l3kernel 3990 (17jul12)

git-svn-id: svn://tug.org/texlive/trunk@27108 c570f23f-e606-0410-a88d-b1316a301751

77 files changed, 32544 insertions, 23781 deletions

diff --git a/Master/texmf-dist/doc/latex/l3kernel/README b/Master/texmf-dist/doc/latex/l3kernel/README
index 51a7f2857b0..7a42e1451a9 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/README
+++ b/Master/texmf-dist/doc/latex/l3kernel/README
@@ -73,7 +73,6 @@ the team members are
   * Johannes Braams
   * David Carlisle
   * Robin Fairbairns
-  * Morten Høgholm
   * Bruno Le Floch
   * Thomas Lotze
   * Frank Mittelbach
@@ -86,6 +85,7 @@ Former members of The LaTeX3 Project team were
 
   * Michael Downes
   * Denys Duchier
+  * Morten Høgholm
   * Alan Jeffrey
   * Martin Schröder
 
@@ -94,5 +94,7 @@ by e-mail: <latex-team@latex-project.org>; for general LaTeX3 discussion
 the [LaTeX-L list](http://news.gmane.org/group/gmane.comp.tex.latex.latex3)
 should be used.
 
---- Copyright 1998-2011
-    The LaTeX3 Project.  All rights reserved ---
\ No newline at end of file
+-----
+
+Copyright (C) 1998-2012 The LaTeX3 Project
+All rights reserved
\ No newline at end of file
diff --git a/Master/texmf-dist/doc/latex/l3kernel/expl3.pdf b/Master/texmf-dist/doc/latex/l3kernel/expl3.pdf
index f920314540e..9edc1f10e3f 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/expl3.pdf
+++ b/Master/texmf-dist/doc/latex/l3kernel/expl3.pdf
diff --git a/Master/texmf-dist/doc/latex/l3kernel/interface3.pdf b/Master/texmf-dist/doc/latex/l3kernel/interface3.pdf
index 8bf1353ee68..16993696c17 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/interface3.pdf
+++ b/Master/texmf-dist/doc/latex/l3kernel/interface3.pdf
diff --git a/Master/texmf-dist/doc/latex/l3kernel/l3docstrip.pdf b/Master/texmf-dist/doc/latex/l3kernel/l3docstrip.pdf
new file mode 100644
index 00000000000..b620c171233
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/l3kernel/l3docstrip.pdf
diff --git a/Master/texmf-dist/doc/latex/l3kernel/l3styleguide.pdf b/Master/texmf-dist/doc/latex/l3kernel/l3styleguide.pdf
index 103dc794e7f..20b3b267c89 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/l3styleguide.pdf
+++ b/Master/texmf-dist/doc/latex/l3kernel/l3styleguide.pdf
diff --git a/Master/texmf-dist/doc/latex/l3kernel/l3styleguide.tex b/Master/texmf-dist/doc/latex/l3kernel/l3styleguide.tex
index a1ef1a42851..18ee23a814c 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/l3styleguide.tex
+++ b/Master/texmf-dist/doc/latex/l3kernel/l3styleguide.tex
@@ -182,4 +182,25 @@ argument is a single token, thus for example
 \end{verbatim}
 remains clear and can be used where appropriate.
 
+\section{Private and internal functions}
+
+Private functions (those starting \cs{__}) should not be used between modules.
+The only exception is where a \enquote{family} of modules share some
+\enquote{internal} methods: this happens most obviously in the kernel itself.
+Any internal functions or variables \emph{must} be documented in the same way
+as public ones.
+
+The \pkg{l3docstrip} method should be used for internal functions in a module.
+This requires a line
+\begin{quote}
+  \ttfamily
+  \%<@@=\meta{module}>
+\end{quote}
+at the start of the source (\texttt{.dtx}) file, with internal functions
+then written in the form
+\begin{verbatim}
+  \cs_new_protected:Npn \@@_function:nn #1#2
+    ...
+\end{verbatim}
+
 \end{document}
diff --git a/Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.pdf b/Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.pdf
index 0839e03a0f5..8ac9a718e85 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.pdf
+++ b/Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.pdf
diff --git a/Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.tex b/Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.tex
index 31b07550060..ac246715add 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.tex
+++ b/Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.tex
@@ -1,6 +1,6 @@
 \iffalse meta-comment
 
-File l3syntax-changes.tex Copyright (C) 2011 The LaTeX3 Project
+File l3syntax-changes.tex Copyright (C) 2011-2012 The LaTeX3 Project
 
 It may be distributed and/or modified under the conditions of the
 LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -20,7 +20,7 @@ The released version of this bundle is available from CTAN.
 
 \usepackage{svn-multi}
 
-\svnid{$Id: l3syntax-changes.tex 2772 2011-09-07 15:07:41Z joseph $}
+\svnid{$Id: l3syntax-changes.tex 3947 2012-07-09 19:51:04Z bruno $}
 \def\filedate{\svnfileyear/\svnfilemonth/\svnfileday}
 
 \title{%
@@ -77,4 +77,24 @@ with an approximate date.
   now trim spaces from each item in the argument.
 \end{itemize}
 
-\end{document}
\ No newline at end of file
+\section{June 2012}
+
+\begin{itemize}
+  \item Access to list functions now indexes from~$1$, not from~$0$.
+  This applies to multiple choices in the \pkg{l3keys} module and
+  the \cs{clist_item:Nn}, \cs{seq_item:Nn} and \cs{tl_item:Nn}
+  functions.
+  \item \cs{tl_trim_spaces:n} now requires a variable number of
+  expansions to fully expand, rather than exactly two.  Of course,
+  \texttt{x}-type expansion still correctly evaluates this function.
+\end{itemize}
+
+\section{July 2012}
+
+\begin{itemize}
+  \item The \cs{tl_if_head_eq_meaning:nN}, \cs{tl_if_head_eq_catcode:nN}
+    and \cs{tl_if_head_eq_charcode:nN} conditionals now never match when
+    their first argument is empty.
+\end{itemize}
+
+\end{document}
diff --git a/Master/texmf-dist/doc/latex/l3kernel/source3.pdf b/Master/texmf-dist/doc/latex/l3kernel/source3.pdf
index a62d8489d51..29dd5ce2332 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/source3.pdf
+++ b/Master/texmf-dist/doc/latex/l3kernel/source3.pdf
diff --git a/Master/texmf-dist/doc/latex/l3kernel/source3.tex b/Master/texmf-dist/doc/latex/l3kernel/source3.tex
index e8b76f8701e..d669eeb079a 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/source3.tex
+++ b/Master/texmf-dist/doc/latex/l3kernel/source3.tex
@@ -103,4 +103,4 @@
   \DelayPrintIndex
 \endgroup
 
-\end{document}
\ No newline at end of file
+\end{document}
diff --git a/Master/texmf-dist/doc/latex/l3kernel/source3body.tex b/Master/texmf-dist/doc/latex/l3kernel/source3body.tex
index bd618e6fa23..c5dbc33a7b3 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/source3body.tex
+++ b/Master/texmf-dist/doc/latex/l3kernel/source3body.tex
@@ -1,6 +1,6 @@
 % \iffalse meta-comment
 %
-%% File: source3body.tex Copyright (C) 1990-2011 The LaTeX3 Project
+%% File: source3body.tex Copyright (C) 1990-2012 The LaTeX3 Project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -393,6 +393,12 @@ and a predicate (|_p|) variant is available, the logical value determined by
 the test is left in the input stream: this will typically be part of a larger
 logical construct.
 
+\section{\TeX{} concepts not supported by \LaTeX3{}}
+
+The \TeX{} concept of an \enquote{\cs{outer}} macro is \emph{not supported}
+at all by \LaTeX3{}. As such, the functions provided here may break when
+used on top of \LaTeXe{} if \cs{outer} tokens are used in the arguments.
+
 \DisableImplementation
 
 \DocInput{l3bootstrap.dtx}
@@ -415,6 +421,28 @@ logical construct.
 \DocInput{l3keys.dtx}
 \DocInput{l3file.dtx}
 \DocInput{l3fp.dtx}
+% To get the various submodules of l3fp to appear in the implementation
+% part only, they have to be added to the documentation list after typesetting
+% the 'user' part just for the main module.
+\ExplSyntaxOn
+\clist_gput_right:Nn \g_docinput_clist
+  {
+    l3fp-aux.dtx ,
+    l3fp-traps.dtx ,
+    l3fp-round.dtx ,
+    l3fp-parse.dtx ,
+    l3fp-logic.dtx ,
+    l3fp-basics.dtx ,
+    l3fp-extended.dtx ,
+    l3fp-expo.dtx ,
+    l3fp-trig.dtx ,
+    l3fp-convert.dtx ,
+    l3fp-assign.dtx ,
+    l3fp-old.dtx ,
+  }
+\ExplSyntaxOff
 \DocInput{l3luatex.dtx}
 
+\DocInput{l3candidates.dtx}
+
 \endinput
diff --git a/Master/texmf-dist/makeindex/l3kernel/l3doc.ist b/Master/texmf-dist/makeindex/l3kernel/l3doc.ist
index 464dc931e12..781c87e50f2 100644
--- a/Master/texmf-dist/makeindex/l3kernel/l3doc.ist
+++ b/Master/texmf-dist/makeindex/l3kernel/l3doc.ist
@@ -15,7 +15,7 @@
 %% Do not distribute a modified version of this file.
 %% 
 %% 
-%% File: l3doc.dtx Copyright (C) 1990-2011 The LaTeX3 project
+%% File: l3doc.dtx Copyright (C) 1990-2012 The LaTeX3 project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
diff --git a/Master/texmf-dist/source/latex/l3kernel/expl3.dtx b/Master/texmf-dist/source/latex/l3kernel/expl3.dtx
index b9a053a8a27..179f45d11c8 100644
--- a/Master/texmf-dist/source/latex/l3kernel/expl3.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/expl3.dtx
@@ -34,22 +34,23 @@
 %% -----------------------------------------------------------------------
 %
 %<*driver|package>
-\RequirePackage{l3names}[2011/12/30]
-%<package>\@ifpackagelater{l3names}{2011/12/30}
+\RequirePackage{l3names}[2012/07/15]
+%<package>\@ifpackagelater{l3names}{2012/07/15}
 %<package>  {}
-%<package>  {
+%<package>  {%
 %<package>    \PackageError{expl3}{Mismatched LaTeX3 packages detected.}
-%<package>      {
+%<package>      {%
 %<package>        Please install an up to date version of l3kernel
-%<package>        using your TeX package manager or from CTAN.\\ \\
-%<package>        Loading expl3 will abort!
-%<package>      }
+%<package>        using your TeX package manager or from CTAN.%
+%<package>        \MessageBreak \MessageBreak
+%<package>        Loading expl3 will abort!%
+%<package>      }%
 %<package>    \endinput
 %<package>  }
 \def\ExplFileName{expl3}
 \def\ExplFileDescription{L3 Experimental code bundle wrapper}
-\def\ExplFileDate{2012/04/23}
-\def\ExplFileVersion{3570}
+\def\ExplFileDate{2012/07/16}
+\def\ExplFileVersion{3990}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -163,8 +164,8 @@
 %     One problem with more traditional \TeX{} coding conventions (as
 %     described in~\cite{A-W:K-TB}) is that the names and syntax of \TeX{}'s
 %     primitive formatting commands are ingeniously designed to be
-%     \enquote{natural} when used directly by the author as document mark-up or in
-%     macros.  Ironically, the ubiquity (and widely recognised
+%     \enquote{natural} when used directly by the author as document mark-up
+%     or in macros.  Ironically, the ubiquity (and widely recognised
 %     superiority) of logical mark-up has meant that such explicit
 %     formatting commands are almost never needed in documents or in
 %     author-defined macros.  Thus they are used almost exclusively by
@@ -309,6 +310,88 @@
 % inferred from the presence or absence of a |g|. See the next subsection for
 % more detail on variable scope.
 %
+% \subsubsection{Separating private and public material}
+%
+% One of the issues with the \TeX{} language is that it doesn't support
+% name spaces and encapsulation other than by convention. As a result
+% nearly every internal command in the \LaTeXe{} kernel has eventually
+% be used by extension packages as an entry point for modifications or
+% extensions. The consequences of this is that nowadays it is next to
+% impossible to change anything in the \LaTeXe{} kernel (even if it is
+% clearly just an internal command) without breaking something.
+%
+% In \pkg{expl3} we hope to improve this situation drastically by
+% clearly separating public interfaces (that extension packages can use
+% and rely on) and private functions and variables (that should not
+% appear outside of their module).  There is (nearly) no way to enforce
+% this without severe computing overhead, so we implement it only
+% through a naming convention, and some support mechanisms.  However, we
+% think that this naming convention is easy to understand and to follow,
+% so that we are confident that this will adopted and provides the
+% desired results.
+%
+% Functions created by a module may either be \enquote{public} (documented
+% with a defined interface) or \enquote{private} (to be used only within
+% that module, and thus not formally documented). It is important that
+% only documented interfaces are used; at the same time, it is necessary to
+% show within the name of a function or variable whether it is public
+% or private.
+%
+% To allow clear separation of these two cases, the following convention
+% is used. Private functions should be defined with |__| added to the beginning
+% of the module name. Thus
+% \begin{verbatim}
+%   \module_foo:nnn
+% \end{verbatim}
+% is a public function which should be documented while
+% \begin{verbatim}
+%   \__module_foo:nnn
+% \end{verbatim}
+% is private to the module, and should \emph{not} be used outside of that
+% module.
+%
+% In the same way, private variables should use two "__" at the start of the
+% module name, such that
+% \begin{verbatim}
+%   \l_module_foo_tl
+% \end{verbatim}
+% is a public variable and
+% \begin{verbatim}
+%   \l__module_foo_tl
+% \end{verbatim}
+% is private.
+%
+% \subsubsection{Using \texttt{@@} and \pkg{l3docstrip} to mark private code}
+%
+% The formal syntax for internal functions allows clear separation of public
+% and private code, but includes redundant information (every internal function
+% or variable includes \texttt{__\meta{module}}). To aid programmers, the
+% \pkg{l3docstrip} program introduces the syntax
+% \begin{quote}
+%   \ttfamily
+%   |%<@@=|\meta{module}|>|
+% \end{quote}
+% which then allows |@@| (and |_@@| in case of variables) to be used as
+% a place holder for \texttt{__\meta{module}} in code. Thus for example
+% \begin{verbatim}
+%   %<@@=foo>
+%   %    \begin{macrocode}
+%   \cs_new:Npn \@@_function:n #1
+%     ...
+%   \tl_new:N \l_@@_my_tl
+%   %    \end{macrocode}
+% \end{verbatim}
+% will be converted by \pkg{l3docstrip} to
+% \begin{verbatim}
+%   \cs_new:Npn \__foo_function:n #1
+%     ...
+%   \tl_new:N \l__foo_my_tl
+% \end{verbatim}
+% on extraction. As you can see both |_@@| and |@@| are mapped to
+% \texttt{__\meta{module}}, because we think that this helps to
+% distinguish variables from functions in the source when the |@@|
+% convention is used.
+%
 % \subsubsection{Variables: scope and type}
 %
 % The \meta{scope} part of the name describes how the variable can be
@@ -323,11 +406,11 @@
 % \end{arg-description}
 %
 % Separate functions are provided to assign data to local and global
-% variables; for example, |\tl_set:Nn| and |\tl_gset:Nn| respectively
+% variables; for example, \cs{tl_set:Nn} and \cs{tl_gset:Nn} respectively
 % set the value of a local or global \enquote{token list} variable.
-% Note that it is a poor \TeX{} practise to intermix local and global
-% assignments to a variable; otherwise you risk exhausting the save stack.
-% \unskip\footnote{See \emph{The \TeX{}book}, p.\,301, for further
+% Note that it is a poor \TeX{} practice to intermix local and global
+% assignments to a variable; otherwise you risk exhausting the save
+% stack.\footnote{See \emph{The \TeX{}book}, p.\,301, for further
 % information.}
 %
 % The \meta{type} will be in the list of available
@@ -335,7 +418,7 @@
 % needed then this will not be the case. However, it is hoped that only
 % the kernel team will need to create new data types.} these include the
 % primitive \TeX{} data-types, such as the various registers, but to
-% these will be added data-types built within the \LaTeX{} programming
+% these are added data-types built within the \LaTeX{} programming
 % system.
 %
 % The data types in \LaTeX3 are:
@@ -349,27 +432,25 @@
 %   \item[dim]    \enquote{rigid} lengths;
 %   \item[fp]     floating-point values;
 %   \item[ior]    an input stream (for reading from a file);
-%   \item[iow]    an output stream (for writing from a file);
+%   \item[iow]    an output stream (for writing to a file);
 %   \item[int]    integer-valued count register;
+%   \item[muskip] math mode \enquote{rubber} lengths;
 %   \item[prop]   property list;
 %   \item[seq]    sequence: a data-type used to implement lists (with
 %                 access at both ends) and stacks;
 %   \item[skip]   \enquote{rubber} lengths;
-%   \item[stream] an input or output stream (for reading from or writing
-%                 to, respectively);
 %   \item[tl]     \enquote{token list variables}: placeholders for token lists.
 % \end{description}
 % When the \meta{type} and \meta{module} are identical (as often happens in
 % the more basic modules) the \meta{module} part is often omitted for
 % aesthetic reasons.
 %
-% The name \enquote{token list} may cause confusion, and so some background is
-% useful.  \TeX{} works with tokens and lists of tokens, rather than
-% characters. It provides two ways to store these token lists: within
-% macros and as token registers (|toks|). The implementation in \LaTeX3 means
-% that
-% |toks| are not required, and that all operations for storing tokens can us
-% the |tl| variable type.
+% The name \enquote{token list} may cause confusion, and so some
+% background is useful.  \TeX{} works with tokens and lists of tokens,
+% rather than characters. It provides two ways to store these token
+% lists: within macros and as token registers (|toks|). The
+% implementation in \LaTeX3 means that |toks| are not required, and that
+% all operations for storing tokens can use the |tl| variable type.
 %
 % Experienced \TeX{} programmers will notice that some of the variable
 % types listed are native \TeX{} registers whilst others are not. In
@@ -400,16 +481,16 @@
 % then using the sequence functions which work in a stack manner
 % (\cs{seq_push:Nn}, \emph{etc}.).
 %
-%  Due to the nature of the underlying \TeX{} implementation, it is
-%  possible to assign values to token list variables and comma lists
-%  without first declaring them. However, this is \emph{not supported
-%  behaviour}. The \LaTeX3 coding convention is that all variables must
-%  be declared before use.
+% Due to the nature of the underlying \TeX{} implementation, it is
+% possible to assign values to token list variables and comma lists
+% without first declaring them. However, this is \emph{not supported
+%   behaviour}. The \LaTeX3 coding convention is that all variables must
+% be declared before use.
 %
-%  The \pkg{expl3} package can be loaded with the |check-declarations| option
-%  to verify that all variables are declared before use. This has a
-%  performance implication and is therefore intended for testing during
-%  development and not for use in production documents.
+% The \pkg{expl3} package can be loaded with the |check-declarations|
+% option to verify that all variables are declared before use. This has
+% a performance implication and is therefore intended for testing during
+% development and not for use in production documents.
 %
 % \subsubsection{Functions: argument specifications}
 %
@@ -443,13 +524,12 @@
 % \end{arg-description}
 % There are two other specifiers with more general meanings:
 % \begin{arg-description}
-%  \item[D] This means: \textbf{Do not use}. This special case is used
-%     for \TeX{} primitives and other commands that are provided for use
-%     only while bootstrapping the \LaTeX{} kernel.  Programmers outside
-%     the kernel team should not use these functions!
+%   \item[D] This means: \textbf{Do not use}. This special case is used
+%     for \TeX{} primitives.  Programmers outside the kernel team should
+%     not use these functions!
 %   \item[w] This means that the argument syntax is \enquote{weird} in that it
 %     does not follow any standard rule.  It is used for functions with
-%     arguments that take non standard forms: examples are \TeX-level
+%     arguments that take non standard forms: examples are \TeX{}-level
 %     delimited arguments and the boolean tests needed after certain
 %     primitive |\if|\ldots{} commands.
 % \end{arg-description}
@@ -468,13 +548,11 @@
 %
 % Let's take a look at some typical operations one might want to
 % perform. Suppose we maintain a stack of open files and we use the
-% stack |\g_ior_file_name_seq| to keep track of them (|io| is the
-% file reading and writing module: it uses the module prefix
-% \texttt{ior} for reading functions and variables). The basic
-% operation here is to push a name onto this stack which could be
-% done by the operation
+% stack |\g_ior_file_name_seq| to keep track of them (\texttt{ior} is
+% the prefix used for the file reading module). The basic operation here
+% is to push a name onto this stack which could be done by the operation
 % \begin{quote}
-%   |\seq_gpush:Nn \g_ior_file_name_seq {#1}|
+%   \cs{seq_gpush:Nn} |\g_ior_file_name_seq {#1}|
 % \end{quote}
 % where |#1| is the filename. In other words, this operation would
 % push the file name as is onto the stack.
@@ -483,20 +561,20 @@
 % a variable of some sort, say |\l_ior_curr_file_tl|. In this case we
 % want to retrieve the value of the variable. If we simply use
 % \begin{quote}
-%   |\seq_gpush:Nn \g_io_file_name_seq \l_io_curr_file_tl|
+%   \cs{seq_gpush:Nn} |\g_ior_file_name_seq| |\l_ior_curr_file_tl|
 % \end{quote}
 % we will not get the value of the variable pushed onto the stack,
 % only the variable name itself. Instead a suitable number of
-% |\exp_after:wN| would be necessary (together with extra braces) to
+% \cs{exp_after:wN} would be necessary (together with extra braces) to
 % change the order of expansion,\footnote{\cs{exp_after:wN} is
-% the \LaTeX3 name for the \TeX{} \tn{expandafter} primitive.}, \emph{i.e.}
+% the \LaTeX3 name for the \TeX{} \tn{expandafter} primitive.} \emph{i.e.}
 % \begin{quote}
-%   |\exp_after:wN|                              \\
-%   |   \seq_gpush:Nn|                           \\
-%   |\exp_after:wN|                              \\
-%   |   \g_io_file_name_seq|                   \\
-%   |\exp_after:wN|                              \\
-%   |   { \l_io_curr_file_tl }|
+%   \cs{exp_after:wN}                              \\
+%   |   |\cs{seq_gpush:Nn}                         \\
+%   \cs{exp_after:wN}                              \\
+%   |   \g_ior_file_name_seq|                      \\
+%   \cs{exp_after:wN}                              \\
+%   |   { \l_ior_curr_file_tl }|
 % \end{quote}
 %
 % The above example is probably the simplest case but already shows
@@ -512,7 +590,7 @@
 % just uses different letters in the arg-spec part of the function to
 % mark the desired behaviour. In the above example one would write
 % \begin{quote}
-%   |\seq_gpush:NV \g_io_file_name_seq \l_io_curr_file_tl|
+%   \cs{seq_gpush:NV} |\g_ior_file_name_seq \l_ior_curr_file_tl|
 % \end{quote}
 % to achieve the desired effect. Here the |V| (the second argument)
 % is for \enquote{retrieve the value of the variable} before passing it to
@@ -524,14 +602,15 @@
 %   \item[c] Character string used as a command name.\\ The argument (a
 %     token or braced token list) must, when fully expanded, produce a
 %     sequence of characters which is then used to construct a command
-%     name (\emph{via}~|\csname| \ldots |\endcsname|). This command name is the
+%     name (\emph{via}~\tn{csname} \ldots \tn{endcsname}).
+%     This command name is the
 %     single token that is passed to the function as the argument. Hence
 %     \begin{quote}
-%       |\seq_gpush:cV { g_file_name_seq } \l_tmpa_tl|
+%       \cs{seq_gpush:cV} |{ g_file_name_seq }| \cs{l_tmpa_tl}
 %     \end{quote}
 %     is equivalent to
 %     \begin{quote}
-%       |\seq_gpush:NV \g_file_name_seq \l_tmpa_tl"|
+%       \cs{seq_gpush:NV} |\g_file_name_seq| \cs{l_tmpa_tl}.
 %     \end{quote}
 %     Remember that \texttt{c} arguments are \emph{fully expanded} by
 %     \TeX{} when creating csnames. This means that (a) the entire
@@ -539,13 +618,14 @@
 %     converted to their content. So the preceding examples are also
 %     equivalent to
 %     \begin{quote}
-%       |\tl_new:N \g_file_seq_name_tl| \\
-%       |\tl_gset:Nn \g_file_seq_name_tl { g_file_name_seq }| \\
-%       |\seq_gpush:cV { \g_file_seq_name_tl } \l_tmpa_tl|.
+%       \cs{tl_new:N} |\g_file_seq_name_tl| \\
+%       \cs{tl_gset:Nn} |\g_file_seq_name_tl { g_file_name_seq }| \\
+%       \cs{seq_gpush:cV} |{| \cs{tl_use:N} |\g_file_seq_name_tl }| \cs{l_tmpa_tl}.
 %     \end{quote}
-%     (Token list variables are expandable and do not require an
-%     accessor function. Other variable types require the appropriate
-%     \cs{<var>_use:N} functions to be used in this context.)
+%     (Token list variables are expandable and we could omit the
+%     accessor function \cs{tl_use:N}.  Other variable types require the
+%     appropriate \cs{<var>_use:N} functions to be used in this
+%     context.)
 %   \item[V]  Value of a variable.\\
 %     This means that the contents of the register in question is used as the
 %     argument, be it an integer, a length-type register, a token list variable
@@ -557,21 +637,22 @@
 %     resulting register to the function.
 %   \item[x]  Fully-expanded token or braced token list.\\
 %     This means that the argument is expanded as in the replacement
-%     text of an~|\edef|, and the expansion is passed to the function as
-%     a braced token list. This means that expansion takes place until
-%     only unexpandable tokens are left.
-%  \item[o]  One-level-expanded token or braced token list.\\
+%     text of an~\tn{edef}, and the expansion is passed to the function as
+%     a braced token list.  Expansion takes place until only unexpandable
+%     tokens are left.  |x|-type arguments cannot be nested.
+%   \item[o]  One-level-expanded token or braced token list.\\
 %     This means that the argument is expanded one level, as by
 %     \tn{expandafter}, and the expansion is passed to the function as a
 %     braced token list.  Note that if the original argument is a braced
 %     token list then only the first token in that list is expanded.
 %     In general, using \texttt{V} should be preferred to using
 %     \texttt{o} for simple variable retrieval.
-%   \item[f] Almost the same as the |x| type except here the token list
+%   \item[f] Expanding the first token recursively in a braced token
+%     list.\\ Almost the same as the |x| type except here the token list
 %     is expanded fully until the first unexpandable token is found and
 %     the rest is left unchanged. Note that if this function finds a
 %     space at the beginning of the argument it will gobble it and not
-%     expand the next argument.
+%     expand the next token.
 % \end{description}
 %
 % \subsection{Simpler means better}
@@ -587,15 +668,15 @@
 %              \csname\cf@encoding \string#1\expandafter\endcsname
 %              \csname ?\string#1\endcsname
 % \end{verbatim}
-% This first piece of code is in essence simply a global |\let| whose
-% two arguments firstly have to be constructed before |\let| is
+% This first piece of code is in essence simply a global \tn{let} whose
+% two arguments firstly have to be constructed before \tn{let} is
 % executed. The |#1| is a control sequence name such as
 % |\textcurrency|. The token to be defined is obtained by
 % concatenating the characters of the current font encoding stored in
 % |\cf@encoding|, which has to be fully expanded, and the name of the
 % symbol. The second token is the same except it uses the default
-% encoding |?|. The result is a mess of interwoven |\expandafter|
-% and |\csname| beloved of all \TeX{} programmers, and the code is
+% encoding |?|. The result is a mess of interwoven \tn{expandafter}
+% and \tn{csname} beloved of all \TeX{} programmers, and the code is
 % essentially unreadable.
 %
 % Using the conventions and functionality outlined here, the task would
@@ -604,7 +685,7 @@
 %   \cs_gset_eq:cc
 %     { \cf@encoding \token_to_str:N  #1 } { ? \token_to_str:N #1 }
 % \end{verbatim}
-% The command |\cs_gset_eq:cc| is a global~|\let| that generates
+% The command \cs{cs_gset_eq:cc} is a global~\tn{let} that generates
 % command names out of both of its arguments before making the
 % definition. This produces code that is far more readable and more
 % likely to be correct first time. (\cs{token_to_str:N} is the \LaTeX3
@@ -623,29 +704,33 @@
 % \end{verbatim}
 % This piece of code is part of the definition of another function. It
 % first produces two things: a token list, by expanding |\group@list| once;
-% and a token whose name comes from~`|sym#3|'.  Then the function~|\in@|
+% and a token whose name comes from~`|sym#3|'.  Then the function~\cs{in@}
 % is called and this tests if its first argument occurs in the token list
 % of its second argument.
 %
 % Again we can improve enormously on the code.  First we shall rename
-% the function~|\in@| according to our conventions.  A function such as
-% this but taking two normal \enquote{\texttt{n}} arguments might reasonably be
-% named |\seq_test_in:Nn|; thus the variant function we need will be
-% defined with the appropriate argument types and its name will be
-% |\seq_test_in:cV|.  Now this code fragment will be simply:
+% the function~\cs{in@}, which tests if its first argument appears
+% within its second argument, according to our conventions.  Such a
+% function takes two normal \enquote{\texttt{n}} arguments and operates
+% on token lists: it might reasonably be named |\tl_test_in:nn|.  Thus
+% the variant function we need will be defined with the appropriate
+% argument types and its name will be |\tl_test_in:cV|.  Now this code
+% fragment will be simply:
 % \begin{verbatim}
-%   \seq_test_in:cV { sym #3 } \l_group_seq
+%   \tl_test_in:cV { sym #3 } \group@list
 % \end{verbatim}
-% Note that, in addition to the lack of |\expandafter|, the space after
-% the~|}| will be silently ignored since all white space is ignored in
-% this programming environment.
+% This code could be improved further by using a sequence |\l_group_seq|
+% rather than the bare token list |\group@list|.  Note that, in addition
+% to the lack of \tn{expandafter}, the space after the~|}| will be
+% silently ignored since all white space is ignored in this programming
+% environment.
 %
 % \subsection{New functions from old}
 %
 % For many common functions the \LaTeX3 kernel will provide variants
 % with a range of argument forms, and similarly it is expected that
 % extension packages providing new functions will make them available in
-% the all the commonly needed forms.
+% all the commonly needed forms.
 %
 % However, there will be occasions where it is necessary to construct a
 % new such variant form; therefore the expansion module provides a
@@ -690,7 +775,7 @@
 % |\demo_cmd_b:xcxcx|, a variant of an existing function
 % |\demo_cmd_b:nnnnn|, that fully
 % expands arguments 1,~3 and~5, and produces commands to pass as
-% arguments 2 and~4 using~|\csname|.
+% arguments 2 and~4 using~\tn{csname}.
 % The definition you need is simply
 % \begin{verbatim}
 %   \cs_generate_variant:Nn \demo_cmd_b:nnnnn { xcxcx }
@@ -715,10 +800,10 @@
 %   \pkg{expl3}.
 % \end{bfseries}
 %
-%  New modules will be added to the distributed version of \pkg{expl3}
-%  as they reach maturity. At present, the \pkg{expl3} bundle consists
-%  of a number of modules, most of which are loaded by including the
-%  line:
+% New modules will be added to the distributed version of \pkg{expl3}
+% as they reach maturity. At present, the \pkg{expl3} bundle consists
+% of a number of modules, most of which are loaded by including the
+% line:
 % \begin{verbatim}
 %   \RequirePackage{expl3}
 % \end{verbatim}
@@ -765,7 +850,7 @@
 %   }
 %   \explpkg{l3prg}{
 %     Program control structures such as boolean data type |bool|, generic
-%     do-while loops, case-switches, sorting routines and stepwise loops.
+%     do-while loops, and conditional flow.
 %   }
 %   \explpkg{l3prop}{
 %     This implements the data-type for \enquote{property lists} that are used, in
@@ -781,8 +866,9 @@
 %     This implements data-types such as queues and stacks.
 %   }
 %   \explpkg{l3skip}{
-%     Implements the \enquote{rubber length} datatype \texttt{skip} and the
-%     \enquote{rigid length} datatype |dim|.
+%     Implements the \enquote{rubber length} datatype \texttt{skip}, the
+%     \enquote{rigid length} datatype |dim|, and the math mode
+%     \enquote{rubber length} datatype \texttt{muskip}.
 %   }
 %   \explpkg{l3tl}{
 %     This implements a basic data-type, called a \textit{token-list
@@ -809,8 +895,9 @@
 %     For example, you may well need \tn{@ifpackageloaded}, as there
 %     is currently no native \LaTeX3 package loading module.
 %   \item User level macros should be generated using the mechanism
-%     available in the \pkg{xparse} package, which is available from CTAN
-%     or the \LaTeX3 SVN repository.
+%     available in the \pkg{xparse} package, which is part of the
+%     \texttt{l3package} bundle, available from CTAN or the \LaTeX3 SVN
+%     repository.
 %   \item At an internal level, most functions should be generated
 %     \tn{long} (using \cs{cs_new:Npn}) rather than \enquote{short} (using
 %     \cs{cs_new_nopar:Npn}). However, functions which take no arguments
@@ -818,7 +905,7 @@
 %   \item Where possible, declare all variables and functions (using
 %     \cs{cs_new:Npn}, \cs{tl_new:N}, etc.) before use.
 %   \item Prefer \enquote{higher-level} functions over \enquote{lower-level},
-%     where possible. So for example use \cs{cs_if_exist:N(TF)} in preference
+%     where possible. So for example use \cs{cs_if_exist:N(TF)} and not
 %     \cs{if_cs_exist:N}.
 %   \item Use space to make code readable. In general, we recommend
 %     a layout such as:
@@ -826,8 +913,8 @@
 %       \cs_new:Npn \foo_bar:Nn #1#2
 %         {
 %           \cs_if_exist:NTF #1
-%             { \foo_bar_aux_i:n {#2} }
-%             { \foo_bar_aux_ii:nn {#2} { literal } }
+%             { \__foo_bar_aux_i:n {#2} }
+%             { \__foo_bar_aux_ii:nn {#2} { literal } }
 %         }
 %     \end{verbatim}
 %     where spaces are used around |{| and |}| except for isolated
@@ -862,11 +949,11 @@
 % function name in the \texttt{.log} file. This is useful for debugging
 % purposes, as it means that there is a complete list of all functions
 % created by each module loaded (with the exceptions of a very small number
-% required by he bootstrap code for \LaTeX3).
+% required by the bootstrap code for \LaTeX3).
 %
 % \DescribeOption{native-drivers}
 % The \texttt{native-drivers} option instructs \LaTeX3 not to use the \LaTeXe{}
-% graphics and colour driver code. Setting this option \texttt{true} uses the
+% graphics driver code. Setting this option \texttt{true} uses the
 % driver code intended for a \LaTeX3 format.
 %
 % \section{The \LaTeX3 Project}
@@ -890,8 +977,8 @@
 % \begin{itemize}
 %   \item Michael Downes
 %   \item Denys Duchier
-%   \item Alan Jeffrey
 %   \item Morten H{\o}gholm
+%   \item Alan Jeffrey
 %   \item Martin Schr{\"o}der
 % \end{itemize}
 %
@@ -945,7 +1032,7 @@
 %    \end{macrocode}
 %
 % \begin{macro}[aux]{\expl@create@bool@option}
-% \begin{variable}
+% \begin{variable}[int]
 %   {
 %     \l@expl@check@declarations@bool ,
 %     \l@expl@log@functions@bool      ,
@@ -965,84 +1052,74 @@
 \expl@create@bool@option { check-declarations } \l@expl@check@declarations@bool
 \expl@create@bool@option { log-functions }      \l@expl@log@functions@bool
 \expl@create@bool@option { native-drivers }     \l@expl@native@drivers@bool
-\ProcessOptions \relax
 \let \expl@create@bool@option \@undefined
+\ProcessOptions \relax
 %    \end{macrocode}
 % \end{variable}
 % \end{macro}
 %
-%    \begin{macrocode}
-\ifodd \l@expl@native@drivers@bool \relax
-\else
-  \RequirePackage { color , graphics }
-\fi
-%    \end{macrocode}
-%
 % We already loaded \pkg{l3names} at the beginning of the \texttt{dtx} file.
 % We now load the base of \LaTeX3, stopping once token list variables are
 % defined.
 %    \begin{macrocode}
-\RequirePackage{ l3basics, l3expan, l3tl }
+\RequirePackage { l3basics, l3expan, l3tl }
 %    \end{macrocode}
 %
-% \begin{macro}{\cs_check_exists:N}
+% \begin{macro}[int]{\__cs_check_exists:N}
 %   When used as a package, there is an option to be picky and to
 %   check definitions exist. This part of the process is done now, so that
 %   variable types based on |tl| (for example |clist|, |seq| and |prop|) will
 %   inherit the appropriate definitions.
 %    \begin{macrocode}
 \ifodd \l@expl@check@declarations@bool \relax
-  \cs_new_protected:Npn \cs_check_exists:N #1
+  \cs_new_protected:Npn \__cs_check_exists:N #1
     {
       \cs_if_exist:NF #1
         {
-          \msg_kernel_error:nnx { check } { non-declared-variable }
+          \__msg_kernel_error:nnx { check } { non-declared-variable }
             { \token_to_str:N #1 }
         }
     }
   \cs_set_protected:Npn \tl_set:Nn #1#2
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_set_nopar:Npx #1 { \exp_not:n {#2} }
     }
   \cs_set_protected:Npn \tl_set:Nx #1#2
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_set_nopar:Npx #1 {#2}
     }
   \cs_set_protected:Npn \tl_gset:Nn #1#2
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_gset_nopar:Npx #1 { \exp_not:n {#2} }
     }
   \cs_set_protected:Npn \tl_gset:Nx #1#2
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_gset_nopar:Npx #1 {#2}
     }
   \cs_set_protected:Npn \tl_set_eq:NN #1#2
     {
-      \cs_check_exists:N #1
-      \cs_check_exists:N #2
+      \__cs_check_exists:N #1
+      \__cs_check_exists:N #2
       \cs_set_eq:NN #1 #2
     }
   \cs_set_protected:Npn \tl_gset_eq:NN #1#2
     {
-      \cs_check_exists:N #1
-      \cs_check_exists:N #2
+      \__cs_check_exists:N #1
+      \__cs_check_exists:N #2
       \cs_gset_eq:NN #1 #2
     }
 \fi
 %    \end{macrocode}
 % \end{macro}
 %
-% The rest of the code can now be loaded.
+% The second part of the file can now be loaded, stopping once the boolean
+% data type is defined.
 %    \begin{macrocode}
-\RequirePackage{
-  l3seq,
-  l3int,
-  l3quark,
-  l3prg}
+\RequirePackage { l3seq, l3int, l3quark, l3prg }
 %    \end{macrocode}
 %
 %  Booleans are not based on token lists but do need checking: another
@@ -1051,62 +1128,65 @@
 \ifodd \l@expl@check@declarations@bool \relax
   \cs_set_protected:Npn \bool_set_true:N #1
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_set_eq:NN #1 \c_true_bool
     }
   \cs_set_protected:Npn \bool_set_false:N #1
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_set_eq:NN #1 \c_false_bool
     }
   \cs_set_protected:Npn \bool_gset_true:N #1
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_gset_eq:NN #1 \c_true_bool
     }
   \cs_set_protected:Npn \bool_gset_false:N #1
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_gset_eq:NN #1 \c_false_bool
     }
   \cs_set_protected:Npn \bool_set_eq:NN  #1
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_set_eq:NN #1
     }
   \cs_set_protected:Npn \bool_gset_eq:NN  #1
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_gset_eq:NN #1
     }
   \cs_set_protected:Npn \bool_set:Nn #1#2
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \tex_chardef:D #1 = \bool_if_p:n {#2}
     }
   \cs_set_protected:Npn \bool_gset:Nn #1#2
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \tex_global:D \tex_chardef:D #1 = \bool_if_p:n {#2}
     }
 \fi
 %    \end{macrocode}
 %
+% Now everything else can be loaded.
 %    \begin{macrocode}
-\RequirePackage{
-  l3clist,
-  l3token,
-  l3prop,
-  l3msg,
-  l3file,
-  l3skip,
-  l3keys,
-  l3fp,
-  l3box,
-  l3coffins,
-  l3color,
-  l3luatex
-}
+\RequirePackage
+  {
+    l3clist,
+    l3token,
+    l3prop,
+    l3msg,
+    l3file,
+    l3skip,
+    l3keys,
+    l3fp,
+    l3box,
+    l3coffins,
+    l3color,
+    l3luatex,
+    l3candidates
+  }
 %    \end{macrocode}
 %
 % The error message for variables cannot be created before now: this means that
@@ -1114,11 +1194,11 @@
 %    \begin{macrocode}
 \bool_if:nT { \l@expl@check@declarations@bool }
   {
-    \msg_kernel_new:nnnn { check } { non-declared-variable }
+    \__msg_kernel_new:nnnn { check } { non-declared-variable }
       { The~variable~#1~has~not~been~declared~\msg_line_context:. }
       {
         Checking~is~active,~and~you~have~tried~do~so~something~like: \\
-        \ \ \tl_set:Nn ~ #1 ~ \iow_char:N \{ ~ ... ~ \iow_char:N \} \\
+        \ \ \tl_set:Nn ~ #1 ~ \{ ~ ... ~ \} \\
         without~first~having: \\
         \ \ \tl_new:N ~ #1  \\
         \\
@@ -1128,10 +1208,19 @@
 %    \end{macrocode}
 %
 % \begin{macro}{\color}
-%   If the native drivers are being used, they can be loaded now. The
-%   \cs{color} macro must be defined for showing coffin poles, so
+%   The \cs{color} macro must be defined for showing coffin poles, so
 %   a no-op version is provided here.
 %    \begin{macrocode}
+\AtBeginDocument
+  {
+    \cs_if_exist:NF \color
+      { \DeclareRobustCommand \color [2] [ ] { } }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+%   If the native drivers are being used, they can be loaded now.
+%    \begin{macrocode}
 \bool_if:nTF { \l@expl@native@drivers@bool }
   {
     \xetex_if_engine:TF
@@ -1144,14 +1233,8 @@
           \file_input:n { l3dvips.def }
         \fi
       }
-    \AtBeginDocument
-      {
-        \cs_if_free:NT \color
-          { \DeclareRobustCommand \color [2] [ ] { } }
-      }
   }
 %    \end{macrocode}
-% \end{macro}
 % \begin{macro}
 %   {
 %     \box_rotate:Nn,
@@ -1160,10 +1243,24 @@
 %     \box_resize_to_wd:Nn,
 %     \box_scale:Nnn
 %   }
-%     If not, alter various definitions to use the \pkg{graphicx} package
-%     instead.
+%   If not, alter various definitions to use the \pkg{graphics} package
+%   instead. The package is loaded right at the start of the hook
+%   as there is otherwise a potential issue with \pkg{(x)color}: see
+%   \url{http://groups.google.com/group/comp.text.tex/msg/c9de8913c756ef4c}.
 %    \begin{macrocode}
   {
+    \tl_gput_left:Nn \@begindocumenthook { \RequirePackage { graphics } }
+    \__msg_kernel_new:nnnn { box } { clipping-not-available }
+      { Box~clipping~not~available. }
+      {
+        The~\box_clip:N~function~is~only~available~when~loading~expl3~
+        with~the~"native-drivers"~option.
+      }
+    \cs_set_protected:Npn \box_clip:N #1
+      {
+        \hbox_set:Nn #1 { \box_use:N #1 }
+        \__msg_kernel_error:nn { box } { clipping-not-available }
+      }
     \cs_set_protected:Npn \box_rotate:Nn #1#2
       { \hbox_set:Nn #1 { \rotatebox {#2} { \box_use:N #1 } } }
     \cs_set_protected:Npn \box_resize:Nnn #1#2#3
@@ -1171,8 +1268,8 @@
         \hbox_set:Nn #1
           {
             \resizebox *
-              { \etex_dimexpr:D #2 \scan_stop: }
-              { \etex_dimexpr:D #3 \scan_stop: }
+              { \__dim_eval:w #2 \__dim_eval_end: }
+              { \__dim_eval:w #3 \__dim_eval_end: }
               { \box_use:N #1 }
           }
       }
@@ -1180,7 +1277,7 @@
       {
         \hbox_set:Nn #1
           {
-            \resizebox * { ! } { \etex_dimexpr:D #2 \scan_stop: }
+            \resizebox * { ! } { \__dim_eval:w #2 \__dim_eval_end: }
               { \box_use:N #1 }
           }
       }
@@ -1188,12 +1285,19 @@
       {
         \hbox_set:Nn #1
           {
-            \resizebox * { \etex_dimexpr:D #2 \scan_stop: } { ! }
+            \resizebox * { \__dim_eval:w #2 \__dim_eval_end: } { ! }
               { \box_use:N #1 }
           }
       }
     \cs_set_protected:Npn \box_scale:Nnn #1#2#3
-      { \hbox_set:Nn #1 { \scalebox {#2} [#3] { \box_use:N #1 } } }
+      {
+        \hbox_set:Nn #1
+          {
+            \exp_last_unbraced:Nx \scalebox
+              { { \fp_eval:n {#2} } [ \fp_eval:n {#3} ] }
+              { \box_use:N #1 }
+          }
+      }
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1205,7 +1309,7 @@
 %    \begin{macrocode}
 \cs_set_protected_nopar:Npn \ExplSyntaxOn
   {
-    \bool_if:NF \l_expl_status_bool
+    \bool_if:NF \l__kernel_expl_bool
       {
         \cs_set_protected_nopar:Npx \ExplSyntaxOff
           {
@@ -1220,7 +1324,7 @@
             \char_set_catcode:nn { 124 } { \char_value_catcode:n { 124 } }
             \char_set_catcode:nn { 126 } { \char_value_catcode:n { 126 } }
             \tex_endlinechar:D = \tex_the:D \tex_endlinechar:D \scan_stop:
-            \bool_set_false:N \l_expl_status_bool
+            \bool_set_false:N \l__kernel_expl_bool
             \cs_set_protected_nopar:Npn \ExplSyntaxOff { }
           }
       }
@@ -1235,7 +1339,7 @@
     \char_set_catcode_other:n            { 124 } % pipe
     \char_set_catcode_space:n            { 126 } % tilde
     \tex_endlinechar:D = 32 \scan_stop:
-    \bool_set_true:N \l_expl_status_bool
+    \bool_set_true:N \l__kernel_expl_bool
   }
 \cs_set_protected_nopar:Npx \ExplSyntaxOff
   {
@@ -1251,4 +1355,4 @@
 %
 % \end{implementation}
 %
-% \PrintIndex
+% \PrintIndex
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3alloc.dtx b/Master/texmf-dist/source/latex/l3kernel/l3alloc.dtx
index d9e59a686a7..6d8f58c86b0 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3alloc.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3alloc.dtx
@@ -1,6 +1,6 @@
 % \iffalse meta-comment
 %
-%% File: l3alloc.dtx Copyright (C) 1990-2011 The LaTeX3 Project
+%% File: l3alloc.dtx Copyright (C) 1990-2012 The LaTeX3 Project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -35,8 +35,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3alloc.dtx 3355 2012-02-09 07:18:22Z joseph $
-  {L3 Experimental register allocation}
+\GetIdInfo$Id: l3alloc.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Register allocation}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -67,7 +67,7 @@
 %
 % \begin{documentation}
 %
-%  Note that this module is only used for generating an pkg{expl3}-based
+%  Note that this module is only used for generating an \pkg{expl3}-based
 %  format. Under \LaTeX{}, the \pkg{etex} package is used for allocation
 %  management.
 %
@@ -83,24 +83,29 @@
 %    \item \TeX{} supports no more than 16 I/O streams for reading
 %      (\tn{read}) and 16 I/O streams for writing (\tn{write}),
 %    \item \TeX{} supports no more than 256 inserts.
-%    \item The other registers (\tn{count}, \tn{dimen},
-%      \tn{skip}, \tn{muskip}, \tn{box}, and \tn{toks})
-%      range from 0 to 32768, but registers numbered above 255 are
+%    \item The other registers (\tn{count}, \tn{dimen}, \tn{skip},
+%      \tn{muskip}, \tn{box}, and \tn{toks}) range from 0 to 32767
+%      (65535 for \LuaTeX{}), but registers numbered above 255 are
 %      accessed somewhat less efficiently.
 %    \item Registers could be allocated both globally and locally; the
-%      use of registers could also be globally or locally. Here we
+%      use of registers could also be global or local. Here we
 %      provide support for globally allocated registers for both
 %      global and local use.
-%    \end{itemize}
+%  \end{itemize}
 %  We also need to allow for some bookkeeping: we need to know which
 %  register was allocated last and which registers can not be
 %  allocated by the standard mechanisms.
 %
-% \begin{function}[updated = 2011-09-05]{\alloc_new:nnnN}
+% \section{Internal functions}
+%
+% Register-based allocation is a low-level process, and is therefore
+% only to be used as part of kernel code.
+%
+% \begin{function}[updated = 2011-09-05]{\__alloc_new:nnnN}
 %   \begin{syntax}
-%     \cs{alloc_new:nnnN} \Arg{type} \Arg{min} \Arg{max} \meta{function}
+%     \cs{__alloc_new:nnnN} \Arg{type} \Arg{min} \Arg{max} \meta{function}
 %   \end{syntax}
-%   Shorthand for allocating new registers. Defines \cs{<type>_new:N} as
+%   Shorthand for allocating new registers. Defines \cs{\meta{type}_new:N} as
 %   and allocator function of the specified \meta{type}, indexed up from
 %   \meta{min} to a \meta{max}, and with assignment carried out by
 %   the \meta{function}. This process will create two token lists,
@@ -110,20 +115,18 @@
 %   numbers which should not be used.
 % \end{function}
 %
-% \section{Internal functions}
-%
-%  \begin{function}[updated = 2011-09-05]{\alloc_setup_type:nnn}
+%  \begin{function}[updated = 2011-09-05]{\__alloc_setup_type:nnn}
 %    \begin{syntax}
-%      \cs{alloc_setup_type:nnn} \Arg{type} \Arg{min} \Arg{max}
+%      \cs{__alloc_setup_type:nnn} \Arg{type} \Arg{min} \Arg{max}
 %    \end{syntax}
 %    Sets up the storage needed for the administration of registers of
 %    \Arg{type}, which will start allocating at \meta{min} and will issue
 %    an error if there is an attempt to allocate past the \meta{max}.
 %  \end{function}
 %
-%  \begin{function}{\alloc_reg:nNN}
+%  \begin{function}{\__alloc_reg:nNN}
 %    \begin{syntax}
-%      \cs{alloc_reg:nNN} \Arg{type} \meta{function} \meta{register}
+%      \cs{__alloc_reg:nNN} \Arg{type} \meta{function} \meta{register}
 %    \end{syntax}
 %    Preforms the allocation for a new \meta{register} of \meta{type},
 %    using the allocator \meta{function} (which will be either a
@@ -140,28 +143,33 @@
 %<*initex>
 %    \end{macrocode}
 %
-% \begin{macro}{\alloc_new:nnnN}
+%    \begin{macrocode}
+%<@@=alloc>
+%    \end{macrocode}
+%
+% \begin{macro}[int]{\@@_new:nnnN}
 %   Shorthand for defining new register types and their allocators:
 %    \begin{macrocode}
-\cs_new_protected:Npn \alloc_new:nnnN #1#2#3#4
+\cs_new_protected:Npn \@@_new:nnnN #1#2#3#4
   {
-    \alloc_setup_type:nnn {#1} {#2} {#3}
-    \cs_new:cpn { #1 _new:N } ##1 { \alloc_reg:nNN {#1} #4 ##1 }
+    \@@_setup_type:nnn {#1} {#2} {#3}
+    \cs_new:cpn { #1 _new:N } ##1 { \@@_reg:nNN {#1} #4 ##1 }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\alloc_setup_type:nnn}
+% \begin{macro}[int]{\@@_setup_type:nnn}
 %   For each type of register we need to \enquote{counters} that hold the
 %   last allocated global register, plus a constant for the maximum
 %   allocation. We also need a sequence to store the \enquote{exceptions}.
+%   All of those variables are internal to the module |#1|.
 %    \begin{macrocode}
-\cs_new_protected:Npn \alloc_setup_type:nnn #1#2#3
+\cs_new_protected:Npn \@@_setup_type:nnn #1#2#3
   {
-    \tl_new:c    { g_ #1 _allocation_tl }
-    \tl_gset:cx  { g_ #1 _allocation_tl }     { \int_eval:n {#2} }
-    \tl_const:cx { c_ #1 _allocation_max_tl } { \int_eval:n {#3} }
-    \seq_new:c   { g_ #1 _allocation_seq }
+    \tl_new:c    { g__ #1 _allocation_tl }
+    \tl_gset:cx  { g__ #1 _allocation_tl }     { \int_eval:n {#2} }
+    \tl_const:cx { c__ #1 _allocation_max_tl } { \int_eval:n {#3} }
+    \seq_new:c   { g__ #1 _allocation_seq }
   }
 %    \end{macrocode}
 % \end{macro}
@@ -176,44 +184,44 @@
 % \end{macro}
 %
 % \begin{macro}
-%   {box_new:N, \dim_new:N, \int_new:N, \muskip_new:N \skip_new:N}
+%   {\box_new:N, \dim_new:N, \int_new:N, \muskip_new:N \skip_new:N}
 %   To get everything to work correctly for inserts, some register types
 %   need to have their allocators set up \enquote{early}. It therefore
 %   makes sense to collect most of them together here.
 %    \begin{macrocode}
 \luatex_if_engine:TF
-  { \alloc_new:nnnN { box } \c_zero \c_max_register_int \tex_chardef:D }
-  { \alloc_new:nnnN { box } \c_zero \c_max_register_int \tex_mathchardef:D }
-\alloc_new:nnnN { dim }    \c_zero \c_max_register_int \tex_dimendef:D
-\alloc_new:nnnN { int }    { 11 }  \c_max_register_int \tex_countdef:D
-\alloc_new:nnnN { muskip } \c_zero \c_max_register_int \tex_muskipdef:D
-\alloc_new:nnnN { skip }   \c_zero \c_max_register_int \tex_skipdef:D
+  { \@@_new:nnnN { box } \c_zero \c_max_register_int \tex_chardef:D }
+  { \@@_new:nnnN { box } \c_zero \c_max_register_int \tex_mathchardef:D }
+\@@_new:nnnN { dim }    \c_zero \c_max_register_int \tex_dimendef:D
+\@@_new:nnnN { int }    { 11 }  \c_max_register_int \tex_countdef:D
+\@@_new:nnnN { muskip } \c_zero \c_max_register_int \tex_muskipdef:D
+\@@_new:nnnN { skip }   \c_zero \c_max_register_int \tex_skipdef:D
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}{\insert_new:N}
-% \begin{macro}[aux]{\alloc_reserve_insert:n}
+% \begin{macro}[aux]{\@@_reserve_insert:n}
 %   For inserts, there is a need to reserve space in various other registers.
 %    \begin{macrocode}
-\alloc_new:nnnN { insert } { 221 } { 254 } \tex_chardef:D
+\@@_new:nnnN { insert } { 221 } { 254 } \tex_chardef:D
 \group_begin:
-  \cs_set_protected:Npn \alloc_reserve_insert:n #1
+  \cs_set_protected:Npn \@@_reserve_insert:n #1
     {
-      \tex_ifnum:D #1 > \c_insert_allocation_max_tl \scan_stop:
+      \tex_ifnum:D #1 > \c__insert_allocation_max_tl \scan_stop:
         \exp_after:wN \use_none:n
       \tex_else:D
         \exp_after:wN \use:n
       \tex_fi:D
         {
-          \seq_put_right:Nn \g_box_allocation_seq  {#1}
-          \seq_put_right:Nn \g_dim_allocation_seq  {#1}
-          \seq_put_right:Nn \g_int_allocation_seq  {#1}
-          \seq_put_right:Nn \g_skip_allocation_seq {#1}
-          \exp_args:Nf \alloc_reserve_insert:n
+          \seq_put_right:Nn \g__box_allocation_seq  {#1}
+          \seq_put_right:Nn \g__dim_allocation_seq  {#1}
+          \seq_put_right:Nn \g__int_allocation_seq  {#1}
+          \seq_put_right:Nn \g__skip_allocation_seq {#1}
+          \exp_args:Nf \@@_reserve_insert:n
             { \etex_numexpr:D #1 + 1 \scan_stop: }
         }
     }
-  \alloc_reserve_insert:n { 221 }
+  \@@_reserve_insert:n { 221 }
 \group_end:
 %    \end{macrocode}
 % \end{macro}
@@ -222,45 +230,45 @@
 % Box $255$ is reserved by \TeX{} for output, so is protected here from
 % use by the allocator.
 %    \begin{macrocode}
-\seq_put_right:Nn \g_box_allocation_seq { 255 }
+\seq_put_right:Nn \g__box_allocation_seq { 255 }
 %    \end{macrocode}
 %
-% \begin{macro}[int]{\alloc_reg:nNN}
+% \begin{macro}[int]{\@@_reg:nNN}
 %   This internal macro performs the actual allocation.
 %    \begin{macrocode}
-\cs_new_protected:Npn \alloc_reg:nNN #1#2#3
+\cs_new_protected:Npn \@@_reg:nNN #1#2#3
   {
-    \chk_if_free_cs:N #3
-    \tex_global:D #2 #3 \tl_use:c { g_ #1 _allocation_tl } \scan_stop:
+    \__chk_if_free_cs:N #3
+    \tex_global:D #2 #3 \tl_use:c { g__ #1 _allocation_tl } \scan_stop:
     \iow_log:x
       {
         \token_to_str:N #3 ~=~ #1 ~register~
-        \tl_use:c { g_ #1 _allocation_tl }
+        \tl_use:c { g__ #1 _allocation_tl }
       }
-    \alloc_next:n {#1}
+    \@@_next:n {#1}
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]{\alloc_next:n}
+% \begin{macro}[aux]{\@@_next:n}
 %   Finding the next register to use is a question of doing an increment
 %   then a check: if we run out of registers then it is a fatal error, so
 %   there is no need to unwind the change. (The check could be done
 %   first but that needs an additional calculation.) There is a built-in
 %   loop to handle reserved allocation positions.
 %    \begin{macrocode}
-\cs_new_protected:Npn \alloc_next:n #1
+\cs_new_protected:Npn \@@_next:n #1
   {
-    \tl_gset:cx { g_ #1 _allocation_tl }
-      { \int_eval:n { \tl_use:c { g_ #1 _allocation_tl } + 1 } }
+    \tl_gset:cx { g__ #1 _allocation_tl }
+      { \int_eval:n { \tl_use:c { g__ #1 _allocation_tl } + 1 } }
     \int_compare:nNnTF
-      { \tl_use:c { g_ #1 _allocation_tl } }
-      > { \tl_use:c { c_ #1 _allocation_max_tl } }
-      { \msg_kernel_fatal:nnx { kernel } { out-of-registers } {#1} }
+      { \tl_use:c { g__ #1 _allocation_tl } }
+      > { \tl_use:c { c__ #1 _allocation_max_tl } }
+      { \__msg_kernel_fatal:nnx { kernel } { out-of-registers } {#1} }
       {
-        \seq_if_in:cxT { g_ #1 _allocation_seq }
-          { \tl_use:c { g_ #1 _allocation_tl } }
-          { \alloc_next:n {#1} }
+        \seq_if_in:cxT { g__ #1 _allocation_seq }
+          { \tl_use:c { g__ #1 _allocation_tl } }
+          { \@@_next:n {#1} }
       }
   }
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3basics.dtx b/Master/texmf-dist/source/latex/l3kernel/l3basics.dtx
index f6be95ab725..549ec6de6f8 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3basics.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3basics.dtx
@@ -35,8 +35,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3basics.dtx 3491 2012-03-04 06:13:18Z bruno $
-  {L3 Experimental basic definitions}
+\GetIdInfo$Id: l3basics.dtx 3987 2012-07-15 21:57:39Z joseph $
+  {L3 Basic definitions}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -155,36 +155,36 @@
 % for the formal parameters (|#1|, |#2|, \ldots).
 % \begin{description}
 %   \item[\texttt{new}]
-%     Create a new function with the \texttt{new} primitives,
+%     Create a new function with the \texttt{new} scope,
 %     such as \cs{cs_new:Npn}.  The definition is global and will result in
 %     an error if it is already defined.
 %   \item[\texttt{set}]
-%     Create a new function with the \texttt{set} primitives,
+%     Create a new function with the \texttt{set} scope,
 %     such as \cs{cs_set:Npn}. The definition is restricted to the current
 %     \TeX{} group and will not result in an error if the function is already
 %     defined.
 %   \item[\texttt{gset}]
-%     Create a new function with the \texttt{gset} primitives,
+%     Create a new function with the \texttt{gset} scope,
 %     such as \cs{cs_gset:Npn}. The definition is global and
 %     will not result in an error if the function is already defined.
 % \end{description}
 %
-% Within each set of primitives there are different ways to define a function.
+% Within each set of scope there are different ways to define a function.
 % The differences depend on restrictions on the actual parameters and
 % the expandability of the resulting function.
 % \begin{description}
 %   \item[\texttt{nopar}]
-%      Create a new function with the \texttt{nopar} primitives,
+%      Create a new function with the \texttt{nopar} restriction,
 %      such as \cs{cs_set_nopar:Npn}. The parameter may not contain
 %      \cs{par} tokens.
 %   \item[\texttt{protected}]
-%      Create a new function with the \texttt{protected} primitives,
+%      Create a new function with the \texttt{protected} restriction,
 %      such as \cs{cs_set_protected:Npn}. The parameter may contain
 %      \cs{par} tokens but the function will not expand within an
 %      \texttt{x}-type expansion.
 % \end{description}
 %
-% \subsection{Defining new functions using primitive parameter text}
+% \subsection{Defining new functions using parameter text}
 %
 % \begin{function}{\cs_new:Npn, \cs_new:cpn, \cs_new:Npx, \cs_new:cpx}
 %   \begin{syntax}
@@ -613,11 +613,11 @@
 % \begin{function}
 %   {\cs_new_eq:NN, \cs_new_eq:Nc, \cs_new_eq:cN, \cs_new_eq:cc}
 %   \begin{syntax}
-%     \cs{cs_new_eq:NN} \meta{cs 1} \meta{cs 2}
-%     \cs{cs_new_eq:NN} \meta{cs 1} \meta{token}
+%     \cs{cs_new_eq:NN} \meta{cs_1} \meta{cs_2}
+%     \cs{cs_new_eq:NN} \meta{cs_1} \meta{token}
 %   \end{syntax}
-%   Globally creates \meta{control sequence 1} and sets it to have the same
-%   meaning as \meta{control sequence 2} or <token>.
+%   Globally creates \meta{control sequence_1} and sets it to have the same
+%   meaning as \meta{control sequence_2} or <token>.
 %   The second control sequence may
 %   subsequently be altered without affecting the copy.
 % \end{function}
@@ -625,28 +625,28 @@
 % \begin{function}
 %   {\cs_set_eq:NN, \cs_set_eq:Nc, \cs_set_eq:cN, \cs_set_eq:cc}
 %   \begin{syntax}
-%     \cs{cs_set_eq:NN} \meta{cs 1} \meta{cs 2}
-%     \cs{cs_set_eq:NN} \meta{cs 1} \meta{token}
+%     \cs{cs_set_eq:NN} \meta{cs_1} \meta{cs_2}
+%     \cs{cs_set_eq:NN} \meta{cs_1} \meta{token}
 %   \end{syntax}
-%   Sets \meta{control sequence 1} to have the same meaning as
-%   \meta{control sequence 2} (or <token>).
+%   Sets \meta{control sequence_1} to have the same meaning as
+%   \meta{control sequence_2} (or <token>).
 %   The second control sequence may subsequently be
 %   altered without affecting the copy. The assignment of a meaning
-%   to the \meta{control sequence 1} is restricted to the current
+%   to the \meta{control sequence_1} is restricted to the current
 %   \TeX{} group level.
 % \end{function}
 %
 % \begin{function}
 %   {\cs_gset_eq:NN, \cs_gset_eq:Nc, \cs_gset_eq:cN, \cs_gset_eq:cc}
 %   \begin{syntax}
-%     \cs{cs_gset_eq:NN} \meta{cs 1} \meta{cs 2}
-%     \cs{cs_gset_eq:NN} \meta{cs 1} \meta{token}
+%     \cs{cs_gset_eq:NN} \meta{cs_1} \meta{cs_2}
+%     \cs{cs_gset_eq:NN} \meta{cs_1} \meta{token}
 %   \end{syntax}
-%   Globally sets \meta{control sequence 1} to have the same meaning as
-%   \meta{control sequence 2} (or <token>).
+%   Globally sets \meta{control sequence_1} to have the same meaning as
+%   \meta{control sequence_2} (or <token>).
 %   The second control sequence may subsequently be
 %   altered without affecting the copy. The assignment of a meaning to
-%   the \meta{control sequence 1} is \emph{not} restricted to the current
+%   the \meta{control sequence_1} is \emph{not} restricted to the current
 %   \TeX{} group level: the assignment is global.
 % \end{function}
 %
@@ -938,56 +938,6 @@
 %   in the input stream for further processing.
 % \end{function}
 %
-% \subsection{Decomposing control sequences}
-%
-% \begin{function}[EXP]{\cs_get_arg_count_from_signature:N}
-%   \begin{syntax}
-%     \cs{cs_get_arg_count_from_signature:N} \meta{function}
-%   \end{syntax}
-%   Splits the \meta{function} into the \meta{name} (\emph{i.e.}~the part
-%   before the colon) and the \meta{signature} (\emph{i.e.}~after the colon).
-%   The \meta{number} of tokens in the \meta{signature} is then left in
-%   the input stream. If there was no \meta{signature} then the result is
-%   the marker value $-1$.
-% \end{function}
-%
-% \begin{function}[EXP]{\cs_get_function_name:N}
-%   \begin{syntax}
-%     \cs{cs_get_function_name:N} \meta{function}
-%   \end{syntax}
-%   Splits the \meta{function} into the \meta{name} (\emph{i.e.}~the part
-%   before the colon) and the \meta{signature} (\emph{i.e.}~after the colon).
-%   The \meta{name} is then left in the input stream without the escape
-%   character present made up of tokens with category code $12$
-%   (other).
-% \end{function}
-%
-% \begin{function}[EXP]{\cs_get_function_signature:N}
-%   \begin{syntax}
-%     \cs{cs_get_function_signature:N} \meta{function}
-%   \end{syntax}
-%   Splits the \meta{function} into the \meta{name} (\emph{i.e.}~the part
-%   before the colon) and the \meta{signature} (\emph{i.e.}~after the colon).
-%   The \meta{signature} is then left in the input stream made up of
-%   tokens with category code $12$ (other).
-% \end{function}
-%
-% \begin{function}[EXP]{\cs_split_function:NN}
-%   \begin{syntax}
-%     \cs{cs_split_function:NN} \meta{function} \meta{processor}
-%   \end{syntax}
-%   Splits the \meta{function} into the \meta{name} (\emph{i.e.}~the part
-%   before the colon) and the \meta{signature} (\emph{i.e.}~after the colon).
-%   This information is then placed in the input stream after the
-%   \meta{processor} function in three parts: the \meta{name}, the
-%   \meta{signature} and a logic token indicating if a colon was found
-%   (to differentiate variables from function names). The \meta{name}
-%   will not include the escape character, and both the \meta{name} and
-%   \meta{signature} are made up of tokens with category code $12$
-%   (other). The \meta{processor} should be a function with argument
-%   specification \texttt{:nnN} (plus any trailing arguments needed).
-% \end{function}
-%
 % \section{Predicates and conditionals}
 % \label{sec:predicates}
 %
@@ -1031,7 +981,7 @@
 %     are expandable and have names that end with |_p| in the
 %     description part.  For example,
 %     \begin{quote}
-%       |\cs_if_free_p:N|
+%       \cs{cs_if_free_p:N}
 %     \end{quote}
 %     would be a predicate function for the same type of test as the
 %     conditional described above. It would return \enquote{true} if its
@@ -1100,7 +1050,7 @@
 % \begin{function}[EXP,pTF]
 %   {
 %     \str_if_eq:nn, \str_if_eq:Vn, \str_if_eq:on, \str_if_eq:no,
-%     \str_if_eq:nV, \str_if_eq:VV, \str_if_eq:xx
+%     \str_if_eq:nV, \str_if_eq:VV
 %   }
 %   \begin{syntax}
 %     \cs{str_if_eq_p:nn} \Arg{tl_1} \Arg{tl_2}
@@ -1110,11 +1060,63 @@
 %   basis, and is \texttt{true} if the two lists contain the same
 %   characters in the same order. Thus for example
 %   \begin{verbatim}
-%     \str_if_eq_p:xx { abc } { \tl_to_str:n { abc } }
+%     \str_if_eq_p:no { abc } { \tl_to_str:n { abc } }
+%   \end{verbatim}
+%   is logically \texttt{true}.
+% \end{function}
+%
+% \begin{function}[EXP,pTF, added = 2012-06-05]{\str_if_eq_x:nn}
+%   \begin{syntax}
+%     \cs{str_if_eq_x_p:nn} \Arg{tl_1} \Arg{tl_2}
+%     \cs{str_if_eq_x:nnTF} \Arg{tl_1} \Arg{tl_2} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   Compares the full expansion of two \meta{token lists} on a character by
+%   character basis, and is \texttt{true} if the two lists contain the same
+%   characters in the same order. Thus for example
+%   \begin{verbatim}
+%     \str_if_eq_x_p:nn { abc } { \tl_to_str:n { abc } }
 %   \end{verbatim}
-%   is logically \texttt{true}. All versions of these functions are fully
-%   expandable (including those involving an \texttt{x}-type
-%   expansion).
+%   is logically \texttt{true}.
+% \end{function}
+%
+% \begin{function}[added = 2012-06-03, EXP]{\str_case:nnn, \str_case:onn}
+%   \begin{syntax}
+%     \cs{str_case:nnn} \Arg{test string} \\
+%     ~~|{| \\
+%     ~~~~\Arg{string case_1} \Arg{code case_1} \\
+%     ~~~~\Arg{string case_2} \Arg{code case_2} \\
+%     ~~~~\ldots \\
+%     ~~~~\Arg{string case_n} \Arg{code case_n} \\
+%     ~~|}| \\
+%     ~~\Arg{else code}
+%   \end{syntax}
+%   This function compares the \meta{test string} in turn with each
+%   of the \meta{string cases}. If the two are equal (as described for
+%   \cs{str_if_eq:nnTF} then the
+%   associated \meta{code} is left in the input stream. If none of
+%   the tests are \texttt{true} then the \texttt{else code} will be
+%   left in the input stream.
+% \end{function}
+%
+% \begin{function}[added = 2012-06-05, EXP]{\str_case_x:nnn}
+%   \begin{syntax}
+%     \cs{str_case_x:nnn} \Arg{test string} \\
+%     ~~|{| \\
+%     ~~~~\Arg{string case_1} \Arg{code case_1} \\
+%     ~~~~\Arg{string case_2} \Arg{code case_2} \\
+%     ~~~~\ldots \\
+%     ~~~~\Arg{string case_n} \Arg{code case_n} \\
+%     ~~|}| \\
+%     ~~\Arg{else code}
+%   \end{syntax}
+%   This function comapres the full expansion of the \meta{test string}
+%   in turn with the full expansion of the \meta{string cases}. If the two
+%   full expansions are equal (as described for \cs{str_if_eq:nnTF} then the
+%   associated \meta{code} is left in the input stream. If none of the tests
+%   are \texttt{true} then the \texttt{else code} will be left in the input
+%   stream. The \meta{test string} is expanded in each comparison, and must
+%   always yield the same result: for example, random numbers should
+%   not be used within this string.
 % \end{function}
 %
 % \subsection{Engine-specific conditionals}
@@ -1146,7 +1148,7 @@
 % expand whatever comes after them and others don't. Hence the names
 % for these underlying functions will often contain a |:w| part but
 % higher level functions are often available. See for instance
-% |\int_compare_p:nNn| which is a wrapper for |\if_num:w|.
+% \cs{int_compare_p:nNn} which is a wrapper for \cs{if_int_compare:w}.
 %
 % Certain conditionals deal with specific data types like boxes and
 % fonts and are described there. The ones described below are either
@@ -1167,7 +1169,7 @@
 %   for more.
 %   \begin{texnote}
 %     These are equivalent to their corresponding \TeX\ primitive
-%     conditionals; |\reverse_if:N| is \eTeX's |\unless|.
+%     conditionals; \cs{reverse_if:N} is \eTeX's \tn{unless}.
 %   \end{texnote}
 % \end{function}
 %
@@ -1180,7 +1182,7 @@
 %   <arg_1> and <arg_2> could be functions, variables, tokens; in all cases the
 %   \emph{unexpanded} definitions are compared.
 %   \begin{texnote}
-%     This is \TeX{}'s |\ifx|.
+%     This is \TeX{}'s \tn{ifx}.
 %   \end{texnote}
 % \end{function}
 %
@@ -1223,45 +1225,105 @@
 %
 % \section{Internal kernel functions}
 %
-% \begin{function}{\chk_if_exist_cs:N, \chk_if_exist_cs:c}
+% \begin{function}{\__chk_if_exist_cs:N, \__chk_if_exist_cs:c}
 %   \begin{syntax}
-%     \cs{chk_if_exist_cs:N} \meta{cs}
+%     \cs{__chk_if_exist_cs:N} \meta{cs}
 %   \end{syntax}
 %   This function checks that \meta{cs} exists according to the
 %   criteria for \cs{cs_if_exist_p:N}, and if not raises a kernel-level
 %   error.
 % \end{function}
 %
-% \begin{function}{\chk_if_free_cs:N, \chk_if_free_cs:c}
+% \begin{function}{\__chk_if_free_cs:N, \__chk_if_free_cs:c}
 %   \begin{syntax}
-%     \cs{chk_if_free_cs:N} \meta{cs}
+%     \cs{__chk_if_free_cs:N} \meta{cs}
 %   \end{syntax}
 %   This function checks that \meta{cs} is free according to the
 %   criteria for \cs{cs_if_free_p:N}, and if not raises a kernel-level
 %   error.
 % \end{function}
 %
-% \section{Experimental functions}
+% \begin{function}[EXP]{\__cs_count_signature:N, \__cs_count_signature:c}
+%   \begin{syntax}
+%     \cs{__cs_count_signature:N} \meta{function}
+%   \end{syntax}
+%   Splits the \meta{function} into the \meta{name} (\emph{i.e.}~the part
+%   before the colon) and the \meta{signature} (\emph{i.e.}~after the colon).
+%   The \meta{number} of tokens in the \meta{signature} is then left in
+%   the input stream. If there was no \meta{signature} then the result is
+%   the marker value $-1$.
+% \end{function}
 %
-% \begin{function}[EXP,TF,added=2011-10-10]
-%   {\cs_if_exist_use:N, \cs_if_exist_use:c}
+% \begin{function}[EXP]{\__cs_split_function:NN}
 %   \begin{syntax}
-%     \cs{cs_if_exist_use:NTF} \meta{control sequence} \Arg{true code} \Arg{false code}
+%     \cs{__cs_split_function:NN} \meta{function} \meta{processor}
 %   \end{syntax}
-%   If the \meta{control sequence} exists, leave it in the input stream,
-%   followed by the \meta{true code} (unbraced). Otherwise, leave the
-%   \meta{false} code in the input stream. For example,
-%   \begin{verbatim}
-%     \cs_set:Npn \mypkg_use_character:N #1
-%       { \cs_if_exist_use:cF { mypkg_#1:n } { \mypkg_default:N #1 } }
-%   \end{verbatim}
-%   calls the function |\mypkg_#1:n| if it exists, and falls back to
-%   a default action otherwise. This could also be done (more slowly)
-%   using \cs{prg_case_str:xxn}.
-%   \begin{texnote}
-%     The \texttt{c} variants do not introduce the \meta{control sequence}
-%     in the hash table if it is not there.
-%   \end{texnote}
+%   Splits the \meta{function} into the \meta{name} (\emph{i.e.}~the part
+%   before the colon) and the \meta{signature} (\emph{i.e.}~after the colon).
+%   This information is then placed in the input stream after the
+%   \meta{processor} function in three parts: the \meta{name}, the
+%   \meta{signature} and a logic token indicating if a colon was found
+%   (to differentiate variables from function names). The \meta{name}
+%   will not include the escape character, and both the \meta{name} and
+%   \meta{signature} are made up of tokens with category code $12$
+%   (other). The \meta{processor} should be a function with argument
+%   specification \texttt{:nnN} (plus any trailing arguments needed).
+% \end{function}
+%
+% \begin{function}[EXP]{\__cs_get_function_name:N}
+%   \begin{syntax}
+%     \cs{__cs_get_function_name:N} \meta{function}
+%   \end{syntax}
+%   Splits the \meta{function} into the \meta{name} (\emph{i.e.}~the part
+%   before the colon) and the \meta{signature} (\emph{i.e.}~after the colon).
+%   The \meta{name} is then left in the input stream without the escape
+%   character present made up of tokens with category code $12$
+%   (other).
+% \end{function}
+%
+% \begin{function}[EXP]{\__cs_get_function_signature:N}
+%   \begin{syntax}
+%     \cs{__cs_get_function_signature:N} \meta{function}
+%   \end{syntax}
+%   Splits the \meta{function} into the \meta{name} (\emph{i.e.}~the part
+%   before the colon) and the \meta{signature} (\emph{i.e.}~after the colon).
+%   The \meta{signature} is then left in the input stream made up of
+%   tokens with category code $12$ (other).
+% \end{function}
+%
+% \begin{function}{\__cs_tmp:w}
+%   Function used for various short-term usages, for instance defining
+%   functions whose definition involves tokens which are hard to insert
+%   normally (spaces, charactes with category other).
+% \end{function}
+%
+% \begin{function}{\__kernel_register_show:N, \__kernel_register_show:c}
+%   \begin{syntax}
+%     \cs{\__kernel_register_show:N} \meta{register}
+%   \end{syntax}
+%   Used to show the contents of a \TeX{} register at the terminal, formatted
+%   such that internal parts of the mechanism are not visible.
+% \end{function}
+%
+% \begin{function}{\__prg_case_end:nw}
+%   \begin{syntax}
+%     \cs{__prg_case_end:nw} \Arg{code} \meta{tokens} \cs{q_recursion_stop}
+%   \end{syntax}
+%   Used to terminate case statements (\cs{int_case:nnn}, \emph{etc.})
+%   by removing trailing \meta{tokens} and the end marker
+%   \cs{q_recursion_stop}, and inserting the \meta{code} for the successful
+%   case.
+% \end{function}
+%
+% \begin{function}{\__str_if_eq_x_return:nn}
+%   \begin{syntax}
+%     \cs{__str_if_eq_x_return:nn} \Arg{tl_1} \Arg{tl_2}
+%   \end{syntax}
+%   Compares the full expansion of two \meta{token lists} on a character by
+%   character basis, and is \texttt{true} if the two lists contain the same
+%   characters in the same order. Either \cs{prg_return_true:} or
+%   \cs{prg_return_false:} is then left in the input stream. This is a version
+%   of \cs{str_if_eq_x:nn(TF)} coded for speed.
 % \end{function}
 %
 % \end{documentation}
@@ -1278,7 +1340,7 @@
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
@@ -1370,11 +1432,11 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[EXP]{\if_int_compare:w, \int_to_roman:w}
+% \begin{macro}[EXP]{\if_int_compare:w, \__int_to_roman:w}
 %   For integers.
 %    \begin{macrocode}
 \tex_let:D \if_int_compare:w   \tex_ifnum:D
-\tex_let:D \int_to_roman:w     \tex_romannumeral:D
+\tex_let:D \__int_to_roman:w     \tex_romannumeral:D
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1385,15 +1447,6 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\tex_global:D, \tex_long:D, \etex_protected:D}
-%   Three prefixes for assignments.
-%    \begin{macrocode}
-\tex_let:D \tex_global:D      \tex_global:D
-\tex_let:D \tex_long:D        \tex_long:D
-\tex_let:D \tex_protected:D   \etex_protected:D
-%    \end{macrocode}
-% \end{macro}
-%
 % \begin{macro}[EXP]{\exp_args:Nc}
 %   Discussed in \pkg{l3expan}, but needed much earlier.
 %    \begin{macrocode}
@@ -1403,15 +1456,16 @@
 %
 % \begin{macro}[EXP]{\token_to_str:c, \cs_meaning:c}
 % \begin{macro}{\cs_show:c}
-%   A small number of variants by hand. Some of the necessary functions
+%   A small number of variants defined by hand.
+%   Some of the necessary functions
 %   (\cs{use_i:nn}, \cs{use_ii:nn}, and \cs{exp_args:NNc}) are not
 %   defined at that point yet, but will be defined before those variants
 %   are used.  The \cs{cs_meaning:c} command must check for an undefined
 %   control sequence to avoid defining it mistakenly.  The
 %   \cs{cs_show:c} command is \enquote{protected} because its action is
 %   not expandable. Also, the conversion of its argument to a control
-%   sequence is done within a group to avoid converting it to
-%   \tn{relax}.
+%   sequence is done within a group to avoid showing \tn{relax} for
+%   undefined control sequences.
 %    \begin{macrocode}
 \tex_def:D \token_to_str:c { \exp_args:Nc \token_to_str:N }
 \tex_long:D \tex_def:D \cs_meaning:c #1
@@ -1424,7 +1478,7 @@
     { \exp_args:Nc \cs_meaning:N {#1} }
     { \tl_to_str:n {undefined} }
   }
-\tex_protected:D \tex_def:D \cs_show:c
+\etex_protected:D \tex_def:D \cs_show:c
   { \group_begin: \exp_args:NNc \group_end: \cs_show:N }
 %    \end{macrocode}
 % \end{macro}
@@ -1434,17 +1488,17 @@
 %
 % \begin{variable}{\c_minus_one, \c_zero, \c_sixteen}
 % \begin{variable}{\c_six, \c_seven, \c_twelve}
-%    We need the constants |\c_minus_one| and |\c_sixteen| now for
-%    writing information to the log and the terminal and |\c_zero|
+%    We need the constants \cs{c_minus_one} and \cs{c_sixteen} now for
+%    writing information to the log and the terminal and \cs{c_zero}
 %    which is used by some functions in the \textsf{l3alloc} module. The
 %    rest are defined in the \textsf{l3int} module -- at least for the
-%    ones that can be defined with |\tex_chardef:D| or
-%    |\tex_mathchardef:D|. For other constants the \textsf{l3int} module is
+%    ones that can be defined with \cs{tex_chardef:D} or
+%    \cs{tex_mathchardef:D}. For other constants the \textsf{l3int} module is
 %    required but it can't be used until the allocation has been set
 %    up properly! The actual allocation mechanism is in
 %    \textsf{l3alloc} and as \TeX{} wants to reserve count registers
 %    0--9, the first available one is~10 so we use that for
-%    |\c_minus_one|.
+%    \cs{c_minus_one}.
 %    \begin{macrocode}
 %<*package>
 \tex_let:D \c_minus_one \m@ne
@@ -1453,18 +1507,18 @@
 \tex_countdef:D \c_minus_one = 10 ~
 \c_minus_one = -1 ~
 %</initex>
-\tex_chardef:D \c_sixteen = 16~
-\tex_chardef:D \c_zero    = 0~
-\tex_chardef:D \c_six     = 6~
-\tex_chardef:D \c_seven   = 7~
-\tex_chardef:D \c_twelve  = 12~
+\tex_chardef:D \c_sixteen = 16 ~
+\tex_chardef:D \c_zero    = 0 ~
+\tex_chardef:D \c_six     = 6 ~
+\tex_chardef:D \c_seven   = 7 ~
+\tex_chardef:D \c_twelve  = 12 ~
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 %
 % \begin{variable}{\c_max_register_int}
 %   This is here as this particular integer is needed both in package
-%   mode and to bootstrap \pkg{l3alloc}.
+%   mode and to bootstrap \pkg{l3alloc}, and is documented in \pkg{l3int}.
 %    \begin{macrocode}
 \etex_ifdefined:D \luatex_luatexversion:D
   \tex_chardef:D \c_max_register_int = 65 535 ~
@@ -1486,24 +1540,24 @@
 %     \cs_set_protected_nopar:Npn , \cs_set_protected_nopar:Npx ,
 %     \cs_set_protected:Npn       , \cs_set_protected:Npx
 %   }
-%   All assignment functions in \LaTeX3 should be naturally robust;
+%   All assignment functions in \LaTeX3 should be naturally protected;
 %   after all, the \TeX{} primitives for assignments are and it can be
 %   a cause of problems if others aren't.
 %    \begin{macrocode}
 \tex_let:D \cs_set_nopar:Npn            \tex_def:D
 \tex_let:D \cs_set_nopar:Npx            \tex_edef:D
-\tex_protected:D \cs_set_nopar:Npn \cs_set:Npn
+\etex_protected:D \cs_set_nopar:Npn \cs_set:Npn
   { \tex_long:D \cs_set_nopar:Npn }
-\tex_protected:D \cs_set_nopar:Npn \cs_set:Npx
+\etex_protected:D \cs_set_nopar:Npn \cs_set:Npx
   { \tex_long:D \cs_set_nopar:Npx }
-\tex_protected:D \cs_set_nopar:Npn \cs_set_protected_nopar:Npn
-  { \tex_protected:D \cs_set_nopar:Npn }
-\tex_protected:D \cs_set_nopar:Npn \cs_set_protected_nopar:Npx
-  { \tex_protected:D \cs_set_nopar:Npx }
+\etex_protected:D \cs_set_nopar:Npn \cs_set_protected_nopar:Npn
+  { \etex_protected:D \cs_set_nopar:Npn }
+\etex_protected:D \cs_set_nopar:Npn \cs_set_protected_nopar:Npx
+  { \etex_protected:D \cs_set_nopar:Npx }
 \cs_set_protected_nopar:Npn \cs_set_protected:Npn
-  { \tex_protected:D \tex_long:D \cs_set_nopar:Npn }
+  { \etex_protected:D \tex_long:D \cs_set_nopar:Npn }
 \cs_set_protected_nopar:Npn \cs_set_protected:Npx
-  { \tex_protected:D \tex_long:D \cs_set_nopar:Npx }
+  { \etex_protected:D \tex_long:D \cs_set_nopar:Npx }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1523,13 +1577,13 @@
 \cs_set_protected_nopar:Npn \cs_gset:Npx
   { \tex_long:D \cs_gset_nopar:Npx }
 \cs_set_protected_nopar:Npn \cs_gset_protected_nopar:Npn
-  { \tex_protected:D \cs_gset_nopar:Npn }
+  { \etex_protected:D \cs_gset_nopar:Npn }
 \cs_set_protected_nopar:Npn \cs_gset_protected_nopar:Npx
-  { \tex_protected:D \cs_gset_nopar:Npx }
+  { \etex_protected:D \cs_gset_nopar:Npx }
 \cs_set_protected_nopar:Npn \cs_gset_protected:Npn
-  { \tex_protected:D \tex_long:D \cs_gset_nopar:Npn }
+  { \etex_protected:D \tex_long:D \cs_gset_nopar:Npn }
 \cs_set_protected_nopar:Npn \cs_gset_protected:Npx
-  { \tex_protected:D \tex_long:D \cs_gset_nopar:Npx }
+  { \etex_protected:D \tex_long:D \cs_gset_nopar:Npx }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1544,18 +1598,18 @@
 %
 % \begin{macro}{\use:x}
 %   Fully expands its argument and passes it to the input stream. Uses
-%   the reserved \cs{l_exp_internal_tl} which will be set up in \pkg{l3expan}.
+%   the reserved \cs{l__exp_internal_tl} which will be set up in \pkg{l3expan}.
 %    \begin{macrocode}
 \cs_set_protected:Npn \use:x #1
   {
-    \cs_set_nopar:Npx \l_exp_internal_tl {#1}
-    \l_exp_internal_tl
+    \cs_set_nopar:Npx \l__exp_internal_tl {#1}
+    \l__exp_internal_tl
   }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}[EXP]{\use:n, \use:nn, \use:nnn, \use:nnnn}
-%    These macro grabs its arguments and returns it back to the input
+%    These macros grab their arguments and returns them back to the input
 %    (with outer braces removed).
 %    \begin{macrocode}
 \cs_set:Npn \use:n    #1       {#1}
@@ -1663,20 +1717,25 @@
 % testing and processing must return the \meta{state} this leaves
 % \TeX{} in. Therefore, a simple user interface could be something like
 % \begin{verbatim}
-%   \if_meaning:w #1#2   \prg_return_true:  \else:
-%      \if_meaning:w #1#3  \prg_return_true: \else:
-%      \prg_return_false:
-%  \fi: \fi:
+%   \if_meaning:w #1#2
+%     \prg_return_true:
+%   \else:
+%     \if_meaning:w #1#3
+%       \prg_return_true:
+%     \else:
+%       \prg_return_false:
+%     \fi:
+%   \fi:
 % \end{verbatim}
 % Usually, a \TeX{} programmer would have to insert a number of
-% |\exp_after:wN|s to ensure the state value is returned at exactly
+% \cs{exp_after:wN}s to ensure the state value is returned at exactly
 % the point where the last conditional is finished.  However, that
 % obscures the code and forces the \TeX{} programmer to prove that
 % he/she knows the $2^{n}-1$ table.  We therefore provide the simpler
 % interface.
 %
 % \begin{macro}[EXP]{\prg_return_true:, \prg_return_false:}
-%   The idea here is that \cs{int_to_roman:w} will expand fully any
+%   The idea here is that \cs{__int_to_roman:w} will expand fully any
 %   \cs{else:} and the \cs{fi:} that are waiting to be discarded,
 %   before reaching the \cs{c_zero} which will leave the expansion null.
 %   The code can then leave either the first or second argument in the
@@ -1685,9 +1744,9 @@
 %   to see this.
 %    \begin{macrocode}
 \cs_set_nopar:Npn \prg_return_true:
-  { \exp_after:wN \use_i:nn  \int_to_roman:w }
+  { \exp_after:wN \use_i:nn  \__int_to_roman:w }
 \cs_set_nopar:Npn \prg_return_false:
-  { \exp_after:wN \use_ii:nn \int_to_roman:w}
+  { \exp_after:wN \use_ii:nn \__int_to_roman:w}
 %    \end{macrocode}
 %   An extended state space could be implemented by including a more
 %   elaborate function in place of \cs{use_i:nn}/\cs{use_ii:nn}. Provided
@@ -1701,29 +1760,29 @@
 %     \prg_set_protected_conditional:Npnn ,
 %     \prg_new_protected_conditional:Npnn ,
 %   }
-% \begin{macro}[aux]{\prg_generate_conditional_parm_aux:NNpnn}
+% \begin{macro}[aux]{\__prg_generate_conditional_parm:nnNpnn}
 %   The user functions for the types using parameter text from the
 %   programmer. The various functions only differ by which function is
 %   used for the assignment. For those |Npnn| type functions, we must
 %   grab the parameter text, reading everything up to a left brace
 %   before continuing. Then split the base function into name and
 %   signature, and feed \Arg{name} \Arg{signature} \meta{boolean}
-%   \meta{defining~function} |{parm}| \Arg{parameters} |{TF,...}|
+%   \Arg{set~or~new} \Arg{maybe~protected} \Arg{parameters} |{TF,...}|
 %   \Arg{code} to the auxiliary function responsible for defining all
 %   conditionals.
 %    \begin{macrocode}
 \cs_set_protected_nopar:Npn \prg_set_conditional:Npnn
-  { \prg_generate_conditional_parm_aux:NNpnn \cs_set:Npn }
+  { \__prg_generate_conditional_parm:nnNpnn { set } { } }
 \cs_set_protected_nopar:Npn \prg_new_conditional:Npnn
-  { \prg_generate_conditional_parm_aux:NNpnn \cs_new:Npn }
+  { \__prg_generate_conditional_parm:nnNpnn { new } { } }
 \cs_set_protected_nopar:Npn \prg_set_protected_conditional:Npnn
-  { \prg_generate_conditional_parm_aux:NNpnn \cs_set_protected:Npn }
+  { \__prg_generate_conditional_parm:nnNpnn { set } { _protected } }
 \cs_set_protected_nopar:Npn \prg_new_protected_conditional:Npnn
-  { \prg_generate_conditional_parm_aux:NNpnn \cs_new_protected:Npn }
-\cs_set_protected:Npn \prg_generate_conditional_parm_aux:NNpnn #1#2#3#
+  { \__prg_generate_conditional_parm:nnNpnn { new } { _protected } }
+\cs_set_protected:Npn \__prg_generate_conditional_parm:nnNpnn #1#2#3#4#
   {
-    \cs_split_function:NN #2 \prg_generate_conditional_aux:nnNNnnnn
-    #1 { parm } {#3}
+    \__cs_split_function:NN #3 \__prg_generate_conditional:nnNnnnnn
+    {#1} {#2} {#4}
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1736,204 +1795,248 @@
 %     \prg_set_protected_conditional:Nnn ,
 %     \prg_new_protected_conditional:Nnn ,
 %   }
-% \begin{macro}[aux]{\prg_generate_conditional_count_aux:NNnn}
+% \begin{macro}[aux]
+%   {
+%     \__prg_generate_conditional_count:nnNnn ,
+%     \__prg_generate_conditional_count:nnNnnnn
+%   }
 %   The user functions for the types automatically inserting the correct
 %   parameter text based on the signature. The various functions only
-%   differ by which function is used for the assignment. For those |Nnn|
-%   type functions, we calculate the number of arguments. Then split the
-%   base function into name and signature, and feed \Arg{name}
-%   \Arg{signature} \meta{boolean} \meta{defining~function} |{count}|
-%   \Arg{arg~count} |{TF,...}| \Arg{code} to the auxiliary function
-%   responsible for defining all conditionals.
+%   differ by which function is used for the assignment. Split the base
+%   function into name and signature.  The second auxiliary generates
+%   the parameter text from the number of letters in the signature.
+%   Then feed \Arg{name} \Arg{signature} \meta{boolean} \Arg{set~or~new}
+%   \Arg{maybe~protected} \Arg{parameters} |{TF,...}| \Arg{code} to the
+%   auxiliary function responsible for defining all conditionals.  If
+%   the \meta{signature} has more than $9$ letters, the definition is
+%   aborted since \TeX{} macros have at most $9$ arguments.  The
+%   erroneous case where the function name contains no colon is captured
+%   later.
 %    \begin{macrocode}
 \cs_set_protected_nopar:Npn \prg_set_conditional:Nnn
-  { \prg_generate_conditional_count_aux:NNnn \cs_set:Npn }
+  { \__prg_generate_conditional_count:nnNnn { set } { } }
 \cs_set_protected_nopar:Npn \prg_new_conditional:Nnn
-  { \prg_generate_conditional_count_aux:NNnn \cs_new:Npn }
+  { \__prg_generate_conditional_count:nnNnn { new } { } }
 \cs_set_protected_nopar:Npn \prg_set_protected_conditional:Nnn
-  { \prg_generate_conditional_count_aux:NNnn \cs_set_protected:Npn }
+  { \__prg_generate_conditional_count:nnNnn { set } { _protected } }
 \cs_set_protected_nopar:Npn \prg_new_protected_conditional:Nnn
-  { \prg_generate_conditional_count_aux:NNnn \cs_new_protected:Npn }
-\cs_set_protected:Npn \prg_generate_conditional_count_aux:NNnn #1#2
+  { \__prg_generate_conditional_count:nnNnn { new } { _protected } }
+\cs_set_protected:Npn \__prg_generate_conditional_count:nnNnn #1#2#3
+  {
+    \__cs_split_function:NN #3 \__prg_generate_conditional_count:nnNnnnn
+    {#1} {#2}
+  }
+\cs_set_protected:Npn \__prg_generate_conditional_count:nnNnnnn #1#2#3#4#5
   {
-    \exp_args:Nnf \use:n
+    \__cs_parm_from_arg_count:nnF
+      { \__prg_generate_conditional:nnNnnnnn {#1} {#2} #3 {#4} {#5} }
+      { \tl_count:n {#2} }
       {
-        \cs_split_function:NN #2 \prg_generate_conditional_aux:nnNNnnnn
-        #1 { count }
+        \__msg_kernel_error:nnxx { kernel } { bad-number-of-arguments }
+          { \token_to_str:c { #1 : #2 } }
+          { \tl_count:n {#2} }
+        \use_none:nn
       }
-      { \cs_get_arg_count_from_signature:N #2 }
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\prg_set_eq_conditional:NNn,\prg_new_eq_conditional:NNn}
-%    The obvious setting-equal functions.
-%    \begin{macrocode}
-\cs_set_protected:Npn \prg_set_eq_conditional:NNn #1#2#3
-  { \prg_set_eq_conditional_aux:NNNn \cs_set_eq:cc #1#2 {#3} }
-\cs_set_protected:Npn \prg_new_eq_conditional:NNn #1#2#3
-  { \prg_set_eq_conditional_aux:NNNn \cs_new_eq:cc #1#2 {#3} }
-%    \end{macrocode}
-% \end{macro}
-%
 % \begin{macro}[aux]
 %   {
-%     \prg_generate_conditional_aux:nnNNnnnn,
-%     \prg_generate_conditional_aux:nnw
+%     \__prg_generate_conditional:nnNnnnnn,
+%     \__prg_generate_conditional:nnnnnnw
 %   }
 %   The workhorse here is going through a list of desired forms, \emph{i.e.},
 %   |p|, |TF|, |T| and |F|. The first three arguments come from splitting up
 %   the base form of the conditional, which gives the name, signature
 %   and a boolean to signal whether or not there was a colon in the
-%   name. For the time being, we do not use this piece of information
-%   but could well throw an error. The fourth argument is how to
-%   define this function, the fifth is the text |parm| or |count| for
-%   which version to use to define the functions, the sixth is the
-%   parameters to use (possibly empty) or number of arguments, the
-%   seventh is the list of forms to define, the eight is the
+%   name. In the absence of a colon, we throw an error and don't define
+%   any conditional. The fourth and fifth arguments build up the
+%   defining function.  The sixth is the parameters to use (possibly
+%   empty), the seventh is the list of forms to define, the eigth is the
 %   replacement text which we will augment when defining the forms.
 %    \begin{macrocode}
-\cs_set_protected:Npn \prg_generate_conditional_aux:nnNNnnnn #1#2#3#4#5#6#7#8
+\cs_set_protected:Npn \__prg_generate_conditional:nnNnnnnn #1#2#3#4#5#6#7#8
   {
-    \prg_generate_conditional_aux:nnw {#5}
-      {
-        #4 {#1} {#2} {#6} {#8}
-      }
-      #7 , ? , \q_recursion_stop
+    \if_meaning:w \c_true_bool #3
+      \exp_after:wN \use_i:nn
+    \else:
+      \exp_after:wN \use_ii:nn
+    \fi:
+    {
+      \__prg_generate_conditional:nnnnnnw
+        {#4} {#5} {#1} {#2} {#6} {#8}
+        #7 , , \q_recursion_stop
+    }
+    {
+      \__msg_kernel_error:nnx { kernel } { missing-colon }
+        { \token_to_str:c {#1} }
+    }
   }
 %    \end{macrocode}
-%   Looping through the list of desired forms. First is the text |parm|
-%   or |count|, second is five arguments packed together and third is
-%   the form. Use text and form to call the correct type.
+%   Looping through the list of desired forms.  First are six arguments
+%   and seventh is the form.  Use the form to call the
+%   correct type.  If the form does not exist, the \cs{use:c}
+%   construction results in \tn{relax}, and the error message is
+%   displayed, then \cs{use_none:nnnnnnn} cleans up.  Otherwise, the
+%   error message is removed by the variant form.
 %    \begin{macrocode}
-\cs_set_protected:Npn \prg_generate_conditional_aux:nnw #1#2#3 ,
+\cs_set_protected:Npn \__prg_generate_conditional:nnnnnnw #1#2#3#4#5#6#7 ,
   {
-    \if:w ?#3
+    \if_catcode:w \scan_stop: \etex_detokenize:D {#7} \scan_stop:
       \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
     \fi:
-    \use:c { prg_generate_#3_form_#1:Nnnnn } #2
-    \prg_generate_conditional_aux:nnw {#1} {#2}
+    \use:c { __prg_generate_ \etex_detokenize:D {#7} _form:wnnnnnn }
+        \__msg_kernel_error:nnxx
+          { kernel } { conditional-form-unknown }
+          { \tl_to_str:n {#7} } { \token_to_str:c { #3 : #4 } }
+        \use_none:nnnnnnn
+      \q_stop
+      {#1} {#2} {#3} {#4} {#5} {#6}
+    \__prg_generate_conditional:nnnnnnw {#1} {#2} {#3} {#4} {#5} {#6}
   }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}[aux]
 %   {
-%     \prg_generate_p_form_parm:Nnnnn,
-%     \prg_generate_TF_form_parm:Nnnnn,
-%     \prg_generate_T_form_parm:Nnnnn,
-%     \prg_generate_F_form_parm:Nnnnn
+%     \__prg_generate_p_form:wnnnnnn,
+%     \__prg_generate_TF_form:wnnnnnn,
+%     \__prg_generate_T_form:wnnnnnn,
+%     \__prg_generate_F_form:wnnnnnn
 %   }
-%   How to generate the various forms. The |parm| types here takes the
-%   following arguments: 1: how to define (an N-type), 2: name, 3:
-%   signature, 4: parameter text (or empty), 5: replacement. Remember that
-%   the logic-returning functions expect two arguments to be present after
-%   \cs{c_zero}: notice the construction  of the different variants
-%   relies on this, and that the |TF| variant will be slightly faster
-%   than the |T| version.
-%    \begin{macrocode}
-\cs_set_protected:Npn \prg_generate_p_form_parm:Nnnnn #1#2#3#4#5
+%   How to generate the various forms. Those functions take the
+%   following arguments: 1: \texttt{set} or \texttt{new}, 2: empty or
+%   \texttt{\_protected}, 3: function name 4: signature, 5: parameter
+%   text (or empty), 6: replacement. Remember that the logic-returning
+%   functions expect two arguments to be present after \cs{c_zero}:
+%   notice the construction of the different variants relies on this,
+%   and that the |TF| variant will be slightly faster than the |T|
+%   version.  The |p| form is only valid for expandable tests, we check
+%   for that by making sure that the second argument is empty.
+%    \begin{macrocode}
+\cs_set_protected:Npn \__prg_generate_p_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc #1 { #2 _p: #3 } #4
+    \if_meaning:w \scan_stop: #3 \scan_stop:
+      \exp_after:wN \use_i:nn
+    \else:
+      \exp_after:wN \use_ii:nn
+    \fi:
       {
-        #5 \c_zero
-        \c_true_bool \c_false_bool
+        \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 _p: #5 } #6
+          { #7 \c_zero \c_true_bool \c_false_bool }
       }
-  }
-\cs_set_protected:Npn \prg_generate_T_form_parm:Nnnnn #1#2#3#4#5
-  {
-    \exp_args:Nc #1 { #2 : #3 T } #4
       {
-        #5 \c_zero
-        \use:n \use_none:n
+        \__msg_kernel_error:nnx { kernel } { protected-predicate }
+          { \token_to_str:c { #4 _p: #5 } }
       }
   }
-\cs_set_protected:Npn \prg_generate_F_form_parm:Nnnnn #1#2#3#4#5
+\cs_set_protected:Npn \__prg_generate_T_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc #1 { #2 : #3 F } #4
-      {
-        #5 \c_zero
-        { }
-      }
+    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 T } #6
+      { #7 \c_zero \use:n \use_none:n }
   }
-\cs_set_protected:Npn \prg_generate_TF_form_parm:Nnnnn #1#2#3#4#5
+\cs_set_protected:Npn \__prg_generate_F_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc #1 { #2 : #3 TF } #4
-      { #5 \c_zero }
+    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 F } #6
+      { #7 \c_zero { } }
+  }
+\cs_set_protected:Npn \__prg_generate_TF_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
+  {
+    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 TF } #6
+      { #7 \c_zero }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]
-%   {
-%     \prg_generate_p_form_count:Nnnnn,
-%     \prg_generate_TF_form_count:Nnnnn,
-%     \prg_generate_T_form_count:Nnnnn,
-%     \prg_generate_F_form_count:Nnnnn
-%   }
-%   The |count| form is similar, but of course requires a number rather
-%   than a primitive argument specification.
+% \begin{macro}{\prg_set_eq_conditional:NNn,\prg_new_eq_conditional:NNn}
+%   The setting-equal functions.  Split the base function to be copied,
+%   and feed a first auxiliary \Arg{name} \Arg{signature} \meta{boolean}
+%   \meta{copying~function} \meta{new~function} \Arg{conditions}.
 %    \begin{macrocode}
-\cs_set_protected:Npn \prg_generate_p_form_count:Nnnnn #1#2#3#4#5
+\cs_set_protected:Npn \prg_set_eq_conditional:NNn #1#2
   {
-    \cs_generate_from_arg_count:cNnn { #2 _p: #3 } #1 {#4}
-      {
-        #5 \c_zero
-        \c_true_bool \c_false_bool
-      }
+    \__cs_split_function:NN #2 \__prg_set_eq_conditional:nnNNNn
+    \cs_set_eq:cc #1
   }
-\cs_set_protected:Npn \prg_generate_T_form_count:Nnnnn #1#2#3#4#5
+\cs_set_protected:Npn \prg_new_eq_conditional:NNn #1#2
   {
-    \cs_generate_from_arg_count:cNnn { #2 : #3 T } #1 {#4}
-      {
-        #5 \c_zero
-        \use:n \use_none:n
-      }
-  }
-\cs_set_protected:Npn \prg_generate_F_form_count:Nnnnn #1#2#3#4#5
-  {
-    \cs_generate_from_arg_count:cNnn { #2 : #3 F } #1 {#4}
-      {
-        #5 \c_zero
-        { }
-      }
-  }
-\cs_set_protected:Npn \prg_generate_TF_form_count:Nnnnn #1#2#3#4#5
-  {
-    \cs_generate_from_arg_count:cNnn { #2 : #3 TF } #1 {#4}
-      { #5 \c_zero }
+    \__cs_split_function:NN #2 \__prg_set_eq_conditional:nnNNNn
+    \cs_new_eq:cc #1
   }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}[aux]
-%   {\prg_set_eq_conditional_aux:NNNn, \prg_set_eq_conditional_aux:NNNw}
+%   {
+%     \__prg_set_eq_conditional:nnNNNn   ,
+%     \__prg_set_eq_conditional:nnNnnNNw ,
+%     \__prg_set_eq_conditional_loop:nnnnNw
+%   }
 % \begin{macro}[aux, EXP]
 %   {
-%     \prg_conditional_form_p:nnn  ,
-%     \prg_conditional_form_TF:nnn ,
-%     \prg_conditional_form_T:nnn  ,
-%     \prg_conditional_form_F:nnn  ,
+%     \__prg_conditional_p_form:nnn  ,
+%     \__prg_conditional_TF_form:nnn ,
+%     \__prg_conditional_T_form:nnn  ,
+%     \__prg_conditional_F_form:nnn  ,
 %   }
-%   Manual clist loop over argument |#4|.
-%    \begin{macrocode}
-\cs_set_protected:Npn \prg_set_eq_conditional_aux:NNNn #1#2#3#4
-  { \prg_set_eq_conditional_aux:NNNw #1#2#3#4 , ? , \q_recursion_stop }
-\cs_set_protected:Npn \prg_set_eq_conditional_aux:NNNw #1#2#3#4 ,
+%   Split the function to be defined, and setup a manual clist loop over
+%   argument |#6| of the first auxiliary.  The second auxiliary receives
+%   twice three arguments coming from splitting the function to be
+%   defined and the function to copy.  Make sure that both functions
+%   contained a colon, otherwise we don't know how to build
+%   conditionals, hence abort.  Call the looping macro, with arguments
+%   \Arg{name_1} \Arg{signature_1} \Arg{name_2} \Arg{signature_2}
+%   \meta{copying~function} and followed by the comma list.  At each
+%   step in the loop, make sure that the conditional form we copy is
+%   defined, and copy it, otherwise abort.
+%    \begin{macrocode}
+\cs_set_protected:Npn \__prg_set_eq_conditional:nnNNNn #1#2#3#4#5#6
   {
-    \if:w ? #4 \scan_stop:
+    \__cs_split_function:NN #5 \__prg_set_eq_conditional:nnNnnNNw
+    {#1} {#2} #3 #4
+    #6 , \scan_stop: , \q_recursion_stop
+  }
+\cs_set_protected:Npn \__prg_set_eq_conditional:nnNnnNNw #1#2#3#4#5#6
+  {
+    \if_meaning:w \c_false_bool #3
+      \__msg_kernel_error:nnx { kernel } { missing-colon }
+        { \token_to_str:c {#1} }
+      \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
+    \fi:
+    \if_meaning:w \c_false_bool #6
+      \__msg_kernel_error:nnx { kernel } { missing-colon }
+        { \token_to_str:c {#4} }
       \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
     \fi:
-    #1
-    { \exp_args:NNc \cs_split_function:NN #2 { prg_conditional_form_#4:nnn } }
-    { \exp_args:NNc \cs_split_function:NN #3 { prg_conditional_form_#4:nnn } }
-    \prg_set_eq_conditional_aux:NNNw #1 {#2} {#3}
+    \__prg_set_eq_conditional_loop:nnnnNw {#1} {#2} {#4} {#5}
+  }
+\cs_set_protected:Npn \__prg_set_eq_conditional_loop:nnnnNw #1#2#3#4#5#6 ,
+  {
+    \if_meaning:w \scan_stop: #6 \scan_stop:
+      \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
+    \fi:
+    \cs_if_exist:cTF
+      { \use:c { __prg_conditional_ #6 _form:nn } {#3} {#4} }
+      {
+        #5
+          { \use:c { __prg_conditional_ #6 _form:nn } {#1} {#2} }
+          { \use:c { __prg_conditional_ #6 _form:nn } {#3} {#4} }
+      }
+      {
+        \__msg_kernel_error:nnx { kernel } { command-not-defined }
+          {
+            \token_to_str:c
+              { \use:c { __prg_conditional_ #6 _form:nn } {#3} {#4} }
+          }
+      }
+    \__prg_set_eq_conditional_loop:nnnnNw {#1} {#2} {#3} {#4} #5
   }
-\cs_set:Npn \prg_conditional_form_p:nnn  #1#2#3 { #1 _p : #2 }
-\cs_set:Npn \prg_conditional_form_TF:nnn #1#2#3 { #1    : #2 TF }
-\cs_set:Npn \prg_conditional_form_T:nnn  #1#2#3 { #1    : #2 T }
-\cs_set:Npn \prg_conditional_form_F:nnn  #1#2#3 { #1    : #2 F }
+\cs_set:Npn \__prg_conditional_p_form:nn  #1#2 { #1 _p : #2 }
+\cs_set:Npn \__prg_conditional_TF_form:nn #1#2 { #1    : #2 TF }
+\cs_set:Npn \__prg_conditional_T_form:nn  #1#2 { #1    : #2 T }
+\cs_set:Npn \__prg_conditional_F_form:nn  #1#2 { #1    : #2 F }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1941,7 +2044,7 @@
 % All that is left is to define the canonical boolean true and false.
 % I think Michael originated the idea of expandable boolean tests.  At
 % first these were supposed to expand into either \texttt{TT} or
-% \texttt{TF} to be tested using |\if:w| but this was later changed to
+% \texttt{TF} to be tested using \cs{if:w} but this was later changed to
 % |00| and |01|, so they could be used in logical
 % operations. Later again they were changed to being numerical
 % constants with values of $1$ for true and $0$ for false. We need
@@ -1950,22 +2053,22 @@
 % \begin{variable}{\c_true_bool, \c_false_bool}
 %    Here are the canonical boolean values.
 %    \begin{macrocode}
-\tex_chardef:D \c_true_bool  = 1~
-\tex_chardef:D \c_false_bool = 0~
+\tex_chardef:D \c_true_bool  = 1 ~
+\tex_chardef:D \c_false_bool = 0 ~
 %    \end{macrocode}
 % \end{variable}
 %
 % \subsection{Dissecting a control sequence}
 %
 % \begin{macro}[EXP]{\cs_to_str:N}
-% \begin{macro}[aux, EXP]{\cs_to_str_aux:N, \cs_to_str_aux:w}
+% \begin{macro}[aux, EXP]{\__cs_to_str:N, \__cs_to_str:w}
 %   This converts a control sequence into the character string of its
 %   name, removing the leading escape character. This turns out to be
 %   a non-trivial matter as there a different cases:
 %   \begin{itemize}
 %     \item The usual case of a printable escape character;
 %     \item the case of a non-printable escape characters, e.g., when
-%     the value of |\tex_escapechar:D| is negative;
+%     the value of the \tn{escapechar} is negative;
 %     \item when the escape character is a space.
 %   \end{itemize}
 %   One approach to solve this is to test how many tokens result from
@@ -1979,109 +2082,97 @@
 %   a little more intricate still. When the escape character is printable,
 %   \verb*|\token_to_str:N \ | yields the escape character itself and a space.
 %   The character codes are different, thus the \cs{if:w} test is false,
-%   and \TeX{} reads \cs{cs_to_str_aux:N} after turning the following
+%   and \TeX{} reads \cs{__cs_to_str:N} after turning the following
 %   control sequence into a string; this auxiliary removes the escape
-%   character, and stops the expansion of the initial \cs{int_to_roman:w}.
+%   character, and stops the expansion of the initial \cs{__int_to_roman:w}.
 %   The second case is that the escape character is not printable. Then
 %   the \cs{if:w} test is unfinished after reading a the space from
-%   \verb*|\token_to_str:N \ |, and the auxiliary \cs{cs_to_str_aux:w}
+%   \verb*|\token_to_str:N \ |, and the auxiliary \cs{__cs_to_str:w}
 %   is expanded, feeding |-| as a second character for the test;
 %   the test is false, and \TeX{} skips to \cs{fi:}, then performs
-%   \cs{token_to_str:N}, and stops the \cs{int_to_roman:w} with \cs{c_zero}.
+%   \cs{token_to_str:N}, and stops the \cs{__int_to_roman:w} with \cs{c_zero}.
 %   The last case is that the escape character is itself a space. In this
-%   case, the \cs{if:w} test is true, and the auxiliary \cs{cs_to_str_aux:w}
-%   comes into play, inserting |-\int_value:w|, which expands \cs{c_zero}
-%   to the character |0|. The initial \cs{int_to_roman:w} then sees
+%   case, the \cs{if:w} test is true, and the auxiliary \cs{__cs_to_str:w}
+%   comes into play, inserting |-\__int_value:w|, which expands \cs{c_zero}
+%   to the character |0|. The initial \cs{__int_to_roman:w} then sees
 %   |0|, which is not a terminated number, followed by the escape character,
 %   a space, which is removed, terminating the argument of
-%   \cs{int_to_roman:w}.
+%   \cs{__int_to_roman:w}.
 %   In all three cases, \cs{cs_to_str:N} takes two expansion steps
 %   to be fully expanded.
 %    \begin{macrocode}
 \cs_set_nopar:Npn \cs_to_str:N
   {
-    \int_to_roman:w
-      \if:w \token_to_str:N \ \cs_to_str_aux:w \fi:
-      \exp_after:wN \cs_to_str_aux:N \token_to_str:N
+    \__int_to_roman:w
+      \if:w \token_to_str:N \ \__cs_to_str:w \fi:
+      \exp_after:wN \__cs_to_str:N \token_to_str:N
   }
-\cs_set:Npn \cs_to_str_aux:N #1 { \c_zero }
-\cs_set:Npn \cs_to_str_aux:w #1 \cs_to_str_aux:N
-  { - \int_value:w \fi: \exp_after:wN \c_zero }
+\cs_set:Npn \__cs_to_str:N #1 { \c_zero }
+\cs_set:Npn \__cs_to_str:w #1 \__cs_to_str:N
+  { - \__int_value:w \fi: \exp_after:wN \c_zero }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[EXP]{\cs_split_function:NN}
+% \begin{macro}[EXP, int]{\__cs_split_function:NN}
 % \begin{macro}[aux, EXP]
-%   {\cs_split_function_aux:w, \cs_split_function_auxii:w}
+%   {\__cs_split_function_i:w, \__cs_split_function_ii:w}
 %   This function takes a function name and splits it into name with
 %   the escape char removed and argument specification. In addition to
 %   this, a third argument, a boolean \meta{true} or \meta{false} is
 %   returned with \meta{true} for when there is a colon in the function
 %   and \meta{false} if there is not. Lastly, the second argument of
-%   \cs{cs_split_function:NN} is supposed to be a function
+%   \cs{__cs_split_function:NN} is supposed to be a function
 %   taking three variables, one for name, one for signature, and one
 %   for the boolean.  For example,
-%   |\cs_split_function:NN\foo_bar:cnx\use_i:nnn| as input
-%   becomes |\use_i:nnn {foo_bar}{cnx}\c_true_bool|.
-%
-%   Can't use a literal |:| because it has the wrong catcode here, so
-%   it's transformed from |@| with |\tex_lowercase:D|.
+%   |\__cs_split_function:NN \foo_bar:cnx \use_i:nnn| as input
+%   becomes |\use_i:nnn {foo_bar} {cnx} \c_true_bool|.
+%
+%   We can't use a literal |:| because it has the wrong catcode here, so
+%   it's transformed from |@| with \cs{tex_lowercase:D}.
+%
+%   First ensure that we actually get a properly evaluated string by
+%   expanding \cs{cs_to_str:N} twice.  If the function contained a
+%   colon, the auxiliary takes as |#1| the function name, delimited by
+%   the first colon, then the signature |#2|, delimited by \cs{q_mark},
+%   then \cs{c_true_bool} as |#3|, and |#4| cleans up until \cs{q_stop}.
+%   Otherwise, the |#1| contains the function name and \cs{q_mark}
+%   \cs{c_true_bool}, |#2| is empty, |#3| is \cs{c_false_bool}, and |#4|
+%   cleans up.  In both cases, |#5| is the \meta{processor}.  The second
+%   auxiliary trims the trailing \cs{q_mark} from the function name if
+%   present (that is, if the original function had no colon).
 %    \begin{macrocode}
 \group_begin:
-  \tex_lccode:D  `\@ = `\: \scan_stop:
-  \tex_catcode:D `\@ = 12~
+\tex_lccode:D  `\@ = `\: \scan_stop:
+\tex_catcode:D `\@ = 12 ~
 \tex_lowercase:D
   {
     \group_end:
-%    \end{macrocode}
-%   First ensure that we actually get a properly evaluated str
-%   by expanding \cs{cs_to_str:N} twice.  Insert
-%   extra colon to catch the error cases.
-%    \begin{macrocode}
-    \cs_set:Npn \cs_split_function:NN #1#2
+    \cs_set:Npn \__cs_split_function:NN #1
       {
         \exp_after:wN \exp_after:wN
-        \exp_after:wN \cs_split_function_aux:w
-          \cs_to_str:N #1 @ a \q_stop #2
-      }
-%    \end{macrocode}
-%   If no colon in the name, |#2| is |a| with catcode 11 and |#3| is
-%   empty.  If colon in the name, then either |#2| is a colon or the
-%   first letter of the signature.  The letters here have catcode 12.
-%   If a colon was given we need to a) split off the colon and quark at
-%   the end and b) ensure we return the name, signature and boolean true
-%   We can't use \cs{quark_if_no_value:NTF} yet but this is very safe
-%   anyway as all tokens have catcode~12.
-%    \begin{macrocode}
-    \cs_set:Npn \cs_split_function_aux:w #1 @ #2#3 \q_stop #4
-      {
-        \if_meaning:w a #2
-          \exp_after:wN \use_i:nn
-        \else:
-          \exp_after:wN\use_ii:nn
-        \fi:
-        { #4 {#1} { } \c_false_bool }
-        { \cs_split_function_auxii:w #2#3 \q_stop #4 {#1} }
+        \exp_after:wN \__cs_split_function_i:w
+          \cs_to_str:N #1 \q_mark \c_true_bool
+          @ \q_mark \c_false_bool
+          \q_stop
       }
-    \cs_set:Npn \cs_split_function_auxii:w #1 @a \q_stop #2#3
-      { #2{#3}{#1}\c_true_bool }
-%    \end{macrocode}
-% End of lowercase
-%    \begin{macrocode}
+    \cs_set:Npn \__cs_split_function_i:w #1 @ #2 \q_mark #3#4 \q_stop #5
+      { \__cs_split_function_ii:w #5 #1 \q_mark \q_stop {#2} #3 }
+    \cs_set:Npn \__cs_split_function_ii:w #1#2 \q_mark #3 \q_stop
+      { #1 {#2} }
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[EXP]{\cs_get_function_name:N, \cs_get_function_signature:N}
-%     Now returning the name is trivial: just discard the last two
-%     arguments. Similar for signature.
+% \begin{macro}[EXP, int]
+%   {\__cs_get_function_name:N, \__cs_get_function_signature:N}
+%   Simple wrappers.
 %    \begin{macrocode}
-\cs_set:Npn \cs_get_function_name:N #1
-  { \cs_split_function:NN #1 \use_i:nnn }
-\cs_set:Npn \cs_get_function_signature:N #1
-  { \cs_split_function:NN #1 \use_ii:nnn }
+\cs_set:Npn \__cs_get_function_name:N #1
+  { \__cs_split_function:NN #1 \use_i:nnn }
+\cs_set:Npn \__cs_get_function_signature:N #1
+  { \__cs_split_function:NN #1 \use_ii:nnn }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2089,15 +2180,15 @@
 %
 % A control sequence is said to \emph{exist} (to be used) if has an entry in
 % the hash table and its meaning is different from the primitive
-% |\tex_relax:D| token. A control sequence is said to be \emph{free}
+% \tn{relax} token. A control sequence is said to be \emph{free}
 % (to be defined) if it does not already exist.
 %
 % \begin{macro}[pTF, EXP]{\cs_if_exist:N,\cs_if_exist:c}
 %   Two versions for checking existence. For the |N| form we firstly
-%   check for |\scan_stop:| and then if it is in the hash
-%   table. There is no problem when inputting something like |\else:|
-%   or |\fi:| as \TeX{} will only ever skip input in case the token
-%   tested against is |\scan_stop:|.
+%   check for \cs{scan_stop:} and then if it is in the hash
+%   table. There is no problem when inputting something like \cs{else:}
+%   or \cs{fi:} as \TeX{} will only ever skip input in case the token
+%   tested against is \cs{scan_stop:}.
 %    \begin{macrocode}
 \prg_set_conditional:Npnn \cs_if_exist:N #1 { p , T , F , TF }
   {
@@ -2113,7 +2204,7 @@
   }
 %    \end{macrocode}
 %   For the |c| form we firstly check if it is in the hash table and
-%   then for |\scan_stop:| so that we do not add it to the hash table
+%   then for \cs{scan_stop:} so that we do not add it to the hash table
 %   unless it was already there. Here we have to be careful as the text
 %   to be skipped if the first test is false may contain tokens that
 %   disturb the scanner. Therefore, we ensure that the second test is
@@ -2226,14 +2317,14 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}
-%   {\msg_kernel_error:nnxx, \msg_kernel_error:nnx, \msg_kernel_error:nn}
+% \begin{macro}[int]
+%   {\__msg_kernel_error:nnxx, \__msg_kernel_error:nnx, \__msg_kernel_error:nn}
 %   If an internal error occurs before \LaTeX3 has loaded \pkg{l3msg} then
 %   the code should issue a usable if terse error message and halt. This
 %   can only happen if a coding error is made by the team, so this is
 %   a reasonable response.
 %    \begin{macrocode}
-\cs_set_protected:Npn \msg_kernel_error:nnxx #1#2#3#4
+\cs_set_protected:Npn \__msg_kernel_error:nnxx #1#2#3#4
   {
     \tex_errmessage:D
       {
@@ -2245,10 +2336,10 @@
       }
     \tex_end:D
   }
-\cs_set_protected:Npn \msg_kernel_error:nnx #1#2#3
-  { \msg_kernel_error:nnxx {#1} {#2} {#3} { } }
-\cs_set_protected:Npn \msg_kernel_error:nn #1#2
-  { \msg_kernel_error:nnxx {#1} {#2} { } { } }
+\cs_set_protected:Npn \__msg_kernel_error:nnx #1#2#3
+  { \__msg_kernel_error:nnxx {#1} {#2} {#3} { } }
+\cs_set_protected:Npn \__msg_kernel_error:nn #1#2
+  { \__msg_kernel_error:nnxx {#1} {#2} { } { } }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2256,11 +2347,11 @@
 %   Another one from \pkg{l3msg} which will be altered later.
 %    \begin{macrocode}
 \cs_set_nopar:Npn \msg_line_context:
-  { on~line~\tex_the:D \tex_inputlineno:D }
+  { on~line~ \tex_the:D \tex_inputlineno:D }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\chk_if_free_cs:N, \chk_if_free_cs:c}
+% \begin{macro}[int]{\__chk_if_free_cs:N, \__chk_if_free_cs:c}
 %   This command is called by \cs{cs_new_nopar:Npn} and \cs{cs_new_eq:NN}
 %   \emph{etc.}\
 %   to make sure that the argument sequence is not already in use. If
@@ -2269,46 +2360,46 @@
 %   issued. We have to make sure we don't put the argument into the
 %   conditional processing since it may be an |\if...| type function!
 %    \begin{macrocode}
-\cs_set_protected:Npn \chk_if_free_cs:N #1
+\cs_set_protected:Npn \__chk_if_free_cs:N #1
   {
     \cs_if_free:NF #1
       {
-        \msg_kernel_error:nnxx { kernel } { command-already-defined }
+        \__msg_kernel_error:nnxx { kernel } { command-already-defined }
           { \token_to_str:N #1 } { \token_to_meaning:N #1 }
       }
 }
 %<*package>
 \tex_ifodd:D \l@expl@log@functions@bool
-  \cs_set_protected:Npn \chk_if_free_cs:N #1
+  \cs_set_protected:Npn \__chk_if_free_cs:N #1
     {
       \cs_if_free:NF #1
         {
-          \msg_kernel_error:nnxx { kernel } { command-already-defined }
+          \__msg_kernel_error:nnxx { kernel } { command-already-defined }
             { \token_to_str:N #1 } { \token_to_meaning:N #1 }
         }
       \iow_log:x { Defining~\token_to_str:N #1~ \msg_line_context: }
     }
 \fi:
 %</package>
-\cs_set_protected_nopar:Npn \chk_if_free_cs:c
-  { \exp_args:Nc \chk_if_free_cs:N }
+\cs_set_protected_nopar:Npn \__chk_if_free_cs:c
+  { \exp_args:Nc \__chk_if_free_cs:N }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\chk_if_exist_cs:N, \chk_if_exist_cs:c}
-%    This function issues a warning message when the control sequence
+% \begin{macro}[int]{\__chk_if_exist_cs:N, \__chk_if_exist_cs:c}
+%    This function issues an error message when the control sequence
 %    in its argument does not exist.
 %    \begin{macrocode}
-\cs_set_protected:Npn \chk_if_exist_cs:N #1
+\cs_set_protected:Npn \__chk_if_exist_cs:N #1
   {
     \cs_if_exist:NF #1
       {
-        \msg_kernel_error:nnxx { kernel } { command-not-defined }
-          { \token_to_str:N #1 } { \token_to_meaning:N #1 }
+        \__msg_kernel_error:nnx { kernel } { command-not-defined }
+          { \token_to_str:N #1 }
       }
   }
-\cs_set_protected_nopar:Npn \chk_if_exist_cs:c
-  { \exp_args:Nc \chk_if_exist_cs:N }
+\cs_set_protected_nopar:Npn \__chk_if_exist_cs:c
+  { \exp_args:Nc \__chk_if_exist_cs:N }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2324,22 +2415,22 @@
 %   Function which check that the control sequence is free before
 %   defining it.
 %     \begin{macrocode}
-\cs_set:Npn \cs_tmp:w #1#2
+\cs_set:Npn \__cs_tmp:w #1#2
   {
     \cs_set_protected:Npn #1 ##1
        {
-         \chk_if_free_cs:N ##1
+         \__chk_if_free_cs:N ##1
          #2 ##1
       }
   }
-\cs_tmp:w \cs_new_nopar:Npn           \cs_gset_nopar:Npn
-\cs_tmp:w \cs_new_nopar:Npx           \cs_gset_nopar:Npx
-\cs_tmp:w \cs_new:Npn                 \cs_gset:Npn
-\cs_tmp:w \cs_new:Npx                 \cs_gset:Npx
-\cs_tmp:w \cs_new_protected_nopar:Npn \cs_gset_protected_nopar:Npn
-\cs_tmp:w \cs_new_protected_nopar:Npx \cs_gset_protected_nopar:Npx
-\cs_tmp:w \cs_new_protected:Npn       \cs_gset_protected:Npn
-\cs_tmp:w \cs_new_protected:Npx       \cs_gset_protected:Npx
+\__cs_tmp:w \cs_new_nopar:Npn           \cs_gset_nopar:Npn
+\__cs_tmp:w \cs_new_nopar:Npx           \cs_gset_nopar:Npx
+\__cs_tmp:w \cs_new:Npn                 \cs_gset:Npn
+\__cs_tmp:w \cs_new:Npx                 \cs_gset:Npx
+\__cs_tmp:w \cs_new_protected_nopar:Npn \cs_gset_protected_nopar:Npn
+\__cs_tmp:w \cs_new_protected_nopar:Npx \cs_gset_protected_nopar:Npx
+\__cs_tmp:w \cs_new_protected:Npn       \cs_gset_protected:Npn
+\__cs_tmp:w \cs_new_protected:Npx       \cs_gset_protected:Npx
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2360,14 +2451,14 @@
 %   \cs{cs_set_nopar:Npn}.  This means that there might be a parameter
 %   string between the two arguments.
 %    \begin{macrocode}
-\cs_set:Npn \cs_tmp:w #1#2
+\cs_set:Npn \__cs_tmp:w #1#2
   { \cs_new_protected_nopar:Npn #1 { \exp_args:Nc #2 } }
-\cs_tmp:w \cs_set_nopar:cpn  \cs_set_nopar:Npn
-\cs_tmp:w \cs_set_nopar:cpx  \cs_set_nopar:Npx
-\cs_tmp:w \cs_gset_nopar:cpn \cs_gset_nopar:Npn
-\cs_tmp:w \cs_gset_nopar:cpx \cs_gset_nopar:Npx
-\cs_tmp:w \cs_new_nopar:cpn  \cs_new_nopar:Npn
-\cs_tmp:w \cs_new_nopar:cpx  \cs_new_nopar:Npx
+\__cs_tmp:w \cs_set_nopar:cpn  \cs_set_nopar:Npn
+\__cs_tmp:w \cs_set_nopar:cpx  \cs_set_nopar:Npx
+\__cs_tmp:w \cs_gset_nopar:cpn \cs_gset_nopar:Npn
+\__cs_tmp:w \cs_gset_nopar:cpx \cs_gset_nopar:Npx
+\__cs_tmp:w \cs_new_nopar:cpn  \cs_new_nopar:Npn
+\__cs_tmp:w \cs_new_nopar:cpx  \cs_new_nopar:Npx
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2380,12 +2471,12 @@
 %   Variants of the \cs{cs_set:Npn} versions which make a csname out
 %   of the first arguments. We may also do this globally.
 %    \begin{macrocode}
-\cs_tmp:w \cs_set:cpn  \cs_set:Npn
-\cs_tmp:w \cs_set:cpx  \cs_set:Npx
-\cs_tmp:w \cs_gset:cpn \cs_gset:Npn
-\cs_tmp:w \cs_gset:cpx \cs_gset:Npx
-\cs_tmp:w \cs_new:cpn  \cs_new:Npn
-\cs_tmp:w \cs_new:cpx  \cs_new:Npx
+\__cs_tmp:w \cs_set:cpn  \cs_set:Npn
+\__cs_tmp:w \cs_set:cpx  \cs_set:Npx
+\__cs_tmp:w \cs_gset:cpn \cs_gset:Npn
+\__cs_tmp:w \cs_gset:cpx \cs_gset:Npx
+\__cs_tmp:w \cs_new:cpn  \cs_new:Npn
+\__cs_tmp:w \cs_new:cpx  \cs_new:Npx
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2398,12 +2489,12 @@
 %   Variants of the \cs{cs_set_protected_nopar:Npn} versions which make
 %   a csname out of the first arguments. We may also do this globally.
 %    \begin{macrocode}
-\cs_tmp:w \cs_set_protected_nopar:cpn  \cs_set_protected_nopar:Npn
-\cs_tmp:w \cs_set_protected_nopar:cpx  \cs_set_protected_nopar:Npx
-\cs_tmp:w \cs_gset_protected_nopar:cpn \cs_gset_protected_nopar:Npn
-\cs_tmp:w \cs_gset_protected_nopar:cpx \cs_gset_protected_nopar:Npx
-\cs_tmp:w \cs_new_protected_nopar:cpn  \cs_new_protected_nopar:Npn
-\cs_tmp:w \cs_new_protected_nopar:cpx  \cs_new_protected_nopar:Npx
+\__cs_tmp:w \cs_set_protected_nopar:cpn  \cs_set_protected_nopar:Npn
+\__cs_tmp:w \cs_set_protected_nopar:cpx  \cs_set_protected_nopar:Npx
+\__cs_tmp:w \cs_gset_protected_nopar:cpn \cs_gset_protected_nopar:Npn
+\__cs_tmp:w \cs_gset_protected_nopar:cpx \cs_gset_protected_nopar:Npx
+\__cs_tmp:w \cs_new_protected_nopar:cpn  \cs_new_protected_nopar:Npn
+\__cs_tmp:w \cs_new_protected_nopar:cpx  \cs_new_protected_nopar:Npx
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2416,12 +2507,12 @@
 %   Variants of the \cs{cs_set_protected:Npn} versions which make a csname
 %   out of the first arguments. We may also do this globally.
 %    \begin{macrocode}
-\cs_tmp:w \cs_set_protected:cpn  \cs_set_protected:Npn
-\cs_tmp:w \cs_set_protected:cpx  \cs_set_protected:Npx
-\cs_tmp:w \cs_gset_protected:cpn \cs_gset_protected:Npn
-\cs_tmp:w \cs_gset_protected:cpx \cs_gset_protected:Npx
-\cs_tmp:w \cs_new_protected:cpn  \cs_new_protected:Npn
-\cs_tmp:w \cs_new_protected:cpx  \cs_new_protected:Npx
+\__cs_tmp:w \cs_set_protected:cpn  \cs_set_protected:Npn
+\__cs_tmp:w \cs_set_protected:cpx  \cs_set_protected:Npx
+\__cs_tmp:w \cs_gset_protected:cpn \cs_gset_protected:Npn
+\__cs_tmp:w \cs_gset_protected:cpx \cs_gset_protected:Npx
+\__cs_tmp:w \cs_new_protected:cpn  \cs_new_protected:Npn
+\__cs_tmp:w \cs_new_protected:cpx  \cs_new_protected:Npx
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2456,7 +2547,7 @@
 \cs_new_protected_nopar:Npn \cs_gset_eq:cc { \exp_args:Ncc  \cs_gset_eq:NN }
 \cs_new_protected:Npn \cs_new_eq:NN #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \tex_global:D \cs_set_eq:NN #1
   }
 \cs_new_protected_nopar:Npn \cs_new_eq:cN { \exp_args:Nc  \cs_new_eq:NN }
@@ -2488,57 +2579,88 @@
 %    \end{macrocode}
 % \end{macro}
 %
+% \subsection{Generating parameter text from argument count}
+%
+% \begin{macro}[int]{\__cs_parm_from_arg_count:nnF}
+% \begin{macro}[aux]{\__cs_parm_from_arg_count_test:nnF}
+%   \LaTeX3 provides shorthands to define control sequences and
+%   conditionals with a simple parameter text, derived directly from the
+%   signature, or more generally from knowing the number of arguments,
+%   between~$0$ and~$9$.  This function expands to its first argument,
+%   untouched, followed by a brace group containing the parameter text
+%   |{#|$1$\ldots{}|#|$n$|}|, where $n$ is the result of evaluating the
+%   second argument (as described in \cs{int_eval:n}).  If the second
+%   argument gives a result outside the range $[0,9]$, the third
+%   argument is returned instead, normally an error message.  Some of
+%   the functions use here are not defined yet, but will be defined
+%   before this function is called.
+%    \begin{macrocode}
+\cs_set_protected:Npn \__cs_parm_from_arg_count:nnF #1#2
+  {
+    \exp_args:Nx \__cs_parm_from_arg_count_test:nnF
+      {
+        \exp_after:wN \exp_not:n
+        \if_case:w \__int_eval:w #2 \__int_eval_end:
+             { }
+        \or: { ##1 }
+        \or: { ##1##2 }
+        \or: { ##1##2##3 }
+        \or: { ##1##2##3##4 }
+        \or: { ##1##2##3##4##5 }
+        \or: { ##1##2##3##4##5##6 }
+        \or: { ##1##2##3##4##5##6##7 }
+        \or: { ##1##2##3##4##5##6##7##8 }
+        \or: { ##1##2##3##4##5##6##7##8##9 }
+        \else: { \c_false_bool }
+        \fi:
+      }
+      {#1}
+  }
+\cs_set_protected:Npn \__cs_parm_from_arg_count_test:nnF #1#2
+  {
+    \if_meaning:w \c_false_bool #1
+      \exp_after:wN \use_ii:nn
+    \else:
+      \exp_after:wN \use_i:nn
+    \fi:
+    { #2 {#1} }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
 % \subsection{Defining functions from a given number of arguments}
 %
-% \begin{macro}[EXP]{\cs_get_arg_count_from_signature:N}
-% \begin{macro}[aux, EXP]
-%   {
-%     \cs_get_arg_count_from_signature_aux:nnN,
-%     \cs_get_arg_count_from_signature_auxii:w
-%   }
-%   Counting the number of tokens in the signature, i.e., the number
-%   of arguments the function should take.  If there is no signature,
-%   we return that there is $-1$ arguments to signal an error.
-%   Otherwise we insert the string |9876543210| after the signature.
-%   If the signature is empty, the number we want is $0$ so we remove
-%   the first nine tokens and return the tenth.  Similarly, if the
-%   signature is |nnn| we want to remove the nine tokens |nnn987654|
-%   and return $3$.  Therefore, we simply remove the first nine tokens
-%   and then return the tenth.
-%    \begin{macrocode}
-\cs_new:Npn \cs_get_arg_count_from_signature:N #1
-  { \cs_split_function:NN #1 \cs_get_arg_count_from_signature_aux:nnN }
-\cs_new:Npn \cs_get_arg_count_from_signature_aux:nnN #1#2#3
+% \begin{macro}[EXP, int]{\__cs_count_signature:N, \__cs_count_signature:c}
+% \begin{macro}[aux, EXP]{\__cs_count_signature:nnN}
+%   Counting the number of tokens in the signature, \emph{i.e.}, the
+%   number of arguments the function should take.  Since this is not
+%   used in any time-critical function, we simply use \cs{tl_count:n} if
+%   there is a signature, otherwise $-1$ arguments to signal an error.
+%   We need a variant form right away.
+%    \begin{macrocode}
+\cs_new:Npn \__cs_count_signature:N #1
+  { \int_eval:n { \__cs_split_function:NN #1 \__cs_count_signature:nnN } }
+\cs_new:Npn \__cs_count_signature:nnN #1#2#3
   {
     \if_meaning:w \c_true_bool #3
-      \exp_after:wN \use_i:nn
+      \tl_count:n {#2}
     \else:
-      \exp_after:wN\use_ii:nn
+      \c_minus_one
     \fi:
-    {
-      \exp_after:wN \cs_get_arg_count_from_signature_auxii:w
-        \use_none:nnnnnnnnn  #2 9876543210 \q_stop
-    }
-    { -1 }
-}
-\cs_new:Npn \cs_get_arg_count_from_signature_auxii:w #1#2 \q_stop {#1}
-%    \end{macrocode}
-% A variant form we need right away.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \cs_get_arg_count_from_signature:c
-  { \exp_args:Nc \cs_get_arg_count_from_signature:N }
+  }
+\cs_new_nopar:Npn \__cs_count_signature:c
+  { \exp_args:Nc \__cs_count_signature:N }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[aux]
+% \begin{macro}
 %   {
 %     \cs_generate_from_arg_count:NNnn,
 %     \cs_generate_from_arg_count:cNnn,
 %     \cs_generate_from_arg_count:Ncnn
 %   }
-% \begin{macro}[aux]{\cs_generate_from_arg_count_error_msg:Nn}
-% \begin{macro}[aux]{\cs_generate_from_arg_count_aux:nwn}
 %   We provide a constructor function for defining functions with a
 %   given number of arguments.  For this we need to choose the correct
 %   parameter text and then use that when defining.  Since \TeX{}
@@ -2552,27 +2674,13 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \cs_generate_from_arg_count:NNnn #1#2#3#4
   {
-    \if_case:w \int_eval:w #3 \int_eval_end:
-         \cs_generate_from_arg_count_aux:nwn {}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3##4}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3##4##5}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3##4##5##6}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3##4##5##6##7}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3##4##5##6##7##8}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3##4##5##6##7##8##9}
-    \else:
-      \cs_generate_from_arg_count_error_msg:Nn #1 {#3}
-      \use_i:nnn
-    \fi:
-    {#2#1}
-    {#4}
+    \__cs_parm_from_arg_count:nnF { \use:nnn #2 #1 } {#3}
+      {
+        \__msg_kernel_error:nnxx { kernel } { bad-number-of-arguments }
+          { \token_to_str:N #1 } { \int_eval:n {#3} }
+      }
+      {#4}
   }
-\cs_new_protected:Npn
-  \cs_generate_from_arg_count_aux:nwn #1 #2 \fi: #3
-  { \fi: #3 #1 }
 %    \end{macrocode}
 %   A variant form we need right away, plus one which is used elsewhere but
 %   which is most logically created here.
@@ -2582,17 +2690,6 @@
 \cs_new_protected_nopar:Npn \cs_generate_from_arg_count:Ncnn
   { \exp_args:NNc \cs_generate_from_arg_count:NNnn }
 %    \end{macrocode}
-%   The error message. Elsewhere we use the value of $-1$ to signal a
-%   missing colon in a function, so provide a hint for help on this.
-%    \begin{macrocode}
-\cs_new_protected:Npn \cs_generate_from_arg_count_error_msg:Nn #1#2
-  {
-    \msg_kernel_error:nnxx { kernel } { bad-number-of-arguments }
-      { \token_to_str:N #1 } { \int_eval:n {#2} }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
 % \end{macro}
 %
 % \subsection{Using the signature to define functions}
@@ -2622,7 +2719,7 @@
 %     \cs_set_protected:Npn \cs_set:Nn #1#2
 %       {
 %         \cs_generate_from_arg_count:NNnn #1 \cs_set:Npn
-%           { \cs_get_arg_count_from_signature:N #1 } {#2}
+%           { \__cs_count_signature:N #1 } {#2}
 %       }
 %   \end{verbatim}
 %   In short, to define \cs{cs_set:Nn} we need just use \cs{cs_set:Npn},
@@ -2630,42 +2727,58 @@
 %   make it simpler by temporarily defining a function to do this for
 %   us.
 %    \begin{macrocode}
-\cs_set:Npn \cs_tmp:w #1#2#3
+\cs_set:Npn \__cs_tmp:w #1#2#3
   {
-    \cs_new_protected:cpx { cs_ #1 : #2 } ##1##2
+    \cs_new_protected_nopar:cpx { cs_ #1 : #2 }
       {
-        \exp_not:N \cs_generate_from_arg_count:NNnn ##1
-        \exp_after:wN \exp_not:N \cs:w cs_#1 : #3 \cs_end:
-          { \exp_not:N \cs_get_arg_count_from_signature:N ##1 }{##2}
+        \exp_not:N \__cs_generate_from_signature:NNn
+        \exp_after:wN \exp_not:N \cs:w cs_ #1 : #3 \cs_end:
+      }
+  }
+\cs_new_protected:Npn \__cs_generate_from_signature:NNn #1#2
+  {
+    \__cs_split_function:NN #2 \__cs_generate_from_signature:nnNNNn
+    #1 #2
+  }
+\cs_new_protected:Npn \__cs_generate_from_signature:nnNNNn #1#2#3#4#5#6
+  {
+    \bool_if:NTF #3
+      {
+        \cs_generate_from_arg_count:NNnn
+          #5 #4 { \tl_count:n {#2} } {#6}
+      }
+      {
+        \__msg_kernel_error:nnx { kernel } { missing-colon }
+          { \token_to_str:N #5 }
       }
   }
 %    \end{macrocode}
 %   Then we define the 24 variants beginning with |N|.
 %    \begin{macrocode}
-\cs_tmp:w { set }                  { Nn } { Npn }
-\cs_tmp:w { set }                  { Nx } { Npx }
-\cs_tmp:w { set_nopar }            { Nn } { Npn }
-\cs_tmp:w { set_nopar }            { Nx } { Npx }
-\cs_tmp:w { set_protected }        { Nn } { Npn }
-\cs_tmp:w { set_protected }        { Nx } { Npx }
-\cs_tmp:w { set_protected_nopar }  { Nn } { Npn }
-\cs_tmp:w { set_protected_nopar }  { Nx } { Npx }
-\cs_tmp:w { gset }                 { Nn } { Npn }
-\cs_tmp:w { gset }                 { Nx } { Npx }
-\cs_tmp:w { gset_nopar }           { Nn } { Npn }
-\cs_tmp:w { gset_nopar }           { Nx } { Npx }
-\cs_tmp:w { gset_protected }       { Nn } { Npn }
-\cs_tmp:w { gset_protected }       { Nx } { Npx }
-\cs_tmp:w { gset_protected_nopar } { Nn } { Npn }
-\cs_tmp:w { gset_protected_nopar } { Nx } { Npx }
-\cs_tmp:w { new }                  { Nn } { Npn }
-\cs_tmp:w { new }                  { Nx } { Npx }
-\cs_tmp:w { new_nopar }            { Nn } { Npn }
-\cs_tmp:w { new_nopar }            { Nx } { Npx }
-\cs_tmp:w { new_protected }        { Nn } { Npn }
-\cs_tmp:w { new_protected }        { Nx } { Npx }
-\cs_tmp:w { new_protected_nopar }  { Nn } { Npn }
-\cs_tmp:w { new_protected_nopar }  { Nx } { Npx }
+\__cs_tmp:w { set }                  { Nn } { Npn }
+\__cs_tmp:w { set }                  { Nx } { Npx }
+\__cs_tmp:w { set_nopar }            { Nn } { Npn }
+\__cs_tmp:w { set_nopar }            { Nx } { Npx }
+\__cs_tmp:w { set_protected }        { Nn } { Npn }
+\__cs_tmp:w { set_protected }        { Nx } { Npx }
+\__cs_tmp:w { set_protected_nopar }  { Nn } { Npn }
+\__cs_tmp:w { set_protected_nopar }  { Nx } { Npx }
+\__cs_tmp:w { gset }                 { Nn } { Npn }
+\__cs_tmp:w { gset }                 { Nx } { Npx }
+\__cs_tmp:w { gset_nopar }           { Nn } { Npn }
+\__cs_tmp:w { gset_nopar }           { Nx } { Npx }
+\__cs_tmp:w { gset_protected }       { Nn } { Npn }
+\__cs_tmp:w { gset_protected }       { Nx } { Npx }
+\__cs_tmp:w { gset_protected_nopar } { Nn } { Npn }
+\__cs_tmp:w { gset_protected_nopar } { Nx } { Npx }
+\__cs_tmp:w { new }                  { Nn } { Npn }
+\__cs_tmp:w { new }                  { Nx } { Npx }
+\__cs_tmp:w { new_nopar }            { Nn } { Npn }
+\__cs_tmp:w { new_nopar }            { Nx } { Npx }
+\__cs_tmp:w { new_protected }        { Nn } { Npn }
+\__cs_tmp:w { new_protected }        { Nx } { Npx }
+\__cs_tmp:w { new_protected_nopar }  { Nn } { Npn }
+\__cs_tmp:w { new_protected_nopar }  { Nx } { Npx }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2684,49 +2797,40 @@
 %     \cs_new_protected:cn        , \cs_new_protected:cx        ,
 %     \cs_new_protected_nopar:cn  , \cs_new_protected_nopar:cx  ,
 %   }
-%   Then something similar for the |c| variants.
-%   \begin{verbatim}
-%     \cs_set_protected:Npn \cs_set:cn #1#2
-%       {
-%         \cs_generate_from_arg_count:cNnn {#1} \cs_set:Npn
-%           { \cs_get_arg_count_from_signature:c {#1} } {#2}
-%       }
-%   \end{verbatim}
-%   The 24 |c| variants.
+%   The 24 |c| variants simply use \cs{exp_args:Nc}.
 %    \begin{macrocode}
-\cs_set:Npn \cs_tmp:w #1#2#3
+\cs_set:Npn \__cs_tmp:w #1#2
   {
-    \cs_new_protected:cpx {cs_#1:#2} ##1##2
+    \cs_new_protected_nopar:cpx { cs_ #1 : c #2 }
       {
-        \exp_not:N \cs_generate_from_arg_count:cNnn {##1}
-        \exp_after:wN \exp_not:N \cs:w cs_#1:#3 \cs_end:
-          { \exp_not:N \cs_get_arg_count_from_signature:c {##1} } {##2}
+        \exp_not:N \exp_args:Nc
+        \exp_after:wN \exp_not:N \cs:w cs_ #1 : N #2 \cs_end:
       }
   }
-\cs_tmp:w { set }                  { cn } { Npn }
-\cs_tmp:w { set }                  { cx } { Npx }
-\cs_tmp:w { set_nopar }            { cn } { Npn }
-\cs_tmp:w { set_nopar }            { cx } { Npx }
-\cs_tmp:w { set_protected }        { cn } { Npn }
-\cs_tmp:w { set_protected }        { cx } { Npx }
-\cs_tmp:w { set_protected_nopar }  { cn } { Npn }
-\cs_tmp:w { set_protected_nopar }  { cx } { Npx }
-\cs_tmp:w { gset }                 { cn } { Npn }
-\cs_tmp:w { gset }                 { cx } { Npx }
-\cs_tmp:w { gset_nopar }           { cn } { Npn }
-\cs_tmp:w { gset_nopar }           { cx } { Npx }
-\cs_tmp:w { gset_protected }       { cn } { Npn }
-\cs_tmp:w { gset_protected }       { cx } { Npx }
-\cs_tmp:w { gset_protected_nopar } { cn } { Npn }
-\cs_tmp:w { gset_protected_nopar } { cx } { Npx }
-\cs_tmp:w { new }                  { cn } { Npn }
-\cs_tmp:w { new }                  { cx } { Npx }
-\cs_tmp:w { new_nopar }            { cn } { Npn }
-\cs_tmp:w { new_nopar }            { cx } { Npx }
-\cs_tmp:w { new_protected }        { cn } { Npn }
-\cs_tmp:w { new_protected }        { cx } { Npx }
-\cs_tmp:w { new_protected_nopar }  { cn } { Npn }
-\cs_tmp:w { new_protected_nopar }  { cx } { Npx }
+\__cs_tmp:w { set }                  { n }
+\__cs_tmp:w { set }                  { x }
+\__cs_tmp:w { set_nopar }            { n }
+\__cs_tmp:w { set_nopar }            { x }
+\__cs_tmp:w { set_protected }        { n }
+\__cs_tmp:w { set_protected }        { x }
+\__cs_tmp:w { set_protected_nopar }  { n }
+\__cs_tmp:w { set_protected_nopar }  { x }
+\__cs_tmp:w { gset }                 { n }
+\__cs_tmp:w { gset }                 { x }
+\__cs_tmp:w { gset_nopar }           { n }
+\__cs_tmp:w { gset_nopar }           { x }
+\__cs_tmp:w { gset_protected }       { n }
+\__cs_tmp:w { gset_protected }       { x }
+\__cs_tmp:w { gset_protected_nopar } { n }
+\__cs_tmp:w { gset_protected_nopar } { x }
+\__cs_tmp:w { new }                  { n }
+\__cs_tmp:w { new }                  { x }
+\__cs_tmp:w { new_nopar }            { n }
+\__cs_tmp:w { new_nopar }            { x }
+\__cs_tmp:w { new_protected }        { n }
+\__cs_tmp:w { new_protected }        { x }
+\__cs_tmp:w { new_protected_nopar }  { n }
+\__cs_tmp:w { new_protected_nopar }  { x }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2758,25 +2862,25 @@
 %
 % \subsection{Diagnostic wrapper functions}
 %
-% \begin{macro}{\kernel_register_show:N, \kernel_register_show:c}
-%   Check that the variable, then apply the \tn{showthe} primitive to
+% \begin{macro}[int]{\__kernel_register_show:N, \__kernel_register_show:c}
+%   Check that the variable exists, then apply the \tn{showthe} primitive to
 %   the variable.  The odd-looking \cs{use:n} gives a nicer output.
 %    \begin{macrocode}
-\cs_new:Npn \kernel_register_show:N #1
+\cs_new_protected:Npn \__kernel_register_show:N #1
   {
     \cs_if_exist:NTF #1
       { \tex_showthe:D \use:n {#1} }
       {
-        \msg_kernel_error:nnx { kernel } { variable-not-defined }
+        \__msg_kernel_error:nnx { kernel } { variable-not-defined }
           { \token_to_str:N #1 }
       }
   }
-\cs_new_nopar:Npn \kernel_register_show:c
-  { \exp_args:Nc \kernel_register_show:N }
+\cs_new_protected_nopar:Npn \__kernel_register_show:c
+  { \exp_args:Nc \__kernel_register_show:N }
 %    \end{macrocode}
 % \end{macro}
 %
-%  \subsection{Engine specific definitions}
+% \subsection{Engine specific definitions}
 %
 % \begin{macro}[pTF, EXP]
 %   {\xetex_if_engine:, \luatex_if_engine:, \pdftex_if_engine:}
@@ -2831,7 +2935,7 @@
 %
 % \subsection{String comparisons}
 %
-% \begin{macro}[pTF, EXP]{\str_if_eq:nn, \str_if_eq:xx}
+% \begin{macro}[pTF, EXP]{\str_if_eq:nn, \str_if_eq_x:nn}
 %   Modern engines provide a direct way of comparing two token lists,
 %   but returning a number. This set of conditionals therefore make life
 %   a bit clearer. The \texttt{nn} and \texttt{xx} versions are created
@@ -2844,7 +2948,7 @@
       = \c_zero
       \prg_return_true: \else: \prg_return_false: \fi:
   }
-\prg_new_conditional:Npnn \str_if_eq:xx #1#2 { p , T , F , TF }
+\prg_new_conditional:Npnn \str_if_eq_x:nn #1#2 { p , T , F , TF }
   {
     \if_int_compare:w \pdftex_strcmp:D {#1} {#2} = \c_zero
       \prg_return_true: \else: \prg_return_false: \fi:
@@ -2852,20 +2956,83 @@
 %    \end{macrocode}
 % \end{macro}
 %
+% \begin{macro}[int, EXP]{\__str_if_eq_x_return:nn}
+%   It turns out that we often need to compare a token list
+%   with the result of applying some function to it, and
+%   return with \cs{prg_return_true/false:}. This test is
+%   similar to \cs{str_if_eq:nnTF}, but hard-coded for speed.
+%    \begin{macrocode}
+\cs_new:Npn \__str_if_eq_x_return:nn #1 #2
+  {
+    \if_int_compare:w \pdftex_strcmp:D {#1} {#2} = \c_zero
+      \prg_return_true:
+    \else:
+      \prg_return_false:
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\str_case:nnn, \str_case_x:nnn}
+% \begin{macro}[int, EXP]{\__prg_case_end:nw}
+% \begin{macro}[aux, EXP]
+%   {\__str_case:nw, \__str_case_x:nw, \__str_case_end:nw}
+%   No calculations for strings, otherwise no surprises.
+%    \begin{macrocode}
+\cs_new:Npn \str_case:nnn #1#2#3
+  {
+    \tex_romannumeral:D
+    \__str_case:nw {#1} #2 {#1} {#3} \q_recursion_stop
+  }
+\cs_new:Npn \__str_case:nw #1#2#3
+  {
+    \str_if_eq:nnTF {#1} {#2}
+      { \__str_case_end:nw {#3} }
+      { \__str_case:nw {#1} }
+  }
+\cs_new:Npn \str_case_x:nnn #1#2#3
+  {
+    \tex_romannumeral:D
+    \__str_case_x:nw {#1} #2 {#1} {#3} \q_recursion_stop
+  }
+\cs_new:Npn \__str_case_x:nw #1#2#3
+  {
+    \str_if_eq_x:nnTF {#1} {#2}
+      { \__str_case_end:nw {#3} }
+      { \__str_case_x:nw {#1} }
+  }
+%    \end{macrocode}
+%   Here, |#1| will be the code needed, |#2| will be any remaining case
+%   or cases, and the \cs{c_zero} stops the \tn{romannumeral}.
+%    \begin{macrocode}
+\cs_new:Npn \__prg_case_end:nw #1#2 \q_recursion_stop { \c_zero #1 }
+\cs_new_eq:NN \__str_case_end:nw \__prg_case_end:nw
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
 % \subsection{Breaking out of mapping functions}
 %
-% \begin{macro}[EXP]{\prg_break_point:n, \prg_map_break:, \prg_map_break:n}
+% \begin{macro}[EXP]{\__prg_break_point:Nn, \__prg_map_break:Nn}
 %   In inline mappings, the nesting level must be reset
 %   at the end of the mapping, even when the user decides
 %   to break out. This is done by putting the code that
-%   must be performed as an argument of \cs{prg_break_point:n}.
+%   must be performed as an argument of \cs{__prg_break_point:Nn}.
 %   The breaking functions are then defined to jump to
-%   that point and perform the argument of \cs{prg_break_point:n},
-%   before the user's code (if any).
+%   that point and perform the argument of \cs{__prg_break_point:Nn},
+%   before the user's code (if any).  There is a check that we close the
+%   correct loop, otherwise we continue breaking.
 %    \begin{macrocode}
-\cs_new_eq:NN \prg_break_point:n \use:n
-\cs_new:Npn \prg_map_break: #1 \prg_break_point:n #2 { #2 }
-\cs_new:Npn \prg_map_break:n #1 #2 \prg_break_point:n #3 { #3 #1 }
+\cs_new_eq:NN \__prg_break_point:Nn \use_ii:nn
+\cs_new:Npn \__prg_map_break:Nn #1#2#3 \__prg_break_point:Nn #4#5
+  {
+    #5
+    \if_meaning:w #1 #4
+      \exp_after:wN \use_iii:nnn
+    \fi:
+    \__prg_map_break:Nn #1 {#2}
+  }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2963,6 +3130,24 @@
 %    \end{macrocode}
 % \end{macro}
 %
+% Deprecated 2012-06-05 for removal after 2012-12-31.
+%
+% \begin{macro}[pTF, EXP]{\str_if_eq:xx}
+%   Not really true \texttt{x}-type expansion
+%    \begin{macrocode}
+\cs_new_eq:NN \str_if_eq_p:xx \str_if_eq_x_p:nn
+\cs_new_eq:NN \str_if_eq:xxT  \str_if_eq_x:nnT
+\cs_new_eq:NN \str_if_eq:xxF  \str_if_eq_x:nnF
+\cs_new_eq:NN \str_if_eq:xxTF \str_if_eq_x:nnTF
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\chk_if_free_cs:N}
+%    \begin{macrocode}
+\cs_new_eq:NN \chk_if_free_cs:N \__chk_if_free_cs:N
+%    \end{macrocode}
+% \end{macro}
+%
 %    \begin{macrocode}
 %</initex|package>
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3bootstrap.dtx b/Master/texmf-dist/source/latex/l3kernel/l3bootstrap.dtx
index 43b2d11689f..1fb3ac9454f 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3bootstrap.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3bootstrap.dtx
@@ -1,6 +1,6 @@
 % \iffalse meta-comment
 %
-%% File: l3bootstrap.dtx Copyright (C) 2011 The LaTeX3 project
+%% File: l3bootstrap.dtx Copyright (C) 2011-2012 The LaTeX3 project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -33,22 +33,38 @@
 %%
 %% -----------------------------------------------------------------------
 %
-%<*package>
+%<*driver|package>
+% \begin{macro}{\GetIdInfo}
+% \begin{macro}[aux]{\GetIdInfoAuxI, \GetIdInfoAuxII, \GetIdInfoAuxIII}
+%   The idea here is to extract out the information needed from a standard
+%   \textsc{svn} \texttt{Id} line, but without a line that will get
+%   changed when the file is checked in. Hence the fact that there is
+%   not a line which includes both a dollar sign and the \texttt{Id}
+%   keyword together!
+%    \begin{macrocode}
 \protected\def\GetIdInfo
-  {
+  {%
     \begingroup
-    \catcode 32 = 10 \relax
-    \GetIdInfoAuxI
+      \catcode 32 = 10 %
+      \GetIdInfoAuxI
   }
+%    \end{macrocode}
+%   A first check for a completely empty \textsc{svn} field. If that is
+%   not the case, there is a second case when a file created using
+%   \texttt{svn cp} but has not been checked in. That leaves a special
+%   marker \texttt{-1} version, which has no further data. Dealing correctly
+%   with that is the reason for the space in the line to use
+%   \cs{GetIdInforAuxII}.
+%    \begin{macrocode}
 \protected\def\GetIdInfoAuxI$#1$#2%
-  {
+  {%
     \def\tempa{#1}%
     \def\tempb{Id}%
     \ifx\tempa\tempb
       \def\tempa
         {%
           \endgroup
-          \def\ExplFileDate{9999/99/99}%
+          \def\ExplFileDate{9999/12/31}%
           \def\ExplFileDescription{#2}%
           \def\ExplFileName{[unknown name]}%
           \def\ExplFileExtension{[unknown extension]}%
@@ -58,34 +74,54 @@
       \def\tempa
         {%
           \endgroup
-          \GetIdInfoAuxII$#1${#2}%
+          \def\ExplFileDescription{#2}%
+          \GetIdInfoAuxII$#1 $%
         }%
     \fi
     \tempa
   }
-\protected\def\GetIdInfoAuxII$#1 #2.#3 #4 #5 #6 #7 #8$#9%
+%    \end{macrocode}
+%   Here, |#1| is |Id|, |#2| is the file name, |#3| is the extension,
+%   |#4| is the version, |#5| is the check in date and |#6| is the check in
+%   time and user, plus some trailing spaces. If |#4| is the marker |-1| value
+%   then |#5| and |#6| will be empty.
+%    \begin{macrocode}
+\protected\def\GetIdInfoAuxII$#1 #2.#3 #4 #5 #6$%
   {%
     \def\ExplFileName{#2}%
     \def\ExplFileExtension{#3}%
     \def\ExplFileVersion{#4}%
-    \def\ExplFileDescription{#9}%
-    \GetIdInfoAuxIII#5\relax#3\relax#5\relax#6\relax
+    \begingroup
+      \def\tempa{#4}%
+      \def\tempb{-1}%
+      \ifx\tempa\tempb
+        \def\tempa
+          {%
+            \endgroup
+            \def\ExplFileDate{0000/00/00}%
+          }%
+      \else
+        \def\tempa
+          {%
+            \endgroup
+            \GetIdInfoAuxIII$#5$%
+          }%
+      \fi
+      \tempa
   }
-\protected\def\GetIdInfoAuxIII#1#2#3#4#5#6\relax
+%    \end{macrocode}
+%   Convert an \textsc{svn}-style date into a \LaTeX{}-style one.
+%    \begin{macrocode}
+\protected\def\GetIdInfoAuxIII$#1-#2-#3$%
   {%
-    \ifx#5/%
-      \expandafter\GetIdInfoAuxCVS
-    \else
-      \expandafter\GetIdInfoAuxSVN
-    \fi
+    \def\ExplFileDate{#1/#2/#3}%
   }
-\protected\def\GetIdInfoAuxCVS#1,v\relax#2\relax#3\relax
-  {\def\ExplFileDate{#2}}
-\protected\def\GetIdInfoAuxSVN#1\relax#2-#3-#4\relax#5Z\relax
-  {\def\ExplFileDate{#2/#3/#4}}
-\GetIdInfo$Id: l3bootstrap.dtx 3110 2011-12-29 14:23:48Z joseph $
-  {L3 experimental bootstrap code}
-%</package>
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+\GetIdInfo$Id: l3bootstrap.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Bootstrap code}
+%</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
 \begin{document}
@@ -135,20 +171,7 @@
 %   and underscore (|_|) are treated as \enquote{letters}, thus allowing
 %   access to the names of code functions and variables. Within this
 %   environment, |~| is used to input a space. The \cs{ExplSyntaxOff}
-%   reverts to the document category code regim{\'e}.
-% \end{function}
-%
-% \begin{function}{\ExplSyntaxNamesOn, \ExplSyntaxNamesOff}
-%   \begin{syntax}
-%     \cs{ExplSyntaxNamesOn} \meta{code} \cs{ExplSyntaxNamesOff}
-%   \end{syntax}
-%   The \cs{ExplSyntaxOn} function switches to a category code
-%   regim{\'e} in which the colon (|:|) and underscore (|_|) are treated as
-%   \enquote{letters}, thus allowing access to the names of code functions
-%   and variables. In contrast to \cs{ExplSyntaxOn}, using
-%   \cs{ExplSyntaxNamesOn} does not cause spaces to be ignored.
-%   The \cs{ExplSyntaxNamesOff} reverts to the document category code
-%   regim{\'e}.
+%   reverts to the document category code r{\'e}gime.
 % \end{function}
 %
 % \begin{function}{\ProvidesExplPackage, \ProvidesExplClass, \ProvidesExplFile}
@@ -165,7 +188,7 @@
 %   \tn{makeatletter} within package and class code.)
 % \end{function}
 %
-% \begin{function}{\GetIdInfo}
+% \begin{function}[updated = 2012-06-04]{\GetIdInfo}
 %   \begin{syntax}
 %     |\RequirePackage{l3names}|
 %     \cs{GetIdInfo} |$Id:| \meta{SVN info field} |$| \Arg{description}
@@ -189,6 +212,23 @@
 %   \ProvidesExplPackage{\ExplFileName}
 %     {\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
 % \end{verbatim}
+% 
+% \subsection{Internal functions and variables}
+% 
+% \begin{function}{\__expl_package_check:}
+%   \begin{syntax}
+%     \cs{__expl_package_check:}
+%   \end{syntax}
+%   Used to ensure that all parts of \pkg{expl3} are loaded together
+%   (\emph{i.e.}~as part of \pkg{expl3}). Issues an error if a kernel package
+%   is loaded independently of the bundle.
+% \end{function}
+%
+% \begin{variable}{\l__kernel_expl_bool}
+%   A boolean which records the current code syntax status: \texttt{true} if
+%   currently inside a code environment. This variable should only be
+%   set by \cs{ExplSyntaxOn}/\cs{ExplSyntaxOff}.
+% \end{variable}
 %
 % \end{documentation}
 %
@@ -198,6 +238,7 @@
 %
 %    \begin{macrocode}
 %<*initex|package>
+%<@@=expl>
 %    \end{macrocode}
 %
 % \subsection{Format-specific code}
@@ -223,7 +264,7 @@
 %    \end{macrocode}
 %
 % For \LuaTeX{} the extra primitives need to be enabled before
-% they can be use. No \tn{ifdefined} yet, so do it the old-fashioned
+% they can be used. No \tn{ifdefined} yet, so do it the old-fashioned
 % way. The primitive \tn{strcmp} is simulated using some \Lua{}
 % code, which currently has to be applied to every job as the \Lua{}
 % code is not part of the format. Thanks to Taco Hoekwater for this
@@ -267,7 +308,7 @@
 %</initex>
 %    \end{macrocode}
 %
-% \subsection{Package-specific code}
+% \subsection{Package-specific code part one}
 %
 % The package starts by identifying itself: the information itself is
 % taken from the SVN |Id| string at the start of the source file.
@@ -303,6 +344,64 @@
 \fi
 %</package>
 %    \end{macrocode}
+%    
+% \subsection{The \tn{pdfstrcmp} primitive in \XeTeX{}}
+%
+% Only \pdfTeX{} has a primitive called \tn{pdfstrcmp}. The \XeTeX{}
+% version is just \tn{strcmp}, so there is some shuffling to do.
+%    \begin{macrocode}
+\begingroup\expandafter\expandafter\expandafter\endgroup
+  \expandafter\ifx\csname pdfstrcmp\endcsname\relax
+  \let\pdfstrcmp\strcmp
+\fi
+%    \end{macrocode}
+%    
+% \subsection{Engine requirements}
+%
+% The code currently requires functionality equivalent to \tn{pdfstrcmp}
+% in addition to \eTeX{}. The former is therefore used as a test for
+% a suitable engine.
+%    \begin{macrocode}
+\begingroup\expandafter\expandafter\expandafter\endgroup
+\expandafter\ifx\csname pdfstrcmp\endcsname\relax
+%<*package>
+  \PackageError{expl3}{Required primitives not found}
+    {%
+      LaTeX3 requires the e-TeX primitives and \string\pdfstrcmp.\MessageBreak
+      \MessageBreak
+      These are available in engine versions:\MessageBreak
+      - pdfTeX 1.30\MessageBreak
+      - XeTeX 0.9994\MessageBreak
+      - LuaTeX 0.40\MessageBreak
+      or later.\MessageBreak
+      \MessageBreak
+      Loading of expl3 will abort!%
+    }
+  \expandafter\endinput
+%</package>
+%<*initex>
+  \newlinechar`\^^J\relax
+  \errhelp{%
+      LaTeX3 requires the e-TeX primitives and \pdfstrcmp.^^J%
+      ^^J%
+      These are available in engine versions:^^J%
+      - pdfTeX 1.30^^J%
+      - XeTeX 0.9994^^J%
+      - LuaTeX 0.40^^J%
+      or later.^^J%
+      ^^J%
+      For pdfTeX and XeTeX the '-etex' command-line switch is also
+      needed.^^J%
+       ^^J%
+      Format building will abort!%
+  }
+  \errmessage{Required primitives not found}%
+  \expandafter\end
+%</initex>
+\fi
+%    \end{macrocode}
+%
+% \subsection{Package-specific code part two}
 %
 % \begin{macro}{\ExplSyntaxOff, \ExplSyntaxOn}
 %   Experimental syntax switching is set up here for the package-loading
@@ -322,7 +421,7 @@
     \catcode 124 = \the\catcode 124\relax
     \catcode 126 = \the\catcode 126\relax
     \endlinechar = \the\endlinechar\relax
-    \chardef\csname\detokenize{l_expl_status_bool}\endcsname = 0 \relax
+    \chardef\csname\detokenize{l__kernel_expl_bool}\endcsname = 0 \relax
   }
 \protected\edef\ExplSyntaxOn
   {
@@ -335,82 +434,24 @@
     \catcode 124 = 12 \relax
     \catcode 126 = 10 \relax
     \endlinechar = 32 \relax
-    \chardef\csname\detokenize{l_expl_status_bool}\endcsname = 1 \relax
+    \chardef\csname\detokenize{l__kernel_expl_bool}\endcsname = 1 \relax
   }
 %</package>
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\l_expl_status_bool}
+% \begin{variable}{\l__kernel_expl_bool}
 %   The status for experimental code syntax: this is off at present. This
 %   code is used by both the package and the format.
 %    \begin{macrocode}
-\expandafter\chardef\csname\detokenize{l_expl_status_bool}\endcsname = 0 \relax
+\expandafter\chardef\csname\detokenize{l__kernel_expl_bool}\endcsname = 0 \relax
 %    \end{macrocode}
-%\end{macro}
+%\end{variable}
 %
 % \subsection{Dealing with package-mode meta-data}
 %
 % \begin{macro}{\GetIdInfo}
-% \begin{macro}[aux]
-%   {
-%     \GetIdInfoFull, \GetIdInfoAuxI, \GetIdInfoAuxII, \GetIdInfoAuxIII,
-%     \GetIdInfoAuxCVS, \GetIdInfoAuxSVN
-%   }
-%   Functions for collecting up meta-data from the SVN information
-%   used by the \LaTeX3 Project.
-%    \begin{macrocode}
-%<*package>
-\protected\def\GetIdInfo
-  {
-    \begingroup
-    \catcode 32 = 10 \relax
-    \GetIdInfoAuxI
-  }
-\protected\def\GetIdInfoAuxI$#1$#2%
-  {
-    \def\tempa{#1}%
-    \def\tempb{Id}%
-    \ifx\tempa\tempb
-      \def\tempa
-        {%
-          \endgroup
-          \def\ExplFileDate{9999/99/99}%
-          \def\ExplFileDescription{#2}%
-          \def\ExplFileName{[unknown name]}%
-          \def\ExplFileVersion{999}%
-        }%
-    \else
-      \def\tempa
-        {%
-          \endgroup
-          \GetIdInfoAuxII$#1${#2}%
-        }%
-    \fi
-    \tempa
-  }
-\protected\def\GetIdInfoAuxII$#1 #2.#3 #4 #5 #6 #7 #8$#9%
-  {%
-    \def\ExplFileName{#2}%
-    \def\ExplFileVersion{#4}%
-    \def\ExplFileDescription{#9}%
-    \GetIdInfoAuxIII#5\relax#3\relax#5\relax#6\relax
-  }
-\protected\def\GetIdInfoAuxIII#1#2#3#4#5#6\relax
-  {%
-    \ifx#5/%
-      \expandafter\GetIdInfoAuxCVS
-    \else
-      \expandafter\GetIdInfoAuxSVN
-    \fi
-  }
-\protected\def\GetIdInfoAuxCVS#1,v\relax#2\relax#3\relax
-  {\def\ExplFileDate{#2}}
-\protected\def\GetIdInfoAuxSVN#1\relax#2-#3-#4\relax#5Z\relax
-  {\def\ExplFileDate{#2/#3/#4}}
-%</package>
-%    \end{macrocode}
-% \end{macro}
+%   This is implemented right at the start of \texttt{l3bootstrap.dtx}.
 % \end{macro}
 %
 % \begin{macro}{\ProvidesExplPackage, \ProvidesExplClass, \ProvidesExplFile}
@@ -448,16 +489,16 @@
 \edef\@pushfilename
   {%
     \edef\expandafter\noexpand
-      \csname\detokenize{l_expl_status_stack_tl}\endcsname
+      \csname\detokenize{l_@@_status_stack_tl}\endcsname
       {%
         \noexpand\ifodd\expandafter\noexpand
-          \csname\detokenize{l_expl_status_bool}\endcsname
+          \csname\detokenize{l__kernel_expl_bool}\endcsname
           1%
         \noexpand\else
           0%
         \noexpand\fi
         \expandafter\noexpand
-          \csname\detokenize{l_expl_status_stack_tl}\endcsname
+          \csname\detokenize{l_@@_status_stack_tl}\endcsname
       }%
     \ExplSyntaxOff
     \unexpanded\expandafter{\@pushfilename}%
@@ -466,14 +507,14 @@
   {%
     \unexpanded\expandafter{\@popfilename}%
     \noexpand\if a\expandafter\noexpand\csname
-      \detokenize{l_expl_status_stack_tl}\endcsname a%
+      \detokenize{l_@@_status_stack_tl}\endcsname a%
       \ExplSyntaxOff
     \noexpand\else
       \noexpand\expandafter
         \expandafter\noexpand\csname
-          \detokenize{expl_status_pop:w}\endcsname
+          \detokenize{@@_status_pop:w}\endcsname
           \expandafter\noexpand\csname
-            \detokenize{l_expl_status_stack_tl}\endcsname
+            \detokenize{l_@@_status_stack_tl}\endcsname
           \noexpand\@nil
    \noexpand\fi
   }
@@ -481,28 +522,28 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\l_expl_status_stack_tl}
+% \begin{macro}{\l_@@_status_stack_tl}
 %   As \pkg{expl3} itself cannot be loaded with the code environment
 %   already active, at the end of the package \cs{ExplSyntaxOff} can
 %   safely be called.
 %    \begin{macrocode}
 %<*package>
-\@namedef{\detokenize{l_expl_status_stack_tl}}{0}
+\@namedef{\detokenize{l_@@_status_stack_tl}}{0}
 %</package>
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]{\expl_status_pop:w}
+% \begin{macro}[aux]{\@@_status_pop:w}
 %   The pop auxiliary function removes the first item from the stack,
 %   saves the rest of the stack and then does the test. As
 %   \cs{ExplSyntaxOff} is already defined as a protected macro, there
 %   is no need for \tn{noexpand} here.
 %    \begin{macrocode}
 %<*package>
-\expandafter\edef\csname\detokenize{expl_status_pop:w}\endcsname#1#2\@nil
+\expandafter\edef\csname\detokenize{@@_status_pop:w}\endcsname#1#2\@nil
   {%
     \def\expandafter\noexpand
-      \csname\detokenize{l_expl_status_stack_tl}\endcsname{#2}%
+      \csname\detokenize{l_@@_status_stack_tl}\endcsname{#2}%
     \noexpand\ifodd#1\space
       \noexpand\expandafter\noexpand\ExplSyntaxOn
     \noexpand\else
@@ -513,13 +554,14 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% We want the \pkg{expl3} bundle to be loaded \enquote{as one};
-% this command is
-% used to ensure that one of the |l3| packages isn't loaded on its own.
+% \begin{macro}[int]{\__expl_package_check:}
+%   We want the \pkg{expl3} bundle to be loaded \enquote{as one};
+%   this command is used to ensure that one of the |l3| packages isn't loaded
+%   on its own.
 %    \begin{macrocode}
 %<*package>
 \expandafter\protected\expandafter\def
-  \csname\detokenize{package_check_loaded_expl:}\endcsname
+  \csname\detokenize{__expl_package_check:}\endcsname
   {%
     \@ifpackageloaded{expl3}
       {}
@@ -528,90 +570,16 @@
           {Cannot load the expl3 modules separately}
           {%
             The expl3 modules cannot be loaded separately;\MessageBreak
-            please \string\usepackage\string{expl3\string} instead.
+            please \string\usepackage\string{expl3\string} instead.%
           }%
       }%
   }
 %</package>
 %    \end{macrocode}
-%
-% \subsection{The \tn{pdfstrcmp} primitive in \XeTeX{}}
-%
-% Only \pdfTeX{} has a primitive called \tn{pdfstrcmp}. The \XeTeX{}
-% version is just \tn{strcmp}, so there is some shuffling to do.
-%    \begin{macrocode}
-\begingroup\expandafter\expandafter\expandafter\endgroup
-  \expandafter\ifx\csname pdfstrcmp\endcsname\relax
-  \let\pdfstrcmp\strcmp
-\fi
-%    \end{macrocode}
-%
-% \subsection{Engine requirements}
-%
-% The code currently requires functionality equivalent to \tn{pdfstrcmp}
-% in addition to \eTeX{}. The former is therefore used as a test for
-% a suitable engine.
-%    \begin{macrocode}
-\begingroup\expandafter\expandafter\expandafter\endgroup
-\expandafter\ifx\csname pdfstrcmp\endcsname\relax
-%<*package>
-  \PackageError{l3names}{Required primitive not found: \protect\pdfstrcmp}
-    {%
-      LaTeX3 requires the e-TeX primitives and
-        \string\pdfstrcmp.\MessageBreak
-      These are available in engine versions: \MessageBreak
-      - pdfTeX 1.30 \MessageBreak
-      - XeTeX 0.9994 \MessageBreak
-      - LuaTeX 0.60 \MessageBreak
-      or later. \MessageBreak
-      \MessageBreak
-      Loading of expl3 will abort!
-    }
-%</package>
-%<*initex>
-  \newlinechar`\^^J\relax
-  \errhelp{%
-      LaTeX3 requires the e-TeX primitives and
-        \string\pdfstrcmp. ^^J
-      These are available in engine versions:  ^^J
-      - pdfTeX 1.30  ^^J
-      - XeTeX 0.9994 ^^J
-      - LuaTeX 0.60  ^^J
-      or later. ^^J
-      For pdfTeX and XeTeX the '-etex' command-line switch is also
-      needed.^^J
-       ^^J
-      Format building will abort!
-  }
-%</initex>
-  \expandafter\endinput
-\fi
-%    \end{macrocode}
+% \end{macro}
 %
 % \subsection{The \LaTeX3 code environment}
 %
-% \begin{macro}{\ExplSyntaxNamesOn, \ExplSyntaxNamesOff}
-%   These can be set up early, as they are not used anywhere in the
-%   package or format itself. Using an \tn{edef} here makes the
-%   definitions that bit clearer later.
-%    \begin{macrocode}
-\protected\edef\ExplSyntaxNamesOn
-  {%
-    \expandafter\noexpand
-      \csname\detokenize{char_set_catcode_letter:n}\endcsname{58}%
-    \expandafter\noexpand
-      \csname\detokenize{char_set_catcode_letter:n}\endcsname{95}%
-  }
-\protected\edef\ExplSyntaxNamesOff
-  {%
-    \expandafter\noexpand
-      \csname\detokenize{char_set_catcode_other:n}\endcsname{58}%
-    \expandafter\noexpand
-      \csname\detokenize{char_set_catcode_math_subscript:n}\endcsname{95}%
-  }
-%    \end{macrocode}
-% \end{macro}
-%
 % The code environment is now set up for the format: the package deals
 % with this using \cs{ProvidesExplPackage}.
 %    \begin{macrocode}
@@ -636,7 +604,7 @@
 %<*initex>
 \protected \def \ExplSyntaxOn
   {
-    \bool_if:NF \l_expl_status_bool
+    \bool_if:NF \l__kernel_expl_bool
       {
         \cs_set_protected_nopar:Npx \ExplSyntaxOff
           {
@@ -651,7 +619,7 @@
             \char_set_catcode:nn { 126 } { \char_value_catcode:n { 126 } }
             \tex_endlinechar:D =
               \tex_the:D \tex_endlinechar:D \scan_stop:
-            \bool_set_false:N \l_expl_status_bool
+            \bool_set_false:N \l__kernel_expl_bool
             \cs_set_protected_nopar:Npn \ExplSyntaxOff { }
           }
       }
@@ -665,21 +633,47 @@
     \char_set_catcode_other:n            { 124 } % pipe
     \char_set_catcode_space:n            { 126 } % tilde
     \tex_endlinechar:D = 32 \scan_stop:
-    \bool_set_true:N \l_expl_status_bool
+    \bool_set_true:N \l__kernel_expl_bool
   }
 \protected \def \ExplSyntaxOff { }
 %</initex>
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{variable}{\l_expl_status_bool}
+% \begin{variable}{\l__kernel_expl_bool}
 %   A flag to show the current syntax status.
 %    \begin{macrocode}
 %<*initex>
-\chardef \l_expl_status_bool = 0 ~
+\chardef \l__kernel_expl_bool = 0 ~
 %</initex>
 %    \end{macrocode}
 % \end{variable}
+% 
+% \subsection{Deprecated functions}
+% 
+% Deprecated 2012-06-19 for removal after 2012-12-31.
+%
+% \begin{macro}{\ExplSyntaxNamesOn, \ExplSyntaxNamesOff}
+%   These can be set up early, as they are not used anywhere in the
+%   package or format itself. Using an \tn{edef} here makes the
+%   definitions that bit clearer later.
+%    \begin{macrocode}
+\protected\edef\ExplSyntaxNamesOn
+  {%
+    \expandafter\noexpand
+      \csname\detokenize{char_set_catcode_letter:n}\endcsname{58}%
+    \expandafter\noexpand
+      \csname\detokenize{char_set_catcode_letter:n}\endcsname{95}%
+  }
+\protected\edef\ExplSyntaxNamesOff
+  {%
+    \expandafter\noexpand
+      \csname\detokenize{char_set_catcode_other:n}\endcsname{58}%
+    \expandafter\noexpand
+      \csname\detokenize{char_set_catcode_math_subscript:n}\endcsname{95}%
+  }
+%    \end{macrocode}
+% \end{macro}
 %
 %    \begin{macrocode}
 %</initex|package>
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3box.dtx b/Master/texmf-dist/source/latex/l3kernel/l3box.dtx
index 8ec1f62babe..b578295ac44 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3box.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3box.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3box.dtx 3490 2012-03-04 01:00:53Z bruno $
+\GetIdInfo$Id: l3box.dtx 3986 2012-07-15 19:23:51Z joseph $
   {L3 Experimental boxes}
 %</driver|package>
 %<*driver>
@@ -106,9 +106,9 @@
 %     \box_gset_eq:NN, \box_gset_eq:cN, \box_gset_eq:Nc, \box_gset_eq:cc
 %   }
 %   \begin{syntax}
-%     \cs{box_set_eq:NN} \meta{box1} \meta{box2}
+%     \cs{box_set_eq:NN} \meta{box_1} \meta{box_2}
 %   \end{syntax}
-%   Sets the content of \meta{box1} equal to that of \meta{box2}.
+%   Sets the content of \meta{box_1} equal to that of \meta{box_2}.
 % \end{function}
 %
 % \begin{function}
@@ -117,10 +117,10 @@
 %     \box_set_eq_clear:Nc, \box_set_eq_clear:cc
 %   }
 %   \begin{syntax}
-%     \cs{box_set_eq_clear:NN} \meta{box1} \meta{box2}
+%     \cs{box_set_eq_clear:NN} \meta{box_1} \meta{box_2}
 %   \end{syntax}
-%   Sets the content of \meta{box1} within the current \TeX{} group
-%   equal to that of \meta{box2}, then clears \meta{box2} globally.
+%   Sets the content of \meta{box_1} within the current \TeX{} group
+%   equal to that of \meta{box_2}, then clears \meta{box_2} globally.
 % \end{function}
 %
 % \begin{function}
@@ -129,10 +129,10 @@
 %     \box_gset_eq_clear:Nc, \box_gset_eq_clear:cc
 %   }
 %   \begin{syntax}
-%     \cs{box_gset_eq_clear:NN} \meta{box1} \meta{box2}
+%     \cs{box_gset_eq_clear:NN} \meta{box_1} \meta{box_2}
 %   \end{syntax}
-%   Sets the content of \meta{box1} equal to that of \meta{box2}, then
-%   clears \meta{box2}. These assignments are global.
+%   Sets the content of \meta{box_1} equal to that of \meta{box_2}, then
+%   clears \meta{box_2}. These assignments are global.
 % \end{function}
 %
 % \begin{function}[EXP, pTF, added=2012-03-03]
@@ -255,153 +255,6 @@
 %   \Arg{dimension expression}. This is a global assignment.
 % \end{function}
 %
-% \section{Affine transformations}
-%
-% Affine transformations are changes which (informally) preserve straight
-% lines. Simple translations are affine transformations, but are better handled
-% in \TeX{} by doing the translation first, then inserting an unmodified box.
-% On the other hand, rotation and resizing of boxed material can best be
-% handled by modifying boxes. These transformations are described here.
-%
-% \begin{function}[added = 2011-09-02]{\box_resize:Nnn, \box_resize:cnn}
-%   \begin{syntax}
-%     \cs{box_resize:Nnn} \meta{box} \Arg{x-size} \Arg{y-size}
-%   \end{syntax}
-%   Resize the \meta{box} to \meta{x-size} horizontally and \meta{y-size}
-%   vertically (both of the sizes are dimension expressions).
-%   The \meta{y-size} is the vertical size (height plus depth) of
-%   the box. The updated \meta{box} will be an hbox, irrespective of the nature
-%   of the \meta{box}  before the resizing is applied. Negative sizes will
-%   cause the material in the \meta{box} to be reversed in direction, but the
-%   reference point of the \meta{box} will be unchanged. The resizing applies
-%   within the current \TeX{} group level.
-%
-%   \textbf{This function is experimental}
-% \end{function}
-%
-% \begin{function}[added = 2011-09-02, updated = 2011-10-22]
-%   {\box_resize_to_ht_plus_dp:Nn, \box_resize_to_ht_plus_dp:cn}
-%   \begin{syntax}
-%     \cs{box_resize_to_ht_plus_dp:Nn} \meta{box} \Arg{y-size}
-%   \end{syntax}
-%   Resize the \meta{box} to \meta{y-size} vertically, scaling the horizontal
-%   size by the same amount (\meta{y-size} is a dimension expression).
-%   The \meta{y-size} is the vertical size (height plus depth) of
-%   the box.
-%   The updated \meta{box} will be an hbox, irrespective of the nature
-%   of the \meta{box}  before the resizing is applied. A negative size will
-%   cause the material in the \meta{box} to be reversed in direction, but the
-%   reference point of the \meta{box} will be unchanged. The resizing applies
-%   within the current \TeX{} group level.
-%
-%  \textbf{This function is experimental}
-% \end{function}
-%
-% \begin{function}[added = 2011-09-02, updated = 2011-10-22]
-%   {\box_resize_to_wd:Nn, \box_resize_to_wd:cn}
-%   \begin{syntax}
-%     \cs{box_resize_to_wd:Nn} \meta{box} \Arg{x-size}
-%   \end{syntax}
-%   Resize the \meta{box} to \meta{x-size} horizontally, scaling the vertical
-%   size by the same amount (\meta{x-size} is a dimension expression).
-%   The updated \meta{box} will be an hbox, irrespective of the nature
-%   of the \meta{box}  before the resizing is applied. A negative size will
-%   cause the material in the \meta{box} to be reversed in direction, but the
-%   reference point of the \meta{box} will be unchanged. The resizing applies
-%   within the current \TeX{} group level.
-%
-%  \textbf{This function is experimental}
-% \end{function}
-%
-% \begin{function}[added = 2011-09-02, updated = 2011-10-22]
-%   {\box_rotate:Nn, \box_rotate:cn}
-%   \begin{syntax}
-%     \cs{box_rotate:Nn} \meta{box} \Arg{angle}
-%   \end{syntax}
-%   Rotates the \meta{box} by \meta{angle} (in degrees) anti-clockwise about
-%   its reference point. The reference point of the updated box will be moved
-%   horizontally such that it is at the left side of the smallest rectangle
-%   enclosing the rotated material.
-%   The updated \meta{box} will be an hbox, irrespective of the nature
-%   of the \meta{box} before the rotation is applied. The rotation applies
-%   within the current \TeX{} group level.
-%
-%  \textbf{This function is experimental}
-% \end{function}
-%
-% \begin{function}[added = 2011-09-02, updated = 2011-10-22]
-%   {\box_scale:Nnn, \box_scale:cnn}
-%   \begin{syntax}
-%     \cs{box_scale:Nnn} \meta{box} \Arg{x-scale} \Arg{y-scale}
-%   \end{syntax}
-%   Scales the \meta{box} by factors \meta{x-scale} and \meta{y-scale} in
-%   the horizontal and vertical directions, respectively (both scales are
-%   integer expressions). The updated \meta{box} will be an hbox, irrespective
-%   of the nature of the \meta{box} before the scaling is applied. Negative
-%   scalings will cause the material in the \meta{box} to be reversed in
-%   direction, but the reference point of the \meta{box} will be unchanged.
-%   The scaling applies within the current \TeX{} group level.
-%
-%  \textbf{This function is experimental}
-% \end{function}
-%
-% \section{Viewing part of a box}
-%
-% \begin{function}[added = 2011-11-13]{\box_clip:N, \box_clip:c}
-%   \begin{syntax}
-%     \cs{box_clip:N} \meta{box}
-%   \end{syntax}
-%   Clips the \meta{box} in the output so that only material inside the
-%   bounding box is displayed in the output. The updated \meta{box} will be an
-%   hbox, irrespective of the nature of the \meta{box} before the clipping is
-%   applied. The clipping applies within the current \TeX{} group level.
-%
-%   \textbf{This function is experimental}
-%   \begin{texnote}
-%     Clipping is implemented by the driver, and as such the full content of
-%     the box is places in the output file. Thus clipping does not remove
-%     any information from the raw output, and hidden material can therefore
-%     be viewed by direct examination of the file.
-%   \end{texnote}
-% \end{function}
-%
-% \begin{function}[added = 2011-11-13]
-%   {\box_trim:Nnnnn, \box_trim:cnnnn}
-%   \begin{syntax}
-%     \cs{box_trim:Nnnnn} \meta{box} \Arg{left} \Arg{bottom} \Arg{right} \Arg{top}
-%   \end{syntax}
-%   Adjusts the bounding box of the \meta{box} \meta{left} is removed from
-%   the left-hand edge of the bounding box, \meta{right} from the right-hand
-%   edge and so fourth. All adjustments are \meta{dimension expressions}.
-%   Material output of the bounding box will still be displayed in the output
-%   unless \cs{box_clip:N} is subsequently applied.
-%   The updated \meta{box} will be an
-%   hbox, irrespective of the nature of the \meta{box} before the viewport
-%   operation is applied. The clipping applies within the current \TeX{}
-%   group level.
-%
-%  \textbf{This function is experimental}
-% \end{function}
-%
-% \begin{function}[added = 2011-11-13]
-%   {\box_viewport:Nnnnn, \box_viewport:cnnnn}
-%   \begin{syntax}
-%     \cs{box_viewport:Nnnnn} \meta{box} \Arg{llx} \Arg{lly} \Arg{urx} \Arg{ury}
-%   \end{syntax}
-%   Adjusts the bounding box of the \meta{box} such that it has lower-left
-%   co-ordinates (\meta{llx}, \meta{lly}) and upper-right co-ordinates
-%   (\meta{urx}, \meta{ury}). All four co-ordinate positions are
-%   \meta{dimension expressions}. Material output of the bounding box will
-%   still be displayed in the output unless \cs{box_clip:N} is
-%   subsequently applied.
-%   The updated \meta{box} will be an
-%   hbox, irrespective of the nature of the \meta{box} before the viewport
-%   operation is applied. The clipping applies within the current \TeX{}
-%   group level.
-%
-%  \textbf{This function is experimental}
-% \end{function}
-%
 % \section{Box conditionals}
 %
 % \begin{function}[EXP,pTF]{\box_if_empty:N, \box_if_empty:c}
@@ -460,16 +313,45 @@
 %   code and so should only be used for short-term storage.
 % \end{variable}
 %
+% \begin{variable}{\g_tmpa_box, \g_tmpb_box}
+%   Scratch boxes for global assignment. These are never used by
+%   the kernel code, and so are safe for use with any \LaTeX3-defined
+%   function. However, they may be overwritten by other non-kernel
+%   code and so should only be used for short-term storage.
+% \end{variable}
+%
 % \section{Viewing box contents}
 %
-% \begin{function}{\box_show:N, \box_show:c}
+% \begin{function}[updated = 2012-05-11]{\box_show:N, \box_show:c}
 %   \begin{syntax}
 %      \cs{box_show:N} \meta{box}
 %   \end{syntax}
-%   Writes the contents of \meta{box} to the log file.
-%   \begin{texnote}
-%     This is a wrapper around the \TeX{} primitive \tn{showbox}.
-%   \end{texnote}
+%   Shows full details of the content of the \meta{box} in the terminal.
+% \end{function}
+% 
+% \begin{function}[added = 2012-05-11]{\box_show:Nnn, \box_show:cnn}
+%   \begin{syntax}
+%      \cs{box_show:Nnn} \meta{box} \meta{intexpr_1} \meta{intexpr_2}
+%   \end{syntax}
+%   Display the contents of \meta{box} in the terminal, showing the first
+%   \meta{intexpr_1} items of the box, and descending into \meta{intexpr_2}
+%   group levels.
+% \end{function}
+% 
+% \begin{function}[added = 2012-05-11]{\box_log:N, \box_log:c}
+%   \begin{syntax}
+%      \cs{box_show:N} \meta{box}
+%   \end{syntax}
+%   Writes full details of the content of the \meta{box} to the log.
+% \end{function}
+% 
+% \begin{function}[added = 2012-05-11]{\box_log:Nnn, \box_log:cnn}
+%   \begin{syntax}
+%      \cs{box_show:Nnn} \meta{box} \meta{intexpr_1} \meta{intexpr_2}
+%   \end{syntax}
+%   Writes the contents of \meta{box} to the log, showing the first
+%   \meta{intexpr_1} items of the box, and descending into \meta{intexpr_2}
+%   group levels.
 % \end{function}
 %
 % \section{Horizontal mode boxes}
@@ -671,7 +553,7 @@
 %    \vbox_gset_end:
 %  }
 %    \begin{syntax}
-%      \cs{vbox_begin:Nw} \meta{box} \meta{contents} \cs{vbox_set_end:}
+%      \cs{vbox_set:Nw} \meta{box} \meta{contents} \cs{vbox_set_end:}
 %    \end{syntax}
 %    Typesets the \meta{contents} at natural height and then stores the
 %    result inside the \meta{box}. In contrast
@@ -682,10 +564,10 @@
 %
 % \begin{function}[updated = 2011-10-22]{\vbox_set_split_to_ht:NNn}
 %   \begin{syntax}
-%      \cs{vbox_set_split_to_ht:NNn} \meta{box1} \meta{box2} \Arg{dimexpr}
+%      \cs{vbox_set_split_to_ht:NNn} \meta{box_1} \meta{box_2} \Arg{dimexpr}
 %   \end{syntax}
-%   Sets \meta{box1} to contain material to the height given by the
-%   \meta{dimexpr} by removing content from the top of \meta{box2}
+%   Sets \meta{box_1} to contain material to the height given by the
+%   \meta{dimexpr} by removing content from the top of \meta{box_2}
 %   (which must be a vertical box).
 %   \begin{texnote}
 %     This is the \TeX{} primitive \tn{vsplit}.
@@ -759,29 +641,6 @@
 %   \end{texnote}
 % \end{function}
 %
-% \section{Experimental box functions}
-%
-% \begin{function}[added = 2011-11-21]{\box_show:Nnn, \box_show:cnn}
-%   \begin{syntax}
-%      \cs{box_show:Nnn} \meta{box} \meta{int 1} \meta{int 2}
-%   \end{syntax}
-%   Display the contents of \meta{box} in the terminal,
-%   showing the first \meta{int 1} items of the box,
-%   and descending into \meta{int 1} levels of nesting.
-%   \begin{texnote}
-%     This is a wrapper around the \TeX{} primitives \tn{showbox},
-%     \tn{showboxbreadth} and \tn{showboxdepth}.
-%   \end{texnote}
-% \end{function}
-%
-% \begin{function}[added = 2011-11-22]{\box_show_full:N, \box_show_full:c}
-%   \begin{syntax}
-%      \cs{box_show_full:N} \meta{box}
-%   \end{syntax}
-%   Display the contents of \meta{box} in the terminal,
-%   showing all items in the box.
-% \end{function}
-%
 % \end{documentation}
 %
 % \begin{implementation}
@@ -791,12 +650,16 @@
 %    \begin{macrocode}
 %<*initex|package>
 %    \end{macrocode}
+%    
+%    \begin{macrocode}
+%<@@=box>
+%    \end{macrocode}
 %
 %    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
@@ -814,7 +677,7 @@
 %<*package>
 \cs_new_protected:Npn \box_new:N #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \newbox #1
   }
 %</package>
@@ -863,8 +726,8 @@
   { \tex_setbox:D #1 \tex_copy:D #2 }
 \cs_new_protected:Npn \box_gset_eq:NN
   { \tex_global:D \box_set_eq:NN }
-\cs_generate_variant:Nn \box_set_eq:NN  { cN , Nc , cc }
-\cs_generate_variant:Nn \box_gset_eq:NN { cN , Nc , cc }
+\cs_generate_variant:Nn \box_set_eq:NN  { c , Nc , cc }
+\cs_generate_variant:Nn \box_gset_eq:NN { c , Nc , cc }
 %    \end{macrocode}
 %  \end{macro}
 %  \end{macro}
@@ -888,8 +751,8 @@
   { \tex_setbox:D #1 \tex_box:D #2 }
 \cs_new_protected:Npn \box_gset_eq_clear:NN
   { \tex_global:D  \box_set_eq_clear:NN }
-\cs_generate_variant:Nn \box_set_eq_clear:NN  { cN , Nc , cc }
-\cs_generate_variant:Nn \box_gset_eq_clear:NN { cN , Nc , cc }
+\cs_generate_variant:Nn \box_set_eq_clear:NN  { c , Nc , cc }
+\cs_generate_variant:Nn \box_gset_eq_clear:NN { c , Nc , cc }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -934,11 +797,11 @@
 %   expandable, so the derived functions are not either.
 %    \begin{macrocode}
 \cs_new_protected:Npn \box_set_dp:Nn #1#2
-  { \box_dp:N #1 \dim_eval:w #2 \dim_eval_end: }
+  { \box_dp:N #1 \__dim_eval:w #2 \__dim_eval_end: }
 \cs_new_protected:Npn \box_set_ht:Nn #1#2
-  { \box_ht:N #1 \dim_eval:w #2 \dim_eval_end: }
+  { \box_ht:N #1 \__dim_eval:w #2 \__dim_eval_end: }
 \cs_new_protected:Npn \box_set_wd:Nn #1#2
-  { \box_wd:N #1 \dim_eval:w #2 \dim_eval_end: }
+  { \box_wd:N #1 \__dim_eval:w #2 \__dim_eval_end: }
 \cs_generate_variant:Nn \box_set_ht:Nn { c }
 \cs_generate_variant:Nn \box_set_dp:Nn { c }
 \cs_generate_variant:Nn \box_set_wd:Nn { c }
@@ -968,13 +831,13 @@
 %   Move box material in different directions.
 %    \begin{macrocode}
 \cs_new_protected:Npn \box_move_left:nn #1#2
-  { \tex_moveleft:D \dim_eval:w #1 \dim_eval_end: #2 }
+  { \tex_moveleft:D \__dim_eval:w #1 \__dim_eval_end: #2 }
 \cs_new_protected:Npn \box_move_right:nn #1#2
-  { \tex_moveright:D \dim_eval:w #1 \dim_eval_end: #2 }
+  { \tex_moveright:D \__dim_eval:w #1 \__dim_eval_end: #2 }
 \cs_new_protected:Npn \box_move_up:nn #1#2
-  { \tex_raise:D \dim_eval:w #1 \dim_eval_end: #2 }
+  { \tex_raise:D \__dim_eval:w #1 \__dim_eval_end: #2 }
 \cs_new_protected:Npn \box_move_down:nn #1#2
-  { \tex_lower:D \dim_eval:w #1 \dim_eval_end: #2 }
+  { \tex_lower:D \__dim_eval:w #1 \__dim_eval_end: #2 }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1063,7 +926,8 @@
 %
 % \subsection{Scratch boxes}
 %
-%  \begin{variable}{\l_tmpa_box, \l_tmpb_box}
+%  \begin{variable}{\l_tmpa_box, \l_tmpb_box, \g_tmpa_box, \g_tmpb_box}
+%    Reuse the \LaTeXe{} scratch box in package mode.
 %    \begin{macrocode}
 %<*package>
 \cs_new_eq:NN \l_tmpa_box \@tempboxa
@@ -1072,52 +936,78 @@
 \box_new:N \l_tmpa_box
 %</initex>
 \box_new:N \l_tmpb_box
+\box_new:N \g_tmpa_box
+\box_new:N \g_tmpb_box
 %    \end{macrocode}
 % \end{variable}
 %
 % \subsection{Viewing box contents}
+% 
+% \TeX{}'s \tn{tex_showbox:D} is not really that helpful in many cases, and
+% it is also inconsistent with other \LaTeX3{} \texttt{show} functions as it
+% does not actually shows material in the terminal. So we provide a richer
+% set of functionality.
 %
 % \begin{macro}{\box_show:N, \box_show:c}
-% \testfile*
-%   Check that the variable exists, then show the contents of the box
-%   and write it into the log file. The spurious \cs{use:n} gives
-%   a nicer output.
+% \begin{macro}{\box_show:Nnn, \box_show:cnn}
+%   Essentially a wrapper around the internal function.
 %    \begin{macrocode}
 \cs_new_protected:Npn \box_show:N #1
+  { \box_show:Nnn #1 \c_max_int \c_max_int }
+\cs_generate_variant:Nn \box_show:N { c }
+\cs_new_protected_nopar:Npn \box_show:Nnn
+  { \@@_show:NNnn \c_one }
+\cs_generate_variant:Nn \box_show:Nnn { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% 
+% \begin{macro}{\box_log:N, \box_log:c}
+% \begin{macro}{\box_log:Nnn, \box_log:cnn}
+%   Getting \TeX{} to write to the log without interruption the run is done by
+%   altering the interaction mode. For that, the \eTeX{} extensions are needed.
+%    \begin{macrocode}
+\cs_new_protected:Npn \box_log:N #1
+  { \box_log:Nnn #1 \c_max_int \c_max_int }
+\cs_generate_variant:Nn \box_log:N { c }
+\cs_new_protected:Npn \box_log:Nnn #1#2#3
   {
-    \box_if_exist:NTF #1
-      { \tex_showbox:D \use:n {#1} }
+    \use:x
       {
-        \msg_kernel_error:nnx { kernel } { variable-not-defined }
-          { \token_to_str:N #1 }
+        \etex_interactionmode:D \c_zero
+        \@@_show:NNnn \c_zero \exp_not:N #1
+          { \int_eval:n {#2} } { \int_eval:n {#3} }
+        \etex_interactionmode:D
+            = \tex_the:D \etex_interactionmode:D \scan_stop:
       }
   }
-\cs_generate_variant:Nn \box_show:N { c }
+\cs_generate_variant:Nn \box_log:Nnn { c }
 %    \end{macrocode}
 % \end{macro}
-%
-% \begin{macro}{\box_show:Nnn, \box_show:cnn}
-% \begin{macro}{\box_show_full:N, \box_show_full:c}
-%   Show the contents of a box and write it into the log file,
-%   after setting the parameters \tn{showboxbreadth} and \tn{showboxdepth}
-%   to the values provided by the user.
+% \end{macro}
+% 
+% \begin{macro}[aux]{\@@_show:NNnn}
+%   The internal auxiliary to actually do the output uses a group to deal
+%   with breadth and depth values. The \cs{use:n} here gives better output
+%   appearance. Setting \tn{tex_tracingonline:D} is used to control what
+%   appears in the terminal.
 %    \begin{macrocode}
-\cs_new_protected:Npn \box_show:Nnn #1#2#3
+\cs_new_protected:Npn \@@_show:NNnn #1#2#3#4
   {
     \group_begin:
-      \int_set:Nn \tex_showboxbreadth:D {#2}
-      \int_set:Nn \tex_showboxdepth:D {#3}
-      \int_set_eq:NN \tex_tracingonline:D \c_one
-      \box_show:N #1
+      \int_set:Nn \tex_showboxbreadth:D {#3}
+      \int_set:Nn \tex_showboxdepth:D   {#4}
+      \int_set_eq:NN \tex_tracingonline:D #1
+      \box_if_exist:NTF #2
+        { \tex_showbox:D \use:n {#2} }
+        {
+          \__msg_kernel_error:nnx { kernel } { variable-not-defined }
+            { \token_to_str:N #2 }
+        }
     \group_end:
   }
-\cs_generate_variant:Nn \box_show:Nnn { c }
-\cs_new_protected:Npn \box_show_full:N #1
-  { \box_show:Nnn #1 { \c_max_int } { \c_max_int } }
-\cs_generate_variant:Nn \box_show_full:N { c }
 %    \end{macrocode}
 % \end{macro}
-% \end{macro}
 %
 %  \subsection{Horizontal mode boxes}
 %
@@ -1147,7 +1037,7 @@
 %   Storing material in a horizontal box with a specified width.
 %    \begin{macrocode}
 \cs_new_protected:Npn \hbox_set_to_wd:Nnn #1#2#3
-  { \tex_setbox:D #1 \tex_hbox:D to \dim_eval:w #2 \dim_eval_end: {#3} }
+  { \tex_setbox:D #1 \tex_hbox:D to \__dim_eval:w #2 \__dim_eval_end: {#3} }
 \cs_new_protected:Npn \hbox_gset_to_wd:Nnn
   { \tex_global:D \hbox_set_to_wd:Nnn }
 \cs_generate_variant:Nn \hbox_set_to_wd:Nnn { c }
@@ -1199,7 +1089,7 @@
 %   Put a horizontal box directly into the input stream.
 %    \begin{macrocode}
 \cs_new_protected:Npn \hbox_to_wd:nn #1#2
-   { \tex_hbox:D to \dim_eval:w #1 \dim_eval_end: {#2} }
+   { \tex_hbox:D to \__dim_eval:w #1 \__dim_eval_end: {#2} }
 \cs_new_protected:Npn \hbox_to_zero:n #1 { \tex_hbox:D to \c_zero_skip {#1} }
 %    \end{macrocode}
 %  \end{macro}
@@ -1253,7 +1143,7 @@
 %   Put a vertical box directly into the input stream.
 %    \begin{macrocode}
 \cs_new_protected:Npn \vbox_to_ht:nn #1#2
-  { \tex_vbox:D to \dim_eval:w #1 \dim_eval_end: { #2 \par } }
+  { \tex_vbox:D to \__dim_eval:w #1 \__dim_eval_end: { #2 \par } }
 \cs_new_protected:Npn \vbox_to_zero:n #1
   { \tex_vbox:D to \c_zero_dim { #1 \par } }
 %    \end{macrocode}
@@ -1296,7 +1186,7 @@
 %  Storing material in a vertical box with a specified height.
 %    \begin{macrocode}
 \cs_new_protected:Npn \vbox_set_to_ht:Nnn #1#2#3
-  { \tex_setbox:D #1 \tex_vbox:D to \dim_eval:w #2 \dim_eval_end: { #3 \par } }
+  { \tex_setbox:D #1 \tex_vbox:D to \__dim_eval:w #2 \__dim_eval_end: { #3 \par } }
 \cs_new_protected:Npn \vbox_gset_to_ht:Nnn
   { \tex_global:D \vbox_set_to_ht:Nnn }
 \cs_generate_variant:Nn \vbox_set_to_ht:Nnn  { c }
@@ -1366,614 +1256,7 @@
 %   Splitting a vertical box in two.
 %    \begin{macrocode}
 \cs_new_protected:Npn \vbox_set_split_to_ht:NNn #1#2#3
-  { \tex_setbox:D #1 \tex_vsplit:D #2 to \dim_eval:w #3 \dim_eval_end: }
-%    \end{macrocode}
-% \end{macro}
-%
-% \subsection{Affine transformations}
-%
-% \begin{variable}{\l_box_angle_fp}
-%   When rotating boxes, the angle itself may be needed by the
-%   engine-dependent code. This is done using the \pkg{fp} module so
-%   that the value is tidied up properly.
-%    \begin{macrocode}
-\fp_new:N \l_box_angle_fp
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_box_cos_fp, \l_box_sin_fp}
-%   These are used to hold the calculated sine and cosine values while
-%   carrying out a rotation.
-%    \begin{macrocode}
-\fp_new:N \l_box_cos_fp
-\fp_new:N \l_box_sin_fp
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}
-%   {\l_box_top_dim, \l_box_bottom_dim, \l_box_left_dim, \l_box_right_dim}
-%   These are the positions of the four edges of a box before
-%   manipulation.
-%    \begin{macrocode}
-\dim_new:N \l_box_top_dim
-\dim_new:N \l_box_bottom_dim
-\dim_new:N \l_box_left_dim
-\dim_new:N \l_box_right_dim
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}
-%  {
-%    \l_box_top_new_dim,  \l_box_bottom_new_dim ,
-%    \l_box_left_new_dim, \l_box_right_new_dim
-%  }
-%   These are the positions of the four edges of a box after
-%   manipulation.
-%    \begin{macrocode}
-\dim_new:N \l_box_top_new_dim
-\dim_new:N \l_box_bottom_new_dim
-\dim_new:N \l_box_left_new_dim
-\dim_new:N \l_box_right_new_dim
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_box_internal_box, \l_box_internal_fp}
-%   Scratch space.
-%    \begin{macrocode}
-\box_new:N \l_box_internal_box
-\fp_new:N \l_box_internal_fp
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_box_x_fp, \l_box_y_fp, \l_box_x_new_fp, \l_box_y_new_fp}
-%   Used as the input and output values for a point when manipulation the
-%   location.
-%    \begin{macrocode}
-\fp_new:N \l_box_x_fp
-\fp_new:N \l_box_y_fp
-\fp_new:N \l_box_x_new_fp
-\fp_new:N \l_box_y_new_fp
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{macro}{\box_rotate:Nn}
-% \begin{macro}[aux]{\box_rotate_aux:N}
-% \begin{macro}[aux]{\box_rotate_set_sin_cos:}
-% \begin{macro}[aux]{\box_rotate_x:nnN, \box_rotate_y:nnN}
-% \begin{macro}[aux]
-%   {
-%     \box_rotate_quadrant_one:,   \box_rotate_quadrant_two:,
-%     \box_rotate_quadrant_three:, \box_rotate_quadrant_four:
-%   }
-%   Rotation of a box starts with working out the relevant sine and
-%   cosine. There is then a check to avoid doing any real work for the
-%   trivial rotation.
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_rotate:Nn #1#2
-  {
-    \hbox_set:Nn #1
-      {
-        \group_begin:
-          \fp_set:Nn \l_box_angle_fp {#2}
-          \box_rotate_set_sin_cos:
-          \fp_compare:NNNTF \l_box_sin_fp = \c_zero_fp
-            {
-               \fp_compare:NNNTF \l_box_cos_fp = \c_one_fp
-                 { \box_use:N #1 }
-                 { \box_rotate_aux:N #1 }
-            }
-            { \box_rotate_aux:N #1 }
-        \group_end:
-    }
-  }
-%    \end{macrocode}
-%   The edges of the box are then recorded: the left edge will
-%   always be at zero. Rotation of the four edges then takes place: this is
-%   most efficiently done on a quadrant by quadrant basis.
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_rotate_aux:N #1
-  {
-    \dim_set:Nn \l_box_top_dim    {  \box_ht:N #1 }
-    \dim_set:Nn \l_box_bottom_dim { -\box_dp:N #1 }
-    \dim_set:Nn \l_box_right_dim  {  \box_wd:N #1 }
-    \dim_zero:N \l_box_left_dim
-%    \end{macrocode}
-%   The next step is to work out the $x$ and $y$ coordinates of vertices of
-%   the rotated box in relation to its original coordinates. The box can be
-%   visualized with vertices $B$, $C$, $D$ and $E$ is illustrated
-%   (Figure~\ref{fig:rotation}). The vertex $O$ is the reference point on the
-%   baseline, and in this implementation is also the centre of rotation.
-%   \begin{figure}
-%     \centering
-%     \setlength{\unitlength}{3pt}^^A
-%     \begin{picture}(34,36)(12,44)
-%       \thicklines
-%       \put(20,52){\dashbox{1}(20,21){}}
-%       \put(20,80){\line(0,-1){36}}
-%       \put(12,58){\line(1, 0){34}}
-%       \put(41,59){A}
-%       \put(40,74){B}
-%       \put(21,74){C}
-%       \put(21,49){D}
-%       \put(40,49){E}
-%       \put(21,59){O}
-%     \end{picture}
-%     \caption{Co-ordinates of a box prior to rotation.}
-%     \label{fig:rotation}
-%   \end{figure}
-%   The formulae are, for a point $P$ and angle $\alpha$:
-%   \[
-%     \begin{array}{l}
-%       P'_x = P_x - O_x \\
-%       P'_y = P_y - O_y \\
-%       P''_x =  ( P'_x \cos(\alpha)) - ( P'_y \sin(\alpha) ) \\
-%       P''_y =  ( P'_x \sin(\alpha)) + ( P'_y \cos(\alpha) ) \\
-%       P'''_x = P''_x + O_x + L_x \\
-%       P'''_y = P''_y + O_y
-%    \end{array}
-%   \]
-%   The \enquote{extra} horizontal translation $L_x$ at the end is calculated
-%   so that the leftmost point of the resulting box has $x$-coordinate $0$.
-%   This is desirable as \TeX{} boxes must have the reference point at
-%   the left edge of the box. (As $O$ is always $(0,0)$, this part of the
-%   calculation is omitted here.)
-%    \begin{macrocode}
-    \fp_compare:NNNTF \l_box_sin_fp > \c_zero_fp
-      {
-        \fp_compare:NNNTF \l_box_cos_fp > \c_zero_fp
-          { \box_rotate_quadrant_one: }
-          { \box_rotate_quadrant_two: }
-      }
-      {
-        \fp_compare:NNNTF \l_box_cos_fp < \c_zero_fp
-          { \box_rotate_quadrant_three: }
-          { \box_rotate_quadrant_four: }
-      }
-%    \end{macrocode}
-%   The position of the box edges are now known, but the box at this
-%   stage be misplaced relative to the current \TeX{} reference point. So the
-%   content of the box is moved such that the reference point of the
-%   rotated box will be in the same place as the original.
-%    \begin{macrocode}
-    \hbox_set:Nn \l_box_internal_box { \box_use:N #1 }
-    \hbox_set:Nn \l_box_internal_box
-      {
-        \tex_kern:D -\l_box_left_new_dim
-        \hbox:n
-          {
-            \driver_box_rotate_begin:
-            \box_use:N \l_box_internal_box
-            \driver_box_rotate_end:
-          }
-      }
-%    \end{macrocode}
-%   Tidy up the size of the box so that the material is actually inside
-%   the bounding box. The result can then be used to reset the original
-%   box.
-%    \begin{macrocode}
-    \box_set_ht:Nn \l_box_internal_box {  \l_box_top_new_dim }
-    \box_set_dp:Nn \l_box_internal_box { -\l_box_bottom_new_dim }
-    \box_set_wd:Nn \l_box_internal_box
-      { \l_box_right_new_dim - \l_box_left_new_dim }
-    \box_use:N \l_box_internal_box
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%   A simple conversion from degrees to radians followed by calculation
-%   of the sine and cosine.
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_rotate_set_sin_cos:
-  {
-    \fp_set_eq:NN \l_box_internal_fp \l_box_angle_fp
-    \fp_div:Nn \l_box_internal_fp { 180 }
-    \fp_mul:Nn \l_box_internal_fp { \c_pi_fp }
-    \fp_sin:Nn \l_box_sin_fp { \l_box_internal_fp }
-    \fp_cos:Nn \l_box_cos_fp { \l_box_internal_fp }
-  }
-%    \end{macrocode}
-%   These functions take a general point $(|#1|, |#2|)$ and rotate its
-%   location about the origin, using the previously-set sine and cosine
-%   values. Each function gives only one component of the location of the
-%   updated point. This is because for rotation of a box each step needs
-%   only one value, and so performance is gained by avoiding working
-%   out both $x'$ and $y'$ at the same time. Contrast this with
-%   the equivalent function in the \pkg{l3coffins} module, where both parts
-%   are needed.
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_rotate_x:nnN #1#2#3
-  {
-    \fp_set_from_dim:Nn \l_box_x_fp {#1}
-    \fp_set_from_dim:Nn \l_box_y_fp {#2}
-    \fp_set_eq:NN \l_box_x_new_fp \l_box_x_fp
-    \fp_set_eq:NN \l_box_internal_fp   \l_box_y_fp
-    \fp_mul:Nn \l_box_x_new_fp { \l_box_cos_fp }
-    \fp_mul:Nn \l_box_internal_fp   { \l_box_sin_fp }
-    \fp_sub:Nn \l_box_x_new_fp { \l_box_internal_fp }
-    \dim_set:Nn #3 { \fp_to_dim:N \l_box_x_new_fp }
-  }
-\cs_new_protected:Npn \box_rotate_y:nnN #1#2#3
-  {
-    \fp_set_from_dim:Nn \l_box_x_fp {#1}
-    \fp_set_from_dim:Nn \l_box_y_fp {#2}
-    \fp_set_eq:NN \l_box_y_new_fp \l_box_y_fp
-    \fp_set_eq:NN \l_box_internal_fp   \l_box_x_fp
-    \fp_mul:Nn \l_box_y_new_fp { \l_box_cos_fp }
-    \fp_mul:Nn \l_box_internal_fp   { \l_box_sin_fp }
-    \fp_add:Nn \l_box_y_new_fp { \l_box_internal_fp }
-    \dim_set:Nn #3 { \fp_to_dim:N \l_box_y_new_fp }
-}
-%    \end{macrocode}
-%   Rotation of the edges is done using a different formula for each
-%   quadrant. In every case, the top and bottom edges only need the
-%   resulting $y$-values, whereas the left and right edges need the
-%   $x$-values. Each case is a question of picking out which corner
-%   ends up at with the maximum top, bottom, left and right value. Doing
-%   this by hand means a lot less calculating and avoids lots of
-%   comparisons.
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_rotate_quadrant_one:
-  {
-    \box_rotate_y:nnN \l_box_right_dim \l_box_top_dim
-      \l_box_top_new_dim
-    \box_rotate_y:nnN \l_box_left_dim  \l_box_bottom_dim
-      \l_box_bottom_new_dim
-    \box_rotate_x:nnN \l_box_left_dim  \l_box_top_dim
-      \l_box_left_new_dim
-    \box_rotate_x:nnN \l_box_right_dim \l_box_bottom_dim
-      \l_box_right_new_dim
-  }
-\cs_new_protected:Npn \box_rotate_quadrant_two:
-  {
-    \box_rotate_y:nnN \l_box_right_dim \l_box_bottom_dim
-      \l_box_top_new_dim
-    \box_rotate_y:nnN \l_box_left_dim  \l_box_top_dim
-      \l_box_bottom_new_dim
-    \box_rotate_x:nnN \l_box_right_dim  \l_box_top_dim
-      \l_box_left_new_dim
-    \box_rotate_x:nnN \l_box_left_dim   \l_box_bottom_dim
-      \l_box_right_new_dim
-  }
-\cs_new_protected:Npn \box_rotate_quadrant_three:
-  {
-    \box_rotate_y:nnN \l_box_left_dim  \l_box_bottom_dim
-      \l_box_top_new_dim
-    \box_rotate_y:nnN \l_box_right_dim \l_box_top_dim
-      \l_box_bottom_new_dim
-    \box_rotate_x:nnN \l_box_right_dim \l_box_bottom_dim
-      \l_box_left_new_dim
-    \box_rotate_x:nnN \l_box_left_dim   \l_box_top_dim
-      \l_box_right_new_dim
-  }
-\cs_new_protected:Npn \box_rotate_quadrant_four:
-  {
-    \box_rotate_y:nnN \l_box_left_dim  \l_box_top_dim
-      \l_box_top_new_dim
-    \box_rotate_y:nnN \l_box_right_dim \l_box_bottom_dim
-      \l_box_bottom_new_dim
-    \box_rotate_x:nnN \l_box_left_dim  \l_box_bottom_dim
-      \l_box_left_new_dim
-    \box_rotate_x:nnN \l_box_right_dim \l_box_top_dim
-      \l_box_right_new_dim
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{variable}{\l_box_scale_x_fp, \l_box_scale_y_fp}
-%   Scaling is potentially-different in the two axes.
-%    \begin{macrocode}
-\fp_new:N \l_box_scale_x_fp
-\fp_new:N \l_box_scale_y_fp
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{macro}{\box_resize:Nnn, \box_resize:cnn}
-% \begin{macro}[aux]{\box_resize_aux:Nnn}
-%   Resizing a box starts by working out the various dimensions of the
-%   existing box.
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_resize:Nnn #1#2#3
-  {
-    \hbox_set:Nn #1
-      {
-        \group_begin:
-          \dim_set:Nn \l_box_top_dim    {  \box_ht:N #1 }
-          \dim_set:Nn \l_box_bottom_dim { -\box_dp:N #1 }
-          \dim_set:Nn \l_box_right_dim  {  \box_wd:N #1 }
-          \dim_zero:N \l_box_left_dim
-%    \end{macrocode}
-%   The $x$-scaling and resulting box size is easy enough to work
-%   out: the dimension is that given as |#2|, and the scale is simply the
-%   new width divided by the old one.
-%    \begin{macrocode}
-          \fp_set_from_dim:Nn \l_box_scale_x_fp {#2}
-          \fp_set_from_dim:Nn \l_box_internal_fp { \l_box_right_dim }
-          \fp_div:Nn \l_box_scale_x_fp { \l_box_internal_fp }
-%    \end{macrocode}
-%   The $y$-scaling needs both the height and the depth of the current box.
-%    \begin{macrocode}
-          \fp_set_from_dim:Nn \l_box_scale_y_fp {#3}
-          \fp_set_from_dim:Nn \l_box_internal_fp
-            { \l_box_top_dim - \l_box_bottom_dim }
-          \fp_div:Nn \l_box_scale_y_fp { \l_box_internal_fp }
-%    \end{macrocode}
-%   At this stage, check for trivial scaling. If both scalings are unity, then
-%   the code does nothing. Otherwise, pass on to the auxiliary function to
-%   find the new dimensions.
-%    \begin{macrocode}
-          \fp_compare:NNNTF \l_box_scale_x_fp = \c_one_fp
-            {
-              \fp_compare:NNNTF \l_box_scale_y_fp = \c_one_fp
-                { \box_use:N #1 }
-                { \box_resize_aux:Nnn #1 {#2} {#3} }
-            }
-            { \box_resize_aux:Nnn #1 {#2} {#3} }
-        \group_end:
-      }
-  }
-\cs_generate_variant:Nn \box_resize:Nnn { c }
-%    \end{macrocode}
-%   With at least one real scaling to do, the next phase is to find the new
-%   edge co-ordinates. In the $x$~direction this is relatively easy: just
-%   scale the right edge. This is done using the absolute value of the
-%   scale so that the new edge is in the correct place. In the $y$~direction,
-%   both dimensions have to be scaled, and this again needs the absolute
-%   scale value. Once that is all done, the common resize/rescale code can
-%   be employed.
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_resize_aux:Nnn #1#2#3
-  {
-    \dim_compare:nNnTF {#2} > \c_zero_dim
-      { \dim_set:Nn \l_box_right_new_dim {#2} }
-      { \dim_set:Nn \l_box_right_new_dim { \c_zero_dim - ( #2 ) } }
-    \dim_compare:nNnTF {#3} > \c_zero_dim
-      {
-        \dim_set:Nn \l_box_top_new_dim
-          { \fp_use:N \l_box_scale_y_fp \l_box_top_dim }
-        \dim_set:Nn \l_box_bottom_new_dim
-          { \fp_use:N \l_box_scale_y_fp \l_box_bottom_dim }
-      }
-      {
-        \dim_set:Nn \l_box_top_new_dim
-          { - \fp_use:N \l_box_scale_y_fp \l_box_top_dim }
-        \dim_set:Nn \l_box_bottom_new_dim
-          { - \fp_use:N \l_box_scale_y_fp \l_box_bottom_dim }
-      }
-    \box_resize_common:N #1
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\box_resize_to_ht_plus_dp:Nn, \box_resize_to_ht_plus_dp:cn}
-% \begin{macro}{\box_resize_to_wd:Nn, \box_resize_to_wd:cn}
-%   Scaling to a total height or to a width is a simplified version of the main
-%   resizing operation, with the scale simply copied between the two parts. The
-%   internal auxiliary is called using the scaling value twice, as the sign for
-%   both parts is needed (as this allows the same internal code to be used as
-%   for the general case).
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_resize_to_ht_plus_dp:Nn #1#2
-  {
-    \hbox_set:Nn #1
-      {
-        \group_begin:
-          \dim_set:Nn \l_box_top_dim    {  \box_ht:N #1 }
-          \dim_set:Nn \l_box_bottom_dim { -\box_dp:N #1 }
-          \dim_set:Nn \l_box_right_dim  {  \box_wd:N #1 }
-          \dim_zero:N \l_box_left_dim
-          \fp_set_from_dim:Nn \l_box_scale_y_fp {#2}
-          \fp_set_from_dim:Nn \l_box_internal_fp
-            { \l_box_top_dim - \l_box_bottom_dim }
-          \fp_div:Nn \l_box_scale_y_fp { \l_box_internal_fp }
-          \fp_set_eq:NN \l_box_scale_x_fp \l_box_scale_y_fp
-          \fp_compare:NNNTF \l_box_scale_y_fp = \c_one_fp
-            { \box_use:N #1 }
-            { \box_resize_aux:Nnn #1 {#2} {#2} }
-        \group_end:
-      }
-  }
-\cs_generate_variant:Nn \box_resize_to_ht_plus_dp:Nn { c }
-\cs_new_protected:Npn \box_resize_to_wd:Nn #1#2
-  {
-    \hbox_set:Nn #1
-      {
-        \group_begin:
-          \dim_set:Nn \l_box_top_dim    {  \box_ht:N #1 }
-          \dim_set:Nn \l_box_bottom_dim { -\box_dp:N #1 }
-          \dim_set:Nn \l_box_right_dim  {  \box_wd:N #1 }
-          \dim_zero:N \l_box_left_dim
-          \fp_set_from_dim:Nn \l_box_scale_x_fp {#2}
-          \fp_set_from_dim:Nn \l_box_internal_fp { \l_box_right_dim }
-          \fp_div:Nn \l_box_scale_x_fp { \l_box_internal_fp }
-          \fp_set_eq:NN \l_box_scale_y_fp \l_box_scale_x_fp
-          \fp_compare:NNNTF \l_box_scale_x_fp = \c_one_fp
-            { \box_use:N #1 }
-            { \box_resize_aux:Nnn #1 {#2} {#2} }
-        \group_end:
-      }
-  }
-\cs_generate_variant:Nn \box_resize_to_wd:Nn { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\box_scale:Nnn, \box_scale:cnn}
-% \begin{macro}[aux]{\box_scale_aux:Nnn}
-%   When scaling a box, setting the scaling itself is easy enough. The
-%   new dimensions are also relatively easy to find, allowing only for
-%   the need to keep them positive in all cases. Once that is done then
-%   after a check for the trivial scaling a hand-off can be made to the
-%   common code. The dimension scaling operations are carried out using
-%   the \TeX{} mechanism as it avoids needing to use \texttt{fp}
-%   operations.
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_scale:Nnn #1#2#3
-  {
-    \hbox_set:Nn #1
-      {
-        \group_begin:
-          \fp_set:Nn \l_box_scale_x_fp {#2}
-          \fp_set:Nn \l_box_scale_y_fp {#3}
-          \dim_set:Nn \l_box_top_dim    {  \box_ht:N #1 }
-          \dim_set:Nn \l_box_bottom_dim { -\box_dp:N #1 }
-          \dim_set:Nn \l_box_right_dim  {  \box_wd:N #1 }
-          \dim_zero:N \l_box_left_dim
-          \fp_compare:NNNTF \l_box_scale_x_fp = \c_one_fp
-            {
-              \fp_compare:NNNTF \l_box_scale_y_fp = \c_one_fp
-                { \box_use:N #1 }
-                { \box_scale_aux:Nnn #1 {#2} {#3} }
-            }
-            { \box_scale_aux:Nnn #1 {#2} {#3} }
-        \group_end:
-      }
-  }
-\cs_generate_variant:Nn \box_scale:Nnn { c }
-\cs_new_protected:Npn \box_scale_aux:Nnn #1#2#3
-  {
-    \fp_compare:NNNTF \l_box_scale_y_fp > \c_zero_fp
-      {
-        \dim_set:Nn \l_box_top_new_dim    { #3 \l_box_top_dim }
-        \dim_set:Nn \l_box_bottom_new_dim { #3 \l_box_bottom_dim }
-      }
-      {
-        \dim_set:Nn  \l_box_top_new_dim    { -#3 \l_box_bottom_dim }
-        \dim_set:Nn  \l_box_bottom_new_dim { -#3 \l_box_top_dim }
-      }
-    \fp_compare:NNNTF \l_box_scale_x_fp > \c_zero_fp
-      { \l_box_right_new_dim #2 \l_box_right_dim }
-      { \l_box_right_new_dim -#2 \l_box_right_dim }
-    \box_resize_common:N #1
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[int]{\box_resize_common:N}
-%   The main resize function places in input into a box which will start
-%   of with zero width, and includes the handles for engine rescaling.
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_resize_common:N #1
-  {
-    \hbox_set:Nn \l_box_internal_box
-      {
-        \driver_box_scale_begin:
-        \hbox_overlap_right:n { \box_use:N #1 }
-        \driver_box_scale_end:
-      }
-%    \end{macrocode}
-%   The new height and depth can be applied directly.
-%    \begin{macrocode}
-    \box_set_ht:Nn \l_box_internal_box { \l_box_top_new_dim }
-    \box_set_dp:Nn \l_box_internal_box { \l_box_bottom_new_dim }
-%    \end{macrocode}
-%   Things are not quite as obvious for the width, as the reference point
-%   needs to remain unchanged. For positive scaling factors resizing the
-%   box is all that is needed. However, for case of a negative scaling
-%   the material must be shifted such that the reference point ends up in
-%   the right place.
-%    \begin{macrocode}
-    \fp_compare:NNNTF \l_box_scale_x_fp < \c_zero_fp
-      {
-        \hbox_to_wd:nn { \l_box_right_new_dim }
-          {
-            \tex_kern:D \l_box_right_new_dim
-            \box_use:N \l_box_internal_box
-            \tex_hss:D
-          }
-      }
-      {
-        \box_set_wd:Nn \l_box_internal_box { \l_box_right_new_dim }
-        \box_use:N \l_box_internal_box
-      }
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \subsection{Viewing part of a box}
-%
-% \begin{macro}{\box_clip:N, \box_clip:c}
-%   A wrapper around the driver-dependent code.
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_clip:N #1
-  { \hbox_set:Nn #1 { \driver_box_use_clip:N #1 } }
-\cs_generate_variant:Nn \box_clip:N { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\box_trim:Nnnnn, \box_trim:cnnnn}
-%   Trimming from the left- and right-hand edges of the box is easy. The total
-%   width is set to remove from the right, and a skip will shift the material
-%   to remove from the left.
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_trim:Nnnnn #1#2#3#4#5
-  {
-    \box_set_wd:Nn #1 { \box_wd:N #1 - \dim_eval:n {#4} - \dim_eval:n {#2} }
-    \hbox_set:Nn #1
-      {
-        \skip_horizontal:n { - \dim_eval:n {#2} }
-        \box_use:N #1
-      }
-%    \end{macrocode}
-%   For the height and depth, there is a need to watch the baseline is
-%   respected. Material always has to stay on the correct side, so trimming
-%   has to check that there is enough material to trim.
-%    \begin{macrocode}
-    \dim_compare:nNnTF { \box_dp:N #1 } > {#3}
-      { \box_set_dp:Nn #1 { \box_dp:N #1 - \dim_eval:n {#3} } }
-      {
-        \hbox_set:Nn #1
-          {
-            \box_move_down:nn { \dim_eval:n {#3} - \box_dp:N #1 }
-              { \box_use:N #1 }
-          }
-        \box_set_dp:Nn #1 \c_zero_dim
-      }
-    \dim_compare:nNnTF { \box_ht:N #1 } > {#5}
-      { \box_set_ht:Nn #1 { \box_ht:N #1 - \dim_eval:n {#5} } }
-      {
-        \hbox_set:Nn #1
-          {
-            \box_move_up:nn { \dim_eval:n {#5} - \box_ht:N #1 }
-              { \box_use:N #1 }
-          }
-        \box_set_ht:Nn #1 \c_zero_dim
-      }
-  }
-\cs_generate_variant:Nn \box_trim:Nnnnn { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\box_viewport:Nnnnn, \box_viewport:cnnnn}
-%   The same general logic as for clipping, but with absolute dimensions.
-%   Thus again width is easy and height is harder.
-%    \begin{macrocode}
-\cs_new_protected:Npn \box_viewport:Nnnnn #1#2#3#4#5
-  {
-    \box_set_wd:Nn #1 { \dim_eval:n {#4} - \dim_eval:n {#2} }
-    \hbox_set:Nn #1
-      {
-        \skip_horizontal:n { - \dim_eval:n {#2} }
-        \box_use:N #1
-      }
-    \dim_compare:nNnTF {#3} > \c_zero_dim
-      {
-        \hbox_set:Nn #1 { \box_move_down:nn {#3} { \box_use:N #1 } }
-        \box_set_dp:Nn #1 \c_zero_dim
-      }
-      { \box_set_dp:Nn #1 { - \dim_eval:n {#3} } }
-    \dim_compare:nNnTF {#5} > \c_zero_dim
-      { \box_set_ht:Nn #1 {#5} }
-      {
-        \hbox_set:Nn #1
-          { \box_move_up:nn { -\dim_eval:n {#5} } { \box_use:N #1 } }
-        \box_set_ht:Nn #1 \c_zero_dim
-      }
-  }
-\cs_generate_variant:Nn \box_viewport:Nnnnn { c }
+  { \tex_setbox:D #1 \tex_vsplit:D #2 to \__dim_eval:w #3 \__dim_eval_end: }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1982,7 +1265,9 @@
 % \begin{variable}{\l_last_box}
 %   Deprecated 2011-11-13, for removal by 2012-02-28.
 %    \begin{macrocode}
+%<*deprecated>
 \cs_new_eq:NN \l_last_box \tex_lastbox:D
+%</deprecated>
 %    \end{macrocode}
 % \end{variable}
 %
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3candidates.dtx b/Master/texmf-dist/source/latex/l3kernel/l3candidates.dtx
new file mode 100644
index 00000000000..8afac7cda1f
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3candidates.dtx
@@ -0,0 +1,2828 @@
+% \iffalse meta-comment
+%
+%% File: l3candidates.dtx Copyright(C) 2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver|package>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3candidates.dtx 3633 2012-05-12 20:11:32Z joseph $
+  {L3 Experimental additions to l3kernel}
+%</driver|package>
+%<*driver>
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{^^A
+%   The \textsf{l3candidates} package\\ Experimental additions to
+%   \pkg{l3kernel}^^A
+%   \thanks{This file describes v\ExplFileVersion,
+%     last revised \ExplFileDate.}^^A
+% }
+%
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+%
+% \date{Released \ExplFileDate}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% This module provides a space in which functions can be added to
+% \pkg{l3kernel} (\pkg{expl3}) while still being experimental. As such, the
+% functions here may not remain in their current form, or indeed at all,
+% in \pkg{l3kernel} in the future. In contrast to the material in
+% \pkg{l3experimental}, the functions here are all \emph{small} additions to
+% the kernel. We encourage programmers to test them out and report back on
+% the \texttt{LaTeX-L} mailing list.
+%
+% \section{Additions to \pkg{l3basics}}
+%
+% \begin{function}[EXP,TF]{\cs_if_exist_use:N, \cs_if_exist_use:c}
+%   \begin{syntax}
+%     \cs{cs_if_exist_use:NTF} \meta{control sequence} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   If the \meta{control sequence} exists, leave it in the input stream,
+%   followed by the \meta{true code} (unbraced). Otherwise, leave the
+%   \meta{false} code in the input stream. For example,
+%   \begin{verbatim}
+%     \cs_set:Npn \mypkg_use_character:N #1
+%       { \cs_if_exist_use:cF { mypkg_#1:n } { \mypkg_default:N #1 } }
+%   \end{verbatim}
+%   calls the function |\mypkg_#1:n| if it exists, and falls back to
+%   a default action otherwise. This could also be done (more slowly)
+%   using \cs{str_case_x:nnn}.
+%   \begin{texnote}
+%     The \texttt{c} variants do not introduce the \meta{control sequence}
+%     in the hash table if it is not there.
+%   \end{texnote}
+% \end{function}
+%
+% \section{Additions to \pkg{l3box}}
+%
+% \subsection{Affine transformations}
+%
+% Affine transformations are changes which (informally) preserve straight
+% lines. Simple translations are affine transformations, but are better handled
+% in \TeX{} by doing the translation first, then inserting an unmodified box.
+% On the other hand, rotation and resizing of boxed material can best be
+% handled by modifying boxes. These transformations are described here.
+%
+% \begin{function}{\box_resize:Nnn, \box_resize:cnn}
+%   \begin{syntax}
+%     \cs{box_resize:Nnn} \meta{box} \Arg{x-size} \Arg{y-size}
+%   \end{syntax}
+%   Resize the \meta{box} to \meta{x-size} horizontally and \meta{y-size}
+%   vertically (both of the sizes are dimension expressions).
+%   The \meta{y-size} is the vertical size (height plus depth) of
+%   the box. The updated \meta{box} will be an hbox, irrespective of the nature
+%   of the \meta{box}  before the resizing is applied. Negative sizes will
+%   cause the material in the \meta{box} to be reversed in direction, but the
+%   reference point of the \meta{box} will be unchanged. The resizing applies
+%   within the current \TeX{} group level.
+% \end{function}
+%
+% \begin{function}
+%   {\box_resize_to_ht_plus_dp:Nn, \box_resize_to_ht_plus_dp:cn}
+%   \begin{syntax}
+%     \cs{box_resize_to_ht_plus_dp:Nn} \meta{box} \Arg{y-size}
+%   \end{syntax}
+%   Resize the \meta{box} to \meta{y-size} vertically, scaling the horizontal
+%   size by the same amount (\meta{y-size} is a dimension expression).
+%   The \meta{y-size} is the vertical size (height plus depth) of
+%   the box.
+%   The updated \meta{box} will be an hbox, irrespective of the nature
+%   of the \meta{box}  before the resizing is applied. A negative size will
+%   cause the material in the \meta{box} to be reversed in direction, but the
+%   reference point of the \meta{box} will be unchanged. The resizing applies
+%   within the current \TeX{} group level.
+% \end{function}
+%
+% \begin{function}{\box_resize_to_wd:Nn, \box_resize_to_wd:cn}
+%   \begin{syntax}
+%     \cs{box_resize_to_wd:Nn} \meta{box} \Arg{x-size}
+%   \end{syntax}
+%   Resize the \meta{box} to \meta{x-size} horizontally, scaling the vertical
+%   size by the same amount (\meta{x-size} is a dimension expression).
+%   The updated \meta{box} will be an hbox, irrespective of the nature
+%   of the \meta{box}  before the resizing is applied. A negative size will
+%   cause the material in the \meta{box} to be reversed in direction, but the
+%   reference point of the \meta{box} will be unchanged. The resizing applies
+%   within the current \TeX{} group level.
+% \end{function}
+%
+% \begin{function}{\box_rotate:Nn, \box_rotate:cn}
+%   \begin{syntax}
+%     \cs{box_rotate:Nn} \meta{box} \Arg{angle}
+%   \end{syntax}
+%   Rotates the \meta{box} by \meta{angle} (in degrees) anti-clockwise about
+%   its reference point. The reference point of the updated box will be moved
+%   horizontally such that it is at the left side of the smallest rectangle
+%   enclosing the rotated material.
+%   The updated \meta{box} will be an hbox, irrespective of the nature
+%   of the \meta{box} before the rotation is applied. The rotation applies
+%   within the current \TeX{} group level.
+% \end{function}
+%
+% \begin{function}{\box_scale:Nnn, \box_scale:cnn}
+%   \begin{syntax}
+%     \cs{box_scale:Nnn} \meta{box} \Arg{x-scale} \Arg{y-scale}
+%   \end{syntax}
+%   Scales the \meta{box} by factors \meta{x-scale} and \meta{y-scale} in
+%   the horizontal and vertical directions, respectively (both scales are
+%   integer expressions). The updated \meta{box} will be an hbox, irrespective
+%   of the nature of the \meta{box} before the scaling is applied. Negative
+%   scalings will cause the material in the \meta{box} to be reversed in
+%   direction, but the reference point of the \meta{box} will be unchanged.
+%   The scaling applies within the current \TeX{} group level.
+% \end{function}
+%
+% \subsection{Viewing part of a box}
+%
+% \begin{function}{\box_clip:N, \box_clip:c}
+%   \begin{syntax}
+%     \cs{box_clip:N} \meta{box}
+%   \end{syntax}
+%   Clips the \meta{box} in the output so that only material inside the
+%   bounding box is displayed in the output. The updated \meta{box} will be an
+%   hbox, irrespective of the nature of the \meta{box} before the clipping is
+%   applied. The clipping applies within the current \TeX{} group level.
+%
+%   \textbf{These functions require the \LaTeX3 native drivers: they will
+%   not work with the \LaTeXe{} \pkg{graphics} drivers!}
+%
+%   \begin{texnote}
+%     Clipping is implemented by the driver, and as such the full content of
+%     the box is places in the output file. Thus clipping does not remove
+%     any information from the raw output, and hidden material can therefore
+%     be viewed by direct examination of the file.
+%   \end{texnote}
+% \end{function}
+%
+% \begin{function}{\box_trim:Nnnnn, \box_trim:cnnnn}
+%   \begin{syntax}
+%     \cs{box_trim:Nnnnn} \meta{box} \Arg{left} \Arg{bottom} \Arg{right} \Arg{top}
+%   \end{syntax}
+%   Adjusts the bounding box of the \meta{box} \meta{left} is removed from
+%   the left-hand edge of the bounding box, \meta{right} from the right-hand
+%   edge and so fourth. All adjustments are \meta{dimension expressions}.
+%   Material output of the bounding box will still be displayed in the output
+%   unless \cs{box_clip:N} is subsequently applied.
+%   The updated \meta{box} will be an
+%   hbox, irrespective of the nature of the \meta{box} before the viewport
+%   operation is applied. The adjustment applies within the current \TeX{}
+%   group level.
+% \end{function}
+%
+% \begin{function}{\box_viewport:Nnnnn, \box_viewport:cnnnn}
+%   \begin{syntax}
+%     \cs{box_viewport:Nnnnn} \meta{box} \Arg{llx} \Arg{lly} \Arg{urx} \Arg{ury}
+%   \end{syntax}
+%   Adjusts the bounding box of the \meta{box} such that it has lower-left
+%   co-ordinates (\meta{llx}, \meta{lly}) and upper-right co-ordinates
+%   (\meta{urx}, \meta{ury}). All four co-ordinate positions are
+%   \meta{dimension expressions}. Material output of the bounding box will
+%   still be displayed in the output unless \cs{box_clip:N} is
+%   subsequently applied.
+%   The updated \meta{box} will be an
+%   hbox, irrespective of the nature of the \meta{box} before the viewport
+%   operation is applied. The adjustment applies within the current \TeX{}
+%   group level.
+% \end{function}
+%
+% \subsection{Internal variables}
+%
+% \begin{variable}{\l__box_angle_fp}
+%   The angle through which a box is rotated by \cs{box_rotate:Nn}, given in
+%   degrees counter-clockwise. This value is required by the underlying
+%   driver code in \pkg{l3driver} to carry out the driver-dependent part
+%   of box rotation.
+% \end{variable}
+%
+% \begin{variable}{\l__box_cos_fp, \l__box_sin_fp}
+%   The sine and cosine of the angle through which a box is rotated by
+%   \cs{box_rotate:Nn}: the values refer to the angle counter-clockwise. These
+%   values are required by the underlying driver code in \pkg{l3driver} to
+%   carry out the driver-dependent part of box rotation.
+% \end{variable}
+%
+% \begin{variable}{\l__box_scale_x_fp, \l__box_scale_y_fp}
+%   The scaling factors by which a box is scaled by \cs{box_scale:Nnn}
+%   or \cs{box_resize:Nnn}. These values are required by the underlying
+%   driver code in \pkg{l3driver} to carry out the driver-dependent part
+%   of box rotation.
+% \end{variable}
+%
+% \begin{variable}{\l__box_internal_box}
+%   Box used for affine transformations, which is used to contain rotated
+%   material when applying \cs{box_rotate:Nn}. This box must be correctly
+%   constructed for the driver-dependent code in \pkg{l3driver} to function
+%   correctly.
+% \end{variable}
+%
+% \section{Additions to \pkg{l3clist}}
+%
+% \begin{function}{\clist_item:Nn, \clist_item:cn, \clist_item:nn}
+%   \begin{syntax}
+%     \cs{clist_item:Nn} \meta{comma list} \Arg{integer expression}
+%   \end{syntax}
+%   Indexing items in the \meta{comma list} from~$1$ at the top (left), this
+%   function will evaluate the \meta{integer expression} and leave the
+%   appropriate item from the comma list in the input stream. If the
+%   \meta{integer expression} is negative, indexing occurs from the
+%   bottom (right) of the comma list. When the \meta{integer expression}
+%   is larger than the number of items in the \meta{comma list} (as
+%   calculated by \cs{clist_count:N}) then the function will expand to
+%   nothing.
+%   \begin{texnote}
+%     The result is returned within the \tn{unexpanded}
+%     primitive (\cs{exp_not:n}), which means that the \meta{item}
+%     will not expand further when appearing in an \texttt{x}-type
+%     argument expansion.
+%   \end{texnote}
+% \end{function}
+%
+% \begin{function}
+%   {
+%     \clist_set_from_seq:NN,  \clist_set_from_seq:cN,
+%     \clist_set_from_seq:Nc,  \clist_set_from_seq:cc,
+%     \clist_gset_from_seq:NN, \clist_gset_from_seq:cN,
+%     \clist_gset_from_seq:Nc, \clist_gset_from_seq:cc
+%   }
+%   \begin{syntax}
+%     \cs{clist_set_from_seq:NN} \meta{comma list} \meta{sequence}
+%   \end{syntax}
+%   Sets the \meta{comma list} to be equal to the content of the
+%   \meta{sequence}.
+%   Items which contain either spaces or commas are surrounded by braces.
+% \end{function}
+%
+% \begin{function}
+%   {
+%     \clist_const:Nn, \clist_const:Nx,
+%     \clist_const:cn, \clist_const:cx
+%   }
+%   \begin{syntax}
+%     \cs{clist_const:Nn} \meta{clist~var} \Arg{comma list}
+%   \end{syntax}
+%   Creates a new constant \meta{clist~var} or raises an error
+%   if the name is already taken. The value of the
+%   \meta{clist~var} will be set globally to the
+%   \meta{comma list}.
+% \end{function}
+%
+% \begin{function}[EXP, pTF]{\clist_if_empty:n}
+%   \begin{syntax}
+%     \cs{clist_if_empty_p:n} \Arg{comma list}
+%     \cs{clist_if_empty:nTF} \Arg{comma list} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   Tests if the \meta{comma list} is empty (containing no items).
+%   The rules for space trimming are as for other \texttt{n}-type
+%   comma-list functions, hence the comma list |{~,~,,~}| (without
+%   outer braces) is empty, while |{~,{},}| (without outer braces)
+%   contains one element, which happens to be empty: the comma-list
+%   is not empty.
+% \end{function}
+%
+% \begin{function}[EXP, added = 2012-06-26]{\clist_use:Nnnn}
+%   \begin{syntax}
+%     \cs{clist_use:Nnnn} \meta{clist~var} \Arg{separator~between~two} \Arg{separator~between~more~than~two} \Arg{separator~between~final~two}
+%   \end{syntax}
+%   Places the contents of the \meta{clist~var} in the input stream,
+%   with the appropriate \meta{separator} between the items.  Namely, if
+%   the comma list has more than $2$ items, the \meta{separator between
+%     more than two} is placed between each pair of items except the
+%   last, for which the \meta{separator between final two} is used.  If
+%   the comma list has $2$ items, then they are placed in the input
+%   stream separated by the \meta{separator between two}.  If the comma
+%   list has $1$ item, it is placed in the input stream, and a comma
+%   list with no items produces no output.  An error will be raised if
+%   the variable does not exist or if it is invalid.
+%
+%   For example,
+%   \begin{verbatim}
+%     \clist_set:Nn \l_tmpa_clist { a , b , , c , {de} , f }
+%     \clist_use:Nnnn \l_tmpa_clist { ~and~ } { ,~ } { ,~and~ }
+%   \end{verbatim}
+%   will insert \enquote{\texttt{a, b, c, de, and f}} in the input
+%   stream.  The first separator argument is not used in this case
+%   because the comma list has more than $2$ items.
+%   \begin{texnote}
+%     The result is returned within the \tn{unexpanded}
+%     primitive (\cs{exp_not:n}), which means that the \meta{items}
+%     will not expand further when appearing in an \texttt{x}-type
+%     argument expansion.
+%   \end{texnote}
+% \end{function}
+%
+% \section{Additions to \pkg{l3coffins}}
+%
+% \begin{function}{\coffin_resize:Nnn, \coffin_resize:cnn}
+%   \begin{syntax}
+%     \cs{coffin_resize:Nnn} \meta{coffin} \Arg{width} \Arg{total-height}
+%   \end{syntax}
+%   Resized the \meta{coffin} to \meta{width} and \meta{total-height},
+%   both of which should be given as dimension expressions. These may
+%   include the terms \cs{TotalHeight}, \cs{Height}, \cs{Depth} and
+%   \cs{Width}, which will evaluate to the appropriate dimensions of
+%   the \meta{coffin}.
+% \end{function}
+%
+% \begin{function}{\coffin_rotate:Nn, \coffin_rotate:cn}
+%   \begin{syntax}
+%     \cs{coffin_rotate:Nn} \meta{coffin} \Arg{angle}
+%   \end{syntax}
+%   Rotates the \meta{coffin} by the given \meta{angle} (given in
+%   degrees counter-clockwise). This process will rotate both the
+%   coffin content and poles. Multiple rotations will not result in
+%   the bounding box of the coffin growing unnecessarily.
+% \end{function}
+%
+% \begin{function}{\coffin_scale:Nnn, \coffin_scale:cnn}
+%   \begin{syntax}
+%     \cs{coffin_scale:Nnn} \meta{coffin} \Arg{x-scale} \Arg{y-scale}
+%   \end{syntax}
+%   Scales the \meta{coffin} by a factors \meta{x-scale} and
+%   \meta{y-scale} in the horizontal and vertical directions,
+%   respectively. The two scale factors should be given as real numbers.
+% \end{function}
+%
+% \section{Additions to \pkg{l3file}}
+%
+% \begin{function}[added = 2012-02-11]{\ior_map_inline:Nn}
+%   \begin{syntax}
+%     \cs{ior_map_inline:Nn} \meta{stream} \Arg{inline function}
+%   \end{syntax}
+%   Applies the \meta{inline function} to \meta{lines} obtained by
+%   reading one or more lines (until an equal number of left and right
+%   braces are found) from the \meta{stream}. The \meta{inline function}
+%   should consist of code which will receive the \meta{line} as |#1|.
+% \end{function}
+%
+% \begin{function}[added = 2012-02-11]{\ior_str_map_inline:Nn}
+%   \begin{syntax}
+%     \cs{ior_str_map_inline:Nn} \Arg{stream} \Arg{inline function}
+%   \end{syntax}
+%   Applies the \meta{inline function} to every \meta{line}
+%   in the \meta{sream}. The material is read from the \meta{stream}
+%   as a series of tokens with category code $12$ (other), with the
+%   exception of space characters which are given category code $10$
+%   (space). The \meta{inline function} should consist of code which
+%   will receive the \meta{line} as |#1|.
+% \end{function}
+%
+% \begin{function}[added = 2012-06-29]{\ior_map_break:}
+%   \begin{syntax}
+%     \cs{ior_map_break:}
+%   \end{syntax}
+%   Used to terminate a \cs{ior_map_\ldots} function before all
+%   lines from the \meta{stream} have been processed. This will
+%   normally take place within a conditional statement, for example
+%   \begin{verbatim}
+%     \ior_map_inline:Nn \l_my_ior
+%       {
+%         \str_if_eq:nnTF { #1 } { bingo }
+%           { \ior_map_break: }
+%           {
+%             % Do something useful
+%           }
+%       }
+%   \end{verbatim}
+%   Use outside of a \cs{ior_map_\ldots} scenario will lead to low
+%   level \TeX{} errors.
+%   \begin{texnote}
+%     When the mapping is broken, additional tokens may be inserted by the
+%     internal macro \cs{__prg_break_point:Nn} before further items are taken
+%     from the input stream. This will depend on the design of the mapping
+%     function.
+%   \end{texnote}
+% \end{function}
+%
+% \begin{function}[added = 2012-06-29]{\ior_map_break:n}
+%   \begin{syntax}
+%     \cs{ior_map_break:n} \Arg{tokens}
+%   \end{syntax}
+%   Used to terminate a \cs{ior_map_\ldots} function before all
+%   lines in the \meta{stream} have been processed, inserting
+%   the \meta{tokens} after the mapping has ended. This will
+%   normally take place within a conditional statement, for example
+%   \begin{verbatim}
+%     \ior_map_inline:Nn \l_my_ior
+%       {
+%         \str_if_eq:nnTF { #1 } { bingo }
+%           { \ior_map_break:n { <tokens> } }
+%           {
+%             % Do something useful
+%           }
+%       }
+%   \end{verbatim}
+%   Use outside of a \cs{ior_map_\ldots} scenario will lead to low
+%   level \TeX{} errors.
+%   \begin{texnote}
+%     When the mapping is broken, additional tokens may be inserted by the
+%     internal macro \cs{__prg_break_point:Nn} before the \meta{tokens} are
+%     inserted into the input stream.
+%     This will depend on the design of the mapping function.
+%   \end{texnote}
+% \end{function}
+%
+% \section{Additions to \pkg{l3fp}}
+%
+% \begin{function}
+%   {
+%     \fp_set_from_dim:Nn,  \fp_set_from_dim:cn,
+%     \fp_gset_from_dim:Nn, \fp_gset_from_dim:cn
+%   }
+%   \begin{syntax}
+%     \cs{fp_set_from_dim:Nn} \meta{floating point variable} \Arg{dimexpr}
+%   \end{syntax}
+%   Sets the \meta{floating point variable} to the distance represented
+%   by the \meta{dimension expression} in the units points. This means
+%   that distances given in other units are first converted to points
+%   before being assigned to the \meta{floating point variable}.
+% \end{function}
+%
+% \section{Additions to \pkg{l3prop}}
+%
+% \begin{function}[rEXP]
+%   {\prop_map_tokens:Nn, \prop_map_tokens:cn}
+%   \begin{syntax}
+%     \cs{prop_map_tokens:Nn} \meta{property list} \Arg{code}
+%   \end{syntax}
+%   Analogue of \cs{prop_map_function:NN} which maps several tokens
+%   instead of a single function.  The \meta{code} receives each
+%   key--value pair in the \meta{property list} as two trailing brace
+%   groups. For instance,
+%   \begin{verbatim}
+%     \prop_map_tokens:Nn \l_my_prop { \str_if_eq:nnT { mykey } }
+%   \end{verbatim}
+%   will expand to the value corresponding to \texttt{mykey}: for each
+%   pair in \cs{l_my_prop} the function \cs{str_if_eq:nnT} receives
+%   \texttt{mykey}, the \meta{key} and the \meta{value} as its three
+%   arguments.  For that specific task, \cs{prop_get:Nn} is faster.
+% \end{function}
+%
+% \begin{function}[EXP]{\prop_get:Nn, \prop_get:cn}
+%   \begin{syntax}
+%     \cs{prop_get:Nn} \meta{property list} \Arg{key}
+%   \end{syntax}
+%   Expands to the \meta{value} corresponding to the \meta{key} in
+%   the \meta{property list}. If the \meta{key} is missing, this has
+%   an empty expansion.
+%   \begin{texnote}
+%     This function is slower than the non-expandable analogue
+%     \cs{prop_get:NnN}.
+%     The result is returned within the \tn{unexpanded}
+%     primitive (\cs{exp_not:n}), which means that the \meta{value}
+%     will not expand further when appearing in an \texttt{x}-type
+%     argument expansion.
+%   \end{texnote}
+% \end{function}
+%
+% \section{Additions to \pkg{l3seq}}
+%
+% \begin{function}[EXP]{\seq_item:Nn, \seq_item:cn}
+%   \begin{syntax}
+%     \cs{seq_item:Nn} \meta{sequence} \Arg{integer expression}
+%   \end{syntax}
+%   Indexing items in the \meta{sequence} from~$1$ at the top (left), this
+%   function will evaluate the \meta{integer expression} and leave the
+%   appropriate item from the sequence in the input stream. If the
+%   \meta{integer expression} is negative, indexing occurs from the
+%   bottom (right) of the sequence. When the \meta{integer expression}
+%   is larger than the number of items in the \meta{sequence} (as
+%   calculated by \cs{seq_count:N}) then the function will expand to
+%   nothing.
+%   \begin{texnote}
+%     The result is returned within the \tn{unexpanded}
+%     primitive (\cs{exp_not:n}), which means that the \meta{item}
+%     will not expand further when appearing in an \texttt{x}-type
+%     argument expansion.
+%   \end{texnote}
+% \end{function}
+%
+% \begin{function}[rEXP]
+%   {
+%     \seq_mapthread_function:NNN, \seq_mapthread_function:NcN,
+%     \seq_mapthread_function:cNN, \seq_mapthread_function:ccN
+%   }
+%   \begin{syntax}
+%     \cs{seq_mapthread_function:NNN} \meta{seq_1} \meta{seq_2} \meta{function}
+%   \end{syntax}
+%   Applies \meta{function} to every pair of items
+%   \meta{seq_1-item}--\meta{seq_2-item} from the two sequences, returning
+%   items from both sequences from left to right.   The \meta{function} will
+%   receive two \texttt{n}-type arguments for each iteration. The  mapping
+%   will terminate when
+%   the end of either sequence is reached (\emph{i.e.}~whichever sequence has
+%   fewer items determines how many iterations
+%   occur).
+% \end{function}
+%
+% \begin{function}
+%   {
+%     \seq_set_from_clist:NN,  \seq_set_from_clist:cN,
+%     \seq_set_from_clist:Nc,  \seq_set_from_clist:cc,
+%     \seq_set_from_clist:Nn,  \seq_set_from_clist:cn,
+%     \seq_gset_from_clist:NN, \seq_gset_from_clist:cN,
+%     \seq_gset_from_clist:Nc, \seq_gset_from_clist:cc,
+%     \seq_gset_from_clist:Nn, \seq_gset_from_clist:cn
+%   }
+%   \begin{syntax}
+%     \cs{seq_set_from_clist:NN} \meta{sequence} \meta{comma-list}
+%   \end{syntax}
+%   Sets the \meta{sequence} within the current \TeX{} group to be equal
+%   to the content of the \meta{comma-list}.
+% \end{function}
+%
+% \begin{function}{\seq_reverse:N, \seq_greverse:N}
+%   \begin{syntax}
+%     \cs{seq_reverse:N} \meta{sequence}
+%   \end{syntax}
+%   Reverses the order of items in the \meta{sequence}, and
+%   assigns the result to \meta{sequence}, locally or globally
+%   according to the variant chosen.
+% \end{function}
+%
+% \begin{function}{\seq_set_filter:NNn, \seq_gset_filter:NNn}
+%   \begin{syntax}
+%     \cs{seq_set_filter:NNn} \meta{sequence_1} \meta{sequence_2} \Arg{inline boolexpr}
+%   \end{syntax}
+%   Evaluates the \meta{inline boolexpr} for every \meta{item} stored
+%   within the \meta{sequence_2}. The \meta{inline boolexpr} will
+%   receive the \meta{item} as |#1|. The sequence of all \meta{items}
+%   for which the \meta{inline boolexpr} evaluated to \texttt{true}
+%   is assigned to \meta{sequence_1}.
+%   \begin{texnote}
+%     Contrarily to other mapping functions, \cs{seq_map_break:} cannot
+%     be used in this function, and will lead to low-level \TeX{} errors.
+%   \end{texnote}
+% \end{function}
+%
+% \begin{function}[added = 2011-12-22]
+%   {\seq_set_map:NNn, \seq_gset_map:NNn}
+%   \begin{syntax}
+%     \cs{seq_set_map:NNn} \meta{sequence_1} \meta{sequence_2} \Arg{inline function}
+%   \end{syntax}
+%   Applies \meta{inline function} to every \meta{item} stored
+%   within the \meta{sequence_2}. The \meta{inline function} should
+%   consist of code which will receive the \meta{item} as |#1|.
+%   The sequence resulting from \texttt{x}-expanding
+%   \meta{inline function} applied to each \meta{item}
+%   is assigned to \meta{sequence_1}. As such, the code
+%   in \meta{inline function} should be expandable.
+%   \begin{texnote}
+%     Contrarily to other mapping functions, \cs{seq_map_break:} cannot
+%     be used in this function, and will lead to low-level \TeX{} errors.
+%   \end{texnote}
+% \end{function}
+%
+% \begin{function}[EXP, added = 2012-06-26]{\seq_use:Nnnn}
+%   \begin{syntax}
+%     \cs{seq_use:Nnnn} \meta{seq~var} \Arg{separator~between~two} \Arg{separator~between~more~than~two} \Arg{separator~between~final~two}
+%   \end{syntax}
+%   Places the contents of the \meta{seq~var} in the input stream, with
+%   the appropriate \meta{separator} between the items.  Namely, if the
+%   sequence has more than $2$ items, the \meta{separator between more
+%     than two} is placed between each pair of items except the last,
+%   for which the \meta{separator between final two} is used.  If the
+%   sequence has $2$ items, then they are placed in the input stream
+%   separated by the \meta{separator between two}.  If the sequence has
+%   $1$ item, it is placed in the input stream, and an empty sequence
+%   produces no output.  An error will be raised if the variable does
+%   not exist or if it is invalid.
+%
+%   For example,
+%   \begin{verbatim}
+%     \seq_set_split:Nnn \l_tmpa_seq { | } { a | b | c | {de} | f }
+%     \seq_use:Nnnn \l_tmpa_seq { ~and~ } { ,~ } { ,~and~ }
+%   \end{verbatim}
+%   will insert \enquote{\texttt{a, b, c, de, and f}} in the input
+%   stream.  The first separator argument is not used in this case
+%   because the sequence has more than $2$ items.
+%   \begin{texnote}
+%     The result is returned within the \tn{unexpanded}
+%     primitive (\cs{exp_not:n}), which means that the \meta{items}
+%     will not expand further when appearing in an \texttt{x}-type
+%     argument expansion.
+%   \end{texnote}
+% \end{function}
+%
+% \section{Additions to \pkg{l3skip}}
+%
+% \begin{function}{\skip_split_finite_else_action:nnNN}
+%   \begin{syntax}
+%     \cs{skip_split_finite_else_action:nnNN} \Arg{skipexpr} \Arg{action}
+%     ~~\meta{dimen_1} \meta{dimen_2}
+%   \end{syntax}
+%   Checks if the \meta{skipexpr} contains finite glue. If it does then it
+%   assigns
+%   \meta{dimen_1} the stretch component and \meta{dimen_2} the shrink
+%   component. If
+%   it contains infinite glue set \meta{dimen_1} and \meta{dimen_2} to $0$\,pt
+%   and place |#2| into the input stream: this is usually an error or
+%   warning message of some sort.
+% \end{function}
+%
+% \section{Additions to \pkg{l3tl}}
+%
+% \begin{function}[EXP,pTF]{\tl_if_single_token:n}
+%   \begin{syntax}
+%   \cs{tl_if_single_token_p:n} \Arg{token list}
+%   \cs{tl_if_single_token:nTF} \Arg{token list} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   Tests if the token list consists of exactly one token, \emph{i.e.}~is
+%   either a single space character or a single \enquote{normal} token.
+%   Token groups (|{|\ldots|}|) are not single tokens.
+% \end{function}
+%
+% \begin{function}[EXP]{\tl_reverse_tokens:n}
+%   \begin{syntax}
+%     \cs{tl_reverse_tokens:n} \Arg{tokens}
+%   \end{syntax}
+%   This function, which works directly on \TeX{} tokens, reverses
+%   the order of the \meta{tokens}: the first will be the last and
+%   the last will become first. Spaces are preserved. The reversal
+%   also operates within brace groups, but the braces themselves
+%   are not exchanged, as this would lead to an unbalanced token
+%   list. For instance, \cs{tl_reverse_tokens:n} |{a~{b()}}|
+%   leaves |{)(b}~a| in the input stream. This function requires
+%   two steps of expansion.
+%   \begin{texnote}
+%     The result is returned within the \tn{unexpanded}
+%     primitive (\cs{exp_not:n}), which means that the token
+%     list will not expand further when appearing in an \texttt{x}-type
+%     argument expansion.
+%   \end{texnote}
+% \end{function}
+%
+% \begin{function}[EXP]{\tl_count_tokens:n}
+%   \begin{syntax}
+%     \cs{tl_count_tokens:n} \Arg{tokens}
+%   \end{syntax}
+%   Counts the number of \TeX{} tokens in the \meta{tokens} and leaves
+%   this information in the input stream. Every token, including spaces and
+%   braces, contributes one to the total; thus for instance, the token count of
+%   |a~{bc}| is $6$.
+%   This function requires three expansions,
+%   giving an \meta{integer denotation}.
+% \end{function}
+%
+% \begin{function}[EXP]{\tl_expandable_uppercase:n,\tl_expandable_lowercase:n}
+%   \begin{syntax}
+%     \cs{tl_expandable_uppercase:n} \Arg{tokens}
+%     \cs{tl_expandable_lowercase:n} \Arg{tokens}
+%   \end{syntax}
+%   The \cs{tl_expandable_uppercase:n} function works through all of
+%   the \meta{tokens}, replacing characters in the range |a|--|z|
+%   (with arbitrary category code) by the corresponding letter
+%   in the range |A|--|Z|, with category code $11$ (letter). Similarly,
+%   \cs{tl_expandable_lowercase:n} replaces characters in the range
+%   |A|--|Z| by letters in the range |a|--|z|, and leaves other tokens
+%   unchanged. This function requires two steps of expansion.
+%   \begin{texnote}
+%     Begin-group and end-group characters are normalized and become
+%     |{| and |}|, respectively.
+%     The result is returned within the \tn{unexpanded}
+%     primitive (\cs{exp_not:n}), which means that the token
+%     list will not expand further when appearing in an \texttt{x}-type
+%     argument expansion.
+%   \end{texnote}
+% \end{function}
+%
+% \begin{function}[EXP]{\tl_item:nn, \tl_item:Nn, \tl_item:cn}
+%   \begin{syntax}
+%     \cs{tl_item:nn} \Arg{token list} \Arg{integer expression}
+%   \end{syntax}
+%   Indexing items in the \meta{token list} from~$1$ on the left, this
+%   function will evaluate the \meta{integer expression} and leave the
+%   appropriate item from the \meta{token list} in the input stream.
+%   If the \meta{integer expression} is negative, indexing occurs from
+%   the right of the token list, starting at $-1$ for the right-most item.
+%   If the index is out of bounds, then thr function expands to nothing.
+%   \begin{texnote}
+%     The result is returned within the \tn{unexpanded}
+%     primitive (\cs{exp_not:n}), which means that the \meta{item}
+%     will not expand further when appearing in an \texttt{x}-type
+%     argument expansion.
+%   \end{texnote}
+% \end{function}
+%
+% \section{Additions to \pkg{l3tokens}}
+%
+% \begin{function}{\char_set_active:Npn,  \char_set_active:Npx}
+%   \begin{syntax}
+%      \cs{char_set_active:Npn} \meta{char} \meta{parameters} \Arg{code}
+%   \end{syntax}
+%   Makes \meta{char} an active character to expand to \meta{code} as
+%   replacement text.
+%   Within the \meta{code}, the \meta{parameters} (|#1|, |#2|,
+%   \emph{etc.}) will be replaced by those absorbed. The \meta{char} is
+%   made active within the current \TeX{} group level, and the definition
+%   is also local.
+% \end{function}
+%
+% \begin{function}{\char_gset_active:Npn, \char_gset_active:Npx}
+%   \begin{syntax}
+%      \cs{char_gset_active:Npn} \meta{char} \meta{parameters} \Arg{code}
+%   \end{syntax}
+%   Makes \meta{char} an active character to expand to \meta{code} as
+%   replacement text.
+%   Within the \meta{code}, the \meta{parameters} (|#1|, |#2|,
+%   \emph{etc.}) will be replaced by those absorbed. The \meta{char} is
+%   made active within the current \TeX{} group level, but the definition
+%   is global. This function is therefore suited to cases where an active
+%   character definition should be applied only in some context (where the
+%   \meta{char} is again made active).
+% \end{function}
+%
+% \begin{function}{\char_set_active_eq:NN}
+%   \begin{syntax}
+%      \cs{char_set_active_eq:NN} \meta{char} \meta{function}
+%   \end{syntax}
+%   Makes \meta{char} an active character equivalent in meaning to the
+%   \meta{function} (which may itself be an active character). The \meta{char}
+%   is made active within the current \TeX{} group level, and the definition
+%   is also local.
+% \end{function}
+%
+% \begin{function}{\char_gset_active_eq:NN}
+%   \begin{syntax}
+%      \cs{char_gset_active_eq:NN} \meta{char} \meta{function}
+%   \end{syntax}
+%   Makes \meta{char} an active character equivalent in meaning to the
+%   \meta{function} (which may itself be an active character). The \meta{char}
+%   is made active within the current \TeX{} group level, but the definition
+%   is global. This function is therefore suited to cases where an active
+%   character definition should be applied only in some context (where the
+%   \meta{char} is again made active).
+% \end{function}
+%
+% \begin{function}[TF]{\peek_N_type:}
+%   \begin{syntax}
+%     \cs{peek_N_type:TF} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   Tests if the next \meta{token} in the input stream can be safely
+%   grabbed as an \texttt{N}-type argument. The test will be \meta{false}
+%   if the next \meta{token} is either an explicit or implicit
+%   begin-group or end-group token (with any character code), or
+%   an explicit or implicit space character (with character code $32$
+%   and category code $10$), and \meta{true} in all other cases.
+%   Note that a \meta{true} result ensures that the next \meta{token} is
+%   a valid \texttt{N}-type argument. However, if the next \meta{token}
+%   is for instance \cs{c_space_token}, the test will take the
+%   \meta{false} branch, even though the next \meta{token} is in fact
+%   a valid \texttt{N}-type argument. The \meta{token} will be left
+%   in the input stream after the \meta{true code} or \meta{false code}
+%   (as appropriate to the result of the test).
+% \end{function}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3candidates} Implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<*package>
+\ProvidesExplPackage
+  {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
+\__expl_package_check:
+%</package>
+%    \end{macrocode}
+%
+% \subsection{Additions to \pkg{l3box}}
+%
+%    \begin{macrocode}
+%<@@=box>
+%    \end{macrocode}
+%
+% \subsection{Affine transformations}
+%
+% \begin{variable}{\l_@@_angle_fp}
+%   When rotating boxes, the angle itself may be needed by the
+%   engine-dependent code. This is done using the \pkg{fp} module so
+%   that the value is tidied up properly.
+%    \begin{macrocode}
+\fp_new:N \l_@@_angle_fp
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_cos_fp, \l_@@_sin_fp}
+%   These are used to hold the calculated sine and cosine values while
+%   carrying out a rotation.
+%    \begin{macrocode}
+\fp_new:N \l_@@_cos_fp
+\fp_new:N \l_@@_sin_fp
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}
+%   {\l_@@_top_dim, \l_@@_bottom_dim, \l_@@_left_dim, \l_@@_right_dim}
+%   These are the positions of the four edges of a box before
+%   manipulation.
+%    \begin{macrocode}
+\dim_new:N \l_@@_top_dim
+\dim_new:N \l_@@_bottom_dim
+\dim_new:N \l_@@_left_dim
+\dim_new:N \l_@@_right_dim
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}
+%  {
+%    \l_@@_top_new_dim,  \l_@@_bottom_new_dim ,
+%    \l_@@_left_new_dim, \l_@@_right_new_dim
+%  }
+%   These are the positions of the four edges of a box after
+%   manipulation.
+%    \begin{macrocode}
+\dim_new:N \l_@@_top_new_dim
+\dim_new:N \l_@@_bottom_new_dim
+\dim_new:N \l_@@_left_new_dim
+\dim_new:N \l_@@_right_new_dim
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_internal_box}
+%   Scratch space, but also needed by some parts of the driver.
+%    \begin{macrocode}
+\box_new:N \l_@@_internal_box
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}{\box_rotate:Nn}
+% \begin{macro}[aux]{\@@_rotate:N}
+% \begin{macro}[aux]{\@@_rotate_x:nnN, \@@_rotate_y:nnN}
+% \begin{macro}[aux]
+%   {
+%     \@@_rotate_quadrant_one:,   \@@_rotate_quadrant_two:,
+%     \@@_rotate_quadrant_three:, \@@_rotate_quadrant_four:
+%   }
+%   Rotation of a box starts with working out the relevant sine and
+%   cosine. The actual rotation is in an auxiliary to keep the flow slightly
+%   clearer
+%    \begin{macrocode}
+\cs_new_protected:Npn \box_rotate:Nn #1#2
+  {
+    \hbox_set:Nn #1
+      {
+        \group_begin:
+          \fp_set:Nn \l_@@_angle_fp {#2}
+          \fp_set:Nn \l_@@_sin_fp { sin ( \l_@@_angle_fp * deg ) }
+          \fp_set:Nn \l_@@_cos_fp { cos ( \l_@@_angle_fp * deg ) }
+          \@@_rotate:N #1
+        \group_end:
+    }
+  }
+%    \end{macrocode}
+%   The edges of the box are then recorded: the left edge will
+%   always be at zero. Rotation of the four edges then takes place: this is
+%   most efficiently done on a quadrant by quadrant basis.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_rotate:N #1
+  {
+    \dim_set:Nn \l_@@_top_dim    {  \box_ht:N #1 }
+    \dim_set:Nn \l_@@_bottom_dim { -\box_dp:N #1 }
+    \dim_set:Nn \l_@@_right_dim  {  \box_wd:N #1 }
+    \dim_zero:N \l_@@_left_dim
+%    \end{macrocode}
+%   The next step is to work out the $x$ and $y$ coordinates of vertices of
+%   the rotated box in relation to its original coordinates. The box can be
+%   visualized with vertices $B$, $C$, $D$ and $E$ is illustrated
+%   (Figure~\ref{fig:rotation}). The vertex $O$ is the reference point on the
+%   baseline, and in this implementation is also the centre of rotation.
+%   \begin{figure}
+%     \centering
+%     \setlength{\unitlength}{3pt}^^A
+%     \begin{picture}(34,36)(12,44)
+%       \thicklines
+%       \put(20,52){\dashbox{1}(20,21){}}
+%       \put(20,80){\line(0,-1){36}}
+%       \put(12,58){\line(1, 0){34}}
+%       \put(41,59){A}
+%       \put(40,74){B}
+%       \put(21,74){C}
+%       \put(21,49){D}
+%       \put(40,49){E}
+%       \put(21,59){O}
+%     \end{picture}
+%     \caption{Co-ordinates of a box prior to rotation.}
+%     \label{fig:rotation}
+%   \end{figure}
+%   The formulae are, for a point $P$ and angle $\alpha$:
+%   \[
+%     \begin{array}{l}
+%       P'_x = P_x - O_x \\
+%       P'_y = P_y - O_y \\
+%       P''_x =  ( P'_x \cos(\alpha)) - ( P'_y \sin(\alpha) ) \\
+%       P''_y =  ( P'_x \sin(\alpha)) + ( P'_y \cos(\alpha) ) \\
+%       P'''_x = P''_x + O_x + L_x \\
+%       P'''_y = P''_y + O_y
+%    \end{array}
+%   \]
+%   The \enquote{extra} horizontal translation $L_x$ at the end is calculated
+%   so that the leftmost point of the resulting box has $x$-coordinate $0$.
+%   This is desirable as \TeX{} boxes must have the reference point at
+%   the left edge of the box. (As $O$ is always $(0,0)$, this part of the
+%   calculation is omitted here.)
+%    \begin{macrocode}
+    \fp_compare:nNnTF \l_@@_sin_fp > \c_zero_fp
+      {
+        \fp_compare:nNnTF \l_@@_cos_fp > \c_zero_fp
+          { \@@_rotate_quadrant_one: }
+          { \@@_rotate_quadrant_two: }
+      }
+      {
+        \fp_compare:nNnTF \l_@@_cos_fp < \c_zero_fp
+          { \@@_rotate_quadrant_three: }
+          { \@@_rotate_quadrant_four: }
+      }
+%    \end{macrocode}
+%   The position of the box edges are now known, but the box at this
+%   stage be misplaced relative to the current \TeX{} reference point. So the
+%   content of the box is moved such that the reference point of the
+%   rotated box will be in the same place as the original.
+%    \begin{macrocode}
+    \hbox_set:Nn \l_@@_internal_box { \box_use:N #1 }
+    \hbox_set:Nn \l_@@_internal_box
+      {
+        \tex_kern:D -\l_@@_left_new_dim
+        \hbox:n
+          {
+            \__driver_box_rotate_begin:
+            \box_use:N \l_@@_internal_box
+            \__driver_box_rotate_end:
+          }
+      }
+%    \end{macrocode}
+%   Tidy up the size of the box so that the material is actually inside
+%   the bounding box. The result can then be used to reset the original
+%   box.
+%    \begin{macrocode}
+    \box_set_ht:Nn \l_@@_internal_box {  \l_@@_top_new_dim }
+    \box_set_dp:Nn \l_@@_internal_box { -\l_@@_bottom_new_dim }
+    \box_set_wd:Nn \l_@@_internal_box
+      { \l_@@_right_new_dim - \l_@@_left_new_dim }
+    \box_use:N \l_@@_internal_box
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%   These functions take a general point $(|#1|, |#2|)$ and rotate its
+%   location about the origin, using the previously-set sine and cosine
+%   values. Each function gives only one component of the location of the
+%   updated point. This is because for rotation of a box each step needs
+%   only one value, and so performance is gained by avoiding working
+%   out both $x'$ and $y'$ at the same time. Contrast this with
+%   the equivalent function in the \pkg{l3coffins} module, where both parts
+%   are needed.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_rotate_x:nnN #1#2#3
+  {
+    \dim_set:Nn #3
+      {
+        \fp_to_dim:n
+          {
+                \l_@@_cos_fp * \dim_to_fp:n {#1}
+            - ( \l_@@_sin_fp * \dim_to_fp:n {#2} )
+          }
+      }
+  }
+\cs_new_protected:Npn \@@_rotate_y:nnN #1#2#3
+  {
+    \dim_set:Nn #3
+      {
+        \fp_to_dim:n
+          {
+              \l_@@_sin_fp * \dim_to_fp:n {#1}
+            + \l_@@_cos_fp * \dim_to_fp:n {#2}
+          }
+      }
+  }
+%    \end{macrocode}
+%   Rotation of the edges is done using a different formula for each
+%   quadrant. In every case, the top and bottom edges only need the
+%   resulting $y$-values, whereas the left and right edges need the
+%   $x$-values. Each case is a question of picking out which corner
+%   ends up at with the maximum top, bottom, left and right value. Doing
+%   this by hand means a lot less calculating and avoids lots of
+%   comparisons.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_rotate_quadrant_one:
+  {
+    \@@_rotate_y:nnN \l_@@_right_dim \l_@@_top_dim
+      \l_@@_top_new_dim
+    \@@_rotate_y:nnN \l_@@_left_dim  \l_@@_bottom_dim
+      \l_@@_bottom_new_dim
+    \@@_rotate_x:nnN \l_@@_left_dim  \l_@@_top_dim
+      \l_@@_left_new_dim
+    \@@_rotate_x:nnN \l_@@_right_dim \l_@@_bottom_dim
+      \l_@@_right_new_dim
+  }
+\cs_new_protected:Npn \@@_rotate_quadrant_two:
+  {
+    \@@_rotate_y:nnN \l_@@_right_dim \l_@@_bottom_dim
+      \l_@@_top_new_dim
+    \@@_rotate_y:nnN \l_@@_left_dim  \l_@@_top_dim
+      \l_@@_bottom_new_dim
+    \@@_rotate_x:nnN \l_@@_right_dim  \l_@@_top_dim
+      \l_@@_left_new_dim
+    \@@_rotate_x:nnN \l_@@_left_dim   \l_@@_bottom_dim
+      \l_@@_right_new_dim
+  }
+\cs_new_protected:Npn \@@_rotate_quadrant_three:
+  {
+    \@@_rotate_y:nnN \l_@@_left_dim  \l_@@_bottom_dim
+      \l_@@_top_new_dim
+    \@@_rotate_y:nnN \l_@@_right_dim \l_@@_top_dim
+      \l_@@_bottom_new_dim
+    \@@_rotate_x:nnN \l_@@_right_dim \l_@@_bottom_dim
+      \l_@@_left_new_dim
+    \@@_rotate_x:nnN \l_@@_left_dim   \l_@@_top_dim
+      \l_@@_right_new_dim
+  }
+\cs_new_protected:Npn \@@_rotate_quadrant_four:
+  {
+    \@@_rotate_y:nnN \l_@@_left_dim  \l_@@_top_dim
+      \l_@@_top_new_dim
+    \@@_rotate_y:nnN \l_@@_right_dim \l_@@_bottom_dim
+      \l_@@_bottom_new_dim
+    \@@_rotate_x:nnN \l_@@_left_dim  \l_@@_bottom_dim
+      \l_@@_left_new_dim
+    \@@_rotate_x:nnN \l_@@_right_dim \l_@@_top_dim
+      \l_@@_right_new_dim
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{variable}{\l_@@_scale_x_fp, \l_@@_scale_y_fp}
+%   Scaling is potentially-different in the two axes.
+%    \begin{macrocode}
+\fp_new:N \l_@@_scale_x_fp
+\fp_new:N \l_@@_scale_y_fp
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}{\box_resize:Nnn, \box_resize:cnn}
+% \begin{macro}[aux]{\@@_resize:Nnn}
+%   Resizing a box starts by working out the various dimensions of the
+%   existing box.
+%    \begin{macrocode}
+\cs_new_protected:Npn \box_resize:Nnn #1#2#3
+  {
+    \hbox_set:Nn #1
+      {
+        \group_begin:
+          \dim_set:Nn \l_@@_top_dim    {  \box_ht:N #1 }
+          \dim_set:Nn \l_@@_bottom_dim { -\box_dp:N #1 }
+          \dim_set:Nn \l_@@_right_dim  {  \box_wd:N #1 }
+          \dim_zero:N \l_@@_left_dim
+%    \end{macrocode}
+%   The $x$-scaling and resulting box size is easy enough to work
+%   out: the dimension is that given as |#2|, and the scale is simply the
+%   new width divided by the old one.
+%    \begin{macrocode}
+          \fp_set:Nn \l_@@_scale_x_fp
+            { \dim_to_fp:n {#2} / ( \dim_to_fp:n \l_@@_right_dim ) }
+%    \end{macrocode}
+%   The $y$-scaling needs both the height and the depth of the current box.
+%    \begin{macrocode}
+          \fp_set:Nn \l_@@_scale_y_fp
+            {
+              \dim_to_fp:n {#3} /
+                ( \dim_to_fp:n { \l_@@_top_dim - \l_@@_bottom_dim } )
+            }
+%    \end{macrocode}
+%   Hand off to the auxiliary which does the work.
+%    \begin{macrocode}
+          \@@_resize:Nnn #1 {#2} {#3}
+        \group_end:
+      }
+  }
+\cs_generate_variant:Nn \box_resize:Nnn { c }
+%    \end{macrocode}
+%   With at least one real scaling to do, the next phase is to find the new
+%   edge co-ordinates. In the $x$~direction this is relatively easy: just
+%   scale the right edge. This is done using the absolute value of the
+%   scale so that the new edge is in the correct place. In the $y$~direction,
+%   both dimensions have to be scaled, and this again needs the absolute
+%   scale value. Once that is all done, the common resize/rescale code can
+%   be employed.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_resize:Nnn #1#2#3
+  {
+    \dim_compare:nNnTF {#2} > \c_zero_dim
+      { \dim_set:Nn \l_@@_right_new_dim {#2} }
+      { \dim_set:Nn \l_@@_right_new_dim { \c_zero_dim - ( #2 ) } }
+    \dim_compare:nNnTF {#3} > \c_zero_dim
+      {
+        \dim_set:Nn \l_@@_top_new_dim
+          { \fp_use:N \l_@@_scale_y_fp \l_@@_top_dim }
+        \dim_set:Nn \l_@@_bottom_new_dim
+          { \fp_use:N \l_@@_scale_y_fp \l_@@_bottom_dim }
+      }
+      {
+        \dim_set:Nn \l_@@_top_new_dim
+          { - \fp_use:N \l_@@_scale_y_fp \l_@@_top_dim }
+        \dim_set:Nn \l_@@_bottom_new_dim
+          { - \fp_use:N \l_@@_scale_y_fp \l_@@_bottom_dim }
+      }
+    \@@_resize_common:N #1
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\box_resize_to_ht_plus_dp:Nn, \box_resize_to_ht_plus_dp:cn}
+% \begin{macro}{\box_resize_to_wd:Nn, \box_resize_to_wd:cn}
+%   Scaling to a total height or to a width is a simplified version of the main
+%   resizing operation, with the scale simply copied between the two parts. The
+%   internal auxiliary is called using the scaling value twice, as the sign for
+%   both parts is needed (as this allows the same internal code to be used as
+%   for the general case).
+%    \begin{macrocode}
+\cs_new_protected:Npn \box_resize_to_ht_plus_dp:Nn #1#2
+  {
+    \hbox_set:Nn #1
+      {
+        \group_begin:
+          \dim_set:Nn \l_@@_top_dim    {  \box_ht:N #1 }
+          \dim_set:Nn \l_@@_bottom_dim { -\box_dp:N #1 }
+          \dim_set:Nn \l_@@_right_dim  {  \box_wd:N #1 }
+          \dim_zero:N \l_@@_left_dim
+          \fp_set:Nn \l_@@_scale_y_fp
+            {
+              \dim_to_fp:n {#2} /
+                ( \dim_to_fp:n { \l_@@_top_dim - \l_@@_bottom_dim } )
+            }
+          \fp_set_eq:NN \l_@@_scale_x_fp \l_@@_scale_y_fp
+          \@@_resize:Nnn #1 {#2} {#2}
+        \group_end:
+      }
+  }
+\cs_generate_variant:Nn \box_resize_to_ht_plus_dp:Nn { c }
+\cs_new_protected:Npn \box_resize_to_wd:Nn #1#2
+  {
+    \hbox_set:Nn #1
+      {
+        \group_begin:
+          \dim_set:Nn \l_@@_top_dim    {  \box_ht:N #1 }
+          \dim_set:Nn \l_@@_bottom_dim { -\box_dp:N #1 }
+          \dim_set:Nn \l_@@_right_dim  {  \box_wd:N #1 }
+          \dim_zero:N \l_@@_left_dim
+          \fp_set:Nn \l_@@_scale_x_fp
+            { \dim_to_fp:n {#2} / ( \dim_to_fp:n \l_@@_right_dim ) }
+          \fp_set_eq:NN \l_@@_scale_y_fp \l_@@_scale_x_fp
+          \@@_resize:Nnn #1 {#2} {#2}
+        \group_end:
+      }
+  }
+\cs_generate_variant:Nn \box_resize_to_wd:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\box_scale:Nnn, \box_scale:cnn}
+% \begin{macro}[aux]{\@@_scale:Nnn}
+%   When scaling a box, setting the scaling itself is easy enough. The
+%   new dimensions are also relatively easy to find, allowing only for
+%   the need to keep them positive in all cases. Once that is done then
+%   after a check for the trivial scaling a hand-off can be made to the
+%   common code. The dimension scaling operations are carried out using
+%   the \TeX{} mechanism as it avoids needing to use \texttt{fp}
+%   operations.
+%    \begin{macrocode}
+\cs_new_protected:Npn \box_scale:Nnn #1#2#3
+  {
+    \hbox_set:Nn #1
+      {
+        \group_begin:
+          \fp_set:Nn \l_@@_scale_x_fp {#2}
+          \fp_set:Nn \l_@@_scale_y_fp {#3}
+          \dim_set:Nn \l_@@_top_dim    {  \box_ht:N #1 }
+          \dim_set:Nn \l_@@_bottom_dim { -\box_dp:N #1 }
+          \dim_set:Nn \l_@@_right_dim  {  \box_wd:N #1 }
+          \dim_zero:N \l_@@_left_dim
+          \@@_scale:Nnn #1 {#2} {#3}
+        \group_end:
+      }
+  }
+\cs_generate_variant:Nn \box_scale:Nnn { c }
+\cs_new_protected:Npn \@@_scale:Nnn #1#2#3
+  {
+    \fp_compare:nNnTF \l_@@_scale_y_fp > \c_zero_fp
+      {
+        \dim_set:Nn \l_@@_top_new_dim    { #3 \l_@@_top_dim }
+        \dim_set:Nn \l_@@_bottom_new_dim { #3 \l_@@_bottom_dim }
+      }
+      {
+        \dim_set:Nn  \l_@@_top_new_dim    { -#3 \l_@@_bottom_dim }
+        \dim_set:Nn  \l_@@_bottom_new_dim { -#3 \l_@@_top_dim }
+      }
+    \fp_compare:nNnTF \l_@@_scale_x_fp > \c_zero_fp
+      { \l_@@_right_new_dim #2 \l_@@_right_dim }
+      { \l_@@_right_new_dim -#2 \l_@@_right_dim }
+    \@@_resize_common:N #1
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[aux]{\@@_resize_common:N}
+%   The main resize function places in input into a box which will start
+%   of with zero width, and includes the handles for engine rescaling.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_resize_common:N #1
+  {
+    \hbox_set:Nn \l_@@_internal_box
+      {
+        \__driver_box_scale_begin:
+        \hbox_overlap_right:n { \box_use:N #1 }
+        \__driver_box_scale_end:
+      }
+%    \end{macrocode}
+%   The new height and depth can be applied directly.
+%    \begin{macrocode}
+    \box_set_ht:Nn \l_@@_internal_box { \l_@@_top_new_dim }
+    \box_set_dp:Nn \l_@@_internal_box { \l_@@_bottom_new_dim }
+%    \end{macrocode}
+%   Things are not quite as obvious for the width, as the reference point
+%   needs to remain unchanged. For positive scaling factors resizing the
+%   box is all that is needed. However, for case of a negative scaling
+%   the material must be shifted such that the reference point ends up in
+%   the right place.
+%    \begin{macrocode}
+    \fp_compare:nNnTF \l_@@_scale_x_fp < \c_zero_fp
+      {
+        \hbox_to_wd:nn { \l_@@_right_new_dim }
+          {
+            \tex_kern:D \l_@@_right_new_dim
+            \box_use:N \l_@@_internal_box
+            \tex_hss:D
+          }
+      }
+      {
+        \box_set_wd:Nn \l_@@_internal_box { \l_@@_right_new_dim }
+        \box_use:N \l_@@_internal_box
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Viewing part of a box}
+%
+% \begin{macro}{\box_clip:N, \box_clip:c}
+%   A wrapper around the driver-dependent code.
+%    \begin{macrocode}
+\cs_new_protected:Npn \box_clip:N #1
+  { \hbox_set:Nn #1 { \__driver_box_use_clip:N #1 } }
+\cs_generate_variant:Nn \box_clip:N { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\box_trim:Nnnnn, \box_trim:cnnnn}
+%   Trimming from the left- and right-hand edges of the box is easy. The total
+%   width is set to remove from the right, and a skip will shift the material
+%   to remove from the left.
+%    \begin{macrocode}
+\cs_new_protected:Npn \box_trim:Nnnnn #1#2#3#4#5
+  {
+    \box_set_wd:Nn #1 { \box_wd:N #1 - (#4) - (#2) }
+    \hbox_set:Nn #1
+      {
+        \skip_horizontal:n { - \dim_eval:n {#2} }
+        \box_use:N #1
+      }
+%    \end{macrocode}
+%   For the height and depth, there is a need to watch the baseline is
+%   respected. Material always has to stay on the correct side, so trimming
+%   has to check that there is enough material to trim.
+%    \begin{macrocode}
+    \dim_compare:nNnTF { \box_dp:N #1 } > {#3}
+      { \box_set_dp:Nn #1 { \box_dp:N #1 - (#3) } }
+      {
+        \hbox_set:Nn #1
+          { \box_move_down:nn { #3 - \box_dp:N #1 } { \box_use:N #1 } }
+        \box_set_dp:Nn #1 \c_zero_dim
+      }
+    \dim_compare:nNnTF { \box_ht:N #1 } > {#5}
+      { \box_set_ht:Nn #1 { \box_ht:N #1 - (#5) } }
+      {
+        \hbox_set:Nn #1
+          { \box_move_up:nn { #5 - \box_ht:N #1 } { \box_use:N #1 } }
+        \box_set_ht:Nn #1 \c_zero_dim
+      }
+  }
+\cs_generate_variant:Nn \box_trim:Nnnnn { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\box_viewport:Nnnnn, \box_viewport:cnnnn}
+%   The same general logic as for clipping, but with absolute dimensions.
+%   Thus again width is easy and height is harder.
+%    \begin{macrocode}
+\cs_new_protected:Npn \box_viewport:Nnnnn #1#2#3#4#5
+  {
+    \box_set_wd:Nn #1 { (#4) - (#2) }
+    \hbox_set:Nn #1
+      {
+        \skip_horizontal:n { - \dim_eval:n {#2} }
+        \box_use:N #1
+      }
+    \dim_compare:nNnTF {#3} > \c_zero_dim
+      {
+        \hbox_set:Nn #1 { \box_move_down:nn {#3} { \box_use:N #1 } }
+        \box_set_dp:Nn #1 \c_zero_dim
+      }
+      { \box_set_dp:Nn #1 { - \dim_eval:n {#3} } }
+    \dim_compare:nNnTF {#5} > \c_zero_dim
+      { \box_set_ht:Nn #1 {#5} }
+      {
+        \hbox_set:Nn #1
+          { \box_move_up:nn { -\dim_eval:n {#5} } { \box_use:N #1 } }
+        \box_set_ht:Nn #1 \c_zero_dim
+      }
+  }
+\cs_generate_variant:Nn \box_viewport:Nnnnn { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Additions to \pkg{l3clist}}
+%
+%    \begin{macrocode}
+%<@@=clist>
+%    \end{macrocode}
+%
+% \begin{macro}{\clist_item:Nn, \clist_item:cn}
+% \begin{macro}[aux]{\@@_item:nnNn}
+% \begin{macro}[aux]{\@@_item_N_loop:nw}
+%   To avoid needing to test the end of the list at each step,
+%   we first compute the \meta{length} of the list. If the item number
+%   is~$0$, less than $-\meta{length}$, or more than $\meta{length}$,
+%   the result is empty. If it is negative, but not less than $-\meta{length}$,
+%   add $\meta{length}+1$ to the item number before performing the loop.
+%   The loop itself is very simple, return the item if the counter
+%   reached~$1$, otherwise, decrease the counter and repeat.
+%    \begin{macrocode}
+\cs_new:Npn \clist_item:Nn #1#2
+  {
+    \exp_args:Nfo \@@_item:nnNn
+      { \clist_count:N #1 }
+      #1
+      \@@_item_N_loop:nw
+      {#2}
+  }
+\cs_new:Npn \@@_item:nnNn #1#2#3#4
+  {
+    \int_compare:nNnTF {#4} < \c_zero
+      {
+        \int_compare:nNnTF {#4} < { - #1 }
+          { \use_none_delimit_by_q_stop:w }
+          { \exp_args:Nf #3 { \int_eval:n { #4 + \c_one + #1 } } }
+      }
+      {
+        \int_compare:nNnTF {#4} > {#1}
+          { \use_none_delimit_by_q_stop:w }
+          { #3 {#4} }
+      }
+    { } , #2 , \q_stop
+  }
+\cs_new:Npn \@@_item_N_loop:nw #1 #2,
+  {
+    \int_compare:nNnTF {#1} = \c_zero
+      { \use_i_delimit_by_q_stop:nw { \exp_not:n {#2} } }
+      { \exp_args:Nf \@@_item_N_loop:nw { \int_eval:n { #1 - 1 } } }
+  }
+\cs_generate_variant:Nn \clist_item:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\clist_item:nn}
+% \begin{macro}[aux]{
+%     \@@_item_n:nw,
+%     \@@_item_n_loop:nw,
+%     \@@_item_n_end:n,
+%     \@@_item_n_strip:w}
+%   This starts in the same way as \cs{clist_item:Nn} by counting the items
+%   of the comma list. The final item should be space-trimmed before being
+%   brace-stripped, hence we insert a couple of odd-looking
+%   \cs{prg_do_nothing:} to avoid losing braces. Blank items are ignored.
+%    \begin{macrocode}
+\cs_new:Npn \clist_item:nn #1#2
+  {
+    \exp_args:Nf \@@_item:nnNn
+      { \clist_count:n {#1} }
+      {#1}
+      \@@_item_n:nw
+      {#2}
+  }
+\cs_new:Npn \@@_item_n:nw #1
+  { \@@_item_n_loop:nw {#1} \prg_do_nothing: }
+\cs_new:Npn \@@_item_n_loop:nw #1 #2,
+  {
+    \exp_args:No \tl_if_blank:nTF {#2}
+      { \@@_item_n_loop:nw {#1} \prg_do_nothing: }
+      {
+        \int_compare:nNnTF {#1} = \c_zero
+          { \exp_args:No \@@_item_n_end:n {#2} }
+          {
+            \exp_args:Nf \@@_item_n_loop:nw
+              { \int_eval:n { #1 - 1 } }
+              \prg_do_nothing:
+          }
+      }
+  }
+\cs_new:Npn \@@_item_n_end:n #1 #2 \q_stop
+  {
+    \__tl_trim_spaces:nn { \q_mark #1 }
+      { \exp_last_unbraced:No \@@_item_n_strip:w } ,
+  }
+\cs_new:Npn \@@_item_n_strip:w #1 , { \exp_not:n {#1} }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}
+%   {
+%     \clist_set_from_seq:NN, \clist_set_from_seq:cN,
+%     \clist_set_from_seq:Nc, \clist_set_from_seq:cc
+%   }
+% \UnitTested
+% \begin{macro}
+%   {
+%     \clist_gset_from_seq:NN, \clist_gset_from_seq:cN,
+%     \clist_gset_from_seq:Nc, \clist_gset_from_seq:cc
+%   }
+% \UnitTested
+% \begin{macro}[aux]{\@@_set_from_seq:NNNN}
+% \begin{macro}[aux]{\@@_wrap_item:n}
+% \begin{macro}[aux]{\@@_set_from_seq:w}
+%   Setting a comma list from a comma-separated list is done using a simple
+%   mapping. We wrap most items with \cs{exp_not:n}, and a comma. Items which
+%   contain a comma or a space are surrounded by an extra set of braces. The
+%   first comma must be removed, except in the case of an empty comma-list.
+%    \begin{macrocode}
+\cs_new_protected:Npn \clist_set_from_seq:NN
+  { \@@_set_from_seq:NNNN \clist_clear:N  \tl_set:Nx  }
+\cs_new_protected:Npn \clist_gset_from_seq:NN
+  { \@@_set_from_seq:NNNN \clist_gclear:N \tl_gset:Nx }
+\cs_new_protected:Npn \@@_set_from_seq:NNNN #1#2#3#4
+  {
+    \seq_if_empty:NTF #4
+      { #1 #3 }
+      {
+        #2 #3
+          {
+            \exp_last_unbraced:Nf \use_none:n
+              { \seq_map_function:NN #4 \@@_wrap_item:n }
+          }
+      }
+  }
+\cs_new:Npn \@@_wrap_item:n #1
+  {
+    ,
+    \tl_if_empty:oTF { \@@_set_from_seq:w #1 ~ , #1 ~ }
+      { \exp_not:n   {#1}   }
+      { \exp_not:n { {#1} } }
+  }
+\cs_new:Npn \@@_set_from_seq:w #1 , #2 ~ { }
+\cs_generate_variant:Nn \clist_set_from_seq:NN  {     Nc }
+\cs_generate_variant:Nn \clist_set_from_seq:NN  { c , cc }
+\cs_generate_variant:Nn \clist_gset_from_seq:NN {     Nc }
+\cs_generate_variant:Nn \clist_gset_from_seq:NN { c , cc }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}
+%   {
+%     \clist_const:Nn, \clist_const:cn,
+%     \clist_const:Nx, \clist_const:cx
+%   }
+%   Creating and initializing a constant comma list is done in a way
+%   similar to \cs{clist_set:Nn} and \cs{clist_gset:Nn}, being careful
+%   to strip spaces.
+%    \begin{macrocode}
+\cs_new_protected:Npn \clist_const:Nn #1#2
+  { \tl_const:Nx #1 { \@@_trim_spaces:n {#2} } }
+\cs_generate_variant:Nn \clist_const:Nn { c , Nx , cx }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP, pTF]{\clist_if_empty:n}
+% \begin{macro}[aux, EXP]{\@@_if_empty_n:w}
+% \begin{macro}[aux, EXP]{\@@_if_empty_n:wNw}
+%   As usual, we insert a token (here |?|) before grabbing
+%   any argument: this avoids losing braces. The argument
+%   of \cs{tl_if_empty:oTF} is empty if |#1| is |?| followed
+%   by blank spaces (besides, this particular variant of
+%   the emptyness test is optimized). If the item of the
+%   comma list is blank, grab the next one. As soon as one
+%   item is non-blank, exit: the second auxiliary will grab
+%   \cs{prg_return_false:} as |#2|, unless every item in
+%   the comma list was blank and the loop actually got broken
+%   by the trailing |\q_mark \prg_return_false:| item.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \clist_if_empty:n #1 { p , T , F , TF }
+  {
+    \@@_if_empty_n:w ? #1
+    , \q_mark \prg_return_false:
+    , \q_mark \prg_return_true:
+    \q_stop
+  }
+\cs_new:Npn \@@_if_empty_n:w #1 ,
+  {
+    \tl_if_empty:oTF { \use_none:nn #1 ? }
+      { \@@_if_empty_n:w ? }
+      { \@@_if_empty_n:wNw }
+  }
+\cs_new:Npn \@@_if_empty_n:wNw #1 \q_mark #2#3 \q_stop {#2}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\clist_use:Nnnn}
+% \begin{macro}[EXP, aux]
+%   {\@@_use:wwn, \@@_use_ii:nwwwwnwn, \@@_use_iii:nwwn}
+%   First check that the variable exists.  Then count the items in the
+%   comma list.  If it has none, output nothing.  If it has one item,
+%   output that item, brace stripped (note that space-trimming has
+%   already been done when the comma list was assigned).  If it has two,
+%   place the \meta{separator~between~two} in the middle.
+%
+%   Otherwise, \cs{@@_use_ii:nwwwwnwn} takes the following arguments; 1:
+%   a \meta{separator}, 2, 3, 4: three items from the comma list (or
+%   quarks), 5: the rest of the comma list, 6: a \meta{continuation}
+%   function (\texttt{use_ii} or \texttt{use_iii} with its
+%   \meta{separator} argument), 7: junk, and 8: the temporary result,
+%   which is built in a brace group following \cs{q_stop}.  The
+%   \meta{separator} and the first of the three items are placed in the
+%   result, then we use the \meta{continuation}, placing the remaining
+%   two items after it.  When we begin this loop, the three items really
+%   belong to the comma list, the first \cs{q_mark} is taken as a
+%   delimiter to the \texttt{use_ii} function, and the continuation is
+%   \texttt{use_ii} itself.  When we reach the last two items of the
+%   original token list, \cs{q_mark} is taken as a third item, and now
+%   the seconf \cs{q_mark} serves as a delimiter to \texttt{use_ii},
+%   switching to the other \meta{continuation}, \texttt{use_iii}, which
+%   uses the \meta{separator between final two}.
+%    \begin{macrocode}
+\cs_new:Npn \clist_use:Nnnn #1#2#3#4
+  {
+    \clist_if_exist:NTF #1
+      {
+        \int_case:nnn { \clist_count:N #1 }
+          {
+            { 0 } { }
+            { 1 } { \exp_after:wN \@@_use:wwn #1 , , { } }
+            { 2 } { \exp_after:wN \@@_use:wwn #1 , {#2} }
+          }
+          {
+            \exp_after:wN \@@_use_ii:nwwwwnwn
+            \exp_after:wN { \exp_after:wN } #1 ,
+            \q_mark , { \@@_use_ii:nwwwwnwn {#3} }
+            \q_mark , { \@@_use_iii:nwwn {#4} }
+            \q_stop { }
+          }
+      }
+      { \__msg_kernel_expandable_error:nnn { kernel } { bad-variable } {#1} }
+  }
+\cs_new:Npn \@@_use:wwn #1 , #2 , #3 { \exp_not:n { #1 #3 #2 } }
+\cs_new:Npn \@@_use_ii:nwwwwnwn
+    #1#2 , #3 , #4 , #5 \q_mark , #6#7 \q_stop #8
+  { #6 {#3} , {#4} , #5 \q_mark , {#6} #7 \q_stop { #8 #1 #2 } }
+\cs_new:Npn \@@_use_iii:nwwn #1#2 , #3 \q_stop #4
+  { \exp_not:n { #4 #1 #2 } }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Additions to \pkg{l3coffins}}
+%
+%    \begin{macrocode}
+%<@@=coffin>
+%    \end{macrocode}
+%
+% \subsection{Rotating coffins}
+%
+% \begin{variable}{\l_@@_sin_fp}
+% \begin{variable}{\l_@@_cos_fp}
+%   Used for rotations to get the sine and cosine values.
+%    \begin{macrocode}
+\fp_new:N \l_@@_sin_fp
+\fp_new:N \l_@@_cos_fp
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_bounding_prop}
+%   A property list for the bounding box of a coffin. This is only needed
+%   during the rotation, so there is just the one.
+%    \begin{macrocode}
+\prop_new:N \l_@@_bounding_prop
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_bounding_shift_dim}
+%   The shift of the bounding box of a coffin from the real content.
+%    \begin{macrocode}
+\dim_new:N \l_@@_bounding_shift_dim
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_left_corner_dim}
+% \begin{variable}{\l_@@_right_corner_dim}
+% \begin{variable}{\l_@@_bottom_corner_dim}
+% \begin{variable}{\l_@@_top_corner_dim}
+%   These are used to hold maxima for the various corner values: these
+%   thus define the minimum size of the bounding box after rotation.
+%    \begin{macrocode}
+\dim_new:N \l_@@_left_corner_dim
+\dim_new:N \l_@@_right_corner_dim
+\dim_new:N \l_@@_bottom_corner_dim
+\dim_new:N \l_@@_top_corner_dim
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+%
+% \begin{macro}{\coffin_rotate:Nn, \coffin_rotate:cn}
+%   Rotating a coffin requires several steps which can be conveniently
+%   run together. The first step is to convert the angle given in degrees
+%   to one in radians. This is then used to set \cs{l_@@_sin_fp} and
+%   \cs{l_@@_cos_fp}, which are carried through unchanged for the rest
+%   of the procedure.
+%    \begin{macrocode}
+\cs_new_protected:Npn \coffin_rotate:Nn #1#2
+  {
+    \fp_set:Nn \l_@@_sin_fp { sin ( ( #2 ) * deg ) }
+    \fp_set:Nn \l_@@_cos_fp { cos ( ( #2 ) * deg ) }
+%    \end{macrocode}
+%   The corners and poles of the coffin can now be rotated around the
+%    origin. This is best achieved using mapping functions.
+%    \begin{macrocode}
+    \prop_map_inline:cn { l_@@_corners_ \__int_value:w #1 _prop }
+      { \@@_rotate_corner:Nnnn #1 {##1} ##2 }
+    \prop_map_inline:cn { l_@@_poles_ \__int_value:w #1 _prop }
+      { \@@_rotate_pole:Nnnnnn #1 {##1} ##2 }
+%    \end{macrocode}
+%   The bounding box of the coffin needs to be rotated, and to do this
+%   the corners have to be found first. They are then rotated in the same
+%   way as the corners of the coffin material itself.
+%    \begin{macrocode}
+    \@@_set_bounding:N #1
+    \prop_map_inline:Nn \l_@@_bounding_prop
+      { \@@_rotate_bounding:nnn {##1} ##2 }
+%    \end{macrocode}
+%   At this stage, there needs to be a calculation to find where the
+%   corners of the content and the box itself will end up.
+%    \begin{macrocode}
+    \@@_find_corner_maxima:N #1
+    \@@_find_bounding_shift:
+    \box_rotate:Nn #1 {#2}
+%    \end{macrocode}
+%   The correction of the box position itself takes place here. The idea
+%   is that the bounding box for a coffin is tight up to the content, and
+%   has the reference point at the bottom-left. The $x$-direction is
+%   handled by moving the content by the difference in the positions of
+%   the bounding box and the content left edge. The $y$-direction is
+%   dealt with by moving the box down by any depth it has acquired.
+%    \begin{macrocode}
+    \hbox_set:Nn #1
+      {
+        \tex_kern:D \l_@@_bounding_shift_dim
+        \tex_kern:D -\l_@@_left_corner_dim
+        \box_move_down:nn { \l_@@_bottom_corner_dim }
+          { \box_use:N #1 }
+      }
+%    \end{macrocode}
+%   If there have been any previous rotations then the size of the
+%   bounding box will be bigger than the contents. This can be corrected
+%   easily by setting the size of the box to the height and width of the
+%   content.
+%    \begin{macrocode}
+    \box_set_ht:Nn #1
+      { \l_@@_top_corner_dim - \l_@@_bottom_corner_dim }
+    \box_set_dp:Nn #1 { 0 pt }
+    \box_set_wd:Nn #1
+      { \l_@@_right_corner_dim - \l_@@_left_corner_dim }
+%    \end{macrocode}
+%   The final task is to move the poles and corners such that they are
+%   back in alignment with the box reference point.
+%    \begin{macrocode}
+    \prop_map_inline:cn { l_@@_corners_ \__int_value:w #1 _prop }
+      { \@@_shift_corner:Nnnn #1 {##1} ##2 }
+    \prop_map_inline:cn { l_@@_poles_ \__int_value:w #1 _prop }
+      { \@@_shift_pole:Nnnnnn #1 {##1} ##2 }
+  }
+\cs_generate_variant:Nn \coffin_rotate:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_set_bounding:N}
+%   The bounding box corners for a coffin are easy enough to find: this
+%   is the same code as for the corners of the material itself, but
+%   using a dedicated property list.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_set_bounding:N #1
+  {
+    \prop_put:Nnx \l_@@_bounding_prop { tl }
+      { { 0 pt } { \dim_use:N \box_ht:N #1 } }
+    \prop_put:Nnx \l_@@_bounding_prop { tr }
+      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \box_ht:N #1 } }
+    \dim_set:Nn \l_@@_internal_dim { - \box_dp:N #1 }
+    \prop_put:Nnx \l_@@_bounding_prop { bl }
+      { { 0 pt } { \dim_use:N \l_@@_internal_dim } }
+    \prop_put:Nnx \l_@@_bounding_prop { br }
+      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \l_@@_internal_dim } }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_rotate_bounding:nnn}
+% \begin{macro}{\@@_rotate_corner:Nnnn}
+%   Rotating the position of the corner of the coffin is just a case
+%   of treating this as a vector from the reference point. The same
+%   treatment is used for the corners of the material itself and the
+%   bounding box.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_rotate_bounding:nnn #1#2#3
+  {
+    \@@_rotate_vector:nnNN {#2} {#3} \l_@@_x_dim \l_@@_y_dim
+    \prop_put:Nnx \l_@@_bounding_prop {#1}
+      { { \dim_use:N \l_@@_x_dim } { \dim_use:N \l_@@_y_dim } }
+  }
+\cs_new_protected:Npn \@@_rotate_corner:Nnnn #1#2#3#4
+  {
+    \@@_rotate_vector:nnNN {#3} {#4} \l_@@_x_dim \l_@@_y_dim
+    \prop_put:cnx { l_@@_corners_ \__int_value:w #1 _prop } {#2}
+      { { \dim_use:N \l_@@_x_dim } { \dim_use:N \l_@@_y_dim } }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@@_rotate_pole:Nnnnnn}
+%   Rotating a single pole simply means shifting the co-ordinate of
+%   the pole and its direction. The rotation here is about the bottom-left
+%   corner of the coffin.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_rotate_pole:Nnnnnn #1#2#3#4#5#6
+  {
+    \@@_rotate_vector:nnNN {#3} {#4} \l_@@_x_dim \l_@@_y_dim
+    \@@_rotate_vector:nnNN {#5} {#6}
+      \l_@@_x_prime_dim \l_@@_y_prime_dim
+    \@@_set_pole:Nnx #1 {#2}
+      {
+        { \dim_use:N \l_@@_x_dim } { \dim_use:N \l_@@_y_dim }
+        { \dim_use:N \l_@@_x_prime_dim }
+        { \dim_use:N \l_@@_y_prime_dim }
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_rotate_vector:nnNN}
+%   A rotation function, which needs only an input vector (as dimensions)
+%   and an output space. The values \cs{l_@@_cos_fp} and
+%   \cs{l_@@_sin_fp} should previously have been set up correctly.
+%   Working this way means that the floating point work is kept to a
+%   minimum: for any given rotation the sin and cosine values do no
+%   change, after all.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_rotate_vector:nnNN #1#2#3#4
+  {
+    \dim_set:Nn #3
+      {
+        \fp_to_dim:n
+          {
+                \dim_to_fp:n {#1} * \l_@@_cos_fp
+            - ( \dim_to_fp:n {#2} * \l_@@_sin_fp )
+          }
+      }
+    \dim_set:Nn #4
+      {
+        \fp_to_dim:n
+          {
+                \dim_to_fp:n {#1} * \l_@@_sin_fp
+            + ( \dim_to_fp:n {#2} * \l_@@_cos_fp )
+          }
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_find_corner_maxima:N}
+% \begin{macro}[aux]{\@@_find_corner_maxima_aux:nn}
+%   The idea here is to find the extremities of the content of the
+%   coffin. This is done by looking for the smallest values for the bottom
+%   and left corners, and the largest values for the top and right
+%   corners. The values start at the maximum dimensions so that the
+%   case where all are positive or all are negative works out correctly.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_find_corner_maxima:N #1
+  {
+    \dim_set:Nn \l_@@_top_corner_dim   { -\c_max_dim }
+    \dim_set:Nn \l_@@_right_corner_dim { -\c_max_dim }
+    \dim_set:Nn \l_@@_bottom_corner_dim { \c_max_dim }
+    \dim_set:Nn \l_@@_left_corner_dim   { \c_max_dim }
+    \prop_map_inline:cn { l_@@_corners_ \__int_value:w #1 _prop }
+      { \@@_find_corner_maxima_aux:nn ##2 }
+  }
+\cs_new_protected:Npn \@@_find_corner_maxima_aux:nn #1#2
+  {
+    \dim_set_min:Nn \l_@@_left_corner_dim   {#1}
+    \dim_set_max:Nn \l_@@_right_corner_dim  {#1}
+    \dim_set_min:Nn \l_@@_bottom_corner_dim {#2}
+    \dim_set_max:Nn \l_@@_top_corner_dim    {#2}
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@@_find_bounding_shift:}
+% \begin{macro}[aux]{\@@_find_bounding_shift_aux:nn}
+%   The approach to finding the shift for the bounding box is similar to
+%   that for the corners. However, there is only one value needed here and
+%   a fixed input property list, so things are a bit clearer.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_find_bounding_shift:
+  {
+    \dim_set:Nn \l_@@_bounding_shift_dim { \c_max_dim }
+    \prop_map_inline:Nn \l_@@_bounding_prop
+      { \@@_find_bounding_shift_aux:nn ##2 }
+  }
+\cs_new_protected:Npn \@@_find_bounding_shift_aux:nn #1#2
+  { \dim_set_min:Nn \l_@@_bounding_shift_dim {#1} }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@@_shift_corner:Nnnn}
+% \begin{macro}{\@@_shift_pole:Nnnnnn}
+%   Shifting the corners and poles of a coffin means subtracting the
+%   appropriate values from the $x$- and $y$-components. For
+%   the poles, this means that the direction vector is unchanged.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_shift_corner:Nnnn #1#2#3#4
+  {
+    \prop_put:cnx { l_@@_corners_ \__int_value:w #1 _ prop } {#2}
+      {
+        { \dim_eval:n { #3 - \l_@@_left_corner_dim } }
+        { \dim_eval:n { #4 - \l_@@_bottom_corner_dim } }
+      }
+  }
+\cs_new_protected:Npn \@@_shift_pole:Nnnnnn #1#2#3#4#5#6
+  {
+    \prop_put:cnx { l_@@_poles_ \__int_value:w #1 _ prop } {#2}
+      {
+        { \dim_eval:n { #3 - \l_@@_left_corner_dim } }
+        { \dim_eval:n { #4 - \l_@@_bottom_corner_dim } }
+        {#5} {#6}
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Resizing coffins}
+%
+% \begin{variable}{\l_@@_scale_x_fp}
+% \begin{variable}{\l_@@_scale_y_fp}
+%   Storage for the scaling factors in $x$ and $y$, respectively.
+%    \begin{macrocode}
+\fp_new:N \l_@@_scale_x_fp
+\fp_new:N \l_@@_scale_y_fp
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_scaled_total_height_dim}
+% \begin{variable}{\l_@@_scaled_width_dim}
+%   When scaling, the values given have to be turned into absolute values.
+%    \begin{macrocode}
+\dim_new:N \l_@@_scaled_total_height_dim
+\dim_new:N \l_@@_scaled_width_dim
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+%
+% \begin{macro}{\coffin_resize:Nnn, \coffin_resize:cnn}
+%   Resizing a coffin begins by setting up the user-friendly names for
+%   the dimensions of the coffin box. The new sizes are then turned into
+%   scale factor. This is the same operation as takes place for the
+%   underlying box, but that operation is grouped and so the same
+%   calculation is done here.
+%    \begin{macrocode}
+\cs_new_protected:Npn \coffin_resize:Nnn #1#2#3
+  {
+    \@@_set_user_dimensions:N #1
+    \box_resize:Nnn #1 {#2} {#3}
+    \fp_set:Nn \l_@@_scale_x_fp
+      { \dim_to_fp:n {#2} / \dim_to_fp:n \Width }
+    \fp_set:Nn \l_@@_scale_y_fp
+      { \dim_to_fp:n {#3} / \dim_to_fp:n \TotalHeight }
+    \@@_resize_common:Nnn #1 {#2} {#3}
+  }
+\cs_generate_variant:Nn \coffin_resize:Nnn { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_resize_common:Nnn}
+%   The poles and corners of the coffin are scaled to the appropriate
+%   places before actually resizing the underlying box.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_resize_common:Nnn #1#2#3
+  {
+    \prop_map_inline:cn { l_@@_corners_ \__int_value:w #1 _prop }
+      { \@@_scale_corner:Nnnn #1 {##1} ##2 }
+    \prop_map_inline:cn { l_@@_poles_ \__int_value:w #1 _prop }
+      { \@@_scale_pole:Nnnnnn #1 {##1} ##2 }
+%    \end{macrocode}
+%   Negative $x$-scaling values will place the poles in the wrong
+%   location: this is corrected here.
+%    \begin{macrocode}
+    \fp_compare:nNnT \l_@@_scale_x_fp < \c_zero_fp
+      {
+        \prop_map_inline:cn { l_@@_corners_ \__int_value:w #1 _prop }
+          { \@@_x_shift_corner:Nnnn #1 {##1} ##2 }
+        \prop_map_inline:cn { l_@@_poles_ \__int_value:w #1 _prop }
+          { \@@_x_shift_pole:Nnnnnn #1 {##1} ##2 }
+      }
+    \@@_end_user_dimensions:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\coffin_scale:Nnn, \coffin_scale:cnn}
+%   For scaling, the opposite calculation is done to find the new
+%   dimensions for the coffin. Only the total height is needed, as this
+%   is the shift required for corners and poles. The scaling is done
+%   the \TeX{} way as this works properly with floating point values
+%   without needing to use the \texttt{fp} module.
+%    \begin{macrocode}
+\cs_new_protected:Npn \coffin_scale:Nnn #1#2#3
+  {
+    \box_scale:Nnn #1 {#2} {#3}
+    \@@_set_user_dimensions:N #1
+    \fp_set:Nn \l_@@_scale_x_fp {#2}
+    \fp_set:Nn \l_@@_scale_y_fp {#3}
+    \fp_compare:nNnTF \l_@@_scale_y_fp > \c_zero_fp
+      { \l_@@_scaled_total_height_dim #3 \TotalHeight }
+      { \l_@@_scaled_total_height_dim -#3 \TotalHeight }
+    \fp_compare:nNnTF \l_@@_scale_x_fp > \c_zero_fp
+      { \l_@@_scaled_width_dim -#2 \Width }
+      { \l_@@_scaled_width_dim #2 \Width }
+    \@@_resize_common:Nnn #1
+      { \l_@@_scaled_width_dim } { \l_@@_scaled_total_height_dim }
+  }
+\cs_generate_variant:Nn \coffin_scale:Nnn { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_scale_vector:nnNN}
+%   This functions scales a vector from the origin using the pre-set scale
+%   factors in $x$ and $y$. This is a much less complex operation
+%   than rotation, and as a result the code is a lot clearer.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_scale_vector:nnNN #1#2#3#4
+  {
+    \dim_set:Nn #3
+      { \fp_to_dim:n { \dim_to_fp:n {#1} * \l_@@_scale_x_fp } }
+    \dim_set:Nn #4
+      { \fp_to_dim:n { \dim_to_fp:n {#2} * \l_@@_scale_y_fp } }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_scale_corner:Nnnn}
+% \begin{macro}{\@@_scale_pole:Nnnnnn}
+%   Scaling both corners and poles is a simple calculation using the
+%   preceding vector scaling.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_scale_corner:Nnnn #1#2#3#4
+  {
+    \@@_scale_vector:nnNN {#3} {#4} \l_@@_x_dim \l_@@_y_dim
+    \prop_put:cnx { l_@@_corners_ \__int_value:w #1 _prop } {#2}
+      { { \dim_use:N \l_@@_x_dim } { \dim_use:N \l_@@_y_dim } }
+  }
+\cs_new_protected:Npn \@@_scale_pole:Nnnnnn #1#2#3#4#5#6
+  {
+    \@@_scale_vector:nnNN {#3} {#4} \l_@@_x_dim \l_@@_y_dim
+    \@@_set_pole:Nnx #1 {#2}
+      {
+        { \dim_use:N \l_@@_x_dim } { \dim_use:N \l_@@_y_dim }
+        {#5} {#6}
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\@@_x_shift_corner:Nnnn}
+% \begin{macro}{\@@_x_shift_pole:Nnnnnn}
+%   These functions correct for the $x$ displacement that takes
+%   place with a negative horizontal scaling.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_x_shift_corner:Nnnn #1#2#3#4
+  {
+    \prop_put:cnx { l_@@_corners_ \__int_value:w #1 _prop } {#2}
+      {
+        { \dim_eval:n { #3 + \box_wd:N #1 } } {#4}
+      }
+  }
+\cs_new_protected:Npn \@@_x_shift_pole:Nnnnnn #1#2#3#4#5#6
+  {
+    \prop_put:cnx { l_@@_poles_ \__int_value:w #1 _prop } {#2}
+      {
+        { \dim_eval:n #3 + \box_wd:N #1 } {#4}
+        {#5} {#6}
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Additions to \pkg{l3file}}
+%
+%    \begin{macrocode}
+%<@@=ior>
+%    \end{macrocode}
+%
+% \begin{macro}[EXP]{\ior_map_break:, \ior_map_break:n}
+%   Usual map breaking functions.  Those are not yet in \pkg{l3kernel}
+%   proper since the mapping below is the first of its kind.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \ior_map_break:
+  { \__prg_map_break:Nn \ior_map_break: { } }
+\cs_new_nopar:Npn \ior_map_break:n
+  { \__prg_map_break:Nn \ior_map_break: }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ior_map_inline:Nn, \ior_str_map_inline:Nn}
+% \begin{macro}[aux]{\@@_map_inline:NNn}
+% \begin{macro}[aux]{\@@_map_inline:NNNn}
+% \begin{macro}[aux]{\@@_map_inline_loop:NNN}
+% \begin{variable}{\l_@@_internal_tl}
+%   Mapping to an input stream can be done on either a token or a string
+%   basis, hence the set up. Within that, there is a check to avoid reading
+%   past the end of a file, hence the two applications of \cs{ior_if_eof:N}.
+%   This mapping cannot be nested as the stream has only one \enquote{current
+%   line}.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \ior_map_inline:Nn
+  { \@@_map_inline:NNn \ior_get:NN }
+\cs_new_protected_nopar:Npn \ior_str_map_inline:Nn
+  { \@@_map_inline:NNn \ior_get_str:NN }
+\cs_new_protected_nopar:Npn \@@_map_inline:NNn
+  {
+    \int_gincr:N \g__prg_map_int
+    \exp_args:Nc \@@_map_inline:NNNn
+      { __prg_map_ \int_use:N \g__prg_map_int :n }
+  }
+\cs_new_protected:Npn \@@_map_inline:NNNn #1#2#3#4
+  {
+    \cs_set:Npn #1 ##1 {#4}
+    \ior_if_eof:NF #3 { \@@_map_inline_loop:NNN #1#2#3 }
+    \__prg_break_point:Nn \ior_map_break:
+      { \int_gdecr:N \g__prg_map_int }
+  }
+\cs_new_protected:Npn \@@_map_inline_loop:NNN #1#2#3
+  {
+    #2 #3 \l_@@_internal_tl
+    \ior_if_eof:NF #3
+      {
+        \exp_args:No #1 \l_@@_internal_tl
+        \@@_map_inline_loop:NNN #1#2#3
+      }
+  }
+\tl_new:N  \l_@@_internal_tl
+%    \end{macrocode}
+% \end{variable}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Additions to \pkg{l3fp}}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+% \begin{macro}
+%   {
+%     \fp_set_from_dim:Nn,  \fp_set_from_dim:cn,
+%     \fp_gset_from_dim:Nn, \fp_gset_from_dim:cn
+%   }
+%   Use the appropriate function from \pkg{l3fp-convert}.
+%    \begin{macrocode}
+\cs_new_protected:Npn \fp_set_from_dim:Nn #1#2
+  { \tl_set:Nx #1 { \dim_to_fp:n {#2} } }
+\cs_new_protected:Npn \fp_gset_from_dim:Nn #1#2
+  { \tl_gset:Nx #1 { \dim_to_fp:n {#2} } }
+\cs_generate_variant:Nn \fp_set_from_dim:Nn  { c }
+\cs_generate_variant:Nn \fp_gset_from_dim:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Additions to \pkg{l3prop}}
+%
+%    \begin{macrocode}
+%<@@=prop>
+%    \end{macrocode}
+%
+% \begin{macro}[rEXP]{\prop_map_tokens:Nn, \prop_map_tokens:cn}
+% \begin{macro}[aux]{\@@_map_tokens:nwn}
+%   The mapping grabs one key--value pair at a time, and stops when
+%   reaching the marker key \cs{q_recursion_tail}, which
+%   cannot appear in normal keys since those are strings. The odd
+%   construction |\use:n {#1}| allows |#1| to contain any token.
+%    \begin{macrocode}
+\cs_new:Npn \prop_map_tokens:Nn #1#2
+  {
+    \exp_last_unbraced:Nno \@@_map_tokens:nwn {#2} #1
+    \q_recursion_tail \q__prop { }
+    \__prg_break_point:Nn \prop_map_break: { }
+  }
+\cs_new:Npn \@@_map_tokens:nwn #1 \q__prop #2 \q__prop #3
+  {
+    \__quark_if_recursion_tail_break:NN #2 \prop_map_break:
+    \use:n {#1} {#2} {#3}
+    \@@_map_tokens:nwn {#1}
+  }
+\cs_generate_variant:Nn \prop_map_tokens:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\prop_get:Nn, \prop_get:cn}
+% \begin{macro}[aux]{\@@_get_Nn:nwn}
+%   Getting the value corresponding to a key in a property list in an
+%   expandable fashion is a simple instance of mapping some tokens.
+%   Map the function \cs{prop_get:nnn} which takes as its three
+%   arguments the \meta{key} that we are looking for, the current
+%   \meta{key} and the current \meta{value}. If the \meta{keys} match,
+%   the \meta{value} is returned. If none of the keys match, this expands
+%   to nothing.
+%    \begin{macrocode}
+\cs_new:Npn \prop_get:Nn #1#2
+  {
+    \exp_last_unbraced:Noo \@@_get_Nn:nwn
+      { \tl_to_str:n {#2} } #1
+      \tl_to_str:n {#2} \q__prop { }
+    \__prg_break_point:
+  }
+\cs_new:Npn \@@_get_Nn:nwn #1 \q__prop #2 \q__prop #3
+  {
+    \str_if_eq_x:nnTF {#1} {#2}
+      { \__prg_break:n { \exp_not:n {#3} } }
+      { \@@_get_Nn:nwn {#1} }
+  }
+\cs_generate_variant:Nn \prop_get:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Additions to \pkg{l3seq}}
+%
+%    \begin{macrocode}
+%<@@=seq>
+%    \end{macrocode}
+%
+% \begin{macro}{\seq_item:Nn, \seq_item:cn}
+% \begin{macro}[aux]{\@@_item:nnn}
+%   The idea here is to find the offset of the item from the left, then use
+%   a loop to grab the correct item. If the resulting offset is too large,
+%   then the stop code |{ ? \__prg_break: } { }| will be used by the auxiliary,
+%   terminating the loop and returning nothing at all.
+%    \begin{macrocode}
+\cs_new:Npn \seq_item:Nn #1#2
+  {
+    \exp_last_unbraced:Nfo \@@_item:nnn
+      {
+        \int_eval:n
+          {
+            \int_compare:nNnT {#2} < \c_zero
+              { \seq_count:N #1 + \c_one + }
+            #2
+          }
+      }
+    #1
+    { ? \__prg_break: }
+    { }
+    \__prg_break_point:
+  }
+\cs_new:Npn \@@_item:nnn #1#2#3
+  {
+    \use_none:n #2
+    \int_compare:nNnTF {#1} = \c_one
+      { \__prg_break:n { \exp_not:n {#3} } }
+      { \exp_args:Nf \@@_item:nnn { \int_eval:n { #1 - 1 } } }
+  }
+\cs_generate_variant:Nn \seq_item:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}
+%   {
+%     \seq_mapthread_function:NNN, \seq_mapthread_function:NcN,
+%     \seq_mapthread_function:cNN, \seq_mapthread_function:ccN
+%   }
+% \begin{macro}[aux]{\@@_mapthread_function:NN}
+% \begin{macro}[aux]{\@@_mapthread_function:Nnnwnn}
+%   The idea here is to first expand both of the sequences, adding the usual
+%   |{ ? \__prg_break: } { }| to the end of each one. This is most conveniently
+%   done in two steps using an auxiliary function. The mapping then throws
+%   away the first token of |#2| and |#5|, which for items in the sequences
+%   will both be \cs{@@_item:n}. The function to be mapped will then be
+%   applied to the two entries. When the code hits the end of one of the
+%   sequences, the break material will stop the entire loop and tidy up. This
+%   avoids needing to find the count of the two sequences, or worrying about
+%   which is longer.
+%    \begin{macrocode}
+\cs_new:Npn \seq_mapthread_function:NNN #1#2#3
+  {
+    \exp_after:wN \@@_mapthread_function:NN
+      \exp_after:wN #3
+      \exp_after:wN #1
+      #2
+      { ? \__prg_break: } { }
+    \__prg_break_point:
+  }
+\cs_new:Npn \@@_mapthread_function:NN #1#2
+  {
+    \exp_after:wN \@@_mapthread_function:Nnnwnn
+      \exp_after:wN #1
+      #2
+      { ? \__prg_break: } { }
+      \q_stop
+  }
+\cs_new:Npn \@@_mapthread_function:Nnnwnn #1#2#3#4 \q_stop #5#6
+  {
+    \use_none:n #2
+    \use_none:n #5
+    #1 {#3} {#6}
+    \@@_mapthread_function:Nnnwnn #1 #4 \q_stop
+  }
+\cs_generate_variant:Nn \seq_mapthread_function:NNN {     Nc }
+\cs_generate_variant:Nn \seq_mapthread_function:NNN { c , cc }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}
+%   {
+%     \seq_set_from_clist:NN, \seq_set_from_clist:cN,
+%     \seq_set_from_clist:Nc, \seq_set_from_clist:cc,
+%     \seq_set_from_clist:Nn, \seq_set_from_clist:cn
+%   }
+% \begin{macro}
+%   {
+%     \seq_gset_from_clist:NN, \seq_gset_from_clist:cN,
+%     \seq_gset_from_clist:Nc, \seq_gset_from_clist:cc,
+%     \seq_gset_from_clist:Nn, \seq_gset_from_clist:cn
+%   }
+%   Setting a sequence from a comma-separated list is done using a simple
+%   mapping.
+%    \begin{macrocode}
+\cs_new_protected:Npn \seq_set_from_clist:NN #1#2
+  {
+    \tl_set:Nx #1
+      { \clist_map_function:NN #2 \@@_wrap_item:n }
+  }
+\cs_new_protected:Npn \seq_set_from_clist:Nn #1#2
+  {
+    \tl_set:Nx #1
+      { \clist_map_function:nN {#2} \@@_wrap_item:n }
+  }
+\cs_new_protected:Npn \seq_gset_from_clist:NN #1#2
+  {
+    \tl_gset:Nx #1
+      { \clist_map_function:NN #2 \@@_wrap_item:n }
+  }
+\cs_new_protected:Npn \seq_gset_from_clist:Nn #1#2
+  {
+    \tl_gset:Nx #1
+      { \clist_map_function:nN {#2} \@@_wrap_item:n }
+  }
+\cs_generate_variant:Nn \seq_set_from_clist:NN  {     Nc }
+\cs_generate_variant:Nn \seq_set_from_clist:NN  { c , cc }
+\cs_generate_variant:Nn \seq_set_from_clist:Nn  { c      }
+\cs_generate_variant:Nn \seq_gset_from_clist:NN {     Nc }
+\cs_generate_variant:Nn \seq_gset_from_clist:NN { c , cc }
+\cs_generate_variant:Nn \seq_gset_from_clist:Nn { c      }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}
+%   {\seq_reverse:N, \seq_reverse:c, \seq_greverse:N, \seq_greverse:c}
+% \begin{macro}[aux]{\@@_tmp:w}
+% \begin{macro}[aux]{\@@_reverse:NN}
+% \begin{macro}[aux]{\@@_reverse_item:nwn}
+%   Previously, \cs{seq_reverse:N} was coded by collecting the items
+%   in reverse order after an \cs{exp_stop_f:} marker.
+%   \begin{verbatim}
+%     \cs_new_protected:Npn \seq_reverse:N #1
+%       {
+%         \cs_set_eq:NN \@@_item:n \@@_reverse_item:nw
+%         \tl_set:Nf #2 { #2 \exp_stop_f: }
+%       }
+%     \cs_new:Npn \@@_reverse_item:nw #1 #2 \exp_stop_f:
+%       {
+%         #2 \exp_stop_f:
+%         \@@_item:n {#1}
+%       }
+%   \end{verbatim}
+%   At first, this seems optimal, since we can forget about each item
+%   as soon as it is placed after \cs{exp_stop_f:}. Unfortunately,
+%   \TeX{}'s usual tail recursion does not take place in this case:
+%   since the following \cs{@@_reverse_item:nw} only reads
+%   tokens until \cs{exp_stop_f:}, and never reads the
+%   |\@@_item:n {#1}| left by the previous call, \TeX{} cannot
+%   remove that previous call from the stack, and in particular
+%   must retain the various macro parameters in memory, until the
+%   end of the replacement text is reached. The stack is thus
+%   only flushed after all the \cs{@@_reverse_item:nw} are
+%   expanded. Keeping track of the arguments of all those calls
+%   uses up a memory quadratic in the length of the sequence.
+%   \TeX{} can then not cope with more than a few thousand items.
+%
+%   Instead, we collect the items in the argument
+%   of \cs{exp_not:n}. The previous calls are cleanly removed
+%   from the stack, and the memory consumption becomes linear.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_tmp:w { }
+\cs_new_protected_nopar:Npn \seq_reverse:N
+  { \@@_reverse:NN \tl_set:Nx }
+\cs_new_protected_nopar:Npn \seq_greverse:N
+  { \@@_reverse:NN \tl_gset:Nx }
+\cs_new_protected:Npn \@@_reverse:NN #1 #2
+  {
+    \cs_set_eq:NN \@@_tmp:w \@@_item:n
+    \cs_set_eq:NN \@@_item:n \@@_reverse_item:nwn
+    #1 #2 { #2 \exp_not:n { } }
+    \cs_set_eq:NN \@@_item:n \@@_tmp:w
+  }
+\cs_new:Npn \@@_reverse_item:nwn #1 #2 \exp_not:n #3
+  {
+    #2
+    \exp_not:n { \@@_item:n {#1} #3 }
+  }
+\cs_generate_variant:Nn \seq_reverse:N  { c }
+\cs_generate_variant:Nn \seq_greverse:N { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\seq_set_filter:NNn, \seq_gset_filter:NNn}
+% \begin{macro}[aux]{\@@_set_filter:NNNn}
+%   Similar to \cs{seq_map_inline:Nn}, without a
+%   \cs{__prg_break_point:} because the user's code
+%   is performed within the evaluation of a boolean expression,
+%   and skipping out of that would break horribly.
+%   The \cs{@@_wrap_item:n} function inserts the relevant
+%   \cs{@@_item:n} without expansion in the input stream,
+%   hence in the \texttt{x}-expanding assignment.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \seq_set_filter:NNn
+  { \@@_set_filter:NNNn \tl_set:Nx }
+\cs_new_protected_nopar:Npn \seq_gset_filter:NNn
+  { \@@_set_filter:NNNn \tl_gset:Nx }
+\cs_new_protected:Npn \@@_set_filter:NNNn #1#2#3#4
+  {
+    \@@_push_item_def:n { \bool_if:nT {#4} { \@@_wrap_item:n {##1} } }
+    #1 #2 { #3 }
+    \@@_pop_item_def:
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\seq_set_map:NNn,\seq_gset_map:NNn}
+% \begin{macro}[aux]{\@@_set_map:NNNn}
+%   Very similar to \cs{seq_set_filter:NNn}. We could actually
+%   merge the two within a single function, but it would have weird
+%   semantics.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \seq_set_map:NNn
+  { \@@_set_map:NNNn \tl_set:Nx }
+\cs_new_protected_nopar:Npn \seq_gset_map:NNn
+  { \@@_set_map:NNNn \tl_gset:Nx }
+\cs_new_protected:Npn \@@_set_map:NNNn #1#2#3#4
+  {
+    \@@_push_item_def:n { \exp_not:N \@@_item:n {#4} }
+    #1 #2 { #3 }
+    \@@_pop_item_def:
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\seq_use:Nnnn}
+% \begin{macro}[EXP, aux]
+%   {\@@_use:NnNnn, \@@_use_ii:nwwwwnwn, \@@_use_iii:nwwn}
+%   See \cs{clist_use:Nnnn} for a general explanation.  The main
+%   difference is that we use \cs{@@_item:n} as a delimiter rather than
+%   commas.  We also need to add \cs{@@_item:n} at various places.
+%    \begin{macrocode}
+\cs_new:Npn \seq_use:Nnnn #1#2#3#4
+  {
+    \seq_if_exist:NTF #1
+      {
+        \int_case:nnn { \seq_count:N #1 }
+          {
+            { 0 } { }
+            { 1 } { \exp_after:wN \@@_use:NnNnn #1 \@@_item:n { } { } }
+            { 2 } { \exp_after:wN \@@_use:NnNnn #1 {#2} }
+          }
+          {
+            \exp_after:wN \@@_use_ii:nwwwwnwn
+            \exp_after:wN { \exp_after:wN } #1 \@@_item:n
+            \q_mark { \@@_use_ii:nwwwwnwn {#3} }
+            \q_mark { \@@_use_iii:nwwn {#4} }
+            \q_stop { }
+          }
+      }
+      { \__msg_kernel_expandable_error:nnn { kernel } { bad-variable } {#1} }
+  }
+\cs_new:Npn \@@_use:NnNnn \@@_item:n #1 \@@_item:n #2#3
+  { \exp_not:n { #1 #3 #2 } }
+\cs_new:Npn \@@_use_ii:nwwwwnwn
+    #1 \@@_item:n #2 \@@_item:n #3 \@@_item:n #4#5
+    \q_mark #6#7 \q_stop #8
+  {
+    #6 \@@_item:n {#3} \@@_item:n {#4} #5
+    \q_mark {#6} #7 \q_stop { #8 #1 #2 }
+  }
+\cs_new:Npn \@@_use_iii:nwwn #1 \@@_item:n #2 #3 \q_stop #4
+  { \exp_not:n { #4 #1 #2 } }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Additions to \pkg{l3skip}}
+%
+%    \begin{macrocode}
+%<@@=skip>
+%    \end{macrocode}
+%
+% \begin{macro}{\skip_split_finite_else_action:nnNN}
+%   This macro is useful when performing error checking in certain
+%   circumstances. If the \meta{skip} register holds finite glue it sets
+%   |#3| and |#4| to the stretch and shrink component, resp. If it holds
+%   infinite glue set |#3| and |#4| to zero and issue the special action
+%   |#2| which is probably an error message.
+%   Assignments are local.
+%    \begin{macrocode}
+\cs_new:Npn \skip_split_finite_else_action:nnNN #1#2#3#4
+  {
+    \skip_if_finite:nTF {#1}
+      {
+        #3 = \etex_gluestretch:D #1 \scan_stop:
+        #4 = \etex_glueshrink:D  #1 \scan_stop:
+      }
+      {
+        #3 = \c_zero_skip
+        #4 = \c_zero_skip
+        #2
+      }
+  }
+%    \end{macrocode}
+%  \end{macro}
+%
+%  \subsection{Additions to \pkg{l3tl}}
+%
+%    \begin{macrocode}
+%<@@=tl>
+%    \end{macrocode}
+%
+% \begin{macro}[EXP,pTF]{\tl_if_single_token:n}
+%   There are four cases: empty token list, token list starting with
+%   a normal token, with a brace group, or with a space token.
+%   If the token list starts with a normal token, remove it
+%   and check for emptyness. Otherwise, compare with a single
+%   space, only case where we have a single token.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \tl_if_single_token:n #1 { p , T , F , TF }
+  {
+    \tl_if_head_is_N_type:nTF {#1}
+      { \__str_if_eq_x_return:nn { \exp_not:o { \use_none:n #1 } } { } }
+      { \__str_if_eq_x_return:nn { \exp_not:n {#1} } { ~ } }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\tl_reverse_tokens:n}
+% \begin{macro}[EXP,aux]{\@@_reverse_group:nn}
+%   The same as \cs{tl_reverse:n} but with recursion within brace groups.
+%    \begin{macrocode}
+\cs_new:Npn \tl_reverse_tokens:n #1
+  {
+    \etex_unexpanded:D \exp_after:wN
+      {
+        \tex_romannumeral:D
+        \@@_act:NNNnn
+          \@@_reverse_normal:nN
+          \@@_reverse_group:nn
+          \@@_reverse_space:n
+          { }
+          {#1}
+      }
+  }
+\cs_new:Npn \@@_reverse_group:nn #1
+  {
+    \@@_act_group_recurse:Nnn
+      \@@_act_reverse_output:n
+      { \tl_reverse_tokens:n }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}[EXP,aux]{\@@_act_group_recurse:Nnn}
+%   In many applications of \cs{@@_act:NNNnn}, we need to recursively
+%   apply some transformation within brace groups, then output. In this
+%   code, |#1| is the output function, |#2| is the transformation,
+%   which should expand in two steps, and |#3| is the group.
+%    \begin{macrocode}
+\cs_new:Npn \@@_act_group_recurse:Nnn #1#2#3
+  {
+    \exp_args:Nf #1
+      { \exp_after:wN \exp_after:wN \exp_after:wN { #2 {#3} } }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\tl_count_tokens:n}
+% \begin{macro}[EXP,aux]{\@@_act_count_normal:nN,
+%     \@@_act_count_group:nn,\@@_act_count_space:n}
+%   The token coung is computed through an \cs{int_eval:n} construction.
+%   Each \texttt{1+} is output to the \emph{left}, into the integer
+%   expression, and the sum is ended by the \cs{c_zero} inserted by
+%   \cs{@@_act_end:wn}. Somewhat a hack.
+%    \begin{macrocode}
+\cs_new:Npn \tl_count_tokens:n #1
+  {
+    \int_eval:n
+      {
+        \@@_act:NNNnn
+          \@@_act_count_normal:nN
+          \@@_act_count_group:nn
+          \@@_act_count_space:n
+          { }
+          {#1}
+      }
+  }
+\cs_new:Npn \@@_act_count_normal:nN #1 #2 { 1 + }
+\cs_new:Npn \@@_act_count_space:n #1 { 1 + }
+\cs_new:Npn \@@_act_count_group:nn #1 #2
+  { 2 + \tl_count_tokens:n {#2} + }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{variable}{\c_@@_act_uppercase_tl, \c_@@_act_lowercase_tl}
+%   These constants contain the correspondance between lowercase
+%   and uppercase letters, in the form |aAbBcC...| and |AaBbCc...|
+%   respectively.
+%    \begin{macrocode}
+\tl_const:Nn \c_@@_act_uppercase_tl
+  {
+    aA bB cC dD eE fF gG hH iI jJ kK lL mM
+    nN oO pP qQ rR sS tT uU vV wW xX yY zZ
+  }
+\tl_const:Nn \c_@@_act_lowercase_tl
+  {
+    Aa Bb Cc Dd Ee Ff Gg Hh Ii Jj Kk Ll Mm
+    Nn Oo Pp Qq Rr Ss Tt Uu Vv Ww Xx Yy Zz
+  }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}[EXP]{\tl_expandable_uppercase:n,\tl_expandable_lowercase:n}
+% \begin{macro}[EXP,aux]{\@@_act_case_normal:nN,
+%     \@@_act_case_group:nn,\@@_act_case_space:n}
+%   The only difference between uppercasing and lowercasing is
+%   the table of correspondance that is used. As for other
+%   token list actions, we feed \cs{@@_act:NNNnn} three
+%   functions, and this time, we use the \meta{parameters}
+%   argument to carry which case-changing we are applying.
+%   A space is simply output. A normal token is compared
+%   to each letter in the alphabet using \cs{str_if_eq:nn}
+%   tests, and converted if necessary to upper/lowercase,
+%   before being output. For a group, we must perform the
+%   conversion within the group (the \cs{exp_after:wN} trigger
+%   \tn{romannumeral}, which expands fully to give the
+%   converted group), then output.
+%    \begin{macrocode}
+\cs_new:Npn \tl_expandable_uppercase:n #1
+  {
+    \etex_unexpanded:D \exp_after:wN
+      {
+        \tex_romannumeral:D
+          \@@_act_case_aux:nn { \c_@@_act_uppercase_tl } {#1}
+      }
+  }
+\cs_new:Npn \tl_expandable_lowercase:n #1
+  {
+    \etex_unexpanded:D \exp_after:wN
+      {
+        \tex_romannumeral:D
+          \@@_act_case_aux:nn { \c_@@_act_lowercase_tl } {#1}
+      }
+  }
+\cs_new:Npn \@@_act_case_aux:nn
+  {
+    \@@_act:NNNnn
+      \@@_act_case_normal:nN
+      \@@_act_case_group:nn
+      \@@_act_case_space:n
+  }
+\cs_new:Npn \@@_act_case_space:n #1 { \@@_act_output:n {~} }
+\cs_new:Npn \@@_act_case_normal:nN #1 #2
+  {
+    \exp_args:Nf \@@_act_output:n
+      {
+        \exp_args:NNo \str_case:nnn #2 {#1}
+          { \exp_stop_f: #2 }
+      }
+  }
+\cs_new:Npn \@@_act_case_group:nn #1 #2
+  {
+    \exp_after:wN \@@_act_output:n \exp_after:wN
+      { \exp_after:wN { \tex_romannumeral:D \@@_act_case_aux:nn {#1} {#2} } }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\tl_item:nn, \tl_item:Nn, \tl_item:cn}
+% \begin{macro}[aux]{\@@_item:nn}
+%   The idea here is to find the offset of the item from the left, then use
+%   a loop to grab the correct item. If the resulting offset is too large,
+%   then \cs{quark_if_recursion_tail_stop:n} terminates the loop, and returns
+%   nothing at all.
+%    \begin{macrocode}
+\cs_new:Npn \tl_item:nn #1#2
+  {
+    \exp_args:Nf \@@_item:nn
+      {
+        \int_eval:n
+          {
+            \int_compare:nNnT {#2} < \c_zero
+              { \tl_count:n {#1} + \c_one + }
+            #2
+          }
+      }
+    #1
+    \q_recursion_tail
+    \__prg_break_point:
+  }
+\cs_new:Npn \@@_item:nn #1#2
+  {
+    \__quark_if_recursion_tail_break:nN {#2} \__prg_break:
+    \int_compare:nNnTF {#1} = \c_one
+      { \__prg_break:n { \exp_not:n {#2} } }
+      { \exp_args:Nf \@@_item:nn { \int_eval:n { #1 - 1 } } }
+  }
+\cs_new_nopar:Npn \tl_item:Nn { \exp_args:No \tl_item:nn }
+\cs_generate_variant:Nn \tl_item:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Additions to \pkg{l3tokens}}
+%
+%    \begin{macrocode}
+%<@@=char>
+%    \end{macrocode}
+%
+% \begin{macro}{\char_set_active:Npn,\char_set_active:Npx}
+% \begin{macro}{\char_gset_active:Npn,\char_gset_active:Npx}
+% \begin{macro}{\char_set_active_eq:NN,\char_gset_active_eq:NN}
+%    \begin{macrocode}
+\group_begin:
+  \char_set_catcode_active:N \^^@
+  \cs_set:Npn \char_tmp:NN #1#2
+    {
+      \cs_new:Npn #1 ##1
+        {
+          \char_set_catcode_active:n { `##1 }
+          \group_begin:
+          \char_set_lccode:nn { `\^^@ } { `##1 }
+          \tl_to_lowercase:n { \group_end: #2 ^^@ }
+        }
+    }
+  \char_tmp:NN \char_set_active:Npn    \cs_set:Npn
+  \char_tmp:NN \char_set_active:Npx    \cs_set:Npx
+  \char_tmp:NN \char_gset_active:Npn   \cs_gset:Npn
+  \char_tmp:NN \char_gset_active:Npx   \cs_gset:Npx
+  \char_tmp:NN \char_set_active_eq:NN  \cs_set_eq:NN
+  \char_tmp:NN \char_gset_active_eq:NN \cs_gset_eq:NN
+\group_end:
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+%    \begin{macrocode}
+%<@@=peek>
+%    \end{macrocode}
+%
+% \begin{macro}[TF]{\peek_N_type:}
+% \begin{macro}{\@@_execute_branches_N_type:}
+%   The next token is normal if it is neither a begin-group token,
+%   nor an end-group token, nor a charcode-$32$ space token.
+%   Note that implicit begin-group tokens, end-group tokens, and
+%   spaces are also recognized as non-\texttt{N}-type.
+%   Here, there is no \meta{search token}, so we feed a dummy
+%   \cs{scan_stop:} to the \cs{peek_token_generic::NN} functions.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_execute_branches_N_type:
+  {
+    \bool_if:nTF
+      {
+        \token_if_eq_catcode_p:NN \l_peek_token \c_group_begin_token ||
+        \token_if_eq_catcode_p:NN \l_peek_token \c_group_end_token   ||
+        \token_if_eq_meaning_p:NN \l_peek_token \c_space_token
+      }
+      { \@@_false:w }
+      { \@@_true:w }
+  }
+\cs_new_protected_nopar:Npn \peek_N_type:TF
+  { \@@_token_generic:NNTF \@@_execute_branches_N_type: \scan_stop: }
+\cs_new_protected_nopar:Npn \peek_N_type:T
+  { \@@_token_generic:NNT  \@@_execute_branches_N_type: \scan_stop: }
+\cs_new_protected_nopar:Npn \peek_N_type:F
+  { \@@_token_generic:NNF  \@@_execute_branches_N_type: \scan_stop: }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintIndex
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3clist.dtx b/Master/texmf-dist/source/latex/l3kernel/l3clist.dtx
index 31a429e61ef..5fbb63f89d9 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3clist.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3clist.dtx
@@ -37,8 +37,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3clist.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental comma separated lists}
+\GetIdInfo$Id: l3clist.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Comma separated lists}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -88,7 +88,9 @@
 % \end{verbatim}
 % will leave \texttt{true} in the input stream. To include an item
 % which contains a comma, or starts or ends with a space,
-% surround it with braces.
+% surround it with braces.  The sequence data type should be preferred
+% to comma lists if items are to contain |{|, |}|, or |#| (assuming the
+% usual \TeX{} category codes apply).
 %
 % \section{Creating and initialising comma lists}
 %
@@ -118,7 +120,7 @@
 %     \cs{clist_clear_new:N} \meta{comma list}
 %   \end{syntax}
 %   Ensures that the \meta{comma list} exists globally by applying
-%   \cs{clsit_new:N} if necessary, then applies \cs{clist_(g)clear:N} to leave
+%   \cs{clist_new:N} if necessary, then applies \cs{clist_(g)clear:N} to leave
 %   the list empty.
 % \end{function}
 %
@@ -130,10 +132,10 @@
 %     \clist_gset_eq:Nc, \clist_gset_eq:cc
 %   }
 %   \begin{syntax}
-%     \cs{clist_set_eq:NN} \meta{comma list1} \meta{comma list2}
+%     \cs{clist_set_eq:NN} \meta{comma list_1} \meta{comma list_2}
 %   \end{syntax}
-%   Sets the content of \meta{comma list1} equal to that of
-%   \meta{comma list2}.
+%   Sets the content of \meta{comma list_1} equal to that of
+%   \meta{comma list_2}.
 % \end{function}
 %
 % \begin{function}
@@ -142,11 +144,11 @@
 %     \clist_gconcat:NNN, \clist_gconcat:ccc
 %   }
 %   \begin{syntax}
-%     \cs{clist_concat:NNN} \meta{comma list1} \meta{comma list2} \meta{comma list3}
+%     \cs{clist_concat:NNN} \meta{comma list_1} \meta{comma list_2} \meta{comma list_3}
 %   \end{syntax}
-%   Concatenates the content of \meta{comma list2} and \meta{comma list3}
-%   together and saves the result in \meta{comma list1}. The items in
-%   \meta{comma list2} will be placed at the left side of the new comma list.
+%   Concatenates the content of \meta{comma list_2} and \meta{comma list_3}
+%   together and saves the result in \meta{comma list_1}. The items in
+%   \meta{comma list_2} will be placed at the left side of the new comma list.
 % \end{function}
 %
 % \begin{function}[EXP, pTF, added=2012-03-03]
@@ -173,7 +175,7 @@
 %     \clist_gset:co, \clist_gset:cx
 %   }
 %   \begin{syntax}
-%     \cs{clist_set:Nn} \meta{comma list} |{|\meta{item1},\ldots{},\meta{item$_n$}|}|
+%     \cs{clist_set:Nn} \meta{comma list} |{|\meta{item_1},\ldots{},\meta{item_n}|}|
 %   \end{syntax}
 %   Sets \meta{comma list} to contain the \meta{items},
 %   removing any previous content from the variable.
@@ -192,7 +194,7 @@
 %     \clist_gput_left:co, \clist_gput_left:cx
 %   }
 %   \begin{syntax}
-%     \cs{clist_put_left:Nn} \meta{comma list} |{|\meta{item1},\ldots{},\meta{item$_n$}|}|
+%     \cs{clist_put_left:Nn} \meta{comma list} |{|\meta{item_1},\ldots{},\meta{item_n}|}|
 %   \end{syntax}
 %   Appends the \meta{items} to the left of the \meta{comma list}.
 %   Spaces are removed from both sides of each item.
@@ -210,22 +212,12 @@
 %     \clist_gput_right:co, \clist_gput_right:cx
 %   }
 %   \begin{syntax}
-%     \cs{clist_put_right:Nn} \meta{comma list} |{|\meta{item1},\ldots{},\meta{item$_n$}|}|
+%     \cs{clist_put_right:Nn} \meta{comma list} |{|\meta{item_1},\ldots{},\meta{item_n}|}|
 %   \end{syntax}
 %   Appends the \meta{items} to the right of the \meta{comma list}.
 %   Spaces are removed from both sides of each item.
 % \end{function}
 %
-% \section{Using comma lists}
-%
-% \begin{function}[EXP]{\clist_use:N, \clist_use:c}
-%   \begin{syntax}
-%     \cs{clist_use:N} \meta{comma list}
-%   \end{syntax}
-%   Places the \meta{comma list} directly into the input stream,
-%   including the commas, thus treating it as a \meta{token list}.
-% \end{function}
-%
 % \section{Modifying comma lists}
 %
 % While comma lists are normally used as ordered lists, it may be
@@ -281,17 +273,6 @@
 %   Tests if the \meta{comma list} is empty (containing no items).
 % \end{function}
 %
-% \begin{function}[EXP,pTF]
-%   {\clist_if_eq:NN, \clist_if_eq:Nc, \clist_if_eq:cN, \clist_if_eq:cc}
-%   \begin{syntax}
-%     \cs{clist_if_eq_p:NN} \meta{clist_1} \meta{clist_2}
-%     \cs{clist_if_eq:NNTF} \meta{clist_1} \meta{clist_2} \Arg{true code} \Arg{false code}
-%   \end{syntax}
-%   Compares the content of two \meta{comma lists} and
-%   is logically \texttt{true} if the two contain the same list of
-%   entries in the same order.
-% \end{function}
-%
 % \begin{function}[updated = 2011-09-06, TF]
 %   {
 %      \clist_if_in:Nn, \clist_if_in:NV, \clist_if_in:No,
@@ -326,16 +307,16 @@
 % If the result of trimming spaces is empty, the item is ignored.
 % Otherwise, if the item is surrounded by braces, one set is removed,
 % and the result is passed to the mapped function. Thus, if your
-% comma list that is being mapped is \verb*|{a , {b }, ,{}, {c},}|
+% comma list that is being mapped is \verb*|{a , {{b} }, ,{}, {c},}|
 % then the arguments passed to the mapped function are
-% `\verb*|a|', `\verb*|{b }|', an empty argument, and `\verb*|c|'.
+% `\verb*|a|', `\verb*|{b} |', an empty argument, and `\verb*|c|'.
 %
 % When the comma list is given as an \texttt{N}-type argument, spaces
 % have already been trimmed on input, and items are simply stripped
 % of one set of braces if any. This case is more efficient than using
 % \texttt{n}-type comma lists.
 %
-% \begin{function}[rEXP]
+% \begin{function}[rEXP, updated = 2012-06-29]
 %   {\clist_map_function:NN, \clist_map_function:cN, \clist_map_function:nN}
 %   \begin{syntax}
 %     \cs{clist_map_function:NN} \meta{comma list} \meta{function}
@@ -348,7 +329,7 @@
 %   One mapping may be nested inside another.
 % \end{function}
 %
-% \begin{function}
+% \begin{function}[updated = 2012-06-29]
 %   {\clist_map_inline:Nn, \clist_map_inline:cn, \clist_map_inline:nn}
 %   \begin{syntax}
 %     \cs{clist_map_inline:Nn} \meta{comma list} \Arg{inline function}
@@ -360,7 +341,7 @@
 %   are returned from left to right.
 % \end{function}
 %
-% \begin{function}
+% \begin{function}[updated = 2012-06-29]
 %   {\clist_map_variable:NNn, \clist_map_variable:cNn, \clist_map_variable:nNn}
 %   \begin{syntax}
 %     \cs{clist_map_variable:NNn} \meta{comma list} \meta{tl~var.} \Arg{function using tl~var.}
@@ -373,7 +354,7 @@
 %   are returned from left to right.
 % \end{function}
 %
-% \begin{function}[rEXP]{\clist_map_break:}
+% \begin{function}[rEXP, updated = 2012-06-29]{\clist_map_break:}
 %   \begin{syntax}
 %     \cs{clist_map_break:}
 %   \end{syntax}
@@ -394,13 +375,13 @@
 %   level \TeX{} errors.
 %   \begin{texnote}
 %     When the mapping is broken, additional tokens may be inserted by the
-%     internal macro \cs{prg_break_point:n} before further items are taken
+%     internal macro \cs{__prg_break_point:Nn} before further items are taken
 %     from the input stream. This will depend on the design of the mapping
 %     function.
 %   \end{texnote}
 % \end{function}
 %
-% \begin{function}[rEXP]{\clist_map_break:n}
+% \begin{function}[updated = 2012-06-29, rEXP]{\clist_map_break:n}
 %   \begin{syntax}
 %     \cs{clist_map_break:n} \Arg{tokens}
 %   \end{syntax}
@@ -422,12 +403,23 @@
 %   level \TeX{} errors.
 %   \begin{texnote}
 %     When the mapping is broken, additional tokens may be inserted by the
-%     internal macro \cs{prg_break_point:n} before the \meta{tokens} are
+%     internal macro \cs{__prg_break_point:Nn} before the \meta{tokens} are
 %     inserted into the input stream.
 %     This will depend on the design of the mapping function.
 %   \end{texnote}
 % \end{function}
 %
+% \begin{function}[EXP, added = 2012-07-13]
+%   {\clist_count:N, \clist_count:c, \clist_count:n}
+%   \begin{syntax}
+%     \cs{clist_count:N} \meta{comma list}
+%   \end{syntax}
+%   Leaves the number of items in the \meta{comma list} in the input
+%   stream as an \meta{integer denotation}. The total number of items
+%   in a \meta{comma list} will include those which are duplicates,
+%   \emph{i.e.}~every item in a \meta{comma list} is unique.
+% \end{function}
+%
 % \section{Comma lists as stacks}
 %
 % Comma lists can be used as stacks, where data is pushed to and popped
@@ -437,22 +429,28 @@
 % in the previous section: a comma list should either be used as an
 % ordered data type or as a stack, but not in both ways.
 %
-% \begin{function}{\clist_get:NN, \clist_get:cN}
+% \begin{function}[updated = 2012-05-14]{\clist_get:NN, \clist_get:cN}
 %   \begin{syntax}
 %     \cs{clist_get:NN} \meta{comma list} \meta{token list variable}
 %   \end{syntax}
 %   Stores the left-most item from a \meta{comma list} in the
 %   \meta{token list variable} without removing it from the
 %   \meta{comma list}. The \meta{token list variable} is assigned locally.
+%   If the \meta{comma list} is empty the \meta{token list variable} will
+%   contain the marker value \cs{q_no_value}.
 % \end{function}
 %
-% \begin{function}{\clist_get:NN, \clist_get:cN}
+% \begin{function}[TF, added = 2012-05-14]{\clist_get:NN, \clist_get:cN}
 %   \begin{syntax}
-%     \cs{clist_get:NN} \meta{comma list} \meta{token list variable}
+%     \cs{clist_get:NNTF} \meta{comma list} \meta{token list variable} \Arg{true code} \Arg{false code}
 %   \end{syntax}
-%   Stores the right-most item from a \meta{comma list} in the
-%   \meta{token list variable} without removing it from the
-%   \meta{comma list}. The \meta{token list variable} is assigned locally.
+%   If the \meta{comma list} is empty, leaves the \meta{false code} in the
+%   input stream.  The value of the \meta{token list variable} is
+%   not defined in this case and should not be relied upon.  If the
+%   \meta{comma list} is non-empty, stores the top item from the
+%   \meta{comma list} in the \meta{token list variable} without removing it
+%   from the \meta{comma list}. The \meta{token list variable} is assigned
+%   locally.
 % \end{function}
 %
 % \begin{function}[updated = 2011-09-06]{\clist_pop:NN, \clist_pop:cN}
@@ -476,6 +474,32 @@
 %   the \meta{token list variable} is local.
 % \end{function}
 %
+% \begin{function}[TF, added = 2012-05-14]{\clist_pop:NN, \clist_pop:cN}
+%   \begin{syntax}
+%     \cs{clist_pop:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   If the \meta{comma list} is empty, leaves the \meta{false code} in the
+%   input stream.  The value of the \meta{token list variable} is
+%   not defined in this case and should not be relied upon.  If the
+%   \meta{comma list} is non-empty, pops the top item from the
+%   \meta{comma list} in the \meta{token list variable}, \emph{i.e.}~removes
+%   the item from the \meta{comma list}. Both the \meta{comma list} and the
+%   \meta{token list variable} are assigned locally.
+% \end{function}
+%
+% \begin{function}[TF, added = 2012-05-14]{\clist_gpop:NN, \clist_gpop:cN}
+%   \begin{syntax}
+%     \cs{clist_gpop:NNTF} \meta{comma list} \meta{token list variable} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   If the \meta{comma list} is empty, leaves the \meta{false code} in the
+%   input stream.  The value of the \meta{token list variable} is
+%   not defined in this case and should not be relied upon.  If the
+%   \meta{comma list} is non-empty, pops the top item from the
+%   \meta{comma list} in the \meta{token list variable}, \emph{i.e.}~removes
+%   the item from the \meta{comma list}. The \meta{comma list} is modified
+%   globally, while the \meta{token list variable} is assigned locally.
+% \end{function}
+%
 % \begin{function}
 %   {
 %     \clist_push:Nn,  \clist_push:NV,  \clist_push:No,  \clist_push:Nx,
@@ -506,7 +530,11 @@
 %   Displays the entries in the comma list in the terminal.
 % \end{function}
 %
-% \section{Scratch comma lists}
+% \section{Constant and scratch comma lists}
+%
+% \begin{variable}[added = 2012-07-02]{\c_empty_clist}
+%   Constant that is always empty.
+% \end{variable}
 %
 % \begin{variable}[added = 2011-09-06]{\l_tmpa_clist, \l_tmpb_clist}
 %   Scratch comma lists for local assignment. These are never used by
@@ -522,97 +550,6 @@
 %   code and so should only be used for short-term storage.
 % \end{variable}
 %
-% \section{Experimental comma list functions}
-%
-% This section contains functions which may or may not be retained, depending
-% on how useful they are found to be.
-%
-% \begin{function}[added = 2011-06-25, updated = 2011-09-06, EXP]
-%   {\clist_length:N, \clist_length:c, \clist_length:n}
-%   \begin{syntax}
-%     \cs{clist_length:N} \meta{comma list}
-%   \end{syntax}
-%   Leaves the number of items in the \meta{comma list} in the input
-%   stream as an \meta{integer denotation}. The total number of items
-%   in a \meta{comma list} will include those which are duplicates,
-%   \emph{i.e.}~every item in a \meta{comma list} is unique.
-% \end{function}
-%
-% \begin{function}[updated = 2012-01-08, EXP]
-%   {\clist_item:Nn, \clist_item:cn, \clist_item:nn}
-%   \begin{syntax}
-%     \cs{clist_item:Nn} \meta{comma list} \Arg{integer expression}
-%   \end{syntax}
-%   Indexing items in the \meta{comma list} from $0$ at the top (left), this
-%   function will evaluate the \meta{integer expression} and leave the
-%   appropriate item from the comma list in the input stream. If the
-%   \meta{integer expression} is negative, indexing occurs from the
-%   bottom (right) of the comma list. When the \meta{integer expression}
-%   is larger than the number of items in the \meta{comma list} (as
-%   calculated by \cs{clist_length:N}) then the function will expand to
-%   nothing.
-%   \begin{texnote}
-%     The result is returned within the \tn{unexpanded}
-%     primitive (\cs{exp_not:n}), which means that the \meta{item}
-%     will not expand further when appearing in an x-type
-%     argument expansion.
-%   \end{texnote}
-% \end{function}
-%
-% \begin{function}[updated = 2011-08-31]
-%   {
-%     \clist_set_from_seq:NN,  \clist_set_from_seq:cN,
-%     \clist_set_from_seq:Nc,  \clist_set_from_seq:cc,
-%     \clist_gset_from_seq:NN, \clist_gset_from_seq:cN,
-%     \clist_gset_from_seq:Nc, \clist_gset_from_seq:cc
-%   }
-%   \begin{syntax}
-%     \cs{clist_set_from_seq:NN} \meta{comma list} \meta{sequence}
-%   \end{syntax}
-%   Sets the \meta{comma list} to be equal to the content of the
-%   \meta{sequence}.
-%   Items which contain either spaces or commas are surrounded by braces.
-% \end{function}
-%
-% \begin{function}[added = 2011-11-26]
-%   {
-%     \clist_const:Nn, \clist_const:Nx,
-%     \clist_const:cn, \clist_const:cx
-%   }
-%   \begin{syntax}
-%     \cs{clist_const:Nn} \meta{clist~var} \Arg{comma list}
-%   \end{syntax}
-%   Creates a new constant \meta{clist~var} or raises an error
-%   if the name is already taken. The value of the
-%   \meta{clist~var} will be set globally to the
-%   \meta{comma list}.
-% \end{function}
-%
-% \begin{function}[EXP, pTF, added = 2011-12-07]{\clist_if_empty:n}
-%   \begin{syntax}
-%     \cs{clist_if_empty_p:n} \Arg{comma list}
-%     \cs{clist_if_empty:nTF} \Arg{comma list} \Arg{true code} \Arg{false code}
-%   \end{syntax}
-%   Tests if the \meta{comma list} is empty (containing no items).
-%   The rules for space trimming are as for other \texttt{n}-type
-%   comma-list functions, hence the comma list |{~,~,,~}| (without
-%   outer braces) is empty, while |{~,{},}| (without outer braces)
-%   contains one element, which happens to be empty: the comma-list
-%   is not empty.
-% \end{function}
-%
-% \section{Internal comma-list functions}
-%
-% \begin{function}[added = 2011-07-09, rEXP]{\clist_trim_spaces:n}
-%   \begin{syntax}
-%     \cs{clist_trim_spaces:n} \Arg{comma list}
-%   \end{syntax}
-%   Removes leading and trailing spaces from each \meta{item} in the
-%   \meta{comma list}, leaving the resulting modified list in the
-%   input stream. This is used by the functions which add data
-%   into a comma list.
-% \end{function}
-%
 % \end{documentation}
 %
 % \begin{implementation}
@@ -626,25 +563,36 @@
 %    \end{macrocode}
 %
 %    \begin{macrocode}
+%<@@=clist>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
-% \begin{variable}{\l_clist_internal_clist}
+% \begin{variable}{\c_empty_clist}
+%   An empty comma list is simply an empty token list.
+%    \begin{macrocode}
+\cs_new_eq:NN \c_empty_clist \c_empty_tl
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_internal_clist}
 %   Scratch space for various internal uses. This comma list variable
 %   cannot be declared as such because it comes before \cs{clist_new:N}
 %    \begin{macrocode}
-\tl_new:N \l_clist_internal_clist
+\tl_new:N \l_@@_internal_clist
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{macro}[aux]{\clist_tmp:w}
+% \begin{macro}[aux]{\@@_tmp:w}
 %   A temporary function for various purposes.
 %    \begin{macrocode}
-\cs_new_protected:Npn \clist_tmp:w { }
+\cs_new_protected:Npn \@@_tmp:w { }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -714,16 +662,16 @@
 % \UnitTested
 % \begin{macro}{\clist_gconcat:NNN, \clist_gconcat:ccc}
 % \UnitTested
-% \begin{macro}[aux]{\clist_concat_aux:NNNN}
-%   Concatenating sequences is not quite as easy as it seems, as
+% \begin{macro}[aux]{\@@_concat:NNNN}
+%   Concatenating comma lists is not quite as easy as it seems, as
 %   there needs to be the correct addition of a comma to the output. So
 %   a little work to do.
 %    \begin{macrocode}
 \cs_new_protected_nopar:Npn \clist_concat:NNN
-  { \clist_concat_aux:NNNN \tl_set:Nx }
+  { \@@_concat:NNNN \tl_set:Nx }
 \cs_new_protected_nopar:Npn \clist_gconcat:NNN
-  { \clist_concat_aux:NNNN \tl_gset:Nx }
-\cs_new_protected:Npn \clist_concat_aux:NNNN #1#2#3#4
+  { \@@_concat:NNNN \tl_gset:Nx }
+\cs_new_protected:Npn \@@_concat:NNNN #1#2#3#4
   {
     #1 #2
       {
@@ -755,73 +703,58 @@
 %
 % \subsection{Removing spaces around items}
 %
-% \begin{macro}[int,EXP]{\clist_trim_spaces_generic:nw}
-% \begin{macro}[aux]{\clist_trim_spaces_generic_aux:w}
-% \begin{macro}[aux]{\clist_trim_spaces_generic_aux_ii:nn}
-%   Used as `\cs{clist_trim_spaces_generic:nw} \Arg{code}
-%   \cs{q_mark} \meta{item} |,|' (including the comma).
+% \begin{macro}[int,EXP]{\@@_trim_spaces_generic:nw}
+% \begin{macro}[aux]{\@@_trim_spaces_generic:nn}
+%   \begin{syntax}
+%     \cs{@@_trim_spaces_generic:nw} \Arg{code} \cs{q_mark} \meta{item} |,|
+%   \end{syntax}
 %   This expands to the \meta{code}, followed by a brace group
-%   containing the \meta{item}, with leading and trailing spaces removed.
-%   The calling function is responsible for inserting \cs{q_mark}
-%   in front of the \meta{item}, as well as testing for the end of the list.
-%   See \cs{tl_trim_spaces:n} for a partial explanation of what
-%   is happening here. We changed \cs{tl_trim_spaces_aux_iv:w}
-%   into \cs{clist_trim_spaces_generic_aux:w} compared to
-%   \cs{tl_trim_spaces:n}, and dropped a \cs{q_mark}, which is
-%   already included in the argument |##2|.
+%   containing the \meta{item}, with leading and trailing spaces
+%   removed.  The calling function is responsible for inserting
+%   \cs{q_mark} in front of the \meta{item}, as well as testing for the
+%   end of the list.  We reuse a \pkg{l3tl} internal function, whose
+%   first argument must start with \cs{q_mark}.  That trims the item
+%   |#2|, then feeds the result (after having to do an \texttt{o}-type
+%   expansion) to \cs{@@_trim_spaces_generic:nn} which places the
+%   \meta{code} in front of the \meta{trimmed item}.
 %    \begin{macrocode}
-\cs_set:Npn \clist_tmp:w #1
+\cs_new:Npn \@@_trim_spaces_generic:nw #1#2 ,
   {
-    \cs_new:Npn \clist_trim_spaces_generic:nw ##1 ##2 ,
-      {
-        \tl_trim_spaces_aux_i:w
-        ##2
-        \q_nil
-        \q_mark #1 { }
-        \q_mark \tl_trim_spaces_aux_ii:w
-        \tl_trim_spaces_aux_iii:w
-        #1 \q_nil
-        \clist_trim_spaces_generic_aux:w
-        \q_stop
-        {##1}
-      }
+    \__tl_trim_spaces:nn {#2}
+      { \exp_args:No \@@_trim_spaces_generic:nn } {#1}
   }
-\clist_tmp:w {~}
-\cs_new:Npn \clist_trim_spaces_generic_aux:w #1 \q_nil #2 \q_stop
-  { \exp_args:No \clist_trim_spaces_generic_aux_ii:nn { \use_none:n #1 } }
-\cs_new:Npn \clist_trim_spaces_generic_aux_ii:nn #1 #2 { #2 {#1} }
+\cs_new:Npn \@@_trim_spaces_generic:nn #1#2 { #2 {#1} }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
-% \end{macro}
 %
-% \begin{macro}[int,rEXP]{\clist_trim_spaces:n}
-% \begin{macro}[aux]{\clist_trim_spaces_aux:nn}
-%   The first argument of \cs{clist_trim_spaces_aux:nn} is initially empty,
+% \begin{macro}[int,rEXP]{\@@_trim_spaces:n}
+% \begin{macro}[aux]{\@@_trim_spaces_ii:nn}
+%   The first argument of \cs{@@_trim_spaces_ii:nn} is initially empty,
 %   and later a comma, namely, as soon as we have added an item to the
 %   resulting list. The auxiliary tests for the end of the list,
 %   and also prevents empty arguments from finding their way into the
 %   output.
 %    \begin{macrocode}
-\cs_new:Npn \clist_trim_spaces:n #1
+\cs_new:Npn \@@_trim_spaces:n #1
   {
-    \clist_trim_spaces_generic:nw
-      { \clist_trim_spaces_aux:nn { } }
+    \@@_trim_spaces_generic:nw
+      { \@@_trim_spaces_ii:nn { } }
       \q_mark #1 ,
     \q_recursion_tail, \q_recursion_stop
   }
-\cs_new:Npn \clist_trim_spaces_aux:nn #1 #2
+\cs_new:Npn \@@_trim_spaces_ii:nn #1 #2
   {
     \quark_if_recursion_tail_stop:n {#2}
     \tl_if_empty:nTF {#2}
       {
-        \clist_trim_spaces_generic:nw
-          { \clist_trim_spaces_aux:nn {#1} } \q_mark
+        \@@_trim_spaces_generic:nw
+          { \@@_trim_spaces_ii:nn {#1} } \q_mark
       }
       {
         #1 \exp_not:n {#2}
-        \clist_trim_spaces_generic:nw
-          { \clist_trim_spaces_aux:nn { , } } \q_mark
+        \@@_trim_spaces_generic:nw
+          { \@@_trim_spaces_ii:nn { , } } \q_mark
       }
   }
 %    \end{macrocode}
@@ -846,9 +779,9 @@
 %   }
 %    \begin{macrocode}
 \cs_new_protected:Npn \clist_set:Nn #1#2
-  { \tl_set:Nx #1 { \clist_trim_spaces:n {#2} } }
+  { \tl_set:Nx #1 { \@@_trim_spaces:n {#2} } }
 \cs_new_protected:Npn \clist_gset:Nn #1#2
-  { \tl_gset:Nx #1 { \clist_trim_spaces:n {#2} } }
+  { \tl_gset:Nx #1 { \@@_trim_spaces:n {#2} } }
 \cs_generate_variant:Nn \clist_set:Nn  { NV , No , Nx , c , cV , co , cx }
 \cs_generate_variant:Nn \clist_gset:Nn { NV , No , Nx , c , cV , co , cx }
 %    \end{macrocode}
@@ -871,18 +804,18 @@
 %     \clist_gput_left:co, \clist_gput_left:cx
 %   }
 % \UnitTested
-% \begin{macro}[aux]{\clist_put_left_aux:NNNn}
+% \begin{macro}[aux]{\@@_put_left:NNNn}
 %   Comma lists cannot hold empty values: there are therefore a couple
 %   of sanity checks to avoid accumulating commas.
 %    \begin{macrocode}
 \cs_new_protected_nopar:Npn \clist_put_left:Nn
-  { \clist_put_left_aux:NNNn \clist_concat:NNN \clist_set:Nn }
+  { \@@_put_left:NNNn \clist_concat:NNN \clist_set:Nn }
 \cs_new_protected_nopar:Npn \clist_gput_left:Nn
-  { \clist_put_left_aux:NNNn \clist_gconcat:NNN \clist_set:Nn }
-\cs_new_protected:Npn \clist_put_left_aux:NNNn #1#2#3#4
+  { \@@_put_left:NNNn \clist_gconcat:NNN \clist_set:Nn }
+\cs_new_protected:Npn \@@_put_left:NNNn #1#2#3#4
   {
-    #2 \l_clist_internal_clist {#4}
-    #1 #3 \l_clist_internal_clist #3
+    #2 \l_@@_internal_clist {#4}
+    #1 #3 \l_@@_internal_clist #3
   }
 \cs_generate_variant:Nn \clist_put_left:Nn  {     NV , No , Nx }
 \cs_generate_variant:Nn \clist_put_left:Nn  { c , cV , co , cx }
@@ -909,16 +842,16 @@
 %     \clist_gput_right:co, \clist_gput_right:cx
 %   }
 % \UnitTested
-% \begin{macro}[aux]{\clist_put_right_aux:NNNn}
+% \begin{macro}[aux]{\@@_put_right:NNNn}
 %    \begin{macrocode}
 \cs_new_protected_nopar:Npn \clist_put_right:Nn
-  { \clist_put_right_aux:NNNn \clist_concat:NNN \clist_set:Nn }
+  { \@@_put_right:NNNn \clist_concat:NNN \clist_set:Nn }
 \cs_new_protected_nopar:Npn \clist_gput_right:Nn
-  { \clist_put_right_aux:NNNn \clist_gconcat:NNN \clist_gset:Nn }
-\cs_new_protected:Npn \clist_put_right_aux:NNNn #1#2#3#4
+  { \@@_put_right:NNNn \clist_gconcat:NNN \clist_gset:Nn }
+\cs_new_protected:Npn \@@_put_right:NNNn #1#2#3#4
   {
-    #2 \l_clist_internal_clist {#4}
-    #1 #3 #3 \l_clist_internal_clist
+    #2 \l_@@_internal_clist {#4}
+    #1 #3 #3 \l_@@_internal_clist
   }
 \cs_generate_variant:Nn \clist_put_right:Nn  {     NV , No , Nx }
 \cs_generate_variant:Nn \clist_put_right:Nn  { c , cV , co , cx }
@@ -933,13 +866,19 @@
 %
 % \begin{macro}{\clist_get:NN, \clist_get:cN}
 % \UnitTested
-% \begin{macro}[aux]{\clist_get_aux:wN}
+% \begin{macro}[aux]{\@@_get:wN}
 %   Getting an item from the left of a comma list is pretty easy: just
 %   trim off the first item using the comma.
 %    \begin{macrocode}
 \cs_new_protected:Npn \clist_get:NN #1#2
-  { \exp_after:wN \clist_get_aux:wN #1 , \q_stop #2 }
-\cs_new_protected:Npn \clist_get_aux:wN #1 , #2 \q_stop #3
+  {
+    \if_meaning:w #1 \c_empty_clist
+      \tl_set:Nn #2 { \q_no_value }
+    \else:
+      \exp_after:wN \@@_get:wN #1 , \q_stop #2
+    \fi:
+  }
+\cs_new_protected:Npn \@@_get:wN #1 , #2 \q_stop #3
   { \tl_set:Nn #3 {#1} }
 \cs_generate_variant:Nn \clist_get:NN { c }
 %    \end{macrocode}
@@ -951,28 +890,39 @@
 % \begin{macro}{\clist_gpop:NN, \clist_gpop:cN}
 % \UnitTested
 % \begin{macro}[aux]
-%   {\clist_pop_aux:NNN, \clist_pop_aux:NwNNN, \clist_pop_aux:wNN}
-%   The aim here is to get the popped item as |#1| in the auxiliary, with
-%   |#2| containing either the remainder of the list \emph{or} \cs{q_nil}
-%   if there were insufficient items. That keeps the number of auxiliary
-%   functions down.
+%   {\@@_pop:NNN, \@@_pop:wwNNN, \@@_pop:wN}
+%   An empty clist leads to \cs{q_no_value}, otherwise grab until the
+%   first comma and assign to the variable.  The second argument of
+%   \cs{@@_pop:wwNNN} is a comma list ending in a comma and
+%   \cs{q_mark}, unless the original clist contained exactly one item:
+%   then the argument is just \cs{q_mark}.  The next auxiliary picks
+%   either \cs{exp_not:n} or \cs{use_none:n} as |#2|, ensuring that the
+%   result can safely be an empty comma list.
 %    \begin{macrocode}
 \cs_new_protected_nopar:Npn \clist_pop:NN
-  { \clist_pop_aux:NNN \tl_set:Nf }
+  { \@@_pop:NNN \tl_set:Nx }
 \cs_new_protected_nopar:Npn \clist_gpop:NN
-  { \clist_pop_aux:NNN \tl_gset:Nf }
-\cs_new_protected:Npn \clist_pop_aux:NNN #1#2#3
+  { \@@_pop:NNN \tl_gset:Nx }
+\cs_new_protected:Npn \@@_pop:NNN #1#2#3
   {
-    \exp_after:wN \clist_pop_aux:wNNN #2 , \q_nil \q_stop #1#2#3
+    \if_meaning:w #2 \c_empty_clist
+      \tl_set:Nn #3 { \q_no_value }
+    \else:
+      \exp_after:wN \@@_pop:wwNNN #2 , \q_mark \q_stop #1#2#3
+    \fi:
   }
-\cs_new_protected:Npn \clist_pop_aux:wNNN #1 , #2 \q_stop #3#4#5
+\cs_new_protected:Npn \@@_pop:wwNNN #1 , #2 \q_stop #3#4#5
   {
     \tl_set:Nn #5 {#1}
-    \quark_if_nil:nTF {#2}
-      { #3 #4 { } }
-      { #3 #4 { \clist_pop_aux:w \exp_stop_f: #2 } }
+    #3 #4
+      {
+        \@@_pop:wN \prg_do_nothing:
+          #2 \exp_not:o
+          , \q_mark \use_none:n
+        \q_stop
+      }
   }
-\cs_new_protected:Npn \clist_pop_aux:w #1 , \q_nil {#1}
+\cs_new:Npn \@@_pop:wN #1 , \q_mark #2 #3 \q_stop { #2 {#1} }
 \cs_generate_variant:Nn \clist_pop:NN  { c }
 \cs_generate_variant:Nn \clist_gpop:NN { c }
 %    \end{macrocode}
@@ -980,6 +930,49 @@
 % \end{macro}
 % \end{macro}
 %
+% \begin{macro}[TF]{\clist_get:NN, \clist_get:cN}
+% \begin{macro}[TF]{\clist_pop:NN, \clist_pop:cN}
+% \begin{macro}[TF]{\clist_gpop:NN, \clist_gpop:cN}
+% \begin{macro}[aux]{\@@_pop_TF:NNN}
+%   The same, as branching code: very similar to the above.
+%    \begin{macrocode}
+\prg_new_protected_conditional:Npnn \clist_get:NN #1#2 { T , F , TF }
+  {
+    \if_meaning:w #1 \c_empty_clist
+      \prg_return_false:
+    \else:
+      \exp_after:wN \@@_get:wN #1 , \q_stop #2
+      \prg_return_true:
+    \fi:
+  }
+\cs_generate_variant:Nn \clist_get:NNT  { c }
+\cs_generate_variant:Nn \clist_get:NNF  { c }
+\cs_generate_variant:Nn \clist_get:NNTF { c }
+\prg_new_protected_conditional:Npnn \clist_pop:NN #1#2 { T , F , TF }
+  { \@@_pop_TF:NNN \tl_set:Nx #1 #2 }
+\prg_new_protected_conditional:Npnn \clist_gpop:NN #1#2 { T , F , TF }
+  { \@@_pop_TF:NNN \tl_gset:Nx #1 #2 }
+\cs_new_protected:Npn \@@_pop_TF:NNN #1#2#3
+  {
+    \if_meaning:w #2 \c_empty_clist
+      \prg_return_false:
+    \else:
+      \exp_after:wN \@@_pop:wwNNN #2 , \q_mark \q_stop #1#2#3
+      \prg_return_true:
+    \fi:
+  }
+\cs_generate_variant:Nn \clist_pop:NNT   { c }
+\cs_generate_variant:Nn \clist_pop:NNF   { c }
+\cs_generate_variant:Nn \clist_pop:NNTF  { c }
+\cs_generate_variant:Nn \clist_gpop:NNT  { c }
+\cs_generate_variant:Nn \clist_gpop:NNF  { c }
+\cs_generate_variant:Nn \clist_gpop:NNTF { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
 % \begin{macro}{
 %   \clist_push:Nn, \clist_push:NV, \clist_push:No, \clist_push:Nx,
 %   \clist_push:cn, \clist_push:cV, \clist_push:co, \clist_push:cx
@@ -990,7 +983,7 @@
 %   \clist_gpush:cn, \clist_gpush:cV, \clist_gpush:co, \clist_gpush:cx
 % }
 % \UnitTested
-%   Pushing to a sequence is the same as adding on the left.
+%   Pushing to a comma list is the same as adding on the left.
 %    \begin{macrocode}
 \cs_new_eq:NN \clist_push:Nn  \clist_put_left:Nn
 \cs_new_eq:NN \clist_push:NV  \clist_put_left:NV
@@ -1012,23 +1005,12 @@
 % \end{macro}
 % \end{macro}
 %
-% \subsection{Using comma lists}
-%
-% \begin{macro}{\clist_use:N, \clist_use:c}
-% \UnitTested
-%   The approach is the same as for \cs{tl_use:N}.
-%    \begin{macrocode}
-\cs_new_eq:NN \clist_use:N \tl_use:N
-\cs_new_eq:NN \clist_use:c \tl_use:c
-%    \end{macrocode}
-% \end{macro}
-%
 % \subsection{Modifying comma lists}
 %
-% \begin{variable}{\l_clist_internal_remove_clist}
+% \begin{variable}{\l_@@_internal_remove_clist}
 %   An internal comma list for the removal routines.
 %    \begin{macrocode}
-\clist_new:N \l_clist_internal_remove_clist
+\clist_new:N \l_@@_internal_remove_clist
 %    \end{macrocode}
 % \end{variable}
 %
@@ -1036,22 +1018,22 @@
 % \UnitTested
 % \begin{macro}{\clist_gremove_duplicates:N, \clist_gremove_duplicates:c}
 % \UnitTested
-% \begin{macro}[aux]{\clist_remove_duplicates_aux:NN}
+% \begin{macro}[aux]{\@@_remove_duplicates:NN}
 %   Removing duplicates means making a new list then copying it.
 %    \begin{macrocode}
 \cs_new_protected:Npn \clist_remove_duplicates:N
-  { \clist_remove_duplicates_aux:NN \clist_set_eq:NN }
+  { \@@_remove_duplicates:NN \clist_set_eq:NN }
 \cs_new_protected:Npn \clist_gremove_duplicates:N
-  { \clist_remove_duplicates_aux:NN \clist_gset_eq:NN }
-\cs_new_protected:Npn \clist_remove_duplicates_aux:NN #1#2
+  { \@@_remove_duplicates:NN \clist_gset_eq:NN }
+\cs_new_protected:Npn \@@_remove_duplicates:NN #1#2
   {
-    \clist_clear:N \l_clist_internal_remove_clist
+    \clist_clear:N \l_@@_internal_remove_clist
     \clist_map_inline:Nn #2
       {
-        \clist_if_in:NnF \l_clist_internal_remove_clist {##1}
-          { \clist_put_right:Nn \l_clist_internal_remove_clist {##1} }
+        \clist_if_in:NnF \l_@@_internal_remove_clist {##1}
+          { \clist_put_right:Nn \l_@@_internal_remove_clist {##1} }
       }
-    #1 #2 \l_clist_internal_remove_clist
+    #1 #2 \l_@@_internal_remove_clist
   }
 \cs_generate_variant:Nn \clist_remove_duplicates:N  { c }
 \cs_generate_variant:Nn \clist_gremove_duplicates:N { c }
@@ -1064,21 +1046,21 @@
 % \UnitTested
 % \begin{macro}{\clist_gremove_all:Nn, \clist_gremove_all:cn}
 % \UnitTested
-% \begin{macro}[aux]{\clist_remove_all_aux:NNn}
-% \begin{macro}[aux]{\clist_remove_all_aux:w}
-% \begin{macro}[aux]{\clist_remove_all_aux:}
+% \begin{macro}[aux]{\@@_remove_all:NNn}
+% \begin{macro}[aux]{\@@_remove_all:w}
+% \begin{macro}[aux]{\@@_remove_all:}
 %   The method used here is very similar to \cs{tl_replace_all:Nnn}.
 %   Build a function delimited by the \meta{item} that should be removed,
 %   surrounded with commas, and call that function followed by
 %   the expanded comma list, and another copy of the \meta{item}.
 %   The loop is controlled by the argument grabbed by
-%   \cs{clist_remove_all_aux:w}: when the item was found,
+%   \cs{@@_remove_all:w}: when the item was found,
 %   the \cs{q_mark} delimiter used is the one inserted by
-%   \cs{clist_tmp:w}, and \cs{use_none_delimit_by_q_stop:w}
+%   \cs{@@_tmp:w}, and \cs{use_none_delimit_by_q_stop:w}
 %   is deleted. At the end, the final \meta{item} is
-%   grabbed, and the argument of \cs{clist_tmp:w} contains
-%   \cs{q_mark}: in that case, \cs{clist_remove_all_aux:w}
-%   removes the second \cs{q_mark} (inserted by \cs{clist_tmp:w}),
+%   grabbed, and the argument of \cs{@@_tmp:w} contains
+%   \cs{q_mark}: in that case, \cs{@@_remove_all:w}
+%   removes the second \cs{q_mark} (inserted by \cs{@@_tmp:w}),
 %   and lets \cs{use_none_delimit_by_q_stop:w} act.
 %
 %   No brace is lost because items are always grabbed with a leading comma.
@@ -1090,20 +1072,20 @@
 %   the second step removes it.
 %    \begin{macrocode}
 \cs_new_protected:Npn \clist_remove_all:Nn
-  { \clist_remove_all_aux:NNn \tl_set:Nx }
+  { \@@_remove_all:NNn \tl_set:Nx }
 \cs_new_protected:Npn \clist_gremove_all:Nn
-  { \clist_remove_all_aux:NNn \tl_gset:Nx }
-\cs_new_protected:Npn \clist_remove_all_aux:NNn #1#2#3
+  { \@@_remove_all:NNn \tl_gset:Nx }
+\cs_new_protected:Npn \@@_remove_all:NNn #1#2#3
   {
-    \cs_set:Npn \clist_tmp:w ##1 , #3 ,
+    \cs_set:Npn \@@_tmp:w ##1 , #3 ,
       {
         ##1
         , \q_mark , \use_none_delimit_by_q_stop:w ,
-        \clist_remove_all_aux:
+        \@@_remove_all:
       }
     #1 #2
       {
-        \exp_after:wN \clist_remove_all_aux:
+        \exp_after:wN \@@_remove_all:
         #2 , \q_mark , #3 , \q_stop
       }
     \clist_if_empty:NF #2
@@ -1115,9 +1097,9 @@
           }
       }
   }
-\cs_new:Npn \clist_remove_all_aux:
-  { \exp_after:wN \clist_remove_all_aux:w \clist_tmp:w , }
-\cs_new:Npn \clist_remove_all_aux:w #1 , \q_mark , #2 , { \exp_not:n {#1} }
+\cs_new:Npn \@@_remove_all:
+  { \exp_after:wN \@@_remove_all:w \@@_tmp:w , }
+\cs_new:Npn \@@_remove_all:w #1 , \q_mark , #2 , { \exp_not:n {#1} }
 \cs_generate_variant:Nn \clist_remove_all:Nn  { c }
 \cs_generate_variant:Nn \clist_gremove_all:Nn { c }
 %    \end{macrocode}
@@ -1138,43 +1120,31 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[pTF]
-%   {\clist_if_eq:NN, \clist_if_eq:Nc, \clist_if_eq:cN, \clist_if_eq:cc}
-% \UnitTested
-%   Simple copies from the token list variable material.
-%    \begin{macrocode}
-\prg_new_eq_conditional:NNn \clist_if_eq:NN \tl_if_eq:NN { p , T , F , TF }
-\prg_new_eq_conditional:NNn \clist_if_eq:Nc \tl_if_eq:Nc { p , T , F , TF }
-\prg_new_eq_conditional:NNn \clist_if_eq:cN \tl_if_eq:cN { p , T , F , TF }
-\prg_new_eq_conditional:NNn \clist_if_eq:cc \tl_if_eq:cc { p , T , F , TF }
-%    \end{macrocode}
-% \end{macro}
-%
 % \begin{macro}[TF]
 %   {
 %     \clist_if_in:Nn, \clist_if_in:NV, \clist_if_in:No,
 %     \clist_if_in:cn, \clist_if_in:cV, \clist_if_in:co,
 %     \clist_if_in:nn, \clist_if_in:nV, \clist_if_in:no
 %   }
-% \begin{macro}[aux]{\clist_if_in_return:nn}
+% \begin{macro}[aux]{\@@_if_in_return:nn}
 % \UnitTested
 %   See description of the \cs{tl_if_in:Nn} function for details.
 %   We simply surround the comma list, and the item, with commas.
 %    \begin{macrocode}
 \prg_new_protected_conditional:Npnn \clist_if_in:Nn #1#2 { T  , F , TF }
   {
-    \exp_args:No \clist_if_in_return:nn #1 {#2}
+    \exp_args:No \@@_if_in_return:nn #1 {#2}
   }
 \prg_new_protected_conditional:Npnn \clist_if_in:nn #1#2 { T  , F , TF }
   {
-    \clist_set:Nn \l_clist_internal_clist {#1}
-    \exp_args:No \clist_if_in_return:nn \l_clist_internal_clist {#2}
+    \clist_set:Nn \l_@@_internal_clist {#1}
+    \exp_args:No \@@_if_in_return:nn \l_@@_internal_clist {#2}
   }
-\cs_new_protected:Npn \clist_if_in_return:nn #1#2
+\cs_new_protected:Npn \@@_if_in_return:nn #1#2
   {
-    \cs_set:Npn \clist_tmp:w ##1 ,#2, { }
+    \cs_set:Npn \@@_tmp:w ##1 ,#2, { }
     \tl_if_empty:oTF
-      { \clist_tmp:w ,#1, {} {} ,#2, }
+      { \@@_tmp:w ,#1, {} {} ,#2, }
       { \prg_return_false: } { \prg_return_true: }
   }
 \cs_generate_variant:Nn \clist_if_in:NnT  {     NV , No }
@@ -1194,28 +1164,28 @@
 %
 % \begin{macro}{\clist_map_function:NN, \clist_map_function:cN}
 % \UnitTested
-% \begin{macro}[aux]{\clist_map_function_aux:Nw}
+% \begin{macro}[aux]{\@@_map_function:Nw}
 %   If the variable is empty, the mapping is skipped (otherwise,
 %   that comma-list would be seen as consisting of one empty item).
 %   Then loop over the comma-list, grabbing one comma-delimited
 %   item at a time. The end is marked by \cs{q_recursion_tail}.
-%   The auxiliary function \cs{clist_map_function_aux:Nw} is used
+%   The auxiliary function \cs{@@_map_function:Nw} is used
 %   directly in \cs{clist_map_inline:Nn}. Change with care.
 %    \begin{macrocode}
 \cs_new:Npn \clist_map_function:NN #1#2
   {
     \clist_if_empty:NF #1
       {
-        \exp_last_unbraced:NNo \clist_map_function_aux:Nw #2 #1
+        \exp_last_unbraced:NNo \@@_map_function:Nw #2 #1
           , \q_recursion_tail ,
-        \prg_break_point:n { }
+        \__prg_break_point:Nn \clist_map_break: { }
       }
   }
-\cs_new:Npn \clist_map_function_aux:Nw #1#2 ,
+\cs_new:Npn \@@_map_function:Nw #1#2 ,
   {
-    \quark_if_recursion_tail_break:n {#2}
+    \__quark_if_recursion_tail_break:nN {#2} \clist_map_break:
     #1 {#2}
-    \clist_map_function_aux:Nw #1
+    \@@_map_function:Nw #1
   }
 \cs_generate_variant:Nn \clist_map_function:NN { c }
 %    \end{macrocode}
@@ -1224,31 +1194,31 @@
 %
 % \begin{macro}{\clist_map_function:nN}
 % \UnitTested
-% \begin{macro}[aux]{\clist_map_function_n_aux:Nn}
-% \begin{macro}{\clist_map_aux_unbrace:Nw}
+% \begin{macro}[aux]{\@@_map_function_n:Nn}
+% \begin{macro}[aux]{\@@_map_unbrace:Nw}
 %   The \texttt{n}-type mapping function is a bit more awkward,
-%   since spaces mustbe trimmed from each item.
-%   Space trimming is again based on \cs{clist_trim_spaces_generic:nw}.
-%   The auxiliary \cs{clist_map_function_n_aux:Nn} receives
+%   since spaces must be trimmed from each item.
+%   Space trimming is again based on \cs{@@_trim_spaces_generic:nw}.
+%   The auxiliary \cs{@@_map_function_n:Nn} receives
 %   as arguments the function, and the result of removing leading
 %   and trailing spaces from the item which lies until the next comma.
 %   Empty items are ignored, then one level of braces is removed
-%   by \cs{clist_map_aux_unbrace:Nw}.
+%   by \cs{@@_map_unbrace:Nw}.
 %    \begin{macrocode}
 \cs_new:Npn \clist_map_function:nN #1#2
   {
-    \clist_trim_spaces_generic:nw { \clist_map_function_n_aux:Nn #2 }
+    \@@_trim_spaces_generic:nw { \@@_map_function_n:Nn #2 }
     \q_mark #1, \q_recursion_tail,
-    \prg_break_point:n { }
+    \__prg_break_point:Nn \clist_map_break: { }
   }
-\cs_new:Npn \clist_map_function_n_aux:Nn #1 #2
+\cs_new:Npn \@@_map_function_n:Nn #1 #2
   {
-    \quark_if_recursion_tail_break:n {#2}
-    \tl_if_empty:nF {#2} { \clist_map_aux_unbrace:Nw #1 #2, }
-    \clist_trim_spaces_generic:nw { \clist_map_function_n_aux:Nn #1 }
+    \__quark_if_recursion_tail_break:nN {#2} \clist_map_break:
+    \tl_if_empty:nF {#2} { \@@_map_unbrace:Nw #1 #2, }
+    \@@_trim_spaces_generic:nw { \@@_map_function_n:Nn #1 }
     \q_mark
   }
-\cs_new:Npn \clist_map_aux_unbrace:Nw #1 #2, { #1 {#2} }
+\cs_new:Npn \@@_map_unbrace:Nw #1 #2, { #1 {#2} }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1274,18 +1244,19 @@
   {
     \clist_if_empty:NF #1
       {
-        \int_gincr:N \g_prg_map_int
-        \cs_gset:cpn { clist_map_ \int_use:N \g_prg_map_int :n } ##1 {#2}
-        \exp_last_unbraced:Nco \clist_map_function_aux:Nw
-          { clist_map_ \int_use:N \g_prg_map_int :n }
+        \int_gincr:N \g__prg_map_int
+        \cs_gset:cpn { __prg_map_ \int_use:N \g__prg_map_int :w } ##1 {#2}
+        \exp_last_unbraced:Nco \@@_map_function:Nw
+          { __prg_map_ \int_use:N \g__prg_map_int :w }
           #1 , \q_recursion_tail ,
-        \prg_break_point:n { \int_gdecr:N \g_prg_map_int }
+        \__prg_break_point:Nn \clist_map_break:
+          { \int_gdecr:N \g__prg_map_int }
       }
   }
 \cs_new_protected:Npn \clist_map_inline:nn #1
   {
-    \clist_set:Nn \l_clist_internal_clist {#1}
-    \clist_map_inline:Nn \l_clist_internal_clist
+    \clist_set:Nn \l_@@_internal_clist {#1}
+    \clist_map_inline:Nn \l_@@_internal_clist
   }
 \cs_generate_variant:Nn \clist_map_inline:Nn { c }
 %    \end{macrocode}
@@ -1295,7 +1266,7 @@
 % \begin{macro}{\clist_map_variable:NNn, \clist_map_variable:cNn}
 % \UnitTested
 % \begin{macro}{\clist_map_variable:nNn}
-% \begin{macro}[aux]{\clist_map_variable_aux:Nnw}
+% \begin{macro}[aux]{\@@_map_variable:Nnw}
 %   As for other comma-list mappings, filter out the case of
 %   an empty list. Same approach as \cs{clist_map_function:Nn},
 %   additionally we store each item in the given variable.
@@ -1307,23 +1278,23 @@
     \clist_if_empty:NF #1
       {
         \exp_args:Nno \use:nn
-          { \clist_map_variable_aux:Nnw #2 {#3} }
+          { \@@_map_variable:Nnw #2 {#3} }
           #1
           , \q_recursion_tail , \q_recursion_stop
-        \prg_break_point:n { }
+        \__prg_break_point:Nn \clist_map_break: { }
       }
   }
 \cs_new_protected:Npn \clist_map_variable:nNn #1
   {
-    \clist_set:Nn \l_clist_internal_clist {#1}
-    \clist_map_variable:NNn \l_clist_internal_clist
+    \clist_set:Nn \l_@@_internal_clist {#1}
+    \clist_map_variable:NNn \l_@@_internal_clist
   }
-\cs_new_protected:Npn \clist_map_variable_aux:Nnw #1#2#3,
+\cs_new_protected:Npn \@@_map_variable:Nnw #1#2#3,
   {
     \tl_set:Nn #1 {#3}
     \quark_if_recursion_tail_stop:N #1
     \use:n {#2}
-    \clist_map_variable_aux:Nnw #1 {#2}
+    \@@_map_variable:Nnw #1 {#2}
   }
 \cs_generate_variant:Nn \clist_map_variable:NNn { c }
 %    \end{macrocode}
@@ -1331,293 +1302,99 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\clist_map_break:}
-% \begin{macro}{\clist_map_break:n}
-%   The break statements are simply copies.
+% \begin{macro}{\clist_map_break:, \clist_map_break:n}
+%   The break statements use the general \cs{__prg_map_break:Nn} mechanism.
 %    \begin{macrocode}
-\cs_new_eq:NN \clist_map_break:  \prg_map_break:
-\cs_new_eq:NN \clist_map_break:n \prg_map_break:n
+\cs_new_nopar:Npn \clist_map_break:
+  { \__prg_map_break:Nn \clist_map_break: { } }
+\cs_new_nopar:Npn \clist_map_break:n
+  { \__prg_map_break:Nn \clist_map_break: }
 %    \end{macrocode}
 % \end{macro}
-% \end{macro}
-%
-% \subsection{Viewing comma lists}
-%
-% \begin{macro}{\clist_show:N, \clist_show:c}
-% \begin{macro}{\clist_show:n}
-%   Apply the general \cs{msg_aux_show:Nnx}. In the case
-%   of an \texttt{n}-type comma-list, first store it
-%   in a scratch variable, then show that variable,
-%   omitting its name from the $4$-th argument.
-%    \begin{macrocode}
-\cs_new_protected:Npn \clist_show:N #1
-  {
-    \msg_aux_show:Nnx
-      #1
-      { clist }
-      { \clist_map_function:NN #1 \msg_aux_show:n }
-  }
-\cs_new_protected:Npn \clist_show:n #1
-  {
-    \clist_set:Nn \l_clist_internal_clist {#1}
-    \msg_aux_show:Nnx
-      \l_clist_internal_clist
-      { clist }
-      { \clist_map_function:NN \l_clist_internal_clist \msg_aux_show:n }
-  }
-\cs_generate_variant:Nn \clist_show:N { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Scratch comma lists}
-%
-% \begin{variable}{\l_tmpa_clist, \l_tmpb_clist}
-% \begin{variable}{\g_tmpa_clist, \g_tmpb_clist}
-%   Temporary comma list variables.
-%    \begin{macrocode}
-\clist_new:N \l_tmpa_clist
-\clist_new:N \l_tmpb_clist
-\clist_new:N \g_tmpa_clist
-\clist_new:N \g_tmpb_clist
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \subsection{Experimental functions}
-%
-% \begin{macro}{\clist_length:N, \clist_length:c}
-% \begin{macro}{\clist_length:n}
-% \begin{macro}[aux]{\clist_length_aux:w}
+% 
+% \begin{macro}{\clist_count:N, \clist_count:c, \clist_count:n}
+% \begin{macro}[aux]{\@@_count:n}
+% \begin{macro}[aux]{\@@_count:w}
 %   Counting the items in a comma list is done using the same approach as for
-%   other length functions: turn each entry into a \texttt{+1} then use
+%   other token count functions: turn each entry into a \texttt{+1} then use
 %   integer evaluation to actually do the mathematics.
 %   In the case of an \texttt{n}-type comma-list, we could of course use
 %   \cs{clist_map_function:nN}, but that is very slow, because it carefully
 %   removes spaces. Instead, we loop manually, and skip blank items
 %   (but not |{}|, hence the extra spaces).
 %    \begin{macrocode}
-\cs_new:Npn \clist_length:N #1
+\cs_new:Npn \clist_count:N #1
   {
     \int_eval:n
       {
         0
-        \clist_map_function:NN #1 \clist_length_aux:n
+        \clist_map_function:NN #1 \@@_count:n
       }
   }
-\cs_new:Npn \clist_length_aux:n #1 { +1 }
-\cs_new:Npx \clist_length:n #1
+\cs_generate_variant:Nn \clist_count:N { c }
+\cs_new:Npx \clist_count:n #1
   {
     \exp_not:N \int_eval:n
       {
         0
-        \exp_not:N \clist_length_n_aux:w \c_space_tl
+        \exp_not:N \@@_count:w \c_space_tl
         #1 \exp_not:n { , \q_recursion_tail , \q_recursion_stop }
       }
   }
-\cs_new:Npx \clist_length_n_aux:w #1 ,
+\cs_new:Npn \@@_count:n #1 { + \c_one }
+\cs_new:Npx \@@_count:w #1 ,
   {
     \exp_not:n { \exp_args:Nf \quark_if_recursion_tail_stop:n } {#1}
     \exp_not:N \tl_if_blank:nF {#1} { + \c_one }
-    \exp_not:N \clist_length_n_aux:w \c_space_tl
+    \exp_not:N \@@_count:w \c_space_tl
   }
-\cs_generate_variant:Nn \clist_length:N { c }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\clist_item:Nn, \clist_item:cn}
-% \begin{macro}[aux]{\clist_item_aux:nnNn}
-% \begin{macro}[aux]{\clist_item_N_loop:nw}
-%   To avoid needing to test the end of the list at each step,
-%   we first compute the \meta{length} of the list. If the item number
-%   is less than $-\meta{length}$ or more than $\meta{length}-1$,
-%   the result is empty. If it is negative, but not less than $-\meta{length}$,
-%   add the \meta{length} to the item number before performing the loop.
-%   The loop itself is very simple, return the item if the counter
-%   reached zero, otherwise, decrease the counter and repeat.
-%    \begin{macrocode}
-\cs_new:Npn \clist_item:Nn #1#2
-  {
-    \exp_args:Nfo \clist_item_aux:nnNn
-      { \clist_length:N #1 }
-      #1
-      \clist_item_N_loop:nw
-      {#2}
-  }
-\cs_new:Npn \clist_item_aux:nnNn #1#2#3#4
-  {
-    \int_compare:nNnTF {#4} < \c_zero
-      {
-        \int_compare:nNnTF {#4} < { - #1 }
-          { \use_none_delimit_by_q_stop:w }
-          { \exp_args:Nf #3 { \int_eval:n { #4 + #1 } } }
-      }
-      {
-        \int_compare:nNnTF {#4} < {#1}
-          { #3 {#4} }
-          { \use_none_delimit_by_q_stop:w }
-      }
-    #2, \q_stop
-  }
-\cs_new:Npn \clist_item_N_loop:nw #1 #2,
-  {
-    \int_compare:nNnTF {#1} = \c_zero
-      { \use_i_delimit_by_q_stop:nw { \exp_not:n {#2} } }
-      { \exp_args:Nf \clist_item_N_loop:nw { \int_eval:n { #1 - 1 } } }
-  }
-\cs_generate_variant:Nn \clist_item:Nn { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\clist_item:nn}
-% \begin{macro}[aux]{
-%     \clist_item_n_aux:nw,
-%     \clist_item_n_loop:nw,
-%     \clist_item_n_end:n,
-%     \clist_item_n_strip:w}
-%   This starts in the same way as \cs{clist_item:Nn} by checking the length
-%   of the comma list. The final item should be space-trimmed before being
-%   brace-stripped, hence we insert a couple of odd-looking
-%   \cs{prg_do_nothing:} to avoid losing braces. Blank items are ignored.
-%    \begin{macrocode}
-\cs_new:Npn \clist_item:nn #1#2
-  {
-    \exp_args:Nf \clist_item_aux:nnNn
-      { \clist_length:n {#1} }
-      {#1}
-      \clist_item_n_aux:nw
-      {#2}
-  }
-\cs_new:Npn \clist_item_n_aux:nw #1
-  { \clist_item_n_loop:nw {#1} \prg_do_nothing: }
-\cs_new:Npn \clist_item_n_loop:nw #1 #2,
-  {
-    \exp_args:No \tl_if_blank:nTF {#2}
-      { \clist_item_n_loop:nw {#1} \prg_do_nothing: }
-      {
-        \int_compare:nNnTF {#1} = \c_zero
-          { \exp_args:No \clist_item_n_end:n {#2} }
-          {
-            \exp_args:Nf \clist_item_n_loop:nw
-              { \int_eval:n { #1 - 1 } }
-              \prg_do_nothing:
-          }
-      }
-  }
-\cs_new:Npn \clist_item_n_end:n #1 #2 \q_stop
-  {
-    \exp_after:wN \exp_after:wN \exp_after:wN \clist_item_n_strip:w
-    \tl_trim_spaces:n {#1} ,
-  }
-\cs_new:Npn \clist_item_n_strip:w #1 , { \exp_not:n {#1} }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
+% \subsection{Viewing comma lists}
 %
-% \begin{macro}
-%   {
-%     \clist_set_from_seq:NN, \clist_set_from_seq:cN,
-%     \clist_set_from_seq:Nc, \clist_set_from_seq:cc
-%   }
-% \UnitTested
-% \begin{macro}
-%   {
-%     \clist_gset_from_seq:NN, \clist_gset_from_seq:cN,
-%     \clist_gset_from_seq:Nc, \clist_gset_from_seq:cc
-%   }
-% \UnitTested
-% \begin{macro}[aux]{\clist_set_from_seq_aux:NNNN}
-% \begin{macro}[aux]{\clist_wrap_item:n}
-%   Setting a comma list from a comma-separated list is done using a simple
-%   mapping. We wrap most items with \cs{exp_not:n}, and a comma. Items which
-%   contain a comma or a space are surrounded by an extra set of braces. The
-%   first comma must be removed, except in the case of an empty comma-list.
+% \begin{macro}{\clist_show:N, \clist_show:c}
+% \begin{macro}{\clist_show:n}
+%   Apply the general \cs{__msg_show_variable:Nnn}. In the case
+%   of an \texttt{n}-type comma-list, first store it
+%   in a scratch variable, then show that variable,
+%   omitting its name from the $4$-th argument.
 %    \begin{macrocode}
-\cs_new_protected:Npn \clist_set_from_seq:NN
-  { \clist_set_from_seq_aux:NNNN \clist_clear:N  \tl_set:Nx  }
-\cs_new_protected:Npn \clist_gset_from_seq:NN
-  { \clist_set_from_seq_aux:NNNN \clist_gclear:N \tl_gset:Nx }
-\cs_new_protected:Npn \clist_set_from_seq_aux:NNNN #1#2#3#4
+\cs_new_protected:Npn \clist_show:N #1
   {
-    \seq_if_empty:NTF #4
-      { #1 #3 }
-      {
-        #2 #3
-          {
-            \exp_last_unbraced:Nf \use_none:n
-              { \seq_map_function:NN #4 \clist_wrap_item:n }
-          }
-      }
+    \__msg_show_variable:Nnn
+      #1
+      { clist }
+      { \clist_map_function:NN #1 \__msg_show_item:n }
   }
-\cs_new:Npn \clist_wrap_item:n #1
+\cs_new_protected:Npn \clist_show:n #1
   {
-    ,
-    \tl_if_empty:oTF { \clist_set_from_seq_aux:w #1 ~ , #1 ~ }
-      { \exp_not:n   {#1}   }
-      { \exp_not:n { {#1} } }
+    \clist_set:Nn \l_@@_internal_clist {#1}
+    \__msg_show_variable:Nnn
+      \l_@@_internal_clist
+      { clist }
+      { \clist_map_function:NN \l_@@_internal_clist \__msg_show_item:n }
   }
-\cs_new:Npn \clist_set_from_seq_aux:w #1 , #2 ~ { }
-\cs_generate_variant:Nn \clist_set_from_seq:NN  {     Nc }
-\cs_generate_variant:Nn \clist_set_from_seq:NN  { c , cc }
-\cs_generate_variant:Nn \clist_gset_from_seq:NN {     Nc }
-\cs_generate_variant:Nn \clist_gset_from_seq:NN { c , cc }
+\cs_generate_variant:Nn \clist_show:N { c }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
-% \end{macro}
-% \end{macro}
 %
-% \begin{macro}
-%   {
-%     \clist_const:Nn, \clist_const:cn,
-%     \clist_const:Nx, \clist_const:cx
-%   }
-%   Creating and initializing a constant comma list is done in a way
-%   similar to \cs{clist_set:Nn} and \cs{clist_gset:Nn}, being careful
-%   to strip spaces.
-%    \begin{macrocode}
-\cs_new_protected:Npn \clist_const:Nn #1#2
-  { \tl_const:Nx #1 { \clist_trim_spaces:n {#2} } }
-\cs_generate_variant:Nn \clist_const:Nn { c , Nx , cx }
-%    \end{macrocode}
-% \end{macro}
+% \subsection{Scratch comma lists}
 %
-% \begin{macro}[EXP, pTF]{\clist_if_empty:n}
-% \begin{macro}[aux, EXP]{\clist_if_empty_n_aux:w}
-% \begin{macro}[aux, EXP]{\clist_if_empty_n_aux:wNw}
-%   As usual, we insert a token (here |?|) before grabbing
-%   any argument: this avoids losing braces. The argument
-%   of \cs{tl_if_empty:oTF} is empty if |#1| is |?| followed
-%   by blank spaces (besides, this particular variant of
-%   the emptyness test is optimized). If the item of the
-%   comma list is blank, grab the next one. As soon as one
-%   item is non-blank, exit: the second auxiliary will grab
-%   \cs{prg_return_false:} as |#2|, unless every item in
-%   the comma list was blank and the loop actually got broken
-%   by the trailing |\q_mark \prg_return_false:| item.
+% \begin{variable}{\l_tmpa_clist, \l_tmpb_clist}
+% \begin{variable}{\g_tmpa_clist, \g_tmpb_clist}
+%   Temporary comma list variables.
 %    \begin{macrocode}
-\prg_new_conditional:Npnn \clist_if_empty:n #1 { p , T , F , TF }
-  {
-    \clist_if_empty_n_aux:w ? #1
-    , \q_mark \prg_return_false:
-    , \q_mark \prg_return_true:
-    \q_stop
-  }
-\cs_new:Npn \clist_if_empty_n_aux:w #1 ,
-  {
-    \tl_if_empty:oTF { \use_none:nn #1 ? }
-      { \clist_if_empty_n_aux:w ? }
-      { \clist_if_empty_n_aux:wNw }
-  }
-\cs_new:Npn \clist_if_empty_n_aux:wNw #1 \q_mark #2#3 \q_stop {#2}
+\clist_new:N \l_tmpa_clist
+\clist_new:N \l_tmpb_clist
+\clist_new:N \g_tmpa_clist
+\clist_new:N \g_tmpb_clist
 %    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
+% \end{variable}
+% \end{variable}
 %
 % \subsection{Deprecated interfaces}
 %
@@ -1664,7 +1441,7 @@
 %   }
 %   Since clist items are now always stripped from their surrounding
 %   spaces, it is redundant to provide these functions.
-%   The \cs{clist_trim_spaces:n} function is now internal,
+%   The \cs{@@_trim_spaces:n} function is now internal,
 %   deprecated for use outside the kernel.
 %    \begin{macrocode}
 %<*deprecated>
@@ -1676,6 +1453,38 @@
 %    \end{macrocode}
 % \end{macro}
 %
+% Deprecated on 2012-05-10, for removal by 2012-08-31.
+%
+% \begin{macro}[pTF]
+%   {\clist_if_eq:NN, \clist_if_eq:Nc, \clist_if_eq:cN, \clist_if_eq:cc}
+%   Simple copies from the token list variable material.
+%    \begin{macrocode}
+\prg_new_eq_conditional:NNn \clist__if_eq:NN \tl_if_eq:NN { p , T , F , TF }
+\prg_new_eq_conditional:NNn \clist_if_eq:Nc \tl_if_eq:Nc { p , T , F , TF }
+\prg_new_eq_conditional:NNn \clist_if_eq:cN \tl_if_eq:cN { p , T , F , TF }
+\prg_new_eq_conditional:NNn \clist_if_eq:cc \tl_if_eq:cc { p , T , F , TF }
+%    \end{macrocode}
+% \end{macro}
+% 
+% Deprecated 2012-05-13 for removal by 2012-11-31.
+%  
+% \begin{macro}{\clist_length:N, \clist_length:c, \clist_length:n}
+%    \begin{macrocode}
+\cs_new_eq:NN \clist_length:N \clist_count:N
+\cs_new_eq:NN \clist_length:n \clist_count:c
+\cs_new_eq:NN \clist_length:c \clist_count:n
+%    \end{macrocode}
+% \end{macro}
+%
+% Deprecated 2012-05-19 for removal by 2012-11-31.
+%
+% \begin{macro}{\clist_use:N, \clist_use:c}
+%    \begin{macrocode}
+\cs_new_eq:NN \clist_use:N \tl_use:N
+\cs_new_eq:NN \clist_use:c \tl_use:c
+%    \end{macrocode}
+% \end{macro}
+%
 %    \begin{macrocode}
 %</initex|package>
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx b/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
index 54575bde8ce..b4242b6d8ed 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
@@ -36,8 +36,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3coffins.dtx 3482 2012-03-03 18:48:06Z bruno $
-  {L3 Experimental coffin code layer}
+\GetIdInfo$Id: l3coffins.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Coffin code layer}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -94,10 +94,19 @@
 % \begin{function}[added = 2011-08-17]
 %  {\coffin_set_eq:NN, \coffin_set_eq:Nc, \coffin_set_eq:cN, \coffin_set_eq:cc}
 %   \begin{syntax}
-%    \cs{coffin_set_eq:NN} \meta{coffin1} \meta{coffin2}
+%    \cs{coffin_set_eq:NN} \meta{coffin_1} \meta{coffin_2}
 %   \end{syntax}
-%   Sets both the content and poles of \meta{coffin1} equal to those
-%   of \meta{coffin2} within the current \TeX\ group level.
+%   Sets both the content and poles of \meta{coffin_1} equal to those
+%   of \meta{coffin_2} within the current \TeX\ group level.
+% \end{function}
+%
+% \begin{function}[EXP, pTF, added = 2012-06-20]
+%   {\coffin_if_exist:N, \coffin_if_exist:c}
+%   \begin{syntax}
+%     \cs{coffin_if_exist_p:N} \meta{box}
+%     \cs{coffin_if_exist:NTF} \meta{box} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   Tests whether the \meta{coffin} is currently defined.
 % \end{function}
 %
 % \section{Setting coffin content and poles}
@@ -127,7 +136,7 @@
 %   environment in a coffin.
 % \end{function}
 %
-% \begin{function}[added = 2011-08-17, updated = 2011-09-03]
+% \begin{function}[added = 2011-08-17, updated = 2012-05-22]
 %   {\vcoffin_set:Nnn, \vcoffin_set:cnn}
 %   \begin{syntax}
 %     \cs{vcoffin_set:Nnn} \meta{coffin} \Arg{width} \Arg{material}
@@ -138,7 +147,7 @@
 %   size of the typeset material.
 % \end{function}
 %
-% \begin{function}[added = 2011-09-10]
+% \begin{function}[added = 2011-09-10, updated = 2012-05-22]
 %   {\vcoffin_set:Nnw, \vcoffin_set:cnw, \vcoffin_set_end:}
 %   \begin{syntax}
 %     \cs{vcoffin_set:Nnw} \meta{coffin} \Arg{width} \meta{material} \cs{vcoffin_set_end:}
@@ -180,42 +189,6 @@
 %   the \meta{coffin}.
 % \end{function}
 %
-% \section{Coffin transformations}
-%
-% \begin{function}[added = 2011-09-02]{\coffin_resize:Nnn, \coffin_resize:cnn}
-%   \begin{syntax}
-%     \cs{coffin_resize:Nnn} \meta{coffin} \Arg{width} \Arg{total-height}
-%   \end{syntax}
-%   Resized the \meta{coffin} to \meta{width} and \meta{total-height},
-%   both of which should be given as dimension expressions. These may
-%   include the terms \cs{TotalHeight}, \cs{Height}, \cs{Depth} and
-%   \cs{Width}, which will evaluate to the appropriate dimensions of
-%   the \meta{coffin}.
-%
-%  \textbf{This function is experimental.}
-% \end{function}
-%
-% \begin{function}[added = 2011-09-02]{\coffin_rotate:Nn, \coffin_rotate:cn}
-%   \begin{syntax}
-%     \cs{coffin_rotate:Nn} \meta{coffin} \Arg{angle}
-%   \end{syntax}
-%   Rotates the \meta{coffin} by the given \meta{angle} (given in
-%   degrees counter-clockwise). This process will rotate both the
-%   coffin content and poles. Multiple rotations will not result in
-%   the bounding box of the coffin growing unnecessarily.
-% \end{function}
-%
-% \begin{function}[added = 2011-09-02]{\coffin_scale:Nnn, \coffin_scale:cnn}
-%   \begin{syntax}
-%     \cs{coffin_scale:Nnn} \meta{coffin} \Arg{x-scale} \Arg{y-scale}
-%   \end{syntax}
-%   Scales the \meta{coffin} by a factors \meta{x-scale} and
-%   \meta{y-scale} in the horizontal and vertical directions,
-%   respectively. The two scale factors should be given as real numbers.
-%
-%  \textbf{This function is experimental.}
-% \end{function}
-%
 % \section{Joining and using coffins}
 %
 % \begin{function}
@@ -225,19 +198,19 @@
 %   }
 %   \begin{syntax}
 %     \cs{coffin_attach:NnnNnnnn}
-%     ~~\meta{coffin1} \Arg{coffin1-pole1} \Arg{coffin1-pole2}
-%     ~~\meta{coffin2} \Arg{coffin2-pole1} \Arg{coffin2-pole2}
+%     ~~\meta{coffin_1} \Arg{coffin_1-pole_1} \Arg{coffin_1-pole_2}
+%     ~~\meta{coffin_2} \Arg{coffin_2-pole_1} \Arg{coffin_2-pole_2}
 %     ~~\Arg{x-offset} \Arg{y-offset}
 %   \end{syntax}
 %   This function attaches <coffin_2> to <coffin_1> such that the bounding box
-%   of \meta{coffin1} is not altered, \emph{i.e.}~\meta{coffin2} can
+%   of \meta{coffin_1} is not altered, \emph{i.e.}~\meta{coffin_2} can
 %   protrude outside of the bounding box of the coffin. The alignment
-%   is carried out by first calculating \meta{handle1}, the
-%   point of intersection of \meta{coffin1-pole1} and
-%   \meta{coffin1-pole2}, and \meta{handle2}, the point of intersection
-%   of \meta{coffin2-pole1} and \meta{coffin2-pole2}. \meta{coffin2} is
-%   then attached to \meta{coffin1} such that the relationship between
-%   \meta{handle1} and \meta{handle2} is described by the \meta{x-offset}
+%   is carried out by first calculating \meta{handle_1}, the
+%   point of intersection of \meta{coffin_1-pole_1} and
+%   \meta{coffin_1-pole_2}, and \meta{handle_2}, the point of intersection
+%   of \meta{coffin_2-pole_1} and \meta{coffin_2-pole_2}. \meta{coffin_2} is
+%   then attached to \meta{coffin_1} such that the relationship between
+%   \meta{handle_1} and \meta{handle_2} is described by the \meta{x-offset}
 %   and \meta{y-offset}. The two offsets should be given as dimension
 %   expressions.
 % \end{function}
@@ -249,19 +222,19 @@
 %   }
 %   \begin{syntax}
 %     \cs{coffin_join:NnnNnnnn}
-%     ~~\meta{coffin1} \Arg{coffin1-pole1} \Arg{coffin1-pole2}
-%     ~~\meta{coffin2} \Arg{coffin2-pole1} \Arg{coffin2-pole2}
+%     ~~\meta{coffin_1} \Arg{coffin_1-pole_1} \Arg{coffin_1-pole_2}
+%     ~~\meta{coffin_2} \Arg{coffin_2-pole_1} \Arg{coffin_2-pole_2}
 %     ~~\Arg{x-offset} \Arg{y-offset}
 %   \end{syntax}
 %   This function joins <coffin_2> to <coffin_1> such that the bounding box
-%   of \meta{coffin1} may expand. The new bounding
+%   of \meta{coffin_1} may expand. The new bounding
 %   box will cover the area containing the bounding boxes of the two
 %   original coffins. The alignment is carried out by first calculating
-%   \meta{handle1}, the point of intersection of \meta{coffin1-pole1} and
-%   \meta{coffin1-pole2}, and \meta{handle2}, the point of intersection
-%   of \meta{coffin2-pole1} and \meta{coffin2-pole2}. \meta{coffin2} is
-%   then attached to \meta{coffin1} such that the relationship between
-%   \meta{handle1} and \meta{handle2} is described by the \meta{x-offset}
+%   \meta{handle_1}, the point of intersection of \meta{coffin_1-pole_1} and
+%   \meta{coffin_1-pole_2}, and \meta{handle_2}, the point of intersection
+%   of \meta{coffin_2-pole_1} and \meta{coffin_2-pole_2}. \meta{coffin_2} is
+%   then attached to \meta{coffin_1} such that the relationship between
+%   \meta{handle_1} and \meta{handle_2} is described by the \meta{x-offset}
 %   and \meta{y-offset}. The two offsets should be given as dimension
 %   expressions.
 % \end{function}
@@ -272,7 +245,7 @@
 %     ~~\Arg{x-offset} \Arg{y-offset}
 %   \end{syntax}
 %   Typesetting is carried out by first calculating \meta{handle}, the
-%   point of intersection of \meta{pole1} and \meta{pole2}. The coffin
+%   point of intersection of \meta{pole_1} and \meta{pole_2}. The coffin
 %   is then typeset such that the relationship between the current
 %   reference point in the document and the \meta{handle} is described
 %   by the \meta{x-offset} and \meta{y-offset}. The two offsets should
@@ -310,7 +283,7 @@
 % \section{Coffin diagnostics}
 %
 % \begin{function}[updated = 2011-09-02]
-%   {\coffin_display_handles:cn, \coffin_display_handles:cn}
+%   {\coffin_display_handles:Nn, \coffin_display_handles:cn}
 %   \begin{syntax}
 %     \cs{coffin_display_handles:Nn} \meta{coffin} \Arg{colour}
 %   \end{syntax}
@@ -329,8 +302,8 @@
 %     \cs{coffin_mark_handle:Nnnn} \meta{coffin} \Arg{pole_1} \Arg{pole_2} \Arg{colour}
 %   \end{syntax}
 %   This function first calculates the \meta{handle} for the
-%   \meta{coffin} as defined by the intersection of \meta{pole1} and
-%   \meta{pole2}. It then marks the position of the \meta{handle}
+%   \meta{coffin} as defined by the intersection of \meta{pole_1} and
+%   \meta{pole_2}. It then marks the position of the \meta{handle}
 %   on the \meta{coffin}. The \meta{handle} will be labelled as part of
 %   this process: the location of the \meta{handle} and the label are
 %   both printed in the \meta{colour} specified.
@@ -353,6 +326,19 @@
 %   the later, rather than the absolute values, which determines the
 %   direction of the pole.
 % \end{function}
+% 
+% \subsection{Constants and variables}
+%
+% \begin{variable}{\c_empty_coffin}
+%   A permanently empty coffin.
+% \end{variable}
+% 
+% \begin{variable}[added = 2012-06-19]{\l_tmpa_coffin, \l_tmpb_coffin}
+%   Scratch coffins for local assignment. These are never used by
+%   the kernel code, and so are safe for use with any \LaTeX3-defined
+%   function. However, they may be overwritten by other non-kernel
+%   code and so should only be used for short-term storage.
+% \end{variable}
 %
 % \end{documentation}
 %
@@ -363,183 +349,148 @@
 %    \begin{macrocode}
 %<*initex|package>
 %    \end{macrocode}
+%    
+%    \begin{macrocode}
+%<@@=coffin>
+%    \end{macrocode}
 %
 %    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
 % \subsection{Coffins: data structures and general variables}
 %
-% \begin{variable}{\l_coffin_internal_box}
-% \begin{variable}{\l_coffin_internal_dim}
-% \begin{variable}{\l_coffin_internal_fp}
-% \begin{variable}{\l_coffin_internal_tl}
+% \begin{variable}{\l_@@_internal_box}
+% \begin{variable}{\l_@@_internal_dim}
+% \begin{variable}{\l_@@_internal_tl}
 %   Scratch variables.
 %    \begin{macrocode}
-\box_new:N \l_coffin_internal_box
-\dim_new:N \l_coffin_internal_dim
-\fp_new:N  \l_coffin_internal_fp
-\tl_new:N  \l_coffin_internal_tl
+\box_new:N \l_@@_internal_box
+\dim_new:N \l_@@_internal_dim
+\tl_new:N  \l_@@_internal_tl
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 % \end{variable}
-% \end{variable}
 %
-% \begin{variable}{\c_coffin_corners_prop}
+% \begin{variable}{\c_@@_corners_prop}
 %   The \enquote{corners}; of a coffin define the real content, as
 %   opposed to the \TeX{} bounding box. They all start off in the same
 %   place, of course.
 %    \begin{macrocode}
-\prop_new:N \c_coffin_corners_prop
-\prop_put:Nnn \c_coffin_corners_prop { tl } { { 0 pt } { 0 pt } }
-\prop_put:Nnn \c_coffin_corners_prop { tr } { { 0 pt } { 0 pt } }
-\prop_put:Nnn \c_coffin_corners_prop { bl } { { 0 pt } { 0 pt } }
-\prop_put:Nnn \c_coffin_corners_prop { br } { { 0 pt } { 0 pt } }
+\prop_new:N \c_@@_corners_prop
+\prop_put:Nnn \c_@@_corners_prop { tl } { { 0 pt } { 0 pt } }
+\prop_put:Nnn \c_@@_corners_prop { tr } { { 0 pt } { 0 pt } }
+\prop_put:Nnn \c_@@_corners_prop { bl } { { 0 pt } { 0 pt } }
+\prop_put:Nnn \c_@@_corners_prop { br } { { 0 pt } { 0 pt } }
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\c_coffin_poles_prop}
+% \begin{variable}{\c_@@_poles_prop}
 %   Pole positions are given for horizontal, vertical and reference-point
 %   based values.
 %    \begin{macrocode}
-\prop_new:N \c_coffin_poles_prop
-\tl_set:Nn \l_coffin_internal_tl { { 0 pt } { 0 pt } { 0 pt } { 1000 pt } }
-\prop_put:Nno \c_coffin_poles_prop { l }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { hc } { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { r }  { \l_coffin_internal_tl }
-\tl_set:Nn \l_coffin_internal_tl { { 0 pt } { 0 pt } { 1000 pt } { 0 pt } }
-\prop_put:Nno \c_coffin_poles_prop { b }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { vc } { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { t }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { B }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { H }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { T }  { \l_coffin_internal_tl }
+\prop_new:N \c_@@_poles_prop
+\tl_set:Nn \l_@@_internal_tl { { 0 pt } { 0 pt } { 0 pt } { 1000 pt } }
+\prop_put:Nno \c_@@_poles_prop { l }  { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { hc } { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { r }  { \l_@@_internal_tl }
+\tl_set:Nn \l_@@_internal_tl { { 0 pt } { 0 pt } { 1000 pt } { 0 pt } }
+\prop_put:Nno \c_@@_poles_prop { b }  { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { vc } { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { t }  { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { B }  { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { H }  { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { T }  { \l_@@_internal_tl }
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_calc_a_fp}
-% \begin{variable}{\l_coffin_calc_b_fp}
-% \begin{variable}{\l_coffin_calc_c_fp}
-% \begin{variable}{\l_coffin_calc_d_fp}
-% \begin{variable}{\l_coffin_calc_result_fp}
-%   Used for calculations of intersections and in other internal places.
+% \begin{variable}{\l_@@_slope_x_fp}
+% \begin{variable}{\l_@@_slope_y_fp}
+%   Used for calculations of intersections.
 %    \begin{macrocode}
-\fp_new:N \l_coffin_calc_a_fp
-\fp_new:N \l_coffin_calc_b_fp
-\fp_new:N \l_coffin_calc_c_fp
-\fp_new:N \l_coffin_calc_d_fp
-\fp_new:N \l_coffin_calc_result_fp
+\fp_new:N \l_@@_slope_x_fp
+\fp_new:N \l_@@_slope_y_fp
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
 %
-% \begin{variable}{\l_coffin_error_bool}
+% \begin{variable}{\l_@@_error_bool}
 %   For propagating errors so that parts of the code can work around them.
 %    \begin{macrocode}
-\bool_new:N \l_coffin_error_bool
+\bool_new:N \l_@@_error_bool
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_offset_x_dim}
-% \begin{variable}{\l_coffin_offset_y_dim}
+% \begin{variable}{\l_@@_offset_x_dim}
+% \begin{variable}{\l_@@_offset_y_dim}
 %   The offset between two sets of coffin handles when typesetting. These
 %   values are corrected from those requested in an alignment for the
 %   positions of the handles.
 %    \begin{macrocode}
-\dim_new:N \l_coffin_offset_x_dim
-\dim_new:N \l_coffin_offset_y_dim
+\dim_new:N \l_@@_offset_x_dim
+\dim_new:N \l_@@_offset_y_dim
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_pole_a_tl}
-% \begin{variable}{\l_coffin_pole_b_tl}
+% \begin{variable}{\l_@@_pole_a_tl}
+% \begin{variable}{\l_@@_pole_b_tl}
 %   Needed for finding the intersection of two poles.
 %    \begin{macrocode}
-\tl_new:N \l_coffin_pole_a_tl
-\tl_new:N \l_coffin_pole_b_tl
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_coffin_sin_fp}
-% \begin{variable}{\l_coffin_cos_fp}
-%   Used for rotations to get the sine and cosine values.
-%    \begin{macrocode}
-\fp_new:N \l_coffin_sin_fp
-\fp_new:N \l_coffin_cos_fp
+\tl_new:N \l_@@_pole_a_tl
+\tl_new:N \l_@@_pole_b_tl
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_x_dim}
-% \begin{variable}{\l_coffin_y_dim}
-% \begin{variable}{\l_coffin_x_prime_dim}
-% \begin{variable}{\l_coffin_y_prime_dim}
+% \begin{variable}{\l_@@_x_dim}
+% \begin{variable}{\l_@@_y_dim}
+% \begin{variable}{\l_@@_x_prime_dim}
+% \begin{variable}{\l_@@_y_prime_dim}
 %   For calculating intersections and so forth.
 %    \begin{macrocode}
-\dim_new:N \l_coffin_x_dim
-\dim_new:N \l_coffin_y_dim
-\dim_new:N \l_coffin_x_prime_dim
-\dim_new:N \l_coffin_y_prime_dim
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_coffin_x_fp}
-% \begin{variable}{\l_coffin_y_fp}
-% \begin{variable}{\l_coffin_x_prime_fp}
-% \begin{variable}{\l_coffin_y_prime_fp}
-%   Used for calculations where there are clear $x$- and
-%   $y$-components, for example during vector rotation.
-%    \begin{macrocode}
-\fp_new:N \l_coffin_x_fp
-\fp_new:N \l_coffin_y_fp
-\fp_new:N \l_coffin_x_prime_fp
-\fp_new:N \l_coffin_y_prime_fp
+\dim_new:N \l_@@_x_dim
+\dim_new:N \l_@@_y_dim
+\dim_new:N \l_@@_x_prime_dim
+\dim_new:N \l_@@_y_prime_dim
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 % \end{variable}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_Depth_dim}
-% \begin{variable}{\l_coffin_Height_dim}
-% \begin{variable}{\l_coffin_TotalHeight_dim}
-% \begin{variable}{\l_coffin_Width_dim}
+% \begin{variable}{\l_@@_Depth_dim}
+% \begin{variable}{\l_@@_Height_dim}
+% \begin{variable}{\l_@@_TotalHeight_dim}
+% \begin{variable}{\l_@@_Width_dim}
 %   Dimensions for the various parts of a coffin.
 %    \begin{macrocode}
-\dim_new:N \l_coffin_Depth_dim
-\dim_new:N \l_coffin_Height_dim
-\dim_new:N \l_coffin_TotalHeight_dim
-\dim_new:N \l_coffin_Width_dim
+\dim_new:N \l_@@_Depth_dim
+\dim_new:N \l_@@_Height_dim
+\dim_new:N \l_@@_TotalHeight_dim
+\dim_new:N \l_@@_Width_dim
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 % \end{variable}
 % \end{variable}
 %
-% \begin{macro}{\coffin_saved_Depth:}
-% \begin{macro}{\coffin_saved_Height:}
-% \begin{macro}{\coffin_saved_TotalHeight:}
-% \begin{macro}{\coffin_saved_Width:}
+% \begin{macro}{\@@_saved_Depth:}
+% \begin{macro}{\@@_saved_Height:}
+% \begin{macro}{\@@_saved_TotalHeight:}
+% \begin{macro}{\@@_saved_Width:}
 %   Used to save the meaning of \cs{Depth}, \cs{Height}, \cs{TotalHeight}
 %   and \cs{Width}.
 %    \begin{macrocode}
-\cs_new_nopar:Npn \coffin_saved_Depth:       { }
-\cs_new_nopar:Npn \coffin_saved_Height:      { }
-\cs_new_nopar:Npn \coffin_saved_TotalHeight: { }
-\cs_new_nopar:Npn \coffin_saved_Width:       { }
+\cs_new_nopar:Npn \@@_saved_Depth:       { }
+\cs_new_nopar:Npn \@@_saved_Height:      { }
+\cs_new_nopar:Npn \@@_saved_TotalHeight: { }
+\cs_new_nopar:Npn \@@_saved_Width:       { }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -552,25 +503,40 @@
 % placing material in them. This all relies on the following data
 % structures.
 %
-% \begin{macro}{\coffin_if_exist:NT}
+% \begin{macro}[EXP, pTF]{\coffin_if_exist:N, \coffin_if_exist:c}
 %   Several of the higher-level coffin functions will give multiple
 %   errors if the coffin does not exist. A cleaner way to handle this
 %   is provided here: both the box and the coffin structure are
 %   checked.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_if_exist:NT #1#2
+\prg_new_conditional:Npnn \coffin_if_exist:N #1 { p , T , F , TF }
   {
     \cs_if_exist:NTF #1
       {
-        \cs_if_exist:cTF { l_coffin_poles_ \int_value:w #1 _prop }
-          { #2 }
-          {
-            \msg_kernel_error:nnx { coffins } { unknown-coffin }
-              { \token_to_str:N #1 }
-          }
+        \cs_if_exist:cTF { l_@@_poles_ \__int_value:w #1 _prop }
+          { \prg_return_true: }
+          { \prg_return_false: }
       }
+      { \prg_return_false: }
+  }
+\cs_generate_variant:Nn \coffin_if_exist_p:N { c }
+\cs_generate_variant:Nn \coffin_if_exist:NT  { c }
+\cs_generate_variant:Nn \coffin_if_exist:NF  { c }
+\cs_generate_variant:Nn \coffin_if_exist:NTF { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_if_exist:NT}
+%   Several of the higher-level coffin functions will give multiple
+%   errors if the coffin does not exist. So a wrapper is provided to deal
+%   with this correctly, issuing an error on erroneous use.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_if_exist:NT #1#2
+  {
+    \coffin_if_exist:NTF #1
+      { #2 }
       {
-        \msg_kernel_error:nnx { coffins } { unknown-coffin }
+        \__msg_kernel_error:nnx { kernel } { unknown-coffin }
           { \token_to_str:N #1 }
       }
   }
@@ -583,10 +549,10 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_clear:N #1
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
         \box_clear:N #1
-        \coffin_reset_structure:N #1
+        \@@_reset_structure:N #1
       }
   }
 \cs_generate_variant:Nn \coffin_clear:N { c }
@@ -603,12 +569,12 @@
 \cs_new_protected:Npn \coffin_new:N #1
   {
     \box_new:N #1
-    \prop_clear_new:c { l_coffin_corners_ \int_value:w #1 _prop }
-    \prop_clear_new:c { l_coffin_poles_   \int_value:w #1 _prop }
-    \prop_gset_eq:cN { l_coffin_corners_ \int_value:w #1 _prop }
-      \c_coffin_corners_prop
-    \prop_gset_eq:cN { l_coffin_poles_ \int_value:w #1 _prop }
-      \c_coffin_poles_prop
+    \prop_clear_new:c { l_@@_corners_ \__int_value:w #1 _prop }
+    \prop_clear_new:c { l_@@_poles_   \__int_value:w #1 _prop }
+    \prop_gset_eq:cN { l_@@_corners_ \__int_value:w #1 _prop }
+      \c_@@_corners_prop
+    \prop_gset_eq:cN { l_@@_poles_ \__int_value:w #1 _prop }
+      \c_@@_poles_prop
   }
 \cs_generate_variant:Nn \coffin_new:N { c }
 %    \end{macrocode}
@@ -620,7 +586,7 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \hcoffin_set:Nn #1#2
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
         \hbox_set:Nn #1
           {
@@ -629,9 +595,9 @@
               #2
             \color_group_end:
           }
-        \coffin_reset_structure:N #1
-        \coffin_update_poles:N #1
-        \coffin_update_corners:N #1
+        \@@_reset_structure:N #1
+        \@@_update_poles:N #1
+        \@@_update_corners:N #1
       }
   }
 \cs_generate_variant:Nn \hcoffin_set:Nn { c }
@@ -642,32 +608,38 @@
 %   Setting vertical coffins is more complex. First, the material is
 %   typeset with a given width. The default handles and poles are set as
 %   for a horizontal coffin, before finding the top baseline using a
-%   temporary box.
+%   temporary box. No \cs{color_ensure_current:} here as that would add a
+%   whatsit to the start of the vertical box and mess up the location of the
+%   \texttt{T}~pole (see \emph{\TeX{} by Topic} for discussion of the
+%   \tn{vtop} primitive, used to do the measuring).
 %    \begin{macrocode}
 \cs_new_protected:Npn \vcoffin_set:Nnn #1#2#3
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
         \vbox_set:Nn #1
           {
             \dim_set:Nn \tex_hsize:D {#2}
+%<*package>
+            \dim_set_eq:NN \linewidth   \tex_hsize:D
+            \dim_set_eq:NN \columnwidth \tex_hsize:D
+%</package>
             \color_group_begin:
-              \color_ensure_current:
               #3
             \color_group_end:
           }
-        \coffin_reset_structure:N #1
-        \coffin_update_poles:N #1
-        \coffin_update_corners:N #1
-        \vbox_set_top:Nn \l_coffin_internal_box { \vbox_unpack:N #1 }
-        \coffin_set_pole:Nnx #1 { T }
+        \@@_reset_structure:N #1
+        \@@_update_poles:N #1
+        \@@_update_corners:N #1
+        \vbox_set_top:Nn \l_@@_internal_box { \vbox_unpack:N #1 }
+        \@@_set_pole:Nnx #1 { T }
           {
             { 0 pt }
-            { \dim_eval:n { \box_ht:N #1 - \box_ht:N \l_coffin_internal_box } }
+            { \dim_eval:n { \box_ht:N #1 - \box_ht:N \l_@@_internal_box } }
             { 1000 pt }
             { 0 pt }
           }
-        \box_clear:N \l_coffin_internal_box
+        \box_clear:N \l_@@_internal_box
       }
   }
 \cs_generate_variant:Nn \vcoffin_set:Nnn { c }
@@ -681,16 +653,16 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \hcoffin_set:Nw #1
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
         \hbox_set:Nw #1 \color_group_begin: \color_ensure_current:
           \cs_set_protected_nopar:Npn \hcoffin_set_end:
             {
                 \color_group_end:
               \hbox_set_end:
-              \coffin_reset_structure:N #1
-              \coffin_update_poles:N #1
-              \coffin_update_corners:N #1
+              \@@_reset_structure:N #1
+              \@@_update_poles:N #1
+              \@@_update_corners:N #1
             }
       }
   }
@@ -706,29 +678,33 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \vcoffin_set:Nnw #1#2
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
         \vbox_set:Nw #1
           \dim_set:Nn \tex_hsize:D {#2}
+%<*package>
+            \dim_set_eq:NN \linewidth   \tex_hsize:D
+            \dim_set_eq:NN \columnwidth \tex_hsize:D
+%</package>
           \color_group_begin: \color_ensure_current:
           \cs_set_protected:Npn \vcoffin_set_end:
             {
                 \color_group_end:
               \vbox_set_end:
-              \coffin_reset_structure:N #1
-              \coffin_update_poles:N #1
-              \coffin_update_corners:N #1
-              \vbox_set_top:Nn \l_coffin_internal_box { \vbox_unpack:N #1 }
-              \coffin_set_pole:Nnx #1 { T }
+              \@@_reset_structure:N #1
+              \@@_update_poles:N #1
+              \@@_update_corners:N #1
+              \vbox_set_top:Nn \l_@@_internal_box { \vbox_unpack:N #1 }
+              \@@_set_pole:Nnx #1 { T }
                 {
                   { 0 pt }
                   {
-                    \dim_eval:n { \box_ht:N #1 - \box_ht:N \l_coffin_internal_box }
+                    \dim_eval:n { \box_ht:N #1 - \box_ht:N \l_@@_internal_box }
                   }
                   { 1000 pt }
                   { 0 pt }
                 }
-              \box_clear:N \l_coffin_internal_box
+              \box_clear:N \l_@@_internal_box
             }
       }
   }
@@ -747,10 +723,10 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_set_eq:NN #1#2
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
         \box_set_eq:NN #1 #2
-        \coffin_set_eq_structure:NN #1 #2
+        \@@_set_eq_structure:NN #1 #2
       }
   }
 \cs_generate_variant:Nn \coffin_set_eq:NN { c , Nc , cc }
@@ -758,20 +734,28 @@
 % \end{macro}
 %
 % \begin{variable}{\c_empty_coffin}
-% \begin{variable}{\l_coffin_aligned_coffin}
-% \begin{variable}{\l_coffin_aligned_internal_coffin}
+% \begin{variable}{\l_@@_aligned_coffin}
+% \begin{variable}{\l_@@_aligned_internal_coffin}
 %   Special coffins: these cannot be set up earlier as they need
 %   \cs{coffin_new:N}. The empty coffin is set as a box as the full
 %   coffin-setting system needs some material which is not yet available.
 %    \begin{macrocode}
 \coffin_new:N \c_empty_coffin
 \hbox_set:Nn  \c_empty_coffin { }
-\coffin_new:N \l_coffin_aligned_coffin
-\coffin_new:N \l_coffin_aligned_internal_coffin
+\coffin_new:N \l_@@_aligned_coffin
+\coffin_new:N \l_@@_aligned_internal_coffin
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 % \end{variable}
+% 
+% \begin{variable}{\l_tmpa_coffin, \l_tmpb_coffin}
+%   The usual scratch space.
+%    \begin{macrocode}
+\coffin_new:N \l_tmpa_coffin
+\coffin_new:N \l_tmpb_coffin
+%    \end{macrocode}
+% \end{variable}
 %
 % \subsection{Measuring coffins}
 %
@@ -794,16 +778,16 @@
 %
 % \subsection{Coffins: handle and pole management}
 %
-% \begin{macro}{\coffin_get_pole:NnN}
+% \begin{macro}{\@@_get_pole:NnN}
 %   A simple wrapper around the recovery of a coffin pole, with some
 %   error checking and recovery built-in.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_get_pole:NnN #1#2#3
+\cs_new_protected:Npn \@@_get_pole:NnN #1#2#3
   {
     \prop_get:cnNF
-      { l_coffin_poles_ \int_value:w #1 _prop } {#2} #3
+      { l_@@_poles_ \__int_value:w #1 _prop } {#2} #3
       {
-        \msg_kernel_error:nnxx { coffins } { unknown-coffin-pole }
+        \__msg_kernel_error:nnxx { kernel } { unknown-coffin-pole }
           {#2} { \token_to_str:N #1 }
         \tl_set:Nn #3 { { 0 pt } { 0 pt } { 0 pt } { 0 pt } }
       }
@@ -811,42 +795,42 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\coffin_reset_structure:N}
+% \begin{macro}{\@@_reset_structure:N}
 %   Resetting the structure is a simple copy job.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_reset_structure:N #1
+\cs_new_protected:Npn \@@_reset_structure:N #1
   {
-    \prop_set_eq:cN { l_coffin_corners_ \int_value:w #1 _prop }
-      \c_coffin_corners_prop
-    \prop_set_eq:cN { l_coffin_poles_ \int_value:w #1 _prop }
-      \c_coffin_poles_prop
+    \prop_set_eq:cN { l_@@_corners_ \__int_value:w #1 _prop }
+      \c_@@_corners_prop
+    \prop_set_eq:cN { l_@@_poles_ \__int_value:w #1 _prop }
+      \c_@@_poles_prop
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\coffin_set_eq_structure:NN,\coffin_gset_eq_structure:NN}
+% \begin{macro}{\@@_set_eq_structure:NN,\@@_gset_eq_structure:NN}
 % Setting coffin structures equal simply means copying the property
 % list.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_set_eq_structure:NN #1#2
+\cs_new_protected:Npn \@@_set_eq_structure:NN #1#2
   {
-    \prop_set_eq:cc { l_coffin_corners_ \int_value:w #1 _prop }
-      { l_coffin_corners_ \int_value:w #2 _prop }
-    \prop_set_eq:cc { l_coffin_poles_ \int_value:w #1 _prop }
-      { l_coffin_poles_ \int_value:w #2 _prop }
+    \prop_set_eq:cc { l_@@_corners_ \__int_value:w #1 _prop }
+      { l_@@_corners_ \__int_value:w #2 _prop }
+    \prop_set_eq:cc { l_@@_poles_ \__int_value:w #1 _prop }
+      { l_@@_poles_ \__int_value:w #2 _prop }
   }
-\cs_new_protected:Npn \coffin_gset_eq_structure:NN #1#2
+\cs_new_protected:Npn \@@_gset_eq_structure:NN #1#2
   {
-    \prop_gset_eq:cc { l_coffin_corners_ \int_value:w #1 _prop }
-      { l_coffin_corners_ \int_value:w #2 _prop }
-    \prop_gset_eq:cc { l_coffin_poles_ \int_value:w #1 _prop }
-      { l_coffin_poles_ \int_value:w #2 _prop }
+    \prop_gset_eq:cc { l_@@_corners_ \__int_value:w #1 _prop }
+      { l_@@_corners_ \__int_value:w #2 _prop }
+    \prop_gset_eq:cc { l_@@_poles_ \__int_value:w #1 _prop }
+      { l_@@_poles_ \__int_value:w #2 _prop }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\coffin_set_user_dimensions:N}
-% \begin{macro}{\coffin_end_user_dimensions:}
+% \begin{macro}{\@@_set_user_dimensions:N}
+% \begin{macro}{\@@_end_user_dimensions:}
 % \begin{macro}{\Depth}
 % \begin{macro}{\Height}
 % \begin{macro}{\TotalHeight}
@@ -854,27 +838,27 @@
 %   These make design-level names for the dimensions of a coffin easy to
 %   get at.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_set_user_dimensions:N #1
+\cs_new_protected:Npn \@@_set_user_dimensions:N #1
   {
-    \cs_set_eq:NN \coffin_saved_Height:      \Height
-    \cs_set_eq:NN \coffin_saved_Depth:       \Depth
-    \cs_set_eq:NN \coffin_saved_TotalHeight: \TotalHeight
-    \cs_set_eq:NN \coffin_saved_Width:       \Width
-    \cs_set_eq:NN \Height      \l_coffin_Height_dim
-    \cs_set_eq:NN \Depth       \l_coffin_Depth_dim
-    \cs_set_eq:NN \TotalHeight \l_coffin_TotalHeight_dim
-    \cs_set_eq:NN \Width       \l_coffin_Width_dim
+    \cs_set_eq:NN \@@_saved_Height:      \Height
+    \cs_set_eq:NN \@@_saved_Depth:       \Depth
+    \cs_set_eq:NN \@@_saved_TotalHeight: \TotalHeight
+    \cs_set_eq:NN \@@_saved_Width:       \Width
+    \cs_set_eq:NN \Height      \l_@@_Height_dim
+    \cs_set_eq:NN \Depth       \l_@@_Depth_dim
+    \cs_set_eq:NN \TotalHeight \l_@@_TotalHeight_dim
+    \cs_set_eq:NN \Width       \l_@@_Width_dim
     \dim_set:Nn \Height      { \box_ht:N #1 }
     \dim_set:Nn \Depth       { \box_dp:N #1 }
     \dim_set:Nn \TotalHeight { \box_ht:N #1 + \box_dp:N #1 }
     \dim_set:Nn \Width       { \box_wd:N #1 }
   }
-\cs_new_protected_nopar:Npn \coffin_end_user_dimensions:
+\cs_new_protected_nopar:Npn \@@_end_user_dimensions:
   {
-    \cs_set_eq:NN \Height      \coffin_saved_Height:
-    \cs_set_eq:NN \Depth       \coffin_saved_Depth:
-    \cs_set_eq:NN \TotalHeight \coffin_saved_TotalHeight:
-    \cs_set_eq:NN \Width       \coffin_saved_Width:
+    \cs_set_eq:NN \Height      \@@_saved_Height:
+    \cs_set_eq:NN \Depth       \@@_saved_Depth:
+    \cs_set_eq:NN \TotalHeight \@@_saved_TotalHeight:
+    \cs_set_eq:NN \Width       \@@_saved_Width:
   }
 %    \end{macrocode}
 % \end{macro}
@@ -887,7 +871,7 @@
 % \begin{macro}
 %   {\coffin_set_horizontal_pole:Nnn, \coffin_set_horizontal_pole:cnn}
 % \begin{macro}{\coffin_set_vertical_pole:Nnn,\coffin_set_vertical_pole:cnn}
-% \begin{macro}{\coffin_set_pole:Nnn, \coffin_set_pole:Nnx}
+% \begin{macro}{\@@_set_pole:Nnn, \@@_set_pole:Nnx}
 %   Setting the pole of a coffin at the user/designer level requires a
 %   bit more care. The idea here is to provide a reasonable interface to
 %   the system, then to do the setting with full expansion. The
@@ -895,93 +879,93 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_set_horizontal_pole:Nnn #1#2#3
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
-        \coffin_set_user_dimensions:N #1
-        \coffin_set_pole:Nnx #1 {#2}
+        \@@_set_user_dimensions:N #1
+        \@@_set_pole:Nnx #1 {#2}
           {
             { 0 pt } { \dim_eval:n {#3} }
             { 1000 pt } { 0 pt }
           }
-        \coffin_end_user_dimensions:
+        \@@_end_user_dimensions:
       }
   }
 \cs_new_protected:Npn \coffin_set_vertical_pole:Nnn #1#2#3
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
-        \coffin_set_user_dimensions:N #1
-        \coffin_set_pole:Nnx #1 {#2}
+        \@@_set_user_dimensions:N #1
+        \@@_set_pole:Nnx #1 {#2}
           {
             { \dim_eval:n {#3} } { 0 pt }
             { 0 pt } { 1000 pt }
           }
-        \coffin_end_user_dimensions:
+        \@@_end_user_dimensions:
       }
   }
-\cs_new_protected:Npn \coffin_set_pole:Nnn #1#2#3
-  { \prop_put:cnn { l_coffin_poles_ \int_value:w #1 _prop } {#2} {#3} }
+\cs_new_protected:Npn \@@_set_pole:Nnn #1#2#3
+  { \prop_put:cnn { l_@@_poles_ \__int_value:w #1 _prop } {#2} {#3} }
 \cs_generate_variant:Nn \coffin_set_horizontal_pole:Nnn { c }
 \cs_generate_variant:Nn \coffin_set_vertical_pole:Nnn { c }
-\cs_generate_variant:Nn \coffin_set_pole:Nnn { Nnx }
+\cs_generate_variant:Nn \@@_set_pole:Nnn { Nnx }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\coffin_update_corners:N}
+% \begin{macro}{\@@_update_corners:N}
 %   Updating the corners of a coffin is straight-forward as at this stage
 %   there can be no rotation. So the corners of the content are just those
 %   of the underlying \TeX{} box.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_update_corners:N #1
+\cs_new_protected:Npn \@@_update_corners:N #1
   {
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { tl }
+    \prop_put:cnx { l_@@_corners_ \__int_value:w #1 _prop } { tl }
       { { 0 pt } { \dim_use:N \box_ht:N #1 } }
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { tr }
+    \prop_put:cnx { l_@@_corners_ \__int_value:w #1 _prop } { tr }
       { { \dim_use:N \box_wd:N #1 } { \dim_use:N \box_ht:N #1 } }
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { bl }
+    \prop_put:cnx { l_@@_corners_ \__int_value:w #1 _prop } { bl }
       { { 0 pt } { \dim_eval:n { - \box_dp:N #1 } } }
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { br }
+    \prop_put:cnx { l_@@_corners_ \__int_value:w #1 _prop } { br }
       { { \dim_use:N \box_wd:N #1 } { \dim_eval:n { - \box_dp:N #1 } } }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\coffin_update_poles:N}
+% \begin{macro}{\@@_update_poles:N}
 %   This function is called when a coffin is set, and updates the poles to
 %   reflect the nature of size of the box. Thus this function only alters
 %   poles where the default position is dependent on the size of the box.
 %   It also does not set poles which are relevant only to vertical
 %   coffins.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_update_poles:N #1
+\cs_new_protected:Npn \@@_update_poles:N #1
   {
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { hc }
+    \prop_put:cnx { l_@@_poles_ \__int_value:w #1 _prop } { hc }
       {
         { \dim_eval:n { 0.5 \box_wd:N #1 } }
         { 0 pt } { 0 pt } { 1000 pt }
       }
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { r }
+    \prop_put:cnx { l_@@_poles_ \__int_value:w #1 _prop } { r }
       {
         { \dim_use:N \box_wd:N #1 }
         { 0 pt } { 0 pt } { 1000 pt }
       }
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { vc }
+    \prop_put:cnx { l_@@_poles_ \__int_value:w #1 _prop } { vc }
       {
         { 0 pt }
         { \dim_eval:n { ( \box_ht:N #1 - \box_dp:N #1 ) / 2 } }
         { 1000 pt }
         { 0 pt }
       }
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { t }
+    \prop_put:cnx { l_@@_poles_ \__int_value:w #1 _prop } { t }
       {
         { 0 pt }
         { \dim_use:N \box_ht:N #1 }
         { 1000 pt }
         { 0 pt }
       }
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { b }
+    \prop_put:cnx { l_@@_poles_ \__int_value:w #1 _prop } { b }
       {
         { 0 pt }
         { \dim_eval:n { - \box_dp:N #1 } }
@@ -994,27 +978,27 @@
 %
 % \subsection{Coffins: calculation of pole intersections}
 %
-% \begin{macro}{\coffin_calculate_intersection:Nnn}
-% \begin{macro}[aux]{\coffin_calculate_intersection:nnnnnnnn}
-% \begin{macro}[aux]{\coffin_calculate_intersection_aux:nnnnnN}
+% \begin{macro}{\@@_calculate_intersection:Nnn}
+% \begin{macro}[aux]{\@@_calculate_intersection:nnnnnnnn}
+% \begin{macro}[aux]{\@@_calculate_intersection_aux:nnnnnN}
 %   The lead off in finding intersections is to recover the two poles
 %   and then hand off to the auxiliary for the actual calculation. There
 %   may of course not be an intersection, for which an error trap is
 %   needed.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_calculate_intersection:Nnn #1#2#3
+\cs_new_protected:Npn \@@_calculate_intersection:Nnn #1#2#3
   {
-    \coffin_get_pole:NnN #1 {#2} \l_coffin_pole_a_tl
-    \coffin_get_pole:NnN #1 {#3} \l_coffin_pole_b_tl
-    \bool_set_false:N \l_coffin_error_bool
+    \@@_get_pole:NnN #1 {#2} \l_@@_pole_a_tl
+    \@@_get_pole:NnN #1 {#3} \l_@@_pole_b_tl
+    \bool_set_false:N \l_@@_error_bool
     \exp_last_two_unbraced:Noo
-      \coffin_calculate_intersection:nnnnnnnn
-        \l_coffin_pole_a_tl \l_coffin_pole_b_tl
-    \bool_if:NT \l_coffin_error_bool
+      \@@_calculate_intersection:nnnnnnnn
+        \l_@@_pole_a_tl \l_@@_pole_b_tl
+    \bool_if:NT \l_@@_error_bool
       {
-        \msg_kernel_error:nn { coffins } { no-pole-intersection }
-        \dim_zero:N \l_coffin_x_dim
-        \dim_zero:N \l_coffin_y_dim
+        \__msg_kernel_error:nn { kernel } { no-pole-intersection }
+        \dim_zero:N \l_@@_x_dim
+        \dim_zero:N \l_@@_y_dim
       }
   }
 %    \end{macrocode}
@@ -1029,7 +1013,7 @@
 %   is either horizontal or vertical then one or more of $c$, $d$,
 %   $c'$ and $d'$ will be zero and a special case is needed.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_calculate_intersection:nnnnnnnn
+\cs_new_protected:Npn \@@_calculate_intersection:nnnnnnnn
   #1#2#3#4#5#6#7#8
   {
     \dim_compare:nNnTF {#3} = { \c_zero_dim }
@@ -1039,9 +1023,9 @@
 %   second pole: if it is also vertical then there is an error.
 %    \begin{macrocode}
       {
-        \dim_set:Nn \l_coffin_x_dim {#1}
+        \dim_set:Nn \l_@@_x_dim {#1}
         \dim_compare:nNnTF {#7} = \c_zero_dim
-          { \bool_set_true:N \l_coffin_error_bool }
+          { \bool_set_true:N \l_@@_error_bool }
 %    \end{macrocode}
 %   The second pole may still be horizontal, in which case the
 %   $y$-component of the intersection will be $b'$. If not,
@@ -1053,10 +1037,10 @@
 %    \begin{macrocode}
           {
             \dim_compare:nNnTF {#8} = \c_zero_dim
-              { \dim_set:Nn \l_coffin_y_dim {#6} }
+              { \dim_set:Nn \l_@@_y_dim {#6} }
               {
-                \coffin_calculate_intersection_aux:nnnnnN
-                  {#1} {#5} {#6} {#7} {#8} \l_coffin_y_dim
+                \@@_calculate_intersection_aux:nnnnnN
+                  {#1} {#5} {#6} {#7} {#8} \l_@@_y_dim
               }
           }
       }
@@ -1068,12 +1052,12 @@
       {
         \dim_compare:nNnTF {#4} = \c_zero_dim
           {
-            \dim_set:Nn \l_coffin_y_dim {#2}
+            \dim_set:Nn \l_@@_y_dim {#2}
             \dim_compare:nNnTF {#8} = { \c_zero_dim }
-              { \bool_set_true:N \l_coffin_error_bool }
+              { \bool_set_true:N \l_@@_error_bool }
               {
                 \dim_compare:nNnTF {#7} = \c_zero_dim
-                  { \dim_set:Nn \l_coffin_x_dim {#5} }
+                  { \dim_set:Nn \l_@@_x_dim {#5} }
 %    \end{macrocode}
 %   The formula for the case where the second pole is neither horizontal
 %   nor vertical is
@@ -1083,8 +1067,8 @@
 %   which is again handled by the same auxiliary.
 %    \begin{macrocode}
                   {
-                    \coffin_calculate_intersection_aux:nnnnnN
-                      {#2} {#6} {#5} {#8} {#7} \l_coffin_x_dim
+                    \@@_calculate_intersection_aux:nnnnnN
+                      {#2} {#6} {#5} {#8} {#7} \l_@@_x_dim
                   }
               }
           }
@@ -1097,32 +1081,30 @@
           {
             \dim_compare:nNnTF {#7} = \c_zero_dim
               {
-                \dim_set:Nn \l_coffin_x_dim {#5}
-                \coffin_calculate_intersection_aux:nnnnnN
-                  {#5} {#1} {#2} {#3} {#4} \l_coffin_y_dim
+                \dim_set:Nn \l_@@_x_dim {#5}
+                \@@_calculate_intersection_aux:nnnnnN
+                  {#5} {#1} {#2} {#3} {#4} \l_@@_y_dim
               }
               {
                 \dim_compare:nNnTF {#8} = \c_zero_dim
                   {
-                    \dim_set:Nn \l_coffin_x_dim {#6}
-                    \coffin_calculate_intersection_aux:nnnnnN
-                      {#6} {#2} {#1} {#4} {#3} \l_coffin_x_dim
+                    \dim_set:Nn \l_@@_x_dim {#6}
+                    \@@_calculate_intersection_aux:nnnnnN
+                      {#6} {#2} {#1} {#4} {#3} \l_@@_x_dim
                   }
 %    \end{macrocode}
 %   If none of the special cases apply then there is still a need to
 %   check that there is a unique intersection between the two pole. This
 %   is the case if they have different slopes.
 %    \begin{macrocode}
-                {
-                    \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#3}
-                    \fp_set_from_dim:Nn \l_coffin_calc_b_fp {#4}
-                    \fp_set_from_dim:Nn \l_coffin_calc_c_fp {#7}
-                    \fp_set_from_dim:Nn \l_coffin_calc_d_fp {#8}
-                    \fp_div:Nn \l_coffin_calc_b_fp \l_coffin_calc_a_fp
-                    \fp_div:Nn \l_coffin_calc_d_fp \l_coffin_calc_c_fp
+                  {
+                    \fp_set:Nn \l_@@_slope_x_fp
+                      { \dim_to_fp:n {#4} / \dim_to_fp:n {#3} }
+                    \fp_set:Nn \l_@@_slope_y_fp
+                      { \dim_to_fp:n {#8} / \dim_to_fp:n {#7} }
                     \fp_compare:nNnTF
-                      \l_coffin_calc_b_fp = \l_coffin_calc_d_fp
-                      { \bool_set_true:N \l_coffin_error_bool }
+                      \l_@@_slope_x_fp = \l_@@_slope_y_fp
+                      { \bool_set_true:N \l_@@_error_bool }
 %    \end{macrocode}
 %   All of the tests pass, so there is the full complexity of the
 %   calculation:
@@ -1137,29 +1119,23 @@
 %   $x$-position.
 %    \begin{macrocode}
                       {
-                        \fp_set_from_dim:Nn \l_coffin_calc_result_fp {#6}
-                        \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#2}
-                        \fp_sub:Nn \l_coffin_calc_result_fp
-                          { \l_coffin_calc_a_fp }
-                        \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#1}
-                        \fp_mul:Nn \l_coffin_calc_a_fp
-                          { \l_coffin_calc_b_fp }
-                        \fp_add:Nn \l_coffin_calc_result_fp
-                          { \l_coffin_calc_a_fp }
-                        \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#5}
-                        \fp_mul:Nn \l_coffin_calc_a_fp
-                          { \l_coffin_calc_d_fp }
-                        \fp_sub:Nn \l_coffin_calc_result_fp
-                          { \l_coffin_calc_a_fp }
-                        \fp_sub:Nn \l_coffin_calc_b_fp
-                          { \l_coffin_calc_d_fp }
-                        \fp_div:Nn \l_coffin_calc_result_fp
-                          { \l_coffin_calc_b_fp }
-                        \dim_set:Nn \l_coffin_x_dim
-                          { \fp_to_dim:N \l_coffin_calc_result_fp }
-                        \coffin_calculate_intersection_aux:nnnnnN
-                          { \l_coffin_x_dim }
-                          {#5} {#6} {#8} {#7} \l_coffin_y_dim
+                        \dim_set:Nn \l_@@_x_dim
+                          {
+                            \fp_to_dim:n
+                              {
+                                (
+                                      \dim_to_fp:n {#1} * \l_@@_slope_x_fp
+                                  - ( \dim_to_fp:n {#5} * \l_@@_slope_y_fp )
+                                  -   \dim_to_fp:n {#2}
+                                  +   \dim_to_fp:n {#6}
+                                )
+                                /
+                                ( \l_@@_slope_x_fp - \l_@@_slope_y_fp )
+                            }
+                          }
+                        \@@_calculate_intersection_aux:nnnnnN
+                          { \l_@@_x_dim }
+                          {#5} {#6} {#8} {#7} \l_@@_y_dim
                       }
                   }
               }
@@ -1170,24 +1146,23 @@
 %   The formula for finding the intersection point is in most cases the
 %   same. The formula here is
 %   \[
-%     \#6 = \frac{\#5}{\#4} \left ( \#1 - \#2 \right ) + \#3
+%     \#6 = \#4 \cdot \left( \frac { \#1 - \#2 } { \#5 } \right)\#3
 %   \]
 %   Thus |#4| and |#5| should be the directions of the pole while
 %   |#2| and |#3| are co-ordinates.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_calculate_intersection_aux:nnnnnN
-  #1#2#3#4#5#6
+\cs_new_protected:Npn \@@_calculate_intersection_aux:nnnnnN #1#2#3#4#5#6
   {
-    \fp_set_from_dim:Nn \l_coffin_calc_result_fp {#1}
-    \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#2}
-    \fp_set_from_dim:Nn \l_coffin_calc_b_fp {#3}
-    \fp_set_from_dim:Nn \l_coffin_calc_c_fp {#4}
-    \fp_set_from_dim:Nn \l_coffin_calc_d_fp {#5}
-    \fp_sub:Nn \l_coffin_calc_result_fp { \l_coffin_calc_a_fp }
-    \fp_div:Nn \l_coffin_calc_result_fp { \l_coffin_calc_d_fp }
-    \fp_mul:Nn \l_coffin_calc_result_fp { \l_coffin_calc_c_fp }
-    \fp_add:Nn \l_coffin_calc_result_fp { \l_coffin_calc_b_fp }
-    \dim_set:Nn #6 { \fp_to_dim:N \l_coffin_calc_result_fp }
+    \dim_set:Nn #6
+      {
+        \fp_to_dim:n
+          {
+            \dim_to_fp:n {#4} *
+            ( \dim_to_fp:n {#1} - \dim_to_fp:n {#2} ) /
+            \dim_to_fp:n {#5}
+            + \dim_to_fp:n {#3}
+          }
+      }
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1209,8 +1184,8 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_join:NnnNnnnn #1#2#3#4#5#6#7#8
   {
-    \coffin_align:NnnNnnnnN
-      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_coffin_aligned_coffin
+    \@@_align:NnnNnnnnN
+      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_@@_aligned_coffin
 %    \end{macrocode}
 %   Correct the placement of the reference point. If the $x$-offset
 %   is negative then the reference point of the second box is to the left
@@ -1219,46 +1194,46 @@
 %   than the sum of the $x$-offset and the width of the second box.
 %   So a second kern may be needed.
 %    \begin{macrocode}
-    \hbox_set:Nn \l_coffin_aligned_coffin
+    \hbox_set:Nn \l_@@_aligned_coffin
       {
-        \dim_compare:nNnT { \l_coffin_offset_x_dim } < \c_zero_dim
-          { \tex_kern:D -\l_coffin_offset_x_dim }
-        \hbox_unpack:N \l_coffin_aligned_coffin
-        \dim_set:Nn \l_coffin_internal_dim
-          { \l_coffin_offset_x_dim - \box_wd:N #1 + \box_wd:N #4 }
-        \dim_compare:nNnT \l_coffin_internal_dim < \c_zero_dim
-          { \tex_kern:D -\l_coffin_internal_dim }
+        \dim_compare:nNnT { \l_@@_offset_x_dim } < \c_zero_dim
+          { \tex_kern:D -\l_@@_offset_x_dim }
+        \hbox_unpack:N \l_@@_aligned_coffin
+        \dim_set:Nn \l_@@_internal_dim
+          { \l_@@_offset_x_dim - \box_wd:N #1 + \box_wd:N #4 }
+        \dim_compare:nNnT \l_@@_internal_dim < \c_zero_dim
+          { \tex_kern:D -\l_@@_internal_dim }
       }
 %    \end{macrocode}
 %   The coffin structure is reset, and the corners are cleared: only
 %   those from the two parent coffins are needed.
 %    \begin{macrocode}
-   \coffin_reset_structure:N \l_coffin_aligned_coffin
+   \@@_reset_structure:N \l_@@_aligned_coffin
     \prop_clear:c
-      {  l_coffin_corners_ \int_value:w \l_coffin_aligned_coffin _ prop }
-    \coffin_update_poles:N \l_coffin_aligned_coffin
+      {  l_@@_corners_ \__int_value:w \l_@@_aligned_coffin _ prop }
+    \@@_update_poles:N \l_@@_aligned_coffin
 %    \end{macrocode}
 %   The structures of the parent coffins are now transferred to the new
 %   coffin, which requires that the appropriate offsets are applied. That
 %   will then depend on whether any shift was needed.
 %    \begin{macrocode}
-    \dim_compare:nNnTF \l_coffin_offset_x_dim < \c_zero_dim
+    \dim_compare:nNnTF \l_@@_offset_x_dim < \c_zero_dim
       {
-        \coffin_offset_poles:Nnn #1 { -\l_coffin_offset_x_dim } { 0 pt }
-        \coffin_offset_poles:Nnn #4 { 0 pt } { \l_coffin_offset_y_dim }
-        \coffin_offset_corners:Nnn #1 { -\l_coffin_offset_x_dim } { 0 pt }
-        \coffin_offset_corners:Nnn #4 { 0 pt } { \l_coffin_offset_y_dim }
+        \@@_offset_poles:Nnn #1 { -\l_@@_offset_x_dim } { 0 pt }
+        \@@_offset_poles:Nnn #4 { 0 pt } { \l_@@_offset_y_dim }
+        \@@_offset_corners:Nnn #1 { -\l_@@_offset_x_dim } { 0 pt }
+        \@@_offset_corners:Nnn #4 { 0 pt } { \l_@@_offset_y_dim }
       }
       {
-        \coffin_offset_poles:Nnn #1 { 0 pt } { 0 pt }
-        \coffin_offset_poles:Nnn #4
-          { \l_coffin_offset_x_dim } { \l_coffin_offset_y_dim }
-        \coffin_offset_corners:Nnn #1 { 0 pt } { 0 pt }
-        \coffin_offset_corners:Nnn #4
-          { \l_coffin_offset_x_dim } { \l_coffin_offset_y_dim }
+        \@@_offset_poles:Nnn #1 { 0 pt } { 0 pt }
+        \@@_offset_poles:Nnn #4
+          { \l_@@_offset_x_dim } { \l_@@_offset_y_dim }
+        \@@_offset_corners:Nnn #1 { 0 pt } { 0 pt }
+        \@@_offset_corners:Nnn #4
+          { \l_@@_offset_x_dim } { \l_@@_offset_y_dim }
       }
-    \coffin_update_vertical_poles:NNN #1 #4 \l_coffin_aligned_coffin
-    \coffin_set_eq:NN #1 \l_coffin_aligned_coffin
+    \@@_update_vertical_poles:NNN #1 #4 \l_@@_aligned_coffin
+    \coffin_set_eq:NN #1 \l_@@_aligned_coffin
   }
 \cs_generate_variant:Nn \coffin_join:NnnNnnnn { c , Nnnc , cnnc }
 %    \end{macrocode}
@@ -1278,37 +1253,37 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_attach:NnnNnnnn #1#2#3#4#5#6#7#8
   {
-    \coffin_align:NnnNnnnnN
-      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_coffin_aligned_coffin
-    \box_set_ht:Nn \l_coffin_aligned_coffin { \box_ht:N #1 }
-    \box_set_dp:Nn \l_coffin_aligned_coffin { \box_dp:N #1 }
-    \box_set_wd:Nn \l_coffin_aligned_coffin { \box_wd:N #1 }
-    \coffin_reset_structure:N \l_coffin_aligned_coffin
+    \@@_align:NnnNnnnnN
+      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_@@_aligned_coffin
+    \box_set_ht:Nn \l_@@_aligned_coffin { \box_ht:N #1 }
+    \box_set_dp:Nn \l_@@_aligned_coffin { \box_dp:N #1 }
+    \box_set_wd:Nn \l_@@_aligned_coffin { \box_wd:N #1 }
+    \@@_reset_structure:N \l_@@_aligned_coffin
     \prop_set_eq:cc
-      { l_coffin_corners_ \int_value:w \l_coffin_aligned_coffin _prop }
-      { l_coffin_corners_ \int_value:w #1 _prop }
-    \coffin_update_poles:N  \l_coffin_aligned_coffin
-    \coffin_offset_poles:Nnn #1 { 0 pt } { 0 pt }
-    \coffin_offset_poles:Nnn #4
-      { \l_coffin_offset_x_dim } { \l_coffin_offset_y_dim }
-    \coffin_update_vertical_poles:NNN #1 #4 \l_coffin_aligned_coffin
-    \coffin_set_eq:NN #1 \l_coffin_aligned_coffin
+      { l_@@_corners_ \__int_value:w \l_@@_aligned_coffin _prop }
+      { l_@@_corners_ \__int_value:w #1 _prop }
+    \@@_update_poles:N  \l_@@_aligned_coffin
+    \@@_offset_poles:Nnn #1 { 0 pt } { 0 pt }
+    \@@_offset_poles:Nnn #4
+      { \l_@@_offset_x_dim } { \l_@@_offset_y_dim }
+    \@@_update_vertical_poles:NNN #1 #4 \l_@@_aligned_coffin
+    \coffin_set_eq:NN #1 \l_@@_aligned_coffin
   }
 \cs_new_protected:Npn \coffin_attach_mark:NnnNnnnn #1#2#3#4#5#6#7#8
   {
-    \coffin_align:NnnNnnnnN
-      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_coffin_aligned_coffin
-    \box_set_ht:Nn \l_coffin_aligned_coffin { \box_ht:N #1 }
-    \box_set_dp:Nn \l_coffin_aligned_coffin { \box_dp:N #1 }
-    \box_set_wd:Nn \l_coffin_aligned_coffin { \box_wd:N #1 }
-    \box_set_eq:NN #1 \l_coffin_aligned_coffin
+    \@@_align:NnnNnnnnN
+      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_@@_aligned_coffin
+    \box_set_ht:Nn \l_@@_aligned_coffin { \box_ht:N #1 }
+    \box_set_dp:Nn \l_@@_aligned_coffin { \box_dp:N #1 }
+    \box_set_wd:Nn \l_@@_aligned_coffin { \box_wd:N #1 }
+    \box_set_eq:NN #1 \l_@@_aligned_coffin
   }
 \cs_generate_variant:Nn \coffin_attach:NnnNnnnn { c , Nnnc , cnnc }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\coffin_align:NnnNnnnnN}
+% \begin{macro}{\@@_align:NnnNnnnnN}
 %   The internal function aligns the two coffins into a third one, but
 %   performs no corrections on the resulting coffin poles. The process
 %   begins by finding the points of intersection for the poles for each
@@ -1319,30 +1294,30 @@
 %   input coffins. The default poles are then set up, but the final result
 %   will depend on how the bounding box is being handled.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_align:NnnNnnnnN #1#2#3#4#5#6#7#8#9
+\cs_new_protected:Npn \@@_align:NnnNnnnnN #1#2#3#4#5#6#7#8#9
   {
-    \coffin_calculate_intersection:Nnn #4 {#5} {#6}
-    \dim_set:Nn \l_coffin_x_prime_dim { \l_coffin_x_dim }
-    \dim_set:Nn \l_coffin_y_prime_dim { \l_coffin_y_dim }
-    \coffin_calculate_intersection:Nnn #1 {#2} {#3}
-    \dim_set:Nn \l_coffin_offset_x_dim
-      { \l_coffin_x_dim - \l_coffin_x_prime_dim + #7 }
-    \dim_set:Nn \l_coffin_offset_y_dim
-      { \l_coffin_y_dim - \l_coffin_y_prime_dim + #8 }
-    \hbox_set:Nn \l_coffin_aligned_internal_coffin
+    \@@_calculate_intersection:Nnn #4 {#5} {#6}
+    \dim_set:Nn \l_@@_x_prime_dim { \l_@@_x_dim }
+    \dim_set:Nn \l_@@_y_prime_dim { \l_@@_y_dim }
+    \@@_calculate_intersection:Nnn #1 {#2} {#3}
+    \dim_set:Nn \l_@@_offset_x_dim
+      { \l_@@_x_dim - \l_@@_x_prime_dim + #7 }
+    \dim_set:Nn \l_@@_offset_y_dim
+      { \l_@@_y_dim - \l_@@_y_prime_dim + #8 }
+    \hbox_set:Nn \l_@@_aligned_internal_coffin
       {
         \box_use:N #1
         \tex_kern:D -\box_wd:N #1
-        \tex_kern:D \l_coffin_offset_x_dim
-        \box_move_up:nn { \l_coffin_offset_y_dim } { \box_use:N #4 }
+        \tex_kern:D \l_@@_offset_x_dim
+        \box_move_up:nn { \l_@@_offset_y_dim } { \box_use:N #4 }
       }
-    \coffin_set_eq:NN #9 \l_coffin_aligned_internal_coffin
+    \coffin_set_eq:NN #9 \l_@@_aligned_internal_coffin
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\coffin_offset_poles:Nnn}
-% \begin{macro}[aux]{\coffin_offset_pole:Nnnnnnn}
+% \begin{macro}{\@@_offset_poles:Nnn}
+% \begin{macro}[aux]{\@@_offset_pole:Nnnnnnn}
 %   Transferring structures from one coffin to another requires that the
 %   positions are updated by the offset between the two coffins. This is
 %   done by mapping to the property list of the source coffins, moving
@@ -1353,22 +1328,22 @@
 %   or handle names, and that multiple alignments do not result in a
 %   whole set of values.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_offset_poles:Nnn #1#2#3
+\cs_new_protected:Npn \@@_offset_poles:Nnn #1#2#3
   {
-    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-      { \coffin_offset_pole:Nnnnnnn #1 {##1} ##2 {#2} {#3} }
+    \prop_map_inline:cn { l_@@_poles_ \__int_value:w #1 _prop }
+      { \@@_offset_pole:Nnnnnnn #1 {##1} ##2 {#2} {#3} }
   }
-\cs_new_protected:Npn \coffin_offset_pole:Nnnnnnn #1#2#3#4#5#6#7#8
+\cs_new_protected:Npn \@@_offset_pole:Nnnnnnn #1#2#3#4#5#6#7#8
   {
-    \dim_set:Nn \l_coffin_x_dim { #3 + #7 }
-    \dim_set:Nn \l_coffin_y_dim { #4 + #8 }
+    \dim_set:Nn \l_@@_x_dim { #3 + #7 }
+    \dim_set:Nn \l_@@_y_dim { #4 + #8 }
     \tl_if_in:nnTF {#2} { - }
-      { \tl_set:Nn \l_coffin_internal_tl { {#2} } }
-      { \tl_set:Nn \l_coffin_internal_tl { { #1 - #2 } } }
-    \exp_last_unbraced:NNo \coffin_set_pole:Nnx \l_coffin_aligned_coffin
-      { \l_coffin_internal_tl }
+      { \tl_set:Nn \l_@@_internal_tl { {#2} } }
+      { \tl_set:Nn \l_@@_internal_tl { { #1 - #2 } } }
+    \exp_last_unbraced:NNo \@@_set_pole:Nnx \l_@@_aligned_coffin
+      { \l_@@_internal_tl }
       {
-        { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim }
+        { \dim_use:N \l_@@_x_dim } { \dim_use:N \l_@@_y_dim }
         {#5} {#6}
       }
   }
@@ -1376,21 +1351,21 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\coffin_offset_corners:Nnn}
-% \begin{macro}[aux]{\coffin_offset_corners:Nnnnn}
+% \begin{macro}{\@@_offset_corners:Nnn}
+% \begin{macro}[aux]{\@@_offset_corner:Nnnnn}
 %   Saving the offset corners of a coffin is very similar, except that
 %   there is no need to worry about naming: every corner can be saved
 %   here as order is unimportant.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_offset_corners:Nnn #1#2#3
+\cs_new_protected:Npn \@@_offset_corners:Nnn #1#2#3
   {
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_offset_corner:Nnnnn #1 {##1} ##2 {#2} {#3} }
+    \prop_map_inline:cn { l_@@_corners_ \__int_value:w #1 _prop }
+      { \@@_offset_corner:Nnnnn #1 {##1} ##2 {#2} {#3} }
   }
-\cs_new_protected:Npn \coffin_offset_corner:Nnnnn #1#2#3#4#5#6
+\cs_new_protected:Npn \@@_offset_corner:Nnnnn #1#2#3#4#5#6
   {
     \prop_put:cnx
-      { l_coffin_corners_ \int_value:w \l_coffin_aligned_coffin _prop }
+      { l_@@_corners_ \__int_value:w \l_@@_aligned_coffin _prop }
       { #1 - #2 }
       {
         { \dim_eval:n { #3 + #5 } }
@@ -1401,46 +1376,46 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\coffin_update_vertical_poles:NNN}
-% \begin{macro}[aux]{\coffin_update_T:nnnnnnnnN}
-% \begin{macro}[aux]{\coffin_update_B:nnnnnnnnN}
+% \begin{macro}{\@@_update_vertical_poles:NNN}
+% \begin{macro}[aux]{\@@_update_T:nnnnnnnnN}
+% \begin{macro}[aux]{\@@_update_B:nnnnnnnnN}
 %   The \texttt{T} and \texttt{B} poles will need to be recalculated
 %   after alignment. These functions find the larger absolute value for
 %   the poles, but this is of course only logical when the poles are
 %   horizontal.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_update_vertical_poles:NNN #1#2#3
+\cs_new_protected:Npn \@@_update_vertical_poles:NNN #1#2#3
   {
-    \coffin_get_pole:NnN #3 { #1 -T } \l_coffin_pole_a_tl
-    \coffin_get_pole:NnN #3 { #2 -T } \l_coffin_pole_b_tl
-    \exp_last_two_unbraced:Noo \coffin_update_T:nnnnnnnnN
-      \l_coffin_pole_a_tl \l_coffin_pole_b_tl #3
-    \coffin_get_pole:NnN #3 { #1 -B } \l_coffin_pole_a_tl
-    \coffin_get_pole:NnN #3 { #2 -B } \l_coffin_pole_b_tl
-    \exp_last_two_unbraced:Noo \coffin_update_B:nnnnnnnnN
-      \l_coffin_pole_a_tl \l_coffin_pole_b_tl #3
+    \@@_get_pole:NnN #3 { #1 -T } \l_@@_pole_a_tl
+    \@@_get_pole:NnN #3 { #2 -T } \l_@@_pole_b_tl
+    \exp_last_two_unbraced:Noo \@@_update_T:nnnnnnnnN
+      \l_@@_pole_a_tl \l_@@_pole_b_tl #3
+    \@@_get_pole:NnN #3 { #1 -B } \l_@@_pole_a_tl
+    \@@_get_pole:NnN #3 { #2 -B } \l_@@_pole_b_tl
+    \exp_last_two_unbraced:Noo \@@_update_B:nnnnnnnnN
+      \l_@@_pole_a_tl \l_@@_pole_b_tl #3
   }
-\cs_new_protected:Npn \coffin_update_T:nnnnnnnnN #1#2#3#4#5#6#7#8#9
+\cs_new_protected:Npn \@@_update_T:nnnnnnnnN #1#2#3#4#5#6#7#8#9
   {
     \dim_compare:nNnTF {#2} < {#6}
       {
-        \coffin_set_pole:Nnx #9 { T }
+        \@@_set_pole:Nnx #9 { T }
           { { 0 pt } {#6} { 1000 pt } { 0 pt } }
       }
       {
-        \coffin_set_pole:Nnx #9 { T }
+        \@@_set_pole:Nnx #9 { T }
           { { 0 pt } {#2} { 1000 pt } { 0 pt } }
       }
   }
-\cs_new_protected:Npn \coffin_update_B:nnnnnnnnN #1#2#3#4#5#6#7#8#9
+\cs_new_protected:Npn \@@_update_B:nnnnnnnnN #1#2#3#4#5#6#7#8#9
   {
     \dim_compare:nNnTF {#2} < {#6}
       {
-        \coffin_set_pole:Nnx #9 { B }
+        \@@_set_pole:Nnx #9 { B }
           { { 0 pt } {#2}  { 1000 pt } { 0 pt } }
       }
       {
-        \coffin_set_pole:Nnx #9 { B }
+        \@@_set_pole:Nnx #9 { B }
           { { 0 pt } {#6} { 1000 pt } { 0 pt } }
       }
   }
@@ -1456,556 +1431,120 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_typeset:Nnnnn #1#2#3#4#5
   {
-    \coffin_align:NnnNnnnnN \c_empty_coffin { H } { l }
-      #1 {#2} {#3} {#4} {#5} \l_coffin_aligned_coffin
+    \@@_align:NnnNnnnnN \c_empty_coffin { H } { l }
+      #1 {#2} {#3} {#4} {#5} \l_@@_aligned_coffin
     \hbox_unpack:N \c_empty_box
-    \box_use:N \l_coffin_aligned_coffin
+    \box_use:N \l_@@_aligned_coffin
   }
 \cs_generate_variant:Nn \coffin_typeset:Nnnnn { c }
 %    \end{macrocode}
 % \end{macro}
 %
-% \subsection{Rotating coffins}
-%
-% \begin{variable}{\l_coffin_bounding_prop}
-%   A property list for the bounding box of a coffin. This is only needed
-%   during the rotation, so there is just the one.
-%    \begin{macrocode}
-\prop_new:N \l_coffin_bounding_prop
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_coffin_bounding_shift_dim}
-%   The shift of the bounding box of a coffin from the real content.
-%    \begin{macrocode}
-\dim_new:N \l_coffin_bounding_shift_dim
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_coffin_left_corner_dim}
-% \begin{variable}{\l_coffin_right_corner_dim}
-% \begin{variable}{\l_coffin_bottom_corner_dim}
-% \begin{variable}{\l_coffin_top_corner_dim}
-%   These are used to hold maxima for the various corner values: these
-%   thus define the minimum size of the bounding box after rotation.
-%    \begin{macrocode}
-\dim_new:N \l_coffin_left_corner_dim
-\dim_new:N \l_coffin_right_corner_dim
-\dim_new:N \l_coffin_bottom_corner_dim
-\dim_new:N \l_coffin_top_corner_dim
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{macro}{\coffin_rotate:Nn, \coffin_rotate:cn}
-%   Rotating a coffin requires several steps which can be conveniently
-%   run together. The first step is to convert the angle given in degrees
-%   to one in radians. This is then used to set \cs{l_coffin_sin_fp} and
-%   \cs{l_coffin_cos_fp}, which are carried through unchanged for the rest
-%   of the procedure.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_rotate:Nn #1#2
-  {
-    \fp_set:Nn \l_coffin_internal_fp {#2}
-    \fp_div:Nn \l_coffin_internal_fp { 180 }
-    \fp_mul:Nn \l_coffin_internal_fp { \c_pi_fp }
-    \fp_sin:Nn \l_coffin_sin_fp { \l_coffin_internal_fp }
-    \fp_cos:Nn \l_coffin_cos_fp { \l_coffin_internal_fp }
-%    \end{macrocode}
-%   The corners and poles of the coffin can now be rotated around the
-%    origin. This is best achieved using mapping functions.
-%    \begin{macrocode}
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_rotate_corner:Nnnn #1 {##1} ##2 }
-    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-      { \coffin_rotate_pole:Nnnnnn #1 {##1} ##2 }
-%    \end{macrocode}
-%   The bounding box of the coffin needs to be rotated, and to do this
-%   the corners have to be found first. They are then rotated in the same
-%   way as the corners of the coffin material itself.
-%    \begin{macrocode}
-    \coffin_set_bounding:N #1
-    \prop_map_inline:Nn \l_coffin_bounding_prop
-      { \coffin_rotate_bounding:nnn {##1} ##2 }
-%    \end{macrocode}
-%   At this stage, there needs to be a calculation to find where the
-%   corners of the content and the box itself will end up.
-%    \begin{macrocode}
-    \coffin_find_corner_maxima:N #1
-    \coffin_find_bounding_shift:
-    \box_rotate:Nn #1 {#2}
-%    \end{macrocode}
-%   The correction of the box position itself takes place here. The idea
-%   is that the bounding box for a coffin is tight up to the content, and
-%   has the reference point at the bottom-left. The $x$-direction is
-%   handled by moving the content by the difference in the positions of
-%   the bounding box and the content left edge. The $y$-direction is
-%   dealt with by moving the box down by any depth it has acquired.
-%    \begin{macrocode}
-    \hbox_set:Nn #1
-      {
-        \tex_kern:D \l_coffin_bounding_shift_dim
-        \tex_kern:D -\l_coffin_left_corner_dim
-        \box_move_down:nn { \l_coffin_bottom_corner_dim }
-          { \box_use:N #1 }
-      }
-%    \end{macrocode}
-%   If there have been any previous rotations then the size of the
-%   bounding box will be bigger than the contents. This can be corrected
-%   easily by setting the size of the box to the height and width of the
-%   content.
-%    \begin{macrocode}
-    \box_set_ht:Nn #1
-      { \l_coffin_top_corner_dim - \l_coffin_bottom_corner_dim }
-    \box_set_dp:Nn #1 { 0 pt }
-    \box_set_wd:Nn #1
-      { \l_coffin_right_corner_dim - \l_coffin_left_corner_dim }
-%    \end{macrocode}
-%   The final task is to move the poles and corners such that they are
-%   back in alignment with the box reference point.
-%    \begin{macrocode}
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_shift_corner:Nnnn #1 {##1} ##2 }
-    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-      { \coffin_shift_pole:Nnnnnn #1 {##1} ##2 }
-  }
-\cs_generate_variant:Nn \coffin_rotate:Nn { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_set_bounding:N}
-%   The bounding box corners for a coffin are easy enough to find: this
-%   is the same code as for the corners of the material itself, but
-%   using a dedicated property list.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_set_bounding:N #1
-  {
-   \prop_put:Nnx \l_coffin_bounding_prop { tl }
-      { { 0 pt } { \dim_use:N \box_ht:N #1 } }
-    \prop_put:Nnx \l_coffin_bounding_prop { tr }
-      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \box_ht:N #1 } }
-    \dim_set:Nn \l_coffin_internal_dim { - \box_dp:N #1 }
-    \prop_put:Nnx \l_coffin_bounding_prop { bl }
-      { { 0 pt } { \dim_use:N \l_coffin_internal_dim } }
-    \prop_put:Nnx \l_coffin_bounding_prop { br }
-      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \l_coffin_internal_dim } }
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_rotate_bounding:nnn}
-% \begin{macro}{\coffin_rotate_corner:Nnnn}
-%   Rotating the position of the corner of the coffin is just a case
-%   of treating this as a vector from the reference point. The same
-%   treatment is used for the corners of the material itself and the
-%   bounding box.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_rotate_bounding:nnn #1#2#3
-  {
-    \coffin_rotate_vector:nnNN {#2} {#3} \l_coffin_x_dim \l_coffin_y_dim
-    \prop_put:Nnx \l_coffin_bounding_prop {#1}
-      { { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim } }
-  }
-\cs_new_protected:Npn \coffin_rotate_corner:Nnnn #1#2#3#4
-  {
-    \coffin_rotate_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } {#2}
-      { { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim } }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\coffin_rotate_pole:Nnnnnn}
-%   Rotating a single pole simply means shifting the co-ordinate of
-%   the pole and its direction. The rotation here is about the bottom-left
-%   corner of the coffin.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_rotate_pole:Nnnnnn #1#2#3#4#5#6
-  {
-    \coffin_rotate_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
-    \coffin_rotate_vector:nnNN {#5} {#6}
-      \l_coffin_x_prime_dim \l_coffin_y_prime_dim
-    \coffin_set_pole:Nnx #1 {#2}
-      {
-        { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim }
-        { \dim_use:N \l_coffin_x_prime_dim }
-        { \dim_use:N \l_coffin_y_prime_dim }
-      }
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_rotate_vector:nnNN}
-%   A rotation function, which needs only an input vector (as dimensions)
-%   and an output space. The values \cs{l_coffin_cos_fp} and
-%   \cs{l_coffin_sin_fp} should previously have been set up correctly.
-%   Working this way means that the floating point work is kept to a
-%   minimum: for any given rotation the sin and cosine values do no
-%   change, after all.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_rotate_vector:nnNN #1#2#3#4
-  {
-    \fp_set_from_dim:Nn \l_coffin_x_fp {#1}
-    \fp_set_from_dim:Nn \l_coffin_y_fp {#2}
-    \fp_set_eq:NN \l_coffin_x_prime_fp \l_coffin_x_fp
-    \fp_set_eq:NN \l_coffin_internal_fp     \l_coffin_y_fp
-    \fp_mul:Nn \l_coffin_x_prime_fp { \l_coffin_cos_fp }
-    \fp_mul:Nn \l_coffin_internal_fp     { \l_coffin_sin_fp }
-    \fp_sub:Nn \l_coffin_x_prime_fp { \l_coffin_internal_fp }
-    \fp_set_eq:NN \l_coffin_y_prime_fp \l_coffin_y_fp
-    \fp_set_eq:NN \l_coffin_internal_fp     \l_coffin_x_fp
-    \fp_mul:Nn \l_coffin_y_prime_fp { \l_coffin_cos_fp }
-    \fp_mul:Nn \l_coffin_internal_fp     { \l_coffin_sin_fp }
-    \fp_add:Nn \l_coffin_y_prime_fp { \l_coffin_internal_fp }
-    \dim_set:Nn #3 { \fp_to_dim:N \l_coffin_x_prime_fp }
-    \dim_set:Nn #4 { \fp_to_dim:N \l_coffin_y_prime_fp }
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_find_corner_maxima:N}
-% \begin{macro}[aux]{\coffin_find_corner_maxima_aux:nn}
-%   The idea here is to find the extremities of the content of the
-%   coffin. This is done by looking for the smallest values for the bottom
-%   and left corners, and the largest values for the top and right
-%   corners. The values start at the maximum dimensions so that the
-%   case where all are positive or all are negative works out correctly.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_find_corner_maxima:N #1
-  {
-    \dim_set:Nn \l_coffin_top_corner_dim   { -\c_max_dim }
-    \dim_set:Nn \l_coffin_right_corner_dim { -\c_max_dim }
-    \dim_set:Nn \l_coffin_bottom_corner_dim { \c_max_dim }
-    \dim_set:Nn \l_coffin_left_corner_dim   { \c_max_dim }
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_find_corner_maxima_aux:nn ##2 }
-  }
-\cs_new_protected:Npn \coffin_find_corner_maxima_aux:nn #1#2
-  {
-    \dim_set_min:Nn \l_coffin_left_corner_dim   {#1}
-    \dim_set_max:Nn \l_coffin_right_corner_dim  {#1}
-    \dim_set_min:Nn \l_coffin_bottom_corner_dim {#2}
-    \dim_set_max:Nn \l_coffin_top_corner_dim    {#2}
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\coffin_find_bounding_shift:}
-% \begin{macro}[aux]{\coffin_find_bounding_shift_aux:nn}
-%   The approach to finding the shift for the bounding box is similar to
-%   that for the corners. However, there is only one value needed here and
-%   a fixed input property list, so things are a bit clearer.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \coffin_find_bounding_shift:
-  {
-    \dim_set:Nn \l_coffin_bounding_shift_dim { \c_max_dim }
-    \prop_map_inline:Nn \l_coffin_bounding_prop
-      { \coffin_find_bounding_shift_aux:nn ##2 }
-  }
-\cs_new_protected:Npn \coffin_find_bounding_shift_aux:nn #1#2
-  { \dim_set_min:Nn \l_coffin_bounding_shift_dim {#1} }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\coffin_shift_corner:Nnnn}
-% \begin{macro}{\coffin_shift_pole:Nnnnnn}
-%   Shifting the corners and poles of a coffin means subtracting the
-%   appropriate values from the $x$- and $y$-components. For
-%   the poles, this means that the direction vector is unchanged.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_shift_corner:Nnnn #1#2#3#4
-  {
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _ prop } {#2}
-      {
-        { \dim_eval:n { #3 - \l_coffin_left_corner_dim } }
-        { \dim_eval:n { #4 - \l_coffin_bottom_corner_dim } }
-      }
-  }
-\cs_new_protected:Npn \coffin_shift_pole:Nnnnnn #1#2#3#4#5#6
-  {
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _ prop } {#2}
-      {
-        { \dim_eval:n { #3 - \l_coffin_left_corner_dim } }
-        { \dim_eval:n { #4 - \l_coffin_bottom_corner_dim } }
-        {#5} {#6}
-      }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Resizing coffins}
-%
-% \begin{variable}{\l_coffin_scale_x_fp}
-% \begin{variable}{\l_coffin_scale_y_fp}
-%   Storage for the scaling factors in $x$ and $y$, respectively.
-%    \begin{macrocode}
-\fp_new:N \l_coffin_scale_x_fp
-\fp_new:N \l_coffin_scale_y_fp
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_coffin_scaled_total_height_dim}
-% \begin{variable}{\l_coffin_scaled_width_dim}
-%   When scaling, the values given have to be turned into absolute values.
-%    \begin{macrocode}
-\dim_new:N \l_coffin_scaled_total_height_dim
-\dim_new:N \l_coffin_scaled_width_dim
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \begin{macro}{\coffin_resize:Nnn, \coffin_resize:cnn}
-%   Resizing a coffin begins by setting up the user-friendly names for
-%   the dimensions of the coffin box. The new sizes are then turned into
-%   scale factor. This is the same operation as takes place for the
-%   underlying box, but that operation is grouped and so the same
-%   calculation is done here.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_resize:Nnn #1#2#3
-  {
-    \coffin_set_user_dimensions:N #1
-    \box_resize:Nnn #1 {#2} {#3}
-    \fp_set_from_dim:Nn \l_coffin_scale_x_fp {#2}
-    \fp_set_from_dim:Nn \l_coffin_internal_fp { \Width }
-    \fp_div:Nn \l_coffin_scale_x_fp { \l_coffin_internal_fp }
-    \fp_set_from_dim:Nn \l_coffin_scale_y_fp {#3}
-    \fp_set_from_dim:Nn \l_coffin_internal_fp { \TotalHeight }
-    \fp_div:Nn \l_coffin_scale_y_fp { \l_coffin_internal_fp }
-    \coffin_resize_common:Nnn #1 {#2} {#3}
-  }
-\cs_generate_variant:Nn \coffin_resize:Nnn { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_resize_common:Nnn}
-%   The poles and corners of the coffin are scaled to the appropriate
-%   places before actually resizing the underlying box.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_resize_common:Nnn #1#2#3
-  {
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_scale_corner:Nnnn #1 {##1} ##2 }
-    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-      { \coffin_scale_pole:Nnnnnn #1 {##1} ##2 }
-%    \end{macrocode}
-%   Negative $x$-scaling values will place the poles in the wrong
-%   location: this is corrected here.
-%    \begin{macrocode}
-    \fp_compare:NNNT \l_coffin_scale_x_fp < \c_zero_fp
-      {
-        \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-          { \coffin_x_shift_corner:Nnnn #1 {##1} ##2 }
-        \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-          { \coffin_x_shift_pole:Nnnnnn #1 {##1} ##2 }
-      }
-    \coffin_end_user_dimensions:
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_scale:Nnn, \coffin_scale:cnn}
-%   For scaling, the opposite calculation is done to find the new
-%   dimensions for the coffin. Only the total height is needed, as this
-%   is the shift required for corners and poles. The scaling is done
-%   the \TeX{} way as this works properly with floating point values
-%   without needing to use the \texttt{fp} module.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_scale:Nnn #1#2#3
-  {
-    \box_scale:Nnn #1 {#2} {#3}
-    \coffin_set_user_dimensions:N #1
-    \fp_set:Nn \l_coffin_scale_x_fp {#2}
-    \fp_set:Nn \l_coffin_scale_y_fp {#3}
-    \fp_compare:NNNTF \l_coffin_scale_y_fp > \c_zero_fp
-      { \l_coffin_scaled_total_height_dim #3 \TotalHeight }
-      { \l_coffin_scaled_total_height_dim -#3 \TotalHeight }
-    \fp_compare:NNNTF \l_coffin_scale_x_fp > \c_zero_fp
-      { \l_coffin_scaled_width_dim -#2 \Width }
-      { \l_coffin_scaled_width_dim #2 \Width }
-    \coffin_resize_common:Nnn #1
-      { \l_coffin_scaled_width_dim } { \l_coffin_scaled_total_height_dim }
-  }
-\cs_generate_variant:Nn \coffin_scale:Nnn { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_scale_vector:nnNN}
-%   This functions scales a vector from the origin using the pre-set scale
-%   factors in $x$ and $y$. This is a much less complex operation
-%   than rotation, and as a result the code is a lot clearer.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_scale_vector:nnNN #1#2#3#4
-  {
-    \fp_set_from_dim:Nn \l_coffin_internal_fp {#1}
-    \fp_mul:Nn \l_coffin_internal_fp { \l_coffin_scale_x_fp }
-    \dim_set:Nn #3 { \fp_to_dim:N \l_coffin_internal_fp }
-    \fp_set_from_dim:Nn \l_coffin_internal_fp {#2}
-    \fp_mul:Nn \l_coffin_internal_fp { \l_coffin_scale_y_fp }
-    \dim_set:Nn #4 { \fp_to_dim:N \l_coffin_internal_fp }
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_scale_corner:Nnnn}
-% \begin{macro}{\coffin_scale_pole:Nnnnnn}
-%   Scaling both corners and poles is a simple calculation using the
-%   preceding vector scaling.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_scale_corner:Nnnn #1#2#3#4
-  {
-    \coffin_scale_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } {#2}
-      { { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim } }
-  }
-\cs_new_protected:Npn \coffin_scale_pole:Nnnnnn #1#2#3#4#5#6
-  {
-    \coffin_scale_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
-    \coffin_set_pole:Nnx #1 {#2}
-      {
-        { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim }
-        {#5} {#6}
-      }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\coffin_x_shift_corner:Nnnn}
-% \begin{macro}{\coffin_x_shift_pole:Nnnnnn}
-%   These functions correct for the $x$ displacement that takes
-%   place with a negative horizontal scaling.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_x_shift_corner:Nnnn #1#2#3#4
-  {
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } {#2}
-      {
-        { \dim_eval:n { #3 + \box_wd:N #1 } } {#4}
-    }
-  }
-\cs_new_protected:Npn \coffin_x_shift_pole:Nnnnnn #1#2#3#4#5#6
-  {
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } {#2}
-      {
-        { \dim_eval:n #3 + \box_wd:N #1 } {#4}
-        {#5} {#6}
-      }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
 % \subsection{Coffin diagnostics}
 %
-% \begin{variable}{\l_coffin_display_coffin}
-% \begin{variable}{\l_coffin_display_coord_coffin}
-% \begin{variable}{\l_coffin_display_pole_coffin}
+% \begin{variable}{\l_@@_display_coffin}
+% \begin{variable}{\l_@@_display_coord_coffin}
+% \begin{variable}{\l_@@_display_pole_coffin}
 %   Used for printing coffins with data structures attached.
 %    \begin{macrocode}
-\coffin_new:N \l_coffin_display_coffin
-\coffin_new:N \l_coffin_display_coord_coffin
-\coffin_new:N \l_coffin_display_pole_coffin
+\coffin_new:N \l_@@_display_coffin
+\coffin_new:N \l_@@_display_coord_coffin
+\coffin_new:N \l_@@_display_pole_coffin
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_display_handles_prop}
+% \begin{variable}{\l_@@_display_handles_prop}
 %   This property list is used to print coffin handles at suitable
 %   positions. The offsets are expressed as multiples of the basic offset
 %   value, which therefore acts as a scale-factor.
 %    \begin{macrocode}
-\prop_new:N \l_coffin_display_handles_prop
-\prop_put:Nnn \l_coffin_display_handles_prop { tl }
+\prop_new:N \l_@@_display_handles_prop
+\prop_put:Nnn \l_@@_display_handles_prop { tl }
   { { b } { r } { -1 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { thc }
+\prop_put:Nnn \l_@@_display_handles_prop { thc }
   { { b } { hc } { 0 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { tr }
+\prop_put:Nnn \l_@@_display_handles_prop { tr }
   { { b } { l } { 1 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { vcl }
+\prop_put:Nnn \l_@@_display_handles_prop { vcl }
   { { vc } { r } { -1 } { 0 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { vchc }
+\prop_put:Nnn \l_@@_display_handles_prop { vchc }
   { { vc } { hc } { 0 } { 0 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { vcr }
+\prop_put:Nnn \l_@@_display_handles_prop { vcr }
   { { vc } { l } { 1 } { 0 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { bl }
+\prop_put:Nnn \l_@@_display_handles_prop { bl }
   { { t } { r } { -1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { bhc }
+\prop_put:Nnn \l_@@_display_handles_prop { bhc }
   { { t } { hc } { 0 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { br }
+\prop_put:Nnn \l_@@_display_handles_prop { br }
   { { t } { l } { 1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Tl }
+\prop_put:Nnn \l_@@_display_handles_prop { Tl }
   { { t } { r } { -1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Thc }
+\prop_put:Nnn \l_@@_display_handles_prop { Thc }
   { { t } { hc } { 0 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Tr }
+\prop_put:Nnn \l_@@_display_handles_prop { Tr }
   { { t } { l } { 1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Hl }
+\prop_put:Nnn \l_@@_display_handles_prop { Hl }
   { { vc } { r } { -1 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Hhc }
+\prop_put:Nnn \l_@@_display_handles_prop { Hhc }
   { { vc } { hc } { 0 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Hr }
+\prop_put:Nnn \l_@@_display_handles_prop { Hr }
   { { vc } { l } { 1 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Bl }
+\prop_put:Nnn \l_@@_display_handles_prop { Bl }
   { { b } { r } { -1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Bhc }
+\prop_put:Nnn \l_@@_display_handles_prop { Bhc }
   { { b } { hc } { 0 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Br }
+\prop_put:Nnn \l_@@_display_handles_prop { Br }
   { { b } { l } { 1 } { -1 } }
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_display_offset_dim}
+% \begin{variable}{\l_@@_display_offset_dim}
 %   The standard offset for the label from the handle position when
 %   displaying handles.
 %    \begin{macrocode}
-\dim_new:N  \l_coffin_display_offset_dim
-\dim_set:Nn \l_coffin_display_offset_dim { 2 pt }
+\dim_new:N  \l_@@_display_offset_dim
+\dim_set:Nn \l_@@_display_offset_dim { 2 pt }
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_display_x_dim}
-% \begin{variable}{\l_coffin_display_y_dim}
+% \begin{variable}{\l_@@_display_x_dim}
+% \begin{variable}{\l_@@_display_y_dim}
 %   As the intersections of poles have to be calculated to find which
 %   ones to print, there is a need to avoid repetition. This is done
 %   by saving the intersection into two dedicated values.
 %    \begin{macrocode}
-\dim_new:N \l_coffin_display_x_dim
-\dim_new:N \l_coffin_display_y_dim
+\dim_new:N \l_@@_display_x_dim
+\dim_new:N \l_@@_display_y_dim
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_display_poles_prop}
+% \begin{variable}{\l_@@_display_poles_prop}
 %   A property list for printing poles: various things need to be deleted
 %   from this to get a \enquote{nice} output.
 %    \begin{macrocode}
-\prop_new:N \l_coffin_display_poles_prop
+\prop_new:N \l_@@_display_poles_prop
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_display_font_tl}
+% \begin{variable}{\l_@@_display_font_tl}
 %   Stores the settings used to print coffin data: this keeps things
 %   flexible.
 %    \begin{macrocode}
-\tl_new:N  \l_coffin_display_font_tl
+\tl_new:N  \l_@@_display_font_tl
 %<*initex>
-\tl_set:Nn \l_coffin_display_font_tl { } % TODO
+\tl_set:Nn \l_@@_display_font_tl { } % TODO
 %</initex>
 %<*package>
-\tl_set:Nn \l_coffin_display_font_tl { \sffamily \tiny }
+\tl_set:Nn \l_@@_display_font_tl { \sffamily \tiny }
 %</package>
 %    \end{macrocode}
 % \end{variable}
 %
 % \begin{macro}{\coffin_mark_handle:Nnnn, \coffin_mark_handle:cnnn}
-% \begin{macro}[aux]{\coffin_mark_handle_aux:nnnnNnn}
+% \begin{macro}[aux]{\@@_mark_handle_aux:nnnnNnn}
 %   Marking a single handle is relatively easy. The standard attachment
 %   function is used, meaning that there are two calculations for the
 %   location. However, this is likely to be okay given the load expected.
@@ -2014,7 +1553,7 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_mark_handle:Nnnn #1#2#3#4
   {
-    \hcoffin_set:Nn \l_coffin_display_pole_coffin
+    \hcoffin_set:Nn \l_@@_display_pole_coffin
       {
 %<*initex>
         \hbox:n { \tex_vrule:D width 1 pt height 1 pt \scan_stop: } % TODO
@@ -2025,8 +1564,8 @@
 %</package>
       }
     \coffin_attach_mark:NnnNnnnn #1 {#2} {#3}
-      \l_coffin_display_pole_coffin { hc } { vc } { 0 pt } { 0 pt }
-    \hcoffin_set:Nn \l_coffin_display_coord_coffin
+      \l_@@_display_pole_coffin { hc } { vc } { 0 pt } { 0 pt }
+    \hcoffin_set:Nn \l_@@_display_coord_coffin
       {
 %<*initex>
         % TODO
@@ -2034,37 +1573,37 @@
 %<*package>
         \color {#4}
 %</package>
-        \l_coffin_display_font_tl
+        \l_@@_display_font_tl
         ( \tl_to_str:n { #2 , #3 } )
       }
-    \prop_get:NnN \l_coffin_display_handles_prop
-      { #2 #3 } \l_coffin_internal_tl
-    \quark_if_no_value:NTF \l_coffin_internal_tl
+    \prop_get:NnN \l_@@_display_handles_prop
+      { #2 #3 } \l_@@_internal_tl
+    \quark_if_no_value:NTF \l_@@_internal_tl
       {
-        \prop_get:NnN \l_coffin_display_handles_prop
-          { #3 #2 } \l_coffin_internal_tl
-        \quark_if_no_value:NTF \l_coffin_internal_tl
+        \prop_get:NnN \l_@@_display_handles_prop
+          { #3 #2 } \l_@@_internal_tl
+        \quark_if_no_value:NTF \l_@@_internal_tl
           {
             \coffin_attach_mark:NnnNnnnn #1 {#2} {#3}
-              \l_coffin_display_coord_coffin { l } { vc }
+              \l_@@_display_coord_coffin { l } { vc }
                 { 1 pt } { 0 pt }
           }
           {
-            \exp_last_unbraced:No \coffin_mark_handle_aux:nnnnNnn
-              \l_coffin_internal_tl #1 {#2} {#3}
+            \exp_last_unbraced:No \@@_mark_handle_aux:nnnnNnn
+              \l_@@_internal_tl #1 {#2} {#3}
           }
       }
       {
-        \exp_last_unbraced:No \coffin_mark_handle_aux:nnnnNnn
-          \l_coffin_internal_tl #1 {#2} {#3}
+        \exp_last_unbraced:No \@@_mark_handle_aux:nnnnNnn
+          \l_@@_internal_tl #1 {#2} {#3}
       }
   }
-\cs_new_protected:Npn \coffin_mark_handle_aux:nnnnNnn #1#2#3#4#5#6#7
+\cs_new_protected:Npn \@@_mark_handle_aux:nnnnNnn #1#2#3#4#5#6#7
   {
     \coffin_attach_mark:NnnNnnnn #5 {#6} {#7}
-      \l_coffin_display_coord_coffin {#1} {#2}
-      { #3 \l_coffin_display_offset_dim }
-      { #4 \l_coffin_display_offset_dim }
+      \l_@@_display_coord_coffin {#1} {#2}
+      { #3 \l_@@_display_offset_dim }
+      { #4 \l_@@_display_offset_dim }
   }
 \cs_generate_variant:Nn \coffin_mark_handle:Nnnn { c }
 %    \end{macrocode}
@@ -2072,9 +1611,9 @@
 % \end{macro}
 %
 % \begin{macro}{\coffin_display_handles:Nn, \coffin_display_handles:cn}
-% \begin{macro}[aux]{\coffin_display_handles_aux:nnnnnn}
-% \begin{macro}[aux]{\coffin_display_handles_aux:nnnn}
-% \begin{macro}[aux]{\coffin_display_attach:Nnnnn}
+% \begin{macro}[aux]{\@@_display_handles_aux:nnnnnn}
+% \begin{macro}[aux]{\@@_display_handles_aux:nnnn}
+% \begin{macro}[aux]{\@@_display_attach:Nnnnn}
 %   Printing the poles starts by removing any duplicates, for which the
 %   \texttt{H} poles is used as the definitive version for the baseline
 %   and bottom. Two loops are then used to find the combinations of
@@ -2083,7 +1622,7 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_display_handles:Nn #1#2
   {
-    \hcoffin_set:Nn \l_coffin_display_pole_coffin
+    \hcoffin_set:Nn \l_@@_display_pole_coffin
       {
 %<*initex>
         \hbox:n { \tex_vrule:D width 1 pt height 1 pt \scan_stop: } % TODO
@@ -2093,22 +1632,22 @@
         \rule { 1 pt } { 1 pt }
 %</package>
       }
-    \prop_set_eq:Nc \l_coffin_display_poles_prop
-      { l_coffin_poles_ \int_value:w #1 _prop }
-    \coffin_get_pole:NnN #1 { H } \l_coffin_pole_a_tl
-    \coffin_get_pole:NnN #1 { T } \l_coffin_pole_b_tl
-    \tl_if_eq:NNT \l_coffin_pole_a_tl \l_coffin_pole_b_tl
-      { \prop_del:Nn \l_coffin_display_poles_prop { T } }
-    \coffin_get_pole:NnN #1 { B } \l_coffin_pole_b_tl
-    \tl_if_eq:NNT \l_coffin_pole_a_tl \l_coffin_pole_b_tl
-      { \prop_del:Nn \l_coffin_display_poles_prop { B } }
-    \coffin_set_eq:NN \l_coffin_display_coffin #1
-    \prop_map_inline:Nn \l_coffin_display_poles_prop
+    \prop_set_eq:Nc \l_@@_display_poles_prop
+      { l_@@_poles_ \__int_value:w #1 _prop }
+    \@@_get_pole:NnN #1 { H } \l_@@_pole_a_tl
+    \@@_get_pole:NnN #1 { T } \l_@@_pole_b_tl
+    \tl_if_eq:NNT \l_@@_pole_a_tl \l_@@_pole_b_tl
+      { \prop_remove:Nn \l_@@_display_poles_prop { T } }
+    \@@_get_pole:NnN #1 { B } \l_@@_pole_b_tl
+    \tl_if_eq:NNT \l_@@_pole_a_tl \l_@@_pole_b_tl
+      { \prop_remove:Nn \l_@@_display_poles_prop { B } }
+    \coffin_set_eq:NN \l_@@_display_coffin #1
+    \prop_map_inline:Nn \l_@@_display_poles_prop
       {
-        \prop_del:Nn \l_coffin_display_poles_prop {##1}
-        \coffin_display_handles_aux:nnnnnn {##1} ##2 {#2}
+        \prop_remove:Nn \l_@@_display_poles_prop {##1}
+        \@@_display_handles_aux:nnnnnn {##1} ##2 {#2}
       }
-    \box_use:N \l_coffin_display_coffin
+    \box_use:N \l_@@_display_coffin
   }
 %    \end{macrocode}
 %   For each pole there is a check for an intersection, which here does
@@ -2116,20 +1655,20 @@
 %   and used to align the pole coffin with the main coffin for output.
 %   The positions are recovered from the preset list if available.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_display_handles_aux:nnnnnn #1#2#3#4#5#6
+\cs_new_protected:Npn \@@_display_handles_aux:nnnnnn #1#2#3#4#5#6
   {
-    \prop_map_inline:Nn \l_coffin_display_poles_prop
+    \prop_map_inline:Nn \l_@@_display_poles_prop
       {
-        \bool_set_false:N \l_coffin_error_bool
-        \coffin_calculate_intersection:nnnnnnnn {#2} {#3} {#4} {#5} ##2
-        \bool_if:NF \l_coffin_error_bool
+        \bool_set_false:N \l_@@_error_bool
+        \@@_calculate_intersection:nnnnnnnn {#2} {#3} {#4} {#5} ##2
+        \bool_if:NF \l_@@_error_bool
           {
-            \dim_set:Nn \l_coffin_display_x_dim { \l_coffin_x_dim }
-            \dim_set:Nn \l_coffin_display_y_dim { \l_coffin_y_dim }
-            \coffin_display_attach:Nnnnn
-              \l_coffin_display_pole_coffin { hc } { vc }
+            \dim_set:Nn \l_@@_display_x_dim { \l_@@_x_dim }
+            \dim_set:Nn \l_@@_display_y_dim { \l_@@_y_dim }
+            \@@_display_attach:Nnnnn
+              \l_@@_display_pole_coffin { hc } { vc }
               { 0 pt } { 0 pt }
-            \hcoffin_set:Nn \l_coffin_display_coord_coffin
+            \hcoffin_set:Nn \l_@@_display_coord_coffin
               {
 %<*initex>
                 % TODO
@@ -2137,40 +1676,40 @@
 %<*package>
                 \color {#6}
 %</package>
-                \l_coffin_display_font_tl
+                \l_@@_display_font_tl
                 ( \tl_to_str:n { #1 , ##1 } )
               }
-            \prop_get:NnN \l_coffin_display_handles_prop
-              { #1 ##1 } \l_coffin_internal_tl
-            \quark_if_no_value:NTF \l_coffin_internal_tl
+            \prop_get:NnN \l_@@_display_handles_prop
+              { #1 ##1 } \l_@@_internal_tl
+            \quark_if_no_value:NTF \l_@@_internal_tl
               {
-                \prop_get:NnN \l_coffin_display_handles_prop
-                  { ##1 #1 } \l_coffin_internal_tl
-                \quark_if_no_value:NTF \l_coffin_internal_tl
+                \prop_get:NnN \l_@@_display_handles_prop
+                  { ##1 #1 } \l_@@_internal_tl
+                \quark_if_no_value:NTF \l_@@_internal_tl
                   {
-                    \coffin_display_attach:Nnnnn
-                      \l_coffin_display_coord_coffin { l } { vc }
+                    \@@_display_attach:Nnnnn
+                      \l_@@_display_coord_coffin { l } { vc }
                       { 1 pt } { 0 pt }
                   }
                   {
                     \exp_last_unbraced:No
-                      \coffin_display_handles_aux:nnnn
-                      \l_coffin_internal_tl
+                      \@@_display_handles_aux:nnnn
+                      \l_@@_internal_tl
                   }
               }
               {
-                \exp_last_unbraced:No \coffin_display_handles_aux:nnnn
-                  \l_coffin_internal_tl
+                \exp_last_unbraced:No \@@_display_handles_aux:nnnn
+                  \l_@@_internal_tl
               }
           }
       }
   }
-\cs_new_protected:Npn \coffin_display_handles_aux:nnnn #1#2#3#4
+\cs_new_protected:Npn \@@_display_handles_aux:nnnn #1#2#3#4
   {
-    \coffin_display_attach:Nnnnn
-      \l_coffin_display_coord_coffin {#1} {#2}
-      { #3 \l_coffin_display_offset_dim }
-      { #4 \l_coffin_display_offset_dim }
+    \@@_display_attach:Nnnnn
+      \l_@@_display_coord_coffin {#1} {#2}
+      { #3 \l_@@_display_offset_dim }
+      { #4 \l_@@_display_offset_dim }
   }
 \cs_generate_variant:Nn \coffin_display_handles:Nn { c }
 %    \end{macrocode}
@@ -2179,29 +1718,29 @@
 %   and stored for the display coffin the code simply uses it directly,
 %   with no calculation.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_display_attach:Nnnnn #1#2#3#4#5
+\cs_new_protected:Npn \@@_display_attach:Nnnnn #1#2#3#4#5
   {
-    \coffin_calculate_intersection:Nnn #1 {#2} {#3}
-    \dim_set:Nn \l_coffin_x_prime_dim { \l_coffin_x_dim }
-    \dim_set:Nn \l_coffin_y_prime_dim { \l_coffin_y_dim }
-    \dim_set:Nn \l_coffin_offset_x_dim
-      { \l_coffin_display_x_dim - \l_coffin_x_prime_dim + #4 }
-    \dim_set:Nn \l_coffin_offset_y_dim
-      { \l_coffin_display_y_dim - \l_coffin_y_prime_dim + #5 }
-    \hbox_set:Nn \l_coffin_aligned_coffin
+    \@@_calculate_intersection:Nnn #1 {#2} {#3}
+    \dim_set:Nn \l_@@_x_prime_dim { \l_@@_x_dim }
+    \dim_set:Nn \l_@@_y_prime_dim { \l_@@_y_dim }
+    \dim_set:Nn \l_@@_offset_x_dim
+      { \l_@@_display_x_dim - \l_@@_x_prime_dim + #4 }
+    \dim_set:Nn \l_@@_offset_y_dim
+      { \l_@@_display_y_dim - \l_@@_y_prime_dim + #5 }
+    \hbox_set:Nn \l_@@_aligned_coffin
       {
-        \box_use:N \l_coffin_display_coffin
-        \tex_kern:D -\box_wd:N \l_coffin_display_coffin
-        \tex_kern:D \l_coffin_offset_x_dim
-        \box_move_up:nn { \l_coffin_offset_y_dim } { \box_use:N #1 }
+        \box_use:N \l_@@_display_coffin
+        \tex_kern:D -\box_wd:N \l_@@_display_coffin
+        \tex_kern:D \l_@@_offset_x_dim
+        \box_move_up:nn { \l_@@_offset_y_dim } { \box_use:N #1 }
       }
-    \box_set_ht:Nn \l_coffin_aligned_coffin
-      { \box_ht:N \l_coffin_display_coffin }
-    \box_set_dp:Nn \l_coffin_aligned_coffin
-      { \box_dp:N \l_coffin_display_coffin }
-    \box_set_wd:Nn \l_coffin_aligned_coffin
-      { \box_wd:N \l_coffin_display_coffin }
-    \box_set_eq:NN \l_coffin_display_coffin \l_coffin_aligned_coffin
+    \box_set_ht:Nn \l_@@_aligned_coffin
+      { \box_ht:N \l_@@_display_coffin }
+    \box_set_dp:Nn \l_@@_aligned_coffin
+      { \box_dp:N \l_@@_display_coffin }
+    \box_set_wd:Nn \l_@@_aligned_coffin
+      { \box_wd:N \l_@@_display_coffin }
+    \box_set_eq:NN \l_@@_display_coffin \l_@@_aligned_coffin
   }
 %    \end{macrocode}
 % \end{macro}
@@ -2216,13 +1755,13 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_show_structure:N #1
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
-        \msg_aux_show:Nnx #1 { coffins }
+        \__msg_show_variable:Nnn #1 { coffins }
           {
             \prop_map_function:cN
-              { l_coffin_poles_ \int_value:w #1 _prop }
-              \msg_aux_show_unbraced:nn
+              { l_@@_poles_ \__int_value:w #1 _prop }
+              \__msg_show_item_unbraced:nn
           }
       }
   }
@@ -2233,7 +1772,7 @@
 % \subsection{Messages}
 %
 %    \begin{macrocode}
-\msg_kernel_new:nnnn { coffins } { no-pole-intersection }
+\__msg_kernel_new:nnnn { kernel } { no-pole-intersection }
   { No~intersection~between~coffin~poles. }
   {
     \c_msg_coding_error_text_tl
@@ -2241,17 +1780,17 @@
     but~they~do~not~have~a~unique~meeting~point:~
     the~value~(0~pt,~0~pt)~will~be~used.
   }
-\msg_kernel_new:nnnn { coffins } { unknown-coffin }
+\__msg_kernel_new:nnnn { kernel } { unknown-coffin }
   { Unknown~coffin~'#1'. }
   { The~coffin~'#1'~was~never~defined. }
-\msg_kernel_new:nnnn { coffins } { unknown-coffin-pole }
+\__msg_kernel_new:nnnn { kernel } { unknown-coffin-pole }
   { Pole~'#1'~unknown~for~coffin~'#2'. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~was~asked~to~find~a~typesetting~pole~for~a~coffin,~
     but~either~the~coffin~does~not~exist~or~the~pole~name~is~wrong.
   }
-\msg_kernel_new:nnn { coffins } { show }
+\__msg_kernel_new:nnn { kernel } { show-coffins }
   {
     Size~of~coffin~\token_to_str:N #1 : \\
     > ~ ht~=~\dim_use:N \box_ht:N #1 \\
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3color.dtx b/Master/texmf-dist/source/latex/l3kernel/l3color.dtx
index 2089859d4e3..e8aa1f5d050 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3color.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3color.dtx
@@ -1,6 +1,6 @@
 % \iffalse meta-comment
 %
-%% File: l3color.dtx Copyright(C) 2011 The LaTeX3 Project
+%% File: l3color.dtx Copyright(C) 2011,2012 The LaTeX3 Project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -36,7 +36,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3color.dtx 2776 2011-09-07 18:33:19Z joseph $
+\GetIdInfo$Id: l3color.dtx 3986 2012-07-15 19:23:51Z joseph $
   {L3 Experimental colour support}
 %</driver|package>
 %<*driver>
@@ -111,7 +111,7 @@
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
@@ -135,10 +135,27 @@
 %    \begin{macrocode}
 %<*initex>
 \cs_new_protected_nopar:Npn \color_ensure_current:
-  { \driver_color_ensure_current: }
+  { \__driver_color_ensure_current: }
 %</initex>
+%    \end{macrocode}
+%   In package mode, the driver code may not be loaded. To keep down
+%   dependencies, if there is no driver code available and no \cs{set@color}
+%   then colour is not in use and this function can be a no-op.
+%    \begin{macrocode}
 %<*package>
-\cs_new_protected_nopar:Npn \color_ensure_current: { \set@color }
+\cs_new_protected_nopar:Npn \color_ensure_current: { }
+\AtBeginDocument
+  {
+    \cs_if_exist:NTF \__driver_color_ensure_current:
+      {
+        \cs_set_protected_nopar:Npn \color_ensure_current:
+          { \__driver_color_ensure_current: }
+      }
+      {
+        \cs_if_exist:NT \set@color
+          { \cs_set_protected_nopar:Npn \color_ensure_current: { \set@color } }
+      }
+  }
 %</package>
 %    \end{macrocode}
 % \end{macro}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3doc.dtx b/Master/texmf-dist/source/latex/l3kernel/l3doc.dtx
index 8eec496836e..137d75f056f 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3doc.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3doc.dtx
@@ -1,6 +1,6 @@
 % \iffalse meta-comment
 %
-%% File: l3doc.dtx Copyright (C) 1990-2011 The LaTeX3 project
+%% File: l3doc.dtx Copyright (C) 1990-2012 The LaTeX3 project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -55,7 +55,7 @@ Do not distribute a modified version of this file.
 % stop docstrip adding \endinput
 \postamble
 \endpostamble
-\generate{\file{l3doc.cls}{\from{l3doc.dtx}{class}}}
+\generate{\file{l3doc.cls}{\from{l3doc.dtx}{class,cfg}}}
 \generate{\file{l3doc.ist}{\from{l3doc.dtx}{docist}}}
 \ifx\fmtname\nameofplainTeX
   \expandafter\endbatchfile
@@ -64,10 +64,6 @@ Do not distribute a modified version of this file.
 \fi
 %</driver>
 %
-%<*driver|class>
-\RequirePackage{expl3,xparse,calc}
-%</driver|class>
-%
 % Need to protect the file metadata for any modules that load l3doc.
 % This is restored after "\ProvideExplClass" below.
 %    \begin{macrocode}
@@ -78,7 +74,11 @@ Do not distribute a modified version of this file.
 %    \end{macrocode}
 %
 %<*driver|class>
-\GetIdInfo$Id: l3doc.dtx 3491 2012-03-04 06:13:18Z bruno $
+\RequirePackage{expl3,xparse,calc}
+%</driver|class>
+%
+%<*driver|class>
+\GetIdInfo$Id: l3doc.dtx 3989 2012-07-16 01:15:43Z bruno $
           {L3 Experimental documentation class}
 %</driver|class>
 %
@@ -265,7 +265,7 @@ Do not distribute a modified version of this file.
 % when the DTX file is "\DocInput"; use "\DisableDocumentation"/"\DisableImplementation"
 % to omit the contents of those environments.
 %
-% Note that \cmd\DocInput\ now takes comma-separated arguments, and \cmd\DocInputAgain\
+% Note that "\DocInput" now takes comma-separated arguments, and "\DocInputAgain"
 % can be used to re-input all DTX files previously input in this way.
 %
 % \subsection{Describing functions in the documentation}
@@ -463,16 +463,6 @@ Do not distribute a modified version of this file.
 %<*class>
 %    \end{macrocode}
 %
-% The Guilty Parties.
-%    \begin{macrocode}
-\cs_new_nopar:Npn\Team{%
-  The~\LaTeX3~Project\thanks{%
-  Frank~Mittelbach,~Denys~Duchier,~Chris~Rowley,~
-  Rainer~Sch\"opf,~Johannes~Braams,~Michael~Downes,~
-  David~Carlisle,~Alan~Jeffrey,~Morten~H\o{}gholm,~Thomas~Lotze,~
-  Javier~Bezos,~Will~Robertson,~Joseph~Wright,~Bruno~Le~Floch}}
-%    \end{macrocode}
-%
 % \subsection{Variables}
 %
 %    \begin{macrocode}
@@ -518,6 +508,19 @@ Do not distribute a modified version of this file.
 \bool_new:N \g_doc_checktest_bool
 %    \end{macrocode}
 %
+% Temporaries:
+%    \begin{macrocode}
+\seq_new:N \g_doc_tmpa_seq
+\tl_new:N \l_doc_tmpa_tl
+\tl_new:N \l_doc_tmpb_tl
+\int_new:N \l_doc_tmpa_int
+%    \end{macrocode}
+%
+% Other:
+%    \begin{macrocode}
+\bool_new:N \l_doc_tested_bool
+%    \end{macrocode}
+%
 % \subsection{expl3 extras}
 %
 % \begin{macro}
@@ -526,18 +529,20 @@ Do not distribute a modified version of this file.
 %     \coffin_gset_eq:cN, \coffin_gset_eq:cc
 %   }
 %   Setting two coffins equal is just a wrapper around other functions.
+%   Slightly naughty use of an internal coffin function here, but \ldots
 %    \begin{macrocode}
 \cs_set_protected_nopar:Npn \coffin_gset_eq:NN #1#2
   {
     \coffin_if_exist:NT #1
       {
         \box_gset_eq:NN #1 #2
-        \coffin_gset_eq_structure:NN #1 #2
+        \__coffin_gset_eq_structure:NN #1 #2
       }
   }
 \cs_generate_variant:Nn \coffin_gset_eq:NN { c , Nc , cc }
 %    \end{macrocode}
 % \end{macro}
+% 
 %
 % \subsection{Options and configuration}
 %
@@ -571,16 +576,18 @@ Do not distribute a modified version of this file.
 \ExecuteOptions{full,a4paper,nocheck,nochecktest,lm-default}
 %    \end{macrocode}
 %
-% Input a local configuration file, if it exists.
+% Input a local configuration file, if it exists, with a message to the console that this has happened. Since we distribute a cfg file with the class, this should usually always be true. Therefore, check for \cs{ExplMakeTitle} (defined in `our' cfg file) and only output the informational message if it's not found.
 %
 %    \begin{macrocode}
-\InputIfFileExists{l3doc.cfg}
+\msg_new:nnn {l3doc} {input-cfg}
   {
-    \typeout{*************************************^^J
-             *~Local~config~file~l3doc.cfg~used   ^^J
-             *************************************}
+    Local~config~file~l3doc.cfg~loaded.
+  }
+\file_if_exist:nT {l3doc.cfg}
+  {
+    \file_input:n {l3doc.cfg}
+    \msg_info:nn {l3doc} {input-cfg}
   }
-  { \@input{l3doc.ltx} }
 %    \end{macrocode}
 %
 %    \begin{macrocode}
@@ -597,6 +604,7 @@ Do not distribute a modified version of this file.
   {
     array,
     alphalph,
+    amsmath,
     booktabs,
     color,
     colortbl,
@@ -679,9 +687,9 @@ Do not distribute a modified version of this file.
 %    \begin{macrocode}
 \setcounter{StandardModuleDepth}{1}
 \@addtoreset{CodelineNo}{part}
-\cs_set_nopar:Npn \theCodelineNo {
-  \textcolor[gray]{0.5}{ \sffamily\tiny\arabic{CodelineNo} }
-}
+\tl_replace_once:Nnn \theCodelineNo
+ { \HDorg@theCodelineNo }
+ { \textcolor[gray]{0.5} { \sffamily\tiny\arabic{CodelineNo} } }
 %    \end{macrocode}
 %
 %
@@ -762,13 +770,29 @@ Do not distribute a modified version of this file.
 %    \end{macrocode}
 %
 % \begin{macro}{\cmd,\cs}
-% |\cmd{\foo}| Prints |\foo| verbatim. It may be used inside moving
-% arguments. |\cs{foo}| also prints |\foo|, for those who prefer that
-% syntax.
-%    \begin{macrocode}
-\cs_set_nopar:Npn \cmd #1 { \cs{\expandafter\cmd@to@cs\string#1} }
-\cs_set_nopar:Npn \cmd@to@cs #1#2 { \char\number`#2\relax }
-\DeclareRobustCommand \cs [1] { \texttt { \char`\\ #1 } }
+%   |\cmd{\foo}| Prints |\foo| verbatim. It may be used inside moving
+%   arguments. |\cs{foo}| also prints |\foo|, for those who prefer that
+%   syntax.  There is a bit of shuffling around to make sure that |_|
+%   has the catcode that \cs{doc_replace_at_at:N} expects, without
+%   rescanning the whole argument.  For that we store in
+%   \cs{l_doc_tmpb_tl} a single underscore with the current catcode,
+%   then replace all such underscores by letter underscores in |#1|
+%   (stored in the |tmpa| token list).  After calling
+%   \cs{doc_replace_at_at:N}, we replace the underscores back to their
+%   old meaning before using the token list.
+%    \begin{macrocode}
+\cs_set_nopar:Npn \cmd #1 { \cs{\expandafter \doc_cmd_to_cs:w \string#1} }
+\cs_set_nopar:Npn \doc_cmd_to_cs:w #1#2 { \char\number`#2\relax }
+\DeclareRobustCommand \cs [1]
+  {
+    \tl_set_rescan:Nnn \l_doc_tmpb_tl { } { _ }
+    \tl_set:Nn \l_doc_tmpa_tl {#1}
+    \tl_replace_all:NVn \l_doc_tmpa_tl \l_doc_tmpb_tl { _ }
+    \doc_replace_at_at:N \l_doc_tmpa_tl
+    \tl_replace_all:NnV \l_doc_tmpa_tl { _ } \l_doc_tmpb_tl
+    \texttt { \char`\\ \tl_use:N \l_doc_tmpa_tl}
+  }
+\cs_generate_variant:Nn \tl_replace_all:Nnn { NV , NnV }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -823,7 +847,7 @@ Do not distribute a modified version of this file.
 % \begin{macro}{\DisableDocumentation,\DisableImplementation}
 %    \begin{macrocode}
 \cs_new:Npn \doc_implementation: {
-  \cs_set:Npn \variable {\macro[var]}
+  \DeclareDocumentCommand {\variable} { O{} } { \doc_macro:n { var , ##1 } }
   \cs_set_eq:NN \endvariable \endmacro
 }
 \cs_new:Npn \doc_docu: {
@@ -931,8 +955,9 @@ Do not distribute a modified version of this file.
     \char_set_catcode_ignore:N \ % space
     \char_set_catcode_ignore:N \^^M
     \char_set_catcode_ignore:N \^^I
-
-    \function_aux:n
+    \exp_after:wN
+  \group_end:
+  \function_aux:n
   }
   {
     \vcoffin_set_end:
@@ -989,8 +1014,6 @@ Do not distribute a modified version of this file.
 %    \begin{macrocode}
 \cs_set_nopar:Npn \function_aux:n #1 {
 
-  \group_end:
-
   \tl_set:Nn \l_doc_function_input_tl {#1}
 
   \dim_zero:N \l_doc_trial_width_dim
@@ -1027,7 +1050,7 @@ Do not distribute a modified version of this file.
 % about the functions being typeset and their variants.
 % The property list uses a specific format: the keys contained are the function `names' (stripped of signature) with values specified by a comma-separated list containing two brace groups per item:
 % \begin{center}
-% ">  {my_function}  =>  { {" \meta{Nargs 1} "}{" \meta{sig.\ 1} "} , {" \meta{Nargs 2} "}{" \meta{sig.\ 2} "} , ... }"
+% |>  {my_function}  =>  {| \Arg{Nargs_1} \Arg{sig_1} |,| \Arg{Nargs_2} \Arg{sig_2} |, ... }|
 % \end{center}
 % This somewhat arcane syntax is chosen to distinguish between all variants of control sequence that may be being documented here. (With or without \textsf{expl3} function syntax.)
 %    \begin{macrocode}
@@ -1048,22 +1071,22 @@ Do not distribute a modified version of this file.
 					  % finally, for regular old csnames:
 						\exp_args:NNf \prop_get:NnNTF
 						  \l_doc_functions_block_prop
-						  { \cs_get_function_name:N #1 } \l_doc_tmp_tl
+						  { \__cs_get_function_name:N #1 } \l_doc_tmpb_tl
 						{
 							\prop_put:Nxx \l_doc_functions_block_prop
-								{ \cs_get_function_name:N #1 }
+								{ \__cs_get_function_name:N #1 }
 								{
-								  \l_doc_tmp_tl ,
-								  {\cs_get_arg_count_from_signature:N #1}
-								  {\cs_get_function_signature:N #1}
+								  \l_doc_tmpb_tl ,
+								  {\__cs_count_signature:N #1}
+								  {\__cs_get_function_signature:N #1}
 								}
 						}
 						{
 							\prop_put:Nxx \l_doc_functions_block_prop
-								{ \cs_get_function_name:N #1 }
+								{ \__cs_get_function_name:N #1 }
 								{
-								  {\cs_get_arg_count_from_signature:N #1}
-								  {\cs_get_function_signature:N #1}
+								  {\__cs_count_signature:N #1}
+								  {\__cs_get_function_signature:N #1}
 								}
 						}
 					}
@@ -1072,7 +1095,7 @@ Do not distribute a modified version of this file.
       {
         % for now don't bother splitting into variants:
         \tl_gclear:N \l_doc_function_name_prefix_tl
-				\prop_put:Nxx \l_doc_functions_block_prop	{ #1 } { {-1} {} }
+				\prop_put:Nxx \l_doc_functions_block_prop	{ \tl_to_str:n {#1} } { {-1} {} }
       }
   }
 
@@ -1091,13 +1114,13 @@ Do not distribute a modified version of this file.
 \cs_new:Nn \doc_typeset_functions:nn
   {
     \clist_gset:Nn \l_doc_variants_clist {#2}
-    \clist_gpop:NN \l_doc_variants_clist \l_doc_tmp_tl
+    \clist_gpop:NN \l_doc_variants_clist \l_doc_tmpb_tl
     \exp_args:Nc \doc_typeset_functions_aux:N
       {
          #1
-         \int_compare:nT { \exp_after:wN \use_i:nn \l_doc_tmp_tl > -1 } {:}
-         \int_compare:nT { \exp_after:wN \use_i:nn \l_doc_tmp_tl >  0 }
-           { \exp_after:wN \use_ii:nn \l_doc_tmp_tl }
+         \int_compare:nT { \exp_after:wN \use_i:nn \l_doc_tmpb_tl > -1 } {:}
+         \int_compare:nT { \exp_after:wN \use_i:nn \l_doc_tmpb_tl >  0 }
+           { \exp_after:wN \use_ii:nn \l_doc_tmpb_tl }
       }
     \\
   }
@@ -1105,18 +1128,22 @@ Do not distribute a modified version of this file.
 \cs_new_nopar:Nn \doc_typeset_functions_aux:N
 {
   \bool_if:NT \l_doc_meta_pTF_bool {
+    \tl_set:Nx \l_doc_pTF_name_tl
+      { \l_doc_function_name_prefix_tl \doc_predicate_from_base:N #1 }
+    \doc_special_main_index:o { \l_doc_pTF_name_tl }
+    \seq_gput_right:Nx \g_doc_functions_seq
+      { \tl_to_str:N \l_doc_pTF_name_tl }
     \tl_set:Nx \l_doc_pTF_name_tl { \doc_predicate_from_base:N #1 }
-    \doc_special_main_index:o { \tl_to_str:N \l_doc_pTF_name_tl }
-    \seq_gput_right:Nx \g_doc_functions_seq { \l_doc_function_name_prefix_tl \l_doc_pTF_name_tl }
   }
 
-  \bool_if:NTF \l_doc_meta_TF_bool {
-    \doc_special_main_index:o { \token_to_str:N #1 TF }
-    \seq_gput_right:Nx \g_doc_functions_seq { \token_to_str:N #1 TF }
-  }{
-    \doc_special_main_index:o { \token_to_str:N #1 }
-    \seq_gput_right:Nx \g_doc_functions_seq { \tl_to_str:n {#1}  }
-  }
+  \tl_set:Nx \l_doc_tmpa_tl
+    {
+      \l_doc_function_name_prefix_tl
+      \cs_to_str:N #1
+      \bool_if:NT \l_doc_meta_TF_bool { \tl_to_str:n {TF} }
+    }
+  \doc_special_main_index:o { \l_doc_tmpa_tl }
+  \seq_gput_right:No \g_doc_functions_seq { \l_doc_tmpa_tl }
 
   \bool_if:NTF \l_doc_meta_pTF_bool {
 
@@ -1139,24 +1166,19 @@ Do not distribute a modified version of this file.
 % \begin{macro}[internal]{\doc_typeset_function_block:N}
 %    \begin{macrocode}
 \cs_set_nopar:Nn \doc_typeset_function_block:N {
-  \tl_gset:Nx \l_doc_function_name_tl { \cs_get_function_name:N #1 }
-  \tl_gset:Nx \l_doc_function_sig_tl { \cs_get_function_signature:N #1 }
+  \tl_gset:Nx \l_doc_function_name_tl { \__cs_get_function_name:N #1 }
+  \tl_gset:Nx \l_doc_function_sig_tl { \__cs_get_function_signature:N #1 }
   \tl_gset:Nx \g_doc_macro_tl { \l_doc_function_name_prefix_tl \l_doc_function_name_tl }
 
   \doc_typeset_function_basename:N #1
   \bool_if:NT \l_doc_meta_TF_bool { \doc_typeset_TF: }
   \doc_typeset_expandability:
   \clist_if_empty:NF \l_doc_variants_clist { \doc_typeset_variants: }
-  \bool_if:NT \g_doc_full_bool { \doc_label_function: }
+  \bool_if:NT \g_doc_full_bool { \doc_label_function:N #1 }
 
 }
 \cs_set:Nn \doc_typeset_function_basename:N
-  {
-    \g_doc_macro_tl
-    \int_compare:nT { \cs_get_arg_count_from_signature:N #1 >  -1 } { : }
-    \int_compare:nT { \cs_get_arg_count_from_signature:N #1 >   0 }
-      { \l_doc_function_sig_tl }
-  }
+  { \l_doc_function_name_prefix_tl \cs_to_str:N #1 }
 \cs_set:Nn \doc_typeset_expandability:
   {
     &
@@ -1173,12 +1195,12 @@ Do not distribute a modified version of this file.
   {
     \\
     \doc_typeset_aux:n \g_doc_macro_tl :
-    \int_compare:nTF { \clist_length:N \l_doc_variants_clist == 1 }
+    \int_compare:nTF { \clist_count:N \l_doc_variants_clist == 1 }
       { \exp_after:wN \use_ii:nn \l_doc_variants_clist }
       {
         \textrm(
-          \clist_pop:NN \l_doc_variants_clist \l_doc_tmp_tl
-          \exp_after:wN \use_ii:nn \l_doc_tmp_tl
+          \clist_pop:NN \l_doc_variants_clist \l_doc_tmpb_tl
+          \exp_after:wN \use_ii:nn \l_doc_tmpb_tl
           \clist_map_inline:Nn \l_doc_variants_clist {\textrm| \use_ii:nn ##1}
         \textrm)
       }
@@ -1193,15 +1215,12 @@ Do not distribute a modified version of this file.
       \hyperlink{rexpstar} {\ding{73}} % hollow star
     }
   }
-\cs_set:Nn \doc_label_function:
+\cs_set:Nn \doc_label_function:N
   {
-    \exp_args:NNf \tl_replace_all:Nnn \g_doc_macro_tl {\token_to_str:N _} {/}
-    \exp_args:NNf \tl_replace_all:Nnn \g_doc_macro_tl {\@backslashchar} {}
-    \exp_args:Nx \label
-      {
-        doc/function//\g_doc_macro_tl
-        \tl_if_empty:NF \l_doc_function_sig_tl { : \l_doc_function_sig_tl }
-      }
+    \tl_set:Nx \l_doc_tmpa_tl { \l_doc_function_name_prefix_tl \cs_to_str:N #1 }
+    \exp_args:NNf \tl_replace_all:Nnn \l_doc_tmpa_tl {\token_to_str:N _} {/}
+    \exp_args:NNf \tl_remove_all:Nn \l_doc_tmpa_tl {\@backslashchar}
+    \exp_args:Nx \label {doc/function//\l_doc_tmpa_tl}
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1339,11 +1358,14 @@ Do not distribute a modified version of this file.
       { \bool_set_true:N \l_doc_macro_TF_bool } ,
     pTF .code:n =
       { \bool_set_true:N \l_doc_macro_pTF_bool } ,
+    tested .code:n =
+      { } ,
   }
 %    \end{macrocode}
 %
 %    \begin{macrocode}
-\renewcommand \macro [1][] {
+\RenewDocumentCommand { \macro } { O{} } { \doc_macro:n {#1} }
+\cs_new_protected:Npn \doc_macro:n #1 {
 
   \int_compare:nNnTF \currentgrouplevel=2
     { \int_gzero:N \g_doc_nested_macro_int }
@@ -1412,7 +1434,7 @@ Do not distribute a modified version of this file.
 %    \begin{macrocode}
 \cs_set:Nn \doc_predicate_from_base:N
   {
-    \cs_get_function_name:N #1 _p: \cs_get_function_signature:N #1
+    \__cs_get_function_name:N #1 _p: \__cs_get_function_signature:N #1
   }
 \cs_set:Npn \doc_predicate_from_base:w #1 : #2 \q_nil
   {
@@ -1427,10 +1449,15 @@ Do not distribute a modified version of this file.
 % \begin{arguments}
 % \item Macro/function/whatever name; input has already been sanitised.
 % \end{arguments}
+% \cs{l_doc_at_replaced_macro_tl} stores the macro name after
+% replacement of |@@|.
 %    \begin{macrocode}
+\tl_new:N \l_doc_at_replaced_macro_tl
 \cs_set_nopar:Npn \doc_macro_single:n #1 {
   \int_incr:N \l_doc_macro_int
-  \tl_set:Nx \saved@macroname { \token_to_str:N #1 }
+  \tl_set:Nx \l_doc_at_replaced_macro_tl { \token_to_str:N #1 }
+  \doc_replace_at_at:N \l_doc_at_replaced_macro_tl
+  \tl_set_eq:NN \saved@macroname \l_doc_at_replaced_macro_tl
   \topsep\MacroTopsep
   \trivlist
   \cs_set_nopar:Npn \makelabel ##1 { \llap{##1} }
@@ -1457,33 +1484,33 @@ Do not distribute a modified version of this file.
   }
 
   \bool_if:NF \l_doc_macro_aux_bool {
-    \tl_gset:Nx \l_doc_macro_tl { \tl_to_str:n {#1} }
+    \tl_gset:Nx \l_doc_macro_tl { \tl_to_str:N \l_doc_at_replaced_macro_tl }
     \exp_args:NNf \tl_greplace_all:Nnn \l_doc_macro_tl {\token_to_str:N _} {/}
     \exp_args:NNf \tl_greplace_all:Nnn \l_doc_macro_tl {\@backslashchar} {}
   }
 
   \use:x {
     \exp_not:N \item [ \exp_not:N \doc_print_macroname:n {
-      \tl_to_str:n {#1}
+      \tl_to_str:N \l_doc_at_replaced_macro_tl
     }]
   }
   \global\advance \c@CodelineNo \@ne
 
   \bool_if:NF \l_doc_macro_aux_bool {
     \bool_if:NTF \l_doc_macro_TF_bool {
-      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:n { #1 TF } }
-      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:n { #1 T  } }
-      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:n { #1 F  } }
+      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:N \l_doc_at_replaced_macro_tl \tl_to_str:n {TF} }
+      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:N \l_doc_at_replaced_macro_tl \tl_to_str:n {T } }
+      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:N \l_doc_at_replaced_macro_tl \tl_to_str:n { F} }
     }{
-      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:n {#1} }
+      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:N \l_doc_at_replaced_macro_tl }
     }
   }
   \bool_if:NTF \l_doc_macro_TF_bool {
-    \SpecialMainIndex{#1 TF}\nobreak
-    \DoNotIndex{#1 TF}
+    \exp_args:Nx \SpecialMainIndex{ \tl_to_str:N \l_doc_at_replaced_macro_tl TF}\nobreak
+    \exp_args:Nx \DoNotIndex{ \tl_to_str:N \l_doc_at_replaced_macro_tl TF}
   }{
-    \SpecialMainIndex{#1}\nobreak
-    \DoNotIndex{#1}
+    \exp_args:Nx \SpecialMainIndex{ \tl_to_str:N \l_doc_at_replaced_macro_tl }\nobreak
+    \exp_args:Nx \DoNotIndex{ \tl_to_str:N \l_doc_at_replaced_macro_tl }
   }
 
   \global\advance \c@CodelineNo \m@ne
@@ -1496,7 +1523,8 @@ Do not distribute a modified version of this file.
 \tl_clear:N \l_doc_macro_tl
 \cs_set_nopar:Npn \doc_print_macroname:n #1 {
   \strut
-  \int_compare:nTF { \tl_length:n {#1} <= 28 }
+  \HD@target
+  \int_compare:nTF { \tl_count:n {#1} <= 28 }
     { \MacroFont } { \MacroLongFont }
 
   % INEFFICIENT: (!)
@@ -1581,15 +1609,16 @@ Do not distribute a modified version of this file.
 % \end{macro}
 %
 % \begin{macro}{\TestMissing}
+%   Note: There \cs{l_doc_macro_input_clist} may contain unconverted |@@|.
 %    \begin{macrocode}
 \cs_generate_variant:Nn \prop_gput:Nnn {NVx}
 \DeclareDocumentCommand \TestMissing {m} {
   \prop_if_in:NVTF \g_doc_missing_tests_prop \l_doc_macro_input_clist
   {
-    \prop_get:NVN \g_doc_missing_tests_prop \l_doc_macro_input_clist \l_tmpa_tl
+    \prop_get:NVN \g_doc_missing_tests_prop \l_doc_macro_input_clist \l_doc_tmpa_tl
     \prop_gput:NVx \g_doc_missing_tests_prop \l_doc_macro_input_clist
     {
-      *~ \l_tmpa_tl
+      *~ \l_doc_tmpa_tl
       ^^J \exp_not:n {\space\space\space\space\space\space}
       *~ #1
     }
@@ -1599,11 +1628,45 @@ Do not distribute a modified version of this file.
 %    \end{macrocode}
 % \end{macro}
 %
+% \begin{variable}{\g_doc_module_name_tl}
+% \begin{macro}[int]{\doc_replace_at_at:N}
+%    \begin{macrocode}
+\tl_new:N \g_doc_module_name_tl
+\cs_new_protected:Npn \doc_replace_at_at:N #1 {
+    \tl_if_empty:NF \g_doc_module_name_tl
+      {
+        \tl_replace_all:Non #1 { \token_to_str:N @ } { @ }
+        \tl_replace_all:Non #1 { \token_to_str:N _ } { _ }
+        \tl_replace_all:Nox #1 { _@@ } { __ \g_doc_module_name_tl }
+        \tl_replace_all:Nox #1 { @@ } { __ \g_doc_module_name_tl }
+      }
+}
+\cs_generate_variant:Nn \tl_replace_all:Nnn { Non, Nox }
+%    \end{macrocode}
+% \end{macro}
+% \end{variable}
+%
 % \begin{macro}{\endmacro}
+%   The \cs{doc_endmacro_wrap_each:N} puts each item of the sequence |#1|
+%   in \cs{texttt} font and with a trailing TF if needed.  This should
+%   go inline in the definition of \cs{endmacro}, but somehow the |#|
+%   doesn't go through some \LaTeXe{} internals.
 %    \begin{macrocode}
-\cs_set:Nn \doc_macro_wrap:n
+\cs_new_protected:Nn \doc_endmacro_build_seq:N
+  {
+    \seq_gclear:N #1
+    \clist_map_inline:Nn \l_doc_macro_input_clist
+      {
+        \tl_set:Nn \l_doc_tmpa_tl {##1}
+        \doc_replace_at_at:N \l_doc_tmpa_tl
+        \seq_gput_right:No #1 { \l_doc_tmpa_tl }
+      }
+  }
+\cs_set_protected:Nn \doc_endmacro_wrap_each:N
   {
-    #1 \bool_if:NT \l_doc_macro_TF_bool {TF}
+    \bool_if:NTF \l_doc_macro_TF_bool
+      { \seq_gset_map:NNn #1 #1 { \exp_not:N \texttt { ##1 TF } } }
+      { \seq_gset_map:NNn #1 #1 { \exp_not:N \texttt { ##1 } } }
   }
 \cs_set:Nn \doc_texttt_comma:n {\,,~\texttt{#1}}
 \cs_set:Npn \endmacro {
@@ -1611,29 +1674,14 @@ Do not distribute a modified version of this file.
   {
   \par\nobreak\noindent{\footnotesize(\emph{
     End~ definition~ for~
-    \prg_case_int:nnn { \clist_length:N \l_doc_macro_input_clist }
-    {
-      {1} { \texttt{ \doc_macro_wrap:n { \clist_use:N \l_doc_macro_input_clist } }. }
-      {2}
+    \doc_endmacro_build_seq:N \g_doc_tmpa_seq
+    \doc_endmacro_wrap_each:N \g_doc_tmpa_seq
+    \int_compare:nTF { \seq_count:N \g_doc_tmpa_seq <= 3 }
       {
-        \tl_set:Nx \l_clist_first_tl { \clist_item:Nn \l_doc_macro_input_clist {0} }
-        \tl_set:Nx \l_clist_last_tl { \clist_item:Nn \l_doc_macro_input_clist {1} }
-        \texttt{\doc_macro_wrap:n\l_clist_first_tl}\,~ and~ \texttt{\doc_macro_wrap:n\l_clist_last_tl}\,.
+        \seq_use:Nnnn \g_doc_tmpa_seq
+          { \,~and~ } { \,,~ } { \,,~and~ }
       }
-      {3}
-      {
-        \tl_set:Nx \l_clist_first_tl { \clist_item:Nn \l_doc_macro_input_clist {0} }
-        \tl_set:Nx \l_clist_mid_tl   { \clist_item:Nn \l_doc_macro_input_clist {1} }
-        \tl_set:Nx \l_clist_last_tl  { \clist_item:Nn \l_doc_macro_input_clist {2} }
-        \texttt{\doc_macro_wrap:n\l_clist_first_tl}\,,~
-        \texttt{\doc_macro_wrap:n\l_clist_mid_tl}\,,~
-        and~ \texttt{\doc_macro_wrap:n\l_clist_last_tl}\,.
-      }
-    }
-    {
-      \tl_set:Nx \l_clist_first_tl { \clist_item:Nn \l_doc_macro_input_clist {0} }
-      \texttt{\doc_macro_wrap:n\l_clist_first_tl}\,~and~others.
-    }
+      { \seq_item:Nn \g_doc_tmpa_seq {1}\,~and~others. }
     \bool_if:nT {
       !\l_doc_macro_aux_bool &&
       !\l_doc_macro_internal_bool &&
@@ -1656,7 +1704,7 @@ Do not distribute a modified version of this file.
   {
     \seq_gput_right:Nx \g_doc_not_tested_seq
     {
-      \l_doc_macro_input_clist
+      \seq_use:Nnnn \g_doc_tmpa_seq { , } { , } { , }
       \bool_if:NT \l_doc_macro_pTF_bool {~(pTF)}
       \bool_if:NT \l_doc_macro_TF_bool {~(TF)}
     }
@@ -1665,6 +1713,70 @@ Do not distribute a modified version of this file.
 %    \end{macrocode}
 % \end{macro}
 %
+% \begin{environment}{macrocode}
+% \begin{macro}[aux]{\doc_xmacro_code:n}
+%   Hook into the \texttt{macrocode} environment in a dirty way:
+%   \cs{xmacro@code} is responsible for grabbing (and tokenizing) the
+%   body of the environment.  Redefine it to pass what it grabs to
+%   \cs{doc_xparse_code:n}.  This new macro replaces all |@@| by the
+%   appropriate module name.  One exceptional case is the
+%   |<@@=|\meta{module}|>| lines themselves, where |@@| should not be
+%   modified.  Actually, we search for such lines, to set the module
+%   name automatically.  We need to be careful: no |<@@=| should appear
+%   as such in the code below since \pkg{l3doc} is also typeset using
+%   this code.
+%    \begin{macrocode}
+\group_begin:
+  \char_set_catcode_escape:N \/
+  \char_set_catcode_other:N \^^A
+  \char_set_catcode_active:N \^^S
+  \char_set_catcode_active:N \^^B
+  \char_set_catcode_other:N \^^L
+  \char_set_catcode_other:N \^^R
+  \char_set_lccode:nn { `\^^A } { `\% }
+  \char_set_lccode:nn { `\^^S } { `\  }
+  \char_set_lccode:nn { `\^^B } { `\\ }
+  \char_set_lccode:nn { `\^^L } { `\{ }
+  \char_set_lccode:nn { `\^^R } { `\} }
+  \tl_to_lowercase:n
+    {
+      \group_end:
+      \cs_set_protected:Npn \xmacro@code
+          #1 ^^A ^^S^^S^^S^^S ^^Bend ^^Lmacrocode^^R
+        { \doc_xmacro_code:n {#1} /end{macrocode} }
+    }
+\group_begin:
+  \char_set_catcode_active:N \<
+  \char_set_catcode_active:N \>
+  \cs_new_protected:Npn \doc_xmacro_code:n #1
+    {
+      \tl_if_in:nnTF {#1} { < @ @ = }
+        { \doc_xmacro_code:w #1 \q_stop }
+        {
+          \tl_set:Nn \l_doc_tmpa_tl {#1}
+          \doc_replace_at_at:N \l_doc_tmpa_tl
+          \tl_use:N \l_doc_tmpa_tl
+        }
+    }
+  \cs_new_protected:Npn \doc_xmacro_code:w #1 < @ @ = #2 > #3 \q_stop
+    {
+      \tl_set:Nn \l_doc_tmpa_tl {#1}
+      \doc_replace_at_at:N \l_doc_tmpa_tl
+
+      \tl_gset:Nn \g_doc_module_name_tl {#2}
+      \tl_put_right:Nn \l_doc_tmpa_tl { < @ @ = #2 > }
+
+      \tl_set:Nn \l_doc_tmpb_tl {#3}
+      \doc_replace_at_at:N \l_doc_tmpb_tl
+      \tl_put_right:No \l_doc_tmpa_tl { \l_doc_tmpb_tl }
+
+      \tl_use:N \l_doc_tmpa_tl
+    }
+\group_end:
+%    \end{macrocode}
+% \end{macro}
+% \end{environment}
+%
 % \begin{macro}{\DescribeOption}
 % For describing package options. Due to Joseph Wright.
 % Name/usage might change soon.
@@ -1987,40 +2099,44 @@ Do not distribute a modified version of this file.
 % Print all defined and documented macros/functions.
 %
 %    \begin{macrocode}
-\iow_open:Nn \g_write_func_stream { \jobname.cmds }
+\iow_new:N \g_doc_func_iow
 %    \end{macrocode}
 %
 %    \begin{macrocode}
 \cs_new_nopar:Npn \doc_show_functions_defined: {
   \bool_if:nT { \g_doc_implementation_bool && \g_doc_checkfunc_bool } {
     \typeout{ ======================================== ^^J }
+    \iow_open:Nn \g_doc_func_iow { \c_job_name_tl .cmds }
 
-    \tl_clear:N \l_tmpa_tl
+    \tl_clear:N \l_doc_tmpa_tl
     \seq_map_inline:Nn \g_doc_functions_seq {
       \seq_if_in:NnT \g_doc_macros_seq {##1} {
-        \tl_put_right:Nn \l_tmpa_tl { ##1 ^^J }
-        \iow_now:Nn \g_write_func_stream { ##1 }
+        \tl_put_right:Nn \l_doc_tmpa_tl { ##1 ^^J }
+        \iow_now:Nn \g_doc_func_iow { > ~ ##1 }
       }
     }
-    \iow_close:N \g_write_func_stream
+
     \doc_functions_typeout:n {
       Functions~both~documented~and~defined:^^J (In~order~of~being~documented)
     }
 
     \seq_map_inline:Nn \g_doc_functions_seq {
       \seq_if_in:NnF \g_doc_macros_seq {##1} {
-        \tl_put_right:Nn \l_tmpa_tl { ##1 ^^J }
+        \tl_put_right:Nn \l_doc_tmpa_tl { ##1 ^^J }
+        \iow_now:Nn \g_doc_func_iow { ! ~ ##1}
       }
     }
     \doc_functions_typeout:n { Functions~documented~but~not~defined: }
 
     \seq_map_inline:Nn \g_doc_macros_seq {
       \seq_if_in:NnF \g_doc_functions_seq {##1} {
-        \tl_put_right:Nn \l_tmpa_tl { ##1 ^^J }
+        \tl_put_right:Nn \l_doc_tmpa_tl { ##1 ^^J }
+        \iow_now:Nn \g_doc_func_iow { ? ~ ##1}
       }
     }
     \doc_functions_typeout:n { Functions~defined~but~not~documented: }
 
+    \iow_close:N \g_doc_func_iow
     \typeout{ ======================================== }
   }
 }
@@ -2029,12 +2145,12 @@ Do not distribute a modified version of this file.
 %
 %    \begin{macrocode}
 \cs_set_nopar:Npn \doc_functions_typeout:n #1 {
-  \tl_if_empty:NF \l_tmpa_tl {
+  \tl_if_empty:NF \l_doc_tmpa_tl {
     \typeout{
       -------------------------------------- ^^J #1 ^^J
-      -------------------------------------- ^^J \l_tmpa_tl
+      -------------------------------------- ^^J \l_doc_tmpa_tl
     }
-    \tl_clear:N \l_tmpa_tl
+    \tl_clear:N \l_doc_tmpa_tl
   }
 }
 %    \end{macrocode}
@@ -2046,23 +2162,23 @@ Do not distribute a modified version of this file.
     \bool_if:nT { !(\seq_if_empty_p:N  \g_doc_not_tested_seq) ||
                   !(\prop_if_empty_p:N \g_doc_missing_tests_prop) }
     {
-      \tl_clear:N \l_tmpa_tl
+      \tl_clear:N \l_doc_tmpa_tl
       \prop_if_empty:NF \g_doc_missing_tests_prop
       {
-        \tl_put_right:Nn \l_tmpa_tl
+        \tl_put_right:Nn \l_doc_tmpa_tl
         {
           ^^J^^JThe~ following~ macro(s)~ have~ incomplete~ tests:^^J
         }
         \prop_map_inline:Nn \g_doc_missing_tests_prop
         {
-          \tl_put_right:Nn \l_tmpa_tl
+          \tl_put_right:Nn \l_doc_tmpa_tl
           {^^J\space\space\space\space ##1
            ^^J\space\space\space\space\space\space ##2}
         }
       }
       \seq_if_empty:NF \g_doc_not_tested_seq
       {
-        \tl_put_right:Nn \l_tmpa_tl
+        \tl_put_right:Nn \l_doc_tmpa_tl
         {
           ^^J^^J
           The~ following~ macro(s)~ do~ not~ have~ any~ tests:^^J
@@ -2071,12 +2187,12 @@ Do not distribute a modified version of this file.
         {
           \clist_map_inline:nn {##1}
           {
-            \tl_put_right:Nn \l_tmpa_tl {^^J\space\space\space\space ####1}
+            \tl_put_right:Nn \l_doc_tmpa_tl {^^J\space\space\space\space ####1}
           }
         }
         \int_set:Nn \l_tmpa_int {\etex_interactionmode:D}
         \errorstopmode
-        \ClassError{l3doc}{\l_tmpa_tl}{}
+        \ClassError{l3doc}{\l_doc_tmpa_tl}{}
         \int_set:Nn \etex_interactionmode:D {\l_tmpa_int}
       }
     }
@@ -2111,39 +2227,31 @@ Do not distribute a modified version of this file.
 %    \end{macrocode}
 %
 %
-% \begin{macro}{\doc_special_main_index:n,\doc_special_main_index:o,\hdpgindex}
+% \begin{macro}{\doc_special_main_index:n,\doc_special_main_index:o, \doc_special_main_index:x}
 % Heiko's replacement to play nicely with |hypdoc|:
 %    \begin{macrocode}
 
 \cs_set_nopar:Npn \doc_special_main_index:n #1 {
+  \HD@target
   \index{
     \@gobble#1
     \actualchar
     \string\verb\quotechar*\verbatimchar#1\verbatimchar
     \encapchar
-    hdpgindex{\thepage}{usage}
-  }
-}
-\cs_set_nopar:Npn \doc_special_main_index:o { \exp_args:No \doc_special_main_index:n }
-%    \end{macrocode}
-%    \begin{macrocode}
-\cs_set_nopar:Npn \hdpgindex #1#2#3 {
-  \csname\ifx\\#2\\relax\else#2\fi\endcsname{
-    \hyperlink{page.#1}{#3}
+    hdclindex{\the\c@HD@hypercount}{usage}
   }
 }
+\cs_generate_variant:Nn \doc_special_main_index:n { o , x }
 %    \end{macrocode}
 % \end{macro}
 %
 %    \begin{macrocode}
-\g@addto@macro \PrintIndex { \AtEndDocument{ \typeout{^^J
-  ========================================^^J
-  Generate~the~index~by~executing^^J
-  \c_space_tl \c_space_tl \c_space_tl \c_space_tl
-  makeindex~-s~l3doc.ist~-o~\jobname.ind~\jobname.idx^^J
-  ========================================^^J
-  }}
-}
+\msg_new:nnn {l3doc} {print-index-howto}
+  {
+    Generate~the~index~by~executing\\
+    \iow_indent:n { makeindex~-s~l3doc.ist~-o~\c_job_name_tl .ind~\c_job_name_tl .idx }
+  }
+\tl_gput_right:Nn \PrintIndex { \AtEndDocument{ \msg_info:nn {l3doc} {print-index-howto} } }
 %    \end{macrocode}
 %
 % \subsection{Change history}
@@ -2160,14 +2268,12 @@ Do not distribute a modified version of this file.
 %    \end{macrocode}
 %
 %    \begin{macrocode}
-\g@addto@macro \PrintChanges { \AtEndDocument{ \typeout{^^J
-  ========================================^^J
-  Generate~the~change~list~by~executing^^J
-  \c_space_tl \c_space_tl \c_space_tl \c_space_tl
-   makeindex~-s~gglo.ist~~-o~\jobname.gls~\jobname.glo^^J
-  ========================================^^J
-  }}
-}
+\msg_new:nnn {l3doc} {print-changes-howto}
+  {
+    Generate~the~change~list~by~executing\\
+    \iow_indent:n { makeindex~-s~gglo.ist~-o~\c_job_name_tl .gls~\c_job_name_tl .glo }
+  }
+\tl_gput_right:Nn \PrintChanges { \AtEndDocument{ \msg_info:nn {l3doc} {print-changes-howto} } }
 %    \end{macrocode}
 %
 %^^A The standard \changes command modified slightly to better cope with
@@ -2190,7 +2296,7 @@ Do not distribute a modified version of this file.
 %^^A                                 :\levelchar #3}}%
 %^^A  \@tempa\endgroup\@esphack}
 %
-% \subsection{cfg}
+% \subsection{Default configuration}
 %
 %    \begin{macrocode}
 \bool_if:NTF \g_doc_full_bool {
@@ -2210,6 +2316,79 @@ Do not distribute a modified version of this file.
 %</class>
 %    \end{macrocode}
 %
+% \subsection{Internal macros for \LaTeX3 sources}
+%
+% These definitions are only used by the \LaTeX3 documentation;
+% they are not necessary for third-party users of l3doc.
+% In time this will be broken into a separate package that is specifically
+% loaded in the various expl3 modules, etc.
+%
+%    \begin{macrocode}
+%<*cfg>
+%    \end{macrocode}
+%
+% The Guilty Parties.
+%    \begin{macrocode}
+\cs_new_nopar:Npn\Team{%
+  The~\LaTeX3~Project\thanks{%
+  Frank~Mittelbach,~Denys~Duchier,~Chris~Rowley,~
+  Rainer~Sch\"opf,~Johannes~Braams,~Michael~Downes,~
+  David~Carlisle,~Alan~Jeffrey,~Morten~H\o{}gholm,~Thomas~Lotze,~
+  Javier~Bezos,~Will~Robertson,~Joseph~Wright,~Bruno~Le~Floch}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\NewDocumentCommand{\ExplMakeTitle}{mm}
+ {
+   \title
+     {
+        The~\pkg{#1}~package \\ #2
+        \thanks{This~file~describes~v\ExplFileVersion,~
+          last~revised~\ExplFileDate.}
+     }
+   \author{The~\LaTeX3~Project\thanks{E-mail:~
+     \href{mailto:latex-l@listserv.uni-heidelberg.de}
+          {latex-l@listserv.uni-heidelberg.de}}}
+   \date{Released~\ExplFileDate}
+   \maketitle
+ }
+%    \end{macrocode}
+%
+% \subsection{Text extras}
+%
+%    \begin{macrocode}
+\DeclareDocumentCommand\ie{}{\emph{i.e.}}
+\DeclareDocumentCommand\eg{}{\emph{e.g.}}
+\DeclareDocumentCommand\Ie{}{\emph{I.e.}}
+\DeclareDocumentCommand\Eg{}{\emph{E.g.}}
+%    \end{macrocode}
+%
+% \subsection{Math extras}
+%
+% For \pkg{l3fp}.
+% 
+%    \begin{macrocode}
+\AtBeginDocument
+  {
+    \clist_map_inline:nn
+      {
+        asin, acos, atan, acot,
+        asinh, acosh, atanh, acoth, round, floor, ceil
+      }
+      { \exp_args:Nc \DeclareMathOperator{#1}{#1} }
+  }
+%    \end{macrocode}
+%    
+% \begin{macro}{\nan}
+%    \begin{macrocode}
+\NewDocumentCommand { \nan } { } { \text { \texttt { nan } } }
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</cfg>
+%    \end{macrocode}
+%
 %
 % \subsection{Makeindex configuration}
 %
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3docstrip.dtx b/Master/texmf-dist/source/latex/l3kernel/l3docstrip.dtx
new file mode 100644
index 00000000000..5e2ba0a5e63
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3docstrip.dtx
@@ -0,0 +1,277 @@
+% \iffalse
+%
+%% File l3dosctrip.dtx Copyright (C) 2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver|program>
+\def\ExplFileDate{2012/06/08}
+\def\ExplFileName{l3docstrip}
+\def\ExplFileVersion{3787}
+%</driver|program>
+%<*driver>
+% The same approach as used in \textsf{DocStrip}: if \cs{documentclass}
+% is undefined then skip the driver, allowing the file to be used to extract
+% \texttt{l3docstrip.tex} from \texttt{l3docstrip.dtx} directly. This works
+% as the \cs{fi} is only seen if \LaTeX{} is not in use. The odd \cs{jobname}
+% business allows the extraction to work with \LaTeX{} provided an appropriate
+% \texttt{.ins} file is set up.
+%<*gobble>
+\ifx\jobname\relax\let\documentclass\undefined\fi
+\ifx\documentclass\undefined
+\else \csname fi\endcsname
+%</gobble>
+  \def\filename{docstrip.dtx}
+  \documentclass[full]{l3doc}
+  \begin{document}
+    \DocInput{\jobname.dtx}
+  \end{document}
+%<*gobble>
+\fi
+%</gobble>
+%</driver>
+% \fi
+%
+% \title{^^A
+%   The \pkg{l3docstrip} package\\ Code extraction and manipulation^^A
+%   \thanks{This file describes v\ExplFileVersion,
+%      last revised \ExplFileDate.}^^A
+% }
+%
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+%
+% \date{Released \ExplFileDate}
+%
+% \maketitle
+%
+% \begin{documentation}
+% 
+% \section{Extending \textsf{DocStrip}}
+% 
+% The \pkg{l3docstrip} module adds \LaTeX3 extensions to the \textsf{DocStrip}
+% program for extracting code from \texttt{.dtx}. As such, this documentation
+% should be read along with that for \textsf{DocStrip}.
+% 
+% \section{Internal functions and variables}
+% 
+% An important consideration for \LaTeX3 development is separating out public
+% and internal functions. Functions and variables which are private to one
+% module should not be used or modified by any other module. As \TeX{} does
+% not have any formal namespacing system, this requires a convention for
+% indicating which functions in a code-level module are public and which are
+% private.
+% 
+% Using \pkg{l3docstrip} allows internal functions to be indicated using a
+% \enquote{two part} system. Within the \texttt{.dtx} file, internal functions
+% may be indicated using |@@| in place of the module name, for example
+% \begin{verbatim}
+%    \cs_new_protected:Npn \@@_some_function:nn #1#2
+%      {
+%        % Some code here
+%      }
+%    \tl_new:N \l_@@_internal_tl
+% \end{verbatim}
+%
+% To extract the code using \pkg{l3docstrip}, the \enquote{guard} concept
+% used by \textsf{DocStrip} is extended by introduction of the syntax
+% \texttt{\%<@@=\meta{module}}. The \meta{module} name will be used when the
+% code is extracted to replace the |@@|, so that
+% \begin{verbatim}
+%   %<*package>
+%   %<@@=foo>
+%   \cs_new_protected:Npn \@@_some_function:nn #1#2
+%      {
+%        % Some code here
+%      }
+%   \tl_new:N \l_@@_internal_tl
+%   %</package>  
+% \end{verbatim}
+% will be extracted as
+% \begin{verbatim}
+%   \cs_new_protected:Npn \__foo_some_function:nn #1#2
+%      {
+%        % Some code here
+%      }
+%   \tl_new:N \l__foo_internal_tl
+% \end{verbatim}
+% where the |__| indicates that the functions and variables are internal
+% to the \texttt{foo} module.
+% 
+% \end{documentation}
+% 
+% \begin{implementation}
+%
+% \section{\pkg{l3docstrip} implementation}
+% 
+%    \begin{macrocode}
+%<*program>
+%    \end{macrocode}
+%
+% We start by loading the existing \textsf{DocStrip} code using the \TeX{}
+% input convention.
+%    \begin{macrocode}
+\input docstrip %
+%    \end{macrocode}
+%
+% \begin{macro}{\checkOption}
+%   The \cs{checkOption} macro is defined by \textsf{DocStrip} and is redefined
+%   here to accommodate the new \texttt{\%<@} syntax.
+% 
+%   When the macros that process a line have found that the line starts with 
+%   \enquote{\texttt{\%<}}, a guard line has been encountered. The first
+%   character of a guard can be an asterisk (\texttt{*}), a slash (\texttt{/}),
+%   a plus (\texttt{+}), a minus (\texttt{-}), a less-than sign (\texttt{<})
+%   starting verbatim mode, a commercial at (\texttt{@}) or any other character
+%   that can be found in an option name. This means that we have to peek at the
+%   next token and decide what kind of guard we have. We reinsert |#1| as it
+%   may be needed by \cs{doOption}.
+%    \begin{macrocode}
+\def\checkOption<#1{%
+  \ifcase
+    \ifx*#10\else \ifx/#11\else
+    \ifx+#12\else \ifx-#13\else
+    \ifx<#14\else \ifx @#15\else 6\fi\fi\fi\fi\fi\fi\relax
+  \expandafter\starOption\or
+  \expandafter\slashOption\or
+  \expandafter\plusOption\or
+  \expandafter\minusOption\or
+  \expandafter\verbOption\or
+  \expandafter\moduleOption\or
+  \expandafter\doOption\fi
+  #1%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\moduleOption}
+%   In the case where the line starts |%<@|: the defined syntax requires that
+%   this continues to |%<@@=|. At the moment, we assume that the syntax will
+%   be correct and |#1| here is the module name for substitution into any
+%   internal functions in the extracted material.
+%    \begin{macrocode}
+\def\moduleOption @@=#1>#2\endLine{%
+  \maybeMsg{<@@=#1>}%
+  \prepareActiveModule{#1}%
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\prepareActiveModule}
+% \begin{macro}{\replaceModuleInLine}
+%   Here, we set up to do the search-and-replace when doing the extraction.
+%   The argument (|#1|) is the replacement text to use, or if empty an
+%   indicator that no replacement should be done. The search material is
+%   one of |__@@|, |_@@| or |@@|, done in order such that all three will end
+%   up the same in the output. The replacement function is initialised as a
+%   do-nothing for the case where |%<@@=| is never seen.
+%    \begin{macrocode}
+\begingroup
+  \catcode`\_ = 12 %
+  \long\gdef\prepareActiveModule#1{%
+    \ifx\relax#1\relax
+       \let\replaceModuleInLine\empty
+    \else
+      \def\replaceModuleInLine{%
+        \replaceAllIn\inLine{__@@}{__#1}%
+        \replaceAllIn\inLine{_@@}{__#1}%
+        \replaceAllIn\inLine{@@}{__#1}%
+      }%  
+    \fi
+  }
+\endgroup
+\let\replaceModuleInLine\empty
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\replaceAllIn}
+% \begin{macro}{\replaceAllInAuxI}
+% \begin{macro}{\replaceAllInAuxII}
+% \begin{macro}{\replaceAllInAuxIII}
+%   The code here is a simple search-and-replace routine for a macro |#1|,
+%   replacing |#2| by |#3|. As set up here, there is an assumption that nothing
+%   is going to be expandable, which is reasonable as \pkg{l3docstrip} deals
+%   with \enquote{string} material.
+%    \begin{macrocode}
+\long\def\replaceAllIn#1#2#3{%
+  \long\def\tempa##1##2#2{%
+    ##2\qMark\replaceAllInAuxIII#3##1%
+  }%
+  \edef#1{\expandafter\replaceAllInAuxI#1\qMark#2\qStop}%
+}
+\def\replaceAllInAuxI{%
+  \expandafter\replaceAllInAuxII\tempa\replaceAllInAuxI\empty
+}
+\long\def\replaceAllInAuxII#1\qMark#2{#1}
+\long\def\replaceAllInAuxIII#1\qStop{}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\normalLine}
+%   The \cs{normalLine} macro is present in \textsf{DocStrip} but is modified
+%   here to include the search-and-replace macro \cs{replaceModuleInLine}. The
+%   macro \cs{normalLine} writes its argument (which has to be delimited with
+%   |\endLine|) on all active output files, i.e.~those with off-counters equal
+%   to zero. The counter \cs{codeLinesPassed} is incremented by~$1$ for
+%   statistics (the guards for this used in \textsf{DocStrip} are retained).
+%    \begin{macrocode}
+\def\normalLine#1\endLine{%
+%<*stats>
+  \advance\codeLinesPassed\@ne
+%</stats>
+  \maybeMsg{.}%
+  \def\inLine{#1}%
+  \replaceModuleInLine
+  \let\do\putline@do
+  \activefiles
+}
+%    \end{macrocode}
+% \end{macro}
+% 
+%    \begin{macrocode}
+%</program>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintIndex
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3drivers.dtx b/Master/texmf-dist/source/latex/l3kernel/l3drivers.dtx
index 2729cad13ca..817a616897f 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3drivers.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3drivers.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3drivers.dtx 3158 2012-01-09 00:47:42Z bruno $
+\GetIdInfo$Id: l3drivers.dtx 3986 2012-07-15 19:23:51Z joseph $
   {L3 Experimental drivers}
 %</driver|package>
 %<*driver>
@@ -89,9 +89,9 @@
 %
 % \section{Box clipping}
 %
-% \begin{function}[added = 2011-11-11]{\driver_box_use_clip:N}
+% \begin{function}[added = 2011-11-11]{\__driver_box_use_clip:N}
 %   \begin{syntax}
-%     \cs{driver_box_use_clip:N} \meta{box}
+%     \cs{__driver_box_use_clip:N} \meta{box}
 %   \end{syntax}
 %   Inserts the content of the \meta{box} at the current insertion point
 %   such that any material outside of the bounding box will not be displayed
@@ -101,32 +101,32 @@
 %
 % \section{Box rotation and scaling}
 %
-% \begin{function}[added = 2011-09-01]
-%  {\driver_box_rotate_begin:, \driver_box_rotate_end:}
+% \begin{function}[added = 2011-09-01, updated = 2012-05-18]
+%  {\__driver_box_rotate_begin:, \__driver_box_rotate_end:}
 %   \begin{syntax}
-%     \cs{driver_box_rotate_begin:}
-%     \cs{box_use:N} \cs{l_box_internal_box}
-%     \cs{driver_box_rotate_end:}
+%     \cs{__driver_box_rotate_begin:}
+%     \cs{box_use:N} \cs{l__box_internal_box}
+%     \cs{__driver_box_rotate_end:}
 %   \end{syntax}
 %   Rotates the \meta{box material} anti-clockwise around the current
 %   insertion point. The angle of rotation (in degrees counter-clockwise)
 %   and the sine and cosine of this angle should be stored in
-%   \cs{l_box_angle_fp}, \cs{l_box_sin_fp} and \cs{l_box_cos_fp},
+%   \cs{l__box_angle_fp}, \cs{l__box_sin_fp} and \cs{l__box_cos_fp},
 %   respectively. Typically, the box material inserted between the beginning
-%   and end markers will be stored in \cs{l_box_internal_box}: this fact is
+%   and end markers will be stored in \cs{l__box_internal_box}: this fact is
 %   required by some drivers to obtain the correct output.
 % \end{function}
 %
-% \begin{function}[added = 2011-09-02]
-%   {\driver_box_scale_begin:, \driver_box_scale_end:}
+% \begin{function}[added = 2011-09-02, updated = 2012-05-18]
+%   {\__driver_box_scale_begin:, \__driver_box_scale_end:}
 %   \begin{syntax}
-%     \cs{driver_box_scale_begin:}
+%     \cs{__driver_box_scale_begin:}
 %     \meta{box material}
-%     \cs{driver_box_scale_end:}
+%     \cs{__driver_box_scale_end:}
 %   \end{syntax}
 %   Scales the \meta{box material} (which should be either a \cs{box_use:N}
 %   or \cs{hbox:n} construct). The \meta{box material} is scaled by the values
-%   stored in \cs{l_box_scale_x_fp} and \cs{l_box_scale_y_fp} in the
+%   stored in \cs{l__box_scale_x_fp} and \cs{l__box_scale_y_fp} in the
 %   horizontal and vertical directions, respectively. This function is
 %   also reused when resizing boxes: at a driver level, only scalings are
 %   supported and so the higher-level code must convert the absolute sizes
@@ -135,9 +135,10 @@
 %
 % \section{Colour support}
 %
-% \begin{function}[added = 2011-09-03]{\driver_color_ensure_current:}
+% \begin{function}[added = 2011-09-03, updated = 2012-05-18]
+%   {\__driver_color_ensure_current:}
 %   \begin{syntax}
-%     \cs{driver_color_ensure_current:}
+%     \cs{__driver_color_ensure_current:}
 %   \end{syntax}
 %   Ensures that the colour used to typeset material is that which was
 %   set when the material was placed in a box. This function is therefore
@@ -154,6 +155,7 @@
 %
 %    \begin{macrocode}
 %<*initex|package>
+%<@@=driver>
 %    \end{macrocode}
 %
 %    \begin{macrocode}
@@ -171,7 +173,7 @@
   {l3pdfmode.def}{\ExplFileDate}{\ExplFileVersion}
   {L3~Experimental~driver:~xdvipdfmx}
 %</xdvipdfmx>
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
@@ -208,50 +210,62 @@
 %
 % \subsection{Driver utility functions}
 %
-% \begin{macro}{\driver_graphic_state_save:}
-% \begin{macro}{\driver_graphic_state_restore:}
+% \begin{macro}{\@@_graphic_state_save:, \@@_graphic_state_restore:}
 %   All of the drivers have a stack for saving the graphic state. These
-%   have slightly different interfaces. As \texttt{dvips} does not
-%   automatically save the current location, this is set up here.
+%   have slightly different interfaces. For both \texttt{dvips} and
+%   \texttt{xdvipdfmx} this is done using an appropriate special.
 %    \begin{macrocode}
-\cs_new_protected:Npn \driver_graphic_state_save:
+%<*dvips|xdvipdfmx>
+\cs_new_protected_nopar:Npn \@@_graphic_state_save:
 %<*dvips>
   { \tex_special:D { ps:gsave } }
 %</dvips>
-%<*pdfmode>
-  { \pdftex_pdfsave:D }
-%</pdfmode>
 %<*xdvipdfmx>
   { \tex_special:D { pdf:bcontent } }
 %</xdvipdfmx>
-\cs_new_protected:Npn \driver_graphic_state_restore:
+\cs_new_protected_nopar:Npn \@@_graphic_state_restore:
 %<*dvips>
   { \tex_special:D { ps:grestore } }
 %</dvips>
-%<*pdfmode>
-  { \pdftex_pdfrestore:D }
-%</pdfmode>
 %<*xdvipdfmx>
   { \tex_special:D { pdf:econtent } }
 %</xdvipdfmx>
+%</dvips|xdvipdfmx>
+%    \end{macrocode}
+%   For direct PDF output there is also a need to worry about the version
+%   of \pdfTeX{} in use: the \tn{pdfsave} primitive was only introduced
+%   in version~1.40.0.
+%    \begin{macrocode}
+%<*pdfmode>
+\cs_if_exist:NTF \pdftex_pdfsave:D
+  {
+    \cs_new_eq:NN \@@_graphic_state_save:    \pdftex_pdfsave:D
+    \cs_new_eq:NN \@@_graphic_state_restore: \pdftex_pdfrestore:D
+  }
+  {
+    \cs_new_protected_nopar:Npn \@@_graphic_state_save:
+      { \pdftex_pdfliteral:D { q } }
+    \cs_new_protected_nopar:Npn \@@_graphic_state_restore:
+      { \pdftex_pdfliteral:D { Q } }
+  }
+%</pdfmode>
 %    \end{macrocode}
-% \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\driver_pdf_literal:n, \driver_pdf_literal_direct:n}
+% \begin{macro}{\@@_pdf_literal:n, \@@_pdf_literal_direct:n}
 %   Both direct PDF mode and \texttt{xdvipdfmx} make use of direct PDF
 %   special insertion. These are slightly different in the two cases.
 %   The |direct| versions do not save the current matrix.
 %    \begin{macrocode}
 %<*pdfmode|xdvipdfmx>
-\cs_new_protected:Npn \driver_pdf_literal:n #1
+\cs_new_protected:Npn \@@_pdf_literal:n #1
 %<*pdfmode>
   { \pdftex_pdfliteral:D {#1} }
 %</pdfmode>
 %<*xdvipdfmx>
   { \tex_special:D { pdf:content~ #1 } }
 %</xdvipdfmx>
-\cs_new_protected:Npn \driver_pdf_literal_direct:n #1
+\cs_new_protected:Npn \@@_pdf_literal_direct:n #1
 %<*pdfmode>
   { \pdftex_pdfliteral:D direct~{#1} }
 %</pdfmode>
@@ -262,12 +276,12 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\driver_ps_literal:n}
+% \begin{macro}{\@@_ps_literal:n}
 %   The same concept for PostScript: these are \enquote{direct} by default,
 %   but by keeping the same name life should be a little clearer.
 %    \begin{macrocode}
 %<*dvips>
-\cs_new_protected:Npn \driver_ps_literal:n #1
+\cs_new_protected:Npn \@@_ps_literal:n #1
   { \tex_special:D { ps: #1 } }
 %</dvips>
 %    \end{macrocode}
@@ -275,7 +289,7 @@
 %
 % \subsection{Box clipping}
 %
-% \begin{macro}{\driver_box_use_clip:N}
+% \begin{macro}{\@@_box_use_clip:N}
 %   The overall logic to clipping a box is the same in all cases. The general
 %   method is to save the current location, define a clipping path equivalent
 %   to the bounding box, then insert the content at the current position
@@ -285,9 +299,9 @@
 %   as much code as possible and uses the same conversions (and so same
 %   rounding errors) in all three cases.
 %    \begin{macrocode}
-\cs_new_protected:Npn \driver_box_use_clip:N #1
+\cs_new_protected:Npn \@@_box_use_clip:N #1
   {
-    \driver_graphic_state_save:
+    \@@_graphic_state_save:
 %    \end{macrocode}
 %   The business end of the code sets up the clip box, using the higher-level
 %   rectangle operators rather than the lower level direct line drawing. This
@@ -301,21 +315,21 @@
 %   \TeX{} current positions).
 %    \begin{macrocode}
 %<*dvips>
-    \driver_ps_literal:n
+    \@@_ps_literal:n
       {
         /savedmatrix~matrix~currentmatrix~def~
         currentpoint~translate~
         Resolution~72~div~VResolution~72~div~scale
       }
-    \driver_ps_literal:n
+    \@@_ps_literal:n
       {
         0~
-        -\dim_strip_bp:n { \box_dp:N #1 } ~neg~
-         \dim_strip_bp:n { \box_wd:N #1 } ~
-         \dim_strip_bp:n { \box_ht:N #1 + \box_dp:N #1 } ~neg~
+        \__dim_strip_bp:n { \box_dp:N #1 } ~
+        \__dim_strip_bp:n { \box_wd:N #1 } ~
+        \__dim_strip_bp:n { - \box_ht:N #1 - \box_dp:N #1 } ~
         rectclip
       }
-    \driver_ps_literal:n { savedmatrix~setmatrix }
+    \@@_ps_literal:n { savedmatrix~setmatrix }
 %</dvips>
 %    \end{macrocode}
 %   The PDF box is easier to define as it is automatically in big points and
@@ -323,12 +337,12 @@
 %   locations automatically.
 %    \begin{macrocode}
 %<*pdfmode|xdvipdfmx>
-    \driver_pdf_literal_direct:n
+    \@@_pdf_literal_direct:n
       {
         0 ~
-        -\dim_strip_bp:n { \box_dp:N #1 } ~
-         \dim_strip_bp:n { \box_wd:N #1 } ~
-         \dim_strip_bp:n { \box_ht:N #1 + \box_dp:N #1 } ~
+        \__dim_strip_bp:n { - \box_dp:N #1 } ~
+        \__dim_strip_bp:n { \box_wd:N #1 } ~
+        \__dim_strip_bp:n { \box_ht:N #1 + \box_dp:N #1 } ~
         re~W~n
       }
 %</pdfmode|xdvipdfmx>
@@ -337,7 +351,7 @@
 %   and then insert the necessary width.
 %    \begin{macrocode}
     \hbox_overlap_right:n { \box_use:N #1 }
-    \driver_graphic_state_restore:
+    \@@_graphic_state_restore:
     \skip_horizontal:n { \box_wd:N #1 }
   }
 %    \end{macrocode}
@@ -345,16 +359,7 @@
 %
 % \subsection{Box rotation and scaling}
 %
-% \begin{variable}{\l_driver_internal_fp}
-%  Needed for a safe sign inversion in PDF mode.
-%    \begin{macrocode}
-%<*pdfmode|xdvipdfmx>
-\fp_new:N \l_driver_internal_fp
-%</pdfmode|xdvipdfmx>
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{macro}{\driver_box_rotate_begin:, \driver_box_rotate_end:}
+% \begin{macro}{\@@_box_rotate_begin:, \@@_box_rotate_end:}
 %   The driver for \texttt{dvips} works with a simple rotation angle.
 %   In PDF mode, an affine matrix is used instead. The transformation for
 %   \texttt{xdvipdfmx} can be done either way: to have some code sharing,
@@ -362,137 +367,189 @@
 %   shared in this way). For the \texttt{dvips}, that odd-looking
 %   |currentpoint| at the beginning is used to put this data onto the
 %   stack for |neg exch neg exch translate| to pick up.
+%   
+%   In both cases, some rounding code is included to limit the floating
+%   point values to five decimal places. There is no point using any more
+%   as \TeX{}'s dimensions are of that precision, and the extra figures
+%   will simply bloat the PDF and make values harder to trace. In the
+%   case where the sine and cosine are used, we store the rounded values to
+%   avoid rounding twice. There are also a couple of comparisons to ensure
+%   that |-0| is not written to the output, as this avoids any issues with
+%   problematic display programs.
 %    \begin{macrocode}
-\cs_new_protected:Npn \driver_box_rotate_begin:
+\cs_new_protected_nopar:Npn \@@_box_rotate_begin:
   {
-    \driver_graphic_state_save:
+    \@@_graphic_state_save:
 %<*dvips>
-    \driver_ps_literal:n
+    \@@_ps_literal:n
       {
         currentpoint~
         currentpoint~translate~
-        \fp_use:N \l_box_angle_fp \c_space_tl neg~rotate~
+        \fp_compare:nTnTF \l__box_angle_fp = \c_zero_fp
+          { 0 }
+          { \fp_eval:n { round ( - \l__box_angle_fp , 5 ) } }
+        ~rotate~
         neg~exch~neg~exch~translate
       }
 %</dvips>
 %<*pdfmode|xdvipdfmx>
-    \box_set_wd:Nn \l_box_internal_box \c_zero_dim
-    \fp_set_eq:NN \l_driver_internal_fp \l_box_sin_fp
-    \fp_neg:N \l_driver_internal_fp
-%<*pdfmode>
-    \pdftex_pdfsetmatrix:D
-%</pdfmode>
-%<*xdvipdfmx>
-    \driver_pdf_literal_direct:n
-%</xdvipdfmx>
+    \box_set_wd:Nn \l__box_internal_box \c_zero_dim
+    \fp_set:Nn \l__box_cos_fp
       {
-        \fp_use:N \l_box_cos_fp \c_space_tl
-        \fp_use:N \l_box_sin_fp \c_space_tl
-        \fp_use:N \l_driver_internal_fp \c_space_tl
-        \fp_use:N \l_box_cos_fp
-%<*xdvipdfmx>
-        \c_space_tl 0~0~cm
-%</xdvipdfmx>
+        \fp_compare:nNnTF \l__box_cos_fp = \c_zero_fp
+          { 0 }
+          { round ( \l__box_cos_fp , 5 ) }
+      }
+    \fp_set:Nn \l__box_sin_fp { round ( \l__box_sin_fp , 5 ) }
+    \@@_pdf_matrix:n
+      {
+        \fp_use:N \l__box_cos_fp \c_space_tl
+        \fp_compare:nNnTF \l__box_sin_fp = \c_zero_fp
+          { 0~0 }
+          {
+            \fp_use:N \l__box_sin_fp
+            \c_space_tl
+            \fp_eval:n { -\l__box_sin_fp }
+          }
+        \c_space_tl
+        \fp_use:N \l__box_cos_fp
       }
 %</pdfmode|xdvipdfmx>
   }
 %    \end{macrocode}
-% The end of a rotation means tidying up the output grouping.
+%   The end of a rotation means tidying up the output grouping.
 %    \begin{macrocode}
-\cs_new_eq:NN \driver_box_rotate_end: \driver_graphic_state_restore:
+\cs_new_eq:NN \@@_box_rotate_end: \@@_graphic_state_restore:
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\driver_box_scale_begin:, \driver_box_scale_end:}
+% \begin{macro}{\@@_box_scale_begin:, \@@_box_scale_end:}
 %   Scaling is not dissimilar to rotation, but the calculations are somewhat
 %   less complex.
 %    \begin{macrocode}
-\cs_new_protected:Npn \driver_box_scale_begin:
+\cs_new_protected_nopar:Npn \@@_box_scale_begin:
   {
-    \driver_graphic_state_save:
+    \fp_set:Nn \l__box_scale_x_fp { round ( \l__box_scale_x_fp , 5 ) }
+    \fp_set:Nn \l__box_scale_y_fp { round ( \l__box_scale_y_fp , 5 ) }
+    \@@_graphic_state_save:
 %<*dvips>
-    \driver_ps_literal:n
+    \@@_ps_literal:n
       {
         currentpoint~
         currentpoint~translate~
-        \fp_use:N \l_box_scale_x_fp \c_space_tl
-        \fp_use:N \l_box_scale_y_fp \c_space_tl scale~
+        \fp_use:N \l__box_scale_x_fp \c_space_tl
+        \fp_use:N \l__box_scale_y_fp \c_space_tl scale~
         neg~exch~neg~exch~translate
       }
 %</dvips>
 %<*pdfmode|xdvipdfmx>
-%<*pdfmode>
-    \pdftex_pdfsetmatrix:D
-%</pdfmode>
-%<*xdvipdfmx>
-    \driver_pdf_literal_direct:n
-%</xdvipdfmx>
+    \@@_pdf_matrix:n
       {
-        \fp_use:N \l_box_scale_x_fp \c_space_tl
+        \fp_use:N \l__box_scale_x_fp \c_space_tl
         0~0~
-        \fp_use:N \l_box_scale_y_fp
-%<*xdvipdfmx>
-        \c_space_tl 0~0~cm
-%</xdvipdfmx>
+        \fp_use:N \l__box_scale_y_fp
       }
 %</pdfmode|xdvipdfmx>
   }
-\cs_new_eq:NN \driver_box_scale_end: \driver_graphic_state_restore:
+\cs_new_eq:NN \@@_box_scale_end: \@@_graphic_state_restore:
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\@@_pdf_matrix:n}
+%   Here the appropriate function is set up to insert an affine matrix
+%   into the PDF. With a new enough \pdfTeX{} (version~1.40.0 or later)
+%   there is a primitive for this, which only needs the rotation/scaling/skew
+%   part. With an older \pdfTeX{} or with \texttt{xdvipdfmx} the matrix
+%   also has to include a translation part: that is always zero and so is
+%   built in here.
+%    \begin{macrocode}
+%<*pdfmode>
+\cs_if_exist:NTF \pdftex_pdfsetmatrix:D
+  {
+    \cs_new_protected:Npn \@@_pdf_matrix:n #1
+      { \pdftex_pdfsetmatrix:D {#1} }
+  }
+  {
+    \cs_new_protected:Npn \@@_pdf_matrix:n #1
+      { \@@_pdf_literal:n { #1 \c_space_tl 0~0~cm } }
+  }
+%</pdfmode>
+%<*xdvipdfmx>
+\cs_new_protected:Npn \@@_pdf_matrix:n #1
+  { \@@_pdf_literal_direct:n { #1 \c_space_tl 0~0~cm } }
+%</xdvipdfmx>
 %    \end{macrocode}
 % \end{macro}
 %
 % \subsection{Colour support}
 %
-% \begin{variable}{\l_driver_current_color_tl}
+% \begin{variable}{\l_@@_current_color_tl}
 %   The current colour is needed by all of the engines, but the way this
 %   is stored varies.
 %    \begin{macrocode}
-\tl_new:N \l_driver_current_color_tl
+\tl_new:N \l_@@_current_color_tl
 %<*dvips>
-\tl_set:Nn \l_driver_current_color_tl { Black }
+\tl_set:Nn \l_@@_current_color_tl { Black }
 %</dvips>
 %<*pdfmode>
-\tl_set:Nn \l_driver_current_color_tl { 0~g~0~G }
+\tl_set:Nn \l_@@_current_color_tl { 0~g~0~G }
 %</pdfmode>
 %<*xdvipdfmx>
-\tl_set:Nn \l_driver_current_color_tl { gray~0 }
+\tl_set:Nn \l_@@_current_color_tl { gray~0 }
 %</xdvipdfmx>
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_driver_color_stack_int}
-%   \pdfTeX{} and \LuaTeX{} have multiple stacks available, and the colour
-%   stack therefore needs a number.
+% \begin{variable}{\l_@@_color_stack_int}
+%   \pdfTeX{} (version~1.40.0 or later) and \LuaTeX{} have multiple stacks
+%   available, and the colour stack therefore needs a number.
 %    \begin{macrocode}
 %<*pdfmode>
-\int_new:N \l_driver_color_stack_int
+\int_new:N \l_@@_color_stack_int
 %</pdfmode>
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{macro}{\driver_color_ensure_current:}
-% \begin{macro}[aux]{\driver_color_reset:}
+% \begin{macro}{\@@_color_ensure_current:}
+% \begin{macro}[aux]{\@@_color_reset:}
 %   Setting the current colour depends on the nature of the colour stack
 %   available. In all cases there is a need to reset the colour after
 %   the current group.
 %    \begin{macrocode}
-\cs_new_protected:Npn \driver_color_ensure_current:
-  {
 %<*dvips|xdvipdfmx>
-    \tex_special:D { color~push~\l_driver_current_color_tl }
-%</dvips|xdvipdfmx>
-%<*pdfmode>
-    \pdftex_pdfcolorstack:D \l_driver_color_stack_int push
-      { \l_driver_current_color_tl }
-%</pdfmode>
-    \group_insert_after:N \driver_color_reset:
+\cs_new_protected_nopar:Npn \@@_color_ensure_current:
+  {
+    \tex_special:D { color~push~\l_@@_current_color_tl }
+    \group_insert_after:N \@@_color_reset:
   }
-\cs_new_protected:Npn \driver_color_reset:
-%<*dvips|xdvipdfmx>
+\cs_new_protected_nopar:Npn \@@_color_reset:
   { \tex_special:D { color~pop } }
 %</dvips|xdvipdfmx>
+%    \end{macrocode}
+%   Once again there is a version switch for \pdfTeX{}, as the
+%   \tn{pdfcolorstack} primitive was introduced in version~1.40.0.
+%    \begin{macrocode}
 %<*pdfmode>
-  { \pdftex_pdfcolorstack:D \l_driver_color_stack_int pop }
+\cs_if_exist:NTF \pdftex_pdfcolorstack:D
+  {
+    \cs_new_protected_nopar:Npn \@@_color_ensure_current:
+      {
+        \pdftex_pdfcolorstack:D \l_@@_color_stack_int push
+          { \l_@@_current_color_tl }
+        \group_insert_after:N \@@_color_reset:
+      }
+    \cs_new_protected_nopar:Npn \@@_color_reset:
+      { \pdftex_pdfcolorstack:D \l_@@_color_stack_int pop }
+  }
+  {
+    \cs_new_protected_nopar:Npn \@@_color_ensure_current:
+      {
+        \@@_pdf_literal:n { \l_@@_current_color_tl }
+        \group_insert_after:N \@@_color_reset:
+      }
+    \cs_new_protected_nopar:Npn \@@_color_reset:
+      { \@@_pdf_literal:n { \l_@@_current_color_tl } }
+  }
 %</pdfmode>
 %    \end{macrocode}
 % \end{macro}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3expan.dtx b/Master/texmf-dist/source/latex/l3kernel/l3expan.dtx
index 01024ff6593..8e14807cfcf 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3expan.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3expan.dtx
@@ -35,8 +35,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3expan.dtx 3460 2012-02-26 12:16:41Z will $
-  {L3 Experimental argument expansion}
+\GetIdInfo$Id: l3expan.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Argument expansion}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -85,17 +85,17 @@
 %
 % Internally preprocessing of arguments is done with functions from the
 % |\exp_| module.  They all look alike, an example would be
-% |\exp_args:NNo|. This function has three arguments, the first and the
+% \cs{exp_args:NNo}. This function has three arguments, the first and the
 % second are a single tokens, while the third argument should be given
-% in braces. Applying |\exp_args:NNo| will expand the content of third
+% in braces. Applying \cs{exp_args:NNo} will expand the content of third
 % argument once before any expansion of the first and second arguments.
-% If |\seq_gpush:No| was not define it could be coded in the following way:
+% If \cs{seq_gpush:No} was not defined it could be coded in the following way:
 % \begin{verbatim}
 %   \exp_args:NNo \seq_gpush:Nn
 %      \g_file_name_stack
 %      \l_tmpa_tl
 % \end{verbatim}
-% In other words, the first argument to |\exp_args:NNo| is the base
+% In other words, the first argument to \cs{exp_args:NNo} is the base
 % function and the other arguments are preprocessed and then passed to
 % this base function. In the example the first argument to the base
 % function should be a single token which is left unchanged while the
@@ -106,17 +106,17 @@
 %   |\cs_new_nopar:Npn\seq_gpush:No{\exp_args:NNo\seq_gpush:Nn}|
 % \end{quote}
 % Providing variants in this way in style files is uncritical as the
-% |\cs_new_nopar:Npn| function will silently accept definitions whenever the
+% \cs{cs_new_nopar:Npn} function will silently accept definitions whenever the
 % new definition is identical to an already given one. Therefore adding
 % such definition to later releases of the kernel will not make such
 % style files obsolete.
 %
 % The steps above may be automated by using the function
-% |\cs_generate_variant:Nn|, described next.
+% \cs{cs_generate_variant:Nn}, described next.
 %
 % \section{Methods for defining variants}
 %
-% \begin{function}[updated = 2011-09-15]{\cs_generate_variant:Nn}
+% \begin{function}[updated = 2012-06-21]{\cs_generate_variant:Nn}
 %   \begin{syntax}
 %     \cs{cs_generate_variant:Nn} \meta{parent control sequence} \Arg{variant argument specifiers}
 %   \end{syntax}
@@ -165,7 +165,7 @@
 %     Arguments that need full expansion (\emph{i.e.}, are denoted
 %     with |x|) should be avoided if possible as they can not be
 %     processed expandably, \emph{i.e.}, functions of this type will
-%     not work correctly in arguments that are itself subject to |x|
+%     not work correctly in arguments that are themselves subject to |x|
 %     expansion.
 %   \item
 %     In general, unless in the last position, multi-token arguments
@@ -176,6 +176,7 @@
 %     not expanded.
 % \end{itemize}
 %
+% ^^A Bruno: We should drop part of that paragraph eventually.
 % The |V| type returns the value of a register, which can be one of
 % |tl|, |num|, |int|, |skip|, |dim|, |toks|, or built-in \TeX{}
 % registers. The |v| type is the same except it first creates a
@@ -204,13 +205,13 @@
 % Unfortunately this only puts
 % |\exp_args:NNc \cs_set_eq:NN \aaa {b \l_tmpa_tl b}| into |\l_tmpb_tl|
 % and not |\cs_set_eq:NN \aaa = \blurb| as we probably wanted. Using
-% |\tl_set:Nx| is not an option as that will die horribly. Instead
+% \cs{tl_set:Nx} is not an option as that will die horribly. Instead
 % we can do a
 % \begin{quote}
 %   |\tl_set:Nf \l_tmpb_tl {\cs_set_eq:Nc \aaa { b \l_tmpa_tl b } }|
 % \end{quote}
 % which puts the desired result in |\l_tmpb_tl|. It requires
-% |\toks_set:Nf| to be defined as
+% \cs{tl_set:Nf} to be defined as
 % \begin{quote}
 %   |\cs_set_nopar:Npn \tl_set:Nf { \exp_args:NNf \tl_set:Nn }|
 % \end{quote}
@@ -315,7 +316,7 @@
 %     \exp_args:NVV
 %   }
 %   \begin{syntax}
-%     \cs{exp_args:NNc} \meta{token1} \meta{token2} \Arg{tokens}
+%     \cs{exp_args:NNc} \meta{token_1} \meta{token_2} \Arg{tokens}
 %   \end{syntax}
 %   These optimized functions absorb three arguments and expand the second and
 %   third as detailed by their argument specifier. The first argument
@@ -355,7 +356,7 @@
 %     \exp_args:Nxx
 %   }
 %   \begin{syntax}
-%     \cs{exp_args:NNx} \meta{token1} \meta{token2} \Arg{tokens}
+%     \cs{exp_args:NNx} \meta{token_1} \meta{token_2} \Arg{tokens}
 %   \end{syntax}
 %   These functions absorb three arguments and expand the second and
 %   third as detailed by their argument specifier. The first argument
@@ -376,7 +377,7 @@
 %     \exp_args:Ncco
 %   }
 %   \begin{syntax}
-%     \cs{exp_args:NNNo} \meta{token1} \meta{token2} \meta{token3} \Arg{tokens}
+%     \cs{exp_args:NNNo} \meta{token_1} \meta{token_2} \meta{token_3} \Arg{tokens}
 %   \end{syntax}
 %   These optimized functions absorb four arguments and expand the second, third
 %   and fourth as detailed by their argument specifier. The first
@@ -393,7 +394,7 @@
 %     \exp_args:Nooo,
 %   }
 %   \begin{syntax}
-%     \cs{exp_args:NNNo} \meta{token1} \meta{token2} \meta{token3} \Arg{tokens}
+%     \cs{exp_args:NNNo} \meta{token_1} \meta{token_2} \meta{token_3} \Arg{tokens}
 %   \end{syntax}
 %   These functions absorb four arguments and expand the second, third
 %   and fourth as detailed by their argument specifier. The first
@@ -413,7 +414,7 @@
 %     \exp_args:Nccx
 %   }
 %   \begin{syntax}
-%     \cs{exp_args:NNnx} \meta{token1} \meta{token2} \Arg{tokens_1} \Arg{tokens_2}
+%     \cs{exp_args:NNnx} \meta{token_1} \meta{token_2} \Arg{tokens_1} \Arg{tokens_2}
 %   \end{syntax}
 %   These functions absorb four arguments and expand the second, third
 %   and fourth as detailed by their argument specifier. The first
@@ -441,7 +442,7 @@
 %     \exp_last_unbraced:NnNo
 %     }
 %   \begin{syntax}
-%     \cs{exp_last_unbraced:Nno} \meta{token} \meta{tokens1} \meta{tokens2}
+%     \cs{exp_last_unbraced:Nno} \meta{token} \meta{tokens_1} \meta{tokens_2}
 %    \end{syntax}
 %   These functions absorb the number of arguments given by their
 %   specification, carry out the expansion
@@ -469,7 +470,7 @@
 %
 % \begin{function}[EXP]{\exp_last_two_unbraced:Noo}
 %   \begin{syntax}
-%     \cs{exp_last_two_unbraced:Noo} \meta{token} \meta{tokens1} \Arg{tokens_2}
+%     \cs{exp_last_two_unbraced:Noo} \meta{token} \meta{tokens_1} \Arg{tokens_2}
 %   \end{syntax}
 %   This function absorbs three arguments and expand the second and third
 %   once. The first argument of the function is then the next item on the
@@ -480,14 +481,14 @@
 %
 % \begin{function}[EXP]{\exp_after:wN}
 %   \begin{syntax}
-%     \cs{exp_after:wN} \meta{token1} \meta{token2}
+%     \cs{exp_after:wN} \meta{token_1} \meta{token_2}
 %   \end{syntax}
-%   Carries out a single expansion of \meta{token2} (which may consume
+%   Carries out a single expansion of \meta{token_2} (which may consume
 %   arguments) prior to the expansion
-%   of \meta{token1}. If \meta{token2} is a \TeX{} primitive, it will
-%   be executed rather than expanded, while if \meta{token2} has not
+%   of \meta{token_1}. If \meta{token_2} is a \TeX{} primitive, it will
+%   be executed rather than expanded, while if \meta{token_2} has not
 %   expansion (for example, if it is a character) then it will be left
-%   unchanged. It is important to notice that \meta{token1} may be
+%   unchanged. It is important to notice that \meta{token_1} may be
 %   \emph{any} single token, including group-opening and -closing
 %   tokens (|{| or |}| assuming normal \TeX{} category codes). Unless
 %   specifically required, expansion should be carried out using an
@@ -529,11 +530,11 @@
 %   \begin{syntax}
 %     \cs{exp_not:n} \Arg{tokens}
 %   \end{syntax}
-%   Prevents expansion of the \meta{tokens} in a context where they would
-%   otherwise
-%   be expanded, for example an |x|-type argument.
+%   Prevents expansion of the \meta{tokens} in a context where they
+%   would otherwise be expanded, for example an |x|-type argument.
 %   \begin{texnote}
-%     This is the \eTeX{} \tn{unexpanded} primitive.
+%     This is the \eTeX{} \tn{unexpanded} primitive.  Hence its argument
+%     \emph{must} be surrounded by braces.
 %   \end{texnote}
 % \end{function}
 %
@@ -591,24 +592,12 @@
 %
 % \section{Internal functions and variables}
 %
-% \begin{variable}{\l_exp_internal_tl}
+% \begin{variable}{\l__exp_internal_tl}
 %   The |\exp_| module has its private variables to temporarily store
 %   results of the argument expansion. This is done to avoid interference
 %   with other functions using temporary variables.
 % \end{variable}
 %
-% \begin{function}[EXP]{\exp_eval_register:N, \exp_eval_register:c}
-%   \begin{syntax}
-%     \cs{exp_eval_register:N} \meta{variable}
-%   \end{syntax}
-%   These functions evaluates a \meta{variable} as part of a |V| or |v|
-%   expansion (respectively), preceded by \cs{c_zero} which stops
-%   the expansion of a previous \tn{romannumeral}.
-%   A \meta{variable} might exist as
-%   one of two things: a parameter-less non-long, non-protected macro
-%   or a built-in \TeX{} register such as |\count|.
-% \end{function}
-%
 % \begin{function}{\::n, \::N, \::c, \::o, \::f, \::x, \::v, \::V, \:::}
 %   \begin{syntax}
 %     |\cs_set_nopar:Npn \exp_args:Ncof { \::c \::o \::f \::: }|
@@ -618,15 +607,6 @@
 %   visible in the log and so forth.
 % \end{function}
 %
-% \begin{function}{\cs_generate_internal_variant:n}
-%   \begin{syntax}
-%     \cs{cs_generate_internal_variant:n} \meta{arg~spec}
-%   \end{syntax}
-%   Tests if the function |\exp_args:N|\meta{arg~spec} exists, and defines it
-%   if it does not. The \meta{arg~spec} should be a series of one or more
-%   of the letters |N|, |c|, |n|, |o|, |V|, |v|, |f| and |x|.
-% \end{function}
-%
 % \end{documentation}
 %
 % \begin{implementation}
@@ -636,13 +616,17 @@
 %    \begin{macrocode}
 %<*initex|package>
 %    \end{macrocode}
+%    
+%    \begin{macrocode}
+%<@@=exp>
+%    \end{macrocode}
 %
 %    We start by ensuring that the required packages are loaded.
 %    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
@@ -659,23 +643,23 @@
 % In this section a general mechanism for defining functions to handle
 % argument handling is defined.  These general expansion functions are
 % expandable unless |x| is used.  (Any version of |x| is going to have
-% to use one of the \LaTeX3 names for |\cs_set_nopar:Npx| at some point, and
-% so is never going to be expandable.\footnote{However, some
-% primitives have certain characteristics that means that their
-% arguments undergo an \texttt{x} type expansion but the primitive
-% is in fact still expandable. We shall make it very clear when such
-% a function is expandable.})
+% to use one of the \LaTeX3 names for \cs{cs_set_nopar:Npx} at some
+% point, and so is never going to be expandable.\footnote{Some
+%   primitives have certain characteristics that means that their
+%   arguments undergo an expansion similar to an \texttt{x} type
+%   expansion but the primitive is in fact still expandable. We make it
+%   very clear when such a function is expandable.})
 %
 % The definition of expansion functions with this technique happens
 % in section~\ref{sec:gendef}.
 % In section~\ref{sec:handtune} some common cases are coded by a more direct
-% method for efficiency, typically using calls to |\exp_after:wN|.
+% method for efficiency, typically using calls to \cs{exp_after:wN}.
 %
-% \begin{variable}{\l_exp_internal_tl}
+% \begin{variable}{\l_@@_internal_tl}
 %   We need a scratch token list variable.
 %   We don't use |tl| methods so that \pkg{l3expan} can be loaded earlier.
 %    \begin{macrocode}
-\cs_new_nopar:Npn \l_exp_internal_tl { }
+\cs_new_nopar:Npn \l_@@_internal_tl { }
 %    \end{macrocode}
 % \end{variable}
 %
@@ -686,12 +670,12 @@
 %
 % An argument manipulator |\::|\meta{Z} always has signature |#1\:::#2#3|
 % where |#1| holds the remaining argument manipulations to be performed,
-% |\:::| serves as an end marker for the list of manipulations, |#2|
+% \cs{:::} serves as an end marker for the list of manipulations, |#2|
 % is the carried over result of the previous expansion steps and |#3| is
 % the argument about to be processed.
 %
-% \begin{macro}[aux, EXP]{\exp_arg_next:nnn}
-% \begin{macro}[aux, EXP]{\exp_arg_next:Nnn}
+% \begin{macro}[aux, EXP]{\@@_arg_next:nnn}
+% \begin{macro}[aux, EXP]{\@@_arg_next:Nnn}
 %   |#1| is the result of an expansion step, |#2| is the remaining
 %   argument manipulations and |#3| is the current result of the
 %   expansion chain.  This auxiliary function moves |#1| back after
@@ -702,8 +686,8 @@
 %   only the |c| of the final argument manipulation variants does not
 %   require a set of braces.
 %    \begin{macrocode}
-\cs_new:Npn \exp_arg_next:nnn #1#2#3 { #2 \::: { #3 {#1} } }
-\cs_new:Npn \exp_arg_next:Nnn #1#2#3 { #2 \::: { #3 #1 } }
+\cs_new:Npn \@@_arg_next:nnn #1#2#3 { #2 \::: { #3 {#1} } }
+\cs_new:Npn \@@_arg_next:Nnn #1#2#3 { #2 \::: { #3 #1 } }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -736,7 +720,7 @@
 %   as control sequence without expansion.
 %    \begin{macrocode}
 \cs_new:Npn \::c #1 \::: #2#3
-  { \exp_after:wN \exp_arg_next:Nnn \cs:w #3 \cs_end: {#1} {#2} }
+  { \exp_after:wN \@@_arg_next:Nnn \cs:w #3 \cs_end: {#1} {#2} }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -744,7 +728,7 @@
 %   This function is used to expand an argument once.
 %    \begin{macrocode}
 \cs_new:Npn \::o #1 \::: #2#3
-  { \exp_after:wN \exp_arg_next:nnn \exp_after:wN {#3} {#1} {#2} }
+  { \exp_after:wN \@@_arg_next:nnn \exp_after:wN {#3} {#1} {#2} }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -755,13 +739,13 @@
 %   expands everything in its way to find something terminating the
 %   number and thereby expands the function in front of it. This
 %   scanning procedure is terminated once the expansion hits
-%   something non-expandable or a space. We introduce |\exp_stop_f:|
+%   something non-expandable or a space. We introduce \cs{exp_stop_f:}
 %   to mark such an end of expansion marker; in case the scanner hits
 %   a number, this number also terminates the scanning and is left
 %   untouched. In the example shown earlier the scanning was stopped
 %   once \TeX{} had fully expanded |\cs_set_eq:Nc \aaa { b \l_tmpa_tl b }|
 %   into |\cs_set_eq:NN \aaa = \blurb| which then turned out to contain
-%   the non-expandable token |\cs_set_eq:NN|.  Since the expansion of
+%   the non-expandable token \cs{cs_set_eq:NN}.  Since the expansion of
 %   \tn{romannumeral} |-`0| is \meta{null}, we wind up with a fully
 %   expanded list, only \TeX{} has not tried to execute any of the
 %   non-expandable tokens. This is what differentiates this function
@@ -769,7 +753,7 @@
 %    \begin{macrocode}
 \cs_new:Npn \::f #1 \::: #2#3
   {
-    \exp_after:wN \exp_arg_next:nnn
+    \exp_after:wN \@@_arg_next:nnn
       \exp_after:wN { \tex_romannumeral:D -`0 #3 }
       {#1} {#2}
   }
@@ -783,8 +767,8 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \::x #1 \::: #2#3
   {
-    \cs_set_nopar:Npx \l_exp_internal_tl { {#3} }
-    \exp_after:wN \exp_arg_next:nnn \l_exp_internal_tl {#1} {#2}
+    \cs_set_nopar:Npx \l_@@_internal_tl { {#3} }
+    \exp_after:wN \@@_arg_next:nnn \l_@@_internal_tl {#1} {#2}
   }
 %    \end{macrocode}
 % \end{macro}
@@ -801,22 +785,22 @@
 %    \begin{macrocode}
 \cs_new:Npn \::V #1 \::: #2#3
   {
-    \exp_after:wN \exp_arg_next:nnn
-      \exp_after:wN { \tex_romannumeral:D \exp_eval_register:N #3 }
+    \exp_after:wN \@@_arg_next:nnn
+      \exp_after:wN { \tex_romannumeral:D \@@_eval_register:N #3 }
       {#1} {#2}
 }
 \cs_new:Npn \::v # 1\::: #2#3
   {
-    \exp_after:wN \exp_arg_next:nnn
-      \exp_after:wN { \tex_romannumeral:D \exp_eval_register:c {#3} }
+    \exp_after:wN \@@_arg_next:nnn
+      \exp_after:wN { \tex_romannumeral:D \@@_eval_register:c {#3} }
       {#1} {#2}
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int, EXP]{\exp_eval_register:N, \exp_eval_register:c}
-% \begin{macro}[aux, EXP]{\exp_eval_error_msg:w}
+% \begin{macro}[int, EXP]{\@@_eval_register:N, \@@_eval_register:c}
+% \begin{macro}[aux, EXP]{\@@_eval_error_msg:w}
 %   This function evaluates a register. Now a register might exist as
 %   one of two things: A parameter-less macro or a built-in \TeX{}
 %   register such as |\count|. For the \TeX{} registers we have to
@@ -824,19 +808,19 @@
 %   expand them once. The trick is to find out when to use
 %   \tn{the} and when not to. What we do here is try to find out
 %   whether the token will expand to something else when hit with
-%   |\exp_after:wN|. The technique is to compare the meaning of the
-%   register in question when it has been prefixed with |\exp_not:N|
+%   \cs{exp_after:wN}. The technique is to compare the meaning of the
+%   register in question when it has been prefixed with \cs{exp_not:N}
 %   and the register itself. If it is a macro, the prefixed
-%   |\exp_not:N| will temporarily turn it into the primitive
-%   |\scan_stop:|.
+%   \cs{exp_not:N} will temporarily turn it into the primitive
+%   \cs{scan_stop:}.
 %    \begin{macrocode}
-\cs_new:Npn \exp_eval_register:N #1
+\cs_new:Npn \@@_eval_register:N #1
   {
     \exp_after:wN \if_meaning:w \exp_not:N #1 #1
 %    \end{macrocode}
 %   If the token was not a macro it may be a malformed variable from a
 %   |c| expansion in which case it is equal to the primitive
-%   |\scan_stop:|. In that case we throw an error. We could let \TeX{}
+%   \cs{scan_stop:}. In that case we throw an error. We could let \TeX{}
 %   do it for us but that would result in the rather obscure
 %   \begin{quote}
 %     |! You can't use `\relax' after \the.|
@@ -845,7 +829,7 @@
 %   went wrong. We provide something more sensible.
 %    \begin{macrocode}
       \if_meaning:w \scan_stop: #1
-        \exp_eval_error_msg:w
+        \@@_eval_error_msg:w
       \fi:
 %    \end{macrocode}
 %   The next bit requires some explanation. The function must be
@@ -856,15 +840,15 @@
 %   |\exp_after:wN \c_zero \tex_the:D #1| and if it is a macro we
 %   need to execute |\exp_after:wN \c_zero #1|. We therefore issue
 %   the longer of the two sequences and if the register is a macro, we
-%   remove the |\tex_the:D|.
+%   remove the \cs{tex_the:D}.
 %    \begin{macrocode}
     \else:
       \exp_after:wN \use_i_ii:nnn
     \fi:
     \exp_after:wN \c_zero \tex_the:D #1
   }
-\cs_new:Npn \exp_eval_register:c #1
-  { \exp_after:wN \exp_eval_register:N \cs:w #1 \cs_end: }
+\cs_new:Npn \@@_eval_register:c #1
+  { \exp_after:wN \@@_eval_register:N \cs:w #1 \cs_end: }
 %    \end{macrocode}
 %   Clean up nicely, then call the undefined control sequence. The
 %   result is an error message looking like this:
@@ -875,11 +859,11 @@
 %     l.55 \tl_set:Nv \l_tmpa_tl {undefined_tl}
 %   \end{verbatim}
 %    \begin{macrocode}
-\cs_new:Npn \exp_eval_error_msg:w #1 \tex_the:D #2
+\cs_new:Npn \@@_eval_error_msg:w #1 \tex_the:D #2
   {
       \fi:
     \fi:
-    \msg_expandable_kernel_error:nnn { kernel } { bad-var } {#2}
+    \__msg_kernel_expandable_error:nnn { kernel } { bad-variable } {#2}
     \c_zero
   }
 %    \end{macrocode}
@@ -891,7 +875,7 @@
 %
 % One of the most important features of these functions is that they
 % are fully expandable and therefore allow to prefix them with
-% |\tex_global:D| for example.
+% \cs{tex_global:D} for example.
 %
 % \begin{macro}[EXP]{\exp_args:No}
 % \begin{macro}[EXP]{\exp_args:NNo}
@@ -940,12 +924,12 @@
 \cs_new:Npn \exp_args:Nv #1#2
   {
     \exp_after:wN #1 \exp_after:wN
-      { \tex_romannumeral:D \exp_eval_register:c {#2} }
+      { \tex_romannumeral:D \@@_eval_register:c {#2} }
   }
 \cs_new:Npn \exp_args:NV #1#2
   {
     \exp_after:wN #1 \exp_after:wN
-      { \tex_romannumeral:D \exp_eval_register:N #2 }
+      { \tex_romannumeral:D \@@_eval_register:N #2 }
   }
 %    \end{macrocode}
 % \end{macro}
@@ -971,13 +955,13 @@
   {
     \exp_after:wN #1
     \exp_after:wN #2
-    \exp_after:wN { \tex_romannumeral:D \exp_eval_register:c {#3} }
+    \exp_after:wN { \tex_romannumeral:D \@@_eval_register:c {#3} }
   }
 \cs_new:Npn \exp_args:NNV #1#2#3
   {
     \exp_after:wN #1
     \exp_after:wN #2
-    \exp_after:wN { \tex_romannumeral:D \exp_eval_register:N #3 }
+    \exp_after:wN { \tex_romannumeral:D \@@_eval_register:N #3 }
   }
 \cs_new:Npn \exp_args:Nco #1#2#3
   {
@@ -995,8 +979,8 @@
   {
     \exp_after:wN #1
     \exp_after:wN { \tex_romannumeral:D \exp_after:wN
-      \exp_eval_register:N \exp_after:wN #2 \exp_after:wN }
-    \exp_after:wN { \tex_romannumeral:D \exp_eval_register:N #3 }
+      \@@_eval_register:N \exp_after:wN #2 \exp_after:wN }
+    \exp_after:wN { \tex_romannumeral:D \@@_eval_register:N #3 }
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1013,7 +997,7 @@
     \exp_after:wN #1
     \exp_after:wN #2
     \exp_after:wN #3
-    \exp_after:wN { \tex_romannumeral:D \exp_eval_register:N #4 }
+    \exp_after:wN { \tex_romannumeral:D \@@_eval_register:N #4 }
   }
 \cs_new:Npn \exp_args:NcNc #1#2#3#4
   {
@@ -1114,7 +1098,7 @@
 %
 % \subsection{Last-unbraced versions}
 %
-% \begin{macro}[aux, EXP]{\exp_arg_last_unbraced:nn}
+% \begin{macro}[aux, EXP]{\@@_arg_last_unbraced:nn}
 % \begin{macro}[aux, EXP]{\::f_unbraced}
 % \begin{macro}[aux, EXP]{\::o_unbraced}
 % \begin{macro}[aux, EXP]{\::V_unbraced}
@@ -1123,28 +1107,28 @@
 %   There are a few places where the last argument needs to be available
 %   unbraced. First some helper macros.
 %    \begin{macrocode}
-\cs_new:Npn \exp_arg_last_unbraced:nn #1#2 { #2#1 }
+\cs_new:Npn \@@_arg_last_unbraced:nn #1#2 { #2#1 }
 \cs_new:Npn \::f_unbraced \::: #1#2
   {
-    \exp_after:wN \exp_arg_last_unbraced:nn
+    \exp_after:wN \@@_arg_last_unbraced:nn
       \exp_after:wN { \tex_romannumeral:D -`0 #2 } {#1}
   }
 \cs_new:Npn \::o_unbraced \::: #1#2
-  { \exp_after:wN \exp_arg_last_unbraced:nn \exp_after:wN {#2} {#1} }
+  { \exp_after:wN \@@_arg_last_unbraced:nn \exp_after:wN {#2} {#1} }
 \cs_new:Npn \::V_unbraced \::: #1#2
   {
-    \exp_after:wN \exp_arg_last_unbraced:nn
-      \exp_after:wN { \tex_romannumeral:D \exp_eval_register:N #2 } {#1}
+    \exp_after:wN \@@_arg_last_unbraced:nn
+      \exp_after:wN { \tex_romannumeral:D \@@_eval_register:N #2 } {#1}
   }
 \cs_new:Npn \::v_unbraced \::: #1#2
   {
-    \exp_after:wN \exp_arg_last_unbraced:nn
-      \exp_after:wN { \tex_romannumeral:D \exp_eval_register:c {#2} } {#1}
+    \exp_after:wN \@@_arg_last_unbraced:nn
+      \exp_after:wN { \tex_romannumeral:D \@@_eval_register:c {#2} } {#1}
   }
 \cs_new_protected:Npn \::x_unbraced \::: #1#2
   {
-    \cs_set_nopar:Npx \l_exp_internal_tl { \exp_not:n {#1} #2 }
-    \l_exp_internal_tl
+    \cs_set_nopar:Npx \l_@@_internal_tl { \exp_not:n {#1} #2 }
+    \l_@@_internal_tl
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1173,9 +1157,9 @@
 %   general system is in place.
 %    \begin{macrocode}
 \cs_new:Npn \exp_last_unbraced:NV #1#2
-  { \exp_after:wN #1 \tex_romannumeral:D \exp_eval_register:N #2 }
+  { \exp_after:wN #1 \tex_romannumeral:D \@@_eval_register:N #2 }
 \cs_new:Npn \exp_last_unbraced:Nv #1#2
-  { \exp_after:wN #1 \tex_romannumeral:D \exp_eval_register:c {#2} }
+  { \exp_after:wN #1 \tex_romannumeral:D \@@_eval_register:c {#2} }
 \cs_new:Npn \exp_last_unbraced:No #1#2 { \exp_after:wN #1 #2 }
 \cs_new:Npn \exp_last_unbraced:Nf #1#2
   { \exp_after:wN #1 \tex_romannumeral:D -`0 #2 }
@@ -1185,13 +1169,13 @@
   {
     \exp_after:wN #1
     \cs:w #2 \exp_after:wN \cs_end:
-    \tex_romannumeral:D \exp_eval_register:N #3
+    \tex_romannumeral:D \@@_eval_register:N #3
   }
 \cs_new:Npn \exp_last_unbraced:NNV #1#2#3
   {
     \exp_after:wN #1
     \exp_after:wN #2
-    \tex_romannumeral:D \exp_eval_register:N #3
+    \tex_romannumeral:D \@@_eval_register:N #3
   }
 \cs_new:Npn \exp_last_unbraced:NNo #1#2#3
   { \exp_after:wN #1 \exp_after:wN #2 #3 }
@@ -1200,7 +1184,7 @@
     \exp_after:wN #1
     \exp_after:wN #2
     \exp_after:wN #3
-    \tex_romannumeral:D \exp_eval_register:N #4
+    \tex_romannumeral:D \@@_eval_register:N #4
   }
 \cs_new:Npn \exp_last_unbraced:NNNo #1#2#3#4
   { \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN #3 #4 }
@@ -1227,6 +1211,7 @@
 % \end{macro}
 %
 % \begin{macro}[EXP]{\exp_last_two_unbraced:Noo}
+% \begin{macro}[EXP, aux]{\@@_last_two_unbraced:noN}
 %   If |#2| is a single token then this can be implemented as
 %   \begin{verbatim}
 %     \cs_new:Npn \exp_last_two_unbraced:Noo #1 #2 #3
@@ -1236,11 +1221,12 @@
 %   shuffle is used to ensure that |#2| can be multiple tokens.
 %    \begin{macrocode}
 \cs_new:Npn \exp_last_two_unbraced:Noo #1#2#3
-  { \exp_after:wN \exp_last_two_unbraced_aux:noN \exp_after:wN {#3} {#2} #1 }
-\cs_new:Npn \exp_last_two_unbraced_aux:noN #1#2#3
+  { \exp_after:wN \@@_last_two_unbraced:noN \exp_after:wN {#3} {#2} #1 }
+\cs_new:Npn \@@_last_two_unbraced:noN #1#2#3
    { \exp_after:wN #3 #2 #1 }
 %    \end{macrocode}
 % \end{macro}
+% \end{macro}
 %
 % \subsection{Preventing expansion}
 %
@@ -1257,12 +1243,12 @@
 \cs_new:Npn \exp_not:V #1
   {
     \etex_unexpanded:D \exp_after:wN
-      { \tex_romannumeral:D \exp_eval_register:N #1 }
+      { \tex_romannumeral:D \@@_eval_register:N #1 }
   }
 \cs_new:Npn \exp_not:v #1
   {
     \etex_unexpanded:D \exp_after:wN
-      { \tex_romannumeral:D \exp_eval_register:c {#1} }
+      { \tex_romannumeral:D \@@_eval_register:c {#1} }
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1273,94 +1259,197 @@
 %
 % \subsection{Defining function variants}
 %
+%    \begin{macrocode}
+%<@@=cs>
+%    \end{macrocode}
+%
 % \begin{macro}{\cs_generate_variant:Nn}
-% \begin{macro}[aux]{\cs_generate_variant_aux:nnNNn}
-% \begin{macro}[aux]{\cs_generate_variant_aux:Nnnw}
-% \begin{macro}[aux]{\cs_generate_variant_aux:NNn}
 %   \begin{arguments}
-%     \item Base form of a function; \emph{e.g.},~|\tl_set:Nn|
+%     \item Base form of a function; \emph{e.g.},~\cs{tl_set:Nn}
 %     \item One or more variant argument specifiers; e.g., |{Nx,c,cx}|
 %   \end{arguments}
-%   Test whether the base function is protected or not
-%   and define \cs{cs_tmp:w} as either \cs{cs_new_nopar:Npx} or
-%   \cs{cs_new_protected_nopar:Npx}, then used to define all the
-%   variants.
-%   Split up the original base function to grab its name and signature
-%   consisting of $k$ letters. Then we wish to iterate through the list
-%   of variant argument specifiers, and for each one construct a new
-%   function name using the original base name, the variant signature
-%   consisting of $l$ letters and the last $k-l$ letters of the base
-%   signature. For example, for a base function |\tl_set:Nn| which
-%   needs a |c| variant form, we want the new signature to be |cn|.
+%   After making sure that the base form exists, test whether it is
+%   protected or not and define \cs{@@_tmp:w} as either
+%   \cs{cs_new_nopar:Npx} or \cs{cs_new_protected_nopar:Npx}, which is
+%   then used to define all the variants (except those involving
+%   \texttt{x}-expansion, always protected).  Split up the original base
+%   function only once, to grab its name and signature.  Then we wish to
+%   iterate through the comma list of variant argument specifiers, which
+%   we first convert to a string: the reason is explained later.
 %    \begin{macrocode}
-\cs_new_protected:Npn \cs_generate_variant:Nn #1
+\cs_new_protected:Npn \cs_generate_variant:Nn #1#2
   {
-    \chk_if_exist_cs:N #1
-    \cs_generate_variant_aux:N #1
-    \cs_split_function:NN #1 \cs_generate_variant_aux:nnNNn
-    #1
+    \__chk_if_exist_cs:N #1
+    \@@_generate_variant:N #1
+    \exp_after:wN \@@_split_function:NN
+    \exp_after:wN #1
+    \exp_after:wN \@@_generate_variant:nnNN
+    \exp_after:wN #1
+    \etex_detokenize:D {#2} , ? , \q_recursion_stop
   }
 %    \end{macrocode}
-%   We discard the boolean |#3| and then set off a loop through the desired
-%   variant forms. The original function is retained as |#4| for efficiency.
+% \end{macro}
+%
+% \begin{macro}[aux]{\@@_generate_variant:N}
+% \begin{macro}[aux]{\@@_generate_variant:w}
+%   The idea here is to pick up protected parent functions, using the
+%   nature of the meaning string that they generate.  If |\protected|
+%   appears in the meaning, the first \cs{q_mark} is taken as an
+%   argument, and |#3| is \cs{cs_new_protected_nopar:Npx}, otherwise it
+%   is \cs{cs_new_nopar:Npx}.
 %    \begin{macrocode}
-\cs_new_protected:Npn \cs_generate_variant_aux:nnNNn #1#2#3#4#5
-  { \cs_generate_variant_aux:Nnnw #4 {#1}{#2} #5 , ? , \q_recursion_stop }
+\group_begin:
+  \tex_lccode:D `\Z = `\d \scan_stop:
+  \tex_lccode:D `\? =`\\ \scan_stop:
+  \tex_catcode:D `\P = 12 \scan_stop:
+  \tex_catcode:D `\R = 12 \scan_stop:
+  \tex_catcode:D `\O = 12 \scan_stop:
+  \tex_catcode:D `\T = 12 \scan_stop:
+  \tex_catcode:D `\E = 12 \scan_stop:
+  \tex_catcode:D `\C = 12 \scan_stop:
+  \tex_catcode:D `\Z = 12 \scan_stop:
+\tex_lowercase:D
+  {
+    \group_end:
+    \cs_new_protected:Npn \@@_generate_variant:N #1
+      {
+        \exp_after:wN \@@_generate_variant:w
+          \token_to_meaning:N #1
+          \q_mark \cs_new_protected_nopar:Npx
+          ? PROTECTEZ
+          \q_mark \cs_new_nopar:Npx
+          \q_stop
+      }
+    \cs_new_protected:Npn \@@_generate_variant:w
+        #1 ? PROTECTEZ #2 \q_mark #3 #4 \q_stop
+      {
+        \cs_set_eq:NN \@@_tmp:w #3
+      }
+  }
 %    \end{macrocode}
-%   Next is the real work to be done. We now have 1: original function,
-%   2: base name, 3: base signature, 4: beginning of variant signature.
-%   To construct the new
-%   csname and the |\exp_args:Ncc| form, we need the variant signature.
-%   In our example, we wanted to discard the first two letters of the
-%   base signature because the variant form started with |cc|. This is
-%   the same as putting first |cc| in the signature and then
-%   |\use_none:nn| followed by the base signature |NNn|. Depending on
-%   the number of characters in |#4|, the relevant \cs{use_none:n\ldots{}n}
-%   is called.
-%
-%   Firstly though, we check whether to terminate the loop.
-%   Then build the variant function once, to avoid repeating this
-%   relatively expensive operation. Then recurse.
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[aux]{\@@_generate_variant:nnNN}
+%   \begin{arguments}
+%     \item Base name.
+%     \item Base signature.
+%     \item Boolean.
+%     \item Base function.
+%   \end{arguments}
+%   We discard the boolean and then set off a loop through the desired
+%   variant forms. The original function is retained as |#4| for
+%   efficiency.
 %    \begin{macrocode}
-\cs_new_protected:Npn \cs_generate_variant_aux:Nnnw #1#2#3#4 ,
+\cs_new_protected:Npn \@@_generate_variant:nnNN #1#2#3#4
+  { \@@_generate_variant:Nnnw #4 {#1}{#2} }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux]{\@@_generate_variant:Nnnw}
+%   \begin{arguments}
+%     \item Base function.
+%     \item Base name.
+%     \item Base signature.
+%     \item Beginning of variant signature.
+%   \end{arguments}
+%   First check whether to terminate the loop over variant forms.  Then
+%   build the variant function name once, to avoid repeating this
+%   relatively expensive operation. Then recurse, calling
+%   \cs{@@_generate_variant:Nnnw} with the three same arguments (and a
+%   new item from the comma list of variant forms).
+%
+%   For each variant form, construct a new function name using the
+%   original base name, the variant signature consisting of $l$ letters
+%   and the last $k-l$ letters of the base signature (of length $k$).
+%   For example, for a base function \cs{prop_put:Nnn} which needs a
+%   |cV| variant form, we want the new signature to be |cVn|.  This
+%   could be done by placing the variant form letters, then
+%   \cs{use_none:nn} followed by the signature (the choice of
+%   \cs{use_none:nn} would depend on the variant form).  However, this
+%   would crash badly if the base signature is mistakenly shorter than
+%   the variant form (this includes cases where the base function had no
+%   colon).  Instead, we do a loop which at each step removes a
+%   character from the base signature and leaves one from the variant
+%   form behind it in a \cs{cs:w} \ldots{} \cs{cs_end:} construction.
+%   This \texttt{c}-type expansion is not done using \cs{exp_args:NNc}
+%   because some error-reporting mechanism must escape out of this
+%   construction.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_generate_variant:Nnnw #1#2#3#4 ,
   {
     \if:w ? #4
       \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
     \fi:
-    \exp_args:NNc \cs_generate_variant_aux:NNn
-      #1
-      {
-        #2 : #4
-        \exp_after:wN \use_i_delimit_by_q_stop:nw
-        \use_none:nnnnnnnnn #4
-        \use_none:nnnnnnnnn
-        \use_none:nnnnnnnn
-        \use_none:nnnnnnn
-        \use_none:nnnnnn
-        \use_none:nnnnn
-        \use_none:nnnn
-        \use_none:nnn
-        \use_none:nn
-        \use_none:n
-        { }
+    \exp_after:wN \@@_generate_variant:NNn
+    \exp_after:wN #1
+      \cs:w
+        #2 :
+        \@@_generate_variant_loop:NwN
+          ? #3
+          \q_mark #4 \@@_generate_variant_loop_end:w
+          \q_mark \@@_generate_variant_loop_error:wnNNnn
         \q_stop
-        #3
-      }
+      \cs_end:
       {#4}
-    \cs_generate_variant_aux:Nnnw #1 {#2} {#3}
+    \@@_generate_variant:Nnnw #1 {#2} {#3}
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]{\@@_generate_variant_loop:NwN}
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_generate_variant_loop_end:w,
+%     \@@_generate_variant_loop_error:wnNNnn
+%   }
+%   Normally, the loop takes one character of the base signature and one
+%   from the variant form (after \cs{q_mark}), and leaves the latter one
+%   in the input stream.  This stops when |#3| is the \texttt{loop_end}
+%   auxiliary, which, once left in the input stream, cleans up the rest
+%   of the csname construction.  In case the base signature was in fact
+%   shorter, one reaches the point where |#1| is the \cs{q_mark} which
+%   is supposed to separate the base signature from the variant form.
+%   Then |#2| is delimited by the next \cs{q_mark}, and the
+%   \texttt{loop_error} auxiliary is taken as |#3|.  This function
+%   fetches appropriate arguments for an error message, and places it
+%   outside the csname construction.
+%
+%   Note in the definition of \cs{@@_generate_variant:Nnnw} the base
+%   signature is preceeded by a question mark.  This shifts the base
+%   signature and variant form to compensate for the presence of the
+%   \texttt{loop_end} auxiliary at the end of the variant form.
+%    \begin{macrocode}
+\cs_new:Npn \@@_generate_variant_loop:NwN #1 #2 \q_mark #3
+  { #3 \@@_generate_variant_loop:NwN #2 \q_mark }
+\cs_new:Npn \@@_generate_variant_loop_end:w #1#2 \q_mark #3 \q_stop {#2}
+\cs_new:Npn \@@_generate_variant_loop_error:wnNNnn
+    #1 \q_stop \cs_end: #2 #3#4#5#6
+  {
+    \cs_end: {#2}
+    \__msg_kernel_error:nnxx { kernel } { variant-too-long }
+      { \tl_to_str:n {#2} } { \token_to_str:N #4 }
+    #3 #4 {#5} {#6}
   }
 %    \end{macrocode}
-%   Check if the variant form has already been defined.
-%   If not, then define it and then additionally check if
-%   the |\exp_args:N| form needed is defined.
-%   Otherwise tell that it was already defined.
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[aux]{\@@_generate_variant:NNn}
+%   If the variant form has already been defined, log its existence.
+%   Otherwise, make sure that the |\exp_args:N #3| form is defined, and
+%   if it contains |x|, change \cs{@@_tmp:w} locally to
+%   \cs{cs_new_protected_nopar:Npx}.  Then define the variant by
+%   combining the |\exp_args:N #3| variant and the base function.
 %    \begin{macrocode}
-\cs_new_protected:Npn \cs_generate_variant_aux:NNn #1 #2 #3
+\cs_new_protected:Npn \@@_generate_variant:NNn #1 #2 #3
   {
     \cs_if_free:NTF #2
       {
-        \cs_tmp:w #2 { \exp_not:c { exp_args:N #3 } \exp_not:N #1 }
-        \cs_generate_internal_variant:n {#3}
+        \group_begin:
+          \@@_generate_internal_variant:n {#3}
+          \@@_tmp:w #2 { \exp_not:c { exp_args:N #3 } \exp_not:N #1 }
+        \group_end:
       }
       {
         \iow_log:x
@@ -1373,86 +1462,65 @@
   }
 %    \end{macrocode}
 % \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
 %
-% \begin{macro}[aux]{\cs_generate_variant_aux:N}
-% \begin{macro}[aux]{\cs_generate_variant_aux:w}
-%   The idea here is to pick up protected parent functions, using the
-%   nature of the meaning string that they generate. The test here is
-%   almost the same as \cs{tl_if_empty:nTF}, but has to be hard-coded as
-%   that function is not yet available and because it has to match both
-%   long and short macros.
+% \begin{macro}[int]{\@@_generate_internal_variant:n}
+% \begin{macro}[aux]{\@@_generate_internal_variant:wwnw}
+% \begin{macro}[aux, rEXP]{\@@_generate_internal_variant_loop:n}
+%   Test if |\exp_args:N #1| is already defined and if not define it via
+%   the |\::| commands using the chars in |#1|.  If |#1| contains an |x|
+%   (this is the place where having converted the original comma-list
+%   argument to a string is very important), the result should be
+%   protected, and the next variant to be defined using that internal
+%   variant should be protected.
 %    \begin{macrocode}
 \group_begin:
-  \tex_lccode:D `\Z = `\d \scan_stop:
-  \tex_lccode:D `\? =`\\ \scan_stop:
-  \tex_catcode:D `\P = 12 \scan_stop:
-  \tex_catcode:D `\R = 12 \scan_stop:
-  \tex_catcode:D `\O = 12 \scan_stop:
-  \tex_catcode:D `\T = 12 \scan_stop:
-  \tex_catcode:D `\E = 12 \scan_stop:
-  \tex_catcode:D `\C = 12 \scan_stop:
-  \tex_catcode:D `\Z = 12 \scan_stop:
+  \tex_catcode:D `\X = 12 \scan_stop:
+  \tex_lccode:D `\N = `\N \scan_stop:
 \tex_lowercase:D
   {
     \group_end:
-    \cs_new_protected:Npn \cs_generate_variant_aux:N #1
-      {
-        \exp_after:wN \cs_generate_variant_aux:w
-          \token_to_meaning:N #1
-          \q_mark \cs_new_protected_nopar:Npx
-          ? PROTECTEZ
-          \q_mark \cs_new_nopar:Npx
-          \q_stop
-      }
-    \cs_new_protected:Npn \cs_generate_variant_aux:w
-        #1 ? PROTECTEZ #2 \q_mark #3 #4 \q_stop
+    \cs_new_protected:Npn \@@_generate_internal_variant:n #1
       {
-        \cs_set_eq:NN \cs_tmp:w #3
+        \@@_generate_internal_variant:wwnNwnn
+          #1 \q_mark
+            { \cs_set_eq:NN \@@_tmp:w \cs_new_protected_nopar:Npx }
+            \cs_new_protected_nopar:cpx
+          X \q_mark
+            { }
+            \cs_new_nopar:cpx
+        \q_stop
+          { exp_args:N #1 }
+          { \@@_generate_internal_variant_loop:n #1 { : \use_i:nn } }
       }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[int]{\cs_generate_internal_variant:n}
-% \begin{macro}[aux, rEXP]{\cs_generate_internal_variant_aux:N}
-%   Test if |exp_args:N #1| is already defined
-%   and if not define it via the
-%   |\::| commands using the chars in |#1|
-%    \begin{macrocode}
-\cs_new_protected:Npn \cs_generate_internal_variant:n #1
-  {
-    \cs_if_free:cT { exp_args:N #1 }
+    \cs_new_protected:Npn \@@_generate_internal_variant:wwnNwnn
+        #1 X #2 \q_mark #3 #4 #5 \q_stop #6 #7
       {
-        \cs_new:cpx { exp_args:N #1 }
-          { \cs_generate_internal_variant_aux:N #1 : }
+        #3
+        \cs_if_free:cT {#6} { #4 {#6} {#7} }
       }
   }
 %    \end{macrocode}
 %   This command grabs char by char outputting |\::#1| (not expanded
-%   further) until we see a |:|. That colon is in fact also turned into
-%   |\:::| so that the required structure for |\exp_args...| commands
-%   is correctly terminated.
+%   further).  We avoid tests by putting a trailing |: \use_i:nn|, which
+%   leaves \cs{cs_end:} and removes the looping macro.  The colon is in
+%   fact also turned into \cs{:::} so that the required structure for
+%   |\exp_args:N...| commands is correctly terminated.
 %    \begin{macrocode}
-\cs_new:Npn \cs_generate_internal_variant_aux:N #1
+\cs_new:Npn \@@_generate_internal_variant_loop:n #1
   {
-    \exp_not:c { :: #1 }
-    \if_meaning:w : #1
-      \exp_after:wN \use_none:n
-    \fi:
-    \cs_generate_internal_variant_aux:N
+    \exp_after:wN \exp_not:N \cs:w :: #1 \cs_end:
+    \@@_generate_internal_variant_loop:n
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
+% \end{macro}
 %
 %\subsection{Variants which cannot be created earlier}
 %
 % \begin{macro}[EXP,pTF]
 %   {\str_if_eq:Vn, \str_if_eq:on, \str_if_eq:nV, \str_if_eq:no, \str_if_eq:VV}
+% \begin{macro}[EXP]{\str_case:onn}
 %   These cannot come earlier as they need \cs{cs_generate_variant:Nn}.
 %    \begin{macrocode}
 \cs_generate_variant:Nn \str_if_eq_p:nn {  V ,  o }
@@ -1463,8 +1531,10 @@
 \cs_generate_variant:Nn \str_if_eq:nnF  { nV , no , VV }
 \cs_generate_variant:Nn \str_if_eq:nnTF {  V ,  o }
 \cs_generate_variant:Nn \str_if_eq:nnTF { nV , no , VV }
+\cs_generate_variant:Nn \str_case:nnn { o }
 %    \end{macrocode}
 % \end{macro}
+% \end{macro}
 %
 %    \begin{macrocode}
 %</initex|package>
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3file.dtx b/Master/texmf-dist/source/latex/l3kernel/l3file.dtx
index 9b8bd6b1a0a..919281bd552 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3file.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3file.dtx
@@ -35,8 +35,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3file.dtx 3520 2012-03-09 19:34:07Z joseph $
-  {L3 Experimental file and I/O operations}
+\GetIdInfo$Id: l3file.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 File and I/O operations}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -78,6 +78,13 @@
 % \enquote{current path} for \TeX{} is somewhat broader than that for other
 % programs.
 %
+% For functions which expect a \meta{file name} argument, this argument
+% may contain both literal items and expandable content, which should on
+% full expansion be the desired file name.  Any active characters (as
+% declared in \cs{l_char_active_seq}) will \emph{not} be expanded,
+% allowing the direct use of these in file names.
+% Spaces are not allowed in file names.
+%
 % \section{File operation functions}
 %
 % \begin{variable}{\g_file_current_name_tl}
@@ -95,11 +102,6 @@
 %   Searches for \meta{file name} using the current \TeX{} search
 %   path and the additional paths controlled by
 %   \cs{file_path_include:n}).
-%   \begin{texnote}
-%     The \meta{file name} may contain both literal items and expandable
-%     content, which should on full expansion be the desired file name.
-%     The expansion occurs when \TeX{} searches for the file.
-%   \end{texnote}
 % \end{function}
 %
 % \begin{function}[updated = 2012-02-10]{\file_add_path:nN}
@@ -108,16 +110,9 @@
 %   \end{syntax}
 %   Searches for \meta{file name} in the path as detailed for
 %   \cs{file_if_exist:nTF}, and if found sets the \meta{tl var} the
-%   fully-qualified name of the file, \emph{i.e}.~the path and file name.
+%   fully-qualified name of the file, \emph{i.e.}~the path and file name.
 %   If the file is not found then the \meta{tl var} will contain the
 %   marker \cs{q_no_value}.
-%   \begin{texnote}
-%     The \meta{file name} may contain both literal items and expandable
-%     content, which should on full expansion be the desired file name.
-%     Any active characters (as declared in \cs{l_char_active_seq}) will
-%     \emph{not} be expanded, allowing the direct use of these in
-%     file names.
-%   \end{texnote}
 % \end{function}
 %
 % \begin{function}[updated = 2012-02-17]{\file_input:n}
@@ -128,30 +123,29 @@
 %   \cs{file_if_exist:nTF}, and if found reads in the file as
 %   additional \LaTeX{} source. All files read are recorded
 %   for information and the file name stack is updated by this
-%   function. An error will be raised if the file is not found
-%   \begin{texnote}
-%     The \meta{file name} may contain both literal items and expandable
-%     content, which should on full expansion be the desired file name.
-%     Any active characters (as declared in \cs{l_char_active_seq}) will
-%     \emph{not} be expanded, allowing the direct use of these in
-%     file names.
-%   \end{texnote}
+%   function. An error will be raised if the file is not found.
 % \end{function}
 %
-% \begin{function}{\file_path_include:n}
+% \begin{function}[updated = 2012-07-04]{\file_path_include:n}
 %   \begin{syntax}
 %     \cs{file_path_include:n} \Arg{path}
 %   \end{syntax}
 %   Adds \meta{path} to the list of those used to search when reading
 %   files. The assignment is local.
+%   The \meta{path} is processed in the same way as a \meta{file name},
+%   \emph{i.e.}, with \texttt{x}-type expansion except active
+%   characters.  Spaces are not allowed in the \meta{path}.
 % \end{function}
 %
-% \begin{function}{\file_path_remove:n}
+% \begin{function}[updated = 2012-07-04]{\file_path_remove:n}
 %   \begin{syntax}
 %     \cs{file_path_remove:n} \Arg{path}
 %   \end{syntax}
 %   Removes \meta{path} from the list of those used to search when reading
 %   files. The assignment is local.
+%   The \meta{path} is processed in the same way as a \meta{file name},
+%   \emph{i.e.}, with \texttt{x}-type expansion except active
+%   characters.  Spaces are not allowed in the \meta{path}.
 % \end{function}
 %
 % \begin{function}{\file_list:}
@@ -171,16 +165,20 @@
 % close streams when they are no longer needed, to release them for other
 % processes.
 %
+% Note that I/O operations are global: streams should all be declared
+% with global names and treated accordingly.
+%
 % \begin{function}[added = 2011-09-26, updated = 2011-12-27]
 %   {\ior_new:N, \ior_new:c, \iow_new:N, \iow_new:c}
 %   \begin{syntax}
-%     \cs{ior_new:Nn} \meta{stream}
+%     \cs{ior_new:N} \meta{stream}
+%     \cs{iow_new:N} \meta{stream}
 %   \end{syntax}
 %   Globally reserves the name of the \meta{stream}, either for reading
-%   or for writing as appropriate. The \meta{stream} is not opened until the
-%   appropriate \cs{\ldots_open:Nn} function is used. Attempting to use
-%   a \meta{stream} which has not been opened will result in a \TeX{}
-%   error.
+%   or for writing as appropriate. The \meta{stream} is not opened until
+%   the appropriate \cs{\ldots_open:Nn} function is used. Attempting to
+%   use a \meta{stream} which has not been opened is an error, and the
+%   \meta{stream} will behave as the corresponding \cs{c_term_\ldots}.
 % \end{function}
 %
 % \begin{function}[updated = 2012-02-10]{\ior_open:Nn, \ior_open:cn}
@@ -192,14 +190,7 @@
 %   open it is closed before the new operation begins. The
 %   \meta{stream} is available for access immediately and will remain
 %   allocated to \meta{file name} until a \cs{ior_close:N} instruction
-%   is given or the file ends.
-%   \begin{texnote}
-%     The \meta{file name} may contain both literal items and expandable
-%     content, which should on full expansion be the desired file name.
-%     Any active characters (as declared in \cs{l_char_active_seq}) will
-%     \emph{not} be expanded, allowing the direct use of these in
-%     file names.
-%   \end{texnote}
+%   is given or the \TeX{} run ends.
 % \end{function}
 %
 % \begin{function}[updated = 2012-02-09]{\iow_open:Nn, \iow_open:cn}
@@ -211,34 +202,20 @@
 %   open it is closed before the new operation begins. The
 %   \meta{stream} is available for access immediately and will remain
 %   allocated to \meta{file name} until a \cs{iow_close:N} instruction
-%   is given or the file ends. Opening a file for writing will clear
+%   is given or the \TeX{} run ends. Opening a file for writing will clear
 %   any existing content in the file (\emph{i.e.}~writing is \emph{not}
 %   additive).
-%   \begin{texnote}
-%     The \meta{file name} may contain both literal items and expandable
-%     content, which should on full expansion be the desired file name.
-%     Any active characters (as declared in \cs{l_char_active_seq}) will
-%     \emph{not} be expanded, allowing the direct use of these in
-%     file names.
-%   \end{texnote}
 % \end{function}
 %
-% \begin{function}[updated = 2011-12-27]{\ior_close:N, \ior_close:c}
+% \begin{function}[updated = 2012-07-03]
+%   {\ior_close:N, \ior_close:c, \iow_close:N, \iow_close:c}
 %   \begin{syntax}
 %     \cs{ior_close:N} \meta{stream}
-%   \end{syntax}
-%   Closes the \meta{stream}. Streams should always be closed when
-%   they are finished with as this ensures that they remain available
-%   to other programmer.
-% \end{function}
-%
-% \begin{function}[updated = 2011-12-27]{\iow_close:N, \iow_close:c}
-%   \begin{syntax}
 %     \cs{iow_close:N} \meta{stream}
 %   \end{syntax}
 %   Closes the \meta{stream}. Streams should always be closed when
 %   they are finished with as this ensures that they remain available
-%   to other programmer.
+%   to other programmers.
 % \end{function}
 %
 % \begin{function}{\ior_list_streams:, \iow_list_streams:}
@@ -250,38 +227,38 @@
 %   stream: intended for tracking down problems.
 % \end{function}
 %
-% \section{Reading from files}
+% \subsection{Reading from files}
 %
-% \begin{function}{\ior_to:NN,\ior_gto:NN}
+% \begin{function}[added = 2012-06-24]{\ior_get:NN}
 %   \begin{syntax}
-%     \cs{ior_to:NN} \meta{stream} \meta{token list variable}
+%     \cs{ior_get:NN} \meta{stream} \meta{token list variable}
 %   \end{syntax}
-%   Functions that reads one or more lines (until an equal number of left
+%   Function that reads one or more lines (until an equal number of left
 %   and right braces are found) from the input \meta{stream} and stores
-%   the result in the \meta{token list} variable, locally or globally. If the
+%   the result locally in the \meta{token list} variable. If the
 %   \meta{stream} is not open, input is requested from the terminal.
 %   The material read from the \meta{stream} will be tokenized by
 %   \TeX{} according to the category codes in force when the function
 %   is used.
 %   \begin{texnote}
-%     This protected macro expands to the \TeX{} primitives \tn{read}
-%     or \tn{global}\tn{read} along with the |to| keyword.
+%     This protected macro expands to the \TeX{} primitive \tn{read}
+%     along with the |to| keyword.
 %   \end{texnote}
 % \end{function}
 %
-% \begin{function}{\ior_str_to:NN,\ior_str_gto:NN}
+% \begin{function}[added = 2012-06-24]{\ior_get_str:NN}
 %   \begin{syntax}
-%     \cs{ior_str_to:NN} \meta{stream} \meta{token list variable}
+%     \cs{ior_get_str:NN} \meta{stream} \meta{token list variable}
 %   \end{syntax}
-%   Functions that reads one line from the input \meta{stream} and stores
-%   the result in the \meta{token list} variable, locally or globally. If the
+%   Function that reads one line from the input \meta{stream} and stores
+%   the result locally in the \meta{token list} variable. If the
 %   \meta{stream} is not open, input is requested from the terminal.
-%   The material read from the \meta{stream} as a series of tokens with
+%   The material is read from the \meta{stream} as a series of tokens with
 %   category code $12$ (other), with the exception of space
 %   characters which are given category code $10$ (space).
 %   \begin{texnote}
-%     This protected macro expands to the \eTeX{} primitives \tn{readline}
-%     or \tn{global}\tn{readline} along with the |to| keyword.
+%     This protected macro expands to the \eTeX{} primitive \tn{readline}
+%     along with the |to| keyword.
 %   \end{texnote}
 % \end{function}
 %
@@ -297,17 +274,13 @@
 %
 % \section{Writing to files}
 %
-% \begin{function}{\iow_now:Nn, \iow_now:Nx}
+% \begin{function}[updated = 2012-06-05]{\iow_now:Nn, \iow_now:Nx}
 %   \begin{syntax}
 %     \cs{iow_now:Nn} \meta{stream} \Arg{tokens}
 %   \end{syntax}
 %   This functions writes \meta{tokens} to the specified
 %   \meta{stream} immediately (\emph{i.e.}~the write operation is called
 %   on expansion of \cs{iow_now:Nn}).
-%   \begin{texnote}
-%     \cs{iow_now:Nx} is a protected macro which expands to
-%     the two \TeX{} primitives \tn{immediate}\tn{write}.
-%   \end{texnote}
 % \end{function}
 %
 % \begin{function}{\iow_log:n, \iow_log:x}
@@ -355,9 +328,9 @@
 %
 % \begin{function}[EXP]{\iow_char:N}
 %   \begin{syntax}
-%     \cs{iow_char:N} \meta{token}
+%     \cs{iow_char:N} |\|\meta{char}
 %   \end{syntax}
-%   Inserts \meta{token} into the output stream. Useful when trying to
+%   Inserts \meta{char} into the output stream. Useful when trying to
 %   write difficult characters such as |%|, |{|, |}|,
 %   \emph{etc.}~in messages, for example:
 %   \begin{verbatim}
@@ -376,47 +349,59 @@
 %   expansion (\emph{e.g.}~in the second argument of \cs{iow_now:Nn}).
 % \end{function}
 %
-% \section{Wrapping lines in output}
+% \subsection{Wrapping lines in output}
 %
-% \begin{function}[updated = 2011-09-21]{\iow_wrap:xnnnN}
+% \begin{function}[added = 2012-06-28]{\iow_wrap:nnnN}
 %   \begin{syntax}
-%     \cs{iow_wrap:xnnnN} \Arg{text} \Arg{run-on text} \Arg{run-on length} \Arg{set up} \meta{function}
+%     \cs{iow_wrap:nnnN} \Arg{text} \Arg{run-on text} \Arg{set up} \meta{function}
 %   \end{syntax}
 %   This function will wrap the \meta{text} to a fixed number of
 %   characters per line. At the start of each line which is wrapped,
-%   the \meta{run-on text} will be inserted.  The line length targeted
-%   will be the value of \cs{l_iow_line_length_int} minus the
-%   \meta{run-on length}. The later value should be the number of
-%   characters in the \meta{run-on text}. Additional functions may be
-%   added to the wrapping by using the \meta{set up}, which is executed
-%   before the wrapping takes place. The result of the wrapping operation
-%   is passed as a braced argument to the \meta{function}, which will
-%   typically be a wrapper around a writing operation. Within the
-%   \meta{text},
+%   the \meta{run-on text} will be inserted.  The line character count
+%   targeted will be the value of \cs{l_iow_line_count_int} minus the
+%   number of characters in the \meta{run-on text}.  The \meta{text} and
+%   \meta{run-on text} are exhaustively expanded by the function, with the
+%   following substitutions:
 %   \begin{itemize}
-%   \item |\\| may be used to force a new line,
-%   \item \verb|\ | may be used to represent a forced space
-%     (for example after a control sequence),
-%   \item |\#|, |\%|, |\{|, |\}|, |\~| may be used to represent
-%     the corresponding character,
-%   \item \cs{iow_indent:n} may be used to indent a part of the
-%     message.
+%     \item |\\| may be used to force a new line,
+%     \item \verb*|\ | may be used to represent a forced space
+%       (for example after a control sequence),
+%     \item |\#|, |\%|, |\{|, |\}|, |\~| may be used to represent
+%       the corresponding character,
+%     \item \cs{iow_indent:n} may be used to indent a part of the
+%       message.
 %   \end{itemize}
-%   Both the wrapping process and the subsequent write operation
-%   will perform \texttt{x}-type expansion. For this reason, material which
-%   is to be written \enquote{as is} should be given as the argument to
-%   \cs{token_to_str:N} or \cs{tl_to_str:n} (as appropriate) within
-%   the \meta{text}. The output of \cs{iow_wrap:xnnnN} (\emph{i.e.}~the
-%   argument passed to the \meta{function}) will consist of characters of
-%   category code $12$ (other) and $10$ (space) only. This means that the
+%   Additional functions may be added to the wrapping by using the
+%   \meta{set up}, which is executed before the wrapping takes place: this
+%   may include overriding the substitutions listed.
+%   
+%   Any expandable material in the \meta{text} which is not to be expanded
+%   on wrapping should be converted to a string using \cs{token_to_str:N},
+%   \cs{tl_to_str:n}, \cs{tl_to_str:N}, \emph{etc.}
+%   
+%   The result of the wrapping operation is passed as a braced argument to the
+%   \meta{function}, which will typically be a wrapper around a write
+%   operation. The output of \cs{iow_wrap:nnnN} (\emph{i.e.}~the argument
+%   passed to the \meta{function}) will consist of characters of category
+%   \enquote{other} (category code~12), with the exception of spaces which
+%   will have category \enquote{space} (category code~10). This means that the
 %   output will \emph{not} expand further when written to a file.
+%   
+%   \begin{texnote}
+%     Internally, \cs{iow_wrap:nnnN} carries out an \texttt{x}-type expansion
+%     on the \meta{text} to expand it. This is done in such a way that
+%     \cs{exp_not:N} or \cs{exp_not:n} \emph{could} be used to prevent
+%     expansion of material. However, this is less conceptually clear than
+%     conversion to a string, which is therefore the supported method for
+%     handling expandable material in the \meta{text}.
+%   \end{texnote}
 % \end{function}
 %
 % \begin{function}[added = 2011-09-21]{\iow_indent:n}
 %   \begin{syntax}
 %     \cs{iow_indent:n} \Arg{text}
 %   \end{syntax}
-%   In the context of \cs{iow_wrap:xnnnN} (for instance in messages),
+%   In the context of \cs{iow_wrap:nnnN} (for instance in messages),
 %   indents \meta{text} by four spaces. This function will not cause
 %   a line break, and only affects lines which start within the scope
 %   of the \meta{text}. In case the indented \meta{text} should appear
@@ -424,8 +409,9 @@
 %   line breaks.
 % \end{function}
 %
-% \begin{variable}{\l_iow_line_length_int}
-%   The maximum length of a line to be written by the \cs{iow_wrap:xxnnN}
+% \begin{variable}[added = 2012-06-24]{\l_iow_line_count_int}
+%   The maximum number of characters in a line to be written
+%   by the \cs{iow_wrap:nnnN}
 %   function. This value depends on the \TeX{} system in use: the standard
 %   value is $78$, which is typically correct for unmodified \TeX{}live
 %   and MiK\TeX{} systems.
@@ -436,11 +422,11 @@
 %   (\enquote{other}), and character code $32$ (space).
 % \end{variable}
 %
-% \section{Constant input--output streams}
+% \subsection{Constant input--output streams}
 %
 % \begin{variable}{\c_term_ior}
 %   Constant input stream for reading from the terminal. Reading from this
-%   stream using \cs{ior_to:NN} or similar will result in a prompt from
+%   stream using \cs{ior_get:NN} or similar will result in a prompt from
 %   \TeX{} of the form
 %   \begin{verbatim}
 %     <tl>=
@@ -452,123 +438,61 @@
 %   (plus the log), respectively.
 % \end{variable}
 %
-% \section{Experimental functions}
-%
-% \begin{function}[added = 2012-02-11]{\ior_map_inline:Nn}
-%   \begin{syntax}
-%     \cs{ior_map_inline:Nn} \meta{stream} \Arg{inline function}
-%   \end{syntax}
-%   Applies the \meta{inline function} to \meta{items} obtained by
-%   reading one or more lines (until an equal number of left and right
-%   braces are found) from the \meta{stream}. The \meta{inline function}
-%   should consist of code which will receive the \meta{line} as |#1|.
-% \end{function}
+% \subsection{Primitive conditionals}
 %
-% \begin{function}[added = 2012-02-11]{\ior_str_map_inline:nn}
+% \begin{function}[EXP]{\if_eof:w}
 %   \begin{syntax}
-%     \cs{ior_str_map_inline:Nn} \Arg{stream} \Arg{inline function}
+%     \cs{if_eof:w} \meta{stream}
+%     ~~\meta{true code}
+%     \cs{else:}
+%     ~~\meta{false code}
+%     \cs{fi:}
 %   \end{syntax}
-%   Applies the \meta{inline function} to every \meta{line}
-%   in the \meta{file}. The material is read from the \meta{stream}
-%   as a series of tokens with category code $12$ (other), with the
-%   exception of space characters which are given category code $10$
-%   (space). The \meta{inline function} should consist of code which
-%   will receive the \meta{line} as |#1|.
+%   Tests if the \meta{stream} returns \enquote{end of file}, which is true
+%   for non-existent files. The \cs{else:} branch is optional.
+%   \begin{texnote}
+%     This is the \TeX{} primitive \tn{ifeof}.
+%   \end{texnote}
 % \end{function}
 %
-% \section{Internal file functions}
-%
-% \begin{variable}{\g_file_stack_seq}
-%   Stores the stack of nested files loaded using \cs{file_input:n}. This
-%   is needed to restore the appropriate file name to
-%   \cs{g_file_current_name_tl} at the end of each file.
-% \end{variable}
+% \subsection{Internal file functions and variables}
 %
-% \begin{variable}{\g_file_record_seq}
-%   Stores the name of every file loaded using \cs{file_input:n}. In
-%   contrast to \cs{g_file_stack_seq}, no items are ever removed from this
-%   sequence.
+% \begin{variable}{\l__file_internal_name_ior}
+%   Used to test for the existence of files when opening.
 % \end{variable}
 %
-% \begin{variable}{\l_file_internal_name_tl}
+% \begin{variable}{\l__file_internal_name_tl}
 %   Used to return the full name of a file for internal use.
 % \end{variable}
 %
-% \begin{variable}{\l_file_search_path_seq}
-%   The sequence of file paths to search when loading a file.
-% \end{variable}
-%
-% \begin{variable}{\l_file_internal_saved_path_seq}
-%   When loaded on top of \LaTeXe{}, there is a need to save the search
-%   path so that \tn{input@path} can be used as appropriate.
-% \end{variable}
-%
-% \begin{variable}[added = 2011-09-06]{\l_file_internal_seq}
-%   When loaded on top of \LaTeXe{}, there is a need to convert
-%   the comma lists \tn{input@path} and \tn{@filelist} to sequences.
-% \end{variable}
-%
-% \section{Internal input--output functions}
-%
-% \begin{function}[added = 2012-02-09]{\file_name_sanitize:nn}
+% \begin{function}[added = 2012-02-09]{\__file_name_sanitize:nn}
 %   \begin{syntax}
-%     \cs{file_name_sanitize:nn} \Arg{name} \Arg{tokens}
+%     \cs{__file_name_sanitize:nn} \Arg{name} \Arg{tokens}
 %   \end{syntax}
 %   Exhaustively-expands the \meta{name} with the exception of any
-%   category \meta{active} (catcode~$12$) tokens, which are not expanded.
+%   category \meta{active} (catcode~$13$) tokens, which are not expanded.
 %   The list of \meta{active} tokens is taken from \cs{l_char_active_seq}.
 %   The \meta{sanitized name} is then inserted (in braces) after the
 %   \meta{tokens}, which should further process the file name. If any
 %   spaces are found in the name after expansion, an error is raised.
 % \end{function}
 %
-% \begin{function}[EXP]{\if_eof:w}
-%   \begin{syntax}
-%     \cs{if_eof:w} \meta{stream}
-%     ~~\meta{true code}
-%     \cs{else:}
-%     ~~\meta{false code}
-%     \cs{fi:}
-%   \end{syntax}
-%   Tests if the \meta{stream} returns \enquote{end of file}, which is true
-%   for non-existent files. The \cs{else:} branch is optional.
-%   \begin{texnote}
-%     This is the \TeX{} primitive \tn{ifeof}.
-%   \end{texnote}
-% \end{function}
+% \subsection{Internal input--output functions}
 %
-% \begin{function}[added = 2012-01-23]
-%   {\ior_open_unsafe:Nn, \ior_open_unsafe:No, \iow_open_unsafe:Nn}
+% \begin{function}[added = 2012-01-23]{\__ior_open:Nn, \__ior_open:No}
 %   \begin{syntax}
-%     \cs{ior_open_unsafe:Nn} \meta{stream} \Arg{file name}
+%     \cs{__ior_open:Nn} \meta{stream} \Arg{file name}
 %   \end{syntax}
-%   These functions have identical syntax to the generally-available
-%   versions without the |_unsafe| suffix. However, these functions do not
-%   take precautions against active characters in the \meta{file name}: they
-%   are therefore intended to be used by higher-level functions which
-%   have already fully expanded the \meta{file name} and which need to
-%   perform multiple open or close operations. See for example the
+%   This function has identical syntax to the public version. However,
+%   is does not take precautions against active characters in the
+%   \meta{file name}, and it does not attempt to add a \meta{path} to
+%   the \meta{file name}: it is therefore intended to be used by
+%   higher-level
+%   functions which have already fully expanded the \meta{file name} and which
+%   need to perform multiple open or close operations. See for example the
 %   implementation of \cs{file_add_path:Nn},
 % \end{function}
 %
-% \begin{function}{\ior_raw_new:N, \ior_raw_new:c}
-%   \begin{syntax}
-%     \cs{ior_raw_new:N} \meta{stream}
-%   \end{syntax}
-%   Directly allocates a new stream for reading, bypassing the stack
-%   system. This is to be used only when a new stream is required at a
-%   \TeX{} level, when a new stream is requested by the stack itself.
-% \end{function}
-%
-% \begin{function}{\iow_raw_new:N, \iow_raw_new:c}
-%   \begin{syntax}
-%     \cs{iow_raw_new:N} \meta{stream}
-%   \end{syntax}
-%   Directly allocates a new stream for writing, bypassing the stack
-%   system. This is to be used only when a new stream is required at a
-%   \TeX{} level, when a new stream is requested by the stack itself.
-% \end{function}
-%
 % \end{documentation}
 %
 % \begin{implementation}
@@ -582,10 +506,14 @@
 %    \end{macrocode}
 %
 %    \begin{macrocode}
+%<@@=file>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
@@ -593,12 +521,10 @@
 %
 % \begin{variable}{\g_file_current_name_tl}
 %   The name of the current file should be available at all times.
-%    \begin{macrocode}
-\tl_new:N \g_file_current_name_tl
-%    \end{macrocode}
 %   For the format the file name needs to be picked up at the start of the
 %   file. In package mode the current file name is collected from \LaTeXe{}.
 %    \begin{macrocode}
+\tl_new:N \g_file_current_name_tl
 %<*initex>
 \tex_everyjob:D \exp_after:wN
   {
@@ -612,91 +538,92 @@
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\g_file_stack_seq}
+% \begin{variable}{\g_@@_stack_seq}
 %   The input list of files is stored as a sequence stack.
 %    \begin{macrocode}
-\seq_new:N \g_file_stack_seq
+\seq_new:N \g_@@_stack_seq
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\g_file_record_seq}
-%   The total list of files used is recorded separately from the current file
-%   stack, as nothing is ever popped from this list.
-%    \begin{macrocode}
-\seq_new:N \g_file_record_seq
-%    \end{macrocode}
-% The current file name should be included in the file list!
+% \begin{variable}{\g_@@_record_seq}
+%   The total list of files used is recorded separately from the current
+%   file stack, as nothing is ever popped from this list.  The current
+%   file name should be included in the file list!  In format mode, this
+%   is done at the very start of the \TeX{} run.  In package mode we
+%   will eventually copy the contents of \cs{@filelist}.
 %    \begin{macrocode}
+\seq_new:N \g_@@_record_seq
 %<*initex>
 \tex_everyjob:D \exp_after:wN
   {
     \tex_the:D \tex_everyjob:D
-    \seq_gput_right:NV \g_file_record_seq \g_file_current_name_tl
+    \seq_gput_right:NV \g_@@_record_seq \g_file_current_name_tl
   }
 %</initex>
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_file_internal_name_tl}
+% \begin{variable}{\l_@@_internal_name_tl}
 %   Used to return the fully-qualified name of a file.
 %    \begin{macrocode}
-\tl_new:N \l_file_internal_name_tl
+\tl_new:N \l_@@_internal_name_tl
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_file_search_path_seq}
+% \begin{variable}{\l_@@_search_path_seq}
 %   The current search path.
 %    \begin{macrocode}
-\seq_new:N \l_file_search_path_seq
+\seq_new:N \l_@@_search_path_seq
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_file_internal_saved_path_seq}
+% \begin{variable}{\l_@@_saved_search_path_seq}
 %   The current search path has to be saved for package use.
 %    \begin{macrocode}
 %<*package>
-\seq_new:N \l_file_internal_saved_path_seq
+\seq_new:N \l_@@_saved_search_path_seq
 %</package>
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_file_internal_seq}
+% \begin{variable}{\l_@@_internal_seq}
 %   Scratch space for comma list conversion in package mode.
 %    \begin{macrocode}
 %<*package>
-\seq_new:N \l_file_internal_seq
+\seq_new:N \l_@@_internal_seq
 %</package>
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{macro}[int]{\file_name_sanitize:nn}
+% \begin{macro}[aux]{\@@_name_sanitize:nn}
 %   For converting a token list to a string where active characters are treated
 %   as strings from the start.
 %    \begin{macrocode}
-\cs_new_protected:Npn \file_name_sanitize:nn #1#2
+\cs_new_protected:Npn \@@_name_sanitize:nn #1#2
   {
     \group_begin:
       \seq_map_inline:Nn \l_char_active_seq
         { \cs_set_nopar:Npx ##1 { \token_to_str:N ##1 } }
-      \tl_set:Nx \l_file_internal_name_tl {#1}
-      \tl_set:Nx \l_file_internal_name_tl
-        { \tl_to_str:N \l_file_internal_name_tl }
-      \tl_if_in:NnTF \l_file_internal_name_tl { ~ }
+      \tl_set:Nx \l_@@_internal_name_tl {#1}
+      \tl_set:Nx \l_@@_internal_name_tl
+        { \tl_to_str:N \l_@@_internal_name_tl }
+      \tl_if_in:NnT \l_@@_internal_name_tl { ~ }
         {
-          \msg_kernel_error:nnx { file } { space-in-file-name }
-            { \l_file_internal_name_tl }
+          \__msg_kernel_error:nnx { kernel } { space-in-file-name }
+            { \l_@@_internal_name_tl }
+          \tl_remove_all:Nn \l_@@_internal_name_tl { ~ }
         }
       \use:x
         {
           \group_end:
-          \exp_not:n {#2} { \l_file_internal_name_tl }
+          \exp_not:n {#2} { \l_@@_internal_name_tl }
         }
   }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}{\file_add_path:nN}
-% \begin{macro}[aux]{\file_add_path_aux:nN, \file_add_path_search:nN}
+% \begin{macro}[aux]{\@@_add_path:nN, \@@_add_path_search:nN}
 %   The way to test if a file exists is to try to open it: if it does not
 %   exist then \TeX{} will report end-of-file. For files which are in the
 %   current directory, this is straight-forward.  For other locations, a
@@ -705,33 +632,31 @@
 %   |#2| is returned empty.
 %    \begin{macrocode}
 \cs_new_protected:Npn \file_add_path:nN #1
-  { \file_name_sanitize:nn {#1} { \file_add_path_aux:nN } }
-\cs_new_protected:Npn \file_add_path_aux:nN #1#2
+  { \@@_name_sanitize:nn {#1} { \@@_add_path:nN } }
+\cs_new_protected:Npn \@@_add_path:nN #1#2
   {
-    \ior_open_unsafe:Nn \g_file_internal_ior {#1}
-    \ior_if_eof:NTF \g_file_internal_ior
-      { \file_add_path_search:nN {#1} #2 }
-      {
-        \ior_close:N \g_file_internal_ior
-        \tl_set:Nn #2 {#1}
-      }
+    \__ior_open:Nn \g__file_internal_ior {#1}
+    \ior_if_eof:NTF \g__file_internal_ior
+      { \@@_add_path_search:nN {#1} #2 }
+      { \tl_set:Nn #2 {#1} }
+    \ior_close:N \g__file_internal_ior
   }
-\cs_new_protected:Npn \file_add_path_search:nN #1#2
+\cs_new_protected:Npn \@@_add_path_search:nN #1#2
   {
-    \tl_set:Nn #2 { \q_no_value }
+    \tl_set:Nn #2 { \q_no_value  }
 %<*package>
     \cs_if_exist:NT \input@path
       {
-        \seq_set_eq:NN \l_file_internal_saved_path_seq \l_file_search_path_seq
-        \seq_set_from_clist:NN \l_file_internal_seq \input@path
-        \seq_concat:NNN \l_file_search_path_seq
-          \l_file_search_path_seq \l_file_internal_seq
+        \seq_set_eq:NN \l_@@_saved_search_path_seq \l_@@_search_path_seq
+        \seq_set_split:NnV \l_@@_internal_seq { , } \input@path
+        \seq_concat:NNN \l_@@_search_path_seq
+          \l_@@_search_path_seq \l_@@_internal_seq
       }
 %</package>
-    \seq_map_inline:Nn \l_file_search_path_seq
+    \seq_map_inline:Nn \l_@@_search_path_seq
       {
-        \ior_open_unsafe:Nn \g_file_internal_ior { ##1 #1 }
-        \ior_if_eof:NF \g_file_internal_ior
+        \__ior_open:Nn \g__file_internal_ior { ##1 #1 }
+        \ior_if_eof:NF \g__file_internal_ior
           {
             \tl_set:Nx #2 { ##1 #1 }
             \seq_map_break:
@@ -739,9 +664,8 @@
       }
 %<*package>
     \cs_if_exist:NT \input@path
-      { \seq_set_eq:NN \l_file_search_path_seq \l_file_internal_saved_path_seq }
+      { \seq_set_eq:NN \l_@@_search_path_seq \l_@@_saved_search_path_seq }
 %</package>
-    \ior_close:N \g_file_internal_ior
   }
 %    \end{macrocode}
 % \end{macro}
@@ -751,12 +675,12 @@
 %   The test for the existence of a file is a wrapper around the function to
 %   add a path to a file. If the file was found, the path will contain
 %   something, whereas if the file was not located then the return value
-%   will be empty.
+%   will be \cs{q_no_value}.
 %    \begin{macrocode}
 \prg_new_protected_conditional:Npnn \file_if_exist:n #1 { T , F , TF }
   {
-    \file_add_path:nN {#1} \l_file_internal_name_tl
-    \quark_if_no_value:NTF \l_file_internal_name_tl
+    \file_add_path:nN {#1} \l_@@_internal_name_tl
+    \quark_if_no_value:NTF \l_@@_internal_name_tl
       { \prg_return_false: }
       { \prg_return_true: }
   }
@@ -764,78 +688,124 @@
 % \end{macro}
 %
 % \begin{macro}{\file_input:n}
-% \begin{macro}[aux]{\file_input_aux:n \file_input_aux:V, \file_input_error:n}
+% \begin{macro}[aux]{\@@_input:n \@@_input:V}
+% \begin{macro}[aux, EXP]{\@@_input_aux:w}
+% \begin{macro}[aux]{\@@_input_aux:n, \@@_input_aux:o}
 %   Loading a file is done in a safe way, checking first that the file
-%   exists and loading only if it does.
+%   exists and loading only if it does.  Push the file name on the
+%   \cs{g_@@_stack_seq}, and add it to the file list, either
+%   \cs{g_@@_record_seq}, or \cs{@filelist} in package mode.
 %    \begin{macrocode}
 \cs_new_protected:Npn \file_input:n #1
   {
-    \file_add_path:nN {#1} \l_file_internal_name_tl
-    \quark_if_no_value:NTF \l_file_internal_name_tl
-      { \file_name_sanitize:nn {#1} { \file_input_error:n } }
-      { \file_input_aux:V \l_file_internal_name_tl }
+    \file_add_path:nN {#1} \l_@@_internal_name_tl
+    \quark_if_no_value:NTF \l_@@_internal_name_tl
+      {
+        \@@_name_sanitize:nn {#1}
+          { \__msg_kernel_error:nnx { kernel } { file-not-found } }
+      }
+      { \@@_input:V \l_@@_internal_name_tl }
   }
-\cs_new_protected:Npn \file_input_aux:n #1
+\cs_new_protected:Npn \@@_input:n #1
+  {
+    \quark_if_nil:oTF { \@@_input_aux:w #1 . \q_nil . \q_stop }
+      { \@@_input_aux:o { \tl_to_str:n { #1 .tex } } }
+      { \@@_input_aux:n {#1} }
+  }
+\cs_generate_variant:Nn \@@_input:n { V }
+\cs_new:Npn \@@_input_aux:w #1 . #2 . #3 \q_stop { #2 }
+\cs_new_protected:Npn \@@_input_aux:n #1
   {
 %<*initex>
-    \seq_gput_right:Nn \g_file_record_seq {#1}
+    \seq_gput_right:Nn \g_@@_record_seq {#1}
 %</initex>
 %<*package>
-    \@addtofilelist {#1}
+    \clist_if_exist:NTF \@filelist
+      { \@addtofilelist {#1} }
+      { \seq_gput_right:Nn \g_@@_record_seq {#1} }
 %</package>
-    \seq_gpush:Nn \g_file_stack_seq \g_file_current_name_tl
+    \seq_gpush:Nn \g_@@_stack_seq \g_file_current_name_tl
     \tl_gset:Nn \g_file_current_name_tl {#1}
     \tex_input:D #1 \c_space_tl
-    \seq_gpop:NN \g_file_stack_seq \g_file_current_name_tl
+    \seq_gpop:NN \g_@@_stack_seq \g_file_current_name_tl
   }
-\cs_generate_variant:Nn \file_input_aux:n { V }
-\cs_new_protected:Npn \file_input_error:n #1
-  { \msg_kernel_error:nnx { file } { file-not-found } {#1} }
+\cs_generate_variant:Nn \@@_input_aux:n { o }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
+% \end{macro}
+% \end{macro}
 %
 % \begin{macro}{\file_path_include:n}
 % \begin{macro}{\file_path_remove:n}
+% \begin{macro}[aux]{\@@_path_include:n}
 %   Wrapper functions to manage the search path.
 %    \begin{macrocode}
 \cs_new_protected:Npn \file_path_include:n #1
+  { \@@_name_sanitize:nn {#1} { \@@_path_include:n } }
+\cs_new_protected:Npn \@@_path_include:n #1
   {
-    \seq_if_in:NnF  \l_file_search_path_seq {#1}
-      { \seq_put_right:Nn \l_file_search_path_seq {#1} }
+    \seq_if_in:NnF \l_@@_search_path_seq {#1}
+      { \seq_put_right:Nn \l_@@_search_path_seq {#1} }
   }
 \cs_new_protected:Npn \file_path_remove:n #1
-  { \seq_remove_all:Nn \l_file_search_path_seq {#1} }
+  {
+    \@@_name_sanitize:nn {#1}
+      { \seq_remove_all:Nn \l_@@_search_path_seq }
+  }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
+% \end{macro}
 %
 % \begin{macro}{\file_list:}
-%   A function to list all files used to the log.
+%   A function to list all files used to the log, without duplicates.
+%   In package mode, if \cs{@filelist} is still defined, we need to take
+%   it into account (we capture it \cs{AtBeginDocument} into
+%   \cs{g_@@_record_seq}), turning each file name into a string.
 %    \begin{macrocode}
 \cs_new_protected_nopar:Npn \file_list:
   {
-    \seq_remove_duplicates:N \g_file_record_seq
+    \seq_set_eq:NN \l_@@_internal_seq \g_@@_record_seq
+%<*package>
+    \clist_if_exist:NT \@filelist
+      {
+        \clist_map_inline:Nn \@filelist
+          {
+            \seq_put_right:No \l_@@_internal_seq
+              { \tl_to_str:n {##1} }
+          }
+      }
+%</package>
+    \seq_remove_duplicates:N \l_@@_internal_seq
     \iow_log:n { *~File~List~* }
-    \seq_map_inline:Nn \g_file_record_seq { \iow_log:n {##1} }
+    \seq_map_inline:Nn \l_@@_internal_seq { \iow_log:n {##1} }
     \iow_log:n { ************* }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-%   When used as a package, there is a need to hold onto the standard
-%   file list as well as the new one here.
+% When used as a package, there is a need to hold onto the standard file
+% list as well as the new one here.  File names recorded in
+% \cs{@filelist} must be turned to strings before being added to
+% \cs{g_@@_record_seq}.
 %    \begin{macrocode}
 %<*package>
 \AtBeginDocument
   {
-    \seq_set_from_clist:NN \l_file_internal_seq \@filelist
-    \seq_gconcat:NNN \g_file_record_seq \g_file_record_seq \l_file_internal_seq
+    \clist_map_inline:Nn \@filelist
+      { \seq_gput_right:No \g_@@_record_seq { \tl_to_str:n {#1} } }
   }
 %</package>
 %    \end{macrocode}
 %
-% \subsection{Input--output variables constants}
+% \subsection{Input operations}
+%
+%    \begin{macrocode}
+%<@@=ior>
+%    \end{macrocode}
+%
+% \subsubsection{Variables and constants}
 %
 % \begin{variable}{\c_term_ior}
 %   Reading from the terminal (with a prompt) is done using a positive
@@ -846,20 +816,10 @@
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\c_log_iow, \c_term_iow}
-%   Here we allocate two output streams for writing to the transcript
-%   file only (\cs{c_log_iow}) and to both the terminal and
-%   transcript file (\cs{c_term_iow}).
-%    \begin{macrocode}
-\cs_new_eq:NN \c_log_iow  \c_minus_one
-\cs_new_eq:NN \c_term_iow \c_sixteen
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\c_iow_streams_tl, \c_ior_streams_tl}
+% \begin{variable}{\c_@@_streams_tl}
 %   The list of streams available, by number.
 %    \begin{macrocode}
-\tl_const:Nn \c_iow_streams_tl
+\tl_const:Nn \c_@@_streams_tl
   {
     \c_zero
     \c_one
@@ -878,151 +838,118 @@
     \c_fourteen
     \c_fifteen
   }
-\cs_new_eq:NN \c_ior_streams_tl \c_iow_streams_tl
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\g_iow_streams_prop, \g_ior_streams_prop}
+% \begin{variable}{\g_@@_streams_prop}
 %   The allocations for streams are stored in property lists, which
 %   are set up to have a \enquote{full} set of allocations from the start.
 %   In package mode, a few slots are always taken, so these are
 %   blocked off from use.
 %    \begin{macrocode}
-\prop_new:N \g_iow_streams_prop
-\prop_new:N \g_ior_streams_prop
+\prop_new:N \g_@@_streams_prop
 %<*package>
-\prop_put:Nnn \g_iow_streams_prop { 0 } { LaTeX2e~reserved }
-\prop_put:Nnn \g_iow_streams_prop { 1 } { LaTeX2e~reserved }
-\prop_put:Nnn \g_iow_streams_prop { 2 } { LaTeX2e~reserved }
-\prop_put:Nnn \g_ior_streams_prop { 0 } { LaTeX2e~reserved }
+\prop_put:Nnn \g_@@_streams_prop { 0 } { LaTeX2e~reserved }
 %</package>
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_iow_stream_int, \l_ior_stream_int}
+% \begin{variable}{\l_@@_stream_int}
 %   Used to track the number allocated to the stream being created:
 %   this is taken from the property list but does alter.
 %    \begin{macrocode}
-\int_new:N \l_iow_stream_int
-\cs_new_eq:NN \l_ior_stream_int \l_iow_stream_int
+\int_new:N \l_@@_stream_int
 %    \end{macrocode}
 % \end{variable}
 %
-% \subsection{Stream management}
+% \subsubsection{Stream management}
 %
-% \begin{macro}[int]{\ior_raw_new:N, \ior_raw_new:c}
-% \begin{macro}[int]{\iow_raw_new:N, \iow_raw_new:c}
-% The lowest level for stream management is actually creating raw \TeX{}
-% streams. As these are very limited (even with \eTeX{}), this should not
-% be addressed directly.
+% \begin{macro}[int]{\@@_new:N, \@@_new:c}
+%   The lowest level for stream management is actually creating raw \TeX{}
+%   streams. As these are very limited (even with \eTeX{}), this should not
+%   be addressed directly.
 %    \begin{macrocode}
 %<*initex>
-\alloc_setup_type:nnn { ior } \c_zero \c_sixteen
-\cs_new_protected:Npn \ior_raw_new:N #1
-  { \alloc_reg:nNN { ior } \tex_chardef:D #1 }
-\alloc_setup_type:nnn { iow } \c_zero \c_sixteen
-\cs_new_protected:Npn \iow_raw_new:N #1
-  { \alloc_reg:nNN { iow } \tex_chardef:D #1 }
+\__alloc_setup_type:nnn { ior } \c_zero \c_sixteen
+\cs_new_protected:Npn \@@_new:N #1
+  { \__alloc_reg:nNN { ior } \tex_chardef:D #1 }
 %</initex>
 %<*package>
-\cs_set_eq:NN \iow_raw_new:N \newwrite
-\cs_set_eq:NN \ior_raw_new:N \newread
+\cs_set_eq:NN \@@_new:N \newread
 %</package>
-\cs_generate_variant:Nn \ior_raw_new:N { c }
-\cs_generate_variant:Nn \iow_raw_new:N { c }
+\cs_generate_variant:Nn \@@_new:N { c }
 %    \end{macrocode}
 % \end{macro}
-% \end{macro}
 %
-% \begin{macro}{\ior_new:N, \ior_new:c, \iow_new:N, \iow_new:c}
+% \begin{macro}{\ior_new:N, \ior_new:c}
 %   Reserving a new stream is done by defining the name as equal to using the
 %   terminal.
 %    \begin{macrocode}
 \cs_new_protected:Npn \ior_new:N #1 { \cs_new_eq:NN #1 \c_term_ior }
 \cs_generate_variant:Nn \ior_new:N { c }
-\cs_new_protected:Npn \iow_new:N #1 { \cs_new_eq:NN #1 \c_term_iow }
-\cs_generate_variant:Nn \iow_new:N { c }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{variable}{\g_file_internal_ior}
-%   Delayed from above so that the mechanisms are in place.
+% \begin{variable}{\g__file_internal_ior}
+%   Delayed from the \texttt{file} section so that the mechanisms are in place.
 %    \begin{macrocode}
-\ior_new:N \g_file_internal_ior
+\ior_new:N \g__file_internal_ior
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{macro}{\ior_open:Nn, \ior_open:cn, \iow_open:Nn, \iow_open:cn}
-% \begin{macro}[int]{\ior_open_aux:Nn}
+% \begin{macro}{\ior_open:Nn, \ior_open:cn}
 % \begin{macro}[TF]{\ior_open:Nn}
-% \begin{macro}[aux]{\ior_open_aux:NnTF}
-% \begin{macro}[int]
-%   {\ior_open_unsafe:Nn, \ior_open_unsafe:No, \iow_open_unsafe:Nn}
-%   In both cases, opening a stream starts with a call to the closing
-%   function: this is safest. There is then a loop through the
-%   allocation number list to find the first free stream number.
-%   When one is found the allocation can take place, the information
-%   can be stored and finally the file can actually be opened. Before
-%   any actual file operations there is a precaution against special
-%   characters in file names. For reading files, there is an intermediate
-%   auxiliary to allow path addition, keeping the internal function fast
-%   and avoiding an infinite loop.
+% \begin{macro}[aux]{\@@_open_aux:Nn}
+% \begin{macro}[aux]{\@@_open_aux:NnTF}
+% \begin{macro}[aux]{\@@_open:Nn, \@@_open:No}
+%   Opening a stream starts with a call to the closing function: this is
+%   safest. There is then a loop through the  allocation number list to find
+%   the first free stream number. When one is found the allocation can take
+%   place, the information can be stored and finally the file can actually be
+%   opened. Before any actual file operations there is a precaution against
+%   special characters in file names. There is an intermediate auxiliary to
+%   allow path addition, keeping the internal function fast and avoiding an
+%   infinite loop.
 %    \begin{macrocode}
 \cs_new_protected:Npn \ior_open:Nn #1#2
-  { \file_name_sanitize:nn {#2} { \ior_open_aux:Nn #1 } }
+  { \__file_name_sanitize:nn {#2} { \@@_open_aux:Nn #1 } }
 \cs_generate_variant:Nn \ior_open:Nn { c }
-\cs_new_protected:Npn \iow_open:Nn #1#2
-  { \file_name_sanitize:nn {#2} { \iow_open_unsafe:Nn #1 } }
-\cs_generate_variant:Nn \iow_open:Nn { c }
-\cs_new_protected:Npn \ior_open_aux:Nn #1#2
+\cs_new_protected:Npn \@@_open_aux:Nn #1#2
   {
-    \file_add_path:nN {#2} \l_file_internal_name_tl
-    \quark_if_no_value:NTF \l_file_internal_name_tl
-      { \file_input_error:n {#2} }
-      { \ior_open_unsafe:No #1 \l_file_internal_name_tl }
+    \file_add_path:nN {#2} \l__file_internal_name_tl
+    \quark_if_no_value:NTF \l__file_internal_name_tl
+      { \__msg_kernel_error:nnx { kernel } { file-not-found } {#2} }
+      { \@@_open:No #1 \l__file_internal_name_tl }
   }
 \prg_new_protected_conditional:Npnn \ior_open:Nn #1#2 { T , F , TF }
-  { \file_name_sanitize:nn {#2} { \ior_open_aux:NnTF #1 } }
-\cs_new_protected:Npn \ior_open_aux:NnTF #1#2
+  { \__file_name_sanitize:nn {#2} { \@@_open_aux:NnTF #1 } }
+\cs_new_protected:Npn \@@_open_aux:NnTF #1#2
   {
-    \file_add_path:nN {#2} \l_file_internal_name_tl
-    \quark_if_no_value:NTF \l_file_internal_name_tl
+    \file_add_path:nN {#2} \l__file_internal_name_tl
+    \quark_if_no_value:NTF \l__file_internal_name_tl
       { \prg_return_false: }
       {
-        \ior_open_unsafe:No #1 \l_file_internal_name_tl
+        \@@_open:No #1 \l__file_internal_name_tl
         \prg_return_true:
       }
   }
 \cs_generate_variant:Nn \ior_open:NnT  { c }
 \cs_generate_variant:Nn \ior_open:NnF  { c }
 \cs_generate_variant:Nn \ior_open:NnTF { c }
-\cs_new_protected:Npn \ior_open_unsafe:Nn #1#2
+\cs_new_protected:Npn \@@_open:Nn #1#2
   {
     \ior_close:N #1
-    \int_set:Nn \l_ior_stream_int \c_sixteen
-    \tl_map_function:NN \c_ior_streams_tl \ior_alloc_read:n
-    \int_compare:nNnTF \l_ior_stream_int = \c_sixteen
-      { \msg_kernel_fatal:nn { ior } { streams-exhausted } }
+    \int_set_eq:NN \l_@@_stream_int \c_sixteen
+    \tl_map_function:NN \c_@@_streams_tl \@@_alloc:n
+    \int_compare:nNnTF \l_@@_stream_int = \c_sixteen
+      { \__msg_kernel_fatal:nn { kernel } { input-streams-exhausted } }
       {
-        \ior_stream_alloc:N #1
-        \prop_gput:NVn \g_ior_streams_prop \l_ior_stream_int {#2}
+        \@@_alloc:N #1
+        \prop_gput:NVn \g_@@_streams_prop \l_@@_stream_int {#2}
         \tex_openin:D #1#2 \scan_stop:
       }
   }
-\cs_generate_variant:Nn \ior_open_unsafe:Nn { No }
-\cs_new_protected:Npn \iow_open_unsafe:Nn #1#2
-  {
-    \iow_close:N #1
-    \int_set:Nn \l_iow_stream_int \c_sixteen
-    \tl_map_function:NN \c_iow_streams_tl \iow_alloc_write:n
-    \int_compare:nNnTF \l_iow_stream_int = \c_sixteen
-      { \msg_kernel_fatal:nn { iow } { streams-exhausted } }
-      {
-        \iow_stream_alloc:N #1
-        \prop_gput:NVn \g_iow_streams_prop \l_iow_stream_int {#2}
-        \tex_immediate:D \tex_openout:D #1#2 \scan_stop:
-      }
-  }
+\cs_generate_variant:Nn \@@_open:Nn { No }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1030,114 +957,321 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[aux]{\ior_alloc_read:n}
-% \begin{macro}[aux]{\iow_alloc_write:n}
-% These functions are used to see if a particular stream is available.
-% The property list contains file names for streams in use, so
-% any unused ones are for the taking.
+% \begin{macro}[aux]{\@@_alloc:n}
+%   See if a particular stream is available: the property list contains file
+%   names for streams in use, so any unused ones are for the taking.
 %    \begin{macrocode}
-\cs_new_protected:Npn \iow_alloc_write:n #1
+\cs_new_protected:Npn \@@_alloc:n #1
   {
-    \prop_if_in:NnF \g_iow_streams_prop {#1}
+    \prop_if_in:NnF \g_@@_streams_prop {#1}
       {
-        \int_set:Nn \l_iow_stream_int {#1}
-        \tl_map_break:
-      }
-  }
-\cs_new_protected:Npn \ior_alloc_read:n #1
-  {
-    \prop_if_in:NnF \g_iow_streams_prop {#1}
-      {
-        \int_set:Nn \l_ior_stream_int {#1}
+        \int_set:Nn \l_@@_stream_int {#1}
         \tl_map_break:
       }
   }
 %    \end{macrocode}
 % \end{macro}
-% \end{macro}
 %
-% \begin{macro}[aux]{\iow_stream_alloc:N, \ior_stream_alloc:N}
-% \begin{macro}[aux]{\iow_stream_alloc_aux:, \ior_stream_alloc_aux:}
-% \begin{variable}{\g_iow_internal_iow, \g_ior_internal_ior}
-%   Allocating a raw stream is much easier in \IniTeX{} mode than for
-%   the package. For the format, all streams will be allocated by
-%   \pkg{l3file} and so there is a simple check to see if a raw
-%   stream is actually available. On the other hand, for the
-%   package there will be non-managed streams. So if the managed
-%   one is not open, a check is made to see if some other managed
-%   stream is available before deciding to open a new one. If a new
-%   one is needed, we get the number allocated by \LaTeXe{} to get
-%   \enquote{back on track} with allocation.
+% \begin{macro}[aux]{\@@_alloc:N}
+% \begin{macro}[aux]{\@@_alloc:}
+% \begin{variable}{\g_@@_internal_ior}
+%   Allocating a raw stream is much easier in \IniTeX{} mode than for the
+%   package. For the format, all streams will be allocated by \pkg{l3file} and
+%   so there is a simple check to see if a raw stream is actually available. On
+%   the other hand, for the package there will be non-managed streams. So if
+%   the managed one is not open, a check is made to see if some other managed
+%   stream is available before deciding to open a new one. If a new one is
+%   needed, we get the number allocated by \LaTeXe{} to get \enquote{back on
+%   track} with allocation.
 %    \begin{macrocode}
-\iow_new:N \g_iow_internal_iow
-\ior_new:N \g_ior_internal_ior
-\cs_new_protected:Npn \iow_stream_alloc:N #1
+\ior_new:N \g_@@_internal_ior
+\cs_new_protected:Npn \@@_alloc:N #1
   {
-    \cs_if_exist:cF { g_iow_ \int_use:N \l_iow_stream_int _iow }
+    \cs_if_exist:cF { g_ior_ \int_use:N \l_@@_stream_int _ior }
       {
 %<*package>
-        \iow_stream_alloc_aux:
-        \int_compare:nNnT \l_iow_stream_int = \c_sixteen
+        \@@_alloc:
+        \int_compare:nNnT \l_@@_stream_int = \c_sixteen
           {
-            \iow_raw_new:N \g_iow_internal_iow
-            \int_set:Nn \l_iow_stream_int { \g_iow_internal_iow }
+            \@@_new:N \g_@@_internal_ior
+            \int_set:Nn \l_@@_stream_int { \g_@@_internal_ior }
             \cs_gset_eq:cN
-              { g_iow_ \int_use:N \l_iow_stream_int _iow } \g_iow_internal_iow
+              { g_ior_ \int_use:N \l_@@_stream_int _ior } \g_@@_internal_ior
           }
 %</package>
 %<*initex>
-        \iow_raw_new:c { g_iow_ \int_use:N \l_iow_stream_int _iow }
+        \@@_new:c { g_ior_ \int_use:N \l_@@_stream_int _ior }
 %</initex>
       }
-    \cs_gset_eq:Nc #1 { g_iow_ \int_use:N \l_iow_stream_int _iow }
+    \cs_gset_eq:Nc #1 { g_ior_ \int_use:N \l_@@_stream_int _ior }
   }
 %<*package>
-\cs_new_protected_nopar:Npn \iow_stream_alloc_aux:
+\cs_new_protected_nopar:Npn \@@_alloc:
   {
-    \int_incr:N \l_iow_stream_int
-    \int_compare:nNnT \l_iow_stream_int < \c_sixteen
+    \int_incr:N \l_@@_stream_int
+    \int_compare:nNnT \l_@@_stream_int < \c_sixteen
       {
-        \cs_if_exist:cTF { g_iow_ \int_use:N \l_iow_stream_int _iow }
+        \cs_if_exist:cTF { g_ior_ \int_use:N \l_@@_stream_int _ior }
           {
-            \prop_if_in:NVT \g_iow_streams_prop \l_iow_stream_int
-              { \iow_stream_alloc_aux: }
+            \prop_if_in:NVT \g_@@_streams_prop \l_@@_stream_int
+              { \@@_alloc: }
           }
-          { \iow_stream_alloc_aux: }
+          { \@@_alloc: }
+      }
+  }
+%</package>
+%    \end{macrocode}
+% \end{variable}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\ior_close:N, \ior_close:c}
+%   Closing a stream is not quite the reverse of opening one. First,
+%   the close operation is easier than the open one, and second as the
+%   stream is actually a number we can use it directly to show that the
+%   slot has been freed up.
+%    \begin{macrocode}
+\cs_new_protected:Npn \ior_close:N #1
+  {
+    \__chk_if_exist_cs:N #1
+    \int_compare:nNnF #1 < \c_zero
+      {
+        \int_compare:nNnF #1 > \c_fifteen
+          {
+            \tex_closein:D #1
+            \prop_gremove:NV \g_@@_streams_prop #1
+            \cs_gset_eq:NN #1 \c_term_ior
+          }
+      }
+  }
+\cs_generate_variant:Nn \ior_close:N { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ior_list_streams:}
+% \begin{macro}[aux]{\@@_list_streams:Nn}
+%   Show the property lists, but with some \enquote{pretty printing}.
+%   See the \pkg{l3msg} module. If there are no open read streams,
+%   issue the message \texttt{show-no-stream}, and show an empty
+%   token list. If there are open read streams, format them with
+%   \cs{__msg_show_item_unbraced:nn}, and with the message
+%   \texttt{show-open-streams}.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \ior_list_streams:
+  { \@@_list_streams:Nn \g_@@_streams_prop { input } }
+\cs_new_protected:Npn \@@_list_streams:Nn #1#2
+  {
+    \__msg_term:nnn { LaTeX / kernel }
+      { \prop_if_empty:NTF #1 { show-no-stream } { show-open-streams } }
+      {#2}
+    \__msg_show_variable:x
+      { \prop_map_function:NN #1 \__msg_show_item_unbraced:nn }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsubsection{Reading input}
+%
+% \begin{macro}[int]{\if_eof:w}
+%   The primitive conditional
+%    \begin{macrocode}
+\cs_new_eq:NN \if_eof:w \tex_ifeof:D
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[pTF]{\ior_if_eof:N}
+%   To test if some particular input stream is exhausted the following
+%   conditional is provided.
+%    \begin{macrocode}
+\prg_new_conditional:Nnn \ior_if_eof:N { p , T , F , TF }
+  {
+    \cs_if_exist:NTF #1
+      {
+        \if_int_compare:w #1 = \c_sixteen
+          \prg_return_true:
+        \else:
+          \if_eof:w #1
+            \prg_return_true:
+          \else:
+            \prg_return_false:
+          \fi:
+        \fi:
       }
+      { \prg_return_true: }
   }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ior_get:NN}
+%   And here we read from files.
+%    \begin{macrocode}
+\cs_new_protected:Npn \ior_get:NN #1#2
+  { \tex_read:D #1 to #2 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\ior_get_str:NN}
+%   Reading as strings is also a primitive wrapper.
+%    \begin{macrocode}
+\cs_new_protected:Npn \ior_get_str:NN #1#2
+  { \etex_readline:D #1 to #2 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Output operations}
+%
+%    \begin{macrocode}
+%<@@=iow>
+%    \end{macrocode}
+%
+% There is a lot of similarity here to the input operations, at least for
+% many of the basics. Thus quite a bit is copied from the earlier material.
+%
+% \subsubsection{Variables and constants}
+%
+% \begin{variable}{\c_log_iow, \c_term_iow}
+%   Here we allocate two output streams for writing to the transcript
+%   file only (\cs{c_log_iow}) and to both the terminal and
+%   transcript file (\cs{c_term_iow}).
+%    \begin{macrocode}
+\cs_new_eq:NN \c_log_iow  \c_minus_one
+\cs_new_eq:NN \c_term_iow \c_sixteen
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\c_@@_streams_tl}
+%   The list of streams available, by number: copied from the input
+%   operations.
+%    \begin{macrocode}
+\cs_new_eq:NN \c_@@_streams_tl \c__ior_streams_tl
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\g_@@_streams_prop}
+%   As for reads, but with more reserved as \LaTeXe{} takes up a few here.
+%    \begin{macrocode}
+\prop_new:N \g_@@_streams_prop
+%<*package>
+\prop_put:Nnn \g_@@_streams_prop { 0 } { LaTeX2e~reserved }
+\prop_put:Nnn \g_@@_streams_prop { 1 } { LaTeX2e~reserved }
+\prop_put:Nnn \g_@@_streams_prop { 2 } { LaTeX2e~reserved }
+%</package>
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_@@_stream_int}
+%   Used to track the number allocated to the stream being created:
+%   this is taken from the property list but does alter. The two allocation
+%   routines only need one register, so we save one here.
+%    \begin{macrocode}
+\cs_new_eq:NN \l_@@_stream_int \l__ior_stream_int
+%    \end{macrocode}
+% \end{variable}
+%
+% \subsection{Stream management}
+%
+% \begin{macro}[aux]{\@@_new:N, \@@_new:c}
+%   The same idea as for input, but with a separate set of functions.
+%    \begin{macrocode}
+%<*initex>
+\__alloc_setup_type:nnn { iow } \c_zero \c_sixteen
+\cs_new_protected:Npn \@@_new:N #1
+  { \__alloc_reg:nNN { iow } \tex_chardef:D #1 }
+%</initex>
+%<*package>
+\cs_set_eq:NN \@@_new:N \newwrite
 %</package>
-\cs_new_protected:Npn \ior_stream_alloc:N #1
+\cs_generate_variant:Nn \@@_new:N { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\iow_new:N, \iow_new:c}
+%   Reserving a new stream is done by defining the name as equal to writing
+%   to the terminal: odd but at least consistent.
+%    \begin{macrocode}
+\cs_new_protected:Npn \iow_new:N #1 { \cs_new_eq:NN #1 \c_term_iow }
+\cs_generate_variant:Nn \iow_new:N { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\iow_open:Nn, \iow_open:cn}
+% \begin{macro}[aux]{\@@_open:Nn}
+%   The same idea as for reading, but without the path.
+%    \begin{macrocode}
+\cs_new_protected:Npn \iow_open:Nn #1#2
+  { \__file_name_sanitize:nn {#2} { \@@_open:Nn #1 } }
+\cs_generate_variant:Nn \iow_open:Nn { c }
+\cs_new_protected:Npn \@@_open:Nn #1#2
   {
-    \cs_if_exist:cF { g_ior_ \int_use:N \l_ior_stream_int _ior }
+    \iow_close:N #1
+    \int_set_eq:NN \l_@@_stream_int \c_sixteen
+    \tl_map_function:NN \c_@@_streams_tl \@@_alloc:n
+    \int_compare:nNnTF \l_@@_stream_int = \c_sixteen
+      { \__msg_kernel_fatal:nn { kernel } { output-streams-exhausted } }
+      {
+        \@@_alloc:N #1
+        \prop_gput:NVn \g_@@_streams_prop \l_@@_stream_int {#2}
+        \tex_immediate:D \tex_openout:D #1#2 \scan_stop:
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[aux]{\@@_alloc:n}
+%   Identical to the input routine, but with the appropriate names used
+%   (when \pkg{l3docstrip} has done it's job!).
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_alloc:n #1
+  {
+    \prop_if_in:NnF \g_@@_streams_prop {#1}
+      {
+        \int_set:Nn \l_@@_stream_int {#1}
+        \tl_map_break:
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux]{\@@_alloc:N}
+% \begin{macro}[aux]{\@@_alloc:}
+% \begin{variable}{\g_@@_internal_iow}
+%   Exactly the same as for reading!
+%    \begin{macrocode}
+\iow_new:N \g_@@_internal_iow
+\cs_new_protected:Npn \@@_alloc:N #1
+  {
+    \cs_if_exist:cF { g_iow_ \int_use:N \l_@@_stream_int _iow }
       {
 %<*package>
-        \ior_stream_alloc_aux:
-        \int_compare:nNnT \l_ior_stream_int = \c_sixteen
+        \@@_alloc:
+        \int_compare:nNnT \l_@@_stream_int = \c_sixteen
           {
-            \ior_raw_new:N \g_ior_internal_ior
-            \int_set:Nn \l_ior_stream_int { \g_ior_internal_ior }
+            \@@_new:N \g_@@_internal_iow
+            \int_set:Nn \l_@@_stream_int { \g_@@_internal_iow }
             \cs_gset_eq:cN
-              { g_ior_ \int_use:N \l_iow_stream_int _ior } \g_ior_internal_ior
+              { g_iow_ \int_use:N \l_@@_stream_int _iow } \g_@@_internal_iow
           }
 %</package>
 %<*initex>
-        \ior_raw_new:c { g_ior_ \int_use:N \l_ior_stream_int _ior }
+        \@@_new:c { g_iow_ \int_use:N \l_@@_stream_int _iow }
 %</initex>
       }
-    \cs_gset_eq:Nc #1 { g_ior_ \int_use:N \l_ior_stream_int _ior }
+    \cs_gset_eq:Nc #1 { g_iow_ \int_use:N \l_@@_stream_int _iow }
   }
 %<*package>
-\cs_new_protected_nopar:Npn \ior_stream_alloc_aux:
+\cs_new_protected_nopar:Npn \@@_alloc:
   {
-    \int_incr:N \l_ior_stream_int
-    \int_compare:nNnT \l_ior_stream_int < \c_sixteen
+    \int_incr:N \l_@@_stream_int
+    \int_compare:nNnT \l_@@_stream_int < \c_sixteen
       {
-        \cs_if_exist:cTF { g_ior_ \int_use:N \l_ior_stream_int _ior }
+        \cs_if_exist:cTF { g_iow_ \int_use:N \l_@@_stream_int _iow }
           {
-            \prop_if_in:NVT \g_ior_streams_prop \l_ior_stream_int
-              { \ior_stream_alloc_aux: }
+            \prop_if_in:NVT \g_@@_streams_prop \l_@@_stream_int
+              { \@@_alloc: }
           }
-          { \ior_stream_alloc_aux: }
+          { \@@_alloc: }
       }
   }
 %</package>
@@ -1146,84 +1280,41 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\ior_close:N, \ior_close:c, \iow_close:N, \iow_close:c}
+% \begin{macro}{\iow_close:N, \iow_close:c}
 %   Closing a stream is not quite the reverse of opening one. First,
 %   the close operation is easier than the open one, and second as the
 %   stream is actually a number we can use it directly to show that the
 %   slot has been freed up.
 %    \begin{macrocode}
-\cs_new_protected:Npn \ior_close:N #1
-  {
-    \cs_if_exist:NT #1
-      {
-        \int_compare:nNnF #1 = \c_minus_one
-          {
-            \int_compare:nNnF #1 = \c_sixteen
-              { \tex_closein:D #1 }
-            \prop_gdel:NV \g_ior_streams_prop #1
-            \cs_gset_eq:NN #1 \c_term_ior
-          }
-      }
-  }
 \cs_new_protected:Npn \iow_close:N #1
   {
-    \cs_if_exist:NT #1
+    \__chk_if_exist_cs:N #1
+    \int_compare:nNnF #1 < \c_zero
       {
-        \int_compare:nNnF #1 = \c_minus_one
+        \int_compare:nNnF #1 > \c_fifteen
           {
-            \int_compare:nNnF #1 = \c_sixteen
-              { \tex_closein:D #1 }
-            \prop_gdel:NV \g_iow_streams_prop #1
+            \tex_closeout:D #1
+            \prop_gremove:NV \g_@@_streams_prop #1
             \cs_gset_eq:NN #1 \c_term_iow
           }
       }
   }
-\cs_generate_variant:Nn \ior_close:N { c }
 \cs_generate_variant:Nn \iow_close:N { c }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\ior_list_streams:}
-%   Show the property lists, but with some \enquote{pretty printing}.
-%   See the \pkg{l3msg} module. If there are no open read streams,
-%   issue the message \texttt{show-no-stream}, and show an empty
-%   token list. If there are open read streams, format them with
-%   \cs{msg_aux_show_unbraced:nn}, and with the message
-%   \texttt{show-open-streams}.
+% \begin{macro}{\iow_list_streams:}
+% \begin{macro}{\@@_list_streams:Nn}
+%   Done as for input, but with a copy of the auxiliary so the name is correct.
 %    \begin{macrocode}
-\cs_new_protected_nopar:Npn \ior_list_streams:
-  { \ior_list_streams_aux:Nn \g_ior_streams_prop { ior } }
 \cs_new_protected_nopar:Npn \iow_list_streams:
-  { \ior_list_streams_aux:Nn \g_iow_streams_prop { iow } }
-\cs_new_protected:Npn \ior_list_streams_aux:Nn #1#2
-  {
-    \msg_aux_use:nn { LaTeX / #2 }
-      { \prop_if_empty:NTF #1 { show-no-stream } { show-open-streams } }
-    \msg_aux_show:x
-      { \prop_map_function:NN #1 \msg_aux_show_unbraced:nn }
-  }
+  { \@@_list_streams:Nn \g_@@_streams_prop { output } }
+\cs_new_eq:NN \@@_list_streams:Nn \__ior_list_streams:Nn
 %    \end{macrocode}
 % \end{macro}
+% \end{macro}
 %
-% Text for the error messages.
-%    \begin{macrocode}
-\msg_kernel_new:nnnn { iow } { streams-exhausted }
-  { Output~streams~exhausted }
-  {
-    TeX~can~only~open~up~to~16~output~streams~at~one~time.\\
-    All~16 are currently~in~use,~and~something~wanted~to~open
-    another~one.
-  }
-\msg_kernel_new:nnnn { ior } { streams-exhausted }
-  { Input~streams~exhausted }
-  {
-    TeX~can~only~open~up~to~16~input~streams~at~one~time.\\
-    All~16 are currently~in~use,~and~something~wanted~to~open
-    another~one.
-  }
-%    \end{macrocode}
-%
-% \subsection{Deferred writing}
+% \subsubsection{Deferred writing}
 %
 % \begin{macro}{\iow_shipout_x:Nn, \iow_shipout_x:Nx}
 %   First the easy part, this is the primitive.
@@ -1234,7 +1325,7 @@
 % \end{macro}
 %
 % \begin{macro}{\iow_shipout:Nn, \iow_shipout:Nx}
-%   With \eTeX{} available deferred writing is easy.
+%   With \eTeX{} available deferred writing without expansion is easy.
 %    \begin{macrocode}
 \cs_new_protected:Npn \iow_shipout:Nn #1#2
   { \iow_shipout_x:Nn #1 { \exp_not:n {#2} } }
@@ -1242,30 +1333,26 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \subsection{Immediate writing}
+% \subsubsection{Immediate writing}
 %
-% \begin{macro}{\iow_now:Nx}
-%   An abbreviation for an often used operation, which immediately
-%   writes its second argument expanded to the output stream.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \iow_now:Nx { \tex_immediate:D \iow_shipout_x:Nn }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\iow_now:Nn}
+% \begin{macro}{\iow_now:Nn, \iow_now:Nx}
 %   This routine writes the second argument onto the output stream without
 %   expansion. If this stream isn't open, the output goes to the terminal
 %   instead. If the first argument is no output stream at all, we get an
-%   internal error.
+%   internal error.  We don't use the expansion done by \tn{write} to
+%   get the |Nx| variant, because it differs in subtle ways from
+%   \texttt{x}-expansion, namely, macro parameter characters would not
+%   need to be doubled.
 %    \begin{macrocode}
 \cs_new_protected:Npn \iow_now:Nn #1#2
-  { \iow_now:Nx #1 { \exp_not:n {#2} } }
+  { \tex_immediate:D \iow_shipout_x:Nn #1 { \exp_not:n {#2} } }
+\cs_generate_variant:Nn \iow_now:Nn { Nx }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}{\iow_log:n, \iow_log:x}
 % \begin{macro}{\iow_term:n, \iow_term:x}
-% Writing to the log and the terminal directly are relatively easy.
+%   Writing to the log and the terminal directly are relatively easy.
 %    \begin{macrocode}
 \cs_set_protected_nopar:Npn \iow_log:x  { \iow_now:Nx \c_log_iow  }
 \cs_new_protected_nopar:Npn \iow_log:n  { \iow_now:Nn \c_log_iow  }
@@ -1275,7 +1362,7 @@
 %\end{macro}
 %\end{macro}
 %
-% \subsection{Special characters for writing}
+% \subsubsection{Special characters for writing}
 %
 % \begin{macro}{\iow_newline:}
 %   Global variable holding the character that forces a new line when
@@ -1292,83 +1379,87 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \subsection{Hard-wrapping lines based on length}
+% \subsubsection{Hard-wrapping lines to a character count}
 %
 % The code here implements a generic hard-wrapping function. This is
 % used by the messaging system, but is designed such that it is
 % available for other uses.
 %
-% \begin{macro}{\l_iow_line_length_int}
-%   This is the \enquote{raw} length of a line which can be written to a
-%   file. The standard value is the line length typically used by
+% \begin{macro}[var, added = 2012-06-24]{\l_iow_line_count_int}
+%   This is the \enquote{raw} number of characters in a line which
+%   can be written to the terminal.
+%   The standard value is the line length typically used by
 %   \TeX{}Live and Mik\TeX{}.
 %    \begin{macrocode}
-\int_new:N  \l_iow_line_length_int
-\int_set:Nn \l_iow_line_length_int { 78 }
+\int_new:N  \l_iow_line_count_int
+\int_set:Nn \l_iow_line_count_int { 78 }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]{\l_iow_target_length_int}
-%   This stores the target line length: the full length minus any
-%   part for a leader at the start of each line.
+% \begin{macro}[aux]{\l_@@_target_count_int}
+%   This stores the target line count: the full number of characters
+%   in a line, minus any part for a leader at the start of each line.
 %    \begin{macrocode}
-\int_new:N \l_iow_target_length_int
+\int_new:N \l_@@_target_count_int
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}[aux]
 %   {
-%     \l_iow_current_line_int,
-%     \l_iow_current_word_int,
-%     \l_iow_current_indentation_int
+%     \l_@@_current_line_int,
+%     \l_@@_current_word_int,
+%     \l_@@_current_indentation_int
 %   }
 %   These store the number of characters in the line and word currently
 %   being constructed, and the current indentation, respectively.
 %    \begin{macrocode}
-\int_new:N \l_iow_current_line_int
-\int_new:N \l_iow_current_word_int
-\int_new:N \l_iow_current_indentation_int
+\int_new:N \l_@@_current_line_int
+\int_new:N \l_@@_current_word_int
+\int_new:N \l_@@_current_indentation_int
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}[aux]
 %   {
-%     \l_iow_current_line_tl,
-%     \l_iow_current_word_tl,
-%     \l_iow_current_indentation_tl
+%     \l_@@_current_line_tl,
+%     \l_@@_current_word_tl,
+%     \l_@@_current_indentation_tl
 %   }
 %   These hold the current line of text and current word,
 %   and a number of spaces for indentation, respectively.
 %    \begin{macrocode}
-\tl_new:N \l_iow_current_line_tl
-\tl_new:N \l_iow_current_word_tl
-\tl_new:N \l_iow_current_indentation_tl
+\tl_new:N \l_@@_current_line_tl
+\tl_new:N \l_@@_current_word_tl
+\tl_new:N \l_@@_current_indentation_tl
 %    \end{macrocode}
 %\end{macro}
 %
-% \begin{macro}[aux]{\l_iow_wrap_tl}
-%   Used for the expansion step before detokenizing.
+% \begin{macro}[aux]{\l_@@_wrap_tl}
+%   Used for the expansion step before detokenizing, and for the output
+%   from wrapping text: fully expanded and with lines which are not
+%   overly long.
 %    \begin{macrocode}
-\tl_new:N \l_iow_wrap_tl
+\tl_new:N \l_@@_wrap_tl
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]{\l_iow_wrapped_tl}
-%   The output from wrapping text: fully expanded and with lines
-%   which are not overly long.
+% \begin{macro}[aux]{\l_@@_newline_tl}
+%   The token list inserted to produce the new line, with the
+%   \meta{run-on text}.
 %    \begin{macrocode}
-\tl_new:N \l_iow_wrapped_tl
+\tl_new:N \l_@@_newline_tl
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]{\l_iow_line_start_bool}
-%   Boolean to avoid adding a space at the beginning of forced newlines.
+% \begin{macro}[aux]{\l_@@_line_start_bool}
+%   Boolean to avoid adding a space at the beginning of forced newlines,
+%   and to know when to add the indentation.
 %    \begin{macrocode}
-\bool_new:N \l_iow_line_start_bool
+\bool_new:N \l_@@_line_start_bool
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]{\c_catcode_other_space_tl}
+% \begin{macro}{\c_catcode_other_space_tl}
 %   Lowercase a character with category code $12$ to produce an
 %   \enquote{other} space. We can do everything within the group,
 %   because \cs{tl_const:Nn} defines its argument globally.
@@ -1381,49 +1472,45 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]{\c_iow_wrap_marker_tl}
-% \begin{macro}[aux]{
-%     \c_iow_wrap_end_marker_tl,
-%     \c_iow_wrap_newline_marker_tl,
-%     \c_iow_wrap_indent_marker_tl,
-%     \c_iow_wrap_unindent_marker_tl}
-% \begin{macro}[aux]{\iow_wrap_new_marker:n}
+% \begin{macro}[aux]{\c_@@_wrap_marker_tl}
+% \begin{macro}[aux]
+%   {
+%     \c_@@_wrap_end_marker_tl,
+%     \c_@@_wrap_newline_marker_tl,
+%     \c_@@_wrap_indent_marker_tl,
+%     \c_@@_wrap_unindent_marker_tl
+%   }
 %   Every special action of the wrapping code is preceeded by
-%   the same recognizable string, \cs{c_iow_wrap_marker_tl}.
+%   the same recognizable string, \cs{c_@@_wrap_marker_tl}.
 %   Upon seeing that \enquote{word}, the wrapping code reads
 %   one space-delimited argument to know what operation to
 %   perform. The setting of \tn{escapechar} here is not
-%   very important, but makes \cs{c_iow_wrap_marker_tl} look
-%   nicer. Note that \cs{iow_wrap_new_marker:n} does not
-%   survive the group, but all constants are defined globally.
+%   very important, but makes \cs{c_@@_wrap_marker_tl} look
+%   nicer.
 %    \begin{macrocode}
 \group_begin:
   \int_set_eq:NN \tex_escapechar:D \c_minus_one
-  \tl_const:Nx \c_iow_wrap_marker_tl
+  \tl_const:Nx \c_@@_wrap_marker_tl
     { \tl_to_str:n { \^^I \^^O \^^W \^^_ \^^W \^^R \^^A \^^P } }
-  \cs_set:Npn \iow_wrap_new_marker:n #1
-    {
-      \tl_const:cx { c_iow_wrap_ #1 _marker_tl }
-        {
-          \c_catcode_other_space_tl
-          \c_iow_wrap_marker_tl
-          \c_catcode_other_space_tl
-          #1
-          \c_catcode_other_space_tl
-        }
-    }
-  \iow_wrap_new_marker:n { end }
-  \iow_wrap_new_marker:n { newline }
-  \iow_wrap_new_marker:n { indent }
-  \iow_wrap_new_marker:n { unindent }
 \group_end:
+\tl_map_inline:nn
+  { { end } { newline } { indent } { unindent } }
+  {
+    \tl_const:cx { c_@@_wrap_ #1 _marker_tl }
+      {
+        \c_catcode_other_space_tl
+        \c_@@_wrap_marker_tl
+        \c_catcode_other_space_tl
+        #1
+        \c_catcode_other_space_tl
+      }
+  }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
-% \end{macro}
 %
 % \begin{macro}{\iow_indent:n}
-% \begin{macro}[aux]{\iow_indent_expandable:n}
+% \begin{macro}[aux]{\@@_indent:n}
 %   We give a dummy (protected) definition to \cs{iow_indent:n}
 %   when outside messages. Within wrapped message, it places
 %   the instruction for increasing the indentation before its
@@ -1432,23 +1519,26 @@
 %   only changes when the next line is started.
 %    \begin{macrocode}
 \cs_new_protected:Npn \iow_indent:n #1 { }
-\cs_new:Npx \iow_indent_expandable:n #1
+\cs_new:Npx \@@_indent:n #1
   {
-    \c_iow_wrap_indent_marker_tl
+    \c_@@_wrap_indent_marker_tl
     #1
-    \c_iow_wrap_unindent_marker_tl
+    \c_@@_wrap_unindent_marker_tl
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\iow_wrap:xnnnN}
-%   The main wrapping function works as follows. The target number of
-%   characters in a line is calculated, before fully-expanding the input
-%   such that |\\| and \verb*|\ | are converted into the appropriate
-%   values. There is then a loop over each word in the input, which
-%   will do the actual wrapping. After the loop, the resulting text is
-%   passed on to the function which has been given as a post-processor.
+% \begin{macro}{\iow_wrap:nnnN}
+%   The main wrapping function works as follows.  First give |\\|,
+%   \verb*|\ | and other formatting commands the correct definition for
+%   messages, before fully-expanding the input.  In package mode, the
+%   expansion uses \LaTeXe{}'s \cs{protect} mechanism.  Afterwards, set
+%   the newline marker (two assignments to fully expand, then convert
+%   to a string) and its length, and initialize some registers.
+%   There is then a loop over each word in the input, which will do the
+%   actual wrapping.  After the loop, the resulting text is passed on to
+%   the function which has been given as a post-processor.
 %   The argument |#4| is available for additional set up steps for
 %   the output. The definition of |\\| and \verb*|\ | use an
 %   \enquote{other} space rather than a normal space, because the latter
@@ -1456,16 +1546,9 @@
 %   expansions. The \cs{tl_to_str:N} step converts the \enquote{other}
 %   space back to a normal space.
 %    \begin{macrocode}
-\cs_new_protected:Npn \iow_wrap:xnnnN #1#2#3#4#5
+\cs_new_protected:Npn \iow_wrap:nnnN #1#2#3#4
   {
     \group_begin:
-      \int_set:Nn \l_iow_target_length_int { \l_iow_line_length_int - ( #3 ) }
-      \int_zero:N \l_iow_current_indentation_int
-      \tl_clear:N \l_iow_current_indentation_tl
-      \int_zero:N \l_iow_current_line_int
-      \tl_clear:N \l_iow_current_line_tl
-      \tl_clear:N \l_iow_wrap_tl
-      \bool_set_true:N \l_iow_line_start_bool
       \int_set_eq:NN \tex_escapechar:D \c_minus_one
       \cs_set_nopar:Npx \{ { \token_to_str:N \{ }
       \cs_set_nopar:Npx \# { \token_to_str:N \# }
@@ -1473,103 +1556,119 @@
       \cs_set_nopar:Npx \% { \token_to_str:N \% }
       \cs_set_nopar:Npx \~ { \token_to_str:N \~ }
       \int_set:Nn \tex_escapechar:D { 92 }
-      \cs_set_eq:NN \\ \c_iow_wrap_newline_marker_tl
+      \cs_set_eq:NN \\ \c_@@_wrap_newline_marker_tl
       \cs_set_eq:NN \  \c_catcode_other_space_tl
-      \cs_set_eq:NN \iow_indent:n \iow_indent_expandable:n
-      #4
+      \cs_set_eq:NN \iow_indent:n \@@_indent:n
+      #3
 %<*initex>
-      \tl_set:Nx \l_iow_wrap_tl {#1}
+      \tl_set:Nx \l_@@_wrap_tl {#1}
 %</initex>
 %<*package>
-      \protected@edef \l_iow_wrap_tl {#1}
+      \protected@edef \l_@@_wrap_tl {#1}
 %</package>
-      \cs_set:Npn \\ { \iow_newline: #2 }
+%    \end{macrocode}
+%   This is a bit of a hack to measure the string length of the run on text
+%   without the \pkg{l3str} module (which is still experimental). This should
+%   be replaced once the string module is finalised with something a little
+%   cleaner.
+%    \begin{macrocode}
+      \tl_set:Nx \l_@@_newline_tl { \iow_newline: #2 }
+      \tl_set:Nx \l_@@_newline_tl { \tl_to_str:N \l_@@_newline_tl }
+      \tl_replace_all:Nnn \l_@@_newline_tl { ~ } { \c_space_tl }
+      \int_set:Nn \l_@@_target_count_int
+        { \l_iow_line_count_int - \tl_count:N \l_@@_newline_tl + \c_one }
+      \int_zero:N \l_@@_current_indentation_int
+      \tl_clear:N \l_@@_current_indentation_tl
+      \int_zero:N \l_@@_current_line_int
+      \tl_clear:N \l_@@_current_line_tl
+      \bool_set_true:N \l_@@_line_start_bool
       \use:x
         {
-          \iow_wrap_loop:w
-          \tl_to_str:N \l_iow_wrap_tl
-          \tl_to_str:N \c_iow_wrap_end_marker_tl
+          \exp_not:n { \tl_clear:N \l_@@_wrap_tl }
+          \@@_wrap_loop:w
+          \tl_to_str:N \l_@@_wrap_tl
+          \tl_to_str:N \c_@@_wrap_end_marker_tl
           \c_space_tl \c_space_tl
           \exp_not:N \q_stop
         }
     \exp_args:NNo \group_end:
-    #5 \l_iow_wrapped_tl
+    #4 \l_@@_wrap_tl
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]{\iow_wrap_loop:w}
+% \begin{macro}[aux]{\@@_wrap_loop:w}
 %   The loop grabs one word in the input, and checks whether it is
 %   the special marker, or a normal word.
 %    \begin{macrocode}
-\cs_new_protected:Npn \iow_wrap_loop:w #1 ~ %
+\cs_new_protected:Npn \@@_wrap_loop:w #1 ~ %
   {
-    \tl_set:Nn \l_iow_current_word_tl {#1}
-    \tl_if_eq:NNTF \l_iow_current_word_tl \c_iow_wrap_marker_tl
-      { \iow_wrap_special:w }
-      { \iow_wrap_word: }
+    \tl_set:Nn \l_@@_current_word_tl {#1}
+    \tl_if_eq:NNTF \l_@@_current_word_tl \c_@@_wrap_marker_tl
+      { \@@_wrap_special:w }
+      { \@@_wrap_word: }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]{\iow_wrap_word:}
-% \begin{macro}[aux]{\iow_wrap_word_fits:}
-% \begin{macro}[aux]{\iow_wrap_word_newline:}
-%   For a normal word, update the line length, then test if the current
+% \begin{macro}[aux]{\@@_wrap_word:}
+% \begin{macro}[aux]{\@@_wrap_word_fits:}
+% \begin{macro}[aux]{\@@_wrap_word_newline:}
+%   For a normal word, update the line count, then test if the current
 %   word would fit in the current line, and call the appropriate function.
 %   If the word fits in the current line, add it to the line, preceded by
 %   a space unless it is the first word of the line.
 %   Otherwise, the current line is added to the result, with the run-on text.
-%   The current word (and its length) are then put in the new line.
+%   The current word (and its character count) are then put in the new line.
 %    \begin{macrocode}
-\cs_new_protected_nopar:Npn \iow_wrap_word:
+\cs_new_protected_nopar:Npn \@@_wrap_word:
   {
-    \int_set:Nn \l_iow_current_word_int
-      { \str_length_skip_spaces:N \l_iow_current_word_tl }
-    \int_add:Nn \l_iow_current_line_int { \l_iow_current_word_int }
-    \int_compare:nNnTF \l_iow_current_line_int < \l_iow_target_length_int
-      { \iow_wrap_word_fits: }
-      { \iow_wrap_word_newline: }
-    \iow_wrap_loop:w
+    \int_set:Nn \l_@@_current_word_int
+      { \__str_count_ignore_spaces:N \l_@@_current_word_tl }
+    \int_add:Nn \l_@@_current_line_int { \l_@@_current_word_int }
+    \int_compare:nNnTF \l_@@_current_line_int < \l_@@_target_count_int
+      { \@@_wrap_word_fits: }
+      { \@@_wrap_word_newline: }
+    \@@_wrap_loop:w
   }
-\cs_new_protected_nopar:Npn \iow_wrap_word_fits:
+\cs_new_protected_nopar:Npn \@@_wrap_word_fits:
   {
-    \bool_if:NTF \l_iow_line_start_bool
+    \bool_if:NTF \l_@@_line_start_bool
       {
-        \bool_set_false:N \l_iow_line_start_bool
-        \tl_put_right:Nx \l_iow_current_line_tl
-          { \l_iow_current_indentation_tl \l_iow_current_word_tl }
-        \int_add:Nn \l_iow_current_line_int
-          { \l_iow_current_indentation_int }
+        \bool_set_false:N \l_@@_line_start_bool
+        \tl_put_right:Nx \l_@@_current_line_tl
+          { \l_@@_current_indentation_tl \l_@@_current_word_tl }
+        \int_add:Nn \l_@@_current_line_int
+          { \l_@@_current_indentation_int }
       }
       {
-        \tl_put_right:Nx \l_iow_current_line_tl
-          { ~ \l_iow_current_word_tl }
-        \int_incr:N \l_iow_current_line_int
+        \tl_put_right:Nx \l_@@_current_line_tl
+          { ~ \l_@@_current_word_tl }
+        \int_incr:N \l_@@_current_line_int
       }
   }
-\cs_new_protected_nopar:Npn \iow_wrap_word_newline:
+\cs_new_protected_nopar:Npn \@@_wrap_word_newline:
   {
-    \tl_put_right:Nx \l_iow_wrapped_tl
-      { \l_iow_current_line_tl \\ }
-    \int_set:Nn \l_iow_current_line_int
+    \tl_put_right:Nx \l_@@_wrap_tl
+      { \l_@@_current_line_tl \l_@@_newline_tl }
+    \int_set:Nn \l_@@_current_line_int
       {
-        \l_iow_current_word_int
-        + \l_iow_current_indentation_int
+        \l_@@_current_word_int
+        + \l_@@_current_indentation_int
       }
-    \tl_set:Nx \l_iow_current_line_tl
-      { \l_iow_current_indentation_tl \l_iow_current_word_tl }
+    \tl_set:Nx \l_@@_current_line_tl
+      { \l_@@_current_indentation_tl \l_@@_current_word_tl }
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[aux]{\iow_wrap_special:w}
-% \begin{macro}[aux]{\iow_wrap_newline:w}
-% \begin{macro}[aux]{\iow_wrap_indent:w}
-% \begin{macro}[aux]{\iow_wrap_unindent:w}
-% \begin{macro}[aux]{\iow_wrap_end:w}
+% \begin{macro}[aux]{\@@_wrap_special:w}
+% \begin{macro}[aux]{\@@_wrap_newline:w}
+% \begin{macro}[aux]{\@@_wrap_indent:w}
+% \begin{macro}[aux]{\@@_wrap_unindent:w}
+% \begin{macro}[aux]{\@@_wrap_end:w}
 %   When the \enquote{special} marker is encountered,
 %   read what operation to perform, as a space-delimited
 %   argument, perform it, and remember to loop.
@@ -1584,37 +1683,37 @@
 %   At the end, we simply save the last line (without the run-on text),
 %   and prevent the loop.
 %    \begin{macrocode}
-\cs_new_protected:Npn \iow_wrap_special:w #1 ~ #2 ~ #3 ~ %
+\cs_new_protected:Npn \@@_wrap_special:w #1 ~ #2 ~ #3 ~ %
   {
-    \use:c { iow_wrap_#1: }
-    \str_if_eq:xxTF { #2~#3 } { ~ \c_iow_wrap_marker_tl }
-      { \iow_wrap_special:w }
-      { \iow_wrap_loop:w #2 ~ #3 ~ }
+    \use:c { @@_wrap_#1: }
+    \str_if_eq_x:nnTF { #2~#3 } { ~ \c_@@_wrap_marker_tl }
+      { \@@_wrap_special:w }
+      { \@@_wrap_loop:w #2 ~ #3 ~ }
   }
-\cs_new_protected_nopar:Npn \iow_wrap_newline:
+\cs_new_protected_nopar:Npn \@@_wrap_newline:
   {
-    \tl_put_right:Nx \l_iow_wrapped_tl
-      { \l_iow_current_line_tl \\ }
-    \int_zero:N \l_iow_current_line_int
-    \tl_clear:N \l_iow_current_line_tl
-    \bool_set_true:N \l_iow_line_start_bool
+    \tl_put_right:Nx \l_@@_wrap_tl
+      { \l_@@_current_line_tl \l_@@_newline_tl }
+    \int_zero:N \l_@@_current_line_int
+    \tl_clear:N \l_@@_current_line_tl
+    \bool_set_true:N \l_@@_line_start_bool
   }
-\cs_new_protected_nopar:Npx \iow_wrap_indent:
+\cs_new_protected_nopar:Npx \@@_wrap_indent:
   {
-    \int_add:Nn \l_iow_current_indentation_int \c_four
-    \tl_put_right:Nx \exp_not:N \l_iow_current_indentation_tl
+    \int_add:Nn \l_@@_current_indentation_int \c_four
+    \tl_put_right:Nx \exp_not:N \l_@@_current_indentation_tl
       { \c_space_tl \c_space_tl \c_space_tl \c_space_tl }
   }
-\cs_new_protected_nopar:Npn \iow_wrap_unindent:
+\cs_new_protected_nopar:Npn \@@_wrap_unindent:
   {
-    \int_sub:Nn \l_iow_current_indentation_int \c_four
-    \tl_set:Nx \l_iow_current_indentation_tl
-      { \prg_replicate:nn \l_iow_current_indentation_int { ~ } }
+    \int_sub:Nn \l_@@_current_indentation_int \c_four
+    \tl_set:Nx \l_@@_current_indentation_tl
+      { \prg_replicate:nn \l_@@_current_indentation_int { ~ } }
   }
-\cs_new_protected_nopar:Npn \iow_wrap_end:
+\cs_new_protected_nopar:Npn \@@_wrap_end:
   {
-    \tl_put_right:Nx \l_iow_wrapped_tl
-      { \l_iow_current_line_tl }
+    \tl_put_right:Nx \l_@@_wrap_tl
+      { \l_@@_current_line_tl }
     \use_none_delimit_by_q_stop:w
   }
 %    \end{macrocode}
@@ -1624,29 +1723,29 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[aux]{\str_length_skip_spaces:N}
-% \begin{macro}[aux]{\str_length_skip_spaces:n}
-% \begin{macro}[aux]{\str_length_loop:NNNNNNNNN}
+% \begin{macro}[aux]{\__str_count_ignore_spaces:N}
+% \begin{macro}[aux]{\__str_count_ignore_spaces:n}
+% \begin{macro}[aux]{\__str_count_loop:NNNNNNNNN}
 %   The wrapping code requires to measure the number of character
-%   in each word. This could be done with \cs{tl_length:n}, but
+%   in each word. This could be done with \cs{tl_count:n}, but
 %   it is ten times faster (literally) to use the code below.
 %    \begin{macrocode}
-\cs_new_nopar:Npn \str_length_skip_spaces:N
-  { \exp_args:No \str_length_skip_spaces:n }
-\cs_new:Npn \str_length_skip_spaces:n #1
+\cs_new_nopar:Npn \__str_count_ignore_spaces:N
+  { \exp_args:No \__str_count_ignore_spaces:n }
+\cs_new:Npn \__str_count_ignore_spaces:n #1
   {
-    \int_value:w \int_eval:w
-      \exp_after:wN \str_length_loop:NNNNNNNNN \tl_to_str:n {#1}
+    \__int_value:w \__int_eval:w
+      \exp_after:wN \__str_count_loop:NNNNNNNNN \tl_to_str:n {#1}
         { X8 } { X7 } { X6 } { X5 } { X4 } { X3 } { X2 } { X1 } { X0 } \q_stop
-    \int_eval_end:
+    \__int_eval_end:
   }
-\cs_new:Npn \str_length_loop:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+\cs_new:Npn \__str_count_loop:NNNNNNNNN #1#2#3#4#5#6#7#8#9
   {
     \if_catcode:w X #9
       \exp_after:wN \use_none_delimit_by_q_stop:w
     \else:
       9 +
-      \exp_after:wN \str_length_loop:NNNNNNNNN
+      \exp_after:wN \__str_count_loop:NNNNNNNNN
     \fi:
   }
 %    \end{macrocode}
@@ -1654,132 +1753,80 @@
 % \end{macro}
 % \end{macro}
 %
-% \subsection{Reading input}
+% \subsection{Messages}
 %
-% \begin{macro}[int]{\if_eof:w}
-%   The primitive conditional
 %    \begin{macrocode}
-\cs_new_eq:NN \if_eof:w \tex_ifeof:D
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[pTF]{\ior_if_eof:N}
-%   To test if some particular input stream is exhausted the following
-%   conditional is provided.
-%    \begin{macrocode}
-\prg_new_conditional:Nnn \ior_if_eof:N { p , T , F , TF }
+\__msg_kernel_new:nnnn { kernel } { file-not-found }
+  { File~'#1'~not~found. }
   {
-    \cs_if_exist:NTF #1
-      {
-        \if_int_compare:w #1 = \c_sixteen
-          \prg_return_true:
-        \else:
-          \if_eof:w #1
-            \prg_return_true:
-          \else:
-            \prg_return_false:
-          \fi:
-        \fi:
-      }
-      { \prg_return_true: }
+    The~requested~file~could~not~be~found~in~the~current~directory,~
+    in~the~TeX~search~path~or~in~the~LaTeX~search~path.
+  }
+\__msg_kernel_new:nnnn { kernel } { input-streams-exhausted }
+  { Input~streams~exhausted }
+  {
+    TeX~can~only~open~up~to~16~input~streams~at~one~time.\\
+    All~16~are~currently~in~use,~and~something~wanted~to~open~
+    another~one.
+  }
+\__msg_kernel_new:nnnn { kernel } { output-streams-exhausted }
+  { Output~streams~exhausted }
+  {
+    TeX~can~only~open~up~to~16~output~streams~at~one~time.\\
+    All~16~are~currently~in~use,~and~something~wanted~to~open~
+    another~one.
+  }
+\__msg_kernel_new:nnnn { kernel } { space-in-file-name }
+  { Space~in~file~name~'#1'. }
+  {
+    Spaces~are~not~permitted~in~files~loaded~by~LaTeX: \\
+    Further~errors~may~follow!
   }
 %    \end{macrocode}
-% \end{macro}
 %
-% \begin{macro}{\ior_to:NN, \ior_gto:NN}
-%   And here we read from files.
-%    \begin{macrocode}
-\cs_new_protected:Npn \ior_to:NN #1#2
-  { \tex_read:D #1 to #2 }
-\cs_new_protected:Npn \ior_gto:NN #1#2
-  { \tex_global:D \tex_read:D #1 to #2 }
-%    \end{macrocode}
-% \end{macro}
+% \subsection{Deprecated functions}
 %
-% \begin{macro}{\ior_str_to:NN, \ior_str_gto:NN}
-%  Reading as strings is also a primitive wrapper.
+% Deprecated on 2012-06-28, for removal by 2012-12-31.
+%
+% \begin{macro}{\iow_wrap:xnnnN}
+%   This was renamed and one unneed argument was removed.
 %    \begin{macrocode}
-\cs_new_protected:Npn \ior_str_to:NN #1#2
-  { \etex_readline:D #1 to #2 }
-\cs_new_protected:Npn \ior_str_gto:NN #1#2
-  { \tex_global:D \etex_readline:D #1 to #2 }
+\cs_new_protected:Npn \iow_wrap:xnnnN #1#2#3#4#5
+  { \iow_wrap:nnnN {#1} {#2} {#4} #5 }
 %    \end{macrocode}
 % \end{macro}
 %
-% \subsection{Experimental functions}
+% Deprecated on 2012-06-24, for removal by 2012-12-31.
 %
-% \begin{macro}{\ior_map_inline:Nn, \ior_str_map_inline:Nn}
-% \begin{macro}[aux]{\ior_str_map_inline_aux:NNn}
-% \begin{macro}[aux]{\ior_str_map_inline_aux:NNNn}
-% \begin{macro}[aux]{\ior_str_map_inline_loop:NNN}
-% \begin{variable}{\l_ior_internal_tl}
-%   Mapping to an input stream can be done on either a token or a string
-%   basis, hence the set up. Within that, there is a check to avoid reading
-%   past the end of a file, hence the two applications of \cs{ior_if_eof:N}.
-%   This mapping cannot be nested as the stream has only one \enquote{current
-%   line}.
+% \begin{variable}{\l_iow_line_length_int}
+%   Simple rename.  Here we copy the \TeX{} register.
 %    \begin{macrocode}
-\cs_new_protected_nopar:Npn \ior_map_inline:Nn
-  { \ior_map_inline_aux:NNn \ior_to:NN }
-\cs_new_protected_nopar:Npn \ior_str_map_inline:Nn
-  { \ior_map_inline_aux:NNn \ior_str_to:NN }
-\cs_new_protected_nopar:Npn \ior_map_inline_aux:NNn
-  {
-    \exp_args:Nc \ior_map_inline_aux:NNNn
-      { ior_map_ \int_use:N \g_prg_map_int :n }
-  }
-\cs_new_protected:Npn \ior_map_inline_aux:NNNn #1#2#3#4
-  {
-    \cs_set:Npn #1 ##1 {#4}
-    \int_gincr:N \g_prg_map_int
-    \ior_if_eof:NF #3 { \ior_map_inline_loop:NNN #1#2#3 }
-    \prg_break_point:n { \int_gdecr:N \g_prg_map_int }
-  }
-\cs_new_protected:Npn \ior_map_inline_loop:NNN #1#2#3
-  {
-    #2 #3 \l_ior_internal_tl
-    \ior_if_eof:NF #3
-      {
-        \exp_args:No #1 \l_ior_internal_tl
-        \ior_map_inline_loop:NNN #1#2#3
-      }
-  }
-\tl_new:N  \l_ior_internal_tl
+\cs_new_eq:NN \l_iow_line_length_int \l_iow_line_count_int
 %    \end{macrocode}
 % \end{variable}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Messages}
 %
+% \begin{macro}{\ior_to:NN, \ior_gto:NN, \ior_str_to:NN, \ior_str_gto:NN}
+%   The local variants are renames, while the global variants are
+%   deprecated and add the \TeX{} primitive \tn{global}.
 %    \begin{macrocode}
-\msg_kernel_new:nnnn { file } { file-not-found }
-  { File~'#1'~not~found. }
-  {
-    The~requested~file~could~not~be~found~in~the~current~directory,~
-    in~the~TeX~search~path~or~in~the~LaTeX~search~path.
-  }
-\msg_kernel_new:nnnn { file } { space-in-file-name }
-  { Space~in~file~name~'#1'. }
-  {
-    Spaces~are~not~permitted~in~files~loaded~by~LaTeX: \\
-    Further~errors~may~follow!
-  }
+\cs_new_eq:NN \ior_to:NN \ior_get:NN
+\cs_new_protected_nopar:Npn \ior_gto:NN { \tex_global:D \ior_to:NN }
+\cs_new_eq:NN \ior_str_to:NN \ior_get_str:NN
+\cs_new_protected_nopar:Npn \ior_str_gto:NN { \tex_global:D \ior_str_to:NN }
 %    \end{macrocode}
-%
-% \subsection{Deprecated functions}
+% \end{macro}
 %
 % Deprecated on 2012-02-10, for removal by 2012-05-31.
 %
 % \begin{macro}{\iow_now_when_avail:Nn, \iow_now_when_avail:Nx}
 % For writing only if the stream requested is open at all.
 %    \begin{macrocode}
+%<*deprecated>
 \cs_new_protected:Npn \iow_now_when_avail:Nn #1
   { \cs_if_free:NTF #1 { \use_none:n } { \iow_now:Nn #1 } }
 \cs_new_protected:Npn \iow_now_when_avail:Nx #1
   { \cs_if_free:NTF #1 { \use_none:n } { \iow_now:Nx #1 } }
+%</deprecated>
 %    \end{macrocode}
 % \end{macro}
 %
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3final.dtx b/Master/texmf-dist/source/latex/l3kernel/l3final.dtx
index c86e9f269db..845d47814d5 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3final.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3final.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3final.dtx 3213 2012-01-20 11:03:46Z joseph $
+\GetIdInfo$Id: l3final.dtx 3986 2012-07-15 19:23:51Z joseph $
   {L3 Experimental format finalisation}
 %</driver|package>
 %<*driver>
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-assign.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-assign.dtx
new file mode 100644
index 00000000000..981e642653b
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-assign.dtx
@@ -0,0 +1,235 @@
+% \iffalse meta-comment
+%%
+%% File: l3fp-assign.dtx Copyright (C) 2011-2012 The LaTeX3 project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp-assign.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Floating-point assignments}
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{The \textsf{l3fp-assign} package\thanks{This file
+%         has version number \ExplFileVersion, last
+%         revised \ExplFileDate.}\\
+% Floating point expressions}
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+% \date{Released \ExplFileDate}
+% \maketitle
+%
+% \begin{documentation}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3fp-assign} implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+% \subsection{Assigning values}
+%
+% \begin{macro}{\fp_new:N}
+%   Floating point variables are initialized to be $+0$.
+%    \begin{macrocode}
+\cs_new_protected:Npn \fp_new:N #1
+  { \cs_new_eq:NN #1 \c_zero_fp }
+\cs_generate_variant:Nn \fp_new:N {c}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}
+%   {
+%     \fp_set:Nn, \fp_set:cn,
+%     \fp_gset:Nn, \fp_gset:cn,
+%     \fp_const:Nn, \fp_const:cn
+%   }
+%   Simply use \cs{@@_parse:n} within various \texttt{x}-expanding
+%   assignments.
+%    \begin{macrocode}
+\cs_new_protected:Npn \fp_set:Nn   #1#2
+  { \tl_set:Nx #1 { \@@_parse:n {#2} } }
+\cs_new_protected:Npn \fp_gset:Nn  #1#2
+  { \tl_gset:Nx #1 { \@@_parse:n {#2} } }
+\cs_new_protected:Npn \fp_const:Nn #1#2
+  { \tl_const:Nx #1 { \@@_parse:n {#2} } }
+\cs_generate_variant:Nn \fp_set:Nn {c}
+\cs_generate_variant:Nn \fp_gset:Nn {c}
+\cs_generate_variant:Nn \fp_const:Nn {c}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}
+%   {
+%     \fp_set_eq:NN , \fp_set_eq:cN , \fp_set_eq:Nc , \fp_set_eq:cc,
+%     \fp_gset_eq:NN, \fp_gset_eq:cN, \fp_gset_eq:Nc, \fp_gset_eq:cc
+%   }
+%   Copying a floating point is the same as copying the underlying token
+%   list.
+%    \begin{macrocode}
+\cs_new_eq:NN \fp_set_eq:NN  \tl_set_eq:NN
+\cs_new_eq:NN \fp_gset_eq:NN \tl_gset_eq:NN
+\cs_generate_variant:Nn \fp_set_eq:NN  { c , Nc , cc }
+\cs_generate_variant:Nn \fp_gset_eq:NN { c , Nc , cc }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\fp_zero:N, \fp_zero:c, \fp_gzero:N, \fp_gzero:c}
+%   Setting a floating point to zero: copy \cs{c_zero_fp}.
+%    \begin{macrocode}
+\cs_new_protected:Npn \fp_zero:N #1 { \fp_set_eq:NN #1 \c_zero_fp }
+\cs_new_protected:Npn \fp_gzero:N #1 { \fp_gset_eq:NN #1 \c_zero_fp }
+\cs_generate_variant:Nn \fp_zero:N  { c }
+\cs_generate_variant:Nn \fp_gzero:N { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}
+%   {\fp_zero_new:N, \fp_zero_new:c, \fp_gzero_new:N, \fp_gzero_new:c}
+%   Set the floating point to zero, or define it if needed.
+%    \begin{macrocode}
+\cs_new_protected:Npn \fp_zero_new:N #1
+  { \fp_if_exist:NTF #1 { \fp_zero:N #1 } { \fp_new:N #1 } }
+\cs_new_protected:Npn \fp_gzero_new:N #1
+  { \fp_if_exist:NTF #1 { \fp_gzero:N #1 } { \fp_new:N #1 } }
+\cs_generate_variant:Nn \fp_zero_new:N  { c }
+\cs_generate_variant:Nn \fp_gzero_new:N { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Updating values}
+%
+% These match the equivalent functions in \pkg{l3int} and \pkg{l3skip}.
+%
+% \begin{macro}
+%   {
+%     \fp_add:Nn, \fp_add:cn, \fp_gadd:Nn, \fp_gadd:cn,
+%     \fp_sub:Nn, \fp_sub:cn, \fp_gsub:Nn, \fp_gsub:cn,
+%   }
+% \begin{macro}[aux]{\@@_add:NNNn}
+%   The auxiliary's arguments are 1: the assignment function, 2: the
+%   operation, 3: the fp variable, 4: the second operand.  The
+%   parentheses around the second operand are needed because |+| and |-|
+%   are not the operations with the lowest priority.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_add:Nn  { \@@_add:NNNn \fp_set:Nn  + }
+\cs_new_protected_nopar:Npn \fp_gadd:Nn { \@@_add:NNNn \fp_gset:Nn + }
+\cs_new_protected_nopar:Npn \fp_sub:Nn  { \@@_add:NNNn \fp_set:Nn  - }
+\cs_new_protected_nopar:Npn \fp_gsub:Nn { \@@_add:NNNn \fp_gset:Nn - }
+\cs_new_protected:Npn \@@_add:NNNn #1#2#3#4 { #1 #3 { #3 #2 (#4) } }
+\cs_generate_variant:Nn \fp_add:Nn  { c }
+\cs_generate_variant:Nn \fp_gadd:Nn { c }
+\cs_generate_variant:Nn \fp_sub:Nn  { c }
+\cs_generate_variant:Nn \fp_gsub:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Showing values}
+%
+% \begin{macro}{\fp_show:N, \fp_show:c, \fp_show:n}
+%   This shows the result of computing its argument.  The
+%   \cs{__msg_show_variable:x} auxiliary expects its input in a slightly odd
+%   form, starting with |>|, and displays the rest.
+%    \begin{macrocode}
+\cs_new_protected:Npn \fp_show:N #1
+  { \__msg_show_variable:x { > \fp_to_tl:N #1 } }
+\cs_new_protected:Npn \fp_show:n #1
+  { \__msg_show_variable:x { > \fp_to_tl:n {#1} } }
+\cs_generate_variant:Nn \fp_show:N { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Some useful constants and scratch variables}
+%
+% \begin{variable}{\c_one_fp, \c_e_fp}
+%   Some constants.
+%    \begin{macrocode}
+\fp_const:Nn \c_e_fp          { 2.718 2818 2845 9045 }
+\fp_const:Nn \c_one_fp        { 1 }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\c_pi_fp, \c_one_degree_fp}
+%   We do not round $\pi$ to the closest multiple of $10^{-15}$, which
+%   would underestimate it by roughly $2.4\cdot 10^{-16}$, but instead
+%   round it up to the next nearest multiple, which is an overestimate
+%   by roughly $7.7\cdot 10^{-16}$.  This particular choice of rounding
+%   has very nice properties: it is exactly divisible by $4$ and by
+%   $180$ as a $16$-digit precision floating point number, hence
+%   ensuring that $\sin(180\mathrm{deg}) = \sin(\pi) = 0$ exactly, with
+%   no rounding artifact.
+%    \begin{macrocode}
+\fp_const:Nn \c_pi_fp         { 3.141 5926 5358 9794 }
+\fp_const:Nn \c_one_degree_fp { 0.0 1745 3292 5199 4330 }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_tmpa_fp, \l_tmpb_fp, \g_tmpa_fp, \g_tmpb_fp}
+%   Scratch variables are simply initialized there.
+%    \begin{macrocode}
+\fp_new:N \l_tmpa_fp
+\fp_new:N \l_tmpb_fp
+\fp_new:N \g_tmpa_fp
+\fp_new:N \g_tmpb_fp
+%    \end{macrocode}
+% \end{variable}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintChanges
+%
+% \PrintIndex
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-aux.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-aux.dtx
new file mode 100644
index 00000000000..566eec13ec5
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-aux.dtx
@@ -0,0 +1,850 @@
+% \iffalse meta-comment
+%
+%% File: l3fp-aux.dtx Copyright(C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp-aux.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Floating-point support functions}
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{^^A
+%   The \textsf{l3fp-aux} package\\ Support for floating points^^A
+%   \thanks{This file describes v\ExplFileVersion,
+%     last revised \ExplFileDate.}^^A
+% }
+%
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+%
+% \date{Released \ExplFileDate}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3fp-aux} implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+% \subsection{Using arguments and semicolons}
+%
+% \begin{macro}[int, EXP]{\@@_use_none_stop_f:n}
+%   This function removes an argument (typically a digit) and replaces
+%   it by \cs{exp_stop_f:}, a marker which stops \texttt{f}-type
+%   expansion.
+%    \begin{macrocode}
+\cs_new:Npn \@@_use_none_stop_f:n #1 { \exp_stop_f: }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_use_s:n, \@@_use_s:nn}
+%   Those functions place a semicolon after one or two arguments
+%   (typically digits).
+%    \begin{macrocode}
+\cs_new:Npn \@@_use_s:n #1 { #1; }
+\cs_new:Npn \@@_use_s:nn #1#2 { #1#2; }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]
+%   {\@@_use_none_until_s:w, \@@_use_i_until_s:nw, \@@_use_ii_until_s:nnw}
+%   Those functions select specific arguments among a set of arguments
+%   delimited by a semicolon.
+%    \begin{macrocode}
+\cs_new:Npn \@@_use_none_until_s:w #1; { }
+\cs_new:Npn \@@_use_i_until_s:nw #1#2; {#1}
+\cs_new:Npn \@@_use_ii_until_s:nnw #1#2#3; {#2}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_reverse_args:Nww}
+%   Many internal functions take arguments delimited by semicolons, and
+%   it is occasionally useful to swap two such arguments.
+%    \begin{macrocode}
+\cs_new:Npn \@@_reverse_args:Nww #1 #2; #3; { #1 #3; #2; }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Constants, and structure of floating points}
+%
+% \begin{macro}[int]{\s_@@, \@@_chk:w}
+%   Floating points numbers all start with \cs{s_@@} \cs{@@_chk:w},
+%   where \cs{s_@@} is equal to the \TeX{} primitive \tn{relax}, and
+%   \cs{@@_chk:w} is protected.  The rest of the floating point number
+%   is made of characters (or \tn{relax}).  This ensures that nothing
+%   expands under \texttt{f}-expansion, nor under \texttt{x}-expansion.
+%   However, when typeset, \cs{s_@@} does nothing, and \cs{@@_chk:w} is
+%   expanded.  We define \cs{@@_chk:w} to produce an error.
+%    \begin{macrocode}
+\__scan_new:N \s_@@
+\cs_new_protected:Npn \@@_chk:w #1 ;
+  {
+    \__msg_kernel_error:nnx { kernel } { misused-fp }
+      { \@@_to_tl:w \s_@@ \@@_chk:w #1 ; }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int]{\s_@@_mark, \s_@@_stop}
+%   Aliases of \cs{tex_relax:D}, used to terminate expressions.
+%    \begin{macrocode}
+\__scan_new:N \s_@@_mark
+\__scan_new:N \s_@@_stop
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int]
+%   {
+%     \s_@@_invalid, \s_@@_underflow, \s_@@_overflow,
+%     \s_@@_division, \s_@@_exact
+%   }
+%   A couple of scan marks used to indicate where special floating point
+%   numbers come from.
+%    \begin{macrocode}
+\__scan_new:N \s_@@_invalid
+\__scan_new:N \s_@@_underflow
+\__scan_new:N \s_@@_overflow
+\__scan_new:N \s_@@_division
+\__scan_new:N \s_@@_exact
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{variable}
+%   {\c_zero_fp, \c_minus_zero_fp, \c_inf_fp, \c_minus_inf_fp, \c_nan_fp}
+%   The special floating points. All of them have the form
+%   \begin{quote}
+%     \cs{s_@@} \cs{@@_chk:w} \meta{case} \meta{sign} \cs{s_@@_...} |;|
+%   \end{quote}
+%   where the dots in \cs{s_@@_...} are one of \texttt{invalid},
+%   \texttt{underflow}, \texttt{overflow}, \texttt{division},
+%   \texttt{exact}, describing how the floating point was created.  We
+%   define the floating points here as \enquote{exact}.
+%    \begin{macrocode}
+\tl_const:Nn \c_zero_fp       { \s_@@ \@@_chk:w 0 0 \s_@@_exact ; }
+\tl_const:Nn \c_minus_zero_fp { \s_@@ \@@_chk:w 0 2 \s_@@_exact ; }
+\tl_const:Nn \c_inf_fp        { \s_@@ \@@_chk:w 2 0 \s_@@_exact ; }
+\tl_const:Nn \c_minus_inf_fp  { \s_@@ \@@_chk:w 2 2 \s_@@_exact ; }
+\tl_const:Nn \c_nan_fp        { \s_@@ \@@_chk:w 3 1 \s_@@_exact ; }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\c_@@_max_exponent_int}
+%   Normal floating point numbers have an exponent at most
+%   \texttt{max_exponent} in absolute value.  Larger numbers are rounded
+%   to $\pm\infty$.  Smaller numbers are subnormal (not implemented yet),
+%   and digits beyond
+%   $10^{-\text{\texttt{max_exponent}}}$ are rounded away, hence the
+%   true minimum exponent is $-\text{\texttt{max_exponent}}-16$;
+%   beyond this, numbers are rounded to zero.  Why this choice of
+%   limits?  When computing $(a\cdot 10^n)^(b\cdot 10^p)$, we need to
+%   evaluate $\log(a\cdot 10^n) = \log(a) + n \log(10)$ as a fixed point
+%   number, which we manipulate as blocks of $4$ digits.  Multiplying
+%   such a fixed point number by $n<10000$ is much cheaper than larger
+%   $n$, because we can multiply $n$ with each block safely.
+%    \begin{macrocode}
+\int_const:Nn \c_@@_max_exponent_int { 10000 }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}[int, EXP]{\@@_zero_fp:N, \@@_inf_fp:N}
+%   In case of overflow or underflow, we have to output
+%   a zero or infinity with a given sign.
+%    \begin{macrocode}
+\cs_new:Npn \@@_zero_fp:N #1 { \s_@@ \@@_chk:w 0 #1 \s_@@_underflow ; }
+\cs_new:Npn \@@_inf_fp:N #1  { \s_@@ \@@_chk:w 2 #1 \s_@@_overflow ; }
+%    \end{macrocode}
+% \end{macro}
+%
+%^^A todo: currently unused.
+% \begin{macro}[int, EXP]{\@@_max_fp:N, \@@_min_fp:N}
+%   In some cases, we need to output the smallest or biggest positive or
+%   negative finite numbers.
+%    \begin{macrocode}
+\cs_new:Npn \@@_min_fp:N #1
+  {
+    \s_@@ \@@_chk:w 1 #1
+      { \int_eval:n { - \c_@@_max_exponent_int } }
+      {1000} {0000} {0000} {0000} ;
+  }
+\cs_new:Npn \@@_max_fp:N #1
+  {
+    \s_@@ \@@_chk:w 1 #1
+      { \int_use:N \c_@@_max_exponent_int }
+      {9999} {9999} {9999} {9999} ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_exponent:w}
+%   For normal numbers, the function expands to the exponent, otherwise
+%   to $0$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_exponent:w \s_@@ \@@_chk:w #1
+  {
+    \if_meaning:w 1 #1
+      \exp_after:wN \@@_use_ii_until_s:nnw
+    \else:
+      \exp_after:wN \@@_use_i_until_s:nw
+      \exp_after:wN 0
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Overflow, underflow, and exact zero}
+%
+%^^A todo: the sign of exact zeros should depend on the rounding mode.
+%
+% \begin{macro}[int, EXP]{\@@_sanitize:Nw, \@@_sanitize:wN}
+% \begin{macro}[aux, EXP]{\@@_sanitize_zero:w}
+%   Expects the sign and the exponent in some order, then the
+%   significand (which we don't touch).  Outputs the corresponding
+%   floating point number, possibly underflowed to $\pm 0$ or overflowed
+%   to $\pm\infty$.  The functions \cs{@@_underflow:w} and
+%   \cs{@@_overflow:w} are defined in \pkg{l3fp-traps}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_sanitize:Nw #1 #2;
+  {
+    \if_case:w \if_int_compare:w #2 > \c_@@_max_exponent_int \c_one \else:
+               \if_int_compare:w #2 < - \c_@@_max_exponent_int \c_two \else:
+               \if_meaning:w 1 #1 \c_three \else: \c_zero \fi: \fi: \fi:
+    \or: \exp_after:wN \@@_overflow:w
+    \or: \exp_after:wN \@@_underflow:w
+    \or: \exp_after:wN \@@_sanitize_zero:w
+    \fi:
+    \s_@@ \@@_chk:w 1 #1 {#2}
+  }
+\cs_new:Npn \@@_sanitize:wN #1; #2 { \@@_sanitize:Nw #2 #1; }
+\cs_new:Npn \@@_sanitize_zero:w \s_@@ \@@_chk:w #1 #2 #3; { \c_zero_fp }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Expanding after a floating point number}
+%
+% \begin{macro}[int, EXP]{\@@_exp_after_o:w}
+% \begin{macro}[int, EXP]{\@@_exp_after_o:nw, \@@_exp_after_f:nw}
+%   \begin{syntax}
+%     \cs{@@_exp_after_o:nw} \Arg{tokens} \meta{floating point} \meta{more tokens}
+%   \end{syntax}
+%   Places \meta{tokens} (empty in the case of \cs{@@_exp_after_o:w})
+%   between the \meta{floating point} and the \meta{more tokens}, then
+%   hits those tokens with either \texttt{o}-expansion (one
+%   \cs{exp_after:wN}) or \texttt{f}-expansion, and leaves the floating
+%   point number unchanged.
+%
+%   We first distinguish normal floating points, which have a mantissa,
+%   from the much simpler special floating points.
+%    \begin{macrocode}
+\cs_new:Npn \@@_exp_after_o:w \s_@@ \@@_chk:w #1
+  {
+    \if_meaning:w 1 #1
+      \exp_after:wN \@@_exp_after_normal:nNNw
+    \else:
+      \exp_after:wN \@@_exp_after_special:nNNw
+    \fi:
+    { }
+    #1
+  }
+\cs_new:Npn \@@_exp_after_o:nw #1 \s_@@ \@@_chk:w #2
+  {
+    \if_meaning:w 1 #2
+      \exp_after:wN \@@_exp_after_normal:nNNw
+    \else:
+      \exp_after:wN \@@_exp_after_special:nNNw
+    \fi:
+    { #1 }
+    #2
+  }
+\cs_new:Npn \@@_exp_after_f:nw #1 \s_@@ \@@_chk:w #2
+  {
+    \if_meaning:w 1 #2
+      \exp_after:wN \@@_exp_after_normal:nNNw
+    \else:
+      \exp_after:wN \@@_exp_after_special:nNNw
+    \fi:
+    { \tex_romannumeral:D -`0 #1 }
+    #2
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_exp_after_special:nNNw}
+%   \begin{syntax}
+%     \cs{@@_exp_after_special:nNNw} \Arg{after} \meta{case} \meta{sign} \meta{scan mark} |;|
+%   \end{syntax}
+%   Special floating point numbers are easy to jump over since they
+%   contain few tokens.
+%    \begin{macrocode}
+\cs_new:Npn \@@_exp_after_special:nNNw #1#2#3#4;
+  {
+    \exp_after:wN \s_@@
+    \exp_after:wN \@@_chk:w
+    \exp_after:wN #2
+    \exp_after:wN #3
+    \exp_after:wN #4
+    \exp_after:wN ;
+    #1
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_exp_after_normal:nNNw}
+%   For normal floating point numbers, life is slightly harder, since we
+%   have many tokens to jump over.  Here it would be slightly better if
+%   the digits were not braced but instead were delimited arguments (for
+%   instance delimited by |,|).  That may be changed some day.
+%    \begin{macrocode}
+\cs_new:Npn \@@_exp_after_normal:nNNw #1 1 #2 #3 #4#5#6#7;
+  {
+    \exp_after:wN \@@_exp_after_normal:Nwwwww
+    \exp_after:wN #2
+    \__int_value:w #3   \exp_after:wN ;
+    \__int_value:w 1 #4 \exp_after:wN ;
+    \__int_value:w 1 #5 \exp_after:wN ;
+    \__int_value:w 1 #6 \exp_after:wN ;
+    \__int_value:w 1 #7 \exp_after:wN ; #1
+  }
+\cs_new:Npn \@@_exp_after_normal:Nwwwww
+    #1 #2; 1 #3 ; 1 #4 ; 1 #5 ; 1 #6 ;
+  { \s_@@ \@@_chk:w 1 #1 {#2} {#3} {#4} {#5} {#6} ; }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Packing digits}
+%
+% When a positive integer |#1| is known to be less than $10^8$, the
+% following trick will split it into two blocks of $4$ digits, padding
+% with zeros on the left.
+% \begin{verbatim}
+%   \cs_new:Npn \pack:NNNNNw #1 #2#3#4#5 #6; { {#2#3#4#5} {#6} }
+%   \exp_after:wN \pack:NNNNNw
+%     \int_use:N \__int_eval:w 1 0000 0000 + #1 ;
+% \end{verbatim}
+% The idea is that adding $10^8$ to the number ensures that it has
+% exactly $9$ digits, and can then easily find which digits correspond
+% to what position in the number. Of course, this can be modified
+% for any number of digits less or equal to~$9$ (we are limited by
+% \TeX{}'s integers). This method is very heavily relied upon in
+% \texttt{l3fp-basics}.
+%
+% More specifically, the auxiliary inserts |+ #1#2#3#4#5 ; {#6}|, which
+% allows us to compute several blocks of $4$ digits in a nested manner,
+% performing carries on the fly.  Say we want to compute $1\,2345 \times
+% 6677\,8899$.  With simplified names, we would do
+% \begin{verbatim}
+%   \exp_after:wN \post_processing:w
+%   \int_use:N \__int_eval:w - 5 0000
+%     \exp_after:wN \pack:NNNNNw
+%     \int_use:N \__int_eval:w 4 9995 0000
+%       + 12345 * 6677
+%       \exp_after:wN \pack:NNNNNw
+%       \int_use:N \__int_eval:w 5 0000 0000
+%         + 12345 * 8899 ;
+% \end{verbatim}
+% The \cs{exp_after:wN} triggers |\int_use:N \__int_eval:w|, which
+% starts a first computation, whose initial value is $- 5\,0000$ (the
+% \enquote{leading shift}).  In that computation appears an
+% \cs{exp_after:wN}, which triggers the nested computation
+% |\int_use:N \__int_eval:w| with starting value $4\,9995\,0000$ (the
+% \enquote{middle shift}).  That, in turn, expands \cs{exp_after:wN}
+% which triggers the third computation.  The third computation's value
+% is $5\,0000\,0000 + 12345 \times 8899$, which has $9$ digits. Adding
+% $5\cdot 10^{8}$ to the product allowed us to know how many digits to
+% expect as long as the numbers to multiply are not too big; it will
+% also work to some extent with negative results.  The \texttt{pack}
+% function puts the last $4$ of those $9$ digits into a brace group,
+% moves the semi-colon delimiter, and inserts a |+|, which combines the
+% carry with the previous computation.  The shifts nicely combine into
+% $5\,0000\,0000 / 10^{4} + 4\,9995\,0000 = 5\,0000\,0000$.  As long as
+% the operands are in some range, the result of this second computation
+% will have $9$ digits.  The corresponding \texttt{pack} function,
+% expanded after the result is computed, braces the last $4$ digits, and
+% leaves |+| \meta{5 digits} for the initial computation.  The
+% \enquote{leading shift} cancels the combination of the other shifts,
+% and the |\post_processing:w| takes care of packing the last few
+% digits.
+%
+% Admittedly, this is quite intricate.  It is probably the key in making
+% \pkg{l3fp} as fast as other pure \TeX{} floating point units despite
+% its increased precision.  In fact, this is used so much that we
+% provide different sets of packing functions and shifts, depending on
+% ranges of input.
+%
+% \begin{macro}[int, EXP]{\@@_pack:NNNNNw}
+% \begin{variable}
+%   {
+%     \c_@@_trailing_shift_int ,
+%     \c_@@_middle_shift_int   ,
+%     \c_@@_leading_shift_int  ,
+%   }
+%   This set of shifts allows for computations involving results in the
+%   range $[-4\cdot 10^{8}, 5\cdot 10^{8}-1]$.  Shifted values all have
+%   exactly $9$ digits.
+%    \begin{macrocode}
+\int_const:Nn \c_@@_leading_shift_int  { - 5 0000 }
+\int_const:Nn \c_@@_middle_shift_int   { 5 0000 *  9999 }
+\int_const:Nn \c_@@_trailing_shift_int { 5 0000 * 10000 }
+\cs_new:Npn \@@_pack:NNNNNw #1 #2#3#4#5 #6; { + #1#2#3#4#5 ; {#6} }
+%    \end{macrocode}
+% \end{variable}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_pack_big:NNNNNNw}
+% \begin{variable}
+%   {
+%     \c_@@_big_trailing_shift_int ,
+%     \c_@@_big_middle_shift_int   ,
+%     \c_@@_big_leading_shift_int  ,
+%   }
+%   This set of shifts allows for computations involving results in the
+%   range $[-5\cdot 10^{8}, 6\cdot 10^{8}-1]$ (actually a bit more).
+%   Shifted values all have exactly $10$ digits.  Note that the upper
+%   bound is due to \TeX{}'s limit of $2^{31}-1$ on integers.  The
+%   shifts are chosen to be roughly the mid-point of $10^{9}$ and
+%   $2^{31}$, the two bounds on $10$-digit integers in \TeX{}.
+%    \begin{macrocode}
+\int_const:Nn \c_@@_big_leading_shift_int  { - 15 2374 }
+\int_const:Nn \c_@@_big_middle_shift_int   { 15 2374 *  9999 }
+\int_const:Nn \c_@@_big_trailing_shift_int { 15 2374 * 10000 }
+\cs_new:Npn \@@_pack_big:NNNNNNw #1#2 #3#4#5#6 #7;
+  { + #1#2#3#4#5#6 ; {#7} }
+%    \end{macrocode}
+% \end{variable}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_pack_twice_four:wNNNNNNNN}
+%   \begin{syntax}
+%     \cs{@@_pack_twice_four:wNNNNNNNN} \meta{tokens} |;| \meta{$\geq 8$ digits}
+%   \end{syntax}
+%   Grabs two sets of $4$ digits and places them before the semi-colon
+%   delimiter.  Putting several copies of this function before a
+%   semicolon will pack more digits since each will take the digits
+%   packed by the others in its first argument.
+%    \begin{macrocode}
+\cs_new:Npn \@@_pack_twice_four:wNNNNNNNN #1; #2#3#4#5 #6#7#8#9
+  { #1 {#2#3#4#5} {#6#7#8#9} ; }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Decimate (dividing by a power of 10)}
+%
+% ^^A begin[todo]
+% \begin{macro}[int, EXP]{\@@_decimate:nNnnnn}
+%   \begin{syntax}
+%     \cs{@@_decimate:nNnnnn} \Arg{shift} \Arg{f_1}
+%     ~~\Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4}
+%   \end{syntax}
+%   Each \meta{X_i} consists in $4$ digits exactly,
+%   and $1000\leq\meta{X_1}<9999$. The first argument determines
+%   by how much we shift the digits. \meta{f_1} is called as follows:
+%   \begin{syntax}
+%     \meta{f_1} \meta{rounding} \Arg{X'_1} \Arg{X'_2} \meta{extra-digits} |;|
+%   \end{syntax}
+%   where $0\leq\meta{X'_i}<10^{8}-1$ are $8$ digit numbers,
+%   forming the truncation of our number. In other words,
+%   \[
+%   \left(
+%     \sum_{i=1}^{4} \meta{X_i} \cdot 10^{-4i} \cdot 10^{-\meta{shift}}
+%     - \meta{X'_1} \cdot 10^{-8} + \meta{X'_2} \cdot 10^{-16}
+%   \right)
+%   \in [0,10^{-16}).
+%   \]
+%   To round properly later, we need to remember some information
+%   about the difference. The \meta{rounding} digit is $0$ if and
+%   only if the difference is exactly $0$, and $5$ if and only if
+%   the difference is exactly $0.5\cdot 10^{-16}$. Otherwise, it
+%   is the (non-$0$, non-$5$) digit closest to $10^{17}$ times the
+%   difference.  In particular, if the shift is $17$ or more, all
+%   the digits are dropped, \meta{rounding} is $1$ (not $0$), and
+%   \meta{X'_1} \meta{X'_2} are both zero.
+%
+%   If the shift is $1$, the \meta{rounding} digit is simply the
+%   only digit that was pushed out of the brace groups (this is
+%   important for subtraction). It would be more natural for the
+%   \meta{rounding} digit to be placed after the \meta{X_i},
+%   but the choice we make involves less reshuffling.
+%
+%   Note that this function fails for negative \meta{shift}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_decimate:nNnnnn #1
+  {
+    \cs:w
+      @@_decimate_
+      \if_int_compare:w \__int_eval:w #1 > \c_sixteen
+        tiny
+      \else:
+        \tex_romannumeral:D \__int_eval:w #1
+      \fi:
+      :Nnnnn
+    \cs_end:
+  }
+%    \end{macrocode}
+%   Each of the auxiliaries see the function \meta{f_1},
+%   followed by $4$ blocks of $4$ digits.
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_decimate_:Nnnnn, \@@_decimate_tiny:Nnnnn}
+%   If the \meta{shift} is zero, or too big, life is very easy.
+%    \begin{macrocode}
+\cs_new:Npn \@@_decimate_:Nnnnn #1 #2#3#4#5
+  { #1 0 {#2#3} {#4#5} ; }
+\cs_new:Npn \@@_decimate_tiny:Nnnnn #1 #2#3#4#5
+  { #1 1 { 0000 0000 } { 0000 0000 } 0 #2#3#4#5 ; }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_decimate_i:Nnnnn,    \@@_decimate_ii:Nnnnn,
+%     \@@_decimate_iii:Nnnnn,  \@@_decimate_iv:Nnnnn,
+%     \@@_decimate_v:Nnnnn,    \@@_decimate_vi:Nnnnn,
+%     \@@_decimate_vii:Nnnnn,  \@@_decimate_viii:Nnnnn,
+%     \@@_decimate_ix:Nnnnn,   \@@_decimate_x:Nnnnn,
+%     \@@_decimate_xi:Nnnnn,   \@@_decimate_xii:Nnnnn,
+%     \@@_decimate_xiii:Nnnnn, \@@_decimate_xiv:Nnnnn,
+%     \@@_decimate_xv:Nnnnn,   \@@_decimate_xvi:Nnnnn
+%   }
+%   \begin{syntax}
+%     \cs{@@_decimate_i:Nnnnn} \meta{f_1} \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4}
+%   \end{syntax}
+%   Shifting happens in two steps: compute the \meta{rounding} digit,
+%   and repack digits into two blocks of $8$. The sixteen functions
+%   are very similar, and defined through \cs{@@_tmp:w}.
+%   The arguments are as follows: |#1| indicates which function is
+%   being defined; after one step of expansion, |#2| yields the
+%   \enquote{extra digits} which are then converted by
+%   \cs{@@_decimate_round:Nw} to the \meta{rounding} digit.
+%   This triggers the \texttt{f}-expansion of
+%   \cs{@@_decimate_pack:nnnnnnnnnnw},\footnote{No, the argument
+%     spec is not a mistake: the function calls an auxiliary to
+%     do half of the job.} responsible for building two blocks of
+%   $8$ digits, and removing the rest. For this to work, |#3|
+%   alternates between braced and unbraced blocks of $4$ digits,
+%   in such a way that the $5$ first and $5$ next token groups
+%   yield the correct blocks of $8$ digits.
+%    \begin{macrocode}
+\cs_new:Npn \@@_tmp:w #1 #2 #3
+  {
+    \cs_new:cpn { @@_decimate_ #1 :Nnnnn } ##1 ##2##3##4##5
+      {
+        \exp_after:wN ##1
+        \__int_value:w
+          \exp_after:wN \@@_decimate_round:Nw #2 ;
+        \@@_decimate_pack:nnnnnnnnnnw #3 ;
+      }
+  }
+\@@_tmp:w {i}   {\use_none:nnn      #50} {    0{#2}#3{#4}#5                }
+\@@_tmp:w {ii}  {\use_none:nn       #5 } {    00{#2}#3{#4}#5               }
+\@@_tmp:w {iii} {\use_none:n        #5 } {    000{#2}#3{#4}#5              }
+\@@_tmp:w {iv}  {                   #5 } {   {0000}#2{#3}#4 #5             }
+\@@_tmp:w {v}   {\use_none:nnn    #4#5 } {   0{0000}#2{#3}#4 #5            }
+\@@_tmp:w {vi}  {\use_none:nn     #4#5 } {   00{0000}#2{#3}#4 #5           }
+\@@_tmp:w {vii} {\use_none:n      #4#5 } {   000{0000}#2{#3}#4 #5          }
+\@@_tmp:w {viii}{                 #4#5 } {  {0000}0000{#2}#3 #4 #5         }
+\@@_tmp:w {ix}  {\use_none:nnn  #3#4+#5} {  0{0000}0000{#2}#3 #4 #5        }
+\@@_tmp:w {x}   {\use_none:nn   #3#4+#5} {  00{0000}0000{#2}#3 #4 #5       }
+\@@_tmp:w {xi}  {\use_none:n    #3#4+#5} {  000{0000}0000{#2}#3 #4 #5      }
+\@@_tmp:w {xii} {               #3#4+#5} { {0000}0000{0000}#2 #3 #4 #5     }
+\@@_tmp:w {xiii}{\use_none:nnn#2#3+#4#5} { 0{0000}0000{0000}#2 #3 #4 #5    }
+\@@_tmp:w {xiv} {\use_none:nn #2#3+#4#5} { 00{0000}0000{0000}#2 #3 #4 #5   }
+\@@_tmp:w {xv}  {\use_none:n  #2#3+#4#5} { 000{0000}0000{0000}#2 #3 #4 #5  }
+\@@_tmp:w {xvi} {             #2#3+#4#5} {{0000}0000{0000}0000 #2 #3 #4 #5 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP, aux]
+%   {\@@_decimate_round:Nw, \@@_decimate_pack:nnnnnnnnnnw}
+%   \cs{@@_decimate_round:Nw} will receive the \enquote{extra digits}
+%   as its argument, and its expansion is triggered by \cs{__int_value:w}.
+%   If the first digit is neither $0$ nor $5$, then it is the \meta{rounding}
+%   digit.  Otherwise, if the remaining digits are not all zero, we need
+%   to add $1$ to that leading digit to get the rounding digit. Some caution
+%   is required, though, because there may be more than $10$
+%   \enquote{extra digits}, and this may overflow \TeX{}'s integers.
+%   Instead of feeding the digits directly to \cs{@@_decimate_round:Nw},
+%   they come split into several blocks, separated by $+$. Hence the first
+%   \cs{__int_eval:w} here.
+%    \begin{macrocode}
+\cs_new:Npn \@@_decimate_round:Nw #1 #2;
+  {
+    \if_int_odd:w \if_meaning:w 0 #1 \c_one \else:
+                  \if_meaning:w 5 #1 \c_one \else:
+                  \c_zero \fi: \fi:
+      \if_int_compare:w \__int_eval:w #2 > \c_zero
+        \__int_eval:w 1 +
+      \fi:
+    \fi:
+    #1
+  }
+%    \end{macrocode}
+%   The computation of the \meta{rounding} digit leaves an unfinished
+%   \cs{__int_value:w}, which expands the following functions. This
+%   allows us to repack nicely the digits we keep. Those digits come
+%   as an alternation of unbraced and braced blocks of $4$ digits,
+%   such that the first $5$ groups of token consist in $4$ single digits,
+%   and one brace group (in some order), and the next $5$ have the same
+%   structure. This is followed by some digits and a semicolon.
+%    \begin{macrocode}
+\cs_new:Npn \@@_decimate_pack:nnnnnnnnnnw #1#2#3#4#5
+  { \@@_decimate_pack_ii:nnnnnnw { #1#2#3#4#5 } }
+\cs_new:Npn \@@_decimate_pack_ii:nnnnnnw #1 #2#3#4#5#6
+  { {#1} {#2#3#4#5#6} }
+%    \end{macrocode}
+% \end{macro}
+% ^^A end[todo]
+%
+% \subsection{Functions for use within primitive conditional branches}
+%
+% The functions described in this section are not pretty and can easily
+% be misused.  When correctly used, each of them removes one \cs{fi:} as
+% part of its parameter text, and puts one back as part of its
+% replacement text.
+%
+% Many computation functions in \pkg{l3fp} must perform tests on the
+% type of floating points that they receive.  This is often done in an
+% \cs{if_case:w} statement or another conditional statement, and only a
+% few cases lead to actual computations: most of the special cases are
+% treated using a few standard functions which we define now.  A typical
+% use context for those functions would be
+% \begin{syntax}
+%   |\if_case:w| \meta{integer} |\exp_stop_f:|
+%   |     \@@_case_return_o:Nw| \meta{fp var}
+%   |\or: \@@_case_use:nw| \Arg{some computation}
+%   |\or: \@@_case_return_same_o:w|
+%   |\or: \@@_case_return:nw| \Arg{something}
+%   |\fi:|
+%   \meta{junk}
+%   \meta{floating point}
+% \end{syntax}
+% In this example, the case $0$ will return the floating point
+% \meta{fp~var}, expanding once after that floating point.  Case $1$
+% will do \meta{some computation} using the \meta{floating point}
+% (presumably compute the operation requested by the user in that
+% non-trivial case).  Case $2$ will return the \meta{floating point}
+% without modifying it, removing the \meta{junk} and expanding once
+% after.  Case $3$ will close the conditional, remove the \meta{junk}
+% and the \meta{floating point}, and expand \meta{something} next.  In
+% other cases, the \enquote{\meta{junk}} is expanded, performing some
+% other operation on the \meta{floating point}.  We provide similar
+% functions with two trailing \meta{floating points}.
+%
+% \begin{macro}[int, EXP]{\@@_case_use:nw}
+%   This function ends a \TeX{} conditional, removes junk until the next
+%   floating point, and places its first argument before that floating
+%   point, to perform some operation on the floating point.
+%    \begin{macrocode}
+\cs_new:Npn \@@_case_use:nw #1#2 \fi: #3 \s_@@ { \fi: #1 \s_@@ }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_case_return:nw}
+%   This function ends a \TeX{} conditional, removes junk and a floating
+%   point, and places its first argument in the input stream.  A quirk
+%   is that we don't define this function requiring a floating point to
+%   follow, simply anything ending in a semicolon.  This, in turn, means
+%   that the \meta{junk} may not contain semicolons.
+%    \begin{macrocode}
+\cs_new:Npn \@@_case_return:nw #1#2 \fi: #3 ; { \fi: #1 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_case_return_o:Nw}
+%   This function ends a \TeX{} conditional, removes junk and a floating
+%   point, and returns its first argument, a \meta{fp~var}, expanding
+%   once after it.
+%    \begin{macrocode}
+\cs_new:Npn \@@_case_return_o:Nw #1#2 \fi: #3 \s_@@ #4 ;
+  { \fi: \exp_after:wN #1 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_case_return_same_o:w}
+%   This function ends a \TeX{} conditional, removes junk, and returns
+%   the following floating point, expanding once after it.
+%    \begin{macrocode}
+\cs_new:Npn \@@_case_return_same_o:w #1 \fi: #2 \s_@@
+  { \fi: \@@_exp_after_o:w \s_@@ }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_case_return_o:Nww}
+%   Same as \cs{@@_case_return_o:Nw} but with two trailing floating
+%   points.
+%    \begin{macrocode}
+\cs_new:Npn \@@_case_return_o:Nww #1#2 \fi: #3 \s_@@ #4 ; #5 ;
+  { \fi: \exp_after:wN #1 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_case_return_ii_o:ww}
+%   Similar to \cs{@@_case_return_same_o:w}, but this returns the second
+%   of two trailing floating point numbers, expanding once after it.
+%    \begin{macrocode}
+\cs_new:Npn \@@_case_return_ii_o:ww #1 \fi: #2 \s_@@ #3 ;
+  { \fi: \@@_exp_after_o:w }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Small integer floating points}
+%
+% \begin{macro}[int, EXP]{\@@_small_int:wTF}
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_small_int_true:wTF,
+%     \@@_small_int_normal:NnwTF,
+%     \@@_small_int_test:NnnwNTF
+%   }
+%   This function tests if its floating point argument is an integer in
+%   the range $[-99999999,99999999]$.  If it is, the result of the
+%   conversion is fed as a braced argument to the \meta{true code}.
+%   Otherwise, the \meta{false code} is performed.  First filter special
+%   cases: neither \texttt{nan} nor infinities are integers.  Normal
+%   numbers with a non-positive exponent are never integers.  When the
+%   exponent is greater than $8$, the number is too large for the range.
+%   Otherwise, decimate, and test the digits after the decimal
+%   separator.  The \cs{use_iii:nnn} remove a trailing |;| and the true
+%   branch, leaving only the false branch.  The \cs{__int_value:w}
+%   appearing in the case where the normal floating point is an integer
+%   takes care of expanding all the conditionals until the trailing |;|.
+%   That integer is fed to \cs{@@_small_int_true:wTF} which places it as
+%   a braced argument of the true branch.
+%    \begin{macrocode}
+\cs_new:Npn \@@_small_int:wTF \s_@@ \@@_chk:w #1
+  {
+    \if_case:w #1 \exp_stop_f:
+           \@@_case_return:nw { \@@_small_int_true:wTF 0 ; }
+    \or:   \exp_after:wN \@@_small_int_normal:NnwTF
+    \else: \@@_case_return:nw \use_ii:nn
+    \fi:
+  }
+\cs_new:Npn \@@_small_int_true:wTF #1; #2#3 { #2 {#1} }
+\cs_new:Npn \@@_small_int_normal:NnwTF #1#2#3;
+  {
+    \if_int_compare:w #2 > \c_zero
+      \if_int_compare:w #2 > \c_eight
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \use_iii:nnn
+      \else:
+        \@@_decimate:nNnnnn { \c_sixteen - #2 }
+          \@@_small_int_test:NnnwNTF
+          #3 #1
+      \fi:
+    \else:
+      \exp_after:wN \use_iii:nnn
+    \fi:
+    ;
+  }
+\cs_new:Npn \@@_small_int_test:NnnwNTF #1#2#3#4; #5
+  {
+    \if_meaning:w 0 #1
+      \exp_after:wN \@@_small_int_true:wTF
+      \__int_value:w \if_meaning:w 2 #5 - \fi: #3
+    \else:
+      \exp_after:wN \use_iii:nnn
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Length of a floating point array}
+%
+% \begin{macro}[int, EXP]{\@@_array_count:w}
+% \begin{macro}[aux, EXP]{\@@_array_count_loop:Nw}
+%   Count the number of items in an array of floating points.  The
+%   technique is very similar to \cs{tl_count:n}, but with the loop
+%   built-in.  Checking for the end of the loop is done with the
+%   |\use_none:n #1| construction.
+%    \begin{macrocode}
+\cs_new:Npn \@@_array_count:w #1 @
+  {
+    \int_use:N \__int_eval:w \c_zero
+      \@@_array_count_loop:Nw #1 { ? \__prg_break: } ;
+      \__prg_break_point:
+    \__int_eval_end:
+  }
+\cs_new:Npn \@@_array_count_loop:Nw #1#2;
+  { \use_none:n #1 + \c_one \@@_array_count_loop:Nw }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Messages}
+%
+% Using a floating point directly is an error.
+%    \begin{macrocode}
+\__msg_kernel_new:nnnn { kernel } { misused-fp }
+  { A~floating~point~with~value~'#1'~was~misused. }
+  {
+    To~obtain~the~value~of~a~floating~point~variable,~use~
+    '\token_to_str:N \fp_to_decimal:N',~
+    '\token_to_str:N \fp_to_scientific:N',~or~other~
+    conversion~functions.
+  }
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintChanges
+%
+% \PrintIndex
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx
new file mode 100644
index 00000000000..0b06d377232
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx
@@ -0,0 +1,1634 @@
+% \iffalse meta-comment
+%
+%% File: l3fp-basics.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp-basics.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Floating-point arithmetic}
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{The \textsf{l3fp-basics} package\thanks{This file
+%         has version number \ExplFileVersion, last
+%         revised \ExplFileDate.}\\
+% Floating point arithmetic}
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+% \date{Released \ExplFileDate}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3fp-basics} Implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+% All operations implemented in this module yield the outcome of
+% rounding the infinitely precise result of the operation to the
+% nearest representable number.
+%
+% ^^A begin[todo]: move
+% \section{Internal storage of floating points numbers}
+%
+% A floating point number \meta{X} is stored as
+% \begin{quote}
+%   \cs{s_@@} \cs{@@_chk:w} \meta{case} \meta{sign} \meta{body} |;|
+% \end{quote}
+% Here, \meta{case} is 0 for $\pm 0$, 1 for normal numbers, 2 for $\pm
+% \infty$, and 3 for \texttt{nan}, and \meta{sign} is $0$ for positive
+% numbers, $1$ for \texttt{nan}s, and $2$ for negative numbers. The
+% \meta{body} of normal numbers is \Arg{exponent} \Arg{X_1} \Arg{X_2}
+% \Arg{X_3} \Arg{X_4}, with
+% \[
+% \meta{X} = (-1)^{\meta{sign}} 10^{-\meta{exponent}} \sum_i
+% \meta{X_i} 10^{-4i}.
+% \]
+% Calculations are done in base $10000$, \emph{i.e.} one myriad.  The
+% \meta{exponent} lies between $\pm\cs{c_@@_max_exponent_int} = \pm
+% \the\csname\detokenize{c__fp_max_exponent_int}\endcsname$ inclusive.
+%
+% Additionally, positive and negative floating point numbers may only be
+% stored with $1000\leq\meta{X_1}<10000$. This requirement is necessary
+% in order to preserve accuracy and speed.
+%
+% ^^A end[todo]
+%
+% ^^A begin[todo]
+%
+% Some algorithms used below end up being quite similar to some
+% described in \enquote{What Every Computer Scientist Should Know About
+%   Floating Point Arithmetic}, by David Goldberg, which can be found at
+% \texttt{http://cr.yp.to/2005-590/goldberg.pdf}. I need to compare them
+% very carefully.
+%
+% ^^A end[todo]
+%
+%^^A todo sanitize, pack.
+%
+% \subsection{Common to several operations}
+%
+% \begin{macro}[EXP]
+%   {
+%     \@@_basics_pack_low:NNNNNw  ,
+%     \@@_basics_pack_high:NNNNNw ,
+%     \@@_basics_pack_high_carry:w
+%   }
+%   Addition and multiplication of mantissas are done in two steps:
+%   first compute a (more or less) exact result,
+%   then round and pack digits in the final (braced) form.
+%   These functions take care of the packing, with special attention
+%   given to the case where rounding has caused a carry.
+%   In \cs{@@_basics_pack_high_carry:w}, |#1| should
+%   always be $0000$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_basics_pack_low:NNNNNw #1 #2#3#4#5 #6;
+  {
+    \if_meaning:w 2 #1
+      + \c_one
+    \fi:
+    ; {#2#3#4#5} {#6} ;
+  }
+\cs_new:Npn \@@_basics_pack_high:NNNNNw #1 #2#3#4#5 #6;
+  {
+    \if_meaning:w 2 #1
+      \@@_basics_pack_high_carry:w
+    \fi:
+    ; {#2#3#4#5} {#6}
+  }
+\cs_new:Npn \@@_basics_pack_high_carry:w \fi: ; #1
+  { \fi: + \c_one ; {1000} }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}
+%   {
+%     \@@_basics_return_nan_nan:NNww ,
+%     \@@_basics_return_zero:NNww    ,
+%     \@@_basics_return_inf:NNww     ,
+%     \@@_basics_return_i:NNNNww     ,
+%     \@@_basics_return_ii:NNNNww    ,
+%     \@@_basics_return_nan:NNNNww
+%   }
+%   \begin{syntax}
+%     \cs{@@_basics_return_...:NNww}
+%     ~~\meta{sign_1} \meta{sign_2} \meta{body_1} |;| \meta{body_2} |;|
+%   \end{syntax}
+%   Used for binary operations, to return a value for some special
+%   cases (common to several operations). All functions expand once
+%   after their arguments.
+%
+%   ^^A todo: redoc, changed.
+%   The \texttt{nan_nan} function combines the \texttt{info} fields
+%   of the two \texttt{nan}.\footnote{Bruno: check that messages are
+%     kept.}
+%   The \texttt{zero} and \texttt{inf} functions return $\pm 0$ or
+%   $\pm\infty$ with a sign equal to the product of the two signs:
+%   three \cs{exp_after:wN} are needed to escape out of the
+%   conditional, and expand once after.
+%   The \texttt{i} and \texttt{ii} functions return one of their
+%   operands and expand after using \cs{@@_exp_after_o:w}.
+%   In some cases, this could be optimized, since we know in advance
+%   what case of number we have. However, it seems better to keep the
+%   number of control sequences low: these functions are called only
+%   in special cases anyways, so performance is not an issue.
+%    \begin{macrocode}
+\cs_new:Npn \@@_basics_return_nan_nan:NNww #1#2 #3; #4;
+  { \@@_exp_after_o:w \s_@@ \@@_chk:w 3 1 #3 ; }
+\cs_new:Npn \@@_basics_return_zero:NNww #1#2 #3; #4;
+  {
+    \if_meaning:w #1 #2
+      \exp_after:wN \exp_after:wN \exp_after:wN \c_zero_fp
+    \else:
+      \exp_after:wN \exp_after:wN \exp_after:wN \c_minus_zero_fp
+    \fi:
+  }
+\cs_new:Npn \@@_basics_return_inf:NNww #1#2 #3; #4;
+  {
+    \if_meaning:w #1 #2
+      \exp_after:wN \exp_after:wN \exp_after:wN \c_inf_fp
+    \else:
+      \exp_after:wN \exp_after:wN \exp_after:wN \c_minus_inf_fp
+    \fi:
+  }
+\cs_new:Npn \@@_basics_return_i:NNNNww #1#2 #3#4 #5; #6;
+  { \@@_exp_after_o:w \s_@@ \@@_chk:w #1 #3 #5; }
+\cs_new:Npn \@@_basics_return_ii:NNNNww #1#2 #3#4 #5; #6;
+  { \@@_exp_after_o:w \s_@@ \@@_chk:w #2 #4 #6; }
+\cs_new:Npn \@@_basics_return_nan:NNww #1#2
+  {
+    \if_meaning:w 1 #1
+      \exp_after:wN \@@_basics_return_i:NNNNww
+    \else:
+      \exp_after:wN \@@_basics_return_ii:NNNNww
+    \fi:
+    3 3 #1 #2
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Addition and subtraction}
+%
+% \begin{macro}[int, EXP]{\@@_+_o:ww}
+%   For addition, everything is easy.  No need to grab the
+%   \meta{body_2}.
+%    \begin{macrocode}
+\cs_new:cpn { @@_+_o:ww }
+    \s_@@ \@@_chk:w #1 #2 #3 ; \s_@@ \@@_chk:w #4 #5
+  { \@@_add_cases:NN #1 #4 #2 #5 #3 ; }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_-_o:ww}
+%   Change the sign of the second argument.
+%    \begin{macrocode}
+\cs_new:cpn { @@_-_o:ww }
+    \s_@@ \@@_chk:w #1 #2 #3 ; \s_@@ \@@_chk:w #4 #5
+  {
+    \exp_after:wN \@@_add_cases:NN
+    \exp_after:wN #1
+    \exp_after:wN #4
+    \exp_after:wN #2
+    \int_use:N \__int_eval:w \c_two - #5 \__int_eval_end:
+    #3 ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Sign, exponent, and special numbers}
+%
+% \begin{macro}[EXP,aux]{\@@_add_cases:NN}
+%   \begin{syntax}
+%     \cs{@@_add_cases:NN} \meta{case_1} \meta{case_2}
+%     ~~\meta{sign_1} \meta{sign_2} \meta{body_1} |;| \meta{body_2} |;|
+%   \end{syntax}
+%   This performs the addition. it also expands the following tokens
+%   on the input stream once.
+%
+%   Whenever \meta{case_1} is different from \meta{case_2}, the result
+%   is simply the floating point number with the highest \meta{case}.
+%   For instance, adding a normal number to a zero gives the normal
+%   number, and adding a \texttt{nan} to any non-\texttt{nan} gives
+%   that \texttt{nan}. Optimizing for addition of normal numbers,
+%   we test for equality and then separate the \enquote{greater than}
+%   and \enquote{less than} branches.
+%    \begin{macrocode}
+\cs_new:Npn \@@_add_cases:NN #1 #2
+  {
+    \if_int_compare:w #1 = #2 \exp_stop_f:
+      \exp_after:wN \@@_add_cases_eq:N
+    \else:
+      \if_int_compare:w #1 < #2 \exp_stop_f:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_basics_return_ii:NNNNww
+      \else:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_basics_return_i:NNNNww
+      \fi:
+      \exp_after:wN #1
+    \fi:
+    #2
+  }
+%    \end{macrocode}
+%   If the first \meta{case} is larger, then the first number remains
+%   untouched, while the second number is ignored. On the other hand,
+%   if the second \meta{case} is larger, the opposite happens: we retain
+%   the second number. In both cases, there needs to be one step of
+%   expansion after.
+%    \begin{macrocode}
+%    \end{macrocode}
+%   We are then ready for the equality case: we split according
+%   to the \meta{case}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_add_cases_eq:N #1
+  {
+    \if_case:w #1 \exp_stop_f:
+         \exp_after:wN \@@_add_zeros:NNww
+    \or: \exp_after:wN \@@_add_normal:NNww
+    \or: \exp_after:wN \@@_add_inf:NNww
+    \or: \exp_after:wN \@@_basics_return_nan_nan:NNww
+    \fi:
+  }
+%    \end{macrocode}
+%   Adding two zeros yields \cs{c_zero_fp}, except if both
+%   zeros were $-0$.\footnote{Bruno: this should depend on the
+%     rounding mode.}
+%    \begin{macrocode}
+\cs_new:Npn \@@_add_zeros:NNww #1#2 #3;
+  {
+    \if_int_compare:w #1 #2 = 02 \exp_stop_f:
+      \@@_case_return_o:Nw \c_zero_fp
+    \else:
+      \@@_case_return_same_o:w
+    \fi:
+    \s_@@ \@@_chk:w 0 #2
+  }
+%    \end{macrocode}
+%   If both infinities have the same sign, just return that infinity,
+%   otherwise, it is an invalid operation.
+%    \begin{macrocode}
+\cs_new:Npn \@@_add_inf:NNww #1#2 #3;
+  {
+    \if_meaning:w #1 #2
+      \@@_case_return_same_o:w
+    \else:
+      \@@_case_use:nw
+        {
+          \@@_invalid_operation:Nnww \c_nan_fp { + }
+            \s_@@ \@@_chk:w 2 #1 #3 ;
+        }
+    \fi:
+    \s_@@ \@@_chk:w 2 #2
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_add_normal:NNww}
+%   \begin{syntax}
+%     \cs{@@_add_normal:NNww} \meta{sign_1} \meta{sign_2}
+%     ~~\Arg{exp_1}  \meta{body_1} |;| \Arg{exp_2} \meta{body_2} |;|
+%   \end{syntax}
+%   We now have two normal numbers to add, and we have to check signs
+%   and exponents more carefully before performing the addition.
+%    \begin{macrocode}
+\cs_new:Npn \@@_add_normal:NNww #1#2
+  {
+    \if_meaning:w #1#2
+      \exp_after:wN \@@_add_npos:Nnwnw
+    \else:
+      \exp_after:wN \@@_sub_npos:Nnwnw
+    \fi:
+    #1
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Absolute addition}
+%
+% In this subsection, we perform the addition
+% of two positive normal numbers.
+%
+% \begin{macro}[EXP]{\@@_add_npos:Nnwnw}
+%   \begin{syntax}
+%     \cs{@@_add_npos:Nnwnw} \meta{sign}
+%     ~~\Arg{exp_1}  \meta{body_1} |;| \Arg{exp_2} \meta{body_2} |;|
+%   \end{syntax}
+%   Since we are doing an addition, \meta{sign} will be the final sign.
+%   The only special case which may arise is the case of an overflow.
+%   This will be checked by \cs{@@_sanitize:Nw} at the end of
+%   the calculation. We start an \cs{__int_eval:w}, responsible for
+%   computing the exponent, which may receive a contribution of |+1|
+%   in case of carry. The exponent should be stopped by |;| followed by
+%   the overall \meta{sign} for the sanitizing to work properly.
+%
+%   Grab and compare the exponents. The smaller number is decimated until
+%   its exponent reaches that of the bigger number. We need to bring the
+%   final sign down in the midst of the calculation to do the rounding
+%   correctly.
+%    \begin{macrocode}
+\cs_new:Npn \@@_add_npos:Nnwnw #1 #2#3; #4
+  {
+    \exp_after:wN \@@_sanitize:Nw
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w
+      \if_int_compare:w #2 > #4 \exp_stop_f:
+        #2
+        \exp_after:wN \@@_add_big_i:wNww \__int_value:w -
+      \else:
+        #4
+        \exp_after:wN \@@_add_big_ii:wNww \__int_value:w
+      \fi:
+      \__int_eval:w #4 - #2 ; #1 #3;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_add_big_i:wNww,
+%     \@@_add_big_ii:wNww}
+%   \begin{syntax}
+%     \cs{@@_add_big_i:wNww} \meta{shift} |;| \meta{sign}
+%     ~~\meta{body_1} |;| \meta{body_2} |;|
+%   \end{syntax}
+%   Shift the mantissa of the small number, and then add with
+%   \cs{@@_add_mantissa:NnnwnnnnN}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_add_big_i:wNww #1; #2 #3; #4;
+  {
+    \@@_decimate:nNnnnn {#1}
+      \@@_add_mantissa:NnnwnnnnN
+      #4
+    #3
+    #2
+  }
+\cs_new:Npn \@@_add_big_ii:wNww #1; #2 #3; #4;
+  {
+    \@@_decimate:nNnnnn {#1}
+      \@@_add_mantissa:NnnwnnnnN
+      #3
+    #4
+    #2
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_add_mantissa:NnnwnnnnN}
+%   \begin{syntax}
+%     \cs{@@_add_mantissa:NnnwnnnnN}
+%     ~~\meta{rounding}
+%     ~~\Arg{Y'_1} \Arg{Y'_2} \meta{extra-digits} |;|
+%     ~~\Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4}
+%     ~~\meta{final sign}
+%   \end{syntax}
+%   To round properly, we must know at which digit the rounding
+%   should occur. This requires to know whether the addition
+%   produces an overall carry or not. Thus, we do the computation
+%   now and check for a carry, then go back and do the rounding.
+%   The rounding may cause a carry in very rare cases such as
+%   $0.99\cdots 95 \to 1.00\cdots 0$, but this situation always
+%   give an exact power of $10$, for which it is easy to correct
+%   the result at the end.
+%    \begin{macrocode}
+\cs_new:Npn \@@_add_mantissa:NnnwnnnnN #1 #2#3 #4; #5#6#7#8
+  {
+    \exp_after:wN \@@_add_mantissa_test:N
+    \int_use:N \__int_eval:w 1#5#6 + #2
+      \exp_after:wN \@@_add_mantissa_pack:NNNNNNN
+      \int_use:N \__int_eval:w 1#7#8 + #3 ; #1
+  }
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\cs_new:Npn \@@_add_mantissa_pack:NNNNNNN #1 #2#3#4#5#6#7
+  {
+    \if:w 2 #1
+      + \c_one
+    \fi:
+    ; #2 #3 #4 #5 #6 #7 ;
+  }
+\cs_new:Npn \@@_add_mantissa_test:N #1
+  {
+    \if:w 2 #1
+      \exp_after:wN \@@_add_mantissa_carry:wwNNNN
+    \else:
+      \exp_after:wN \@@_add_mantissa_no_carry:wwNNNN
+    \fi:
+  }
+%    \end{macrocode}
+%
+%   \begin{quote}
+%     \cs{@@_add_mantissa_no_carry:wwNNNN}
+%     ~~\meta{8d} |;| \meta{6d} |;| \meta{2d} |;|
+%     ~~\meta{rounding} \meta{sign}
+%   \end{quote}
+%   If there's no carry, grab all the digits again, and just
+%   set the rounding correctly.\footnote{Bruno: an optimization
+%     would be to compute whether we need rounding or not,
+%     and only grab digits if there is rounding.}
+%
+%    \begin{macrocode}
+\cs_new:Npn \@@_add_mantissa_no_carry:wwNNNN
+    #1; #2; #3#4 ; #5#6
+  {
+    \exp_after:wN \@@_basics_pack_high:NNNNNw
+    \int_use:N \__int_eval:w 1 #1
+      \exp_after:wN \@@_basics_pack_low:NNNNNw
+      \int_use:N \__int_eval:w 1 #2 #3#4
+        + \@@_round:NNN #6 #4 #5
+        \exp_after:wN ;
+  }
+%    \end{macrocode}
+%
+%   The case where there is a carry is very similar: rounding can even
+%   raise the first digit from $1$ to $2$ (but we don't need to check that).
+%   \begin{quote}
+%     \cs{@@_add_mantissa_carry:wwNNNN}
+%     ~~\meta{8d} |;| \meta{6d} |;| \meta{2d} |;|
+%     ~~\meta{rounding} \meta{sign}
+%   \end{quote}
+%    \begin{macrocode}
+\cs_new:Npn \@@_add_mantissa_carry:wwNNNN
+    #1; #2; #3#4; #5#6
+  {
+    + \c_one
+    \exp_after:wN \@@_add_mantissa_carry_pack:NNNNNNNNw
+    \int_use:N \__int_eval:w 1 #1
+      \exp_after:wN \@@_add_mantissa_carry_pack_ii:NNNNw
+      \int_use:N \__int_eval:w 1 #2#3
+        + \@@_round:NNNN #6 #3 #4 #5
+        \exp_after:wN ;
+  }
+\cs_new:Npn \@@_add_mantissa_carry_pack_ii:NNNNw #1 #2#3#4 #5;
+  {
+    \if:w 2 #1
+      + \c_one
+    \fi:
+    \__int_eval_end:
+    #2#3#4; {#5} ;
+  }
+\cs_new:Npn \@@_add_mantissa_carry_pack:NNNNNNNNw
+    #1#2#3#4 #5#6#7#8 #9; { ; {#1#2#3#4} {#5#6#7#8} {#9} }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Absolute subtraction}
+%
+% \begin{macro}[EXP]{\@@_sub_npos:Nnwnw}
+%   \begin{syntax}
+%     \cs{@@_sub_npos:Nnwnw} \meta{sign}
+%     ~~\Arg{exp_1}  \meta{body_1} |;| \Arg{exp_2} \meta{body_2} |;|
+%   \end{syntax}
+%   Rounding properly in some modes requires to know what the sign
+%   of the result will be. For addition, this was easy. Here, besides
+%   comparing the exponents to know how to decimate, we need to
+%   check carefully which number is bigger when they have the same
+%   exponent.
+%    \begin{macrocode}
+\cs_new:Npn \@@_sub_npos:Nnwnw #1 #2#3; #4 #5;
+  {
+    \exp_after:wN \@@_sanitize:wN
+    \int_use:N \__int_eval:w
+      \if_int_compare:w #2 > #4 \exp_stop_f:
+        #2
+        \exp_after:wN \@@_sub_big_i:wNww \__int_value:w -
+      \else:
+        #4
+        \if_int_compare:w #2 = #4 \exp_stop_f:
+          \@@_sub_exponent_eq:nnnnnnnn #3 #5
+        \else:
+          \exp_after:wN \@@_sub_big_ii:wNww \__int_value:w
+        \fi:
+      \fi:
+      \__int_eval:w #4 - #2 ; #1 #3; #5;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_sub_exponent_eq:nnnnnnnn}
+%    \begin{macrocode}
+\cs_new:Npn \@@_sub_exponent_eq:nnnnnnnn #1#2#3#4 #5#6#7#8
+  {
+    \if_int_compare:w #1#2 > #5#6 \exp_stop_f:
+      \exp_after:wN \@@_sub_big_i:wNww \__int_value:w
+    \else:
+      \if_int_compare:w #1#2 < #5#6 \exp_stop_f:
+        \exp_after:wN \@@_sub_big_ii:wNww \__int_value:w
+      \else:
+        \if_int_compare:w #3#4 > #7#8 \exp_stop_f:
+          \exp_after:wN \@@_sub_big_i:wNww \__int_value:w
+        \else:
+          \if_int_compare:w #3#4 < #7#8 \exp_stop_f:
+            \exp_after:wN \@@_sub_big_ii:wNww \__int_value:w
+          \else:
+            \exp_after:wN \@@_sub_eq:wNww \__int_value:w
+          \fi:
+        \fi:
+      \fi:
+    \fi:
+  }
+\cs_new:Npn \@@_sub_eq:wNww #1; #2 #3; #4;
+  { \exp_after:wN ; \exp_after:wN 1 \exp_after:wN ; }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_sub_big_i:wNww,\@@_sub_big_ii:wNww}
+%   \begin{syntax}
+%     \cs{@@_sub_big_i:wNww} \meta{shift} |;| \meta{sign}
+%     ~~\meta{body_1} |;| \meta{body_2} |;|
+%   \end{syntax}
+%   Shift the mantissa of the small number, and then subtract with
+%   \cs{@@_sub_back_mantissa:NnnwNnnnn}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_sub_big_i:wNww #1; #2 #3; #4;
+  {
+    \@@_decimate:nNnnnn {#1}
+      \@@_sub_back_mantissa:NnnwNnnnn
+      #4
+    #2
+    #3
+  }
+\cs_new:Npn \@@_sub_big_ii:wNww #1; #2 #3; #4;
+  {
+    \exp_after:wN \@@_sub_big_i:wNww
+    \__int_value:w #1 \exp_after:wN ;
+    \int_use:N \__int_eval:w 2 - #2 \__int_eval_end:
+    #4; #3;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_sub_back_mantissa:NnnwNnnnn}
+%   \begin{syntax}
+%     \cs{@@_sub_back_mantissa:NnnwNnnnn}
+%     ~~\meta{rounding} \Arg{Y'_1} \Arg{Y'_2} \meta{extra-digits}
+%     ~~\meta{final sign}
+%     ~~\Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4}
+%   \end{syntax}
+%   At this stage, we know that \meta{Y} is less than \meta{X},
+%   and we know the final sign.
+%    \begin{macrocode}
+\cs_new:Npn \@@_sub_back_mantissa:NnnwNnnnn #1 #2#3 #4; #5 #6#7#8#9
+  {
+    \exp_after:wN \@@_sub_back_mantissa_i:NNwNNNNwN
+    \exp_after:wN #1
+    \exp_after:wN #5
+    \int_use:N \__int_eval:w 2#6#7 - #2 - \c_two +
+      \exp_after:wN \@@_sub_back_mantissa_round:wNN
+      \int_use:N \__int_eval:w 2#8#9 - #3 ; #1 #5
+  }
+%    \end{macrocode}
+%   After the computation, we need to check whether the first digit of
+%   the result is zero. This can only happen if the two numbers had the
+%   same exponent, or exponents differing by $1$. In the latter case,
+%   the \meta{rounding} digit is not quite enough to let us retrieve
+%   the exact result (consider $\cdots25$ and $\cdots15$, both rounded
+%   to $\cdots2$ in the usual mode), so we also move the result of
+%   \cs{@@_round_neg:NNN} upstream as the digit $0$ or $1$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_sub_back_mantissa_round:wNN #1; #2 #3
+  {
+    \exp_after:wN \@@_sub_back_mantissa_iii:N
+    \__int_value:w
+        \exp_after:wN \@@_round_neg:NNN
+        \exp_after:wN #3
+        \use_none:nnnnnnnn #1 #2
+      + #1
+    \exp_after:wN ;
+  }
+\cs_new:Npn \@@_sub_back_mantissa_iii:N #1
+  {
+    \exp_after:wN \@@_sub_back_mantissa_ii:NNNNNNw
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w
+      - #1
+  }
+\cs_new:Npn \@@_sub_back_mantissa_ii:NNNNNNw #1 #2 #3#4#5#6 #7;
+  { #2 ; #1 {#3#4#5#6} {#7} ; }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_sub_back_mantissa_i:NNwNNNNwN}
+%   Here, |#3| should always be $2$, but we have to take is
+%   as a normal undelimited argument since that would break
+%   if |#2| is $2$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_sub_back_mantissa_i:NNwNNNNwN #1#2 #3 #4#5#6#7 #8; #9
+  {
+    \if:w 0 #4
+      \exp_after:wN \@@_sub_back_carry:NNwNnnnn
+      \exp_after:wN #1
+      \exp_after:wN #9
+    \fi:
+    ; #2
+    {#4#5#6#7} {#8}
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_sub_back_carry:NNwNnnnn}
+%   \begin{syntax}
+%     \cs{@@_sub_back_carry:NNwNnnnn}
+%     ~~\meta{rounding} \meta{0 or 1} |;| \meta{final sign}
+%     ~~\Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} |;|
+%   \end{syntax}
+%   This function is called when $\meta{Z_1}\leq 999$. We revert
+%   the carry, which is given by \meta{0 or 1}, and subtract the
+%   \meta{rounding} digit as appropriate, then feed the result,
+%   of the form \meta{$\leq$ 7d} |;| \meta{9d} |;| to
+%   \cs{@@_sub_back_carry_i:wwN}. The result is always exact.
+%    \begin{macrocode}
+\cs_new:Npn \@@_sub_back_carry:NNwNnnnn #1#2 ; #3 #4#5#6#7 ;
+  {
+    \exp_after:wN \@@_sub_back_carry_i:wwN
+    \int_use:N \__int_eval:w #4 #5 - 1 + \exp_after:wN \@@_use_s:n
+    \int_use:N \__int_eval:w 1 #6 #7 0 + #2 0 - #1 ; #3
+  }
+%    \end{macrocode}
+%   Unless the first block is zero, check how many digits is has,
+%   and shift the exponent down by the corresponding amount. Then
+%   pack digits into blocks of $4$ (there are between $10$ and $16$
+%   digits in front of \cs{@@_sub_back_carry_large:NNNNNNNNw}).
+%    \begin{macrocode}
+\cs_new:Npn \@@_sub_back_carry_i:wwN #1 ;
+  {
+    \if:w 0 #1
+      - 8
+      \exp_after:wN \@@_sub_back_carry_small:wN \__int_value:w
+    \else:
+      - \@@_sub_back_carry_ii:NNNNNNNNw #1 1234567;
+      \exp_after:wN \@@_sub_back_carry_large:NNNNNNNNw
+    \fi:
+    #1
+  }
+%    \end{macrocode}
+%   The case where the number is non-zero is slightly easier.
+%    \begin{macrocode}
+\cs_new:Npn \@@_sub_back_carry_ii:NNNNNNNNw #1#2#3#4#5#6#7#8#9; {#8}
+\cs_new:Npn \@@_sub_back_carry_large:NNNNNNNNw #1#2#3#4 #5#6#7#8 #9;
+  {
+    \@@_sub_back_carry_large_ii:NNNNNNNNw
+    #9 000000 ; {#1#2#3#4} {#5#6#7#8}
+  }
+\cs_new:Npn \@@_sub_back_carry_large_ii:NNNNNNNNw #1#2#3#4 #5#6#7#8 #9;
+  { \@@_sub_back_carry_large_iii:nnnnN {#1#2#3#4} {#5#6#7#8} }
+\cs_new:Npn \@@_sub_back_carry_large_iii:nnnnN #1#2 #3#4 #5
+  { ; #5 {#3}{#4} {#1}{#2} ; }
+%    \end{macrocode}
+%   In the case of a \enquote{small} result, what comes after
+%   \cs{@@_sub_back_carry_small:wN} has between $1$
+%   and $9$ digits, and is not zero.
+%    \begin{macrocode}
+\cs_new:Npn \@@_sub_back_carry_small:wN #1;
+  {
+    - \exp_after:wN \@@_use_i_until_s:nw
+      \use_none:nnnnnnnnn #1 012345678;
+    \@@_sub_back_carry_small_ii:NNNNNNNN #1 00000000 ;
+  }
+\cs_new:Npn \@@_sub_back_carry_small_ii:NNNNNNNN #1#2#3#4 #5#6#7#8
+  { \@@_sub_back_carry_small_iii:nnNwN {#1#2#3#4} {#5#6#7#8} }
+\cs_new:Npn \@@_sub_back_carry_small_iii:nnNwN #1 #2 #3 #4; #5
+  { ; #5 {#1} {#2} {#3000} {0000} ; }
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Multiplication}
+%
+% \begin{macro}[int, EXP]{\@@_*_o:ww}
+%   For multiplication, everything is easy.  No need to grab the
+%   \meta{body_2}.
+%    \begin{macrocode}
+\cs_new:cpn { @@_*_o:ww }
+    \s_@@ \@@_chk:w #1 #2 #3 ; \s_@@ \@@_chk:w #4 #5
+  { \@@_mul_cases:NN #1 #4 #2 #5 #3 ; }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Signs, and special numbers}
+%
+% \begin{macro}[EXP,aux]{\@@_mul_cases:NN}
+%   \begin{syntax}
+%     \cs{@@_mul_cases:NN} \meta{case_1} \meta{case_2}
+%     ~~\meta{sign_1} \meta{sign_2} \meta{body_1} |;| \meta{body_2} |;|
+%   \end{syntax}
+%   Expands the following tokens on the input stream once.
+%   The special cases are coded at the start of this module,
+%   and identical to the ones for division.\footnote{Bruno: \texttt{nan}
+%     are not treated properly: $\infty\times 0$ should signal.}
+%^^A todo: use the faster \if_meaning:w.
+%    \begin{macrocode}
+\cs_new:Npn \@@_mul_cases:NN #1 #2
+  {
+    \if_case:w \if_meaning:w 1 #1 #2 \else:
+               \if_meaning:w 1 #2 #1 \else:
+               \if_meaning:w #1#2 #1 \else:
+               \if_int_compare:w \__int_eval:w #1 + #2 > \c_two
+                 3 \else: 4 \fi: \fi: \fi: \fi:
+               \exp_stop_f:
+         \exp_after:wN \@@_basics_return_zero:NNww
+    \or: \exp_after:wN \@@_mul_normal:NNww
+    \or: \exp_after:wN \@@_basics_return_inf:NNww
+    \or: \exp_after:wN \@@_basics_return_nan:NNww
+    \or:
+      \exp_after:wN \@@_mul_invalid:NNNNww
+      \exp_after:wN #1
+      \exp_after:wN #2
+    \fi:
+  }
+\cs_new:Npn \@@_mul_invalid:NNNNww #1#2#3#4#5; #6;
+  {
+    \@@_invalid_operation:Nnww \c_nan_fp { * }
+      \s_@@ \@@_chk:w #1 #3 #5 ;
+      \s_@@ \@@_chk:w #2 #4 #6 ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_mul_normal:NNww}
+%   \begin{syntax}
+%     \cs{@@_mul_normal:NNww} \meta{sign_1} \meta{sign_2}
+%     ~~\Arg{exp_1}  \meta{body_1} |;| \Arg{exp_2} \meta{body_2} |;|
+%   \end{syntax}
+%   We now have two normal numbers to multiply. Combine the signs.
+%    \begin{macrocode}
+\cs_new:Npn \@@_mul_normal:NNww #1#2
+  {
+    \if:w #1#2
+      \exp_after:wN \@@_mul_npos:Nnwnw
+      \exp_after:wN 0
+    \else:
+      \exp_after:wN \@@_mul_npos:Nnwnw
+      \exp_after:wN 2
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Absolute multiplication}
+%
+% In this subsection, we perform the multiplication
+% of two positive normal numbers.
+%
+% \begin{macro}[EXP]{\@@_mul_npos:Nnwnw}
+%   \begin{syntax}
+%     \cs{@@_mul_npos:Nnwnw} \meta{sign}
+%     ~~\Arg{exp_1}  \meta{body_1} |;| \Arg{exp_2} \meta{body_2} |;|
+%   \end{syntax}
+%   As for addition, \meta{sign} is the final sign. After the computation,
+%   \cs{@@_sanitize:Nw} checks for overflow or underflow.
+%   As before, \cs{__int_eval:w} computes the exponent, catching any
+%   shift coming from the computation in the mantissa. Again, the
+%   \meta{sign} is needed for rounding to be done properly, so we move
+%   it around with us. We setup the post-expansion here, triggered by
+%   \cs{@@_mul_mantissa:nnnnNnnnn}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_mul_npos:Nnwnw #1 #2#3; #4 #5;
+  {
+    \exp_after:wN \@@_sanitize:Nw
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w
+      #2 + #4
+      \@@_mul_mantissa:nnnnNnnnn #3 #1 #5
+    \exp_after:wN ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_mul_mantissa:nnnnNnnnn}
+%   \begin{syntax}
+%     \cs{@@_mul_mantissa:nnnnNnnnn}
+%     ~~\Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \meta{sign}
+%     ~~\Arg{Y_1} \Arg{Y_2} \Arg{Y_3} \Arg{Y_4} \meta{;}
+%   \end{syntax}
+%   After one expansion, the token following \meta{Y_4} must be a semicolon
+%   (represented by \meta{;}).
+%
+%   The product of two $16$ digit integers has $31$ or $32$ digits,
+%   but it is impossible to know which one before computing. The place
+%   where we round depends on that number of digits, and may depend
+%   on all digits until the last in some rare cases. The approach is
+%   thus to compute the $5$ first blocks of $4$ digits (the first one
+%   is between $100$ and $9999$ inclusive), and a compact version of
+%   the remaining $3$ blocks. Afterwards, the number of digits is
+%   known, and we can do the rounding within yet another set of
+%   \cs{__int_eval:w}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_mul_mantissa:nnnnNnnnn #1#2#3#4 #5 #6#7#8#9
+  {
+    \exp_after:wN \@@_mul_mantissa_after:NNN
+    \exp_after:wN #5
+    \int_use:N \__int_eval:w 99990000 + #1*#6 +
+      \exp_after:wN \@@_mul_mantissa_keep:NNNNNw
+      \int_use:N \__int_eval:w 99990000 + #1*#7 + #2*#6 +
+        \exp_after:wN \@@_mul_mantissa_keep:NNNNNw
+        \int_use:N \__int_eval:w 99990000 + #1*#8 + #2*#7 + #3*#6 +
+          \exp_after:wN \@@_mul_mantissa_drop:NNNNNw
+          \int_use:N \__int_eval:w  99990000 + #1*#9 + #2*#8 + #3*#7 + #4*#6 +
+            \exp_after:wN \@@_mul_mantissa_drop:NNNNNw
+            \int_use:N \__int_eval:w  99990000 + #2*#9 + #3*#8 + #4*#7 +
+              \exp_after:wN \@@_mul_mantissa_drop:NNNNNw
+              \int_use:N \__int_eval:w  99990000 + #3*#9 + #4*#8 +
+                \exp_after:wN \@@_mul_mantissa_drop:NNNNNw
+                \int_use:N \__int_eval:w 100000000 + #4*#9 \exp_after:wN ;
+  }
+\cs_new:Npn \@@_mul_mantissa_drop:NNNNNw #1#2#3#4#5 #6;
+  { #1#2#3#4#5 ; + #6 }
+\cs_new:Npn \@@_mul_mantissa_keep:NNNNNw #1#2#3#4#5 #6;
+  { #1#2#3#4#5 ; #6 ; }
+%    \end{macrocode}
+%   Once the first \cs{int_use:N} \cs{__int_eval:w}, and all the
+%   \cs{@@_mul_mantissa_...:NNNNNw} have been expanded,
+%   we get
+%   \begin{quote}
+%     \cs{@@_mul_mantissa_after:NNN} \meta{sign} |1|
+%     ~~\meta{digits 1--8} |;| \meta{digits 9--12} |;| \meta{digits 13--16} |;|
+%     ~~|+| \meta{digits 17--20} |+| \meta{digits 21--24}
+%     ~~|+| \meta{digits 25--28} |+| \meta{digits 29--32} |;|
+%   \end{quote}
+%   If the \meta{digit 1} is non-zero, then for rounding we only care
+%   about the digits $16$ and $17$, and whether all other digits are zero
+%   or not (check for exact ties). On the other hand, if \meta{digit 1}
+%   is zero, we care about digits $17$ and $18$, and whether all others are
+%   zero.
+%    \begin{macrocode}
+\cs_new:Npn \@@_mul_mantissa_after:NNN #1 #2 #3
+  {
+    \if:w 0 #3
+      \exp_after:wN \@@_mul_mantissa_small:NNwwwN
+    \else:
+      \exp_after:wN \@@_mul_mantissa_large:NwwNNNN
+    \fi:
+    #1 #3
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_mul_mantissa_large:NwwNNNN}
+%   In this branch, \meta{digit 1} is non-zero. The result is thus
+%   \meta{digits 1--16}, plus some rounding which depends on the digits
+%   $16$, $17$, and whether all subsequent digits are zero or not.
+%   Here, \cs{@@_round_s:NNNw} takes the \meta{sign}, followed by
+%   digits $16$, $17$, and an integer expression which is zero if and
+%   only if all further digits are zero.
+%    \begin{macrocode}
+\cs_new:Npn \@@_mul_mantissa_large:NwwNNNN #1 #2; #3; #4#5#6#7; +
+  {
+    \exp_after:wN \@@_basics_pack_high:NNNNNw
+    \int_use:N \__int_eval:w 1#2
+      \exp_after:wN \@@_basics_pack_low:NNNNNw
+      \int_use:N \__int_eval:w 1#3#4#5#6#7 + \@@_round_s:NNNw #1 #7
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_mul_mantissa_small:NNwwwN}
+%   In this branch, \meta{digit 1} is zero. Our result will thus be
+%   \meta{digits 2--17}, plus some rounding which depends on the digits
+%   $17$, $18$, and whether all subsequent digits are zero or not.
+%   The $8$ digits |1#3| are followed, after expansion of the
+%   \texttt{small_pack} auxiliary, by the next digit, to form a $9$
+%   digit number. Also, rounding may have caused a carry, which is
+%   then converted to \cs{c_ten} rather than the usual \cs{c_one},
+%   because of the shift.
+%    \begin{macrocode}
+\cs_new:Npn \@@_mul_mantissa_small:NNwwwN #1 #2#3; #4; #5; + #6
+  {
+    - \c_one
+    \exp_after:wN \@@_basics_pack_high:NNNNNw
+    \int_use:N \__int_eval:w 1#3
+      \exp_after:wN \@@_mul_mantissa_small_pack:NNNNNNw
+      \int_use:N \__int_eval:w 1#4#5#6 + \@@_round_s:NNNw #1 #6
+  }
+\cs_new:Npn \@@_mul_mantissa_small_pack:NNNNNNw #1#2 #3#4#5#6 #7;
+  {
+    #2
+    \if:w 2 #1
+      + \c_ten
+    \fi:
+    ; {#3#4#5#6} {#7} ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Division}
+%
+% Time is now ripe to tackle the hardest of the four elementary
+% operations: division.
+%
+% \begin{macro}[EXP]{\@@_/_o:ww}
+%   For division we swap the two floating point numbers.
+%    \begin{macrocode}
+\cs_new:cpn { @@_/_o:ww }
+    \s_@@ \@@_chk:w #1 #2 #3 ; \s_@@ \@@_chk:w #4 #5 #6 ;
+  { \@@_div_back_cases:NN #4 #1 #5 #2 #6 ; #3 ; }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Signs, and special numbers}
+%
+% In the case of division, the order of the operands matters,
+% and it turns out to be slightly simpler if we internally
+% compute the \enquote{backwards} division.
+%
+% \begin{macro}[EXP,aux]{\@@_div_back_cases:NN}
+%   \begin{syntax}
+%     \cs{@@_div_back_cases:NN} \meta{case_2} \meta{case_1}
+%     ~~\meta{sign_2} \meta{sign_1} \meta{body_2} |;| \meta{body_1} |;|
+%   \end{syntax}
+%   Expands the following tokens on the input stream once.
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_back_cases:NN #1 #2
+  {
+    \if_case:w \if_int_compare:w #1 = #2 \exp_stop_f:
+                 #1 \exp_stop_f:
+               \else:
+                 \if_int_compare:w #1 < #2 \exp_stop_f:
+                   \if:w 3 #2 \c_four \else: \c_five \fi:
+                 \else:
+                   \if:w 3 #1 \c_six \else: \c_seven \fi:
+                 \fi:
+               \fi:
+         \exp_after:wN \@@_div_back_invalid:NNNww \exp_after:wN 0
+    \or: \exp_after:wN \@@_div_back_normal:NNww
+    \or: \exp_after:wN \@@_div_back_invalid:NNNww \exp_after:wN 2
+    \or: \exp_after:wN \@@_basics_return_nan_nan:NNww
+    \or:
+      \exp_after:wN \@@_basics_return_ii:NNNNww
+      \exp_after:wN #1
+      \exp_after:wN #2
+    \or: \exp_after:wN \@@_basics_return_inf:NNww
+    \or:
+      \exp_after:wN \@@_basics_return_i:NNNNww
+      \exp_after:wN #1
+      \exp_after:wN #2
+    \or: \exp_after:wN \@@_basics_return_zero:NNww
+    \fi:
+  }
+%    \end{macrocode}
+%   Most of the special cases are common with some
+%   previous operations. We only need to write the cases of
+%   $0/0$ and $\infty/\infty$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_back_invalid:NNNww #1#2#3 #4; #5;
+  {
+    \@@_invalid_operation:Nnww \c_nan_fp { / }
+      \s_@@ \@@_chk:w #1 #3 #5 ;
+      \s_@@ \@@_chk:w #1 #2 #4 ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_div_back_normal:NNww}
+%   \begin{syntax}
+%     \cs{@@_div_back_normal:NNww} \meta{sign_1} \meta{sign_2}
+%     ~~\Arg{exp_1}  \meta{body_1} |;| \Arg{exp_2} \meta{body_2} |;|
+%   \end{syntax}
+%   We now have two normal numbers to divide. Combine the signs.
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_back_normal:NNww #1#2
+  {
+    \if:w #1#2
+      \exp_after:wN \@@_div_back_npos:Nnwnw
+      \exp_after:wN 0
+    \else:
+      \exp_after:wN \@@_div_back_npos:Nnwnw
+      \exp_after:wN 2
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Absolute (backwards) division}
+%
+% In this subsection, we perform the division
+% of two positive normal numbers.
+%
+% \begin{macro}[EXP]{\@@_div_back_npos:Nnwnw}
+%   \begin{syntax}
+%     \cs{@@_div_back_npos:Nnwnw} \meta{sign}
+%     ~~\Arg{exp Z} \Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} |;|
+%     ~~\Arg{exp A} \Arg{A_1} \Arg{A_2} \Arg{A_3} \Arg{A_4} |;|
+%   \end{syntax}
+%   We want to compute $A/Z$. As for addition and multiplication,
+%   \meta{sign} is the final sign. Checking for underflow and
+%   overflow is done using the same auxiliary as for multiplication.
+%   As explained just below, we first compute $y$, which is
+%   the $5$ first digits of $Z$, plus $1$, and then compute pieces
+%   of the quotient roughly $4$ digits at a time. Here, |#1| is
+%   a single digit, |#2| and |#7| are the exponents (integers),
+%   |#8| is three brace groups, and all others are each $4$ digits.
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_back_npos:Nnwnw #1 #2 #3#4#5#6; #7 #8;
+  {
+    \exp_after:wN \@@_sanitize:Nw
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w
+      #7 - #2
+      \@@_div_mantissa_i:wNwnn #3; #4;
+      #8 {#3}{#4}{#5}{#6} #1
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+%   We are given two numbers, $A=0.A_{1}A_{2}A_{3}A_{4}$
+%   and $Z=0.Z_{1}Z_{2}Z_{3}Z_{4}$, in blocks of $4$ digits,
+%   and we know that the first digits of $A_{1}$ and of $Z_{1}$
+%   are non-zero. To compute $A/Z$, we proceed as follows.
+%   \begin{itemize}
+%   \item Find an integer $Q_{1} \simeq 10^4 A / Z$.
+%   \item Replace $A$ by $B = 10^4 A - Q_{1} Z$.
+%   \item Find an integer $Q_{2} \simeq 10^4 B / Z$.
+%   \item Replace $B$ by $C = 10^4 B - Q_{2} Z$.
+%   \item Find an integer $Q_{3} \simeq 10^4 C / Z$.
+%   \item Replace $C$ by $D = 10^4 C - Q_{3} Z$.
+%   \item Find an integer $Q_{4} \simeq 10^4 D / Z$.
+%   \item Consider $E = 10^4 D - Q_{4} Z$, and ensure
+%     correct rounding.
+%   \end{itemize}
+%   The calculations of $B$, $C$, $D$, and $E$ can be done
+%   exactly with only $16$ (or $17$) digits.
+%
+%   Unfortunately, things are not as easy as they seem.
+%   Firstly, we make sure that all intermediate steps are positive,
+%   since negative results would require extra calculations at the end.
+%   This requires that $Q_{1} \leq 10^4 A / Z$ etc. A reasonable
+%   attempt would be to define $Q_{1}$ as
+%   \[
+%   \cs{int_eval:n} \left\{
+%     \frac{ A_{1} A_{2} }{ Z_{1} + 1 } - 1 \right\}.
+%   \]
+%   Subtracting $1$ at the end takes care of the fact that e\TeX{}'s
+%   \cs{__int_eval:w} rounds instead of truncating. We add $1$ to $Z_{1}$
+%   because $ Z_{1} \leq 10^4 Z < Z_{1}+1$ and we need $Q_{1}$
+%   to be an underestimate. However, we are now underestimating
+%   $Q_{1}$ too much: it can be wrong by up to $100$, for instance
+%   when $Z = 0.1$ and $A \simeq 1$. Then $B$ could take values up to
+%   $10$ (maybe more), and a few steps down the line, we would run into
+%   arithmetic overflow, since \TeX{} can only handle integers less than
+%   roughly $2\cdot 10^9$.
+%
+%   A better formula is to take
+%   \[
+%   Q_{1} = \cs{int_eval:n} \left\{
+%     \frac{ 10 \cdot A_{1} A_{2} }
+%       { \left\lfloor 10^{-3} \cdot Z_{1} Z_{2} \right\rfloor + 1 }
+%     - 1 \right\}.
+%   \]
+%   This is always less than $10^9 A / (10^5 Z)$, as we wanted.
+%   In words, we take the $5$ first digits of $Z$ into account,
+%   and the $8$ first digits of $A$, using $0$ as a $9$-th digit
+%   rather than the true digit for efficiency reasons. We shall
+%   prove that using this formula to define all the $Q_{i}$
+%   leads to no overflow. For convenience, let us denote
+%   \[
+%   y = \left\lfloor 10^{-3} \cdot Z_{1} Z_{2} \right\rfloor + 1,
+%   \]
+%   so that, taking into account the fact that e\TeX{} rounds ties
+%   away from zero,
+%   \[
+%   Q_{1} = \left\lfloor A_{1}A_{2}0/y - 1/2 \right\rfloor.
+%   \]
+%   Note that $10^4<y\leq 10^5$, and $999 \leq Q_{1} \leq 99989$.
+%   Also note that this formula does not cause an overflow as long as
+%   $A<2.147\cdots$, since the numerator involves an integer slightly
+%   smaller than $10^9A$.
+%
+%   Let us bound $B$:
+%   \begin{align*}
+%   10^5 B
+%   &=
+%   A_{1}A_{2}0 + 10 \cdot 0.A_{3}A_{4}
+%   - 10 \cdot Z_{1}.Z_{2}Z_{3}Z_{4}
+%   \cdot \left\lfloor A_{1}A_{2}0/y - 1/2 \right\rfloor
+%   \\
+%   &<
+%   A_{1}A_{2}0
+%   \cdot \left( 1 - 10 \frac{Z_{1}.Z_{2}Z_{3}Z_{4}}{y} \right)
+%   + \frac{3}{2} \cdot 10 \cdot Z_{1}.Z_{2}Z_{3}Z_{4} + 10
+%   \\
+%   &\leq
+%   \frac{A_{1}A_{2}0 \cdot (y - 10 Z_{1}.Z_{2}Z_{3}Z_{4})}{y}
+%   + \frac{3}{2} y + 10
+%   \\
+%   &\leq
+%   \frac{A_{1}A_{2}0}{y} + \frac{3}{2} y + 10
+%   \leq
+%   \frac{10^9 A}{y} + 1.6 y
+%   \end{align*}
+%   At the last step, we hide $10$ into the second term
+%   for later convenience. The same reasoning yields\footnote{Bruno:
+%     I need to find much better notations. These are not great.}
+%   \begin{align*}
+%     10^5 B &< 10^9 A/y + 1.6 y, \\
+%     10^5 C &< 10^9 B/y + 1.6 y, \\
+%     10^5 D &< 10^9 C/y + 1.6 y, \\
+%     10^5 E &< 10^9 D/y + 1.6 y. \\
+%   \end{align*}
+%   The goal is now to prove that none of $B$, $C$, $D$, and $E$
+%   can go beyond $2.147\cdots$. Simply bounding each term on the
+%   right-hand side separately will not be tight enough: for instance,
+%   we would get $10^5 B < 10^5 + 1.6\cdot 10^5 = 2.6 \cdot 10^5$,
+%   which is too large.
+%
+%   Combining the various inequalities together with $A<1$, we get
+%   \begin{align*}
+%     10^5 B &< 10^9/y + 1.6 y, \\
+%     10^5 C &< 10^{13}/y^2 + 1.6 (y + 10^4), \\
+%     10^5 D &< 10^{17}/y^3 + 1.6 (y + 10^4 + 10^8/y), \\
+%     10^5 E &< 10^{21}/y^4 + 1.6 (y + 10^4 + 10^8/y + 10^{12}/y^2). \\
+%   \end{align*}
+%   All of those bounds are convex functions of $y$ (since every power
+%   of $y$ involved is convex, and hte coefficients are positive), and
+%   thus maximal at one of the end-points of the allowed range
+%   $10^4<y\leq 10^5$. Thus,
+%   \begin{align*}
+%     10^5 B &< \mathrm{max} ( 1.16\cdot 10^5, 1.7 \cdot 10^5), \\
+%     10^5 C &< \mathrm{max} ( 1.32\cdot 10^5, 1.77 \cdot 10^5), \\
+%     10^5 D &< \mathrm{max} ( 1.48\cdot 10^5, 1.777 \cdot 10^5), \\
+%     10^5 E &< \mathrm{max} ( 1.64\cdot 10^5, 1.7777 \cdot 10^5). \\
+%   \end{align*}
+%   All of those bounds are less than $2.147\cdot 10^5$, and
+%   we are thus within \TeX{}'s bounds in all cases!\footnote{Bruno:
+%     but I need to check this very carefully again.}
+%
+%   We will later need to have a bound on the $Q_{i}$. Their
+%   definitions imply that $Q_{1} < 10^9 A/y - 1/2 < 10^5 A$ and
+%   similarly for the other $Q_{i}$. Thus each of them is at most
+%   $177770$.
+%
+%   The last step is to ensure correct rounding. We have
+%   \[
+%   A/Z = \sum_{i=1}^4 \left(10^{-4i} Q_{i}\right) + 10^{-16} E/Z
+%   \]
+%   exactly. Furthermore, we know that the result will be between
+%   $0.1$ (inclusive) and $10$, so we only need to know the integer
+%   part of $E/Z$, and a \enquote{rounding} digit encoding the rest
+%   (see maybe addition for an explanation of why). Equivalently,
+%   we need to find the integer part of $2E/Z$, and determine whether
+%   it was an exact integer or not (this serves to detect ties). Since
+%   \[
+%   \frac{2E}{Z} = 2\frac{10^5 E}{10^5 Z}
+%   \leq 2\frac{10^5 E}{10^4} < 36,
+%   \]
+%   this integer part is between $0$ and $35$ inclusive. We let
+%   e\TeX{} round
+%   \[
+%   P = \cs{int_eval:n} \left\{
+%     2 \frac{E_{1}E_{2}}{Z_{1}Z_{2}} \right\},
+%   \]
+%   which differs from $2E/Z$ by at most
+%   \[
+%   \frac{1}{2}
+%   + 2 \left\lvert \frac{E}{Z} - \frac{E}{10^{-8} Z_{1}Z_{2}}\right\rvert
+%   + 2 \left\lvert \frac{10^8 E - E_{1}E_{2}}{Z_{1}Z_{2}}\right\rvert
+%   < 1,
+%   \]
+%   ($1/2$ comes from e\TeX{}'s rounding) because each absolute value
+%   is less than $10^{-7}$. Thus $P$ is either the correct integer part,
+%   or an overestimate by $1$ (impossible if $2E/Z$ is an integer). It
+%   then suffices to compare $PZ$ with $2E$ to get the integer part of
+%   $2E/Z$ and the information of whether it was an exact quotient or not.
+%
+% \begin{macro}[EXP]{\@@_div_mantissa_i:wNwnn}
+%   \begin{syntax}
+%     \cs{@@_div_mantissa_i:wNwnn}
+%     ~~\meta{Z_1} |;| \meta{Z_2} |;|
+%     ~~\Arg{A_1} \Arg{A_2} \Arg{A_3} \Arg{A_4}
+%     ~~\Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \meta{sign}
+%   \end{syntax}
+%   First compute $y$ from the first $5$ digits of $Z$, and
+%   unbrace \meta{A_1} and \meta{A_2}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_i:wNwnn #1; #2 #3; #4 #5
+  {
+    \exp_after:wN \@@_div_mantissa_ii:ww
+    \int_use:N \__int_eval:w #1#2 + \c_one ;
+    #4 #5 ;
+  }
+%    \end{macrocode}
+%   \begin{quote}
+%     \cs{@@_div_mantissa_ii:ww}
+%     ~~\meta{y} |;| \meta{A_1} \meta{A_2} |;| \Arg{A_3} \Arg{A_4}
+%     ~~\Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \meta{sign}
+%   \end{quote}
+%   Compute $Q_{1}$ by evaluating $\meta{A_1}\meta{A_2}0/y - 1$.
+%   The result will be output to the left, in an \cs{__int_eval:w}
+%   which we start now.
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_ii:ww #1; #2;
+  {
+    \exp_after:wN \@@_div_mantissa_iii:www
+    \__int_value:w #1 \exp_after:wN ;
+    \__int_value:w
+      \exp_after:wN \@@_div_mantissa_calc:Nwwnnnnnn
+      \int_use:N \__int_eval:w #20/#1 + 999999 ; #2 ;
+  }
+%    \end{macrocode}
+%   \begin{quote}
+%     \cs{@@_div_mantissa_calc:Nwwnnnnnn} \meta{$10^6+{}$Q_1} |;|
+%     ~~\meta{A_1} \meta{A_2} |;| \Arg{A_3} \Arg{A_4}
+%     ~~\Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \meta{sign}
+%   \end{quote}
+%   The goal here is to expand to
+%   \begin{quote}
+%     \meta{$10^6+{}$Q_1} |;| \meta{B_1} \meta{B_2} |;| \Arg{B_3} \Arg{B_4}
+%     ~~\Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \meta{sign}
+%   \end{quote}
+%   where $B = 10^4 A - Q_{1} \cdot Z$. More generally, this function
+%   is used with $A\to B$, $B\to C$ and $Q_{1} \to Q_{2}$, etc.
+%
+%   Computing the product $Q_{1} \cdot Z$ is almost simple, since
+%   $Q_{1}$ is rather small, but not quite:
+%   the product of $Q_{1}$ with each block of four digits $Z_{i}$
+%   is within \TeX{}'s bounds, but we wouldn't be able to use the
+%   usual trick of adding a large power of $10$ to ensure that the
+%   number of digits is fixed (see other operations for many examples
+%   of this). Instead, we split off the digit of $10^5$ in $Q_{1}$
+%   (and more generally $Q_{i}$), and do something similar to the
+%   case of the full multiplication.
+%
+%   We know that $0<Q_{i}<1.8\cdot 10^5$, so $10^6+Q_{i}$ starts
+%   with the digit $1$, followed by $\#1 = 1$ or $0$, then |#2|, which
+%   is $5$ more digits. It would be somewhat simpler if we got |#1|
+%   to be two digits, and |#2| four, but we are constrained by the $9$
+%   arguments limit.
+%
+%   The result we want is then (the overall power of $10$ is arbitrary):
+%   \begin{align*}
+%   &10^{-4} ( \#3 - \#2 \cdot \#6 - 10 \cdot \#1 \cdot \#6\#7 )
+%   + 10^{-8} ( \#4 - \#2 \cdot \#7 - 10 \cdot \#1 \cdot \#8 ) \\
+%   &+ 10^{-12}( \#5 - \#2 \cdot \#8 - 10 \cdot \#1 \cdot \#9 )
+%   + 10^{-16}(     - \#2 \cdot \#9 ).
+%   \end{align*}
+%   The factors of $10$ come from the fact that
+%   $Q_{i} = 10\cdot 10^4 \cdot \#1 + \#2$. As usual, to combine
+%   all the terms, we need to choose some shifts which must ensure
+%   that the number of digits of the second, third, and fourth terms
+%   are each fixed. Here, a good choice is $2\cdot 10^9$.
+%   We are flirting with \TeX{}'s limits once more.
+%
+%   If $\#1=0$, then each term in parentheses (omitting the first)
+%   is in the open interval $(-10^9, 10^4)$. Thus, adding
+%   $2\cdot 10^9$ to it gives a $10$ digits number.\footnote{Bruno:
+%     check that the carry from below does not screw that up. This
+%   requires slightly tighter bounds.}
+%
+%   If $\#1=1$, then $\#2 < 7.8 \cdot 10^4$, and each term
+%   in parentheses (omitting the first) is in the interval
+%   $(-8\cdot 10^8, 10^4)$, and we are even safer.
+%
+%   We add the terms containing $\#1$ in a slightly tricky way
+%   for efficiency reasons: if $\#1=0$, no need to do any computation,
+%   while if $\#1=1$ we want $10$ times some number, simply obtained
+%   by appending a $0$ digit.
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_calc:Nwwnnnnnn 1#1#2; #3;#4#5 #6#7#8#9
+  {
+    1 #1 #2 \exp_after:wN ;
+    \int_use:N \__int_eval:w
+      - 200000 + #3 - #2 * #6
+      \if_meaning:w 1 #1
+        - #6#70
+      \fi:
+      +
+      \exp_after:wN \@@_div_mantissa_calc_last:NNNNNN
+      \int_use:N \__int_eval:w
+        1999800000 + #4 - #2*#7
+        \if_meaning:w 1 #1
+          - #80
+        \fi:
+        +
+        \exp_after:wN \@@_div_mantissa_calc_pack:NNNNNNw
+        \int_use:N \__int_eval:w
+          1999800000 + #5 - #2*#8
+          \if_meaning:w 1 #1
+            - #90
+          \fi:
+          +
+          \exp_after:wN \@@_div_mantissa_calc_pack:NNNNNNw
+          \int_use:N \__int_eval:w 2000000000 - #2*#9 ;
+    {#6}{#7}{#8}{#9}
+  }
+\cs_new:Npn \@@_div_mantissa_calc_pack:NNNNNNw #1#2#3#4#5#6 #7;
+  { #1#2#3#4#5#6 ; {#7} }
+\cs_new:Npn \@@_div_mantissa_calc_last:NNNNNN #1#2#3#4#5#6
+  { #1#2#3#4#5#6 \__int_eval_end: }
+%    \end{macrocode}
+%   \begin{quote}
+%     \cs{@@_div_mantissa_iii:www} \meta{y} |;| \meta{$10^6+{}$Q_1} |;|
+%     ~~\meta{B_1} \meta{B_2} |;| \Arg{B_3} \Arg{B_4}
+%     ~~\Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \meta{sign}
+%   \end{quote}
+%   \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_iii:www #1; #2; #3;
+  {
+    \exp_after:wN \@@_div_mantissa_iii_after:w
+    \int_use:N \__int_eval:w #2
+      \exp_after:wN \@@_div_mantissa_iv:www
+      \__int_value:w #1 \exp_after:wN ;
+      \__int_value:w
+        \exp_after:wN \@@_div_mantissa_calc:Nwwnnnnnn
+        \int_use:N \__int_eval:w #30/#1 + 999999 ;
+        #3 ;
+  }
+%    \end{macrocode}
+%   \begin{quote}
+%     \cs{@@_div_mantissa_iv:www} \meta{y} |;| \meta{$10^6+{}$Q_2} |;|
+%     ~~\meta{C_1} \meta{C_2} |;| \Arg{C_3} \Arg{C_4}
+%     ~~\Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \meta{sign}
+%   \end{quote}
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_iv:www #1; #2; #3;
+  {
+    \exp_after:wN \@@_div_mantissa_pack:NNN
+    \int_use:N \__int_eval:w #2
+      \exp_after:wN \@@_div_mantissa_v:www
+      \__int_value:w #1 \exp_after:wN ;
+      \__int_value:w
+        \exp_after:wN \@@_div_mantissa_calc:Nwwnnnnnn
+        \int_use:N \__int_eval:w #30/#1 + 999999 ;
+        #3 ;
+  }
+%    \end{macrocode}
+%   \begin{quote}
+%     \cs{@@_div_mantissa_v:www} \meta{y} |;| \meta{$10^6+{}$Q_3} |;|
+%     ~~\meta{D_1} \meta{D_2} |;| \Arg{D_3} \Arg{D_4}
+%     ~~\Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \meta{sign}
+%   \end{quote}
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_v:www #1; #2; #3;
+  {
+    \exp_after:wN \@@_div_mantissa_pack:NNN
+    \int_use:N \__int_eval:w #2
+      \exp_after:wN \@@_div_mantissa_vi:wwnnnn
+      \__int_value:w
+        \exp_after:wN \@@_div_mantissa_calc:Nwwnnnnnn
+        \int_use:N \__int_eval:w #30/#1 + 999999 ;
+        #3 ;
+  }
+%    \end{macrocode}
+%   \begin{quote}
+%     \cs{@@_div_mantissa_vi:wwnnnn} \meta{$10^6+{}$Q_4} |;|
+%     ~~\meta{E_1} \meta{E_2} |;| \Arg{E_3} \Arg{E_4}
+%     ~~\Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \meta{sign}
+%   \end{quote}
+%   We compute $P$ by rounding $2 E_{1} E_{2}/Z_{1}Z_{2}$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_vi:wwnnnn #1; #2;#3#4 #5#6
+  {
+    \exp_after:wN \@@_div_mantissa_pack:NNN
+    \int_use:N \__int_eval:w #10
+      \exp_after:wN \@@_div_mantissa_vii:wwnnnnnn
+      \int_use:N \__int_eval:w (\c_two*#2)/#5#6 ; % <- P
+      #2;{#3}{#4}
+      {#5}{#6}
+  }
+%    \end{macrocode}
+%   Note that we used |#10| instead of |#2| which we had previously.
+%   Two reasons: firstly, since we dropped $y$, the argument which
+%   holds $Q_{i}$ has changed, and secondly, we will want the
+%   fourth piece of the result to have $5$ digits, including the
+%   \meta{rounding} digit, which we shall compute now from $P$.
+%   \begin{quote}
+%     \cs{@@_div_mantissa_vii:wwnnnnnn} \meta{P} |;|
+%     ~~\meta{E_1} \meta{E_2} |;| \Arg{E_3} \Arg{E_4}
+%     ~~\Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \meta{sign}
+%   \end{quote}
+%   Then compute $2E-PZ$. Once more, we need to be careful and show
+%   that the calculation $\#1\cdot\#5\#6$ below does not cause an
+%   overflow: naively, $P$ can be up to $35$, and $\#5\#6$ up to
+%   $10^8$, but both cannot happen simultaneously. To show that things
+%   are fine, we split in two (non-disjoint) cases.
+%   \begin{itemize}
+%   \item For small $P$, say, $P< 10$, the product obeys
+%     $P\cdot\#5\#6 < 10^8 \cdot P < 10^9 $.
+%   \item For large $P$, say, $P\geq 3$, the rounding error on $P$,
+%     which is at most $1$, is less than a factor of $2$, hence
+%     $P\leq 4E/Z$, and $P\cdot \#5\#6 \leq 4E\cdot 10^8 < 10^9$.
+%   \end{itemize}
+%   Both inequalities could be made tighter if needed.
+%
+%   Note however that $P\cdot \#7\#8$ may overflow,
+%   since the two factors are now independent, and the result may reach
+%   $3.5\cdot 10^9$.
+%
+%   Also, we add $10\cdot P/2$ to the \enquote{fourth piece} of the result
+%   as a first estimate of $10$ times $E/Z$. The goal is that the last digit
+%   (for now $0$ or $5$) should be the \meta{rounding} digit. More precisely,
+%   it will be corrected later by adding or subtracting $1$ depending on
+%   whether $F$ was the correct integer part, or an overestimate (and nothing
+%   is added when the quotient was exact). This does not give the
+%   \enquote{correct} \meta{rounding} digit, but it always gives a digit
+%   in the right \enquote{class} ($0$, $[1,4]$, $5$, or $[6-9]$), enough
+%   for rounding purposes.
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_vii:wwnnnnnn #1; #2;#3#4 #5#6#7#8
+  {
+    + \c_five * #1
+    \exp_after:wN \@@_div_mantissa_ix:Nww
+    \int_use:N \__int_eval:w -20 + 2*#2 - #1*#5#6 +
+      \exp_after:wN \@@_div_mantissa_viii:NNw
+      \int_use:N \__int_eval:w 199980 + 2*#3 - #1*#7 +
+        \exp_after:wN \@@_div_mantissa_viii:NNw
+        \int_use:N \__int_eval:w 200000 + 2*#4 - #1*#8 ; ;
+  }
+\cs_new:Npn \@@_div_mantissa_viii:NNw #1#2#3; { #1#2 ; + #3 }
+%    \end{macrocode}
+%   \begin{quote}
+%     \cs{@@_div_mantissa_ix:Nww}
+%     ~~\meta{F_1} \meta{F_2} |;| |+| \meta{F_3} |+| \meta{F_4} |;| \meta{sign}
+%   \end{quote}
+%   where $F=2E-PZ$. We only need to know whether it is positive,
+%   negative, or exactly zero.
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_ix:Nww #1#2;#3;
+  {
+    \if_meaning:w 0 #1
+      \exp_after:wN \@@_div_mantissa_x:w
+      \int_use:N \__int_eval:w #3
+    \else:
+      \if_meaning:w - #1
+        -
+      \else:
+        +
+      \fi:
+      \c_one
+    \fi:
+    ;
+  }
+\cs_new:Npn \@@_div_mantissa_x:w #1;
+  {
+    \if_int_compare:w #1 > \c_zero
+      + \c_one
+    \fi:
+    ;
+  }
+%    \end{macrocode}
+%   We now obtain the following code, where \TeX{} is in the process
+%   of expanding each of the integer expressions, and thus expands
+%   the function at the bottom before the ones above it.
+%   \begin{quote}
+%     \cs{@@_div_mantissa_iii_after:w}  $10^6 + Q_{1}$
+%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{2}$
+%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{3}$
+%     \cs{@@_div_mantissa_pack:NNN}
+%     $10^7 + 10\cdot Q_{4} + 5 \cdot P + \varepsilon$ |;| \meta{sign}
+%   \end{quote}
+%   Here, $\varepsilon$ is $0$ in case $2E=PZ$ (\emph{i.e.}, $F=0$),
+%   $1$ in case $2E>PZ$, which means that $P$ was the correct value,
+%   but not with an exact quotient, and $-1$ if $2E<PZ$, \emph{i.e.},
+%   $P$ was an overestimate.
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_pack:NNN 1 #1 #2 { + #1 #2 ; }
+%    \end{macrocode}
+%   Once those have been expanded, we get
+%   \begin{quote}
+%     \cs{@@_div_mantissa_iii_after:w} |1| |0| \meta{5d} |;|
+%     ~~\meta{4d} |;| \meta{4d} |;| \meta{5d} |;| \meta{sign}
+%   \end{quote}
+%   The reason we know that the first two digits are |1| and |0|
+%   is that the final result is known to be between $0.1$ (inclusive)
+%   and $10$, hence $\widetilde{Q_{1}}$ (the tilde denoting the
+%   contribution from the other $Q_{i}$) is at most $99999$,
+%   and $10^6+\widetilde{Q_{1}} = 10\cdots$.
+%
+%   It is now time to round. This depends on how many digits
+%   the final result will have.
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_iii_after:w 10 #1
+  {
+    \if_meaning:w 0 #1
+      \exp_after:wN \@@_div_mantissa_small:wwwNNNNwN
+    \else:
+      \exp_after:wN \@@_div_mantissa_large:wwwNNNNwN
+    \fi:
+    #1
+  }
+%    \end{macrocode}
+%   \begin{quote}
+%     \cs{@@_div_mantissa_small:wwwNNNNwN} |0| \meta{4d} |;|
+%     ~~\meta{4d} |;| \meta{4d} |;| \meta{5d} |;| \meta{sign}
+%   \end{quote}
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_small:wwwNNNNwN
+    0 #1; #2; #3; #4#5#6#7#8; #9
+  {
+    \exp_after:wN \@@_basics_pack_high:NNNNNw
+    \int_use:N \__int_eval:w 1 #1#2
+      \exp_after:wN \@@_basics_pack_low:NNNNNw
+      \int_use:N \__int_eval:w 1 #3#4#5#6#7
+        + \@@_round:NNN #9 #7 #8
+        \exp_after:wN ;
+  }
+%    \end{macrocode}
+%   \begin{quote}
+%     \cs{@@_div_mantissa_large:wwwNNNNwN} \meta{5d} |;|
+%     ~~\meta{4d} |;| \meta{4d} |;| \meta{5d} |;| \meta{sign}
+%   \end{quote}
+%   \footnote{Bruno: rename the \enquote{add mantissa carry pack} function.}
+%    \begin{macrocode}
+\cs_new:Npn \@@_div_mantissa_large:wwwNNNNwN
+    #1; #2; #3; #4#5#6#7#8; #9
+  {
+    + \c_one
+    \exp_after:wN \@@_div_mantissa_large_pack:NNNNNNNNw
+    \int_use:N \__int_eval:w 1 #1 #2 %<- 1+9d
+      \exp_after:wN \@@_add_mantissa_carry_pack_ii:NNNNw
+      \int_use:N \__int_eval:w 1 #3 #4 #5 #6
+        + \@@_round:NNNN #9 #6 #7 #8
+        \exp_after:wN ;
+  }
+\cs_new:Npn \@@_div_mantissa_large_pack:NNNNNNNNw
+    1 #1#2#3#4 #5#6#7#8 #9; { ; {#1#2#3#4} {#5#6#7#8} {#9} }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Unary operations}
+%
+% \begin{macro}{\@@_neg:w}
+%   This function flips the sign of the \meta{floating point}
+%   and expands after it in the input stream, just like
+%   \cs{@@_+_o:ww} etc.
+%    \begin{macrocode}
+\cs_new:Npn \@@_neg:w \s_@@ \@@_chk:w #1 #2
+  {
+    \exp_after:wN \@@_exp_after_o:w
+    \exp_after:wN \s_@@
+    \exp_after:wN \@@_chk:w
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w \c_two - #2 \__int_eval_end:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_abs:w}
+%   This function sets the sign of the \meta{floating point} to be
+%   positive, and expands after itself in the input stream, just like
+%   \cs{@@_neg:w}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_abs:w \s_@@ \@@_chk:w #1 #2
+  { \@@_exp_after_o:w \s_@@ \@@_chk:w #1 0 }
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintChanges
+%
+% \PrintIndex
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-convert.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-convert.dtx
new file mode 100644
index 00000000000..057cef4b176
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-convert.dtx
@@ -0,0 +1,476 @@
+% \iffalse meta-comment
+%
+%% File: l3fp-convert.dtx Copyright(C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp-convert.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Floating-point conversion}
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{^^A
+%   The \textsf{l3fp-convert} package\\ Floating point conversion^^A
+%   \thanks{This file describes v\ExplFileVersion,
+%     last revised \ExplFileDate.}^^A
+% }
+%
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+%
+% \date{Released \ExplFileDate}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% ^^A todo: tests
+% ^^A todo: doc functions
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\texttt{l3fp-convert} implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+% \subsection{Trimming trailing zeros}
+%
+% \begin{macro}[int, EXP]{\@@_trim_zeros:w}
+% \begin{macro}[aux, EXP]
+%   {\@@_trim_zeros_loop:w, \@@_trim_zeros_dot:w, \@@_trim_zeros_end:w}
+%   If |#1| ends with a $0$, the \texttt{loop} auxiliary takes that zero
+%   as an end-delimiter for its first argument, and the second argument
+%   is the same \texttt{loop} auxiliary.  Once the last trailing zero is
+%   reached, the second argument will be the \texttt{dot} auxiliary,
+%   which removes a trailing dot if any.  We then cleanup with the
+%   \texttt{end} auxiliary, keeping only the number.
+%    \begin{macrocode}
+\cs_new:Npn \@@_trim_zeros:w #1 ;
+  {
+    \@@_trim_zeros_loop:w #1
+      ; \@@_trim_zeros_loop:w 0; \@@_trim_zeros_dot:w .; \s__stop
+  }
+\cs_new:Npn \@@_trim_zeros_loop:w #1 0; #2 { #2 #1 ; #2 }
+\cs_new:Npn \@@_trim_zeros_dot:w #1 .; { \@@_trim_zeros_end:w #1 ; }
+\cs_new:Npn \@@_trim_zeros_end:w #1 ; #2 \s__stop { #1 }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Scientific notation}
+%
+% \begin{variable}{\c_@@_scientific_inf_tl}
+%   Result of converting $\infty$ to a scientific representation: after
+%   triggering an \enquote{invalid operation} exception,
+%   \cs{fp_to_scientific:n} yields that result, larger than any finite
+%   floating point number.
+%    \begin{macrocode}
+\tl_const:Nx \c_@@_scientific_inf_tl
+  { 1e \int_use:N \c_@@_max_exponent_int }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}
+%   {\fp_to_scientific:N, \fp_to_scientific:c, \fp_to_scientific:n}
+%   The three public functions evaluate their argument, then pass it to
+%   \cs{@@_to_scientific:w}.
+%    \begin{macrocode}
+\cs_new:Npn \fp_to_scientific:N #1 { \exp_after:wN \@@_to_scientific:w #1 }
+\cs_generate_variant:Nn \fp_to_scientific:N { c }
+\cs_new:Npn \fp_to_scientific:n #1
+  {
+    \exp_after:wN \@@_to_scientific:w
+    \tex_romannumeral:D -`0 \@@_parse:n {#1}
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_to_scientific:w,
+%     \@@_to_scientific_normal:wnnnnn,
+%     \@@_to_scientific_normal:wNw
+%   }
+%   Expressing an internal floating point number in scientific notation
+%   is quite easy: no rounding, and the format is very well defined.
+%   First cater for the sign: negative numbers (|#2=2|) start with |-|.
+%   Then filter the special cases: we insert \cs{prg_do_nothing:}
+%   because \cs{@@_invalid_operation:Nnw} expands after taking one
+%   floating point argument.  In the normal case, decrement the exponent
+%   and unbrace the $4$ brace groups, then in a second step grab the
+%   first digit (previously hidden in braces) to order the various parts
+%   correctly.  Finally trim zeros.
+%    \begin{macrocode}
+\cs_new:Npn \@@_to_scientific:w \s_@@ \@@_chk:w #1#2#3 ;
+  {
+    \if_meaning:w 2 #2 \exp_after:wN - \tex_romannumeral:D -`0 \fi:
+    \if_case:w #1 \exp_stop_f:
+         \@@_case_return:nw { \exp_after:wN 0 }
+    \or: \exp_after:wN \@@_to_scientific_normal:wnnnnn
+    \or:
+      \@@_case_use:nw
+        {
+          \@@_invalid_operation:Nnw
+            \c_@@_scientific_inf_tl { fp_to_scientific }
+        }
+    \or:
+      \@@_case_use:nw
+        { \@@_invalid_operation:Nnw 0 { fp_to_scientific } }
+    \fi:
+    \s_@@ \@@_chk:w #1 #2 #3 ; \prg_do_nothing:
+  }
+\cs_new:Npn \@@_to_scientific_normal:wnnnnn
+    \s_@@ \@@_chk:w 1 #1 #2 #3#4#5#6 ; \prg_do_nothing:
+  {
+    \if_int_compare:w #2 = \c_one
+      \exp_after:wN \@@_to_scientific_normal:wNw
+    \else:
+      \exp_after:wN \@@_to_scientific_normal:wNw
+      \exp_after:wN e
+      \int_use:N \__int_eval:w #2 - \c_one
+    \fi:
+    ; #3 #4 #5 #6 ;
+  }
+\cs_new:Npn \@@_to_scientific_normal:wNw #1 ; #2#3;
+  { \@@_trim_zeros:w #2.#3 ; #1 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Decimal representation}
+%
+% \begin{variable}{\c_@@_decimal_inf_tl}
+%   Result of converting $\infty$ to a decimal representation: after
+%   triggering an \enquote{invalid operation} exception,
+%   \cs{fp_to_decimal:n} yields a~$1$ followed by $\ExplSyntaxOn
+%   \int_use:N \c__fp_max_exponent_int$~$0$, larger than any finite
+%   floating point number.  Since the expanded token list is very long,
+%   we use an \texttt{n}-type assignment.
+%    \begin{macrocode}
+\tl_const:Nn \c_@@_decimal_inf_tl
+  {
+    \exp_after:wN \exp_after:wN \exp_after:wN 1
+    \prg_replicate:nn \c_@@_max_exponent_int 0
+  }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}[EXP]
+%   {\fp_to_decimal:N, \fp_to_decimal:c, \fp_to_decimal:n}
+%   All three public variants are based on the same \cs{@@_to_decimal:w}
+%   after evaluating their argument to an internal floating point.
+%    \begin{macrocode}
+\cs_new:Npn \fp_to_decimal:N #1 { \exp_after:wN \@@_to_decimal:w #1 }
+\cs_generate_variant:Nn \fp_to_decimal:N { c }
+\cs_new_nopar:Npn \fp_to_decimal:n
+  {
+    \exp_after:wN \@@_to_decimal:w
+    \tex_romannumeral:D -`0 \@@_parse:n
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP, aux]
+%   {
+%     \@@_to_decimal:w,
+%     \@@_to_decimal_normal:wnnnnn,
+%     \@@_to_decimal_large:Nnnw,
+%     \@@_to_decimal_huge:wnnnn,
+%   }
+%   The structure is similar to \cs{@@_to_scientific:w}.  Insert |-| for
+%   negative numbers.  Zero gives $0$, $\pm\infty$ and \nan{} yield an
+%   \enquote{invalid operation} exception.  Normal numbers with an
+%   exponent in the range $[1,15]$ have that number of digits before the
+%   decimal separator: \enquote{decimate} them, and remove leading zeros
+%   with \cs{__int_value:w}, then trim trailing zeros and dot.  Normal
+%   numbers with an exponent $16$ or larger have no decimal separator,
+%   we only need to add trailing zeros.  When the exponent is
+%   non-positive, the result should be $0.\meta{zeros}\meta{digits}$,
+%   trimmed.
+%    \begin{macrocode}
+\cs_new:Npn \@@_to_decimal:w \s_@@ \@@_chk:w #1#2#3 ;
+  {
+    \if_meaning:w 2 #2 \exp_after:wN - \tex_romannumeral:D -`0 \fi:
+    \if_case:w #1 \exp_stop_f:
+         \@@_case_return:nw { \exp_after:wN 0 }
+    \or: \exp_after:wN \@@_to_decimal_normal:wnnnnn
+    \or:
+      \@@_case_use:nw
+        {
+          \@@_invalid_operation:Nnw
+            \c_@@_decimal_inf_tl { fp_to_decimal }
+        }
+    \or:
+      \@@_case_use:nw
+        { \@@_invalid_operation:Nnw 0 { fp_to_decimal } }
+    \fi:
+    \s_@@ \@@_chk:w #1 #2 #3 ; \prg_do_nothing:
+  }
+\cs_new:Npn \@@_to_decimal_normal:wnnnnn
+    \s_@@ \@@_chk:w 1 #1 #2 #3#4#5#6 ; \prg_do_nothing:
+  {
+    \int_compare:nNnTF {#2} > \c_zero
+      {
+        \int_compare:nNnTF {#2} < \c_sixteen
+          {
+            \@@_decimate:nNnnnn { \c_sixteen - #2 }
+              \@@_to_decimal_large:Nnnw
+          }
+          {
+            \exp_after:wN \exp_after:wN
+            \exp_after:wN \@@_to_decimal_huge:wnnnn
+            \prg_replicate:nn { #2 - \c_sixteen } { 0 } ;
+          }
+        {#3} {#4} {#5} {#6}
+      }
+      {
+        \exp_after:wN \@@_trim_zeros:w
+        \exp_after:wN 0
+        \exp_after:wN .
+        \tex_romannumeral:D -`0 \prg_replicate:nn { - #2 } { 0 }
+        #3#4#5#6 ;
+      }
+  }
+\cs_new:Npn \@@_to_decimal_large:Nnnw #1#2#3#4;
+  {
+    \exp_after:wN \@@_trim_zeros:w \__int_value:w
+      \if_int_compare:w #2 > \c_zero
+        #2
+      \fi:
+      \exp_stop_f:
+      #3.#4 ;
+  }
+\cs_new:Npn \@@_to_decimal_huge:wnnnn #1; #2#3#4#5 { #2#3#4#5 #1 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Token list representation}
+%
+% \begin{macro}[EXP]{\fp_to_tl:N, \fp_to_tl:c, \fp_to_tl:n}
+%   These three public functions evaluate their argument, then pass it
+%   to \cs{@@_to_tl:w}.
+%    \begin{macrocode}
+\cs_new:Npn \fp_to_tl:N #1 { \exp_after:wN \@@_to_tl:w #1 }
+\cs_generate_variant:Nn \fp_to_tl:N { c }
+\cs_new_nopar:Npn \fp_to_tl:n
+  {
+    \exp_after:wN \@@_to_tl:w
+    \tex_romannumeral:D -`0 \@@_parse:n
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP, aux]{\@@_to_tl:w, \@@_to_tl_normal:nnnnn}
+%   A structure similar to \cs{@@_to_scientific:w} and
+%   \cs{@@_to_decimal:w}, but without the \enquote{invalid operation}
+%   exception.  First filter special cases.  We express normal numbers
+%   in decimal notation if the exponent is in the range $[-2,16]$, and
+%   otherwise use scientific notation.  The weird \cs{prg_do_nothing:}
+%   is needed because the \texttt{decimal} and \texttt{scientific}
+%   auxiliaries we use expect it.
+%    \begin{macrocode}
+\cs_new:Npn \@@_to_tl:w \s_@@ \@@_chk:w #1#2
+  {
+    \if_meaning:w 2 #2 \exp_after:wN - \tex_romannumeral:D -`0 \fi:
+    \if_case:w #1 \exp_stop_f:
+           \@@_case_return:nw { 0 }
+    \or:   \exp_after:wN \@@_to_tl_normal:nnnnn
+    \or:   \@@_case_return:nw { inf }
+    \else: \@@_case_return:nw { nan }
+    \fi:
+  }
+\cs_new:Npn \@@_to_tl_normal:nnnnn #1#2 ;
+  {
+    \if_int_compare:w #1 > \c_sixteen
+      \exp_after:wN \@@_to_scientific_normal:wnnnnn
+    \else:
+      \if_int_compare:w #1 < - \c_two
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_to_scientific_normal:wnnnnn
+      \else:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_to_decimal_normal:wnnnnn
+      \fi:
+    \fi:
+    \s_@@ \@@_chk:w 1 0 {#1} #2 ; \prg_do_nothing:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Formatting}
+%
+% ^^A todo
+%
+% \subsection{Convert to dimension or integer}
+%
+% \begin{macro}[EXP]{\fp_to_dim:N, \fp_to_dim:c, \fp_to_dim:n}
+%   These three public functions rely on \cs{fp_to_decimal:n}
+%   internally.
+%    \begin{macrocode}
+\cs_new:Npn \fp_to_dim:N #1 { \fp_to_decimal:N #1 pt }
+\cs_generate_variant:Nn \fp_to_dim:N { c }
+\cs_new:Npn \fp_to_dim:n #1 { \fp_to_decimal:n {#1} pt }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\fp_to_int:N, \fp_to_int:c, \fp_to_int:n}
+%   These three public functions evaluate their argument, then pass it
+%   to \cs{fp_to_int:w}.
+%    \begin{macrocode}
+\cs_new:Npn \fp_to_int:N #1 { \exp_after:wN \@@_to_int:w #1 }
+\cs_generate_variant:Nn \fp_to_int:N { c }
+\cs_new_nopar:Npn \fp_to_int:n
+  {
+    \exp_after:wN \@@_to_int:w
+    \tex_romannumeral:D -`0 \@@_parse:n
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_to_int:w}
+%   To convert to an integer, first round to $0$ places (to the nearest
+%   integer), then express the result as a decimal number: the
+%   definition of \cs{@@_to_decimal:w} is such that there will be no
+%   trailing dot nor zero.
+%    \begin{macrocode}
+\cs_new:Npn \@@_to_int:w #1;
+  {
+    \exp_after:wN \@@_to_decimal:w \tex_romannumeral:D -`0
+    \@@_round:Nwn \@@_round_to_nearest:NNN #1; { 0 } \prg_do_nothing:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Convert from a dimension}
+%
+% \begin{macro}[EXP]{\dim_to_fp:n}
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_from_dim_test:N,
+%     \@@_from_dim:Nw,
+%     \@@_from_dim_ii:wNNnnnnnn,
+%     \@@_from_dim_iii:wnnnnwN,
+%   }
+%   The dimension expression (which can in fact be a glue expression)
+%   is evaluated, converted to a number (\emph{i.e.}, expressed in
+%   scaled points), then multiplied by $2^{-16} = 0.0000152587890625$
+%   to give a value expressed in points. We use the auxiliary function
+%   \begin{quote}
+%     \cs{@@_mul_npos:Nnwnw} \meta{sign} \newline
+%     ~~\Arg{exp_1}  \meta{body_1} |;| \Arg{exp_2} \meta{body_2} |;|
+%   \end{quote}
+%    \begin{macrocode}
+\cs_new:Npn \dim_to_fp:n #1
+  {
+    \exp_after:wN \@@_from_dim_test:N
+    \__int_value:w \etex_glueexpr:D #1 ;
+  }
+\cs_new:Npn \@@_from_dim_test:N #1
+  {
+    \if_meaning:w 0 #1
+      \exp_after:wN \@@_use_i_until_s:nw
+      \exp_after:wN \c_zero_fp
+    \else:
+      \if_meaning:w - #1
+        \exp_after:wN \@@_from_dim:Nw
+        \exp_after:wN 2
+        \__int_value:w
+      \else:
+        \exp_after:wN \@@_from_dim:Nw
+        \exp_after:wN 0
+        \__int_value:w #1
+      \fi:
+    \fi:
+  }
+\cs_new:Npn \@@_from_dim:Nw #1 #2;
+  {
+    \@@_pack_twice_four:wNNNNNNNN \@@_from_dim_ii:wNNnnnnnn ;
+    #2 000 0000 00 {10}987654321; #1
+  }
+\cs_new:Npn \@@_from_dim_ii:wNNnnnnnn #1; #2#3#4#5#6#7#8#9
+  { \@@_from_dim_iii:wnnnnwN #1 {#2#300} {0000} ; }
+\cs_new:Npn \@@_from_dim_iii:wnnnnwN #1; #2#3#4#5#6; #7
+  {
+    \@@_mul_npos:Nnwnw #7 {#5} #1 ;
+    {-4} {1525} {8789} {0625} {0000} ;
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Use and eval}
+%
+% \begin{macro}[EXP]{\fp_use:N, \fp_use:c, \fp_eval:n}
+%   Those public functions are simple copies of the decimal conversions.
+%    \begin{macrocode}
+\cs_new_eq:NN \fp_use:N \fp_to_decimal:N
+\cs_generate_variant:Nn \fp_use:N { c }
+\cs_new_eq:NN \fp_eval:n \fp_to_decimal:n
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\fp_abs:n}
+%   Trivial but useful.
+%    \begin{macrocode}
+\cs_new:Npn \fp_abs:n #1 { \fp_to_decimal:n { abs ( #1 ) } }
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintChanges
+%
+% \PrintIndex
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx
new file mode 100644
index 00000000000..edf9ac2ad35
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx
@@ -0,0 +1,1252 @@
+% \iffalse meta-comment
+%
+%% File: l3fp-expo.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp-expo.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Floating-point exponential-related functions}
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{The \textsf{l3fp-expo} package\thanks{This file
+%         has version number \ExplFileVersion, last
+%         revised \ExplFileDate.}\\
+% Floating point exponential-related functions}
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+% \date{Released \ExplFileDate}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3fp-expo} implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+% \subsection{General comments}
+%
+%^^A todo: redoc
+% The algorithm for computing the logarithm of the significand could be
+% made to use a $5$ terms Taylor series instead of $10$ terms by taking
+% $c = 2000/(\lfloor 200x\rfloor +1) \in [10,95]$ instead of $c\in
+% [1,10]$.  Also, it would then be possible to simplify the computation
+% of $t$, using methods similar to \cs{@@_fixed_div_to_float:ww}.
+% However, we would then have to hard-code the logarithms of $44$ small
+% integers instead of $9$.
+%
+% \subsection{Some constants}
+%
+% ^^A todo: very odd: can I delete ln_ten?
+% \begin{variable}
+%   {
+%     \c_@@_ln_i_fixed_tl ,
+%     \c_@@_ln_ii_fixed_tl ,
+%     \c_@@_ln_iii_fixed_tl ,
+%     \c_@@_ln_iv_fixed_tl ,
+%     \c_@@_ln_vi_fixed_tl ,
+%     \c_@@_ln_vii_fixed_tl ,
+%     \c_@@_ln_viii_fixed_tl ,
+%     \c_@@_ln_ix_fixed_tl ,
+%     \c_@@_ln_x_fixed_tl,
+%     \c_@@_ln_ten_fixed_tl,
+%   }
+%   A few values of the logarithm which are needed in the
+%   implementation.  It turns out that we don't need the value of
+%   $\log(5)$.
+%    \begin{macrocode}
+\tl_const:Nn \c_@@_ln_i_fixed_tl   { {0000}{0000}{0000}{0000}{0000}{0000} }
+\tl_const:Nn \c_@@_ln_ii_fixed_tl  { {6931}{4718}{0559}{9453}{0941}{7232} }
+\tl_const:Nn \c_@@_ln_iii_fixed_tl {{10986}{1228}{8668}{1096}{9139}{5245} }
+\tl_const:Nn \c_@@_ln_iv_fixed_tl  {{13862}{9436}{1119}{8906}{1883}{4464} }
+ % \tl_const:Nn \c_@@_ln_v_fixed_tl   {{16094}{3791}{2434}{1003}{7460}{0759} }
+\tl_const:Nn \c_@@_ln_vi_fixed_tl  {{17917}{5946}{9228}{0550}{0081}{2477} }
+\tl_const:Nn \c_@@_ln_vii_fixed_tl {{19459}{1014}{9055}{3133}{0510}{5353} }
+\tl_const:Nn \c_@@_ln_viii_fixed_tl{{20794}{4154}{1679}{8359}{2825}{1696} }
+\tl_const:Nn \c_@@_ln_ix_fixed_tl  {{21972}{2457}{7336}{2193}{8279}{0490} }
+\tl_const:Nn \c_@@_ln_x_fixed_tl   {{23025}{8509}{2994}{0456}{8401}{7991} }
+ %\tl_const:Nn \c_@@_ln_ten_fixed_tl {{23025}{8509}{2994}{0456}{8401}{7991} }
+%    \end{macrocode}
+% \end{variable}
+%
+% \subsection{Logarithm}
+%
+% \subsubsection{Sign, exponent, and special numbers}
+%
+% \begin{macro}[EXP]{\@@_ln:w}
+%   The logarithm of $\pm 0$ is $-\infty$, raising a division by zero
+%   exception.  The logarithm of negative numbers (including $-\infty$,
+%   but not $-0$) raises the \enquote{invalid} exception.  The logarithm
+%   of $+\infty$ or a \texttt{nan} is itself.  Positive normal numbers
+%   call \cs{@@_ln_npos:w}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_ln:w \s_@@ \@@_chk:w #1 #2
+  {
+    \if_meaning:w 0 #1
+      \@@_case_use:nw
+        { \@@_division_by_zero:Nnw \c_minus_inf_fp { ln } }
+    \fi:
+    \if_meaning:w 2 #2
+      \@@_case_use:nw
+        { \@@_invalid_operation:Nnw \c_nan_fp { ln } }
+    \fi:
+    \if_meaning:w 1 #1 \else:
+      \@@_case_return_same_o:w
+    \fi:
+    \@@_ln_npos:w \s_@@ \@@_chk:w #1#2
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Absolute ln}
+%
+% We are given a positive normal number, of the form $a\cdot 10^{b}$
+% with $a\in[0.1,1)$.  To compute its logarithm, we find a small integer
+% $5\leq c < 50$ such that $0.91 \leq a c / 5 < 1.1$, and use the
+% relation
+% \[
+% \ln (a \cdot 10^b) = b \cdot \ln (10) - \ln (c/5) + \ln (ac/5).
+% \]
+% The logarithms $\ln(10)$ and $\ln(c/5)$ are looked up in a table.  The
+% last term is computed using the following Talor series of $\ln$ near
+% $1$:
+% \[
+% \ln\left(\frac{ac}{5}\right)
+% = \ln\left(\frac{1+t}{1-t}\right)
+% = 2t\left(1 + t^2 \left(\frac{1}{3} + t^2 \left(\frac{1}{5}
+%       + t^2 \left(\frac{1}{7} + t^2 \left( \frac{1}{9} + \cdots
+%         \right)\right)\right)\right)\right)
+% \]
+% where $t=1-10/(ac+5)$.  We can now see one reason for the choice of
+% $ac\sim 5$: then $ac+5=10(1-\epsilon)$ with $-0.05<\epsilon\leq
+% 0.045$, hence
+% \[
+% t = \frac{\epsilon}{1-\epsilon}
+% = \epsilon (1+\epsilon)(1+\epsilon^2)(1+\epsilon^4)\ldots,
+% \]
+% is not too difficult to compute.
+%
+% \begin{macro}{\@@_ln_npos:w}
+%   We catch the case of a significand very close to $0.1$ or to $1$.
+%   In all other cases, the final result is at least $10^{-4}$, and
+%   then an error of $0.5\cdot 10^{-20}$ is acceptable.
+%    \begin{macrocode}
+\cs_new:Npn \@@_ln_npos:w \s_@@ \@@_chk:w 10#1#2#3;
+  { %^^A todo: ln(1) should be "exact zero", not "underflow"
+    \exp_after:wN \@@_sanitize:Nw
+    \__int_value:w % for the overall sign
+      \if_int_compare:w #1 < \c_one
+        2
+      \else:
+        0
+      \fi:
+      \exp_after:wN \exp_stop_f:
+      \int_use:N \__int_eval:w % for the exponent
+        \@@_ln_significand:NNNNnnnN #2#3
+        \@@_ln_exponent:wn {#1}
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_ln_significand:NNNNnnnN}
+%   \begin{syntax}
+%     \cs{@@_ln_significand:NNNNnnnN} \meta{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \meta{continuation}
+%   \end{syntax}
+%   This function expands to
+%   \begin{quote}
+%     \meta{continuation} \Arg{Y_1} \Arg{Y_2} \Arg{Y_3} \Arg{Y_4} \Arg{Y_5} \Arg{Y_6} |;|
+%   \end{quote}
+%   where $Y = - \log X$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_ln_significand:NNNNnnnN #1#2#3#4
+  {
+    \exp_after:wN \@@_ln_x_ii:wnnnn
+    \__int_value:w
+      \if_case:w #1 \exp_stop_f:
+      \or:
+        \if_int_compare:w #2 < \c_four
+          \__int_eval:w \c_ten - #2
+        \else:
+          6
+        \fi:
+      \or: 4
+      \or: 3
+      \or: 2
+      \or: 2
+      \or: 2
+      \else: 1
+      \fi:
+    ; { #1 #2 #3 #4 }
+  }
+%    \end{macrocode}
+%   We have thus found $c$. It is chosen such that $0.7\leq ac < 1.4$
+%   in all cases. Compute $ 1 + x = 1 + ac \in [1.7,2.4)$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_ln_x_ii:wnnnn #1; #2#3#4#5
+  {
+    \exp_after:wN \@@_ln_div_after:Nw
+    \cs:w c_@@_ln_ \tex_romannumeral:D #1 _fixed_tl \exp_after:wN \cs_end:
+    \__int_value:w
+      \exp_after:wN \@@_ln_x_iv:nnnnnnnn
+      \tex_romannumeral:D -`0
+        \exp_after:wN \@@_ln_x_iii_var:NNNNNw
+        \int_use:N \__int_eval:w 9999 9999 + #1*#2#3 +
+          \exp_after:wN \@@_ln_x_iii:NNNNNw
+          \int_use:N \__int_eval:w 1 0000 0000 + #1*#4#5 ;
+    {20000} {0000} {0000} {0000}
+  } %^^A todo: reoptimize (a generalization attempt failed).
+\cs_new:Npn \@@_ln_x_iii:NNNNNw #1 #2#3#4#5 #6; { #1; {#2#3#4#5} {#6} }
+\cs_new:Npn \@@_ln_x_iii_var:NNNNNw #1 #2#3#4#5 #6; { {#1#2#3#4#5} {#6} }
+%    \end{macrocode}
+%   The Taylor series will be expressed in terms of
+%   $t = (x-1)/(x+1) = 1 - 2/(x+1)$. We now compute the
+%   quotient with extended precision, reusing some code
+%   from \cs{@@_/_o:ww}. Note that $1+x$ is known exactly.
+%
+%   To reuse notations from \pkg{l3fp-basics}, we want to
+%   compute $ A / Z $ with $ A = 2 $ and $ Z = x + 1 $.
+%   In \pkg{l3fp-basics}, we considered the case where
+%   both $A$ and $Z$ are arbitrary, in the range $[0.1,1)$,
+%   and we had to monitor the growth of the sequence of
+%   remainders $A$, $B$, $C$, etc. to ensure that no overflow
+%   occured during the computation of the next quotient.
+%   The main source of risk was our choice to define the
+%   quotient as roughly $10^9 \cdot A / 10^5 \cdot Z$: then
+%   $A$ was bound to be below $2.147\cdots$, and this limit
+%   was never far.
+%
+%   In our case, we can simply work with $10^8 \cdot A$ and
+%   $10^4 \cdot Z$, because our reason to work with higher
+%   powers has gone: we needed the integer $y \simeq 10^5 \cdot Z$
+%   to be at least $10^4$, and now, the definition
+%   $y \simeq 10^4 \cdot Z$ suffices.
+%
+%   Let us thus define $y = \left\lfloor 10^4 \cdot Z \right\rfloor + 1
+%   \in ( 1.7 \cdot 10^4, 2.4 \cdot 10^4 ] $, and
+%   \[
+%   Q_{1}
+%   =
+%   \left\lfloor
+%     \frac {\left\lfloor 10^8 \cdot A\right\rfloor} {y} - \frac{1}{2}
+%   \right\rfloor.
+%   \]
+%   (The $1/2$ comes from how e\TeX{} rounds.) As for division, it is
+%   easy to see that $Q_{1} \leq 10^4 A / Z$, \emph{i.e.}, $Q_{1}$
+%   is an underestimate.
+%
+%   Exactly as we did for division, we set $B = 10^4 A - Q_{1}Z$. Then
+%   \begin{align*}
+%     10^4 B
+%     \leq
+%     A_{1}A_{2}.A_{3}A_{4}
+%     - \left( \frac{A_{1}A_{2}}{y} - \frac{3}{2} \right) 10^4 Z
+%     \leq
+%     A_{1}A_{2} \left( 1 - \frac{10^4 Z}{y} \right) + 1 + \frac{3}{2} y
+%     \leq
+%     10^8 \frac{A}{y} + 1 + \frac{3}{2} y
+%   \end{align*}
+%   In the same way, and using $1.7\cdot 10^4\leq y\leq 2.4\cdot 10^4$,
+%   and convexity, we get
+%   \begin{align*}
+%     10^4 A &= 2\cdot 10^4 \\
+%     10^4 B &\leq 10^8 \frac{A}{y} + 1.6 y \leq 4.7\cdot 10^4\\
+%     10^4 C &\leq 10^8 \frac{B}{y} + 1.6 y \leq 5.8\cdot 10^4\\
+%     10^4 D &\leq 10^8 \frac{C}{y} + 1.6 y \leq 6.3\cdot 10^4\\
+%     10^4 E &\leq 10^8 \frac{D}{y} + 1.6 y \leq 6.5\cdot 10^4\\
+%     10^4 F &\leq 10^8 \frac{E}{y} + 1.6 y \leq 6.6\cdot 10^4\\
+%   \end{align*}
+%   Note that we compute more steps than for division: since $t$ is
+%   not the end result, we need to know it with more accuracy
+%   (on the other hand, the ending is much simpler, as we don't
+%   need an exact rounding for transcendental functions, but just
+%   a faithful rounding).\footnote{Bruno: to be completed.}
+%
+%   \begin{quote}
+%     \cs{@@_ln_x_iv:NNNNNwnn}
+%     \meta{1 or 2} \meta{8d} |;| \Arg{4d} \Arg{4d} \meta{fixed-tl}
+%   \end{quote}
+%   The number is $x$. Compute $y$ by adding 1 to the five first digits.
+%    \begin{macrocode}
+\cs_new:Npn \@@_ln_x_iv:nnnnnnnn #1#2#3#4 #5#6#7#8
+  {
+    \exp_after:wN \@@_ln_div_i:w
+    \int_use:N \__int_eval:w #1 + \c_one ;
+    #5 #6 ; {#7} {#8}
+    {#1} {#2} {#3} {#4}
+  }
+\cs_new:Npn \@@_ln_div_i:w #1;
+  {
+    \exp_after:wN \@@_ln_div_ii:www
+    \__int_value:w #1 \exp_after:wN ;
+    \__int_value:w
+      \exp_after:wN \@@_div_mantissa_calc:Nwwnnnnnn
+      \int_use:N \__int_eval:w 999999 + 2 0000 0000 / #1 ; % Q1
+  }
+\cs_set_protected:Npn \@@_tmp:w #1#2
+  {
+    \cs_new:Npn #1 ##1; ##2; ##3; % y; Q1; B1B2; <- for k=1
+      {
+        \exp_after:wN \@@_div_mantissa_pack:NNN
+        \int_use:N \__int_eval:w ##2
+          \exp_after:wN #2
+          \__int_value:w ##1 \exp_after:wN ;
+          \__int_value:w
+            \exp_after:wN \@@_div_mantissa_calc:Nwwnnnnnn
+            \int_use:N \__int_eval:w 999999 + ##3 / ##1 ; % Q2
+            ##3 ;
+      }
+  }
+\@@_tmp:w \@@_ln_div_ii:www \@@_ln_div_iii:www
+\@@_tmp:w \@@_ln_div_iii:www \@@_ln_div_iv:www
+\@@_tmp:w \@@_ln_div_iv:www \@@_ln_div_v:www
+\@@_tmp:w \@@_ln_div_v:www \@@_ln_div_vi:www
+\cs_new:Npn \@@_ln_div_vi:www #1; #2; #3;#4#5 #6#7#8#9 %y;Q5;F1F2;F3F4x1x2x3x4
+  {
+    \exp_after:wN \@@_div_mantissa_pack:NNN
+    \int_use:N \__int_eval:w #2
+      \exp_after:wN \@@_div_mantissa_pack:NNN
+      \int_use:N \__int_eval:w 1000000 + #3 / #1 ; % Q6
+  }
+%    \end{macrocode}
+%   We now have essentially\footnote{Bruno: add a mention that
+%     the error on $Q_{6}$ is bounded by $10$ (probably $6.7$),
+%     and thus corresponds to an error of $10^{-23}$ on the final
+%     result, small enough in all cases.}
+%   \begin{quote}
+%     \cs{@@_ln_div_after:Nw} \meta{fixed tl}
+%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{1}$
+%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{2}$
+%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{3}$
+%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{4}$
+%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{5}$
+%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{6}$ |;|
+%     \meta{exponent} |;| \meta{continuation}
+%   \end{quote}
+%   where \meta{fixed tl} holds the logarithm of a number
+%   in $[1,10]$, and \meta{exponent} is
+%   the exponent. Also, the expansion is done backwards. Then
+%   \cs{@@_div_mantissa_pack:NNN} puts things in the
+%   correct order to add the $Q_{i}$ together and put semicolons
+%   between each piece. Once those have been expanded, we get
+%   \begin{quote}
+%     \cs{@@_ln_div_after:Nw} \meta{fixed-tl} \meta{1d} |;| \meta{4d} |;| \meta{4d} |;| \meta{4d} |;| \meta{4d} |;| \meta{4d} |;| \meta{4d} |;| \meta{exponent} |;|
+%   \end{quote}
+%   ^^A todo: redoc.
+%   Just as with division, we know that the first two digits
+%   are |1| and |0| because of bounds on the final result of
+%   the division $2/(x+1)$, which is between roughly $0.8$ and $1.2$.
+%   We then compute $1-2/(x+1)$, after testing whether $2/(x+1)$ is
+%   greater than or smaller than $1$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_ln_div_after:Nw #1#2;
+  {
+    \if_meaning:w 0 #2
+      \exp_after:wN \@@_ln_t_small:Nw
+    \else:
+      \exp_after:wN \@@_ln_t_large:NNw
+      \exp_after:wN -
+    \fi:
+    #1
+  }
+\cs_new:Npn \@@_ln_t_small:Nw #1 #2; #3; #4; #5; #6; #7;
+  {
+    \exp_after:wN \@@_ln_t_large:NNw
+    \exp_after:wN + % <sign>
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w 9999 - #2 \exp_after:wN ;
+    \int_use:N \__int_eval:w 9999 - #3 \exp_after:wN ;
+    \int_use:N \__int_eval:w 9999 - #4 \exp_after:wN ;
+    \int_use:N \__int_eval:w 9999 - #5 \exp_after:wN ;
+    \int_use:N \__int_eval:w 9999 - #6 \exp_after:wN ;
+    \int_use:N \__int_eval:w 1 0000 - #7 ;
+  }
+%    \end{macrocode}
+%
+%   \begin{quote}
+%     \cs{@@_ln_t_large:NNw} \meta{sign}\meta{fixed tl}  \meta{t_1}|;| \meta{t_2} |;| \meta{t_3}|;| \meta{t_4}|;| \meta{t_5} |;| \meta{t_6}|;| \meta{exponent} |;| \meta{continuation}
+%   \end{quote}
+%   Compute the square $|t|^2$, and keep $|t|$ at the end with its
+%   sign. We know that $|t|<0.1765$, so every piece has at most $4$
+%   digits. However, since we were not careful in \cs{@@_ln_t_small:w},
+%   they can have less than $4$ digits.
+%    \begin{macrocode}
+\cs_new:Npn \@@_ln_t_large:NNw #1 #2 #3; #4; #5; #6; #7; #8;
+  {
+    \exp_after:wN \@@_ln_square_t_after:w
+    \int_use:N \__int_eval:w 9999 0000 + #3*#3
+      \exp_after:wN \@@_ln_square_t_pack:NNNNNw
+      \int_use:N \__int_eval:w 9999 0000 + 2*#3*#4
+        \exp_after:wN \@@_ln_square_t_pack:NNNNNw
+        \int_use:N \__int_eval:w 9999 0000 + 2*#3*#5 + #4*#4
+          \exp_after:wN \@@_ln_square_t_pack:NNNNNw
+          \int_use:N \__int_eval:w 9999 0000 + 2*#3*#6 + 2*#4*#5
+            \exp_after:wN \@@_ln_square_t_pack:NNNNNw
+            \int_use:N \__int_eval:w 1 0000 0000 + 2*#3*#7 + 2*#4*#6 + #5*#5
+              + (2*#3*#8 + 2*#4*#7 + 2*#5*#6) / 1 0000
+              % ; ; ;
+    \exp_after:wN \@@_ln_twice_t_after:w
+    \int_use:N \__int_eval:w -1 + 2*#3
+      \exp_after:wN \@@_ln_twice_t_pack:Nw
+      \int_use:N \__int_eval:w 9999 + 2*#4
+        \exp_after:wN \@@_ln_twice_t_pack:Nw
+        \int_use:N \__int_eval:w 9999 + 2*#5
+          \exp_after:wN \@@_ln_twice_t_pack:Nw
+          \int_use:N \__int_eval:w 9999 + 2*#6
+            \exp_after:wN \@@_ln_twice_t_pack:Nw
+            \int_use:N \__int_eval:w 9999 + 2*#7
+              \exp_after:wN \@@_ln_twice_t_pack:Nw
+              \int_use:N \__int_eval:w 10000 + 2*#8 ; ;
+    { \@@_ln_c:NwNw #1 }
+    #2
+  }
+\cs_new:Npn \@@_ln_twice_t_pack:Nw #1 #2; { + #1 ; {#2} }
+\cs_new:Npn \@@_ln_twice_t_after:w #1; { ;;; {#1} }
+\cs_new:Npn \@@_ln_square_t_pack:NNNNNw #1 #2#3#4#5 #6;
+  { + #1#2#3#4#5 ; {#6} }
+\cs_new:Npn \@@_ln_square_t_after:w 1 0 #1#2#3 #4;
+  { \@@_ln_Taylor:wwNw {0#1#2#3} {#4} }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_ln_Taylor:wwNw}
+%   Denoting $T=t^2$, we get
+%   \begin{quote}
+%     \cs{@@_ln_Taylor:wwNw}
+%     \Arg{T_1} \Arg{T_2} \Arg{T_3} \Arg{T_4} \Arg{T_5} \Arg{T_6} |;| |;|
+%     \Arg{(2t)_1} \Arg{(2t)_2} \Arg{(2t)_3} \Arg{(2t)_4} \Arg{(2t)_5} \Arg{(2t)_6} |;|
+%     |{| \cs{@@_ln_c:NwNn} \meta{sign} |}|
+%     \meta{fixed tl} \meta{exponent} |;| \meta{continuation}
+%   \end{quote}
+%   And we want to compute
+%   \[
+%   \ln\left(\frac{1+t}{1-t}\right)
+%   = 2t\left(1 + T \left(\frac{1}{3} + T \left(\frac{1}{5}
+%         + T \left(\frac{1}{7} + T \left( \frac{1}{9} + \cdots
+%           \right)\right)\right)\right)\right)
+%   \]
+%   The process looks as follows
+%   \begin{verbatim}
+%     \loop 5; A;
+%     \div_int 5; 1.0; \add A; \mul T; {\loop \eval 5-2;}
+%     \add 0.2; A; \mul T; {\loop \eval 5-2;}
+%     \mul B; T; {\loop 3;}
+%     \loop 3; C;
+%   \end{verbatim}
+%   \footnote{Bruno: add explanations.}
+%
+%   This uses the routine for dividing a number by a small integer
+%   (${}<10^4$).
+%    \begin{macrocode}
+\cs_new:Npn \@@_ln_Taylor:wwNw
+  { \@@_ln_Taylor_loop:www 21 ; {0000}{0000}{0000}{0000}{0000}{0000} ; }
+\cs_new:Npn \@@_ln_Taylor_loop:www #1; #2; #3;
+  {
+    \if_int_compare:w #1 = \c_one
+      \@@_ln_Taylor_break:w
+    \fi:
+    \exp_after:wN \@@_fixed_div_int:wwN \c_@@_one_fixed_tl ; #1;
+    \@@_fixed_add:wwN #2;
+    \@@_fixed_mul:wwn #3;
+    {
+      \exp_after:wN \@@_ln_Taylor_loop:www
+      \int_use:N \__int_eval:w #1 - \c_two ;
+    }
+    #3;
+  }
+\cs_new:Npn \@@_ln_Taylor_break:w \fi: #1 \@@_fixed_add:wwN #2#3; #4 ;;
+  {
+    \fi:
+    \exp_after:wN \@@_fixed_mul:wwn
+    \exp_after:wN { \int_use:N \__int_eval:w 10000 + #2 } #3;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_ln_c:NwNw}
+%   \begin{quote}
+%     \cs{@@_ln_c:NwNw} \meta{sign}
+%     \Arg{r_1} \Arg{r_2} \Arg{r_3} \Arg{r_4} \Arg{r_5} \Arg{r_6} |;|
+%     \meta{fixed tl} \meta{exponent} |;| \meta{continuation}
+%   \end{quote}
+%   We are now reduced to finding $\ln c$ and $\meta{exponent}\ln 10$
+%   in a table, and adding it to the mixture. The first step is to
+%   get $\ln c - \ln x = - \ln a$, then we get $|b|\ln 10$ and add
+%   or subtract.
+%
+%   For now, $\ln x$ is given as $\cdot 10^0$. Unless both the exponent
+%   is $1$ and $c=1$, we shift to working in units of $\cdot 10^4$,
+%   since the final result will be at least $\ln 10/7 \simeq
+%   0.35$.\footnote{Bruno: that was wrong at some point, I must check.}
+%    \begin{macrocode}
+\cs_new:Npn \@@_ln_c:NwNw #1 #2; #3
+  {
+    \if_meaning:w + #1
+      \exp_after:wN \exp_after:wN \exp_after:wN \@@_fixed_sub:wwN
+    \else:
+      \exp_after:wN \exp_after:wN \exp_after:wN \@@_fixed_add:wwN
+    \fi:
+    #3 ; #2 ;
+  }
+%    \end{macrocode}
+% \footnote{Bruno: this \emph{\textbf{must}} be updated with correct values!}
+% \end{macro}
+%
+% \begin{macro}{\@@_ln_exponent:wn}
+%   \begin{quote}
+%     \cs{@@_ln_exponent:wn}
+%     \Arg{s_1} \Arg{s_2} \Arg{s_3} \Arg{s_4} \Arg{s_5} \Arg{s_6} |;|
+%     \Arg{exponent}
+%   \end{quote}
+%   Compute \meta{exponent} times $\ln 10$. Apart from the cases where
+%   \meta{exponent} is $0$ or $1$, the result will necessarily be at
+%   least $\ln 10 \simeq 2.3$ in magnitude. We can thus drop the least
+%   significant $4$ digits. In the case of a very large (positive or
+%   negative) exponent, we can (and we need to) drop $4$ additional
+%   digits, since the result is of order $10^4$. Naively, one would
+%   think that in both cases we can drop $4$ more digits than we do,
+%   but that would be slightly too tight for rounding to happen correctly.
+%   Besides, we already have addition and subtraction for $24$ digits
+%   fixed point numbers.
+%    \begin{macrocode}
+\cs_new:Npn \@@_ln_exponent:wn #1; #2
+  {
+    \if_case:w #2 \exp_stop_f:
+      \c_zero \@@_case_return:nw { \@@_fixed_to_float:Nw 2 }
+    \or:
+      \exp_after:wN \@@_ln_exponent_one:ww \__int_value:w
+    \else:
+      \if_int_compare:w #2 > \c_zero
+        \exp_after:wN \@@_ln_exponent_small:NNww
+        \exp_after:wN 0
+        \exp_after:wN \@@_fixed_sub:wwN \__int_value:w
+      \else:
+        \exp_after:wN \@@_ln_exponent_small:NNww
+        \exp_after:wN 2
+        \exp_after:wN \@@_fixed_add:wwN \__int_value:w -
+      \fi:
+    \fi:
+    #2; #1;
+  }
+%    \end{macrocode}
+%   Now we painfully write all the cases.\footnote{Bruno: do rounding.}
+%   No overflow nor underflow can happen, except when computing \texttt{ln(1)}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_ln_exponent_one:ww 1; #1;
+  {
+    \c_zero
+    \exp_after:wN \@@_fixed_sub:wwN \c_@@_ln_x_fixed_tl ; #1;
+    \@@_fixed_to_float:wN 0
+  }
+%    \end{macrocode}
+%   For small exponents, we just drop one block of digits, and set the
+%   exponent of the log to $4$ (minus any shift coming from leading zeros
+%   in the conversion from fixed point to floating point). Note that here
+%   the exponent has been made positive.
+%    \begin{macrocode}
+\cs_new:Npn \@@_ln_exponent_small:NNww #1#2#3; #4#5#6#7#8#9;
+  {
+    \c_four
+    \exp_after:wN \@@_fixed_mul:wwn
+      \c_@@_ln_x_fixed_tl ;
+      {#3}{0000}{0000}{0000}{0000}{0000} ;
+    #2
+      {0000}{#4}{#5}{#6}{#7}{#8};
+    \@@_fixed_to_float:wN #1
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Exponential}
+%
+% \subsubsection{Sign, exponent, and special numbers}
+%
+% \begin{macro}[int, EXP]{\@@_exp:w}
+%    \begin{macrocode}
+\cs_new:Npn \@@_exp:w \s_@@ \@@_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+      \@@_case_return_o:Nw \c_one_fp
+    \or:
+      \exp_after:wN \@@_exp_normal:w
+    \or:
+      \if_meaning:w 0 #2
+        \exp_after:wN \@@_case_return_o:Nw
+        \exp_after:wN \c_inf_fp
+      \else:
+        \exp_after:wN \@@_case_return_o:Nw
+        \exp_after:wN \c_zero_fp
+      \fi:
+    \or:
+      \@@_case_return_same_o:w
+    \fi:
+    \s_@@ \@@_chk:w #1#2
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_exp_normal:w, \@@_exp_pos:Nnwnw}
+%   \begin{macrocode}
+\cs_new:Npn \@@_exp_normal:w \s_@@ \@@_chk:w 1#1
+  {
+    \if_meaning:w 0 #1
+      \@@_exp_pos:NNwnw + \@@_fixed_to_float:wN
+    \else:
+      \@@_exp_pos:NNwnw - \@@_fixed_inv_to_float:wN
+    \fi:
+  }
+\cs_new:Npn \@@_exp_pos:NNwnw #1#2#3 \fi: #4#5;
+  {
+    \fi:
+    \exp_after:wN \@@_sanitize:Nw
+    \exp_after:wN 0
+    \__int_value:w #1 \__int_eval:w
+      \if_int_compare:w #4 < - \c_eight
+        \c_one
+        \exp_after:wN \@@_add_big_i:wNww
+        \int_use:N \__int_eval:w \c_one - #4 ;
+        0 {1000}{0000}{0000}{0000} ; #5;
+        \tex_romannumeral:D
+      \else:
+        \if_int_compare:w #4 > \c_five % cf \c_@@_max_exponent_int
+          \exp_after:wN \@@_exp_overflow:
+          \tex_romannumeral:D
+        \else:
+          \if_int_compare:w #4 < \c_zero
+            \exp_after:wN \use_i:nn
+          \else:
+            \exp_after:wN \use_ii:nn
+          \fi:
+          {
+            \c_zero
+            \@@_decimate:nNnnnn { - #4 }
+              \@@_exp_Taylor:Nnnwn
+          }
+          {
+            \@@_decimate:nNnnnn { \c_sixteen - #4 }
+              \@@_exp_pos_large:NnnNwn
+          }
+          #5
+          {#4}
+          #2 0
+          \tex_romannumeral:D
+        \fi:
+      \fi:
+    \exp_after:wN \c_zero
+  }
+\cs_new:Npn \@@_exp_overflow:
+  { + \c_two * \c_@@_max_exponent_int ; {1000} {0000} {0000} {0000} ; }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_exp_Taylor:Nnnwn}
+% \begin{macro}[aux, EXP]{\@@_exp_Taylor_loop:www, \@@_exp_Taylor_break:Nww}
+%   This function is called for numbers in the range $[10^{-9},
+%   10^{-1})$.  Our only task is to compute the Taylor series.  The
+%   first argument is irrelevant (rounding digit used by some other
+%   functions).  The next three arguments, at least $16$ digits,
+%   delimited by a semicolon, form a fixed point number, so we pack it
+%   in blocks of $4$ digits.
+%    \begin{macrocode}
+\cs_new:Npn \@@_exp_Taylor:Nnnwn #1#2#3 #4; #5
+  {
+    \@@_pack_twice_four:wNNNNNNNN
+    \@@_pack_twice_four:wNNNNNNNN
+    \@@_pack_twice_four:wNNNNNNNN
+    \@@_exp_Taylor_ii:ww
+    ; #2#3#4 0000 0000 ;
+  }
+\cs_new:Npn \@@_exp_Taylor_ii:ww #1; #2;
+  { \@@_exp_Taylor_loop:www 10 ; #1 ; #1 ; \s__stop }
+\cs_new:Npn \@@_exp_Taylor_loop:www #1; #2; #3;
+  {
+    \if_int_compare:w #1 = \c_one
+      \exp_after:wN \@@_exp_Taylor_break:Nww
+    \fi:
+    \@@_fixed_div_int:wwN #3 ; #1 ;
+    \@@_fixed_add_one:wN
+    \@@_fixed_mul:wwn #2 ;
+    {
+      \exp_after:wN \@@_exp_Taylor_loop:www
+      \int_use:N \__int_eval:w #1 - 1 ;
+      #2 ;
+    }
+  }
+\cs_new:Npn \@@_exp_Taylor_break:Nww #1 #2; #3 \s__stop
+  { \@@_fixed_add_one:wN #2 ; }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]
+%   {
+%     \@@_exp_pos_large:NnnNwn ,
+%     \@@_exp_large_after:wwn ,
+%     \@@_exp_large:w ,
+%     \@@_exp_large_v:wN,
+%     \@@_exp_large_iv:wN,
+%     \@@_exp_large_iii:wN,
+%     \@@_exp_large_ii:wN,
+%     \@@_exp_large_i:wN,
+%     \@@_exp_large_:wN,
+%   }
+%   The first two arguments are irrelevant (a rounding digit, and a
+%   brace group with $8$ zeros).  The third argument is the integer part
+%   of our number, then we have the decimal part delimited by a
+%   semicolon, and finally the exponent, in the range $[0,5]$.  Remove
+%   leading zeros from the integer part: putting |#4| in there too
+%   ensures that an integer part of $0$ is also removed.  Then read
+%   digits one by one, looking up $\exp(\meta{digit}\cdot
+%   10^{\meta{exponent}})$ in a table, and multiplying that to the
+%   current total.  The loop is done by having the auxiliary for one
+%   exponent call the auxiliary for the next exponent.  The current
+%   total is expressed by leaving the exponent behind in the input
+%   stream (we are currently within an \cs{__int_eval:w}), and keeping
+%   track of a fixed point number, |#1| for the numbered auxiliaries.
+%   Our usage of \cs{if_case:w} is somewhat dirty for optimization:
+%   \TeX{} jumps to the appropriate case, but we then lose the
+%   \cs{if_case:w} \enquote{by hand}, using \cs{or:} and \cs{fi:} as
+%   delimiters.
+%    \begin{macrocode}
+\cs_new:Npn \@@_exp_pos_large:NnnNwn #1#2#3 #4#5; #6
+  {
+    \exp_after:wN \exp_after:wN
+    \cs:w @@_exp_large_\tex_romannumeral:D #6:wN \exp_after:wN \cs_end:
+    \exp_after:wN \c_@@_one_fixed_tl
+    \exp_after:wN ;
+    \__int_value:w #3 #4 \exp_stop_f:
+    #5 00000 ;
+  }
+\cs_new:Npn \@@_exp_large:w #1 \or: #2 \fi:
+  { \fi: \@@_fixed_mul:wwn #1; }
+\cs_new:Npn \@@_exp_large_v:wN #1; #2
+  {
+    \if_case:w #2 ~           \exp_after:wN \@@_fixed_continue:wn  \or:
+      +  4343 \@@_exp_large:w {8806}{8182}{2566}{2921}{5872}{6150} \or:
+      +  8686 \@@_exp_large:w {7756}{0047}{2598}{6861}{0458}{3204} \or:
+      + 13029 \@@_exp_large:w {6830}{5723}{7791}{4884}{1932}{7351} \or:
+      + 17372 \@@_exp_large:w {6015}{5609}{3095}{3052}{3494}{7574} \or:
+      + 21715 \@@_exp_large:w {5297}{7951}{6443}{0315}{3251}{3576} \or:
+      + 26058 \@@_exp_large:w {4665}{6719}{0099}{3379}{5527}{2929} \or:
+      + 30401 \@@_exp_large:w {4108}{9724}{3326}{3186}{5271}{5665} \or:
+      + 34744 \@@_exp_large:w {3618}{6973}{3140}{0875}{3856}{4102} \or:
+      + 39087 \@@_exp_large:w {3186}{9209}{6113}{3900}{6705}{9685} \or:
+    \fi:
+    #1;
+    \@@_exp_large_iv:wN
+  }
+\cs_new:Npn \@@_exp_large_iv:wN #1; #2
+  {
+    \if_case:w #2 ~          \exp_after:wN \@@_fixed_continue:wn  \or:
+      +  435 \@@_exp_large:w {1970}{0711}{1401}{7046}{9938}{8888} \or:
+      +  869 \@@_exp_large:w {3881}{1801}{9428}{4368}{5764}{8232} \or:
+      + 1303 \@@_exp_large:w {7646}{2009}{8905}{4704}{8893}{1073} \or:
+      + 1738 \@@_exp_large:w {1506}{3559}{7005}{0524}{9009}{7592} \or:
+      + 2172 \@@_exp_large:w {2967}{6283}{8402}{3667}{0689}{6630} \or:
+      + 2606 \@@_exp_large:w {5846}{4389}{5650}{2114}{7278}{5046} \or:
+      + 3041 \@@_exp_large:w {1151}{7900}{5080}{6878}{2914}{4154} \or:
+      + 3475 \@@_exp_large:w {2269}{1083}{0850}{6857}{8724}{4002} \or:
+      + 3909 \@@_exp_large:w {4470}{3047}{3316}{5442}{6408}{6591} \or:
+    \fi:
+    #1;
+    \@@_exp_large_iii:wN
+  }
+\cs_new:Npn \@@_exp_large_iii:wN #1; #2
+  {
+    \if_case:w #2 ~         \exp_after:wN \@@_fixed_continue:wn  \or:
+      +  44 \@@_exp_large:w {2688}{1171}{4181}{6135}{4484}{1263} \or:
+      +  87 \@@_exp_large:w {7225}{9737}{6812}{5749}{2581}{7748} \or:
+      + 131 \@@_exp_large:w {1942}{4263}{9524}{1255}{9365}{8421} \or:
+      + 174 \@@_exp_large:w {5221}{4696}{8976}{4143}{9505}{8876} \or:
+      + 218 \@@_exp_large:w {1403}{5922}{1785}{2837}{4107}{3977} \or:
+      + 261 \@@_exp_large:w {3773}{0203}{0092}{9939}{8234}{0143} \or:
+      + 305 \@@_exp_large:w {1014}{2320}{5473}{5004}{5094}{5533} \or:
+      + 348 \@@_exp_large:w {2726}{3745}{7211}{2566}{5673}{6478} \or:
+      + 391 \@@_exp_large:w {7328}{8142}{2230}{7421}{7051}{8866} \or:
+    \fi:
+    #1;
+    \@@_exp_large_ii:wN
+  }
+\cs_new:Npn \@@_exp_large_ii:wN #1; #2
+  {
+    \if_case:w #2 ~        \exp_after:wN \@@_fixed_continue:wn  \or:
+      +  5 \@@_exp_large:w {2202}{6465}{7948}{0671}{6516}{9579} \or:
+      +  9 \@@_exp_large:w {4851}{6519}{5409}{7902}{7796}{9107} \or:
+      + 14 \@@_exp_large:w {1068}{6474}{5815}{2446}{2146}{9905} \or:
+      + 18 \@@_exp_large:w {2353}{8526}{6837}{0199}{8540}{7900} \or:
+      + 22 \@@_exp_large:w {5184}{7055}{2858}{7072}{4640}{8745} \or:
+      + 27 \@@_exp_large:w {1142}{0073}{8981}{5684}{2836}{6296} \or:
+      + 31 \@@_exp_large:w {2515}{4386}{7091}{9167}{0062}{6578} \or:
+      + 35 \@@_exp_large:w {5540}{6223}{8439}{3510}{0525}{7117} \or:
+      + 40 \@@_exp_large:w {1220}{4032}{9431}{7840}{8020}{0271} \or:
+    \fi:
+    #1;
+    \@@_exp_large_i:wN
+  }
+\cs_new:Npn \@@_exp_large_i:wN #1; #2
+  {
+    \if_case:w #2 ~       \exp_after:wN \@@_fixed_continue:wn  \or:
+      + 1 \@@_exp_large:w {2718}{2818}{2845}{9045}{2353}{6029} \or:
+      + 1 \@@_exp_large:w {7389}{0560}{9893}{0650}{2272}{3043} \or:
+      + 2 \@@_exp_large:w {2008}{5536}{9231}{8766}{7740}{9285} \or:
+      + 2 \@@_exp_large:w {5459}{8150}{0331}{4423}{9078}{1103} \or:
+      + 3 \@@_exp_large:w {1484}{1315}{9102}{5766}{0342}{1116} \or:
+      + 3 \@@_exp_large:w {4034}{2879}{3492}{7351}{2260}{8387} \or:
+      + 4 \@@_exp_large:w {1096}{6331}{5842}{8458}{5992}{6372} \or:
+      + 4 \@@_exp_large:w {2980}{9579}{8704}{1728}{2747}{4359} \or:
+      + 4 \@@_exp_large:w {8103}{0839}{2757}{5384}{0077}{1000} \or:
+    \fi:
+    #1;
+    \@@_exp_large_:wN
+  }
+\cs_new:Npn \@@_exp_large_:wN #1; #2
+  {
+    \if_case:w #2 ~       \exp_after:wN \@@_fixed_continue:wn  \or:
+      + 1 \@@_exp_large:w {1105}{1709}{1807}{5647}{6248}{1171} \or:
+      + 1 \@@_exp_large:w {1221}{4027}{5816}{0169}{8339}{2107} \or:
+      + 1 \@@_exp_large:w {1349}{8588}{0757}{6003}{1039}{8374} \or:
+      + 1 \@@_exp_large:w {1491}{8246}{9764}{1270}{3178}{2485} \or:
+      + 1 \@@_exp_large:w {1648}{7212}{7070}{0128}{1468}{4865} \or:
+      + 1 \@@_exp_large:w {1822}{1188}{0039}{0508}{9748}{7537} \or:
+      + 1 \@@_exp_large:w {2013}{7527}{0747}{0476}{5216}{2455} \or:
+      + 1 \@@_exp_large:w {2225}{5409}{2849}{2467}{6045}{7954} \or:
+      + 1 \@@_exp_large:w {2459}{6031}{1115}{6949}{6638}{0013} \or:
+    \fi:
+    #1;
+    \@@_exp_large_after:wwn
+  }
+\cs_new:Npn \@@_exp_large_after:wwn #1; #2;
+  {
+    \@@_exp_Taylor:Nnnwn ? { } { } 0 #2; {}
+    \@@_fixed_mul:wwn #1;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Power}
+%
+% Raising a number $a$ to a power $b$ leads to many distinct situations.
+% \begin{center}
+%   \begin{tabular}{>{$}c<{$}|*8{>{$}l<{$}}}
+%     a^b    &-\infty&-y     &-n        &\pm 0&+n    &+y     &+\infty&\nan \\
+%     \hline
+%     +\infty&+0     &+0     &+0        &+1&+\infty  &+\infty&+\infty&\nan \\
+%     1<x    &+0     &+x^{-y}&+x^{-n}   &+1&+x^{n}   &+x^{y} &+\infty&\nan \\
+%     +1     &+1     &+1     &+1        &+1&+1       &+1     &+1     &+1   \\
+%     0<x<1  &+\infty&+x^{-y}&+x^{-n}   &+1&+x^{n}   &+x^{y} &+0     &\nan \\
+%     +0     &+\infty&+\infty&+\infty   &+1&+0       &+0     &+0     &\nan \\
+%     -0     &\nan   &\nan   &\pm\infty &+1&\pm 0    &+0     &+0     &\nan \\
+%     -1<-x<0&\nan   &\nan   &\pm x^{-n}&+1&\pm x^{n}&\nan   &+0     &\nan \\
+%     -1     &\nan   &\nan   &\pm 1     &+1&\pm 1    &\nan   &\nan   &\nan \\
+%     -x<-1  &+0     &\nan   &\pm x^{-n}&+1&\pm x^{n}&\nan   &\nan   &\nan \\
+%     -\infty&+0     &+0     &\pm 0     &+1&\pm\infty&\nan   &\nan   &\nan \\
+%     \nan   &\nan   &\nan   &\nan      &+1&\nan     &\nan   &\nan   &\nan \\
+%   \end{tabular}
+% \end{center}
+% One peculiarity of this operation is that $\nan^0 = 1^\nan = 1$,
+% because this relation is obeyed for any number, even $\pm\infty$.
+%
+% \begin{macro}[int, EXP]+\@@_^_o:ww+
+%   We cram a most of the tests into a single function to save csnames.
+%   First treat the case $b=0$: $a^0=1$ for any $a$, even \texttt{nan}.
+%   Then test the sign of $a$.
+%   \begin{itemize}
+%   \item If it is positive, and $a$ is a normal number, call
+%     \cs{@@_pow_normal:ww} followed by the two \texttt{fp} $a$ and $b$.
+%     For $a=+0$ or $+\inf$, call \cs{@@_pow_zero_or_inf:ww} instead, to
+%     return either $+0$ or $+\infty$ as appropriate.
+%   \item If $a$ is a \texttt{nan}, then skip to the next semicolon
+%     (which happens to be conveniently the end of $b$) and return
+%     \texttt{nan}.
+%   \item Finally, if $a$ is negative, compute $|a|^b$
+%     (\cs{@@_pow_normal:ww} which ignores the sign of its first
+%     operand), and keep an extra copy of $a$ and $b$ (the second brace
+%     group, containing \{~$b$~$a$~\}, is inserted between $a$ and $b$).
+%     Then do some tests to find the final sign of the result if it
+%     exists.
+%   \end{itemize}
+%    \begin{macrocode}
+\cs_new:cpn { @@_ \iow_char:N \^ _o:ww }
+    \s_@@ \@@_chk:w #1#2#3; \s_@@ \@@_chk:w #4#5#6;
+  {
+    \if_meaning:w 0 #4
+      \@@_case_return_o:Nw \c_one_fp
+    \fi:
+    \if_case:w #2 \exp_stop_f:
+      \exp_after:wN \use_i:nn
+    \or:
+      \@@_case_return_o:Nw \c_nan_fp
+    \else:
+      \exp_after:wN \@@_pow_neg:www
+      \tex_romannumeral:D -`0 \exp_after:wN \use:nn
+    \fi:
+    {
+      \if_meaning:w 1 #1
+        \exp_after:wN \@@_pow_normal:ww
+      \else:
+        \exp_after:wN \@@_pow_zero_or_inf:ww
+      \fi:
+      \s_@@ \@@_chk:w #1#2#3;
+    }
+    { \s_@@ \@@_chk:w #4#5#6; \s_@@ \@@_chk:w #1#2#3; }
+    \s_@@ \@@_chk:w #4#5#6;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_pow_zero_or_inf:ww}
+%   Raising $-0$ or $-\infty$ to \texttt{nan} yields \texttt{nan}.  For
+%   other powers, the result is $+0$ if $0$ is raised to a positive
+%   power or $\infty$ to a negative power, and $+\infty$ otherwise.  We
+%   can thus know the result by comparing the type of $a$ with the sign
+%   of $b$, since those conveniently take the same possible values, $0$
+%   and~$2$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_pow_zero_or_inf:ww \s_@@ \@@_chk:w #1#2; \s_@@ \@@_chk:w #3#4
+  {
+    \if_meaning:w 1 #4
+      \@@_case_return_same_o:w
+    \fi:
+    \if_meaning:w #1 #4
+      \@@_case_return_o:Nw \c_zero_fp
+    \else:
+      \@@_case_return_o:Nw \c_inf_fp
+    \fi:
+    \s_@@ \@@_chk:w #3#4
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_pow_normal:ww}
+%   We have in front of us $a$, and $b\neq 0$, we know that $a$ is a
+%   normal number, and we wish to compute $\lvert a\rvert^{b}$.  If
+%   $\lvert a\rvert=1$, we return $1$, unless $a=-1$ and $b$ is
+%   \texttt{nan}.  Indeed, returning $1$ at this point would wrongly
+%   raise \enquote{invalid} when the sign is considered.  If $\lvert
+%   a\rvert\neq 1$, test the type of $b$:
+%   \begin{itemize}
+%   \item[0] Impossible, we already filtered $b=\pm 0$.
+%   \item[1] Call \cs{@@_pow_npos:ww}.
+%   \item[2] Return $+\infty$ or $+0$ depending on the sign of $b$ and
+%     whether the exponent of $a$ is positive or not.
+%   \item[3] Return $b$.
+%   \end{itemize}
+%    \begin{macrocode}
+\cs_new:Npn \@@_pow_normal:ww \s_@@ \@@_chk:w 1 #1#2#3; \s_@@ \@@_chk:w #4#5
+  {
+    \if_int_compare:w \pdftex_strcmp:D { #2 #3 }
+              { 1 {1000} {0000} {0000} {0000} } = \c_zero
+      \if_int_compare:w #4 #1 = 32 \exp_stop_f:
+        \exp_after:wN \@@_case_return_ii_o:ww
+      \fi:
+      \@@_case_return_o:Nww \c_one_fp
+    \fi:
+    \if_case:w #4 ~
+    \or:
+      \exp_after:wN \@@_pow_npos:Nww
+      \exp_after:wN #5
+    \or:
+      \if_meaning:w 2 #5 \exp_after:wN \reverse_if:N \fi:
+      \if_int_compare:w #2 > \c_zero
+        \exp_after:wN \@@_case_return_o:Nww
+        \exp_after:wN \c_inf_fp
+      \else:
+        \exp_after:wN \@@_case_return_o:Nww
+        \exp_after:wN \c_zero_fp
+      \fi:
+    \or:
+      \@@_case_return_ii_o:ww
+    \fi:
+    \s_@@ \@@_chk:w 1 #1 {#2} #3 ;
+    \s_@@ \@@_chk:w #4 #5
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% ^^A todo: check that we compute ln to 21 digits!
+% \begin{macro}[aux, EXP]{\@@_pow_npos:Nww}
+%   We now know that $a\neq\pm 1$ is a normal number, and $b$ is a
+%   normal number too.  We want to compute $\lvert a\rvert^{b} = (\lvert
+%   x\rvert\cdot 10^{n})^{y\cdot 10^{p}} = \exp((\log\lvert x\rvert + n
+%   \log 10)\cdot y \cdot 10^{p}) = \exp(z)$.  To compute the
+%   exponential accurately, we need to know the digits of $z$ up to the
+%   $16$-th position.  Since the exponential of $10^{5}$ is infinite, we
+%   only need at most $21$ digits, hence the fixed point result of
+%   \cs{@@_ln:w} is precise enough for our needs.  Start an integer
+%   expression for the decimal exponent of $e^{\lvert z\rvert}$.  If $z$
+%   is negative, negate that decimal exponent, and prepare to take the
+%   inverse when converting from the fixed point to the floating point result.
+%    \begin{macrocode}
+\cs_new:Npn \@@_pow_npos:Nww #1 \s_@@ \@@_chk:w 1#2#3
+  {
+    \exp_after:wN \@@_sanitize:Nw
+    \exp_after:wN 0
+    \__int_value:w
+      \if:w #1 \if_int_compare:w #3 > \c_zero 0 \else: 2 \fi:
+        \exp_after:wN \@@_pow_npos_aux:Nnww
+        \exp_after:wN \@@_fixed_to_float:wN
+      \else:
+        -
+        \exp_after:wN \@@_pow_npos_aux:Nnww
+        \exp_after:wN \@@_fixed_inv_to_float:wN
+      \fi:
+      {#3}
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+%^^A begin[todo]
+% \begin{macro}[aux, EXP]{\@@_pow_npos_aux:Nnww}
+%   The first argument is the conversion function from fixed point to
+%   float.  Then comes an exponent and the $4$ brace groups of $x$,
+%   followed by $b$.  Compute $-\log x$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_pow_npos_aux:Nnww #1#2#3#4; \s_@@ \@@_chk:w 1#5#6#7;
+  {
+    \__int_eval:w
+      \@@_ln_significand:NNNNnnnN #3#4
+      \@@_pow_exponent:wnN {#2}
+      \@@_fixed_mul:wwn #7 {0000}{0000} ;
+      \@@_pow_B:wwN #6;
+      #1 0 % fixed_to_float:wN
+  }
+\cs_new:Npn \@@_pow_exponent:wnN #1; #2
+  {
+    \if_int_compare:w #2 > \c_zero
+      \exp_after:wN \@@_pow_exponent:Nwnnnnnn % n\log 10 - (-\log x)
+      \exp_after:wN +
+    \else:
+      \exp_after:wN \@@_pow_exponent:Nwnnnnnn % -( |n|\log 10 + (-\log x) )
+      \exp_after:wN -
+    \fi:
+    #2; #1;
+  }
+\cs_new:Npn \@@_pow_exponent:Nwnnnnnn #1#2; #3#4#5#6#7#8;
+  { %^^A todo: use that in ln. %^^A todo: log(1.00...) too inaccurate?
+    \exp_after:wN \@@_fixed_mul_after:wwn
+    \int_use:N \__int_eval:w -5 0000
+      \exp_after:wN \@@_fixed_mul_pack:NNNNNw
+      \int_use:N \__int_eval:w 4 9995 0000 #1#2*23025 - #1 #3
+        \exp_after:wN \@@_fixed_mul_pack:NNNNNw
+        \int_use:N \__int_eval:w 4 9995 0000 #1 #2*8509 - #1 #4
+          \exp_after:wN \@@_fixed_mul_pack:NNNNNw
+          \int_use:N \__int_eval:w 4 9995 0000 #1 #2*2994 - #1 #5
+            \exp_after:wN \@@_fixed_mul_pack:NNNNNw
+            \int_use:N \__int_eval:w 4 9995 0000 #1 #2*0456 - #1 #6
+              \exp_after:wN \@@_fixed_mul_pack:NNNNNw
+              \int_use:N \__int_eval:w 5 0000 0000 #1 #2*8401 - #1 #7
+                #1 ( #2*7991 - #8 ) / 1 0000 ; ;
+  }
+\cs_new:Npn \@@_pow_B:wwN #1#2#3#4#5#6; #7;
+  {
+    \if_int_compare:w #7 < \c_zero
+      \exp_after:wN \@@_pow_C_neg:w \__int_value:w -
+    \else:
+      \if_int_compare:w #7 < 22 \exp_stop_f:
+        \exp_after:wN \@@_pow_C_pos:w \__int_value:w
+      \else:
+        \exp_after:wN \@@_pow_C_overflow:w \__int_value:w
+      \fi:
+    \fi:
+    #7 \exp_after:wN ;
+    \int_use:N \__int_eval:w 10 0000 + #1 \__int_eval_end:
+    #2#3#4#5#6 0000 0000 0000 0000 0000 0000 ; %^^A todo: how many 0?
+  }
+\cs_new:Npn \@@_pow_C_overflow:w #1; #2;
+  {
+    + \c_two * \c_@@_max_exponent_int
+    \exp_after:wN \@@_fixed_continue:wn \c_@@_one_fixed_tl ;
+  }
+\cs_new:Npn \@@_pow_C_neg:w #1 ; 1
+  {
+    \exp_after:wN \exp_after:wN \exp_after:wN \@@_pow_C_pack:w
+    \prg_replicate:nn {#1} {0}
+  }
+\cs_new:Npn \@@_pow_C_pos:w #1; 1
+  { \@@_pow_C_pos_loop:wN #1; }
+\cs_new:Npn \@@_pow_C_pos_loop:wN #1; #2
+  {
+    \if_meaning:w 0 #1
+      \exp_after:wN \@@_pow_C_pack:w
+      \exp_after:wN #2
+    \else:
+      \if_meaning:w 0 #2
+        \exp_after:wN \@@_pow_C_pos_loop:wN \__int_value:w
+      \else:
+        \exp_after:wN \@@_pow_C_overflow:w \__int_value:w
+      \fi:
+      \__int_eval:w #1 - \c_one \exp_after:wN ;
+    \fi:
+  }
+\cs_new:Npn \@@_pow_C_pack:w
+  { \exp_after:wN \@@_exp_large_v:wN \c_@@_one_fixed_tl ; }
+%    \end{macrocode}
+% \end{macro}
+%^^A end[todo]
+%
+% \begin{macro}[aux, EXP]{\@@_pow_neg:www, \@@_pow_neg_neg:w}
+%   This function is followed by three floating point numbers: $|a|^b$,
+%   $a\in[-\infty,-0]$, and $b$.  If $b$ is an even integer (case $-1$),
+%   $a^b=|a|^b$.  If $b$ is an odd integer (case $0$), $a^b=-|a|^b$,
+%   obtained by a call to \cs{@@_pow_neg_neg:w}.  Otherwise, the sign is
+%   undefined.  This is invalid, unless $|a|^b$ turns out to be $+0$ or
+%   \texttt{nan}, in which case we return that as $a^b$.  In particular,
+%   since the underflow detection occurs before \cs{@@_pow_neg:www} is
+%   called, |(-0.1)**(12345.6)| will give $+0$ rather than complaining
+%   that the sign is not defined.
+%    \begin{macrocode}
+\cs_new:Npn \@@_pow_neg:www \s_@@ \@@_chk:w #1#2; #3; #4;
+  {
+    \if_case:w \@@_pow_neg_case:w #4 ;
+      \exp_after:wN \@@_pow_neg_neg:w
+    \or:
+      \if_int_compare:w \__int_eval:w #1 / \c_two = \c_one
+        \@@_invalid_operation:Nnww \c_nan_fp { ^ } #3; #4;
+        \tex_romannumeral:D -`0
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_use_none_until_s:w
+      \fi:
+    \fi:
+    \@@_exp_after_o:w
+    \s_@@ \@@_chk:w #1#2;
+  }
+\cs_new:Npn \@@_pow_neg_neg:w \@@_exp_after_o:w \s_@@ \@@_chk:w #1#2
+  {
+    \exp_after:wN \@@_exp_after_o:w
+    \exp_after:wN \s_@@
+    \exp_after:wN \@@_chk:w
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w \c_two - #2 \__int_eval_end:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]
+%   {
+%     \@@_pow_neg_case:w, \@@_pow_neg_case_aux:nnnnn,
+%     \@@_pow_neg_case_aux:NNNNNNNNw
+%   }
+%   This function expects a floating point number, and \enquote{returns}
+%   $-1$ if it is an even integer, $0$ if it is an odd integer, and $1$
+%   if it is not an integer.  Zeros are even, $\pm\infty$ and
+%   \texttt{nan} are non-integers.  The sign of normal numbers is
+%   irrelevant to parity.  If the exponent is greater than sixteen, then
+%   the number is even.  If the exponent is non-positive, the number
+%   cannot be an integer.  We also separate the ranges of exponent
+%   $[1,8]$ and $[9,16]$.  In the former case, check that the last $8$
+%   digits are zero (otherwise we don't have an integer).  In both
+%   cases, consider the appropriate $8$ digits, either |#4#5| or |#2#3|,
+%   remove the first few: we are then left with \meta{digit}
+%   \meta{digits} |;| which would be the digits surrounding the decimal
+%   period.  If the \meta{digits} are non-zero, the number is not an
+%   integer.  Otherwise, check the parity of the \meta{digit} and return
+%   \cs{c_zero} or \cs{c_minus_one}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_pow_neg_case:w \s_@@ \@@_chk:w #1#2#3;
+  {
+    \if_case:w #1 \exp_stop_f:
+           \c_minus_one
+    \or:   \@@_pow_neg_case_aux:nnnnn #3
+    \else: \c_one
+    \fi:
+  }
+\cs_new:Npn \@@_pow_neg_case_aux:nnnnn #1#2#3#4#5
+  {
+    \if_int_compare:w #1 > \c_eight
+      \if_int_compare:w #1 > \c_sixteen
+        \c_minus_one
+      \else:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_pow_neg_case_aux:NNNNNNNNw
+        \prg_replicate:nn { \c_sixteen - #1 } { 0 } #4#5 ;
+      \fi:
+    \else:
+      \if_int_compare:w #1 > \c_zero
+        \if_int_compare:w #4#5 = \c_zero
+          \exp_after:wN \exp_after:wN
+          \exp_after:wN \@@_pow_neg_case_aux:NNNNNNNNw
+          \prg_replicate:nn { \c_eight - #1 } { 0 } #2#3 ;
+        \else:
+          \c_one
+        \fi:
+      \else:
+        \c_one
+      \fi:
+    \fi:
+  }
+\cs_new:Npn \@@_pow_neg_case_aux:NNNNNNNNw #1#2#3#4#5#6#7#8#9;
+  {
+    \if_int_compare:w 0 #9 = \c_zero
+      \if_int_odd:w #8 \exp_stop_f:
+        \c_zero
+      \else:
+        \c_minus_one
+      \fi:
+    \else:
+      \c_one
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintChanges
+%
+% \PrintIndex
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-extended.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-extended.dtx
new file mode 100644
index 00000000000..d38c6de8e17
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-extended.dtx
@@ -0,0 +1,674 @@
+% \iffalse meta-comment
+%
+%% File: l3fp-extended.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp-extended.dtx 2474 2011-06-17 12:54:02Z bruno $
+  {L3 Floating-point extended precision fixed-points}
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{The \textsf{l3fp-extended} package\thanks{This file
+%         has version number \ExplFileVersion, last
+%         revised \ExplFileDate.}\\
+% Fixed points with extended precision for internal use}
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+% \date{Released \ExplFileDate}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3fp-extended} implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+% In this module, we work on (almost) fixed-point numbers with
+% extended ($24$ digits) precision.  This is used in the computation of
+% Taylor series for the logarithm, exponential, and trigonometric
+% functions.  Since we eventually only care about the $16$ first digits
+% of the final result, some of the calculations are not performed with
+% the full $24$-digit precision.  In other words, the last two blocks of
+% each fixed point number may be wrong as long as the error is small
+% enough to be rounded away when converting back to a floating point
+% number.  The fixed point numbers are expressed as
+% \begin{quote}
+%   \Arg{a_1} \Arg{a_2} \Arg{a_3} \Arg{a_4} \Arg{a_5} \Arg{a_6} |;|
+% \end{quote}
+% where each \meta{a_i} is exactly $4$ digits, except
+% \meta{a_1}, which may be any positive \TeX{} integer.  The fixed point
+% number $a$ corresponding to the representation above is $a =
+% \sum_{i=1}^{6} \meta{a_i} \cdot 10^{-4i}$.
+%
+% Most functions we define here have the form
+% \begin{syntax}
+%   \cs{@@_fixed_\meta{calculation}:wwN} \meta{operand_1} |;| \meta{operand_2} |;| \meta{continuation}
+% \end{syntax}
+% They perform the \meta{calculation} on the two \meta{operands}, then
+% feed the result ($6$ brace groups followed by a semicolon) to the
+% \meta{continuation}, responsible for the next step of the calculation.
+% This allows constructions such as
+% \begin{quote}
+%   \cs{@@_fixed_add:wwN} \meta{X_1} |;| \meta{X_2} |;| \\
+%   \cs{@@_fixed_mul:wwn} \meta{X_3} |;| \\
+%   \cs{@@_fixed_add:wwN} \meta{X_4} |;| \\
+% \end{quote}
+% to compute $(X_1+X_2)\cdot X_3 + X_4$.  This turns out to be very
+% appropriate for computing continued fractions and Taylor series.
+%
+% At the end of the calculation, the result is turned back to a floating
+% point number using \cs{@@_fixed_to_float:Nw}.  This function has to
+% change the exponent of the floating point number: it must be used
+% after starting an integer expression for the overall exponent of the
+% result.
+%
+% \begin{variable}{\c_@@_one_fixed_tl}
+%    \begin{macrocode}
+\tl_const:Nn \c_@@_one_fixed_tl
+  { {10000} {0000} {0000} {0000} {0000} {0000} }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}[int, EXP]{\@@_fixed_continue:wn}
+%   This function does nothing.
+%    \begin{macrocode}
+\cs_new:Npn \@@_fixed_continue:wn #1; #2 { #2 #1; }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_fixed_div_int:wwN}
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_fixed_div_int_i:wnN, \@@_fixed_div_int_ii:wnn,
+%     \@@_fixed_div_int_end:wnn, \@@_fixed_div_int_pack:Nw,
+%     \@@_fixed_div_int_after:Nw
+%   }
+%   \begin{syntax}
+%     \cs{@@_fixed_div_int:wwN} \meta{a} |;| \meta{n} |;| \meta{function}
+%   \end{syntax}
+%   Divides the fixed point number \meta{a} by the (small) integer
+%   $0<\meta{n}<10^4$ and feeds the result to the \meta{function}.  The
+%   \texttt{wnN} auxiliary receives $a_{i}$, $n$, and a continuation
+%   function as arguments, and computes a (rather tight) lower bound
+%   $Q_{i}$ for the quotient.  The \texttt{wnn} auxiliary receives
+%   $Q_{i}$, $n$, and $a_{i}$.  It adds $Q_{i}$ to a surrounding integer
+%   expression, and starts a new one.  It also computes $a_{i}-n\cdot
+%   Q_{i}$, putting the result in front of $a_{i+1}$ to serve as the
+%   first argument for a new call to the \texttt{wnN} auxiliary. At the
+%   end, the path we took to the lowest levels rewinds: the
+%   \texttt{pack} auxiliary receives $5$ digits, braces the last $4$,
+%   and carries the leading digit to the level above.  The offsets used
+%   to ensure a given number of digits are as follows: we first subtract
+%   $1$ from the top-level, then add $9999$ at every subsequent level,
+%   and add $2$ to the last level.  This last number is not $1$, because
+%   it compensates for the |- \c_one| in the \texttt{wnN} auxiliary.
+%    \begin{macrocode}
+\cs_new:Npn \@@_fixed_div_int:wwN #1#2#3#4#5#6 ; #7 ; #8
+  {
+    \exp_after:wN \@@_fixed_div_int_after:Nw
+    \exp_after:wN #8
+    \int_use:N \__int_eval:w \c_minus_one
+      \@@_fixed_div_int_i:wnN
+      #1; {#7} \@@_fixed_div_int_ii:wnn
+      #2; {#7} \@@_fixed_div_int_ii:wnn
+      #3; {#7} \@@_fixed_div_int_ii:wnn
+      #4; {#7} \@@_fixed_div_int_ii:wnn
+      #5; {#7} \@@_fixed_div_int_ii:wnn
+      #6; {#7} \@@_fixed_div_int_end:wnn ;
+  }
+\cs_new:Npn \@@_fixed_div_int_i:wnN #1; #2 #3
+  {
+    \exp_after:wN #3
+    \int_use:N \__int_eval:w #1 / #2 - \c_one ;
+    {#2}
+    {#1}
+  }
+\cs_new:Npn \@@_fixed_div_int_ii:wnn #1; #2 #3
+  {
+    + #1
+    \exp_after:wN \@@_fixed_div_int_pack:Nw
+    \int_use:N \__int_eval:w 9999
+      \exp_after:wN \@@_fixed_div_int_i:wnN
+      \int_use:N \__int_eval:w #3 - #1*#2 \__int_eval_end:
+  }
+\cs_new:Npn \@@_fixed_div_int_end:wnn #1; #2 #3 { + #1 + \c_two ; }
+\cs_new:Npn \@@_fixed_div_int_pack:Nw #1 #2; { + #1; {#2} }
+\cs_new:Npn \@@_fixed_div_int_after:Nw #1 #2; { #1 {#2} }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_fixed_add_one:wN}
+%   \begin{syntax}
+%     \cs{@@_fixed_add_one:wN} \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \Arg{X_5} \Arg{X_6} |;| \meta{function}
+%   \end{syntax}
+%    \begin{macrocode}
+\cs_new:Npn \@@_fixed_add_one:wN #1#2; #3
+  {
+    \exp_after:wN #3 \exp_after:wN
+      { \int_use:N \__int_eval:w 10000 + #1 } #2 ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]
+%   {\@@_fixed_add:wwN, \@@_fixed_sub:wwN, \@@_fixed_sub_back:wwN}
+%^^A todo: remove sub_back.
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_fixed_add_i:NNnnnnwnn,
+%     \@@_fixed_add_ii:NnnNnnnnw,
+%     \@@_fixed_add_pack:NNNNNwN,
+%     \@@_fixed_add_after:NNNNNwN
+%   }
+%   \begin{syntax}
+%     \cs{@@_fixed_add:wwN} \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \Arg{X_5} \Arg{X_6} |;| \Arg{Y_1} \Arg{Y_2} \Arg{Y_3} \Arg{Y_4} \Arg{Y_5} \Arg{Y_6} |;| \meta{function}
+%   \end{syntax}
+%   Computes $X+Y$ (resp.\ $X-Y$ and $Y-X$) and feeds the result to
+%   \meta{function}.  The three functions only differ by some signs and
+%   use a common auxiliary.  It would be nice to grab the $12$ brace
+%   groups in one go, only $9$ arguments are allowed.  Start by grabbing
+%   the two signs, $X_{1}, \ldots, X_{4}$, the rest of $X$, and $Y_{1}$
+%   and $Y_{2}$.  The second auxiliary receives the sign of $X$, the
+%   rest of $X$, the sign of $Y$, the rest of $Y$, and the
+%   \meta{function}.  After going down through the various level, we go
+%   back up, packing digits and bringing the \meta{function} (|#9|, then
+%   |#7|) from the end of the argument list to its start.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \@@_fixed_add:wwN { \@@_fixed_add_i:NNnnnnwnn + + }
+\cs_new_nopar:Npn \@@_fixed_sub:wwN { \@@_fixed_add_i:NNnnnnwnn + - }
+\cs_new_nopar:Npn \@@_fixed_sub_back:wwN { \@@_fixed_add_i:NNnnnnwnn - + }
+\cs_new:Npn \@@_fixed_add_i:NNnnnnwnn #1#2 #3#4#5#6 #7; #8#9
+  {
+    \exp_after:wN \@@_fixed_add_after:NNNNNwN
+    \int_use:N \__int_eval:w 1 9999 9998 #1 #3#4 #2 #8#9
+      \exp_after:wN \@@_fixed_add_pack:NNNNNwN
+      \int_use:N \__int_eval:w 1 9999 9998 #1 #5#6
+        \@@_fixed_add_ii:NnnNnnnnw #1 #7 #2
+  }
+\cs_new:Npn \@@_fixed_add_ii:NnnNnnnnw #1 #2#3 #4 #5#6 #7#8 ; #9
+  {
+    #4 #5#6
+    \exp_after:wN \@@_fixed_add_pack:NNNNNwN
+    \int_use:N \__int_eval:w 2 0000 0000 #4 #7#8 #1 #2#3 ; #9 ;
+  }
+\cs_new:Npn \@@_fixed_add_pack:NNNNNwN #1 #2#3#4#5 #6; #7
+  { + #1 ; #7 {#2#3#4#5} {#6} }
+\cs_new:Npn \@@_fixed_add_after:NNNNNwN #1 #2#3#4#5 #6; #7
+  {
+    \exp_after:wN #7
+    \exp_after:wN { \int_use:N \__int_eval:w - 2 0000 + #1#2#3#4#5 }
+    {#6}
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_fixed_mul:wwn}
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_fixed_mul_i:nnnnnnnn   ,
+%     \@@_fixed_mul_pack:NNNNNw    ,
+%     \@@_fixed_mul_after:wwn
+%   }
+%   \begin{syntax}
+%     \cs{@@_fixed_mul:wwn} \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \Arg{X_5} \Arg{X_6} |;| \Arg{Y_1} \Arg{Y_2} \Arg{Y_3} \Arg{Y_4} \Arg{Y_5} \Arg{Y_6} |;| \Arg{tokens}
+%   \end{syntax}
+%   Computes $X\times Y$ and feeds the result to \meta{function}. It
+%   would be nice to grab the $12$ brace groups in one go, but that's
+%   not possible.  On the other hand, we don't need to obtain an exact
+%   rounding, contrarily to the case in \cs{@@_*_o:ww}, so things are
+%   not quite as bad as they may seem.  The parenthesis computing the
+%   seventh group of digits (computed because we need to know its
+%   potentially large carry) is closed by
+%   \cs{@@_fixed_mul_i:nnnnnnnn}, once we access the last two brace
+%   groups, which were not read before. Also, in
+%   \cs{@@_fixed_mul_after:wwn}, |#3| is the continuation
+%   tokens.\footnote{Bruno: insist on the difference compared to
+%     \cs{@@_fixed_add:wwN}.}
+%    \begin{macrocode}
+\cs_new:Npn \@@_fixed_mul:wwn #1#2#3#4 #5; #6#7#8#9
+  {
+    \exp_after:wN \@@_fixed_mul_after:wwn
+    \int_use:N \__int_eval:w \c_@@_leading_shift_int
+      \exp_after:wN \@@_pack:NNNNNw
+      \int_use:N \__int_eval:w \c_@@_middle_shift_int
+        + #1*#6
+        \exp_after:wN \@@_pack:NNNNNw
+        \int_use:N \__int_eval:w \c_@@_middle_shift_int
+          + #1*#7 + #2*#6
+          \exp_after:wN \@@_pack:NNNNNw
+          \int_use:N \__int_eval:w \c_@@_middle_shift_int
+            + #1*#8 + #2*#7 + #3*#6
+            \exp_after:wN \@@_pack:NNNNNw
+            \int_use:N \__int_eval:w \c_@@_middle_shift_int
+              + #1*#9 + #2*#8 + #3*#7 + #4*#6
+              \exp_after:wN \@@_pack:NNNNNw
+              \int_use:N \__int_eval:w \c_@@_trailing_shift_int
+                + #2*#9 + #3*#8 + #4*#7
+                + ( #3*#9 + #4*#8
+                  + \@@_fixed_mul_i:nnnnnnnn #5 {#6}{#7}  {#1}{#2}
+  }
+\cs_new:Npn \@@_fixed_mul_i:nnnnnnnn #1#2 #3#4 #5#6 #7#8
+  { #1*#4 + #2*#3 + #5*#8 + #6*#7 )/10000 + #1*#3 + #5*#7 ; }
+\cs_new:Npn \@@_fixed_mul_pack:NNNNNw
+    #1 #2#3#4#5 #6; { + #1#2#3#4#5 ; {#6} }
+\cs_new:Npn \@@_fixed_mul_after:wwn #1; #2; #3 { #3 {#1} #2 ; }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_fixed_mul_add:wwwn, \@@_fixed_mul_sub_back:wwwn}
+%   \begin{syntax}
+%     \cs{@@_fixed_mul_add:wwn} \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \Arg{X_5} \Arg{X_6} |;| \Arg{Y_1} \Arg{Y_2} \Arg{Y_3} \Arg{Y_4} \Arg{Y_5} \Arg{Y_6} |;| \Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \Arg{Z_5} \Arg{Z_6} |;| \Arg{tokens}
+%   \end{syntax}
+%   These functions compute $X\times Y + Z$ or $Z-X\times Y$ and feed
+%   the result to the \meta{tokens}.  This is tough because we have $18$
+%   brace groups in front of us.
+%    \begin{macrocode}
+\cs_new:Npn \@@_fixed_one_minus_mul:wwn #1; #2#3#4#5;
+  {
+    \exp_after:wN \@@_fixed_mul_after:wwn
+    \int_use:N \__int_eval:w \c_@@_big_leading_shift_int + \c_ten_thousand
+      \exp_after:wN \@@_pack_big:NNNNNNw
+      \int_use:N \__int_eval:w \c_@@_big_middle_shift_int
+        \@@_fixed_mul_add_i:Nnwnnwnnn
+          - 00; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; - 00 ;
+  }
+\cs_new:Npn \@@_fixed_mul_add:wwwn #1; #2#3#4#5; #6#7#8#9
+  {
+    \exp_after:wN \@@_fixed_mul_after:wwn
+    \int_use:N \__int_eval:w \c_@@_big_leading_shift_int + #6
+      \exp_after:wN \@@_pack_big:NNNNNNw
+      \int_use:N \__int_eval:w \c_@@_big_middle_shift_int + #7
+        \@@_fixed_mul_add_i:Nnwnnwnnn
+          + {#8}{#9}; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; +
+  }
+\cs_new:Npn \@@_fixed_mul_sub_back:wwwn #1; #2#3#4#5; #6#7#8#9
+  {
+    \exp_after:wN \@@_fixed_mul_after:wwn
+    \int_use:N \__int_eval:w \c_@@_big_leading_shift_int + #6
+      \exp_after:wN \@@_pack_big:NNNNNNw
+      \int_use:N \__int_eval:w \c_@@_big_middle_shift_int + #7
+        \@@_fixed_mul_add_i:Nnwnnwnnn
+          - {#8}{#9}; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; -
+  }
+\cs_new:Npn \@@_fixed_mul_add_i:Nnwnnwnnn #1 #2#3; #4#5#6; #7#8#9
+  { % sg z3z4; y1y2y3; x1x2x3  x4x5x6; y1y2y3y4y5y6; sg z5z6;
+        #1 #7*#4
+        \exp_after:wN \@@_pack_big:NNNNNNw
+        \int_use:N \__int_eval:w \c_@@_big_middle_shift_int + #2
+          #1 #7*#5 #1 #8*#4
+          \exp_after:wN \@@_pack_big:NNNNNNw
+          \int_use:N \__int_eval:w \c_@@_big_middle_shift_int + #3
+            #1 #7*#6 #1 #8*#5 #1 #9*#4
+            \exp_after:wN \@@_pack_big:NNNNNNw
+            \int_use:N \__int_eval:w \c_@@_big_middle_shift_int
+              #1 \@@_fixed_mul_add_ii:nnnnwnnnn {#7}{#8}{#9}
+  }
+\cs_new:Npn \@@_fixed_mul_add_ii:nnnnwnnnn #1#2#3#4#5; #6#7#8#9
+  { % x1x2x3x4 x5x6; y1y2y3y4  y5y6; sg z5z6;
+    ( #1*#9 + #2*#8 + #3*#7 + #4*#6 )
+    \exp_after:wN \@@_pack_big:NNNNNNw
+    \int_use:N \__int_eval:w \c_@@_big_trailing_shift_int
+      \@@_fixed_mul_add_iii:nnnnwnnwN
+        { #6 + #4*#7 + #3*#8 + #2*#9 + #1 }
+        { #7 + #4*#8 + #3*#9 + #2 }
+        {#1} #5;
+        {#6}
+  }
+\cs_new:Npn \@@_fixed_mul_add_iii:nnnnwnnwN #1#2 #3#4#5; #6#7#8; #9
+  { % {y1+x4*y2+x3*y3+x2*y4+x1} {y2+x4*y3+x3*y4+x2}
+    % x1x5x6; y1y5y6; sg z5z6;
+    % =>
+    % sg (x5*y1+x4*y2+x3*y3+x2*y4+x1*y5)
+    % sg (x6*y1+x5*y2+x4*y3+x3*y4+x2*y5+x1*y6)/10000
+    % + z5z6;
+    #9 (#4* #1 *#7)
+    #9 (#5*#6+#4* #2 *#7+#3*#8) / \c_ten_thousand
+    + \@@_use_s:nn
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+\cs_new:Npn \@@_fixed_to_float:Nw #1#2; { \@@_fixed_to_float:wN #2; #1 }
+%    \end{macrocode}
+%
+% \begin{macro}[int, rEXP]{\@@_fixed_to_float:wN}
+%   \begin{syntax}
+%     \ldots{} \cs{__int_eval:w} \meta{exponent} \cs{@@_fixed_to_float:wN} \Arg{a_1} \Arg{a_2} \Arg{a_3} \Arg{a_4} \Arg{a_5} \Arg{a_6} |;| \meta{sign}
+%   \end{syntax}
+%   yields
+%   \begin{quote}
+%     \meta{exponent'} |;| \Arg{a'_1} \Arg{a'_2} \Arg{a'_3} \Arg{a'_4} |;|
+%   \end{quote}
+%   And the \texttt{to_fixed} version gives six brace groups instead of
+%   $4$, ensuring that $1000\leq\meta{a'_1}\leq 9999$.  At this stage, we
+%   know that \meta{a_1} is positive (otherwise, it is sign of an error
+%   before), and we assume that it is less than $10^8$.\footnote{Bruno:
+%     I must double check this assumption.}
+%
+%^^A todo: round properly when rounding to infinity: I need to know the sign.
+%    \begin{macrocode}
+\cs_new:Npn \@@_fixed_to_float:wN #1#2#3#4#5#6; #7
+  {
+    + \c_four % for the 8-digit-at-the-start thing.
+    \exp_after:wN \exp_after:wN
+    \exp_after:wN \@@_fixed_to_loop:N
+    \exp_after:wN \use_none:n
+    \int_use:N \__int_eval:w
+      1 0000 0000 + #1   \exp_after:wN \@@_use_none_stop_f:n
+      \__int_value:w   1#2 \exp_after:wN \@@_use_none_stop_f:n
+      \__int_value:w 1#3#4 \exp_after:wN \@@_use_none_stop_f:n
+      \__int_value:w 1#5#6
+    \exp_after:wN ;
+    \exp_after:wN ;
+  }
+\cs_new:Npn \@@_fixed_to_loop:N #1
+  {
+    \if_meaning:w 0 #1
+      - \c_one
+      \exp_after:wN \@@_fixed_to_loop:N
+    \else:
+      \exp_after:wN \@@_fixed_to_loop_end:w
+      \exp_after:wN #1
+    \fi:
+  }
+\cs_new:Npn \@@_fixed_to_loop_end:w #1 #2 ;
+  {
+    \if_meaning:w ; #1
+      \exp_after:wN \@@_fixed_to_float_zero:w
+    \else:
+      \exp_after:wN \@@_pack_twice_four:wNNNNNNNN
+      \exp_after:wN \@@_pack_twice_four:wNNNNNNNN
+      \exp_after:wN \@@_fixed_to_float_pack:ww
+      \exp_after:wN ;
+    \fi:
+    #1 #2 0000 0000 0000 0000 ;
+  }
+\cs_new:Npn \@@_fixed_to_float_zero:w ; 0000 0000 0000 0000 ;
+  {
+    - \c_two * \c_@@_max_exponent_int ;
+    {0000} {0000} {0000} {0000} ;
+  }
+\cs_new:Npn \@@_fixed_to_float_pack:ww #1 ; #2#3 ; ;
+  {
+    \if_int_compare:w #2 > \c_four
+      \exp_after:wN \@@_fixed_to_float_round_up:wnnnnw
+    \fi:
+    ; #1 ;
+  }
+\cs_new:Npn \@@_fixed_to_float_round_up:wnnnnw ; #1#2#3#4 ;
+  {
+    \exp_after:wN \@@_basics_pack_high:NNNNNw
+    \int_use:N \__int_eval:w 1 #1#2
+      \exp_after:wN \@@_basics_pack_low:NNNNNw
+      \int_use:N \__int_eval:w 1 #3#4 + \c_one ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[rEXP, int]{\@@_fixed_inv_to_float:wN, \@@_fixed_div_to_float:ww}
+%   Starting from \texttt{fixed_dtf} $A$ |;| $B$ |;| we want to compute
+%   $A/B$, and express it as a floating point number.  Normalize both
+%   numbers by removing leading brace groups of zeros and leaving the
+%   appropriate exponent shift in the input stream.
+%    \begin{macrocode}
+\cs_new:Npn \@@_fixed_inv_to_float:wN #1#2; #3
+  {
+    - \__int_eval:w
+        \if_int_compare:w #1 < \c_one_thousand
+          \@@_fixed_dtf_zeros:wNnnnnnn
+        \fi:
+        \@@_fixed_dtf_no_zero:Nwn + {#1} #2 \s_@@
+        \@@_fixed_dtf_approx:n
+        {10000} {0000} {0000} {0000} {0000} {0000} ;
+  }
+\cs_new:Npn \@@_fixed_div_to_float:ww #1#2; #3#4;
+  {
+    \if_int_compare:w #1 < \c_one_thousand
+      \@@_fixed_dtf_zeros:wNnnnnnn
+    \fi:
+    \@@_fixed_dtf_no_zero:Nwn - {#1} #2 \s_@@
+    {
+      \if_int_compare:w #3 < \c_one_thousand
+        \@@_fixed_dtf_zeros:wNnnnnnn
+      \fi:
+      \@@_fixed_dtf_no_zero:Nwn + {#3} #4 \s_@@
+      \@@_fixed_dtf_approx:n
+    }
+  }
+\cs_new:Npn \@@_fixed_dtf_no_zero:Nwn #1#2 \s_@@ #3 { #3 #2; }
+\cs_new:Npn \@@_fixed_dtf_zeros:wNnnnnnn
+    \fi: \@@_fixed_dtf_no_zero:Nwn #1#2#3#4#5#6#7
+  {
+    \fi:
+    #1 \c_minus_one
+    \exp_after:wN \use_i_ii:nnn
+    \exp_after:wN \@@_fixed_dtf_zeros:NN
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w 10 0000 + #2 \__int_eval_end: #3#4#5#6#7
+    ; 1 ;
+  }
+\cs_new:Npn \@@_fixed_dtf_zeros:NN #1#2
+  {
+    \if_meaning:w 0 #2
+      #1 \c_one
+    \else:
+      \@@_fixed_dtf_zeros_end:wNww #2
+    \fi:
+    \@@_fixed_dtf_zeros:NN #1
+  }
+\cs_new:Npn \@@_fixed_dtf_zeros_end:wNww
+    #1 \fi: \@@_fixed_dtf_zeros:NN #2 #3; #4 \s_@@
+  {
+    \fi:
+    \if_meaning:w ; #1
+      #2 \c_two * \c_@@_max_exponent_int
+      \use_i_ii:nnn
+    \fi:
+    \@@_fixed_dtf_zeros_ii:ww
+    #1#3 0000 0000 0000 0000 0000 0000 ;
+  }
+\cs_new:Npn \@@_fixed_dtf_zeros_ii:ww
+  {
+    \@@_pack_twice_four:wNNNNNNNN
+    \@@_pack_twice_four:wNNNNNNNN
+    \@@_pack_twice_four:wNNNNNNNN
+    \@@_fixed_dtf_zeros_iii:ww
+    ;
+  }
+\cs_new:Npn \@@_fixed_dtf_zeros_iii:ww #1; #2; #3 { #3 #1; }
+%    \end{macrocode}
+%   \newcommand{\eTeXfrac}[2]{\left[\frac{#1}{#2}\right]}
+%   We get
+%   \begin{quote}
+%     \cs{@@_fixed_dtf_approx:n} \meta{B'} |;| \meta{A'} |;|
+%   \end{quote}
+%   where \meta{B'} and \meta{A'} are each $6$ brace groups,
+%   representing fixed point numbers in the range $[0.1,1)$.  Denote by
+%   $x\in[1000,9999]$ and $y\in[0,9999]$ the first two groups of
+%   \meta{B'}.  We first find an estimate $a$ for the inverse of $B'$ by
+%   computing
+%   \begin{align*}
+%     \alpha &= \eTeXfrac{10^{9}}{x+1} \\
+%     \beta  &= \eTeXfrac{10^{9}}{x} \\
+%     a &= 10^{3} \alpha + (\beta-\alpha) \cdot
+%       \left(10^{3}-\eTeXfrac{y}{10}\right) - 1750,
+%   \end{align*}
+%   where $\eTeXfrac{\bullet}{\bullet}$ denotes \eTeX{}'s rounding
+%   division.  The idea is to interpolate between $\alpha$ and $\beta$
+%   with a parameter $y/10^{4}$.  The shift by $1750$ helps to ensure
+%   that $a$ is an underestimate of the correct value.  We will prove
+%   that
+%   \[
+%   1 - 2.255\cdot 10^{-5} < \frac{B'a}{10^{8}} < 1 .
+%   \]
+%   We can then compute the inverse $B'a/10^{8}$ using $1/(1-\epsilon)
+%   \simeq (1+\epsilon)(1+\epsilon^{2})$, which is correct up to a
+%   relative error of $\epsilon^4 < 2.6\cdot 10^{-19}$.  Since we target
+%   a $16$-digit value, this is small enough.
+%
+%   Let us prove the upper bound first.
+%   \begin{align}\label{l3fp-fixed-eTeXfrac}
+%     10^{7} B'a
+%       & < \left(10^{3} x + \eTeXfrac{y}{10} + \frac{3}{2}\right)
+%       \left(\left(10^{3}-\eTeXfrac{y}{10}\right) \beta
+%         + \eTeXfrac{y}{10} \alpha - 1750\right)
+%     \\& < \left(10^{3} x + \eTeXfrac{y}{10} + \frac{3}{2}\right)
+%       \left(\left(10^{3}-\eTeXfrac{y}{10}\right)
+%         \left(\frac{10^{9}}{x} + \frac{1}{2} \right)
+%         + \eTeXfrac{y}{10} \left(\frac{10^{9}}{x+1} + \frac{1}{2} \right)
+%         - 1750\right)
+%     \\& < \left(10^{3} x + \eTeXfrac{y}{10} + \frac{3}{2}\right)
+%       \left(\frac{10^{12}}{x}
+%         - \eTeXfrac{y}{10} \frac{10^{9}}{x(x+1)}
+%         - 1250\right)
+%   \end{align}
+%   We recognize a quadratic polynomial in $[y/10]$ with a negative
+%   leading coefficient, $([y/10]+a)(b-c[y/10]) \leq (b+ca)^2/(4c)$.
+%   Hence,
+%   \[
+%   10^{7} B'a
+%   < \frac{10^{15}}{x(x+1)} \left(
+%     x + \frac{1}{2} + \frac{3}{4} 10^{-3}
+%     - 6.25\cdot 10^{-10} x(x+1) \right)^2
+%   \]
+%   We want to prove that the squared expression is less than $x(x+1)$,
+%   which we do by simplifying the difference, and checking its sign,
+%   \[
+%   x(x+1) - \left(x + \frac{1}{2} + \frac{3}{4} 10^{-3}
+%     - 6.25\cdot 10^{-10} x(x+1) \right)^2
+%   > - \frac{1}{4} (1+1.5\cdot 10^{-3})^2 - 10^{-3} x
+%     + 1.25\cdot 10^{-9} x(x+1)(x+0.5)
+%   > 0.
+%   \]
+%
+%   Now, the lower bound.  The same computation as
+%   \eqref{l3fp-fixed-eTeXfrac} imply
+%   \[
+%     10^{7} B'a
+%       > \left(10^{3} x + \eTeXfrac{y}{10} - \frac{1}{2}\right)
+%       \left(\frac{10^{12}}{x} - \eTeXfrac{y}{10} \frac{10^{9}}{x(x+1)}
+%         - 2250\right)
+%   \]
+%   This time, we want to find the minimum of this quadratic polynomial.
+%   Since the leading coefficient is still negative, the minimum is
+%   reached for one of the extreme values $y=0$ or $y=9999$, and we
+%   easily check the bound for those values.
+%
+%   We have proven that the algorithm will give us a precise enough
+%   answer.  Incidentally, the upper bound that we derived tells us that
+%   $a < 10^{8}/B \leq 10^{9}$, hence we can compute $a$ safely as a
+%   \TeX{} integer, and even add $10^{9}$ to it to ease grabbing of all
+%   the digits.
+%    \begin{macrocode}
+\cs_new:Npn \@@_fixed_dtf_approx:n #1
+  {
+    \exp_after:wN \@@_fixed_dtf_approx_ii:wnn
+    \int_use:N \__int_eval:w 10 0000 0000 / ( #1 + \c_one ) ;
+    {#1}
+  }
+\cs_new:Npn \@@_fixed_dtf_approx_ii:wnn #1; #2#3
+  {
+%<assert>    \assert:n { \tl_count:n {#1} = 6 }
+    \exp_after:wN \@@_fixed_dtf_approx_iii:NNNNNw
+    \int_use:N \__int_eval:w 10 0000 0000 - 1750
+      + #1000 + (10 0000 0000/#2-#1) * (1000-#3/10) ;
+    {#2}{#3}
+  }
+\cs_new:Npn \@@_fixed_dtf_approx_iii:NNNNNw 1#1#2#3#4#5#6; #7; #8;
+  {
+    + \c_four % because of the line below "dtf_epsilon" here.
+    \@@_fixed_mul:wwn {000#1}{#2#3#4#5}{#6}{0000}{0000}{0000} ; #7;
+    \@@_fixed_dtf_epsilon:wN
+    \@@_fixed_mul:wwn {000#1}{#2#3#4#5}{#6}{0000}{0000}{0000} ;
+    \@@_fixed_mul:wwn #8;
+    \@@_fixed_to_float:wN ?
+  }
+\cs_new:Npn \@@_fixed_dtf_epsilon:wN #1#2#3#4#5#6;
+  {
+%<assert>    \assert:n { #1 = 0000 }
+%<assert>    \assert:n { #2 = 9999 }
+    \exp_after:wN \@@_fixed_dtf_epsilon_ii:NNNNNww
+    \int_use:N \__int_eval:w 1 9999 9998 - #3#4 +
+      \exp_after:wN \@@_fixed_dtf_epsilon_pack:NNNNNw
+      \int_use:N \__int_eval:w 2 0000 0000 - #5#6 ; {0000} ;
+  }
+\cs_new:Npn \@@_fixed_dtf_epsilon_pack:NNNNNw #1#2#3#4#5#6;
+  { #1 ; {#2#3#4#5} {#6} }
+\cs_new:Npn \@@_fixed_dtf_epsilon_ii:NNNNNww #1#2#3#4#5#6; #7;
+  {
+    \@@_fixed_mul:wwn %^^A todo: optimize to use \@@_mul_mantissa.
+      {0000} {#2#3#4#5} {#6} #7 ;
+      {0000} {#2#3#4#5} {#6} #7 ;
+    \@@_fixed_add_one:wN
+    \@@_fixed_mul:wwn {10000} {#2#3#4#5} {#6} #7 ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintChanges
+%
+% \PrintIndex
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-logic.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-logic.dtx
new file mode 100644
index 00000000000..2517236fb21
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-logic.dtx
@@ -0,0 +1,393 @@
+% \iffalse meta-comment
+%
+%% File: l3fp-logic.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp-logic.dtx 3504 2012-03-06 06:38:45Z bruno $
+  {L3 Floating-point conditionals}
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{The \textsf{l3fp-logic} package\thanks{This file
+%         has version number \ExplFileVersion, last
+%         revised \ExplFileDate.}\\
+% Floating point conditionals}
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+% \date{Released \ExplFileDate}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3fp-logic} Implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+% \subsection{Existence test}
+%
+% \begin{macro}[pTF]{\fp_if_exist:N, \fp_if_exist:c}
+%   Copies of the \texttt{cs} functions defined in \pkg{l3basics}.
+%    \begin{macrocode}
+\cs_new_eq:NN \fp_if_exist:NTF \cs_if_exist:NTF
+\cs_new_eq:NN \fp_if_exist:NT  \cs_if_exist:NT
+\cs_new_eq:NN \fp_if_exist:NF  \cs_if_exist:NF
+\cs_new_eq:NN \fp_if_exist_p:N \cs_if_exist_p:N
+\cs_new_eq:NN \fp_if_exist:cTF \cs_if_exist:cTF
+\cs_new_eq:NN \fp_if_exist:cT  \cs_if_exist:cT
+\cs_new_eq:NN \fp_if_exist:cF  \cs_if_exist:cF
+\cs_new_eq:NN \fp_if_exist_p:c \cs_if_exist_p:c
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Comparison}
+%
+% \begin{macro}[int, EXP]{\@@_compare:ww}
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_compare_nan:w, \@@_compare_mantissa:ww,
+%     \@@_compare_mantissa:nnnnnnnn
+%   }
+%   \begin{syntax}
+%     \cs{@@_compare:ww} \meta{X} |;| \meta{Y} |;|
+%   \end{syntax}
+%   Expands (in the same way as \cs{int_eval:n}) to $-1$ if $x<y$, $0$
+%   if $x=y$, $1$ if $x>y$, and $2$ otherwise (denoted as $x?y$).  A
+%   trick that will later be useful is that the character codes of |<|,
+%   |=|, |>| and |?| are contiguous, and in the same order as the return
+%   codes of \cs{@@_compare:ww}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_compare:ww \s_@@ \@@_chk:w #1#2#3; \s_@@ \@@_chk:w #4#5#6;
+  {
+    \__int_value:w
+      \if_meaning:w 3 #1 \exp_after:wN \@@_compare_nan:w \fi:
+      \if_meaning:w 3 #4 \exp_after:wN \@@_compare_nan:w \fi:
+      \if_meaning:w 2 #2 - \fi:
+      \if_meaning:w #2 #5
+        \if_meaning:w #1 #4
+          \if_meaning:w 1 #1
+            \@@_compare_mantissa:ww #3; #6;
+          \else:
+            0
+          \fi:
+        \else:
+          \if_int_compare:w #1 < #4 - \fi: 1
+        \fi:
+      \else:
+        \if_meaning:w 0 #1
+          \if_meaning:w 0 #4
+            0
+          \else:
+            1
+          \fi:
+        \else:
+          1
+        \fi:
+      \fi:
+    \exp_stop_f:
+  }
+\cs_new:Npn \@@_compare_nan:w #1 \exp_stop_f: { \c_two }
+\cs_new:Npn \@@_compare_mantissa:ww #1#2; #3#4;
+  {
+    \if_int_compare:w #1 = #3 \exp_stop_f:
+      \@@_compare_mantissa:nnnnnnnn #2 #4
+    \else:
+      \if_int_compare:w #1 < #3 - \fi: 1
+    \fi:
+  }
+\cs_new:Npn \@@_compare_mantissa:nnnnnnnn #1#2#3#4#5#6#7#8
+  {
+    \if_int_compare:w #1 = #5 \exp_stop_f:
+      \if_int_compare:w #2 = #6 \exp_stop_f:
+        \if_int_compare:w #3 = #7 \exp_stop_f:
+          \if_int_compare:w #4 = #8 \exp_stop_f:
+            0
+          \else:
+            \if_int_compare:w #4 < #8 - \fi: 1
+          \fi:
+        \else:
+          \if_int_compare:w #3 < #7 - \fi: 1
+        \fi:
+      \else:
+        \if_int_compare:w #2 < #6 - \fi: 1
+      \fi:
+    \else:
+      \if_int_compare:w #1 < #5 - \fi: 1
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[pTF, EXP]{\fp_compare:nNn}
+% \begin{macro}[aux, EXP]{\@@_compare_aux:wn}
+%   Evaluate |#1| and |#3|, using an auxiliary to expand both, in the
+%   correct order.  Then compare this to |`#2-`=|, which is $-1$ for
+%   |<|, $0$ for |=|, $1$ for |>| and $2$ for |?|.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \fp_compare:nNn #1#2#3 { p , T , F , TF }
+  {
+    \if_int_compare:w
+        \exp_after:wN \@@_compare_aux:wn
+          \tex_romannumeral:D -`0 \@@_parse:n {#3} {#1}
+        = \__int_eval:w `#2 - `= \__int_eval_end:
+      \prg_return_true:
+    \else:
+      \prg_return_false:
+    \fi:
+  }
+\cs_new:Npn \@@_compare_aux:wn #1; #2
+  {
+    \exp_after:wN \@@_compare:ww
+      \tex_romannumeral:D -`0 \@@_parse:n {#2} #1;
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP,pTF]{\fp_compare:n}
+% \begin{macro}[aux,EXP]{\@@_compare_aux:w}
+%   For floating points the comparison operators are treated as
+%   operations, so we simply evaluate then compare with \cs{c_zero_fp}.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \fp_compare:n #1 { p , T , F , TF }
+  {
+    \exp_after:wN \@@_compare_aux:w
+    \tex_romannumeral:D -`0 \@@_parse:n {#1}
+  }
+\cs_new:Npn \@@_compare_aux:w \s_@@ \@@_chk:w #1#2;
+  {
+    \if_meaning:w 0 #1
+      \prg_return_false:
+    \else:
+      \prg_return_true:
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Boolean operations}
+%
+% \begin{macro}[int, EXP]{\@@_not:w}
+%   Return \texttt{true} or \texttt{false}, with two expansions, one to
+%   exit the conditional, and one to please \pkg{l3fp-parse}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_not:w \s_@@ \@@_chk:w #1#2;
+  {
+    \if_meaning:w 0 #1
+      \exp_after:wN \exp_after:wN \exp_after:wN \c_one_fp
+    \else:
+      \exp_after:wN \exp_after:wN \exp_after:wN \c_zero_fp
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]+\@@_&_o:ww+
+% \begin{macro}[int, EXP]+\@@_|_o:ww+
+% \begin{macro}[aux, EXP]{\@@_and_return:wNw}
+%   For \texttt{and}, if the first number is zero, return it (with the
+%   same sign).  Otherwise, return the second one.  For \texttt{or}, the
+%   logic is reversed: if the first number is non-zero, return it,
+%   otherwise return the second number: we achieve that by hi-jacking
+%   \cs{@@_\&_o:ww}, inserting an extra argument, \cs{else:}, before
+%   \cs{s_@@}.  In all cases, expand after the floating point number.
+%    \begin{macrocode}
+\cs_new:cpn { @@_ \iow_char:N \& _o:ww } #1 \s_@@ \@@_chk:w #2#3;
+  {
+    \if_meaning:w 0 #2 #1
+      \@@_and_return:wNw \s_@@ \@@_chk:w #2#3;
+    \fi:
+    \@@_exp_after_o:w
+  }
+\cs_new_nopar:cpx { @@_ \iow_char:N \| _o:ww }
+  { \exp_not:c { @@_ \iow_char:N \& _o:ww } \exp_not:N \else: }
+\cs_new:Npn \@@_and_return:wNw #1; \fi: #2#3; { \fi: #2 #1; }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]
+%   {\@@_ternary:NwwN, \@@_ternary_i:NwwN, \@@_ternary_ii:NwwN}
+%   The first function receives the test and the true branch of the |?:|
+%   ternary operator.  It returns the true branch, unless the test
+%   branch is zero.  In that case, the function returns a very specific
+%   \texttt{nan}.  The second function receives the output of the first
+%   function, and the false branch.  It returns the previous input,
+%   unless that is the special \texttt{nan}, in which case we return the
+%   false branch.
+%^^A todo: optimize.
+%    \begin{macrocode}
+\cs_new:Npn \@@_ternary:NwwN #1 #2@ #3@ #4
+  {
+    \if_meaning:w \@@_parse_infix_::N #4
+      \@@_ternary_loop:Nw
+        #2
+        \s_@@ \@@_chk:w { \@@_ternary_loop_break:w } ;
+      \@@_ternary_break_point:n { \exp_after:wN \@@_ternary_i:NwwN }
+      \exp_after:wN #1
+      \tex_romannumeral:D -`0
+      \@@_parse_exp_after_array:wf #3 \s_@@_stop
+      \exp_after:wN @
+      \tex_romannumeral:D
+        \@@_parse_until:Nw \c_two
+        \@@_parse_expand:w
+    \else:
+      \@@_error:n { Missing~':'~clause~for~'?:'. }
+      \exp_after:wN \@@_parse_until_test:NwN
+      \exp_after:wN #1
+      \tex_romannumeral:D -`0
+      \@@_parse_exp_after_array:wf #3 \s_@@_stop
+      \exp_after:wN #4
+      \exp_after:wN #1
+    \fi:
+  }
+\cs_new:Npn \@@_ternary_loop_break:w #1 \fi: #2 \@@_ternary_break_point:n #3
+  {
+    \c_zero = \c_zero \fi:
+    \exp_after:wN \@@_ternary_ii:NwwN
+  }
+\cs_new:Npn \@@_ternary_loop:Nw \s_@@ \@@_chk:w #1#2;
+  {
+    \if_int_compare:w #1 > \c_zero
+      \exp_after:wN \@@_ternary_map_break:
+    \fi:
+    \@@_ternary_loop:Nw
+  }
+\cs_new:Npn \@@_ternary_map_break: #1 \@@_ternary_break_point:n #2 {#2}
+\cs_new:Npn \@@_ternary_i:NwwN #1#2@#3@#4
+  {
+    \exp_after:wN \@@_parse_until_test:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+    \@@_parse_exp_after_array:wf #2 \s_@@_stop
+    #4 #1
+  }
+\cs_new:Npn \@@_ternary_ii:NwwN #1#2@#3@#4
+  {
+    \exp_after:wN \@@_parse_until_test:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+    \@@_parse_exp_after_array:wf #3 \s_@@_stop
+    #4 #1
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_max:w, \@@_min:w}
+%    \begin{macrocode}
+\cs_new:Npn \@@_max:w #1@
+  {
+    \exp_after:wN \@@_minmax_loop:Nww
+    \exp_after:wN \c_minus_one
+    \c_minus_inf_fp
+    #1
+    \s_@@ \@@_chk:w { 3 \@@_minmax_break:w } ;
+  }
+\cs_new:Npn \@@_min:w #1@
+  {
+    \exp_after:wN \@@_minmax_loop:Nww
+    \exp_after:wN \c_one
+    \c_inf_fp
+    #1
+    \s_@@ \@@_chk:w { 3 \@@_minmax_break:w } ;
+  }
+\cs_new:Npn \@@_minmax_loop:Nww
+    #1 \s_@@ \@@_chk:w #2#3; \s_@@ \@@_chk:w #4#5;
+  {
+    \if_meaning:w 3 #4
+      \if_meaning:w 3 #2
+        \@@_minmax_i:ww
+      \else:
+        \@@_minmax_ii:ww
+      \fi:
+    \else:
+      \if_int_compare:w \@@_compare:ww \s_@@ \@@_chk:w #2#3;
+                               \s_@@ \@@_chk:w #4#5; = #1
+        \@@_minmax_ii:ww
+      \else:
+        \@@_minmax_i:ww
+      \fi:
+    \fi:
+    \@@_minmax_loop:Nww #1
+      \s_@@ \@@_chk:w #2#3;
+      \s_@@ \@@_chk:w #4#5;
+  }
+\cs_new:Npn \@@_minmax_i:ww
+    #1 \@@_minmax_loop:Nww #2 \s_@@ #3; \s_@@ #4;
+  { #1 \@@_minmax_loop:Nww #2 \s_@@ #3; }
+\cs_new:Npn \@@_minmax_ii:ww
+    #1 \@@_minmax_loop:Nww #2 \s_@@ #3; \s_@@ #4;
+  { #1 \@@_minmax_loop:Nww #2 \s_@@ #4; }
+\cs_new:Npn \@@_minmax_break:w #1 \@@_minmax_loop:Nww #2 #3; #4;
+  {
+    \fi:
+    \@@_exp_after_o:w #3;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintChanges
+%
+% \PrintIndex
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-old.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-old.dtx
new file mode 100644
index 00000000000..b195f766d52
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-old.dtx
@@ -0,0 +1,273 @@
+% \iffalse meta-comment
+%
+%% File: l3fp-old.dtx Copyright (C) 2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX3 Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp-old.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Experimental floating-points (old)}
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{^^A
+%   The \pkg{l3fp-old} package\\ Floating-points (old)^^A
+%   \thanks{This file describes v\ExplFileVersion,
+%      last revised \ExplFileDate.}^^A
+% }
+%
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+%
+% \date{Released \ExplFileDate}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3fp-old} implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+% \subsection{Compatibility}
+%
+% \begin{variable}{\c_undefined_fp}
+%   The old floating point number \cs{c_undefined_fp} is now implemented
+%   as a \texttt{nan}.
+%    \begin{macrocode}
+\fp_const:Nn \c_undefined_fp { nan }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}[pTF]{\fp_if_undefined:N}
+%   An old floating point is undefined if it is \texttt{inf} or
+%   \texttt{nan}, \emph{i.e.}, if its type is $2$ or $3$.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF }
+  { \exp_after:wN \@@_if_undefined:w #1 }
+\cs_new:Npn \@@_if_undefined:w \s_@@ \@@_chk:w #1#2;
+  {
+    \if_int_compare:w #1 > \c_one
+      \prg_return_true: \else: \prg_return_false: \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[pTF]{\fp_if_zero:N}
+%   An old floating point is zero if it is $\pm 0$, \emph{i.e.}, its
+%   type is $0$.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF }
+  { \exp_after:wN \@@_if_zero:w #1 }
+\cs_new:Npn \@@_if_zero:w \s_@@ \@@_chk:w #1#2;
+  { \if_meaning:w #1 0 \prg_return_true: \else: \prg_return_false: \fi: }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}
+%   {
+%     \fp_abs:N , \fp_abs:c , \fp_gabs:N , \fp_gabs:c ,
+%     \fp_neg:N , \fp_neg:c , \fp_gneg:N , \fp_gneg:c ,
+%   }
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_abs:N  { \@@_abs:NNN \tl_set:Nx  \@@_abs:w }
+\cs_new_protected_nopar:Npn \fp_gabs:N { \@@_abs:NNN \tl_gset:Nx \@@_abs:w }
+\cs_new_protected_nopar:Npn \fp_neg:N  { \@@_abs:NNN \tl_set:Nx  \@@_neg:w }
+\cs_new_protected_nopar:Npn \fp_gneg:N { \@@_abs:NNN \tl_gset:Nx \@@_neg:w }
+\cs_new_protected:Npn \@@_abs:NNN #1#2#3
+  { #1 #3 { \exp_after:wN #2 #3 \prg_do_nothing: } }
+\cs_generate_variant:Nn \fp_abs:N  { c }
+\cs_generate_variant:Nn \fp_gabs:N { c }
+\cs_generate_variant:Nn \fp_neg:N  { c }
+\cs_generate_variant:Nn \fp_gneg:N { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}
+%   {
+%     \fp_mul:Nn, \fp_mul:cn, \fp_gmul:Nn, \fp_gmul:cn,
+%     \fp_div:Nn, \fp_div:cn, \fp_gdiv:Nn, \fp_gdiv:cn,
+%     \fp_pow:Nn, \fp_pow:cn, \fp_gpow:Nn, \fp_gpow:cn,
+%   }
+% \begin{macro}[aux]{\@@_mul:NNNn}
+%   See \cs{fp_add:Nn} for details.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_mul:Nn  { \@@_mul:NNNn \fp_set:Nn  * }
+\cs_new_protected_nopar:Npn \fp_gmul:Nn { \@@_mul:NNNn \fp_gset:Nn * }
+\cs_new_protected_nopar:Npn \fp_div:Nn  { \@@_mul:NNNn \fp_set:Nn  / }
+\cs_new_protected_nopar:Npn \fp_gdiv:Nn { \@@_mul:NNNn \fp_gset:Nn / }
+\cs_new_protected_nopar:Npn \fp_pow:Nn  { \@@_mul:NNNn \fp_set:Nn  ^ }
+\cs_new_protected_nopar:Npn \fp_gpow:Nn { \@@_mul:NNNn \fp_gset:Nn ^ }
+\cs_new_protected:Npn \@@_mul:NNNn #1#2#3#4 { #1 #3 { #3 #2 (#4) } }
+\cs_generate_variant:Nn \fp_mul:Nn  { c }
+\cs_generate_variant:Nn \fp_gmul:Nn { c }
+\cs_generate_variant:Nn \fp_div:Nn  { c }
+\cs_generate_variant:Nn \fp_gdiv:Nn { c }
+\cs_generate_variant:Nn \fp_pow:Nn  { c }
+\cs_generate_variant:Nn \fp_gpow:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}
+%   {
+%     \fp_exp:Nn, \fp_exp:cn, \fp_gexp:Nn, \fp_gexp:cn,
+%     \fp_ln:Nn , \fp_ln:cn , \fp_gln:Nn , \fp_gln:cn ,
+%     \fp_sin:Nn, \fp_sin:cn, \fp_gsin:Nn, \fp_gsin:cn,
+%     \fp_cos:Nn, \fp_cos:cn, \fp_gcos:Nn, \fp_gcos:cn,
+%     \fp_tan:Nn, \fp_tan:cn, \fp_gtan:Nn, \fp_gtan:cn,
+%   }
+% \begin{macro}[aux]
+%   {\@@_assign_to:nNNNn, \@@_assign_to_i:wNNNn, \@@_assign_to_ii:NnNNN}
+%   Here, an added twist
+%   is that each value computed by these expensive unary operations is
+%   stored as a constant floating point number.
+%    \begin{macrocode}
+\cs_set_protected:Npn \@@_tmp:w #1#2#3#4#5
+  {
+    \cs_new_protected_nopar:Npn #1 { #5 {#4} \tl_set_eq:NN  #3 }
+    \cs_new_protected_nopar:Npn #2 { #5 {#4} \tl_gset_eq:NN #3 }
+    \cs_generate_variant:Nn #1 { c }
+    \cs_generate_variant:Nn #2 { c }
+  }
+\@@_tmp:w \fp_exp:Nn \fp_gexp:Nn \@@_exp:w {exp} \@@_assign_to:nNNNn
+\@@_tmp:w \fp_ln:Nn  \fp_gln:Nn  \@@_ln:w  {ln } \@@_assign_to:nNNNn
+\@@_tmp:w \fp_sin:Nn \fp_gsin:Nn \@@_sin:w {sin} \@@_assign_to:nNNNn
+\@@_tmp:w \fp_cos:Nn \fp_gcos:Nn \@@_cos:w {cos} \@@_assign_to:nNNNn
+\@@_tmp:w \fp_tan:Nn \fp_gtan:Nn \@@_tan:w {tan} \@@_assign_to:nNNNn
+\cs_new_protected:Npn \@@_assign_to:nNNNn #1#2#3#4#5
+  {
+    \exp_after:wN \@@_assign_to_i:wNNNn
+    \tex_romannumeral:D -`0 \@@_parse:n {#5} {#1} #2#3#4
+  }
+\cs_new_protected:Npn \@@_assign_to_i:wNNNn \s_@@ \@@_chk:w #1#2#3; #4
+  {
+    \exp_args:Nc \@@_assign_to_ii:NnNNN
+      { c_@@_ #4 ( #2 \if_meaning:w 1 #1 #3 \fi: ) _fp }
+      { #1#2#3 }
+  }
+\cs_new_protected:Npn \@@_assign_to_ii:NnNNN #1#2#3#4#5
+  {
+    \cs_if_exist:NF #1
+      { \tl_const:Nx #1 { #4 \s_@@ \@@_chk:w #2; } }
+    #3 #5 #1
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[pTF, EXP]{\fp_compare:NNN}
+%   Comparisons used to be easier between floating points stored in
+%   variables. No more.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_compare:NNNTF { \fp_compare:nNnTF }
+\cs_new_protected_nopar:Npn \fp_compare:NNNT  { \fp_compare:nNnT  }
+\cs_new_protected_nopar:Npn \fp_compare:NNNF  { \fp_compare:nNnF  }
+\cs_new_protected_nopar:Npn \fp_compare_p:NNN { \fp_compare_p:nNn }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\fp_round_places:Nn, \fp_ground_places:Nn}
+% \begin{macro}[aux]{\@@_round_places:NNn}
+%   Rounding to a given number of places is easy, since it is provided
+%   by the \pkg{l3fp-round} module.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_round_places:Nn
+  { \@@_round_places:NNn \tl_set:Nx }
+\cs_new_protected_nopar:Npn \fp_ground_places:Nn
+  { \@@_round_places:NNn \tl_gset:Nx }
+\cs_new_protected:Npn \@@_round_places:NNn #1#2#3
+  {
+    #1 #2
+      {
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_round:Nwn
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_round_to_nearest:NNN
+        \exp_after:wN #2
+        \exp_after:wN { \int_use:N \__int_eval:w #3 }
+      }
+  }
+\cs_generate_variant:Nn \fp_round_places:Nn { c }
+\cs_generate_variant:Nn \fp_ground_places:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\fp_round_figures:Nn, \fp_ground_figures:Nn}
+%   Rounding to a given number of figures is the same as rounding to a
+%   number of places, after shifting by the exponent of the argument.
+%    \begin{macrocode}
+\cs_new_protected:Npn \fp_round_figures:Nn #1#2
+  {
+    \@@_round_places:NNn \tl_set:Nx #1
+      { #2 - \exp_after:wN \@@_exponent:w #1 }
+  }
+\cs_new_protected:Npn \fp_ground_figures:Nn #1#2
+  {
+    \@@_round_places:NNn \tl_gset:Nx #1
+      { #2 - \exp_after:wN \@@_exponent:w #1 }
+  }
+\cs_generate_variant:Nn \fp_round_figures:Nn { c }
+\cs_generate_variant:Nn \fp_ground_figures:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintIndex
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-parse.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-parse.dtx
new file mode 100644
index 00000000000..11ec4e11b54
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-parse.dtx
@@ -0,0 +1,2601 @@
+% \iffalse meta-comment
+%
+%% File: l3fp-parse.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp-parse.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Floating-point expression parsing}
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{The \textsf{l3fp-parse} package\thanks{This file
+%         has version number \fileversion, last
+%         revised \filedate.}\\
+% Floating point expression parsing}
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+% \date{Released \filedate}
+%
+% \maketitle
+%
+% ^^A begin[todo]
+%
+% ^^A To typeset the examples of expansion control, I'm using a hand-made
+% ^^A environment.
+% \newcommand{\fpOperation}[1]
+%   {\textcolor[rgb]{.6,.2,.2}{\ttfamily#1}}
+% \newcommand{\fpPrecedence}[1]
+%   {\textcolor[rgb]{.2,.2,.6}{\ttfamily#1}}
+% \newcommand{\fpExpand}[2]
+%   {\underline{\textcolor{red}{#1{#2}}}}
+% \newenvironment{l3fp-code-example}
+%   {\begin{quote}^^A
+%       \edef\^{\string^}^^A
+%       \let\*\fpExpand
+%       \let\o\fpOperation
+%       \let\p\fpPrecedence
+%       \def\!{\begingroup\def\!{\endgroup\par}\color[gray]{0.5}}^^A
+%       \ttfamily\frenchspacing
+%   }{\end{quote}}
+%
+% \begin{documentation}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3fp-parse} implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+% \section{Precedences}
+%
+% In order of evaluation (some distinctions are irrelevant for the order
+% of evaluation, but serve as signals).
+% \begin{itemize}
+% \item[32] Juxtaposition for implicit multiplication.
+% \item[16] Function calls with multiple arguments.
+% \item[15] Function calls expecting exactly one argument.
+% \item[14] Binary |**| and |^| (right to left).
+% \item[12] Unary |+|, |-|, |!| (right to left).
+% \item[10] Binary |*|, |/| and |%|.
+% \item[9] Binary |+| and |-|.
+% \item[7] Comparisons.
+% \item[5] Logical \texttt{and}, denoted by |&&|.
+% \item[4] Logical \texttt{or}, denoted by \verb*+||+.
+% \item[3] Ternary operator |?:|, piece |?|.
+% \item[2] Ternary operator |?:|, piece |:|.
+% \item[1] Commas, and parentheses accepting commas.
+% \item[0] Parentheses expecting exactly one argument.
+% \item[-1] Start and end of the expression.
+% \end{itemize}
+%
+% ^^A todo: change 'mantissa' => 'significand' everywhere.
+% ^^A todo: ask SO when sNaN can arise.
+%
+% \section{Evaluating an expression}
+%
+% \begin{macro}[EXP, int]{\@@_parse:n}
+%   \begin{syntax}
+%     \cs{@@_parse:n} \Arg{floating point expression}
+%   \end{syntax}
+%   This \texttt{f}-expands to the internal floating point number
+%   obtained by evaluating the \meta{floating point expression}.  During
+%   this evaluation, each token is fully \texttt{f}-expanded.
+%   \begin{texnote}
+%     Registers (integers, toks, etc.) are automatically unpacked,
+%     without requiring a function such as \cs{int_use:N}. Invalid
+%     tokens remaining after \texttt{f}-expansion will lead to
+%     unrecoverable low-level TeX errors.\footnote{Bruno: describe what
+%       happens in cases like $2\cs{c_three} = 6$.}
+%   \end{texnote}
+% \end{macro}
+%
+% \section{Work plan}\label{subsec:fp-parse-workplan}
+%
+% The task at hand is non-trivial, and some previous failed attempts have
+% shown me that the code ends up giving unreadable logs, so we'd better get
+% it (almost) right the first time. Let us thus first discuss precisely
+% the design before starting to write the code. To simplify matters,
+% we first consider expressions with integers only.
+%
+% \subsection{Storing results}
+%
+% The main issue in parsing expressions expandably is: \enquote{where
+%   in the input stream should the result be put?}
+%
+% One option is to place the result at the end of the expression,
+% but this has several drawbacks:
+% \begin{itemize}
+% \item firstly it means that for long expressions we would be reaching
+%   all the way to the end of the expression at every step of the
+%   calculation, which can be rather expensive;
+% \item secondly, when parsing parenthesized sub-expressions, we would
+%   naturally place the result after the corresponding closing parenthesis.
+%   But since \cs{@@_parse:n} does not assume that its argument is expanded,
+%   this closing parenthesis may be hidden in a macro, and not present yet,
+%   causing havoc.
+% \end{itemize}
+%
+% The other natural option is to store the result at the start of the
+% expression, and carry it as an argument of each macro. This does not
+% really work either: in order to expand what follows on the input stream,
+% we need to skip at each step over all the tokens in the result using
+% \cs{exp_after:wN}. But this requires adding many \cs{exp_after:wN} to
+% the result at each step, also an expensive process.
+%
+% Hence, we need to go for some fine expansion control: the result is
+% stored \emph{before} the start\ldots{} A toy model that illustrates this
+% idea is to try and add some positive integers which may be hidden
+% within macros, or registers. Assume that one number has already been
+% found, and that we want to parse the next number. The current status
+% of the code may look as follows.
+% \begin{quote}\ttfamily
+%   \cs{exp_after:wN} \cs{add:ww}
+%   \cs{__int_value:w} 12345 \cs{exp_after:wN} ; \newline
+%   \cs{tex_romannumeral:D} -`0 \cs{clean:w} \meta{stuff}
+% \end{quote}
+% Hitting this construction by one step of expansion expands
+% \cs{exp_after:wN}, which triggers the primitive \cs{__int_value:w},
+% which reads an integer, \texttt{12345}. This integer is unfinished,
+% causing the second \cs{exp_after:wN} to expand, and trigger
+% the construction \cs{tex_romannumeral:D} |-`0|, which f-expands
+% \cs{clean:w} (see \pkg{l3expan.dtx} for an explanation). Assume
+% then that \cs{clean:w} is such that it expands \meta{stuff} to
+% \emph{e.g.}, |333444;|. Once \cs{clean:w} is done expanding, we
+% will obtain essentially
+% \begin{quote}\ttfamily
+%   \cs{exp_after:wN} \cs{add:ww} \cs{__int_value:w} 12345 ; 333444 ;
+% \end{quote}
+% where in fact \cs{exp_after:wN} has already been expanded, and
+% \cs{__int_value:w} has already seen \texttt{12345}. Now,
+% \cs{__int_value:w} sees the \texttt{;}, and stops expanding, and
+% we are left with
+% \begin{quote}\ttfamily
+%   \cs{add:ww} 12345 ; 333444 ;
+% \end{quote}
+% which can safely perform the addition by grabbing two arguments
+% delimited by \texttt{;}.
+%
+% On this toy example, we could note that if we were to continue
+% parsing the expression, then the following number should also
+% be cleaned up before the next use of a binary operation such as
+% \cs{add:ww}. Just like \cs{__int_value:w} \texttt{12345}
+% \cs{exp_after:wN} \texttt{;} expanded what follows once, we need
+% \cs{add:ww} to do the calculation, and in the process to expand
+% the following once. This is also true in our real application:
+% all the functions of the form \cs{@@_..._o:ww} expand what
+% follows once. This comes at the cost of leaving tokens in the
+% input stack, and we will need to be careful to waste as little
+% as possible of this precious memory.
+%
+% \subsection{Precedence}
+%
+% A major point to keep in mind when parsing expressions is that
+% different operators have different precedence. The true analog
+% of our toy \cs{clean:w} macro must thus take care of that. For
+% definiteness, let us assume that the operation which prompted
+% \cs{clean:w} was a multiplication. Then \cs{clean:w} (expand
+% and) read digits until the number is ended by some operation.
+% If this is \texttt{+} or~\texttt{-}, then the multiplication
+% should be calculated next, so \cs{clean:w} can simply decide
+% that its job is done. However, if the operator we find is |^|,
+% then this operation must be performed before returning control
+% to the multiplication. This means that we need to \cs{clean:w}
+% the number following |^|, and perform the calculation, then just
+% end our job.
+%
+% Hence, each time a number is cleaned, the precedence of the
+% following operation must be compared to that of the previous
+% operation. The process of course has to happen recursively.
+% For instance, |1+2^3*4| would involve the following steps.
+% \begin{itemize}
+% \item |1| is cleaned up.
+% \item |2| is cleaned up.
+% \item The precedences of |+| and |^| are compared. Since the
+%   latter is higher, the second operand of |^| should be cleaned.
+% \item |3| is cleaned up.
+% \item The precedences of |^| and |*| are compared. Since the
+%   former is higher, the cleaning step stops.
+% \item Compute |2^3 = 8|.
+% \item We now have |1+8*4|, and the operation |+| is still
+%   looking for a second operand. Clean |8|.
+% \item The precedences of |+| and |*| are compared. Since the
+%   latter is higher, the second operand of |*| should be cleaned.
+% \item |4| is cleaned up, and the end of the expression is reached.
+% \item Compute |8*4 = 32|.
+% \item We now have |1+8*4|, and the operation |+| is still
+%   looking for a second operand. Clean |32|, and reach the end
+%   of the expression.
+% \item Compute |1+32 = 33|.
+% \end{itemize}
+% Here, there is some (expensive) redundant work: the results of
+% computations should not need to be cleaned again. Thus the true definition
+% is slightly more elaborate.
+%
+% The precedence of |(| and |)| are defined to be equal, and smaller than
+% the precedence of |+| and |-|, itself smaller than |*| and |/|, smaller,
+% finally, then the power operator |**| (or |^|).
+%
+%
+% \subsection{Infix operators}
+%
+% The implementation that was chosen is slightly wasteful: it causes
+% more nesting than necessary. ^^A todo: clarify.
+% However, it is simpler to implement and to explain than a slightly
+% optimized variant. ^^A todo: implement optimized version; compare.
+%
+% The cornerstone of that method is a pair of functions,
+% \cs{until} and \cs{one}, which both take as their first
+% argument the precedence (an integer) of the last operation.
+% The f-expansion of
+% \begin{quote}
+%   \cs{until} \meta{prec} \cs{one} \meta{prec} \meta{stuff}
+% \end{quote}
+% is the internal floating point obtained by \enquote{cleaning}
+% numbers which follow in the input stream, and performing
+% computations until reaching an operation with a precedence
+% less than or equal to \meta{prec}. This is followed by a control
+% sequence of the form \cs{infix_?}, namely,
+% \begin{quote}
+%   \meta{floating point} \cs{infix_?}
+% \end{quote}
+% where |?| is the operation following that number in the input
+% stream (we thus know that this operation has at most the
+% precedence \meta{prec}, otherwise it would have been performed
+% already).
+%
+% How is that expansion achieved? First, \cs{one} \meta{prec}
+% reads one \meta{floating point} number, and converts it to an
+% internal form, then the following operation, say |*|, is
+% packed in the form \cs{infix_*}, which is fed the \meta{prec}.
+% This function (one per infix operator) compares \meta{prec}
+% with the precedence of the operator we just read (here |*|).
+% If \meta{prec} is higher, our job is finished, and \cs{one}
+% leaves \cs{@@_parse_stop_until:N} so that \cs{until} knows to stop.
+% Otherwise, \cs{infix_*} triggers a new pair
+% \cs{until} \meta{prec(*)} \cs{one} \meta{prec(*)},
+% which produces the second operand \meta{floating point_2}
+% for the multiplication:
+% \begin{quote}
+%   \cs{until} \meta{prec} \meta{floating point} \newline
+%   \texttt{...} \meta{floating point_2} |;| \cs{infix_?}
+% \end{quote}
+% The dots are \cs{@@_parse_apply_binary:NwNwN} |*|.  The boolean
+% tells \cs{until} that it is not done, and it expands
+% (essentially) to
+% \begin{quote}
+%   \cs{until} \meta{prec}
+%   \cs{@@_mul_o:ww} \meta{floating point} \meta{floating point_2}
+%   \cs{tex_romannumeral:D} \texttt{-`0} \cs{infix_?} \meta{prec}
+% \end{quote}
+% making \TeX{} expand \cs{@@_mul_o:ww} before \cs{until}.  As
+% implemented in \pkg{l3fp-basics}, this operation expands what follows
+% its result exactly once. This triggers \cs{tex_romannumeral:D},
+% which fully expands \cs{infix_?} \meta{prec}. This compares
+% the precedence of the next operation, |?|, and \meta{prec},
+% and leaves a boolean (and possibly more things), which is then
+% checked by \cs{until} \meta{prec} to know if the result
+% of the multiplication is the end of the story, or if |?|
+% should be computed as well before \cs{until} \meta{prec} ends.
+%
+% This should be easier to see on an example. To each infix
+% operator, for instance, |*|, is associated the following data:
+% \begin{itemize}
+% \item a test function, \cs{infix_*}, which conditionally continues
+%   the calculation or waits to be hit again by expansion;
+% \item a function \fpOperation{*} (notation for \cs{@@_mul_o:ww})
+%   which performs the actual calculation;
+% \item an integer, \fpPrecedence{*}, which encodes the precedence of
+%   the operator.
+% \end{itemize}
+% The token that is currently being expanded is underlined,
+% and in red. Tokens that have not yet been read (and could
+% still be hidden in macros) are in gray.
+%
+% In a first reading, the disinction between the \meta{precedence}
+% \fpPrecedence{+}, the operation \fpOperation{+}, and the character
+% token |+| should not matter. It is only required to accomodate for
+% multi-token infix operators such as |**|: indeed, when controlling
+% expansion, we need to skip over those tokens using \cs{exp_after:wN},
+% and this only skips one token. Thus |**| needs to be replaced by a
+% single token (either its precedence or its calculating function,
+% depending on the place).
+%
+% To end the computation cleanly, we add a trailing right
+% parenthesis, and give |(| and |)| the lowest precedence,
+% so that \cs{until}\fpPrecedence{(} \cs{one}\fpPrecedence{(}
+% reads numbers and performs operations until meeting a right
+% parenthesis. This is discussed more precisely in the next section.
+%
+% \begin{l3fp-code-example}
+%   \cs{until}\p(    \*\cs{one}\p( \! 11 + 2**3 * 5 - 9 )\!
+%   \cs{until}\p( 1  \*\cs{one}\p( \! 1  + 2**3 * 5 - 9 )\!
+%   \cs{until}\p( 11 \*\cs{one}\p( \!    + 2**3 * 5 - 9 )\!
+%   \cs{until}\p( 11; \*\cs{infix_+}\p( \! 2**3 * 5 - 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ \*\cs{one}\p+ \! 2**3 * 5 - 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ 2 \*\cs{one}\p+ \!  **3 * 5 - 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ 2; \*\cs{infix_**}\p+ \! 3 * 5 - 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ 2;
+%       F \o{**} \cs{until}\p{**} \*\cs{one}\p{**} \! 3 * 5 - 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ 2;
+%       F \o{**} \cs{until}\p{**} 3 \*\cs{one}\p{**} \! * 5 - 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ 2;
+%       F \o{**} \cs{until}\p{**} 3; \*\cs{infix_*}\p{**} \! 5 - 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ 2;
+%       F \o{**} \*\cs{until}\p{**} 3; T \cs{infix_*} \! 5 - 9 )\!
+%   \cs{until}\p( 11; F \o+ \*\cs{until}\p+ 2;
+%       F \o{**} 3; \cs{infix_*} \! 5 - 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ \*\o{**} 2; 3;
+%       \cs{infix_*}\p+ \! 5 - 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ 8; \*\cs{infix_*}\p+ \! 5 - 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ 8;
+%       F \o* \cs{until}\p* \*\cs{one}\p* \! 5 - 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ 8;
+%       F \o* \cs{until}\p* 5 \*\cs{one}\p* \! - 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ 8;
+%       F \o* \cs{until}\p* 5; \*\cs{infix_-}\p* \! 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ 8;
+%       F \o* \*\cs{until}\p* 5; T \cs{infix_-} \! 9 )\!
+%   \cs{until}\p( 11; F \o+ \*\cs{until}\p+ 8; F \o* 5; \cs{infix_-} \! 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ \*\o{*} 8; 5; \cs{infix_-}\p+ \! 9 )\!
+%   \cs{until}\p( 11; F \o+ \cs{until}\p+ 40; \*\cs{infix_-}\p+ \! 9 )\!
+%   \cs{until}\p( 11; F \o+ \*\cs{until}\p+ 40; T \cs{infix_-} \! 9 )\!
+%   \*\cs{until}\p( 11; F \o+ 40; \cs{infix_-} \! 9 )\!
+%   \cs{until}\p( \*\o{+} 11; 40; \cs{infix_-}\p( \! 9 )\!
+%   \cs{until}\p( 51; \*\cs{infix_-}\p( \! 9 )\!
+%   \cs{until}\p( 51; F \o- \cs{until}\p- \*\cs{one}\p- \! 9 )\!
+%   \cs{until}\p( 51; F \o- \cs{until}\p- 9 \*\cs{one}\p- \! )\!
+%   \cs{until}\p( 51; F \o- \cs{until}\p- 9; \*\cs{infix_)}\p- \!\!
+%   \cs{until}\p( 51; F \o- \*\cs{until}\p- 9; T \cs{infix_)} \!\!
+%   \*\cs{until}\p( 51; F \o- 9; \cs{infix_)} \!\!
+%   \cs{until}\p( \*\o{-} 51; 9; \cs{infix_)}\p( \!\!
+%   \cs{until}\p( 42; \*\cs{infix_)}\p( \!\!
+%   \*\cs{until}\p( 42; T \cs{infix_)} \!\!
+%   42; \cs{infix_)} \!\!
+% \end{l3fp-code-example}
+%
+% The only missing step is to clean the output by removing \cs{infix_)},
+% and possibly checking that nothing else remains.
+%
+% \subsection{Prefix operators, parentheses, and functions}
+%
+% Prefix operators (typically the unary |-|) and parentheses are
+% taken care of by the same mechanism, and functions (\texttt{sin},
+% \texttt{exp}, etc.) as well. Finding the argument of the unary
+% |-|, for instance, is very similar to grabbing the second operand
+% of a binary infix operator, with a small subtelty on precedence
+% explained below. Once that argument is found, its sign can be
+% flipped. A left parenthesis is just a prefix operator which
+% removes the closing parenthesis (with some extra checks).
+%
+% Detecting prefix operators is done by \cs{one}. Before looking
+% for a number, it tests the first character. If it is a digit, a
+% dot, or a register, then we have a number. Otherwise, it is put
+% in a function, \cs{prefix_?} (where |?| is roughly that first
+% character), which is expanded. For instance, with a left
+% parenthesis we would have the following.
+% \begin{l3fp-code-example}
+%   \*\cs{one}\p* \! ( 2 + 3 ) \!
+%   \*\cs{prefix_(}\p* \! 2 + 3 ) \!
+%   \o(\p* \cs{until}\p( \*\cs{one}\p( \! 2 + 3 ) \!
+%   ... \!\!
+%   \o(\p* 5; \cs{infix_)} \! \!
+% \end{l3fp-code-example}
+% As usual, the \cs{until}--\cs{one} pair reads and compute
+% until reaching an operator of precedence at most \fpPrecedence{(}.
+% Then \fpOperation{(} removes \cs{infix_)} and looks ahead for
+% the next operation, comparing its precedence with the precedence
+% \fpPrecedence{*} of the previous operation (in fact, this comparison
+% is done by the relevant \cs{infix_?} built from the next operation).
+%
+% To support multi-character function (and constant) names, we
+% may need to put more than one character in the \cs{prefix_?}
+% construction. See implementation for details.
+%
+% Note that contrarily to \cs{infix_?} functions, the \cs{prefix_?}
+% functions perform no test on their argument (which is once more
+% the previous precedence), since we know that we need a number,
+% and must never stop there.
+%
+% Functions are implemented as prefix operators with infinitely high
+% precedence, so that their argument is the first number that can
+% possibly be built. For instance, something like the following could
+% happen in a computation
+% \begin{l3fp-code-example}
+%   \*\cs{one}\p* \! sqrt 4 + 3 ) \!
+%   \*\cs{prefix_sqrt}\p* \! 4 + 3 ) \!
+%   \o{sqrt}\p* \cs{until}\p{$\infty$} \*\cs{one}\p{$\infty$} \! 4 + 3 ) \!
+%   ... \!\!
+%   \o{sqrt}\p* 4; \cs{infix_+} \! 3 ) \!
+%   2; \*\cs{infix_+}\p* \! 3 ) \!
+% \end{l3fp-code-example}
+%
+% Lonely example, to be put somewhere: |2+sin 1 * 3| is $2+(\sin(1)\times 3)$.
+%
+% A further complication arises in the case of the unary |-| sign:
+% |-3**2| should be $-(3^2)=-9$, and not $(-3)^2=9$. Easy, just give
+% |-| a lower precedence, equal to that of the infix |+| and |-|.
+% Unfortunately, this fails in subtle cases such as |3**-2*4|,
+% yielding $3^{-2\times 4}$ instead of the correct $3^{-2}\times 4$.
+% In fact, a unary |-| should only perform operations whose precedence
+% is greater than that of the last operation, as well as
+% |-|.\footnote{Taking into account the precedence of \texttt{-} itself
+%   only matters when it follows a left parenthesis:
+%   \texttt{(-2*4+3)} should give \texttt{((-8)+3)}, not \texttt{(-(8+3))}.}
+% Thus, \cs{prefix_-} \meta{prec} expands to something like
+% \begin{l3fp-code-example}
+%   \o- \meta{prec} \cs{until}\p? \*\cs{one} \p?
+% \end{l3fp-code-example}
+% where \fpPrecedence{?} is the maximum of \meta{prec} and the
+% precedence of |-|. Once the argument of |-| is found, \fpOperation{-}
+% gets its opposite, and leaves it for the previous operation to use.
+%
+% An example with parentheses.
+%
+% \begin{l3fp-code-example}
+%   \cs{until}\p(    \*\cs{one}\p( \! 11 * ( 2 + 3 ) - 9 )\!
+%   \cs{until}\p( 1  \*\cs{one}\p( \! 1  * ( 2 + 3 ) - 9 )\!
+%   \cs{until}\p( 11 \*\cs{one}\p( \!    * ( 2 + 3 ) - 9 )\!
+%   \cs{until}\p( 11; \*\cs{infix_*}\p( \!   ( 2 + 3 ) - 9 )\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \*\cs{one}\p* \! ( 2 + 3 ) - 9 )\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \*\cs{prefix_(}\p* \! 2 + 3 ) - 9 )\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \o(\p* \cs{until}\p( \*\cs{one}\p( \! 2 + 3 ) - 9 )\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \o(\p* \cs{until}\p( 2 \*\cs{one}\p( \! + 3 ) - 9 )\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \o(\p* \cs{until}\p( 2; \*\cs{infix_+}\p( \! 3 ) - 9 )\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \o(\p* \cs{until}\p( 2; F \o+ \cs{until}\p+ \*\cs{one}\p+ \! 3)-9)\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \o(\p* \cs{until}\p( 2; F \o+ \cs{until}\p+ 3 \*\cs{one}\p+ \! )-9)\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \o(\p* \cs{until}\p( 2; F \o+ \cs{until}\p+ 3; \*\cs{infix_)}\p+ \! -9)\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \o(\p* \cs{until}\p( 2; F \o+ \*\cs{until}\p+ 3; T \cs{infix_)} \! -9)\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \o(\p* \*\cs{until}\p( 2; F \o+ 3; \cs{infix_)} \! - 9 )\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \o(\p* \cs{until}\p( \*\o+ 2; 3; \cs{infix_)}\p( \! - 9 )\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \o(\p* \cs{until}\p( 5; \*\cs{infix_)}\p( \! - 9 )\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \o(\p* \*\cs{until}\p( 5; T \cs{infix_)} \! - 9 )\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* \*\o(\p* 5; \cs{infix_)} \! - 9 )\!
+%   \cs{until}\p( 11; F \o* \cs{until}\p* 5; \*\cs{infix_-}\p* \! 9 )\!
+%   \cs{until}\p( 11; F \o* \*\cs{until}\p* 5; T \cs{infix_-} \! 9 )\!
+%   \*\cs{until}\p( 11; F \o* 5; \cs{infix_-} \! 9 )\!
+%   \cs{until}\p( \*\o* 11; 5; \cs{infix_-}\p( \! 9 )\!
+%   \cs{until}\p( 55; \* \cs{infix_-}\p( \! 9 )\!
+%   \cs{until}\p( 55; F \o- \cs{until}\p- \*\cs{one}\p- \! 9 )\!
+%   \cs{until}\p( 55; F \o- \cs{until}\p- 9 \*\cs{one}\p- \! )\!
+%   \cs{until}\p( 55; F \o- \cs{until}\p- 9; \*\cs{infix_)}\p- \!\!
+%   \cs{until}\p( 55; F \o- \*\cs{until}\p- 9; T \cs{infix_)} \!\!
+%   \*\cs{until}\p( 55; F \o- 9; \cs{infix_)} \!\!
+%   \cs{until}\p( \*\o- 55; 9; \cs{infix_)}\p( \!\!
+%   \cs{until}\p( 47; \*\cs{infix_)}\p( \!\!
+%   \*\cs{until}\p( 47; T \cs{infix_)} \!\!
+%   47; \cs{infix_)} \!\!
+% \end{l3fp-code-example}
+%
+% The end of this (sub)section was not revised yet
+%
+% \begin{itemize}
+% \item If it is a sign (|-| or |+|), then any following sign will be
+%   combined with this initial sign, forming \cs{prefix_+} or \cs{prefix_-}.
+% \item If it is a letter, then any following letter is grabbed, forming
+%   for instance \cs{prefix_sin} or \cs{prefix_sinh}.
+% \item Otherwise, only one token\footnote{Some support for multi-character
+%     prefix operator may be added in the future, but right now, I don't
+%     see a use for it. Perhaps, for including comments inside
+%     the computation itself??} is grabbed, for instance \cs{prefix_(}.
+% \end{itemize}
+%
+%^^A todo: make sure that's correct??
+%
+% Functions may take several arguments, possibly an unknown
+% number\footnote{Keyword argument support may be added later.},
+% for instance \texttt{round(1.23456,2)}.
+% \begin{itemize}
+% \item \texttt{round} is made into \cs{prefix_round}, which tries to
+%   grab one number using \cs{one}.
+% \item This builds \cs{prefix_(}, which uses \cs{one} to grab one
+%   number, calculating as necessary. The comma is given the same
+%   precedence as parentheses, and thus ends the calculation of the
+%   argument of \texttt{round}.
+% \item \texttt{round} now has its first argument. It can check whether
+%   the argument was closed by |,| or |)|, and branch accordingly.
+% \item If it was a comma, then the first argument is skipped over,
+%   through an expensive set of \cs{exp_after:wN}, and the second
+%   argument can be grabbed. Here it is simply an integer, easier
+%   to parse by building upon \cs{etex_numexpr:D}.
+% \item The closing parenthesis (or another comma) is seen, and the
+%   control is given back to \cs{prefix_round}.
+% \end{itemize}
+%
+% \subsection{Type detection}
+%
+% The type of data should be detected by reading the first few tokens,
+% before calling a type-specific function to parse it.  Or
+% should the type be obtained after the semicolon which indicates the
+% end of the thing? And placed there?
+%
+% ^^A todo: what did I mean in this paragraph?
+% Also to grab exponents correctly, build \cs{@@_<abc>:w} when seeing
+% some non-numeric |abc| while still looking to complete a number (or
+% other data). Then, if \cs{@@_postfix_<type>_<abc>:w} exists, use it.
+%
+% The internal representation of floating point numbers is quite
+% untypable, and we provide here the tools to convert from a more
+% user-friendly representation to internal floating point numbers,
+% and for various other conversions. Every floating point operation
+% calls those functions to normalize the input, so they must be
+% optimized.
+%
+% \section{Internal representation}
+%
+% Internally, a floating point number \meta{X} is a
+% token list containing
+% \begin{quote}
+%   \cs{s_@@} \cs{@@_chk:w} \meta{case} \meta{sign} \meta{body} |;|
+% \end{quote}
+% Let us explain each piece separately.
+%
+% Internal floating point numbers will be used in expressions,
+% and in this context will be subject to f-expansion. They must
+% leave a recognizable mark after \texttt{f}-expansion, to prevent the
+% floating point number from being re-parsed. Thus, \cs{s_@@}
+% is simply another name for \tn{relax}.
+%
+% Since floating point numbers are always accessed by the various
+% operations using f-expansion, we can safely let them be protected:
+% \texttt{x}-expansion will then leave them untouched.  However, when
+% used directly without an accessor function, floating points should
+% produce an error.  \cs{s_@@} will do nothing, and \cs{@@_chk:w}
+% produces an error.
+%
+% The (decimal part of the) IEEE-754-2008 standard requires the
+% format to be able to represent special floating point numbers
+% besides the usual positive and negative cases. The various
+% possibilities will be distinguished by their \meta{case}, which
+% is a single digit:\footnote{Bruno: I need to implement subnormal
+%   numbers. Also, quiet and signalling \texttt{nan} must be better
+%   distinguished.}
+% \begin{itemize}
+% \item[0] zeros: |+0| and |-0|,
+% \item[1] \enquote{normal} numbers (positive and negative),
+% \item[2] infinities: |+inf| and |-inf|,
+% \item[3] quiet and signalling \texttt{nan}.
+% \end{itemize}
+% The \meta{sign} is |0| (positive) or |2| (negative),
+% except in the case of \texttt{nan}, which have $\meta{sign} = 1$.
+% This ensures that changing the \meta{sign} digit to $2-\meta{sign}$
+% is exactly equivalent to changing the sign of the number.
+%
+% Special floating point numbers have the form
+% \begin{quote}
+%   \cs{s_@@} \cs{@@_chk:w} \meta{case} \meta{sign} \cs{s_@@_...} |;|
+% \end{quote}
+% where \cs{s_@@_...} is a scan mark carrying information about how the
+% number was formed (useful for debugging).
+%
+% Normal floating point numbers ($\meta{case} = 1$) have the form
+% \begin{quote}
+%   \cs{s_@@} \cs{@@_chk:w} 1 \meta{sign} \Arg{exponent}
+%   \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} |;|
+% \end{quote}
+% Here, the \meta{exponent} is an integer, at most
+% $\cs{c_@@_max_exponent_int} =
+%   \the\csname\detokenize{c__fp_max_exponent_int}\endcsname$
+% in absolute value.  The body consists in four
+% blocks of exactly $4$ digits, $ 0000 \leq \meta{X_i} \leq 9999$,
+% such that
+% \[
+% \meta{X}
+% = (-1)^{\meta{sign}} 10^{-\meta{exponent}}
+% \sum_{i=1}^{4} \meta{X_i} 10^{-4i}
+% \]
+% and such that the \meta{exponent} is minimal. This implies
+% $ 1000 \leq \meta{X_1} \leq 9999 $.
+%
+% \begin{table}\centering
+%   \caption{Internal representation of floating point numbers.}
+%   \label{tab:fp-convert-special}
+%   \begin{tabular}{ll}
+%     \toprule
+%     \multicolumn{1}{c}{Representation} & Meaning \\
+%     \midrule
+%     0 0 \cs{s_@@_...}  \texttt{;} & Positive zero.      \\
+%     0 2 \cs{s_@@_...}  \texttt{;} & Negative zero.      \\
+%     1 0 \Arg{exponent} \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \texttt{;}
+%                                   & Positive floating point. \\
+%     1 2 \Arg{exponent} \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \texttt{;}
+%                                   & Negative floating point. \\
+%     2 0 \cs{s_@@_...}  \texttt{;} & Positive infinity.  \\
+%     2 2 \cs{s_@@_...}  \texttt{;} & Negative infinity.  \\
+%     3 1 \cs{s_@@_...}  \texttt{;} & Quiet \texttt{nan}.        \\
+%     3 1 \cs{s_@@_...}  \texttt{;} & Signalling \texttt{nan}.   \\
+%     \bottomrule
+%   \end{tabular}
+% \end{table}
+%
+% \section{Internal parsing functions}
+%
+% \begin{macro}[EXP, int]{\@@_parse_until:Nw}
+%   \begin{syntax}
+%     \cs{tex_romannumeral:D} \cs{@@_parse_until:Nw} \meta{precedence} \cs{@@_parse_expand:w} \meta{tokens}
+%   \end{syntax}
+%   Reads the \meta{tokens}, performing every computation with a
+%   precedence higher than \meta{precedence}, then expands to
+%   \begin{syntax}
+%     \meta{objects} |@| \cs{@@_parse_infix_\meta{operation}:N} \ldots{}
+%   \end{syntax}
+%   where the \meta{op} is the first operation with a lower precedence,
+%   possibly \texttt{end}.
+% \end{macro}
+%
+% \begin{macro}[EXP, int]{\@@_parse_operand:Nw}
+%   \begin{syntax}
+%     \cs{@@_parse_operand:Nw} \meta{precedence} \ldots{}
+%   \end{syntax}
+%   If the following \meta{operation} has a precedence higher than
+%   \meta{precedence}, expands to
+%   \begin{syntax}
+%     \meta{object_1} |@| \cs{@@_parse_apply_binary:NwNwN} \meta{operation} \meta{object_2} |@| \cs{@@_parse_infix_\meta{operation_2}:N} \ldots{}
+%   \end{syntax}
+%   and otherwise expands to
+%   \begin{syntax}
+%     \meta{object} |@| \cs{@@_parse_stop_until:N} \cs{@@_parse_infix_\meta{operation}:N} \ldots{}
+%   \end{syntax}
+% \end{macro}
+%
+% \begin{macro}[EXP, int]{\@@_parse_infix_\meta{operation}:N}
+%   \begin{syntax}
+%     \cs{@@_parse_infix_\meta{operation}:N} \meta{precedence}
+%   \end{syntax}
+%   If the \meta{op} has a precedence higher than \meta{precedence}, expands to
+%   \begin{syntax}
+%     |@| \cs{@@_parse_apply_binary:NwNwN} \meta{operation} \meta{object} |@| \cs{@@_parse_infix_\meta{operation_2}:N}
+%   \end{syntax}
+%   Otherwise expands to
+%   \begin{syntax}
+%     |@| \cs{@@_parse_stop_until:N} \cs{@@_parse_infix_\meta{operation}:N}
+%   \end{syntax}
+% \end{macro}
+%
+% ^^A end[todo]
+%
+% \subsection{Expansion control}
+%
+% At each step in reading a floating point expression, we wish to
+% perform \texttt{f}-expansion.  Normally, spaces stop this
+% \texttt{f}-expansion.  This can be problematic: for instance, the
+% macro |\X| below will not be expanded if we simply do
+% \texttt{f}-expansion.
+% \begin{verbatim}
+%   \DeclareDocumentCommand {\test} {m} { \fp_eval:n {#1} }
+%   \ExplSyntaxOff
+%   \test { 1 + \X }
+% \end{verbatim}
+% To avoid this problem, at every step, we do essentially what
+% \cs{use:f} would do: take an argument, put it back in the input
+% stream, then \texttt{f}-expand it.  This is not a complete solution,
+% since a macro's expansion could contain leading spaces which will stop
+% the \texttt{f}-expansion before further macro calls are performed.
+% However, in practice it should be enough: in particular, floating
+% point numbers will correctly be expanded to the underlying \cs{s_@@}
+% \ldots{} structure.
+%
+%^^A begin[todo]
+% Floating point expressions should behave as much as possible like
+% \eTeX{}-based integer expressions and dimension expressions.  In
+% particular, full-expansion should be performed as the expression is
+% read, token by token, forcing the expansion of protected macros, and
+% ignoring spaces.
+%
+% Full expansion can be done with \cs{tex_romannumeral:D} |-`0|.
+% Unfortunately, this expansion is stopped by spaces.  Thus using simply
+% this will fail on |\fp_eval:n { 1 + ~ \l_tmpa_fp }| since the floating
+% point variable will not be expanded.  Of course, spaces will not
+% appear in a code setting, but may very easily come in document-level
+% input, from which some expressions may come.  We can avoid being
+% stopped by such explicit space characters (and by some braces) if we
+% add \cs{use:n} after~|-`0|.
+%
+% Testing if a character token |#1| is a digit can be done using
+% \begin{verbatim}
+% \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+%   true code
+% \else:
+%   false code
+% \fi:
+% \end{verbatim}
+% To exclude |0|, replace \cs{c_nine} by \cs{c_ten}. The use of
+% \cs{token_to_str:N} ensures that a digit with any catcode is detected.
+%
+%^^A end[todo]
+%
+% \begin{macro}[rEXP, aux]{\@@_parse_expand:w}
+%   \begin{syntax}
+%     \cs{tex_romannumeral:D} \cs{@@_parse_expand:w} \meta{tokens}
+%   \end{syntax}
+%   This function must always come within a \tn{romannumeral} expansion.
+%   The \meta{tokens} should be the part of the expression that we have
+%   not yet read.  This requires in particular closing all conditionals
+%   properly before expanding.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_expand:w #1 { -`0 #1 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP, aux]{\@@_parse_return_semicolon:w}
+%   This very odd function swaps its position with the following
+%   \cs{fi:} and removes \cs{@@_parse_expand:w} normally responsible for
+%   expansion.  That turns out to be useful.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_return_semicolon:w
+    #1 \fi: \@@_parse_expand:w { \fi: ; #1 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Fp object type}
+%
+% \begin{macro}[EXP, int]{\@@_type_from_scan:N}
+%   \begin{syntax}
+%     \cs{@@_type_from_scan:N} \meta{token}
+%   \end{syntax}
+%   Grabs the pieces of the stringified \meta{token} which lies after
+%   the first |s__fp|.  If the \meta{token} does not contain that
+%   string, the result is empty.
+%    \begin{macrocode}
+\group_begin:
+\char_set_catcode_other:N \S
+\char_set_catcode_other:N \F
+\char_set_catcode_other:N \P
+\char_set_lccode:nn { `\- } { `\_ }
+\tl_to_lowercase:n
+  {
+    \group_end:
+    \cs_new:Npn \@@_type_from_scan:N #1
+      {
+        \exp_after:wN \@@_type_from_scan:w
+        \token_to_str:N #1 \q_mark S--FP \q_mark \q_stop
+      }
+    \cs_new:Npn \@@_type_from_scan:w #1 S--FP #2 \q_mark #3 \q_stop {#2}
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Reading digits}
+%
+% \begin{macro}[rEXP, aux]
+%   {
+%     \@@_parse_digits_vii:N  ,
+%     \@@_parse_digits_vi:N   ,
+%     \@@_parse_digits_v:N    ,
+%     \@@_parse_digits_iv:N   ,
+%     \@@_parse_digits_iii:N  ,
+%     \@@_parse_digits_ii:N   ,
+%     \@@_parse_digits_i:N
+%   }
+%   These functions must be called within an \cs{__int_value:w} or
+%   \cs{__int_eval:w} construction.  The first token which follows must be
+%   \texttt{f}-expanded prior to calling those functions.  The functions
+%   read tokens one by one, and output digits into the input stream,
+%   until meeting a non-digit, or up to a number of digits equal to
+%   their index.  The full expansion is
+%   \begin{quote}
+%     \meta{digits} |;| \meta{filling 0} |;| \meta{length}
+%   \end{quote}
+%   where \meta{filling 0} is a string of zeros such that \meta{digits}
+%   \meta{filling 0} has the length given by the index of the function,
+%   and \meta{length} is the number of zeros in the \meta{filling 0}
+%   string.  Each function puts a digit into the input stream and calls
+%   the next function, until we find a non-digit.  We are careful to
+%   pass the tested tokens through \cs{token_to_str:N} to normalize
+%   their category code.
+%    \begin{macrocode}
+\cs_set_protected:Npn \@@_tmp:w #1 #2 #3
+  {
+    \cs_new:cpn { @@_parse_digits_ #1 :N } ##1
+      {
+        \if_int_compare:w \c_nine < 1 \token_to_str:N ##1 \exp_stop_f:
+          \token_to_str:N ##1 \exp_after:wN #2 \tex_romannumeral:D
+        \else:
+          \@@_parse_return_semicolon:w #3 ##1
+        \fi:
+        \@@_parse_expand:w
+      }
+  }
+\@@_tmp:w {vii}  \@@_parse_digits_vi:N   { 0000000 ; 7 }
+\@@_tmp:w {vi}   \@@_parse_digits_v:N    { 000000 ; 6 }
+\@@_tmp:w {v}    \@@_parse_digits_iv:N   { 00000 ; 5 }
+\@@_tmp:w {iv}   \@@_parse_digits_iii:N  { 0000 ; 4 }
+\@@_tmp:w {iii}  \@@_parse_digits_ii:N   { 000 ; 3 }
+\@@_tmp:w {ii}   \@@_parse_digits_i:N    { 00 ; 2 }
+\@@_tmp:w {i}    \@@_parse_digits_:N     { 0 ; 1 }
+\cs_new_nopar:Npn \@@_parse_digits_:N { ; ; 0 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Parsing one operand}
+%
+% At the start of an expression, or just following a binary operation or
+% a function call, we are looking for an operand.  This can be an
+% explicit floating point number, a floating point variable, a \TeX{}
+% register, a function call such as \texttt{sin(3)}, a parenthesized
+% expression, \emph{etc.}  We distinguish the various cases by their
+% first token after \texttt{f}-expansion:
+% \begin{itemize}
+% \item \cs{tex_relax:D} in some form.  That can be an internal
+%   floating point, a premature end, or an unitialized register.
+% \item A register.  We interpret this as the significand of a floating
+%   point number.  This is subtely different from unpacking it, for
+%   instance, \texttt{\cs{c_minus_one}**2} gives $1$, while
+%   \texttt{-1**2} gives $-1$.
+% \item A digit, or a dot.  That marks the start of the significand for
+%   a floating point number.
+% \item A letter (lower or upper-case), which starts an identifier,
+%   either a constant or a function (possibly unknown).
+% \item |+|, |-|, or |!|, unary operators, which resume looking for a
+%   floating point number before acting on it.
+% \item |(|, which makes us parse a subexpression until the
+%   matching~|)|.
+% \item Other characters such as |'| or |"| may be given a meaning
+%   later.  Characters such as |*| or |/| have a meaning as infix
+%   operators but are not valid when we are looking for an operand: for
+%   instance, |3+*4| is not valid.
+% \end{itemize}
+% A category code test separates the first two cases from the others,
+% and they are further distinguished with a meaning test.  We then
+% single out digits.  Letters are detected using their character code.
+% All other characters are taken care of by building a csname from that
+% character and using it to continue parsing.  Unknown characters lead
+% to an error.
+%
+% \begin{macro}[int, EXP]{\@@_parse_operand:Nw}
+%   Function called \cs{one} at other places. It grabs one operand, and
+%   packs the symbol that follows in an \cs{infix_} csname.  |#1| is the
+%   previous \meta{precedence}, and |#2| the first character of the
+%   operand (already \texttt{f}-expanded).
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_operand:Nw #1 #2
+  {
+    \if_catcode:w \tex_relax:D #2
+      \if_meaning:w \tex_relax:D #2
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_parse_operand_relax:NN
+      \else:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_parse_operand_register:NN
+      \fi:
+    \else:
+      \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_parse_operand_digit:NN
+      \else:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_parse_operand_other:NN
+      \fi:
+    \fi:
+    #1 #2
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% ^^A todo: rounding of negative dimensions is probably wrong.
+% \begin{macro}[aux, EXP]
+%   {\@@_parse_operand_register:NN, \@@_parse_operand_register_aux:www}
+%   Find the exponent following the register |#2|, then combine the
+%   value of |#2| (mapping |1pt| to $1$) with the exponent to produce a
+%   floating point number.
+%    \begin{macrocode}
+\group_begin:
+\char_set_catcode_other:N \P
+\char_set_catcode_other:N \T
+\tl_to_lowercase:n
+  {
+    \group_end:
+    \cs_new:Npn \@@_parse_operand_register:NN #1#2
+      {
+        \exp_after:wN \@@_parse_infix_after_operand:NwN
+        \exp_after:wN #1
+        \tex_romannumeral:D -`0
+          \exp_after:wN \@@_parse_operand_register_aux:www
+          \tex_the:D
+            \exp_after:wN #2
+            \exp_after:wN P
+            \exp_after:wN T
+            \exp_after:wN \q_stop
+          \__int_value:w \@@_parse_exponent:N
+      }
+    \cs_new:Npn \@@_parse_operand_register_aux:www #1 PT #2 \q_stop #3 ;
+      { \@@_parse:n { #1 e #3 } }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]
+%   {\@@_parse_operand_relax:NN, \@@_parse_operand_relax_aux:wwnw} The
+%   argument is a token equal to \cs{tex_relax:D}.  This can be
+%   \cs{s_@@}, \cs{s_@@_mark}, or a badly initialized register.  We make
+%   sure that the last argument of \cs{@@_parse_infix:NN} is
+%   correctly expanded.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_operand_relax:NN #1#2
+  {
+      \@@_parse_operand_relax_aux:wwnw
+        #2 \s_@@_mark
+          {
+            \@@_exp_after_o:nw
+              {
+                \tex_romannumeral:D -`0
+                \exp_after:wN \@@_parse_infix:NN
+                \exp_after:wN #1 \tex_romannumeral:D \@@_parse_expand:w
+              }
+            \s_@@
+          }
+        \s_@@ #2
+          {
+            \@@_error:n { Premature~end~in~fp~expression. }
+            \exp_after:wN \c_nan_fp
+            \tex_romannumeral:D -`0
+              \@@_parse_infix:NN #1
+              \s_@@_mark
+          }
+        \s_@@_mark
+          {
+            \@@_error:n { Erroneous~variable~#2 used! }
+            \exp_after:wN \c_nan_fp
+            \tex_romannumeral:D -`0
+              \exp_after:wN \@@_parse_infix:NN
+              \exp_after:wN #1
+              \tex_romannumeral:D \@@_parse_expand:w
+          }
+        \s_@@_mark \s_@@_stop
+  }
+\cs_new:Npn \@@_parse_operand_relax_aux:wwnw
+    #1 \s_@@ #2 \s_@@_mark #3 #4 \s_@@_mark \s_@@_stop { #3 }
+%    \end{macrocode}
+% \end{macro}
+%
+% ^^A begin[todo]
+%
+% \begin{macro}[aux, EXP]{\@@_parse_operand_other:NN}
+%   The interesting bit is \cs{@@_parse_operand_other:NN}. It separates
+%   letters from non-letters and builds the appropriate \cs{prefix}
+%   function. If it is not defined (is \cs{tex_relax:D}), make it
+%   a signalling \texttt{nan}. We don't look for an argument, as the
+%   unknown \enquote{prefix} can also be a (mistyped) constant such
+%   as \texttt{Inf}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_operand_other:NN #1 #2
+  {
+    \if_int_compare:w
+        \__int_eval:w \tex_uccode:D `#2 / 26 = \c_three
+      \exp_after:wN \@@_parse_operand_other_word_aux:Nw
+      \exp_after:wN #1
+      \tex_romannumeral:D
+        \exp_after:wN \@@_parse_letters:NN
+        \exp_after:wN #2
+        \tex_romannumeral:D
+    \else:
+      \exp_after:wN \@@_parse_operand_other_prefix_aux:NNN
+      \exp_after:wN #1
+      \exp_after:wN #2
+      \cs:w @@_parse_prefix_#2:Nw \exp_after:wN \cs_end:
+      \tex_romannumeral:D
+    \fi:
+    \@@_parse_expand:w
+  }
+
+\cs_new:Npn \@@_parse_letters:NN #1#2
+  {
+    \exp_after:wN \c_zero
+    \exp_after:wN #1
+    \tex_romannumeral:D
+      \if_int_compare:w
+          \if_catcode:w \tex_relax:D #2
+            \c_zero
+          \else:
+            \__int_eval:w \tex_uccode:D `#2 / 26
+          \fi:
+          = \c_three
+        \exp_after:wN \@@_parse_letters:NN
+        \exp_after:wN #2
+        \tex_romannumeral:D
+        \exp_after:wN \@@_parse_expand:w
+      \else:
+        \exp_after:wN \c_zero
+        \exp_after:wN ;
+        \exp_after:wN #2
+      \fi:
+  }
+\cs_new:Npn \@@_parse_operand_other_word_aux:Nw #1 #2;
+  {
+    \cs_if_exist_use:cF { @@_parse_word_#2:N }
+      {
+        \__msg_expandable_error:n { Unknown~word~#2. }
+        \exp_after:wN \c_nan_fp
+        \tex_romannumeral:D -`0
+          \@@_parse_infix:NN
+      }
+      #1
+  }
+\cs_new_eq:NN \s_@@_unknown \tex_relax:D
+\cs_new:Npn \@@_parse_operand_other_prefix_aux:NNN #1#2#3
+  {
+    \if_meaning:w \tex_relax:D #3
+      \exp_after:wN \@@_parse_operand_other_prefix_unknown:NNN
+      \exp_after:wN #2
+    \fi:
+    #3 #1
+  }
+\cs_new:Npn \@@_parse_operand_other_prefix_unknown:NNN #1#2#3
+  {
+    \cs_if_exist:cTF { @@_parse_infix_#1:N }
+      {
+        \@@_error:n { Missing~number~before~'#1'. }
+        \exp_after:wN \c_nan_fp
+        \tex_romannumeral:D -`0
+          \@@_parse_infix:NN #3 #1
+      }
+      {
+        \@@_error:n { Unknown~symbol~#1~ignored. }
+        \@@_parse_operand:Nw #3
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% The following forms are accepted:
+% \begin{itemize}
+% \item
+% \item \meta{floating point}
+% \item \meta{integer} |.| \meta{decimal} |e| \meta{exponent}
+% \end{itemize}
+% In both cases, \meta{signs} is a (possibly empty) string of
+% |+| and |-| (with any category code\footnote{Bruno: except
+%   1, 2, 4, 10, 13, and those which cannot be tokens (0, 5, 9),
+%   so really, just 3, 6, 7, 8, 11, 12.}).\footnote{Bruno:
+%   test (and implement) non-other digits.}
+%
+% In the second form, the \meta{integer} is a sequence of digits,
+% whose length is not limited by constraints \TeX{}'s integer
+% registers. It stops at the first non-digit character. The
+% \meta{decimal} part is formed by all digits from the dot
+% (if it exists) until the first non-digit character. The
+% \meta{exponent} part has the form \meta{exponent sign}
+% \meta{exponent body}, where \meta{exponent sign} is any string
+% of |+| or |-|, and \meta{exponent body} is a string of digits,
+% stopping, as usual, at the first non-digit.
+%
+% Any missing part will take the appropriate default value.
+% \begin{itemize}
+% \item A missing \meta{exponent} is considered to be zero.
+% \item A number with no dot has zero decimal part.
+% \item An empty \meta{integer} part or decimal part is zero.
+% \end{itemize}
+%
+% Border cases:
+% \begin{itemize}
+% \item \texttt{e1} is considered as invalid input, and gives
+%   \texttt{qnan}.\footnote{Bruno: now just gives an error.}
+%   This will be important once parsing expressions is
+%   implemented, since \texttt{e-1} would be ambiguous otherwise.
+% \item \texttt{.e3} and \texttt{.} are zero.
+% \end{itemize}
+%
+% Bruno: expansion, not yet. Only f-expansion at the start, and
+% unpacking of registers after signs.
+%
+%
+% Work-plan.
+% \begin{itemize}
+% \item Remove any leading sign and build the \meta{sign} as we go.
+%   If the next character is a letter, go to the \enquote{special}
+%   branch, discussed later.
+% \item Drop leading zeros.
+% \item If the next character is a dot, drop some more zeros,
+%   keeping track of how many were dropped after the dot.
+%   Counting those gives $\meta{exp_1}<0$. Then read the decimal part
+%   with the \cs{@@_from_str_small} functions.
+% \item Otherwise, $\meta{exp_1}=0$, and first read the integer part,
+%   then the decimal part. This is implemented through the more
+%   elaborate \cs{@@_from_str_large} functions.
+% \item Continuing in the same line of expansion, read the exponent
+%   \meta{exp_2}.
+% \item Finally check that nothing is left.\footnote{Bruno: not done yet.}
+% \end{itemize}
+%
+% \begin{macro}[aux, EXP]{\@@_parse_operand_digit:NN}
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_operand_digit:NN #1
+  {
+    \exp_after:wN \@@_parse_infix_after_operand:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+      \exp_after:wN \@@_sanitize:wN
+      \int_use:N \__int_eval:w \c_zero \@@_parse_trim_zeros:N
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% ^^A end[todo]
+%
+% \subsubsection{Trimming leading zeros}
+%
+% \begin{macro}[aux, rEXP]{\@@_parse_trim_zeros:N, \@@_parse_trim_end:w}
+%   This function expects an already expanded token.  It removes any
+%   leading zero, then distinguished three cases: if the first non-zero
+%   token is a digit, then call \cs{@@_parse_large:N} (the significand is
+%   $\geq 1$); if it is |.|, then continue trimming zeros with
+%   \cs{@@_parse_strim_zeros:N}; otherwise, our number is exactly zero,
+%   and we call \cs{@@_parse_zero:} to take care of that case.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_trim_zeros:N #1
+  {
+    \if:w 0 #1
+      \exp_after:wN \@@_parse_trim_zeros:N
+      \tex_romannumeral:D
+    \else:
+      \if:w . #1
+        \exp_after:wN \@@_parse_strim_zeros:N
+        \tex_romannumeral:D
+      \else:
+        \@@_parse_trim_end:w #1
+      \fi:
+    \fi:
+    \@@_parse_expand:w
+  }
+\cs_new:Npn \@@_parse_trim_end:w #1 \fi: \fi: \@@_parse_expand:w
+  {
+      \fi:
+    \fi:
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+      \exp_after:wN \@@_parse_large:N
+    \else:
+      \exp_after:wN \@@_parse_zero:
+    \fi:
+    #1
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]{\@@_parse_strim_zeros:N, \@@_parse_strim_end:w}
+%   If we have removed all digits until a period (or if the body started
+%   with a period), then enter the \enquote{\texttt{small_trim}} loop
+%   which outputs $-1$ for each removed $0$.  Those $-1$ are added to an
+%   integer expression waiting for the exponent.  If the first non-zero
+%   token is a digit, call \cs{@@_parse_small:N} (our significand is
+%   smaller than~$1$), and otherwise, the number is an exact zero.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_strim_zeros:N #1
+  {
+    \if:w 0 #1
+      - \c_one
+      \exp_after:wN \@@_parse_strim_zeros:N
+      \tex_romannumeral:D
+    \else:
+      \@@_parse_strim_end:w #1
+    \fi:
+    \@@_parse_expand:w
+  }
+\cs_new:Npn \@@_parse_strim_end:w #1 \fi: \@@_parse_expand:w
+  {
+    \fi:
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+      \exp_after:wN \@@_parse_small:N
+    \else:
+      \exp_after:wN \@@_parse_zero:
+    \fi:
+    #1
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Exact zero}
+%
+% \begin{macro}[aux, EXP]{\@@_parse_zero:}
+%   After reading a significand of $0$, we need to remove any exponent,
+%   then put a sign of |1| for \cs{@@_sanitize:wN}, denoting an
+%   exact zero.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_zero:
+  {
+    \exp_after:wN ; \exp_after:wN 1
+    \__int_value:w \@@_parse_exponent:N
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Small significand}
+%
+% \begin{macro}[aux, rEXP]{\@@_parse_small:N}
+%   This function is called after we have passed the decimal separator
+%   and removed all leading zeros from the significand.  It is followed
+%   by a non-zero digit (with any catcode).  The goal is to read up to
+%   $16$ digits.  But we can't do that all at once, because
+%   \cs{__int_value:w} (which allows us to collect digits and continue
+%   expanding) can only go up to $9$ digits.  Hence we grab digits in
+%   two steps of $8$ digits.  Since |#1| is a digit, read seven more
+%   digits using \cs{@@_parse_digits_vii:N}.  The \texttt{small_leading}
+%   auxiliary will leave those digits in the \cs{__int_value:w}, and grab
+%   some more, or stop if there are no more digits.  Then the
+%   \texttt{pack_leading} auxiliary puts the various parts in the
+%   appropriate order for the processing further up.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_small:N #1
+  {
+    \exp_after:wN \@@_parse_pack_leading:NNNNNww
+    \int_use:N \__int_eval:w 1 \token_to_str:N #1
+      \exp_after:wN \@@_parse_small_leading:wwNN
+      \__int_value:w 1
+        \exp_after:wN \@@_parse_digits_vii:N
+        \tex_romannumeral:D \@@_parse_expand:w
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]{\@@_parse_small_leading:wwNN}
+%   \begin{syntax}
+%     \cs{@@_parse_small_leading:wwNN} |1| \meta{digits} |;| \meta{zeros} |;| \meta{number~of~zeros}
+%   \end{syntax}
+%   We leave \meta{digits} \meta{zeros} in the input stream: the
+%   functions used to grab digits are such that this constitutes digits
+%   $1$ through $8$ of the significand.  Then prepare to pack $8$ more
+%   digits, with an exponent shift of \cs{c_zero} (this shift is used in
+%   the case of a large significand).  If |#4| is a digit, leave it
+%   behind for the packing function, and read $6$ more digits to reach a
+%   total of $15$ digits: further digits are involved in the rounding.
+%   Otherwise put $8$ zeros in to complete the significand, then look
+%   for an exponent.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_small_leading:wwNN 1 #1 ; #2; #3 #4
+  {
+    #1 #2
+    \exp_after:wN \@@_parse_pack_trailing:NNNNNNww
+    \exp_after:wN \c_zero
+    \int_use:N \__int_eval:w 1
+      \if_int_compare:w \c_nine < 1 \token_to_str:N #4 \exp_stop_f:
+        \token_to_str:N #4
+        \exp_after:wN \@@_parse_small_trailing:wwNN
+        \__int_value:w 1
+          \exp_after:wN \@@_parse_digits_vi:N
+          \tex_romannumeral:D
+      \else:
+        0000 0000 \@@_parse_exponent:Nw #4
+      \fi:
+      \@@_parse_expand:w
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]{\@@_parse_small_trailing:wwNN}
+%   \begin{syntax}
+%     \cs{@@_parse_small_trailing:wwNN} |1| \meta{digits} |;| \meta{zeros} |;| \meta{number~of~zeros} \meta{next~token}
+%   \end{syntax}
+%   Leave digits $10$ to $15$ (arguments |#1| and |#2|) in the input
+%   stream.  If the \meta{next~token} is a digit, it is the $16$th
+%   digit, we keep it, then the \texttt{small_round} auxiliary considers
+%   this digit and all further digits to perform the rounding: the
+%   function expands to nothing or to |+1|.  Otherwise, there is no
+%   $16$-th digit, so we put a $0$, and look for an exponent.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_small_trailing:wwNN 1 #1 ; #2; #3 #4
+  {
+    #1 #2
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #4 \exp_stop_f:
+      \token_to_str:N #4
+      \exp_after:wN \@@_parse_small_round:NN
+      \exp_after:wN #4
+      \tex_romannumeral:D
+    \else:
+      0 \@@_parse_exponent:Nw #4
+    \fi:
+    \@@_parse_expand:w
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]
+%   {
+%     \@@_parse_pack_trailing:NNNNNNww ,
+%     \@@_parse_pack_leading:NNNNNww   ,
+%     \@@_parse_pack_carry:w
+%   }
+%   Those functions are expanded after all the digits are found, we took
+%   care of the rounding, as well as the exponent.  The last argument is
+%   the exponent.  The previous five arguments are $8$ digits which we
+%   pack in groups of $4$, and the argument before that is $1$, except
+%   in the rare case where rounding lead to a carry, in which case the
+%   argument is $2$.  The \texttt{trailing} function has an exponent
+%   shift as its first argument, which we add to the exponent found in
+%   the |e...| syntax.  If the trailing digits cause a carry, the
+%   integer expression for the leading digits is incremented (|+ \c_one|
+%   in the code below).  If the leading digits propagte this carry all
+%   the way up, the function \cs{@@_parse_pack_carry:w} increments the
+%   exponent, and changes the mantissa from |0000...| to |1000...|: this
+%   is simple because such a carry can only occur to give rise to a
+%   power of $10$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_pack_trailing:NNNNNNww #1 #2 #3#4#5#6 #7; #8 ;
+  {
+    \if_meaning:w 2 #2 + \c_one \fi:
+    ; #8 + #1 ; {#3#4#5#6} {#7};
+  }
+\cs_new:Npn \@@_parse_pack_leading:NNNNNww #1 #2#3#4#5 #6; #7;
+  {
+    + #7
+    \if_meaning:w 2 #1 \@@_parse_pack_carry:w \fi:
+    ; 0 {#2#3#4#5} {#6}
+  }
+\cs_new:Npn \@@_parse_pack_carry:w \fi: ; 0 #1
+  { \fi: + \c_one ; 0 {1000} }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Large significand}
+%
+% Parsing a significand larger than $1$ is a little bit more difficult
+% than parsing small significands.  We need to count the number of
+% digits before the decimal separator, and add that to the final
+% exponent.  We also need to test for the presence of a dot each time we
+% run out of digits, and branch to the appropriate \texttt{parse_small}
+% function in those cases.
+%
+% \begin{macro}[aux, EXP]{\@@_parse_large:N}
+%   This function is followed by the first non-zero digit of a
+%   \enquote{large} significand ($\geq 1$).  It is called within an
+%   integer expression for the exponent.  Grab up to $7$ more digits,
+%   for a total of $8$ digits.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_large:N #1
+  {
+    \exp_after:wN \@@_parse_large_leading:wwNN
+    \__int_value:w 1 \token_to_str:N #1
+      \exp_after:wN \@@_parse_digits_vii:N
+      \tex_romannumeral:D \@@_parse_expand:w
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]{\@@_parse_large_leading:wwNN}
+%   \begin{syntax}
+%     \cs{@@_parse_large_leading:wwNN} |1| \meta{digits} |;| \meta{zeros} |;| \meta{number~of~zeros} \meta{next~token}
+%   \end{syntax}
+%   We shift the exponent by the number of digits in |#1|, namely the
+%   target number, $8$, minus the \meta{number of zeros} (number of
+%   digits missing).  Then prepare to pack the $8$ first digits.  If the
+%   \meta{next token} is a digit, read up to $6$ more digits (digits
+%   $10$ to $15$).  If it is a period, try to grab the end of our $8$
+%   first digits, branching to the \texttt{small} functions since the
+%   number of digit does not affect the exponent anymore.  Finally, if
+%   this is the end of the significand, insert the \meta{zeros} to
+%   complete the $8$ first digits, insert $8$ more, and look for an
+%   exponent.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_large_leading:wwNN 1 #1 ; #2; #3 #4
+  {
+    + \c_eight - #3
+    \exp_after:wN \@@_parse_pack_leading:NNNNNww
+    \int_use:N \__int_eval:w 1 #1
+      \if_int_compare:w \c_nine < 1 \token_to_str:N #4 \exp_stop_f:
+        \exp_after:wN \@@_parse_large_trailing:wwNN
+        \__int_value:w 1 \token_to_str:N #4
+          \exp_after:wN \@@_parse_digits_vi:N
+          \tex_romannumeral:D
+      \else:
+        \if:w . #4
+          \exp_after:wN \@@_parse_small_leading:wwNN
+          \__int_value:w 1
+            \cs:w
+              @@_parse_digits_
+              \tex_romannumeral:D #3
+              :N \exp_after:wN
+            \cs_end:
+            \tex_romannumeral:D
+        \else:
+          #2
+          \exp_after:wN \@@_parse_pack_trailing:NNNNNNww
+          \exp_after:wN \c_zero
+          \__int_value:w 1 0000 0000
+          \@@_parse_exponent:Nw #4
+        \fi:
+      \fi:
+      \@@_parse_expand:w
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_parse_large_trailing:wwNN}
+%   \begin{syntax}
+%     \cs{@@_parse_large_trailing:wwNN} |1| \meta{digits} |;| \meta{zeros} |;| \meta{number~of~zeros} \meta{next~token}
+%   \end{syntax}
+%   We have just read $15$ digits.  If the \meta{next token} is a digit,
+%   then the exponent shift caused by this block of $8$ digits is $8$,
+%   first argument to the \texttt{pack_trailing} function.  We keep the
+%   \meta{digits} and this $16$-th digit, and find how this should be
+%   rounded using \cs{@@_parse_large_round:NN}.  Otherwise, the exponent
+%   shift is the number of \meta{digits}, $7$ minus the \meta{number of
+%     zeros}, and we test for a decimal point.  This case happens in
+%   |123451234512345.67| with exactly $15$ digits before the decimal
+%   separator.  Then branch to the appropriate \texttt{small} auxiliary,
+%   grabbing a few more digits to complement the digits we already
+%   grabbed.  Finally, if this is truly the end of the significand, look
+%   for an exponent after using the \meta{zeros} and providing a $16$-th
+%   digit of $0$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_large_trailing:wwNN 1 #1 ; #2; #3 #4
+  {
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #4 \exp_stop_f:
+      \exp_after:wN \@@_parse_pack_trailing:NNNNNNww
+      \exp_after:wN \c_eight
+      \int_use:N \__int_eval:w 1 #1 \token_to_str:N #4
+        \exp_after:wN \@@_parse_large_round:NN
+        \exp_after:wN #4
+        \tex_romannumeral:D
+    \else:
+      \exp_after:wN \@@_parse_pack_trailing:NNNNNNww
+      \int_use:N \__int_eval:w \c_seven - #3 \exp_stop_f:
+      \int_use:N \__int_eval:w 1 #1
+        \if:w . #4
+          \exp_after:wN \@@_parse_small_trailing:wwNN
+          \__int_value:w 1
+            \cs:w
+              @@_parse_digits_
+              \tex_romannumeral:D #3
+              :N \exp_after:wN
+            \cs_end:
+            \tex_romannumeral:D
+        \else:
+          #2 0 \@@_parse_exponent:Nw #4
+        \fi:
+    \fi:
+    \@@_parse_expand:w
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Finding the exponent}
+%
+% Expansion is a little bit tricky here, in part because we accept input
+% where multiplication is implicit.
+% \begin{verbatim}
+%   \@@_parse:n { 3.2 erf(0.1) }
+%   \@@_parse:n { 3.2 e\l_my_int }
+%   \@@_parse:n { 3.2 \c_pi_fp }
+% \end{verbatim}
+% The first case indicates that just looking one character ahead for an
+% \enquote{\texttt{e}} is not enough, since we would mistake the
+% function \texttt{erf} for an exponent of \enquote{\texttt{rf}}.  An
+% alternative would be to look two tokens ahead and check if what
+% follows is a sign or a digit, considering in that case that we must be
+% finding an exponent.  But taking care of the second case requires that
+% we unpack registers after \texttt{e}.  However, blindly expanding the
+% two tokens ahead completely would break the third example (unpacking
+% is even worse).  Indeed, in the course of reading $3.2$, \cs{c_pi_fp}
+% is expanded to \cs{s_@@} \cs{@@_chk:w} |1| |0| |{-1}| |{3141}|
+% $\cdots$ |;| and \cs{s_@@} stops the expansion.  Expanding two tokens
+% ahead would then force the expansion of \cs{@@_chk:w} (despite it
+% being protected), and that function tries to produce an error.
+%
+% What can we do?  Really, the reason why this last case breaks is that
+% just as \TeX{} does, we should read ahead as little as possible.
+% Here, the only case where there may be an exponent is if the first
+% token ahead is |e|.  Then we expand (and possibly unpack) the second
+% token --- and hopefully that is safe.
+%
+% \begin{macro}[aux, rEXP]{\@@_parse_exponent:Nw}
+%   This auxiliary is convenient to smuggle some material through
+%   \cs{fi:} ending conditional processing.  We place those \cs{fi:}
+%   (argument |#2|) at a very odd place becase this allows us to insert
+%   \cs{__int_eval:w} \ldots{} there if needed.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_exponent:Nw #1 #2 \@@_parse_expand:w
+  {
+    \exp_after:wN ;
+    \__int_value:w #2 \@@_parse_exponent:N #1
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]{\@@_parse_exponent:N, \@@_parse_exponent_ii:N}
+%   This function should be called within an \cs{__int_value:w} expansion
+%   (or within an integer expression.  It leaves digits of the exponent
+%   behind it in the input stream, and terminates the expansion with a
+%   semicolon.  If there is no \texttt{e}, leave an exponent of $0$.  If
+%   there is an \texttt{e}, expand the next token to run some tests on
+%   it.  Namely, if the character code of |#1| is greater than that of
+%   |9| (largest code valid for an exponent, less than any code valid
+%   for an identifier), there was in fact no exponent; otherwise, we
+%   search for the sign of the exponent.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_exponent:N #1
+  {
+    \if:w e #1
+      \exp_after:wN \@@_parse_exponent_ii:N
+      \tex_romannumeral:D
+    \else:
+      0 \@@_parse_return_semicolon:w #1
+    \fi:
+    \@@_parse_expand:w
+  }
+\cs_new:Npn \@@_parse_exponent_ii:N #1
+  {
+    \if_int_compare:w \if_catcode:w \tex_relax:D #1
+                \c_zero \else: `#1 \fi: > `9 \exp_stop_f:
+      0 \exp_after:wN ; \exp_after:wN e
+    \else:
+      \exp_after:wN \@@_parse_exponent_sign:N
+    \fi:
+    #1
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]{\@@_parse_exponent_sign:N}
+%   Read signs one by one (if there is any).
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_exponent_sign:N #1
+  {
+    \if:w + \if:w - #1 + \fi: \token_to_str:N #1
+      \exp_after:wN \@@_parse_exponent_sign:N
+      \tex_romannumeral:D \exp_after:wN \@@_parse_expand:w
+    \else:
+      \exp_after:wN \@@_parse_exponent_body:N
+      \exp_after:wN #1
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]{\@@_parse_exponent_body:N}
+%   An exponent can be an explicit integer (most common case), or
+%   various other things (most of which are invalid).
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_exponent_body:N #1
+  {
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+      \token_to_str:N #1
+      \exp_after:wN \@@_parse_exponent_digits:N
+      \tex_romannumeral:D
+    \else:
+      \@@_parse_exponent_keep:NTF #1
+        { \@@_parse_return_semicolon:w #1 }
+        {
+          \exp_after:wN ;
+          \tex_romannumeral:D
+        }
+    \fi:
+    \@@_parse_expand:w
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]{\@@_parse_exponent_digits:N}
+%   Read digits one by one, and leave them behind in the input stream.
+%   When finding a non-digit, stop, and insert a semicolon.  Note that
+%   we don't check for overflow of the exponent, hence there can be a
+%   TeX error.  It is mostly harmless, except when parsing
+%   |0e9876543210|, which should be a valid representation of $0$, but
+%   is not.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_exponent_digits:N #1
+  {
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+      \token_to_str:N #1
+      \exp_after:wN \@@_parse_exponent_digits:N
+      \tex_romannumeral:D
+    \else:
+      \@@_parse_return_semicolon:w #1
+    \fi:
+    \@@_parse_expand:w
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, rEXP]{\@@_parse_exponent_keep:NTF}
+%   This is the last building block for parsing exponents.  The argument
+%   |#1| is already fully expanded, and neither |+| nor |-| nor a digit.
+%   It can be:
+%   \begin{itemize}
+%   \item \cs{s_@@}, marking the start of an internal floating point,
+%     invalid here;
+%   \item another control sequence equal to \tn{relax}, probably a bad
+%     variable;
+%   \item a register: in this case we make sure that it is an integer
+%     register, not a dimension;
+%   \item a character other than |+|, |-| or digits, again, an error.
+%   \end{itemize}
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \@@_parse_exponent_keep:N #1 { TF }
+  {
+    \if_catcode:w \tex_relax:D #1
+      \if_meaning:w \tex_relax:D #1
+        \if_int_compare:w \pdftex_strcmp:D { \s_@@ } { #1 } = \c_zero
+          0 \@@_error:n { Cannot~use~floating~point~after~'e'. }
+          \prg_return_true:
+        \else:
+          0 \@@_error:n { Erroneous~variable~#1 used. }
+          \prg_return_false:
+        \fi:
+      \else:
+        \if_int_compare:w
+            \pdftex_strcmp:D { \__int_value:w #1 } { \tex_the:D #1 }
+            = \c_zero
+          \__int_value:w #1
+        \else:
+          0 \@@_error:n { Cannot~use~a~dimension~(#1)~after~'e'. }
+        \fi:
+        \prg_return_false:
+      \fi:
+    \else:
+      0 \@@_error:n { Missing~exponent~after~'e'. }
+      \prg_return_true:
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% ^^A begin[todo]
+% ^^A todo: \@@_sin:Nn should first _set, then \@@_sin:w,
+% ^^A both for speed, and error reporting.
+% ^^A todo: word 'e' == 'invalid syntax', word 'E' == "use 'e' instead"
+%
+% \subsubsection{Beyond 16 digits: rounding}
+%
+% \begin{macro}[int]{\@@_cfs_round_loop:N}
+%   Used both for \cs{@@_parse_small_round:NN} and
+%   \cs{@@_parse_large_round:NN}.
+%   Should appear after a \cs{__int_eval:w} |0|. Reads digits one by one,
+%   until reaching a non-digit. Adds |+1| for each digit. If all digits
+%   found are |0|, ends the \cs{__int_eval:w} by |;\c_zero|, otherwise
+%   by |;\c_one|. This is done by switching the loop to |round_up|
+%   at the first non-zero digit.
+%
+%    \begin{macrocode}
+\cs_new:Npn \@@_cfs_round_loop:N #1
+  {
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+      + \c_one
+      \if:w 0 #1
+        \exp_after:wN \@@_cfs_round_loop:N
+        \tex_romannumeral:D
+      \else:
+        \exp_after:wN \@@_cfs_round_up:N
+        \tex_romannumeral:D
+      \fi:
+    \else:
+      \@@_parse_return_semicolon:w \c_zero #1
+    \fi:
+    \@@_parse_expand:w
+  }
+\cs_new:Npn \@@_cfs_round_up:N #1
+  {
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+      + 1
+      \exp_after:wN \@@_cfs_round_up:N
+      \tex_romannumeral:D
+    \else:
+      \@@_parse_return_semicolon:w \c_one #1
+    \fi:
+    \@@_parse_expand:w
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \begin{macro}[int]{\@@_parse_large_round:NN}
+%   \begin{syntax}
+%     \cs{@@_parse_large_round:NN} \meta{digit} \meta{more digits}
+%   \end{syntax}
+%   \meta{digit} is the digit that we are currently rounding (we only
+%   care whether it is even or odd).
+%
+%   The goal is to get \cs{c_zero} or \cs{c_one}, check for an exponent
+%   afterwards, and combine it to the number of digits before the decimal
+%   point (which we thus need to keep track of).
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_large_round:NN #1#2
+  {
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f:
+      +
+      \exp_after:wN \@@_round_s:NNNw
+      \exp_after:wN 0
+      \exp_after:wN #1
+      \exp_after:wN #2
+      \int_use:N \__int_eval:w
+        \exp_after:wN \@@_parse_large_round_after:wNN
+        \int_use:N \__int_eval:w \c_one
+          \exp_after:wN \@@_cfs_round_loop:N
+    \else: %^^A could be dot, or e, or other
+      \exp_after:wN \@@_parse_large_round_dot_test:NNw
+      \exp_after:wN #1
+      \exp_after:wN #2
+    \fi:
+  }
+\cs_new:Npn \@@_parse_large_round_dot_test:NNw #1#2
+  {
+    \if:w . #2
+      \exp_after:wN \@@_parse_small_round:NN
+      \exp_after:wN #1
+      \tex_romannumeral:D
+    \else:
+      \@@_parse_exponent:Nw #2
+    \fi:
+    \@@_parse_expand:w
+  }
+%    \end{macrocode}
+%   \begin{syntax}
+%     \cs{@@_parse_large_round_after:wNN} \meta{exp} |;|
+%     ~~\meta{0 or 1} \meta{next~token}
+%   \end{syntax}
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_large_round_after:wNN #1 ; #2 #3
+  {
+    \if:w . #3
+      \exp_after:wN \@@_parse_large_round_after_ii:wN
+      \int_use:N \__int_eval:w #1 +
+        \c_zero * \__int_eval:w \c_zero
+          \exp_after:wN \@@_cfs_round_loop:N
+          \tex_romannumeral:D \exp_after:wN \@@_parse_expand:w
+    \else:
+      + #2
+      \exp_after:wN ;
+      \int_use:N \__int_eval:w #1 +
+        \exp_after:wN \@@_parse_exponent:N
+        \exp_after:wN #3
+    \fi:
+  }
+\cs_new:Npn \@@_parse_large_round_after_ii:wN #1 ; #2
+  {
+    + #2
+    \exp_after:wN ;
+    \int_use:N \__int_eval:w #1 +
+      \@@_parse_exponent:N
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+%
+%
+% \begin{macro}[int]{\@@_parse_small_round:NN}
+%   \begin{syntax}
+%     \cs{@@_parse_small_round:NN} \meta{digit} \meta{more digits}
+%   \end{syntax}
+%   \meta{digit} is the digit that we are currently rounding (we only
+%   care whether it is even or odd).
+%
+%   The goal is to get \cs{c_zero} or \cs{c_one}
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_small_round:NN #1#2
+  {
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f:
+      +
+      \exp_after:wN \@@_round_s:NNNw
+      \exp_after:wN 0
+      \exp_after:wN #1
+      \exp_after:wN #2
+      \int_use:N \__int_eval:w
+        \exp_after:wN \@@_parse_small_round_after:wN
+        \int_use:N \__int_eval:w \c_zero
+          \exp_after:wN \@@_cfs_round_loop:N
+          \tex_romannumeral:D
+    \else:
+      \@@_parse_exponent:Nw #2
+    \fi:
+    \@@_parse_expand:w
+  }
+\cs_new:Npn \@@_parse_small_round_after:wN #1; #2
+  {
+    + #2 \exp_after:wN ;
+    \__int_value:w \@@_parse_exponent:N
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+%
+% \subsection{Main functions}
+%
+% \begin{macro}[int, EXP]{\@@_parse:n}
+% \begin{macro}[aux, EXP]{\@@_parse_after:ww}
+%   Start a \tn{romannumeral} expansion so that \cs{@@_parse:n} expands
+%   in two steps.  The \cs{@@_parse_until:Nw} function will perform
+%   computations until reaching an operation with precedence
+%   \cs{c_minus_one} or less.  Then check that there was indeed nothing
+%   left (this cannot happen), and stop the initial expansion with
+%   \cs{c_zero}.%^^A todo: simplify a bit.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse:n #1
+  {
+    \tex_romannumeral:D
+      \exp_after:wN \@@_parse_after:ww
+      \tex_romannumeral:D
+        \@@_parse_until:Nw \c_minus_one
+        \@@_parse_expand:w #1 \s_@@_mark
+      \s_@@_stop
+  }
+\cs_new:Npn \@@_parse_after:ww #1@ #2 \s_@@_stop
+  {
+%<assert>    \assert_str_eq:nn { #2 } { \@@_parse_infix_end:N \s_@@_mark }
+    \c_zero #1
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_parse_until:Nw}
+% \begin{macro}[aux, EXP]{\@@_parse_until_test:NwN}
+%   The \cs{@@_parse_until}
+%   This is just a shorthand which sets up both \cs{@@_parse_until_test}
+%   and \cs{@@_parse_operand} with the same precedence. Note the
+%   trailing \cs{tex_romannumeral:D}. This function should be
+%   used with much care.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_until:Nw #1
+  {
+    -`0
+    \exp_after:wN \@@_parse_until_test:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+    \exp_after:wN \@@_parse_operand:Nw
+    \exp_after:wN #1
+    \tex_romannumeral:D
+  }
+\cs_new:Npn \@@_parse_until_test:NwN #1 #2 @ #3 { #3 #1 #2 @ }
+\cs_new:Npn \@@_parse_stop_until:N #1 { }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[int]{\@@_parse_until_test:NwN}
+%   \begin{syntax}
+%     \cs{@@_parse_until_test:NwN} \meta{prec} \meta{fp} \meta{bool}
+%   \end{syntax}
+%   If \meta{bool} is true, then \meta{fp} is the floating
+%   point number that we are looking for (it ends with |;|),
+%   and this expands to \meta{fp}. If \meta{bool} is false,
+%   then the input stream actually looks like
+%   \begin{quote}
+%     \cs{@@_parse_until_test:NwN} \meta{prec} \meta{fp_1} \meta{false}
+%     \meta{oper} \meta{fp_2} \cs{infix_?}
+%   \end{quote}
+%   and we must feed \meta{prec} to \cs{infix_?}, and perform
+%   \meta{oper} on \meta{fp_1} and \meta{fp_2}: this
+%   triggers the expansion of \cs{infix_?} \meta{prec}, continuing
+%   the computation (or stopping). In that case, the function \cs{until}
+%   yields
+%   \begin{quote}
+%     \cs{@@_parse_until_test:NwN} \meta{prec}
+%     \meta{oper} \meta{fp_1} \meta{fp_2}
+%     \cs{tex_romannumeral:D} |-`0| \cs{infix_?} \meta{prec}
+%   \end{quote}
+%   expanding \meta{oper} next.
+%    \begin{macrocode}
+%    \end{macrocode}
+% \end{macro}
+%
+% ^^A 3.5\mydim e4**2
+% ^^A todo: add tests that catcode changes don't mess things up.
+%
+% \subsection{Main functions}
+%
+% \begin{macro}[aux, EXP]{\@@_parse_infix_after_operand:NwN}
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_infix_after_operand:NwN #1 #2;
+  {
+    \@@_exp_after_f:nw { \@@_parse_infix:NN #1 }
+    #2;
+  }
+\group_begin:
+  \char_set_catcode_letter:N \*
+  \cs_new:Npn \@@_parse_infix:NN #1 #2
+    {
+      \if_catcode:w \tex_relax:D #2
+        \if_int_compare:w
+            \pdftex_strcmp:D { \s_@@_mark } { #2 }
+            = \c_zero
+          \exp_after:wN \exp_after:wN
+          \exp_after:wN \@@_parse_infix_end:N
+        \else:
+          \exp_after:wN \exp_after:wN
+          \exp_after:wN \@@_parse_infix_juxtapose:N
+        \fi:
+      \else:
+        \if_int_compare:w
+            \__int_eval:w \tex_uccode:D `#2 / 26
+            = \c_three
+          \exp_after:wN \exp_after:wN
+          \exp_after:wN \@@_parse_infix_juxtapose:N
+        \else:
+          \exp_after:wN \@@_parse_infix_check:NNN
+          \cs:w
+            @@_parse_infix_#2:N
+            \exp_after:wN \exp_after:wN \exp_after:wN
+          \cs_end:
+        \fi:
+      \fi:
+      #1
+      #2
+    }
+  \cs_new:Npn \@@_parse_infix_check:NNN #1#2#3
+    {
+      \if_meaning:w \tex_relax:D #1
+        \__msg_expandable_error:n { Missing~*~inserted. }
+        \exp_after:wN \@@_parse_infix_*:N
+        \exp_after:wN #2
+        \exp_after:wN #3
+      \else:
+        \exp_after:wN #1
+        \exp_after:wN #2
+        \tex_romannumeral:D \exp_after:wN \@@_parse_expand:w
+      \fi:
+    }
+\group_end:
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_parse_apply_binary:NwNwN}
+%
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_apply_binary:NwNwN #1 #2#3@ #4 #5#6@ #7
+  {
+    \exp_after:wN \@@_parse_until_test:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+      \cs:w
+        @@
+        \@@_type_from_scan:N #2
+        \@@_type_from_scan:N #5
+        _ #4 _o:ww
+      \cs_end:
+      #2#3 #5#6
+    \tex_romannumeral:D -`0 #7 #1
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]
+%   {\@@_parse_apply_unary_array:NNwN, \@@_parse_apply_unary:NNwN}
+%   Here, |#2| is \emph{e.g.}, \cs{@@_neg_@@:w}, and expands once after the
+%   calculation.\footnote{Bruno: explain.}  The argument |#3| may be an
+%   array, so either we map through all its items, or we feed all items
+%   at once to the custom function.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_apply_unary_array:NNwN #1#2#3@#4
+  {
+    #2 #3 @
+    \tex_romannumeral:D -`0 #4 #1
+  }
+\cs_new:Npn \@@_parse_apply_unary:NNwN #1#2#3@#4
+  {
+    #2 #3
+    \tex_romannumeral:D -`0 #4 #1
+  }
+\cs_new:Npn \@@_parse_unary_type:N #1
+  { \@@_type_from_scan:N #1 :w \cs_end: #1 }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Prefix operators}
+%
+% \subsubsection{Identifiers}
+%
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_parse_word_inf:N, \@@_parse_word_nan:N, \@@_parse_word_pi:N ,
+%     \@@_parse_word_deg:N, \@@_parse_word_em:N ,
+%     \@@_parse_word_ex:N , \@@_parse_word_in:N , \@@_parse_word_pt:N ,
+%     \@@_parse_word_pc:N , \@@_parse_word_cm:N , \@@_parse_word_mm:N ,
+%     \@@_parse_word_dd:N , \@@_parse_word_cc:N , \@@_parse_word_nd:N ,
+%     \@@_parse_word_nc:N , \@@_parse_word_bp:N , \@@_parse_word_sp:N ,
+%     \@@_parse_word_true:N , \@@_parse_word_false:N ,
+%   }
+%   A whole bunch of floating point numbers.
+%    \begin{macrocode}
+\cs_set_protected:Npn \@@_tmp:w #1 #2
+  {
+    \cs_new_nopar:cpn { @@_parse_word_#1:N }
+      { \exp_after:wN #2 \tex_romannumeral:D -`0 \@@_parse_infix:NN }
+  }
+\@@_tmp:w { inf } \c_inf_fp
+\@@_tmp:w { nan } \c_nan_fp
+\@@_tmp:w { pi  } \c_pi_fp
+\@@_tmp:w { deg } \c_one_degree_fp
+\@@_tmp:w { true } \c_one_fp
+\@@_tmp:w { false } \c_zero_fp
+\@@_tmp:w { pt } \c_one_fp
+\cs_set_protected:Npn \@@_tmp:w #1 #2
+  {
+    \cs_new_nopar:cpn { @@_parse_word_#1:N }
+      {
+        \@@_exp_after_f:nw { \@@_parse_infix:NN }
+        \s_@@ \@@_chk:w 10 #2 ;
+      }
+  }
+\@@_tmp:w {in} { {2} {7227} {0000} {0000} {0000} }
+\@@_tmp:w {pc} { {2} {1200} {0000} {0000} {0000} }
+\@@_tmp:w {cm} { {2} {2845} {2755} {9055} {1181} }
+\@@_tmp:w {mm} { {1} {2845} {2755} {9055} {1181} }
+\@@_tmp:w {dd} { {1} {1070} {0085} {6496} {0630} }
+\@@_tmp:w {cc} { {2} {1284} {0102} {7795} {2756} }
+\@@_tmp:w {nd} { {1} {1066} {9783} {4645} {6693} }
+\@@_tmp:w {nc} { {2} {1280} {3740} {1574} {8031} }
+\@@_tmp:w {bp} { {1} {1003} {7500} {0000} {0000} }
+\@@_tmp:w {sp} { {-4} {1525} {8789} {0625} {0000} }
+\tl_map_inline:nn { {em} {ex} }
+  {
+    \cs_new_nopar:cpn { @@_parse_word_#1:N }
+      {
+        \exp_after:wN \dim_to_fp:n \exp_after:wN
+          { \dim_use:N \__dim_eval:w 1 #1 \exp_after:wN }
+        \tex_romannumeral:D -`0 \@@_parse_infix:NN
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]
+%   {
+%     \@@_parse_word_abs:N   ,
+%     \@@_parse_word_cos:N   ,
+%     \@@_parse_word_cot:N   ,
+%     \@@_parse_word_exp:N   ,
+%     \@@_parse_word_ln:N    ,
+%     \@@_parse_word_sin:N   ,
+%     \@@_parse_word_tan:N   ,
+%   }
+%   Unary functions, which are applied to all of their arguments when
+%   receiving an array.
+%    \begin{macrocode}
+\tl_map_inline:nn { {abs} {cos} {cot} {exp} {ln} {sin} {tan} }
+  {
+    \cs_new:cpn { @@_parse_word_#1:N } ##1
+      {
+        \exp_after:wN \@@_parse_apply_unary:NNwN
+        \exp_after:wN ##1
+        \cs:w @@_ #1 \exp_after:wN \@@_parse_unary_type:N
+        \tex_romannumeral:D
+        \@@_parse_until:Nw \c_fifteen
+        \@@_parse_expand:w
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]
+%   {
+%     \@@_parse_word_max:N , \@@_parse_word_min:N   ,
+%     \@@_parse_word_mod:N ,
+%   }
+%   Those functions are also unary, but need to mix all of their
+%   arguments together.
+%    \begin{macrocode}
+\cs_set_protected:Npn \@@_tmp:w #1#2
+  {
+    \cs_new:Npn #1 ##1
+      {
+        \exp_after:wN \@@_parse_apply_unary_array:NNwN
+        \exp_after:wN ##1
+        \exp_after:wN #2
+        \tex_romannumeral:D
+        \@@_parse_until:Nw \c_sixteen \@@_parse_expand:w
+      }
+  }
+\@@_tmp:w \@@_parse_word_max:N \@@_max:w
+\@@_tmp:w \@@_parse_word_min:N \@@_min:w
+ % \@@_tmp:w \@@_parse_word_mod:N \@@_mod:w %^^A todo: not implemented!
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_parse_word_round:N}
+%   This function expects one or two arguments.
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_word_round:N #1#2
+  {
+    \if_meaning:w + #2
+      \@@_parse_round:Nw \@@_round_to_pinf:NNN
+    \else:
+      \if_meaning:w 0 #2
+        \@@_parse_round:Nw \@@_round_to_zero:NNN
+      \else:
+        \if_meaning:w - #2
+          \@@_parse_round:Nw \@@_round_to_ninf:NNN
+        \fi:
+      \fi:
+    \fi:
+    \exp_after:wN \@@_parse_apply_round:NNwN
+    \exp_after:wN #1
+    \exp_after:wN \@@_round_to_nearest:NNN
+    \tex_romannumeral:D
+    \@@_parse_until:Nw \c_sixteen \@@_parse_expand:w #2
+  }
+\cs_new:Npn \@@_parse_round:Nw
+    #1 #2 \@@_round_to_nearest:NNN #3 \@@_parse_expand:w #4
+  { #2 #1 #3 \@@_parse_expand:w }
+\cs_new:Npn \@@_parse_apply_round:NNwN #1#2#3@#4
+  {
+    \if_case:w \__int_eval:w \@@_array_count:w #3@ - \c_one \__int_eval_end:
+         \@@_round:Nwn #2 #3 {0} \tex_romannumeral:D
+    \or: \@@_round:Nww #2 #3 \tex_romannumeral:D
+    \else:
+      \@@_error:n { round()~expects~1~or~2~arguments. }
+      \exp_after:wN \c_nan_fp \tex_romannumeral:D
+    \fi:
+    -`0 #4 #1
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Unary minus, plus, not}
+%
+% \begin{macro}[EXP, aux]{\@@_parse_prefix_+:Nw}
+%   A unary |+| does nothing.
+%    \begin{macrocode}
+\cs_new_eq:cN { @@_parse_prefix_+:Nw } \@@_parse_operand:Nw
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP, aux]{\@@_parse_prefix_-:Nw, \@@_parse_prefix_!:Nw}
+%   Unary |-| is harder.
+%   Boolean not.
+%    \begin{macrocode}
+\cs_set_protected:Npn \@@_tmp:w #1#2
+  {
+    \cs_new:cpn { @@_parse_prefix_#1:Nw } ##1
+      {
+        \exp_after:wN \@@_parse_apply_unary:NNwN
+        \exp_after:wN ##1
+        \cs:w @@_ #2 \exp_after:wN \@@_parse_unary_type:N
+        \tex_romannumeral:D
+        \if_int_compare:w \c_twelve < ##1
+          \@@_parse_until:Nw ##1
+        \else:
+          \@@_parse_until:Nw \c_twelve
+        \fi:
+        \@@_parse_expand:w
+      }
+  }
+\@@_tmp:w - { neg }
+\@@_tmp:w ! { not }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Other prefixes}
+%
+% \begin{macro}[int]{\@@_parse_prefix_(:Nw}
+%    \begin{macrocode}
+\group_begin:
+  \char_set_catcode_letter:N \)
+  \cs_new:cpn { @@_parse_prefix_(:Nw } #1
+    {
+      \exp_after:wN \@@_parse_lparen_after:NwN
+      \exp_after:wN #1
+      \tex_romannumeral:D
+      \if_int_compare:w #1 = \c_sixteen
+        \@@_parse_until:Nw \c_one
+      \else:
+        \@@_parse_until:Nw \c_zero
+      \fi:
+      \@@_parse_expand:w
+    }
+  \cs_new:Npn \@@_parse_lparen_after:NwN #1#2@#3
+    {
+      \token_if_eq_meaning:NNTF #3 \@@_parse_infix_):N
+        {
+          \@@_parse_exp_after_array:wf #2 \s_@@_stop
+          \exp_after:wN \@@_parse_infix:NN
+          \exp_after:wN #1
+          \tex_romannumeral:D \@@_parse_expand:w
+        }
+        {
+          \@@_error:n { Missing~')'~inserted. }
+          #2 @ \@@_parse_stop_until:N #3
+        }
+    }
+\group_end:
+%    \end{macrocode}
+% \end{macro}
+%
+%^^A todo: rename to exp_after_array_f:w
+% \begin{macro}[int, EXP]{\@@_parse_exp_after_array:wf}
+%    \begin{macrocode}
+\cs_new:Npn \@@_parse_exp_after_array:wf #1
+  {
+    \cs:w @@ \@@_type_from_scan:N #1 _exp_after_f:nw \cs_end:
+      { \@@_parse_exp_after_array:wf }
+    #1
+  }
+\cs_new:Npn \@@_stop_exp_after_f:nw #1#2 { }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int]{\@@_parse_prefix_.:Nw}
+%   This function is called when a number starts with a dot.
+%    \begin{macrocode}
+\cs_new:cpn {@@_parse_prefix_.:Nw} #1
+  {
+    \exp_after:wN \@@_parse_infix_after_operand:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+      \exp_after:wN \@@_sanitize:wN
+      \int_use:N \__int_eval:w \c_zero \@@_parse_strim_zeros:N
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Infix operators}
+%
+%   As described in the \enquote{work plan}, each infix operator has an
+%   associated \cs{infix} function, a computing function, and
+%   precedence, given as arguments to \cs{@@_tmp:w}.  The
+%   latter two are only needed when defining the \cs{infix} function.
+%    \begin{macrocode}
+\cs_set_protected:Npn \@@_tmp:w #1#2#3#4
+  {
+    \cs_new:Npn #1 ##1
+      {
+        \if_int_compare:w ##1 < #3
+          \exp_after:wN @
+          \exp_after:wN \@@_parse_apply_binary:NwNwN
+          \exp_after:wN #2
+          \tex_romannumeral:D
+          \@@_parse_until:Nw #4
+          \exp_after:wN \@@_parse_expand:w
+        \else:
+          \exp_after:wN @
+          \exp_after:wN \@@_parse_stop_until:N
+          \exp_after:wN #1
+        \fi:
+      }
+  }
+%    \end{macrocode}
+%
+% \begin{macro}[int, EXP]
+%   {
+%     \@@_parse_infix_+:N, \@@_parse_infix_-:N,
+%     \@@_parse_infix_/:N, \@@_parse_infix_mul:N,
+%     \@@_parse_infix_and:N, \@@_parse_infix_or:N,
+%   }
+%   Using the general mechanism for arithmetic operations.
+%    \begin{macrocode}
+\group_begin:
+  \char_set_catcode_other:N \&
+  \@@_tmp:w \@@_parse_infix_juxtapose:N * \c_thirty_two \c_thirty_two
+  \exp_args:Nc \@@_tmp:w { @@_parse_infix_ / :N } / \c_ten \c_ten
+  \exp_args:Nc \@@_tmp:w { @@_parse_infix_mul:N } * \c_ten \c_ten
+  \exp_args:Nc \@@_tmp:w { @@_parse_infix_ - :N } - \c_nine \c_nine
+  \exp_args:Nc \@@_tmp:w { @@_parse_infix_ + :N } + \c_nine \c_nine
+  \exp_args:Nc \@@_tmp:w { @@_parse_infix_and:N } & \c_five \c_five
+  \exp_args:Nc \@@_tmp:w { @@_parse_infix_ or:N } | \c_four \c_four
+\group_end:
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_parse_infix_*:N}
+% \begin{macro}[int, EXP]+\@@_parse_infix_^:N+
+%   The power operation must be associative in the opposite order from
+%   all others.  For this, we reverse the test, hence treating a
+%   \enquote{previous precedence} of \cs{c_fourteen} as less binding
+%   than |^|.
+%    \begin{macrocode}
+\group_begin:
+  \char_set_catcode_letter:N ^
+  \@@_tmp:w \@@_parse_infix_^:N ^ \c_fifteen \c_fourteen
+  \cs_new:cpn { @@_parse_infix_*:N } #1#2
+    {
+      \if:w * #2
+        \exp_after:wN \@@_parse_infix_^:N
+        \exp_after:wN #1
+      \else:
+        \exp_after:wN \@@_parse_infix_mul:N
+        \exp_after:wN #1
+        \exp_after:wN #2
+      \fi:
+    }
+\group_end:
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]+\@@_parse_infix_|:Nw+
+% \begin{macro}[int, EXP]+\@@_parse_infix_&:Nw+
+%    \begin{macrocode}
+\group_begin:
+  \char_set_catcode_letter:N \|
+  \char_set_catcode_letter:N \&
+  \cs_new:Npn \@@_parse_infix_|:N #1#2
+    {
+      \if:w | #2
+        \exp_after:wN \@@_parse_infix_|:N
+        \exp_after:wN #1
+        \tex_romannumeral:D \exp_after:wN \@@_parse_expand:w
+      \else:
+        \exp_after:wN \@@_parse_infix_or:N
+        \exp_after:wN #1
+        \exp_after:wN #2
+      \fi:
+    }
+  \cs_new:Npn \@@_parse_infix_&:N #1#2
+    {
+      \if:w & #2
+        \exp_after:wN \@@_parse_infix_&:N
+        \exp_after:wN #1
+        \tex_romannumeral:D \exp_after:wN \@@_parse_expand:w
+      \else:
+        \exp_after:wN \@@_parse_infix_and:N
+        \exp_after:wN #1
+        \exp_after:wN #2
+      \fi:
+    }
+\group_end:
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]
+%   {
+%     \@@_parse_infix_<:N, \@@_parse_infix_=:N,
+%     \@@_parse_infix_>:N, \@@_parse_infix_!:N
+%   }
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_parse_infix_excl_aux:NN,
+%     \@@_parse_infix_excl_error:,
+%     \@@_infix_compare:N,
+%     \@@_parse_compare:NNNNNw,
+%     \@@_parse_compare_expand:NNNNNw,
+%     \@@_parse_compare_end:NNNN,
+%     \@@_compare:wNNNNw,
+%   }
+%    \begin{macrocode}
+\cs_new:cpn { @@_parse_infix_<:N } #1
+  {
+    \@@_infix_compare:N #1 \c_one_fp
+      \c_zero_fp  \c_zero_fp \c_zero_fp \c_zero_fp <
+  }
+\cs_new:cpn { @@_parse_infix_=:N } #1
+  {
+    \@@_infix_compare:N #1 \c_one_fp
+      \c_zero_fp \c_zero_fp \c_zero_fp \c_zero_fp =
+  }
+\cs_new:cpn { @@_parse_infix_>:N } #1
+  {
+    \@@_infix_compare:N #1 \c_one_fp
+      \c_zero_fp \c_zero_fp \c_zero_fp \c_zero_fp >
+  }
+\cs_new:cpn { @@_parse_infix_!:N } #1
+  {
+    \exp_after:wN \@@_parse_infix_excl_aux:NN
+    \exp_after:wN #1 \tex_romannumeral:D \@@_parse_expand:w
+  }
+\cs_new:Npn \@@_parse_infix_excl_aux:NN #1#2
+  {
+    \if_catcode:w \tex_relax:D #2
+      \@@_parse_infix_excl_error:
+    \else:
+      \if_int_compare:w `#2 > `? \exp_stop_f:
+        \@@_parse_infix_excl_error:
+      \else:
+        \if_int_compare:w `#2 < `< \exp_stop_f:
+          \@@_parse_infix_excl_error:
+        \fi:
+      \fi:
+    \fi:
+    \@@_infix_compare:N #1 \c_zero_fp
+      \c_one_fp \c_one_fp \c_one_fp \c_one_fp #2
+  }
+\cs_new:Npn \@@_parse_infix_excl_error:
+  { \__msg_expandable_error:n { Missing~relation~symbol~after~'!'. } }
+\cs_new:Npn \@@_infix_compare:N #1
+  {
+    \if_int_compare:w #1 < \c_seven
+      \exp_after:wN \@@_parse_compare:NNNNNw
+    \else:
+      \exp_after:wN @
+      \exp_after:wN \@@_parse_stop_until:N
+      \exp_after:wN \@@_infix_compare:N
+    \fi:
+  }
+\cs_new:Npn \@@_parse_compare:NNNNNw #1#2#3#4#5#6
+  {
+    \if_case:w
+          \if_catcode:w \tex_relax:D #6
+            \c_minus_one
+          \else:
+            \__int_eval:w `#6 - `< \__int_eval_end:
+          \fi:
+         \@@_parse_compare_expand:NNNNNw #1#1#3#4#5
+    \or: \@@_parse_compare_expand:NNNNNw #1#2#1#4#5
+    \or: \@@_parse_compare_expand:NNNNNw #1#2#3#1#5
+    \or: \@@_parse_compare_expand:NNNNNw #1#2#3#4#1
+    \else: \@@_parse_compare_end:NNNN #2#3#4#5#6
+    \fi:
+  }
+\cs_new:Npn \@@_parse_compare_expand:NNNNNw #1#2#3#4#5
+  {
+    \exp_after:wN \@@_parse_compare:NNNNNw
+    \exp_after:wN #1
+    \exp_after:wN #2
+    \exp_after:wN #3
+    \exp_after:wN #4
+    \exp_after:wN #5
+    \tex_romannumeral:D \exp_after:wN \@@_parse_expand:w
+  }
+\cs_new:Npn \@@_parse_compare_end:NNNN #1#2#3#4#5 \fi:
+  {
+    \fi:
+    \exp_after:wN @
+    \exp_after:wN \@@_parse_apply_compare:NwNNNNwN
+    \exp_after:wN #1
+    \exp_after:wN #2
+    \exp_after:wN #3
+    \exp_after:wN #4
+    \tex_romannumeral:D
+    \@@_parse_until:Nw \c_seven \@@_parse_expand:w #5
+  }
+\cs_new:Npn \@@_parse_apply_compare:NwNNNNwN #1 #2@ #3#4#5#6 #7@ #8
+  {
+    \exp_after:wN \@@_parse_until_test:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+      \exp_after:wN \exp_after:wN
+      \exp_after:wN \exp_after:wN
+      \exp_after:wN \exp_after:wN
+      \if_case:w \@@_compare:ww #2 #7 \exp_stop_f:
+             #4
+      \or:   #5
+      \or:   #6
+      \else: #3
+      \fi:
+    \tex_romannumeral:D -`0 #8 #1
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_parse_infix_?:N, \@@_parse_infix_::N}
+%    \begin{macrocode}
+\group_begin:
+  \char_set_catcode_letter:N \?
+  \cs_new:Npn \@@_parse_infix_?:N #1
+    {
+      \if_int_compare:w #1 < \c_three
+        \exp_after:wN @
+        \exp_after:wN \@@_ternary:NwwN
+        \tex_romannumeral:D
+        \@@_parse_until:Nw \c_three
+        \exp_after:wN \@@_parse_expand:w
+      \else:
+        \exp_after:wN @
+        \exp_after:wN \@@_parse_stop_until:N
+        \exp_after:wN \@@_parse_infix_?:N
+      \fi:
+    }
+  \cs_new:Npn \@@_parse_infix_::N #1
+    {
+      \if_int_compare:w #1 < \c_three
+        \__msg_expandable_error:n { Missing~'?'~inserted~for~'?:'. }
+        \exp_after:wN @
+        \exp_after:wN \@@_ternary_ii:NwwN
+        \tex_romannumeral:D
+        \@@_parse_until:Nw \c_two
+        \exp_after:wN \@@_parse_expand:w
+      \else:
+        \exp_after:wN @
+        \exp_after:wN \@@_parse_stop_until:N
+        \exp_after:wN \@@_parse_infix_::N
+      \fi:
+    }
+\group_end:
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]+\@@_parse_infix_):N+
+%   This one is a little bit odd: force every previous operator to end,
+%   regardless of the precedence.  This is very similar to
+%   \cs{@@_parse_infix_end:N}.
+%    \begin{macrocode}
+\group_begin:
+  \char_set_catcode_letter:N \)
+  \cs_new:Npn \@@_parse_infix_):N #1
+    {
+      \if_int_compare:w #1 < \c_zero
+        \@@_error:n { Extra~')'~ignored. }
+        \exp_after:wN \@@_parse_infix:NN
+        \exp_after:wN #1
+        \tex_romannumeral:D \exp_after:wN \@@_parse_expand:w
+      \else:
+        \exp_after:wN @
+        \exp_after:wN \@@_parse_stop_until:N
+        \exp_after:wN \@@_parse_infix_):N
+      \fi:
+    }
+\group_end:
+\cs_new:Npn \@@_parse_infix_end:N #1
+  { @ \@@_parse_stop_until:N \@@_parse_infix_end:N }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]+\@@_parse_infix_,:N+
+%    \begin{macrocode}
+\group_begin:
+  \char_set_catcode_letter:N \,
+  \cs_new:Npn \@@_parse_infix_,:N #1
+    {
+      \if_int_compare:w #1 > \c_one
+        \exp_after:wN @
+        \exp_after:wN \@@_parse_stop_until:N
+        \exp_after:wN \@@_parse_infix_,:N
+      \else:
+        \if_int_compare:w #1 = \c_one
+          \exp_after:wN \@@_parse_infix_comma:w
+          \tex_romannumeral:D
+        \else:
+          \exp_after:wN \@@_parse_infix_comma_gobble:w
+          \tex_romannumeral:D
+        \fi:
+        \@@_parse_until:Nw \c_one
+        \exp_after:wN \@@_parse_expand:w
+      \fi:
+    }
+  \cs_new:Npn \@@_parse_infix_comma:w #1 @
+    { #1 @ \@@_parse_stop_until:N }
+  \cs_new:Npn \@@_parse_infix_comma_gobble:w #1 @
+    {
+      \@@_error:n { Unexpected~comma:~extra~arguments~ignored. }
+      @ \@@_parse_stop_until:N
+    }
+\group_end:
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintChanges
+%
+% \PrintIndex
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-round.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-round.dtx
new file mode 100644
index 00000000000..68df5e1ac17
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-round.dtx
@@ -0,0 +1,424 @@
+% \iffalse meta-comment
+%
+%% File: l3fp-round.dtx Copyright(C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp-round.dtx 3549 2012-03-13 20:54:30Z bruno $
+  {L3 Floating-point rounding}
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{^^A
+%   The \textsf{l3fp-round} package\\ Rounding floating points^^A
+%   \thanks{This file describes v\ExplFileVersion,
+%     last revised \ExplFileDate.}^^A
+% }
+%
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+%
+% \date{Released \ExplFileDate}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3fp-round} implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+% ^^A todo: provide an interface for rounding modes.
+% ^^A todo: provide a \l_@@_rounding_mode_int giving the current mode.
+% ^^A todo: make transcendental function obey the correct rounding mode.
+% ^^A todo: optimize all rounding functions for various rounding modes.
+% ^^A todo: reduce the number of almost identical functions.
+%
+% \subsection{Rounding tools}
+%
+% Floating point operations often yield a result that cannot be exactly
+% represented in a mantissa with $16$ digits.  In that case, we need to
+% round the exact result to a representable number.  The \textsc{ieee}
+% standard defines four rounding modes:
+% \begin{itemize}
+%   \item Round to nearest: round to the representable floating point
+%     number whose absolute difference with the exact result is the
+%     smallest.  If the exact result lies exactly at the mid-point
+%     between two consecutive representable floating point numbers,
+%     round to the floating point number whose last digit is even.
+%   \item Round towards negative infinity: round to the greatest
+%     floating point number not larger than the exact result.
+%   \item Round towards zero: round to a floating point number with the
+%     same sign as the exact result, with the largest absolute value not
+%     larger than the absolute value of the exact result.
+%   \item Round towards positive infinity: round to the least floating
+%     point number not smaller than the exact result.
+% \end{itemize}
+% This is not fully implemented in \pkg{l3fp} yet, and transcendental
+% functions fall back on the \enquote{round to nearest} mode.  All
+% rounding for basic algebra is done through the functions defined in
+% this module, which can be redefined to change their rounding behaviour
+% (but there is not interface for that yet).
+%
+% The rounding tools available in this module are many variations on a
+% base function \cs{@@_round:NNN}, which expands to \cs{c_zero} or
+% \cs{c_one} depending on whether the final result should be rounded up
+% or down.
+% \begin{itemize}
+%   \item \cs{@@_round:NNN} \meta{sign} \meta{digit_1} \meta{digit_2}
+%     can expand to \cs{c_zero} or \cs{c_one}.
+%   \item \cs{@@_round:NNNN} \meta{sign} \meta{digit_1} \meta{digit_2}
+%     \meta{digit_3} can expand to \cs{c_zero} or \cs{c_one}.
+%   \item \cs{@@_round_s:NNNw} \meta{sign} \meta{digit_1} \meta{digit_2}
+%     \meta{more digits} |;| can expand to |\c_zero ;| or |\c_one ;|.
+%   \item \cs{@@_round_neg:NNN} \meta{sign} \meta{digit_1} \meta{digit_2}
+%     can expand to \cs{c_zero} or \cs{c_one}.
+% \end{itemize}
+% See implementation comments for details on the syntax.
+%
+% \begin{macro}[int, rEXP]{\@@_round:NNN}
+% \begin{macro}[aux, rEXP]
+%   {
+%     \@@_round_to_nearest:NNN,
+%     \@@_round_to_ninf:NNN,
+%     \@@_round_to_zero:NNN,
+%     \@@_round_to_pinf:NNN
+%   }
+%   \begin{syntax}
+%     \cs{@@_round:NNN} \meta{final sign} \meta{digit_1} \meta{digit_2}
+%   \end{syntax}
+%   If rounding the number $\meta{final sign}
+%   \meta{digit_1}.\meta{digit_2}$ to an integer rounds it towards zero
+%   (truncates it), this function expands to \cs{c_zero}, and otherwise
+%   to \cs{c_one}.  Typically used within the scope of an
+%   \cs{__int_eval:w}, to add~$1$ if needed, and thereby round
+%   correctly.  The result depends on the rounding mode.
+%
+%   It is very important that \meta{final sign} be the final sign of the
+%   result. Otherwise, the result will be incorrect in the case of
+%   rounding towards~$-\infty$ or towards~$+\infty$. Also recall that
+%   \meta{final sign} is~$0$ for positive, and~$2$ for negative.
+%
+%   By default, the functions below return \cs{c_zero}, but this is
+%   superseded by \cs{@@_round_return_one:}, which instead returns
+%   \cs{c_one}, expanding everything and removing \cs{c_zero} in the
+%   process.  In the case of rounding towards~$\pm\infty$ or
+%   towards~$0$, this is not really useful, but it prepares us for the
+%   \enquote{round to nearest, ties to even} mode.
+%
+%   The \enquote{round to nearest} mode is the default.  If the
+%   \meta{digit_2} is larger than~$5$, then round up.  If it is less
+%   than~$5$, round down.  If it is exactly $5$, then round such that
+%   \meta{digit_1} plus the result is even.  In other words, round up if
+%   \meta{digit_1} is odd.
+%    \begin{macrocode}
+\cs_new:Npn \@@_round_return_one:
+  { \exp_after:wN \c_one \tex_romannumeral:D }
+\cs_new:Npn \@@_round_to_ninf:NNN #1 #2 #3
+  {
+    \if_meaning:w 2 #1
+      \if_int_compare:w #3 > \c_zero
+        \@@_round_return_one:
+      \fi:
+    \fi:
+    \c_zero
+  }
+\cs_new:Npn \@@_round_to_zero:NNN #1 #2 #3 { \c_zero }
+\cs_new:Npn \@@_round_to_pinf:NNN #1 #2 #3
+  {
+    \if_meaning:w 0 #1
+      \if_int_compare:w #3 > \c_zero
+        \@@_round_return_one:
+      \fi:
+    \fi:
+    \c_zero
+  }
+\cs_new:Npn \@@_round_to_nearest:NNN #1 #2 #3
+  {
+    \if_int_compare:w #3 > \c_five
+      \@@_round_return_one:
+    \else:
+      \if_meaning:w 5 #3
+        \if_int_odd:w #2 \exp_stop_f:
+          \@@_round_return_one:
+        \fi:
+      \fi:
+    \fi:
+    \c_zero
+  }
+\cs_new_eq:NN \@@_round:NNN \@@_round_to_nearest:NNN
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP, int]{\@@_round_s:NNNw}
+%   \begin{syntax}
+%     \cs{@@_round_s:NNNw} \meta{final sign} \meta{digit} \meta{more digits} |;|
+%   \end{syntax}
+%   Similar to \cs{@@_round:NNN}, but with an extra semicolon, this
+%   function expands to |\c_zero ;| if rounding $\meta{final sign}
+%   \meta{digit}.\meta{more digits}$ to an integer truncates, and to
+%   |\c_one ;| otherwise.  The \meta{more digits} part must be a digit,
+%   followed by something that does not overflow a \cs{int_use:N}
+%   \cs{__int_eval:w} construction.  The only relevant information about
+%   this piece is whether it is zero or not.
+%    \begin{macrocode}
+\cs_new:Npn \@@_round_s:NNNw #1 #2 #3 #4;
+  {
+    \exp_after:wN \@@_round:NNN
+    \exp_after:wN #1
+    \exp_after:wN #2
+    \int_use:N \__int_eval:w
+      \if_int_odd:w 0 \if_meaning:w 0 #3 1 \fi:
+                      \if_meaning:w 5 #3 1 \fi:
+                \exp_stop_f:
+        \if_int_compare:w \__int_eval:w #4 > \c_zero
+          1 +
+        \fi:
+      \fi:
+      #3
+    ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_round:NNNN}
+%   \begin{syntax}
+%     \cs{@@_round:NNNN} \meta{final sign} \meta{digit} \meta{2d}
+%   \end{syntax}
+%   Identical to \cs{@@_round_s:NNNw} except for a trailing semicolon.
+%   \begin{macrocode}
+\cs_new:Npn \@@_round:NNNN #1 #2 #3 #4
+  {
+    \exp_after:wN \@@_round:NNN
+    \exp_after:wN #1
+    \exp_after:wN #2
+    \int_use:N \__int_eval:w
+      \if_int_odd:w 0 \if_meaning:w 0 #3 1 \fi:
+                      \if_meaning:w 5 #3 1 \fi:
+                \exp_stop_f:
+        \if_int_compare:w #4 > \c_zero
+          1 +
+        \fi:
+      \fi:
+      #3
+    \__int_eval_end:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_round_neg:NNN}
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_round_to_nearest_neg:NNN,
+%     \@@_round_to_ninf_neg:NNN,
+%     \@@_round_to_zero_neg:NNN,
+%     \@@_round_to_pinf_neg:NNN
+%   }
+%   \begin{syntax}
+%     \cs{@@_round_neg:NNN} \meta{final sign} \meta{digit_1} \meta{digit_2}
+%   \end{syntax}
+%   This expands to \cs{c_zero} or \cs{c_one}. Consider a number of
+%   the form $ \meta{final sign}.X\ldots X\meta{digit_1} $ with exactly
+%   $15$ (non-all-zero) digits before \meta{digit_1}, and subtract from it
+%   $\meta{final sign}.0\ldots0\meta{digit_2}$, where there are $16$ zeros.
+%   If in the current rounding mode the result should be rounded down,
+%   then this function returns \cs{c_one}. Otherwise, \emph{i.e.},
+%   if the result is rounded back to the first operand, then this function
+%   returns \cs{c_zero}.
+%
+%   It turns out that this negative \enquote{round to nearest}
+%   is identical to the positive one. And this is the default mode.
+%    \begin{macrocode}
+\cs_new:Npn \@@_round_to_ninf_neg:NNN #1 #2 #3
+  {
+    \if_meaning:w 0 #1
+      \if_int_compare:w #3 > \c_zero
+        \@@_round_return_one:
+      \fi:
+    \fi:
+    \c_zero
+  }
+\cs_new:Npn \@@_round_to_zero_neg:NNN #1 #2 #3
+  {
+    \if_int_compare:w #3 > \c_zero
+      \@@_round_return_one:
+    \fi:
+    \c_zero
+  }
+\cs_new:Npn \@@_round_to_pinf_neg:NNN #1 #2 #3
+  {
+    \if_meaning:w 2 #1
+      \if_int_compare:w #3 > \c_zero
+        \@@_round_return_one:
+      \fi:
+    \fi:
+    \c_zero
+  }
+\cs_new_eq:NN \@@_round_to_nearest_neg:NNN \@@_round_to_nearest:NNN
+\cs_new_eq:NN \@@_round_neg:NNN \@@_round_to_nearest_neg:NNN
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{The \texttt{round} function}
+%
+% ^^A todo: This macro is intermingled with l3fp-parse.
+% ^^A todo: Add explanations.
+% \begin{macro}[int, EXP]{\@@_round:Nww, \@@_round:Nwn}
+% \begin{macro}[aux, EXP]
+%   {
+%     \@@_round_normal:NwNNnw ,
+%     \@@_round_normal_ii:NnnwNNnn ,
+%     \@@_round_pack:Nw ,
+%     \@@_round_normal_iii:NNwNnn ,
+%     \@@_round_normal_end:wwNnn ,
+%     \@@_round_special:NwwNnn ,
+%     \@@_round_special_aux:Nw
+%   }
+%    \begin{macrocode}
+\cs_new:Npn \@@_round:Nww #1#2 ; #3 ;
+  {
+    \@@_small_int:wTF #3; { \@@_round:Nwn #1#2; }
+      {
+        \@@_error:x { {round(x,n)~with~n=} \@@_to_tl:w #3; }
+        \exp_after:wN \c_nan_fp
+      }
+  }
+\cs_new:Npn \@@_round:Nwn #1 \s_@@ \@@_chk:w #2#3#4; #5
+  {
+    \if_meaning:w 1 #2
+      \exp_after:wN \@@_round_normal:NwNNnw
+      \exp_after:wN #1
+      \__int_value:w #5
+    \else:
+      \exp_after:wN \@@_exp_after_o:w
+    \fi:
+    \s_@@ \@@_chk:w #2#3#4;
+  }
+\cs_new:Npn \@@_round_normal:NwNNnw #1#2 \s_@@ \@@_chk:w 1#3#4#5;
+  {
+    \@@_decimate:nNnnnn { \c_sixteen - #4 - #2 }
+      \@@_round_normal_ii:NnnwNNnn #5 #1 #3 {#4} {#2}
+  }
+\cs_new:Npn \@@_round_normal_ii:NnnwNNnn #1#2#3#4; #5#6
+  {
+    \exp_after:wN \@@_round_normal_iii:NNwNnn
+    \int_use:N \__int_eval:w
+      \if_int_compare:w #2 > \c_zero
+        1 \__int_value:w #2
+        \exp_after:wN \@@_round_pack:Nw
+        \int_use:N \__int_eval:w 1#3 +
+      \else:
+        \if_int_compare:w #3 > \c_zero
+          1 \__int_value:w #3 +
+        \fi:
+      \fi:
+      \exp_after:wN #5
+      \exp_after:wN #6
+      \use_none:nnnnnnn #3
+      #1
+      \__int_eval_end:
+      0000 0000 0000 0000 ; #6
+  }
+\cs_new:Npn \@@_round_pack:Nw #1
+  { \if_meaning:w 2 #1 + \c_one \fi: \__int_eval_end: }
+\cs_new:Npn \@@_round_normal_iii:NNwNnn #1 #2
+  {
+    \if_meaning:w 0 #2
+      \exp_after:wN \@@_round_special:NwwNnn
+      \exp_after:wN #1
+    \fi:
+    \@@_pack_twice_four:wNNNNNNNN
+    \@@_pack_twice_four:wNNNNNNNN
+    \@@_round_normal_end:wwNnn
+    ; #2
+  }
+\cs_new:Npn \@@_round_normal_end:wwNnn #1;#2;#3#4#5
+  {
+    \exp_after:wN \@@_exp_after_o:w \tex_romannumeral:D -`0
+    \@@_sanitize:Nw #3 #4 ; #1 ;
+  }
+\cs_new:Npn \@@_round_special:NwwNnn #1#2;#3;#4#5#6
+  {
+    \if_meaning:w 0 #1
+      \@@_case_return:nw
+        { \exp_after:wN \@@_zero_fp:N \exp_after:wN #4 }
+    \else:
+      \exp_after:wN \@@_round_special_aux:Nw
+      \exp_after:wN #4
+      \int_use:N \__int_eval:w \c_one
+        \if_meaning:w 1 #1 -#6 \else: +#5 \fi:
+    \fi:
+    ;
+  }
+\cs_new:Npn \@@_round_special_aux:Nw #1#2;
+  {
+    \exp_after:wN \@@_exp_after_o:w \tex_romannumeral:D -`0
+    \@@_sanitize:Nw #1#2; {1000}{0000}{0000}{0000};
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintChanges
+%
+% \PrintIndex
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-traps.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-traps.dtx
new file mode 100644
index 00000000000..2e3a5e262ba
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-traps.dtx
@@ -0,0 +1,418 @@
+% \iffalse meta-comment
+%%
+%% File: l3fp-traps.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp-traps.dtx 2479 2011-06-19 21:57:25Z bruno $
+  {L3 Floating-point exception trapping}
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{The \textsf{l3fp-traps} package\thanks{This file
+%         has version number \ExplFileVersion, last
+%         revised \ExplFileDate.}\\
+% Trapping floating-point exceptions}
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+% \date{Released \ExplFileDate}
+% \maketitle
+%
+% \begin{documentation}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3fp-traps} Implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+% Exceptions should be accessed by an \texttt{n}-type argument, among
+% \begin{itemize}
+% \item \texttt{invalid_operation}
+% \item \texttt{division_by_zero}
+% \item \texttt{overflow}
+% \item \texttt{underflow}
+% \item \texttt{inexact} (actually never used).
+% \end{itemize}
+%
+% \subsection{Flags}
+%
+% \begin{macro}{\@@_flag_off:n}
+%   Function to turn a flag off.  Simply undefine it.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_flag_off:n #1
+  { \cs_set_eq:cN { l_@@_ #1 _flag_token } \c_undefined:D }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\@@_flag_on:n}
+%   Function to turn a flag on expandably: use \TeX{}'s automatic
+%   assignment to \cs{scan_stop:}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_flag_on:n #1
+  { \exp_args:Nc \use_none:n { l_@@_ #1 _flag_token } }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP,pTF]{\@@_if_flag_on:n}
+%   Returns true if the flag is on, false otherwise.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \@@_if_flag_on:n #1 { p , T , F , TF }
+  {
+    \if_cs_exist:w l_@@_ #1 _flag_token \cs_end:
+      \prg_return_true:
+    \else:
+      \prg_return_false:
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{variable}
+%   {
+%     \l_@@_invalid_operation_flag_token ,
+%     \l_@@_division_by_zero_flag_token  ,
+%     \l_@@_overflow_flag_token          ,
+%     \l_@@_underflow_flag_token         ,
+%   }
+%   The \textsc{ieee} standard defines five exceptions.  We currently
+%   don't support the \enquote{inexact} exception.
+%    \begin{macrocode}
+\cs_new_eq:NN \l_@@_invalid_operation_flag_token \c_undefined:D
+\cs_new_eq:NN \l_@@_division_by_zero_flag_token \c_undefined:D
+\cs_new_eq:NN \l_@@_overflow_flag_token \c_undefined:D
+\cs_new_eq:NN \l_@@_underflow_flag_token \c_undefined:D
+%    \end{macrocode}
+% \end{variable}
+%
+% \subsection{Traps}
+%
+% Exceptions can be trapped to obtain custom behaviour.  When an invalid
+% operation or a division by zero is trapped, the trap receives as
+% arguments the result as an $N$-type floating point number, the
+% function name (multiple letters for prefix operations, or a single
+% symbol for infix operations), and the operand(s).  When an overflow or
+% underflow is trapped, the trap receives the resulting overly large or
+% small floating point number if it is not too big, otherwise it
+% receives $+\infty$.  Currently, the inexact exception is entirely
+% ignored.
+%
+% The behaviour when an exception occurs is controlled by the
+% definitions of the functions
+% \begin{itemize}
+% \item \cs{@@_invalid_operation:Nnw},
+% \item \cs{@@_invalid_operation:Nnww},
+% \item \cs{@@_division_by_zero:Nnw},
+% \item \cs{@@_division_by_zero:Nnww},
+% \item \cs{@@_overflow:w},
+% \item \cs{@@_underflow:w}.
+% \end{itemize}
+% Rather than changing them directly, we provide a user interface as
+% \cs{@@_trap:nn} \Arg{exception} \Arg{way of trapping}, where the
+% \meta{way of trapping} is one of \texttt{error}, \texttt{flag}, or
+% \texttt{none}.
+%
+% \begin{macro}{\@@_trap:nn} %^^A todo: user command => document
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_trap:nn #1#2
+  {
+    \cs_if_exist_use:cF { @@_trap_#1_set_#2: }
+      {
+        \clist_if_in:nnTF
+          { invalid_operation , division_by_zero , overflow , underflow }
+          {#1}
+          {
+            \__msg_kernel_error:nnxx { kernel }
+              { unknown-fpu-trap-type } {#1} {#2}
+          }
+          { \__msg_kernel_error:nnx { kernel } { unknown-fpu-exception } {#1} }
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux]
+%   {
+%     \@@_trap_invalid_operation_set_error: ,
+%     \@@_trap_invalid_operation_set_flag:  ,
+%     \@@_trap_invalid_operation_set_none:  ,
+%     \@@_trap_invalid_operation_set:N      ,
+%   }
+% \begin{macro}[aux]
+%   {
+%     \@@_trap_division_by_zero_set_error: ,
+%     \@@_trap_division_by_zero_set_flag:  ,
+%     \@@_trap_division_by_zero_set_none:  ,
+%     \@@_trap_division_by_zero_set:N      ,
+%   }
+% \begin{macro}[aux]{\@@_trap_invalid_operation_set:Nnn}
+%   We provide three types of trapping for invalid operations and
+%   division by zero: either produce an error and raise the relevant
+%   flag; or only raise the flag; or don't even raise the flag.  In all
+%   cases, the function must produce a result, namely its first
+%   argument, $\pm\infty$ or \nan{}.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_trap_invalid_operation_set_error:
+  { \@@_trap_invalid_operation_set:N \prg_do_nothing: }
+\cs_new_protected_nopar:Npn \@@_trap_invalid_operation_set_flag:
+  { \@@_trap_invalid_operation_set:N \use_none:nn }
+\cs_new_protected_nopar:Npn \@@_trap_invalid_operation_set_none:
+  { \@@_trap_invalid_operation_set:N \use_none:nnnn }
+\cs_new_protected:Npn \@@_trap_invalid_operation_set:N #1
+  {
+    \@@_trap_invalid_operation_set:Nnn #1
+      { invalid_operation } { Invalid~operation~ }
+  }
+\cs_new_protected_nopar:Npn \@@_trap_division_by_zero_set_error:
+  { \@@_trap_division_by_zero_set:N \prg_do_nothing: }
+\cs_new_protected_nopar:Npn \@@_trap_division_by_zero_set_flag:
+  { \@@_trap_division_by_zero_set:N \use_none:nn }
+\cs_new_protected_nopar:Npn \@@_trap_division_by_zero_set_none:
+  { \@@_trap_division_by_zero_set:N \use_none:nnnn }
+\cs_new_protected:Npn \@@_trap_division_by_zero_set:N #1
+  {
+    \@@_trap_invalid_operation_set:Nnn #1
+      { division_by_zero } { Division~by~zero~in~ }
+  }
+\cs_new_protected:Npn \@@_trap_invalid_operation_set:Nnn #1#2#3
+  {
+    \exp_args:Nno \use:n
+      { \cs_set:cpn { @@_ #2 :Nnw } ##1##2##3; }
+      {
+        #1
+        \@@_error:x { { #3 ##2 } ( \@@_to_tl:w ##3; ) }
+        \@@_flag_on:n {#2}
+        \exp_after:wN ##1
+      }
+    \exp_args:Nno \use:n
+      { \cs_set:cpn { @@_ #2 :Nnww } ##1##2##3; ##4; }
+      {
+        #1
+        \@@_error:x
+          {
+            {#3}
+            \tl_if_single:nTF {##2}
+              { ( \@@_to_tl:w ##3; ) ##2 ( \@@_to_tl:w ##4; ) }
+              { { ##2 ( } \@@_to_tl:w ##3; { , ~ } \@@_to_tl:w ##4; ) }
+          }
+        \@@_flag_on:n {#2}
+        \exp_after:wN ##1
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[aux]
+%   {
+%     \@@_trap_overflow_set_error: ,
+%     \@@_trap_overflow_set_flag:  ,
+%     \@@_trap_overflow_set_none:  ,
+%     \@@_trap_overflow_set:N      ,
+%   }
+% \begin{macro}[aux]
+%   {
+%     \@@_trap_underflow_set_error: ,
+%     \@@_trap_underflow_set_flag:  ,
+%     \@@_trap_underflow_set_none:  ,
+%     \@@_trap_underflow_set:N      ,
+%   }
+% \begin{macro}[aux]{\@@_trap_overflow_set:NnNn}
+%   Just as for invalid operations and division by zero, the three
+%   different behaviours are obtained by feeding \cs{prg_do_nothing:},
+%   \cs{use_none:nn} or \cs{use_none:nnnn} to an auxiliary, with a
+%   further auxiliary common to overflow and underflow functions.  In
+%   most cases, the argument of the \cs{@@_overflow:w} and
+%   \cs{@@_underflow:w} functions will be an (almost) normal number
+%   (with an exponent outside the allowed range), and the error message
+%   thus displays that number together with the result to which it
+%   overflowed or underflowed.  For extreme cases such as \texttt{10 **
+%     1e9999}, the exponent would be too large for \TeX{}, and
+%   \cs{@@_overflow:w} receives $\pm \infty$ (\cs{@@_underflow:w} would
+%   receive $\pm 0$); then we cannot do better than simply say an
+%   overflow or underflow occurred.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_trap_overflow_set_error:
+  { \@@_trap_overflow_set:N \prg_do_nothing: }
+\cs_new_protected_nopar:Npn \@@_trap_overflow_set_flag:
+  { \@@_trap_overflow_set:N \use_none:nn }
+\cs_new_protected_nopar:Npn \@@_trap_overflow_set_none:
+  { \@@_trap_overflow_set:N \use_none:nnnn }
+\cs_new_protected:Npn \@@_trap_overflow_set:N #1
+  { \@@_trap_overflow_set:NnNn #1 { overflow } \@@_inf_fp:N { inf } }
+\cs_new_protected_nopar:Npn \@@_trap_underflow_set_error:
+  { \@@_trap_underflow_set:N \prg_do_nothing: }
+\cs_new_protected_nopar:Npn \@@_trap_underflow_set_flag:
+  { \@@_trap_underflow_set:N \use_none:nn }
+\cs_new_protected_nopar:Npn \@@_trap_underflow_set_none:
+  { \@@_trap_underflow_set:N \use_none:nnnn }
+\cs_new_protected:Npn \@@_trap_underflow_set:N #1
+  { \@@_trap_overflow_set:NnNn #1 { underflow } \@@_zero_fp:N { 0 } }
+\cs_new_protected:Npn \@@_trap_overflow_set:NnNn #1#2#3#4
+  {
+    \exp_args:Nno \use:n
+      { \cs_set:cpn { @@_ #2 :w } \s_@@ \@@_chk:w ##1##2##3; }
+      {
+        #1
+        \@@_error:x
+          {
+            \token_if_eq_meaning:NNTF 1 ##1
+              {
+                \@@_to_tl:w \s_@@ \@@_chk:w ##1##2##3; ~ #2 ed ~ to ~
+                \token_if_eq_meaning:NNF 0 ##2 { - } #4 .
+              }
+              { An~#2~occurred. }
+          }
+        \@@_flag_on:n {#2}
+        #3 ##2
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[int]
+%   {
+%     \@@_invalid_operation:Nnw, \@@_invalid_operation:Nnww,
+%     \@@_division_by_zero:Nnw, \@@_division_by_zero:Nnww,
+%     \@@_overflow:w , \@@_underflow:w
+%   }
+%   Initialize the two control sequences (to log properly their
+%   existence).  Then set invalid operations to trigger an error, and
+%   division by zero, overflow, and underflow to act silently on their
+%   flag.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \@@_invalid_operation:Nnw { }
+\cs_new_protected_nopar:Npn \@@_invalid_operation:Nnww { }
+\cs_new_protected_nopar:Npn \@@_division_by_zero:Nnw { }
+\cs_new_protected_nopar:Npn \@@_division_by_zero:Nnww { }
+\cs_new_protected_nopar:Npn \@@_overflow:w { }
+\cs_new_protected_nopar:Npn \@@_underflow:w { }
+\@@_trap:nn { invalid_operation } { error }
+\@@_trap:nn { division_by_zero } { flag }
+\@@_trap:nn { overflow } { flag }
+\@@_trap:nn { underflow } { flag }
+%    \end{macrocode}
+% \end{macro}
+%
+%^^A todo: first arg of @@_invalid_operation:Nnw(w) should be an 'invalid' nan.
+%
+% \subsection{Errors}
+%
+%^^A begin[todo]
+% \begin{macro}[int, EXP]{\@@_error:n, \@@_error:x}
+%   The argument is fully expanded in a way similar to \texttt{x}-type
+%   expansion, but braced groups are simply copied, \cs{exp_not:n} does
+%   not work, spaces are ignored unless braced.  The result of that
+%   weird (but useful) expansion is fed to \cs{__msg_expandable_error:n}.
+%    \begin{macrocode}
+\cs_new_eq:NN \@@_error:n \__msg_expandable_error:n
+\cs_new:Npn \@@_error:x #1
+  {
+    \exp_args:Nf \__msg_expandable_error:n
+      {
+        \@@_error_loop:nwnN { \exp_stop_f: } #1 \prg_do_nothing:
+        \s_@@_mark { } \@@_error_loop:nwnN \s_@@_mark { } \@@_error_end:nw
+      }
+  }
+\cs_new:Npn \@@_error_end:nw #1#2 \@@_error_end:nw { #1 }
+\cs_new:Npn \@@_error_loop:nwnN #1#2 \s_@@_mark #3 #4
+  {
+    \exp_after:wN #4 \tex_romannumeral:D -`0
+    #2
+    \s_@@_mark { #3 #1 } #4
+  }
+%    \end{macrocode}
+% \end{macro}
+% ^^A end[todo]
+%
+% \subsection{Messages}
+%
+% Some messages.
+%    \begin{macrocode}
+\msg_new:nnnn { kernel } { unknown-fpu-exception }
+  { The~FPU~exception~'#1'~is~not~known:~that~trap~will~never~be~triggered. }
+  {
+    The~only~exceptions~to~which~traps~can~be~attached~are \\
+    \iow_indent:n
+      {
+        * ~ invalid_operation \\
+        * ~ division_by_zero \\
+        * ~ overflow \\
+        * ~ underflow
+      }
+  }
+\msg_new:nnnn { kernel } { unknown-fpu-trap-type }
+  { The~FPU~trap~type~'#2'~is~not~known. }
+  {
+    The~trap~type~must~be~one~of \\
+    \iow_indent:n
+      {
+        * ~ error \\
+        * ~ flag \\
+        * ~ none
+      }
+  }
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintChanges
+%
+% \PrintIndex
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx
new file mode 100644
index 00000000000..16a3fb465f6
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx
@@ -0,0 +1,581 @@
+% \iffalse meta-comment
+%
+%% File: l3fp-trig.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver>
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp-trig.dtx 3514 2012-03-08 06:14:48Z bruno $
+  {L3 Floating-point trigonometric functions}
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{The \textsf{l3fp-trig} package\thanks{This file
+%         has version number \ExplFileVersion, last
+%         revised \ExplFileDate.}\\
+% Floating point trigonometric functions}
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+% \date{Released \ExplFileDate}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{Implementation}
+%
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%<@@=fp>
+%    \end{macrocode}
+%
+%^^A todo: check EXP/rEXP everywhere.
+%
+% \subsection{Inverting a floating point number}
+%
+% \begin{macro}[int, EXP]{\@@_one_over:w}
+%   Expects a floating point of the form \cs{s_@@} \ldots{} |;| and
+%   computes its multiplicative inverse.  This is used to compute the
+%   cotangent function very near $0$.
+%    \begin{macrocode}
+\cs_new_nopar:Npx \@@_one_over:w
+  {
+    \exp_not:N \exp_after:wN
+    \exp_not:c { @@_/_o:ww }
+    \exp_not:N \c_one_fp
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Direct trigonometric functions}
+%
+% The approach for all trigonometric functions (sine, cosine, tangent,
+% and cotangent) is the same.
+% \begin{itemize}
+% \item Filter out special cases ($\pm 0$, $\pm\inf$ and \nan{}).
+% \item Keep the sign for later, and work with the absolute value $|x|$
+%   of the argument.
+% \item For numbers less than $1$, shift the mantissa to convert them to
+%   fixed point numbers.  Very small numbers take a slightly different
+%   route.
+% \item For numbers $\geq 1$, subtract a multiple of $\pi/2$ to bring
+%   them to the range to $[0, \pi/2]$.
+% \item Reduce further to $[0, \pi/4]$ using $\sin x = \cos (\pi/2-x)$.
+% \item Use the appropriate power series depending on the octant
+%   $\lfloor\frac{|x|}{\pi/4}\rfloor \mod 8$, the sign, and the function
+%   to compute.
+% \end{itemize}
+%
+% \subsubsection{Sign and special numbers}
+%
+% \begin{macro}[int, EXP]{\@@_sin:w}
+%   The sine of $\pm 0$ or \nan{} is the same floating point number.
+%   The sine of $\pm\infty$ raises an invalid operation exception.
+%   Otherwise, check the exponent, preparing to use
+%   \cs{@@_sin_series:NNwww} for the calculation, with a sign |#2|, and
+%   an initial octant of $0$.  The question mark is an argument which is
+%   not used in this case.
+%    \begin{macrocode}
+\cs_new:Npn \@@_sin:w \s_@@ \@@_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+           \@@_case_return_same_o:w
+    \or:
+      \exp_after:wN \@@_trig_exponent:NNNNwn
+      \exp_after:wN \@@_sin_series:NNwww
+      \exp_after:wN ?
+      \exp_after:wN #2
+      \exp_after:wN \c_zero
+    \or:
+      \@@_case_use:nw
+        { \@@_invalid_operation:Nnw \c_nan_fp { sin } }
+    \else: \@@_case_return_same_o:w
+    \fi:
+    \s_@@ \@@_chk:w #1#2
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_cos:w}
+%   The cosine of $\pm 0$ is $1$.  The cosine of $\pm\infty$ raises an
+%   invalid operation exception.  The cosine of \nan{} is itself.
+%   Otherwise, check the exponent, preparing to use
+%   \cs{@@_sin_series:NNwww} for the calculation, with a positive sign
+%   ($0$), and an initial octant of $2$, because $\cos x = \sin ( \pi/2
+%   + |x|)$.  The question mark is an argument which is not used in this
+%   case.
+%    \begin{macrocode}
+\cs_new:Npn \@@_cos:w \s_@@ \@@_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+           \@@_case_return_o:Nw \c_one_fp
+    \or:
+      \@@_case_use:nw %^^A todo: is that faster than the exp_after route?
+        {
+          \@@_trig_exponent:NNNNwn
+          \@@_sin_series:NNwww
+          ?
+          0
+          \c_two
+        }
+    \or:
+      \@@_case_use:nw
+        { \@@_invalid_operation:Nnw \c_nan_fp { cos } }
+    \else: \@@_case_return_same_o:w
+    \fi:
+    \s_@@ \@@_chk:w #1#2
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_tan:w}
+%   The tangent of $\pm 0$ or \nan{} is the same floating point number.
+%   The tangent of $\pm\infty$ raises an invalid operation exception.
+%   Otherwise, check the exponent, preparing to use
+%   \cs{@@_tan_series:NNwww} for the calculation, with a positive sign
+%   ($0$), and an initial octant of $1$, chosen to be distinct from the
+%   octants for sine and cosine.  See \cs{@@_cot:w} for an
+%   explanation of the $0$ argument.
+%    \begin{macrocode}
+\cs_new:Npn \@@_tan:w \s_@@ \@@_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+           \@@_case_return_same_o:w
+    \or:
+      \exp_after:wN \@@_trig_exponent:NNNNwn
+      \exp_after:wN \@@_tan_series:NNwww
+      \exp_after:wN 0
+      \exp_after:wN #2
+      \exp_after:wN \c_one
+    \or:
+      \@@_case_use:nw
+        { \@@_invalid_operation:Nnw \c_nan_fp { tan } }
+    \else: \@@_case_return_same_o:w
+    \fi:
+    \s_@@ \@@_chk:w #1#2
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_cot:w}
+%   The cotangent of $\pm 0$ is $\pm \infty$ with the same sign,
+%   produced by \cs{@@_one_over:w}.  The cotangent of $\pm\infty$ raises
+%   an invalid operation exception.  The cotangent of \nan{} is itself.
+%   We use $\cot x = - \tan (\pi/2 + x)$, and the initial octant for the
+%   tangent was chosen to be $1$, so the octant here starts at $3$.  The
+%   change in sign is obtained by feeding \cs{@@_tan_series:NNwww} two
+%   signs rather than just the sign of the argument: the first of those
+%   indicates whether we compute tangent or cotangent.  Those signs are
+%   eventually combined.
+%    \begin{macrocode}
+\cs_new:Npn \@@_cot:w \s_@@ \@@_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+           \exp_after:wN \@@_one_over:w
+    \or:
+      \exp_after:wN \@@_trig_exponent:NNNNwn
+      \exp_after:wN \@@_tan_series:NNwww
+      \exp_after:wN 2
+      \exp_after:wN #2
+      \exp_after:wN \c_three
+    \or:
+      \@@_case_use:nw
+        { \@@_invalid_operation:Nnw \c_nan_fp { cot } }
+    \else: \@@_case_return_same_o:w
+    \fi:
+    \s_@@ \@@_chk:w #1#2
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Small and tiny arguments}
+%
+% \begin{macro}[aux, EXP]{\@@_trig_exponent:NNNNwn}
+%   The first four arguments control what trigonometric function we
+%   compute, then follows a normal floating point number.  If the
+%   floating point is smaller than $10^{-8}$, then call the appropriate
+%   \texttt{_epsilon} auxiliary.  Otherwise, call the function |#1|,
+%   with arguments |#2|, |#3|, the octant, computed in an integer
+%   expression starting with |#4|, and a fixed point number obtained
+%   from the floating point number by argument reduction.  Numbers less
+%   than $1$ are converted using \cs{@@_trig_small:w} which simply
+%   shifts the mantissa, while large numbers need argument reduction.
+%    \begin{macrocode}
+\cs_new:Npn \@@_trig_exponent:NNNNwn #1#2#3#4 \s_@@ \@@_chk:w 1#5#6
+  {
+    \if_int_compare:w #6 > - \c_eight
+      \exp_after:wN #1
+      \exp_after:wN #2
+      \exp_after:wN #3
+      \int_use:N \__int_eval:w #4
+        \if_int_compare:w #6 > \c_zero
+          \exp_after:wN \@@_trig_large:w \__int_value:w
+        \else:
+          \exp_after:wN \@@_trig_small:w \__int_value:w
+        \fi:
+    \else:
+      \if_case:w #4
+             \@@_sin_epsilon:w
+      \or:   \@@_sin_epsilon:w
+      \or:   \@@_cos_epsilon:w
+      \else: \@@_cot_epsilon:w
+      \fi:
+      #5
+    \fi:
+    #6 ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]
+%   {\@@_sin_epsilon:w, \@@_cos_epsilon:w, \@@_cot_epsilon:w}
+%   Sine and tangent of tiny numbers give the number itself: the
+%   relative error is less than $5 \cdot 10^{-17}$, which is
+%   appropriate.  Cosine simply gives $1$.  Cotangent computes the
+%   inverse.  This is actually slightly wrong because further terms in
+%   the power series could affect the rounding for cotangent.
+%    \begin{macrocode}
+\cs_new:Npn \@@_sin_epsilon:w #1 \fi: #2 \fi: #3 ;
+  { \fi: \fi: \@@_exp_after_o:w \s_@@ \@@_chk:w 1 #2 {#3} }
+\cs_new:Npn \@@_cos_epsilon:w #1 \fi: #2 \fi: #3 ; #4 ;
+  { \fi: \fi: \exp_after:wN \c_one_fp }
+\cs_new:Npn \@@_cot_epsilon:w \fi: #1 \fi: #2 ;
+  { \fi: \fi: \@@_one_over:w \s_@@ \@@_chk:w 1 #1 {#2} }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_trig_small:w, \@@_trig_small_aux:wwNN}
+%   Floating point numbers less than $1$ are converted to fixed point
+%   numbers by shifting the mantissa.  Since we have already filtered
+%   out numbers less than $10^{-8}$, no digit is lost in converting to
+%   a fixed point number.
+%    \begin{macrocode}
+\cs_new:Npn \@@_trig_small:w #1;
+  {
+    \exp_after:wN \exp_after:wN \exp_after:wN \@@_trig_small_aux:wwNN
+    \prg_replicate:nn { - #1 } { 0 } ;
+  }
+\cs_new:Npn \@@_trig_small_aux:wwNN #1; #2#3#4#5;
+  {
+    \@@_pack_twice_four:wNNNNNNNN
+    \@@_pack_twice_four:wNNNNNNNN
+    \@@_pack_twice_four:wNNNNNNNN
+    .
+    ;
+    #1#2#3#4#5 0000 0000;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsubsection{Reduction of large arguments}
+%
+% In the case of a floating point argument greater or equal to $1$, we
+% need to perform argument reduction.
+%
+% \begin{macro}[aux, rEXP]
+%   {
+%     \@@_trig_large:w, \@@_trig_large_i:www,
+%     \@@_trig_large_ii:wnnnnnn, \@@_trig_large_break:w
+%   }
+%   We shift the mantissa by one digit at a time, subtracting a multiple
+%   of $2\pi$ at each step.  We use a value of $2\pi$ rounded up,
+%   consistent with the choice of \cs{c_pi_fp}.  This is not quite
+%   correct from an accuracy perspective, but has the nice property that
+%   $\sin(180\mathrm{deg}) = 0$ exactly.  The arguments of
+%   \cs{@@_trig_large_i:www} are a leading block of up to $5$ digits,
+%   three brace groups of $4$ digits each, and the exponent, decremented
+%   at each step.  The multiple of $2\pi$ to subtract is estimated as
+%   $\lfloor |#1| / 6283\rfloor$ (the formula chosen always gives a
+%   non-negative integer).  The subtraction has a form similar to our
+%   usual multiplications (see \pkg{l3fp-basics} or
+%   \pkg{l3fp-extended}).  Once the exponent reaches $0$, we are done
+%   subtracting $2\pi$, and we call \cs{@@_trig_octant_loop:nw} to do
+%   the reduction by $\pi/2$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_trig_large:w #1; #2#3;
+  { \@@_trig_large_i:www #2; #3 ;  #1; }
+\cs_new:Npn \@@_trig_large_i:www #1; #2; #3;
+  {
+    \if_meaning:w 0 #3 \@@_trig_large_break:w \fi:
+    \exp_after:wN \@@_trig_large_ii:wnnnnnn
+    \int_use:N \__int_eval:w ( #1 - 3141 ) / 6283 ;
+    {#1} #2;
+    \int_use:N \__int_eval:w \c_minus_one + #3;
+  }
+\cs_new:Npn \@@_trig_large_ii:wnnnnnn #1; #2#3#4#5;
+  {
+    \exp_after:wN \@@_trig_large_i:www
+    \int_use:N \__int_eval:w -5 0000 + #20 - #1*62831
+      \exp_after:wN \@@_fixed_mul_pack:NNNNNw
+      \int_use:N \__int_eval:w 4 9995 0000 + #30 - #1*8530
+        \exp_after:wN \@@_fixed_mul_pack:NNNNNw
+        \int_use:N \__int_eval:w 4 9995 0000 + #40 - #1*7179
+          \exp_after:wN \@@_fixed_mul_pack:NNNNNw
+          \int_use:N \__int_eval:w 5 0000 0000 + #50 - #1*5880
+    \exp_after:wN ;
+    \exp_after:wN ;
+  }
+\cs_new:Npn \@@_trig_large_break:w \fi: #1; #2;
+  { \fi: \@@_trig_octant_loop:nw #2 {0000} {0000} ; }
+%    \end{macrocode}
+% \end{macro}
+%
+%^^A todo: optimize: we don't need 6x4 digits here, only 4x4.
+%
+% \begin{macro}[aux, rEXP]
+%   {
+%     \@@_trig_octant_loop:nw, \@@_trig_octant_break:w,
+%     \@@_trig_octant_neg:w
+%   }
+%   We receive a fixed point number as argument.  As long as it is
+%   greater than $1.5707$ (a slight underestimate of $\pi/2$), subtract
+%   $\pi/2$, and leave |+ \c_two| in the integer expression for the
+%   octant.  Once it becomes smaller, if it is greater than $0.7854$
+%   (overestimate of $\pi/4$), then compute $\pi/2 - x$ and increment
+%   the octant.  If it is negative, correct this by changing the sign
+%   and decrementing the octant (by adding $7$).  The result is in all
+%   cases in the range $[0, 0.7854]$, appropriate for a series
+%   expansion.
+%    \begin{macrocode}
+\cs_new:Npn \@@_trig_octant_loop:nw #1#2;
+  {
+    \if_int_compare:w #1 < 15707 \exp_stop_f:
+      \@@_trig_octant_break:w
+    \fi:
+    + \c_two
+    \@@_fixed_sub_back:wwN
+      {15707} {9632} {6794} {8970} {0000} {0000} ;
+      {#1} #2;
+    \@@_trig_octant_loop:nw
+  }
+\cs_new:Npn \@@_trig_octant_break:w #1 \fi: + #2#3 #4; #5#6; #7;
+  {
+    \fi:
+    \if_int_compare:w #5 < 7854 \exp_stop_f:
+      \if_int_compare:w #5 < \c_zero
+        \exp_after:wN \@@_trig_octant_neg:w
+      \fi:
+      \exp_after:wN \@@_use_i_until_s:nw
+      \exp_after:wN .
+    \fi:
+    + \c_one
+    \@@_fixed_sub:wwN
+    {15707} {9632} {6794} {8970} {0000} {0000} ;
+    {#5} #6 ; . ;
+  }
+\cs_new:Npn \@@_trig_octant_neg:w #1\fi: #2; #3#4#5#6#7#8; #9
+  {
+    \fi:
+    + \c_seven
+    \exp_after:wN \@@_fixed_add_after:NNNNNwN
+    \int_use:N \__int_eval:w 1 9999 9998 - #30000 - #4
+      \exp_after:wN \@@_fixed_add_pack:NNNNNwN
+      \int_use:N \__int_eval:w 1 9999 9998 - #5#6
+        \exp_after:wN \@@_fixed_add_pack:NNNNNwN
+        \int_use:N \__int_eval:w 2 0000 0000 - #7#8 ; {#9} ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Computing the power series}
+%
+% \begin{macro}[aux, EXP]{\@@_sin_series:NNwww, \@@_sin_series_aux:Nnww}
+%   Here we receive an unused |?|, a \meta{sign} ($0$ or $2$), a
+%   (non-negative) \meta{octant} delimited by a dot, a \meta{fixed
+%     point} number, and junk delimited by a semicolon.  The auxiliary
+%   receives:
+%   \begin{itemize}
+%   \item The final sign, which depends on the octant |#3| and the
+%     original sign |#2|,
+%   \item The octant |#3|, which will control the series we use.
+%   \item The square |#4 * #4| of the argument, computed with
+%     \cs{@@_fixed_mul:wwn}.
+%   \item The number itself.
+%   \end{itemize}
+%   If the octant is in $\{1,2,5,6,\ldots{}\}$, we are near an extremum
+%   of the function and we use the series
+%   \[
+%   \cos(x) = 1 - x^2 \bigg( \frac{1}{2!} - x^2 \bigg( \frac{1}{4!}
+%   - x^2 \bigg( \cdots \bigg) \bigg) \bigg) .
+%   \]
+%   Otherwise, the series
+%   \[
+%   \sin(x) = x \bigg( 1 - x^2 \bigg( \frac{1}{3!} - x^2 \bigg(
+%   \frac{1}{5!} - x^2 \bigg( \cdots \bigg) \bigg) \bigg) \bigg)
+%   \]
+%   is used.  Finally, the fixed point number is converted to a floating
+%   point number with the given sign, and we check for overflow or
+%   underflow. %^^A todo: can over/underflow really happen??
+%    \begin{macrocode}
+\cs_new:Npn \@@_sin_series:NNwww #1#2#3 . #4; #5;
+  {
+    \@@_fixed_mul:wwn #4; #4;
+    {
+      \exp_after:wN \@@_sin_series_aux:Nnww
+      \__int_value:w
+        \if_int_odd:w \__int_eval:w ( #3 + \c_two ) / \c_four \__int_eval_end:
+          #2
+        \else:
+          \if_meaning:w #2 0 2 \else: 0 \fi:
+        \fi:
+      {#3}
+    }
+    #4 ;
+  }
+\cs_new:Npn \@@_sin_series_aux:Nnww #1#2 #3; #4;
+  {
+    \if_int_odd:w \__int_eval:w #2 / \c_two \__int_eval_end:
+      \exp_after:wN \use_i:nn
+    \else:
+      \exp_after:wN \use_ii:nn
+    \fi:
+    {
+      \@@_fixed_continue:wn {0000}{0000}{0000}{0001}{5619}{2070}; % 1/18!
+      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0000}{0477}{9477}{3324};
+      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0011}{4707}{4559}{7730};
+      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0000}{2087}{6756}{9878}{6810};
+      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0027}{5573}{1922}{3985}{8907};
+      \@@_fixed_mul_sub_back:wwwn #3; {0000}{2480}{1587}{3015}{8730}{1587};
+      \@@_fixed_mul_sub_back:wwwn #3; {0013}{8888}{8888}{8888}{8888}{8889};
+      \@@_fixed_mul_sub_back:wwwn #3; {0416}{6666}{6666}{6666}{6666}{6667};
+      \@@_fixed_mul_sub_back:wwwn #3; {5000}{0000}{0000}{0000}{0000}{0000};
+      \@@_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
+    }
+    {
+      \@@_fixed_continue:wn {0000}{0000}{0000}{0028}{1145}{7254}; % 1/17!
+      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0000}{7647}{1637}{3182};
+      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0160}{5904}{3836}{8216};
+      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0002}{5052}{1083}{8544}{1719};
+      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0275}{5731}{9223}{9858}{9065};
+      \@@_fixed_mul_sub_back:wwwn #3; {0001}{9841}{2698}{4126}{9841}{2698};
+      \@@_fixed_mul_sub_back:wwwn #3; {0083}{3333}{3333}{3333}{3333}{3333};
+      \@@_fixed_mul_sub_back:wwwn #3; {1666}{6666}{6666}{6666}{6666}{6667};
+      \@@_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
+      \@@_fixed_mul:wwn #4;
+    }
+    {
+      \exp_after:wN \@@_sanitize:Nw
+      \exp_after:wN #1
+      \int_use:N \__int_eval:w \@@_fixed_to_float:wN
+    }
+    #1
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_tan_series:NNwww, \@@_tan_series_aux:Nnww}
+%   Similar to \cs{@@_sin_series:NNwww}, but with slightly different
+%   rules to find the sign.  The result is expressed as a ratio of
+%   polynomials, of the form
+%   \[
+%   \tan(x) \simeq
+%   \frac{x (1 - x^2 (a_1 - x^2 (a_2 - x^2 (a_3 - x^2 (a_4 - x^2 a_5)))))}
+%     {1 - x^2 (b_1 - x^2 (b_2 - x^2 (b_3 - x^2 (b_4 - x^2 b_5))))} .
+%   \]
+%   The ratio of the two fixed point numbers is converted to a floating
+%   point number directly to avoid rounding issues.  The two fixed
+%   points may be exchanged before computing the ratio, depending on the
+%   quadrant.
+%    \begin{macrocode}
+\cs_new:Npn \@@_tan_series:NNwww #1#2#3. #4; #5;
+  {
+    \@@_fixed_mul:wwn #4; #4;
+    {
+      \exp_after:wN \@@_tan_series_aux:Nnww
+      \__int_value:w
+        \if_int_odd:w \__int_eval:w #3 / \c_two \__int_eval_end:
+          \exp_after:wN \reverse_if:N
+        \fi:
+        \if_meaning:w #1#2 2 \else: 0 \fi:
+      {#3}
+    }
+    #4 ;
+  }
+\cs_new:Npn \@@_tan_series_aux:Nnww #1 #2 #3; #4;
+  {
+    \@@_fixed_continue:wn {0000}{0000}{1527}{3493}{0856}{7059};
+    \@@_fixed_mul_sub_back:wwwn #3; {0000}{0159}{6080}{0274}{5257}{6472};
+    \@@_fixed_mul_sub_back:wwwn #3; {0002}{4571}{2320}{0157}{2558}{8481};
+    \@@_fixed_mul_sub_back:wwwn #3; {0115}{5830}{7533}{5397}{3168}{2147};
+    \@@_fixed_mul_sub_back:wwwn #3; {1929}{8245}{6140}{3508}{7719}{2982};
+    \@@_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
+    \@@_fixed_mul:wwn #4;
+      {
+        \@@_fixed_continue:wn {0000}{0007}{0258}{0681}{9408}{4706};
+        \@@_fixed_mul_sub_back:wwwn #3; {0000}{2343}{7175}{1399}{6151}{7670};
+        \@@_fixed_mul_sub_back:wwwn #3; {0019}{2638}{4588}{9232}{8861}{3691};
+        \@@_fixed_mul_sub_back:wwwn #3; {0536}{6357}{0691}{4344}{6852}{4252};
+        \@@_fixed_mul_sub_back:wwwn #3; {5263}{1578}{9473}{6842}{1052}{6315};
+        \@@_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
+          {
+            \exp_after:wN \@@_sanitize:Nw
+            \exp_after:wN #1
+            \int_use:N \__int_eval:w
+              \reverse_if:N \if_int_odd:w
+                  \__int_eval:w (#2 - \c_one) / \c_two \__int_eval_end:
+                \exp_after:wN \@@_reverse_args:Nww
+              \fi:
+              \@@_fixed_div_to_float:ww
+          }
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintChanges
+%
+% \PrintIndex 
\ No newline at end of file
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp.dtx
index 64a6b39252f..68f71f540cc 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp.dtx
@@ -1,6 +1,6 @@
 % \iffalse meta-comment
 %
-%% File: l3fp.dtx Copyright (C) 2010-2012 The LaTeX3 Project
+%% File: l3fp.dtx Copyright (C) 2011-2012 The LaTeX3 Project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -29,27 +29,31 @@
 %%   Snapshots taken from the repository represent work in progress and may
 %%   not work or may contain conflicting material!  We therefore ask
 %%   people _not_ to put them into distributions, archives, etc. without
-%%   prior consultation with the LaTeX3 Project.
+%%   prior consultation with the LaTeX3 Project Team.
 %%
 %% -----------------------------------------------------------------------
+%%
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3fp.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental floating-point operations}
+\GetIdInfo$Id: l3fp.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Floating points}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
+\usepackage{amsmath}
+\providecommand\nan{\texttt{NaN}}
 \begin{document}
   \DocInput{\jobname.dtx}
 \end{document}
 %</driver>
 % \fi
 %
+%
 % \title{^^A
-%   The \pkg{l3fp} package\\ Floating-point operations^^A
+%   The \textsf{l3fp} package: floating points^^A
 %   \thanks{This file describes v\ExplFileVersion,
-%      last revised \ExplFileDate.}^^A
+%     last revised \ExplFileDate.}^^A
 % }
 %
 % \author{^^A
@@ -67,5497 +71,868 @@
 %
 % \begin{documentation}
 %
-% A floating point number is one which is stored as a mantissa and
-% a separate exponent. This module implements arithmetic using radix
-% $10$ floating point numbers. This means that the mantissa should
-% be a real number in the range $1 \le \expandafter\mathopen\string|
-% x \expandafter\mathclose\string| < 10$, with the
-% exponent given as an integer between $-99$ and $99$. In the
-% input, the exponent part is represented starting with an \texttt{e}.
-% As this is a low-level module, error-checking is minimal. Numbers
-% which are too large for the floating point unit to handle will result
-% in errors, either from \TeX{} or from \LaTeX{}. The \LaTeX{} code does not
-% check that the input will not overflow, hence the possibility of a
-% \TeX{} error. On the other hand, numbers which are too small will be
-% dropped, which will mean that extra decimal digits will simply be
-% lost.
-%
-% When parsing numbers, any missing parts will be interpreted as
-% zero. So for example
-%\begin{verbatim}
-%  \fp_set:Nn \l_my_fp { }
-%  \fp_set:Nn \l_my_fp { . }
-%  \fp_set:Nn \l_my_fp { - }
+% A floating point number is one which is stored as a mantissa and a
+% separate exponent.  The module implements expandably a wide set of
+% arithmetic, trigonometric, and other operations on floating point
+% numbers, to be used within floating point expressions.  Floating point
+% expressions support the following operations with their usual
+% precedence.
+% \begin{itemize}
+%   \item Basic arithmetic: addition $x+y$, subtraction $x-y$,
+%     multiplication $x*y$, division $x/y$, and parentheses.
+%   \item Trigonometry: $\sin x$, $\cos x$, $\tan x$, $\cot x$.
+%   \item Exponentials: $\exp x$, $\ln x$, $x^y$.
+%   \item Comparison operators: $x<y$, $x<=y$, $x>?y$, $x!=y$ \emph{etc.}
+%   \item Boolean logic: negation $!x$, conjunction $\&\&$, disjunction
+%     $\vert\vert$, ternary operator $x?y:z$.
+%   \item [\emph{not yet}] Inverse trigonometric functions:
+%     $\operatorname{asin} x$, $\operatorname{acos} x$,
+%     $\operatorname{atan} x$, $\operatorname{acot} x$.
+%   \item [\emph{not yet}] Hyperbolic functions and their inverse
+%     functions: $\sinh x$, $\cosh x$, $\tanh x$, $\coth x$, and
+%     $\operatorname{asinh} x$, $\operatorname{acosh} x$,
+%     $\operatorname{atanh} x$, $\operatorname{acoth} x$.
+%   \item Extrema: $\max(x,y,\ldots)$, $\min(x,y,\ldots)$,
+%     $\operatorname{abs}(x)$.
+%   \item Rounding functions: $\operatorname{round}(x,n)$ round to
+%     closest, $\operatorname{round} 0(x,n)$ round towards zero,
+%     $\operatorname{round}\pm(x,n)$ round towards $\pm\infty$.  And
+%     (\emph{not yet}) modulo, and \enquote{quantize}.
+%   \item Constants: \texttt{pi}, \texttt{deg} (one degree in radians).
+%   \item Dimensions, automatically expressed in points, \emph{e.g.},
+%     \texttt{pc} is $12$.
+%   \item Automatic conversion (no need for \cs{\meta{type}_use:N}) of
+%     integer, dimension, and skip variables to floating points,
+%     expressing dimensions in points and ignoring the stretch and
+%     shrink components of skips.
+% \end{itemize}
+% Floating point numbers can be given either explicitly (in a form such
+% as |1.234e-34|, or |-.0001|), or as a stored floating point variable,
+% which is automatically replaced by its current value.  See
+% section~\ref{sec:fp-floats} for a description of what a floating point is,
+% section~\ref{sec:fp-precedence} for details about how an expression is
+% parsed, and section~\ref{sec:fp-operations} to know what the various
+% operations do.  Some operations may raise exceptions (error messages),
+% described in section~\ref{sec:fp-exceptions}.
+%
+% An example of use could be the following.
+% \begin{verbatim}
+%   \LaTeX{} can now compute: $ \frac{\sin (3.5)}{2} + 2\cdot 10^{-3}
+%   = \ExplSyntaxOn \fp_to_decimal:n {sin 3.5 /2 + 2e-3} $.
+% \end{verbatim}
+% But in all fairness, this module is mostly meant as an underlying tool
+% for higher-level commands.  For example, one could provide a function
+% to typeset nicely the result of floating point computations.
+% \begin{verbatim}
+%   \usepackage{xparse, siunitx}
+%   \ExplSyntaxOn
+%   \NewDocumentCommand { \calcnum } { m }
+%     { \num { \fp_to_scientific:n {#1} } }
+%   \ExplSyntaxOff
+%   \calcnum { 2 pi * sin ( 2.3 ^ 5 ) }
 % \end{verbatim}
-% will all be interpreted as zero values without raising an error.
-%
-% Operations which give an undefined result (such as division by
-% $0$) will not lead to errors. Instead special marker values are
-% returned, which can be tested for using for example
-% \cs{fp_if_undefined:N(TF)}. In this way it is possible to work with
-% asymptotic functions without first checking the input. If these
-% special values are carried forward in calculations they will be
-% treated as $0$.
-%
-% Floating point numbers are stored in the \texttt{fp} floating point
-% variable type. This has a standard range of functions for
-% variable management.
-%
-% \section{Floating-point variables}
 %
-% \begin{function}{\fp_new:N, \fp_new:c}
-%   \begin{syntax}
-%     \cs{fp_new:N} \meta{floating point variable}
-%   \end{syntax}
-%   Creates a new \meta{floating point variable} or raises an error if
-%   the name is already taken. The declaration is global. The
-%   \meta{floating point} will initially be set to  |+0.000000000e0|
-%   (the zero floating point).
-% \end{function}
+% \section{Creating and initialising floating point variables}
 %
-% \begin{function}{\fp_const:Nn, \fp_const:cn}
+% \begin{function}[updated = 2012-05-08]{\fp_new:N, \fp_new:c}
 %   \begin{syntax}
-%     \cs{fp_const:Nn} \meta{floating point variable} \Arg{value}
+%     \cs{fp_new:N} \meta{fp~var}
 %   \end{syntax}
-%   Creates a new constant \meta{floating point variable} or raises an
-%   error  if the name is already taken. The value of the
-%   \meta{floating point variable} will be set globally to the
-%   \meta{value}.
+%   Creates a new \meta{fp~var} or raises an error if the name is
+%   already taken. The declaration is global. The \meta{fp~var} will
+%   initially be $+0$.
 % \end{function}
 %
-% \begin{function}
-%   {
-%     \fp_set_eq:NN,  \fp_set_eq:cN,  \fp_set_eq:Nc,  \fp_set_eq:cc,
-%     \fp_gset_eq:NN, \fp_gset_eq:cN, \fp_gset_eq:Nc, \fp_gset_eq:cc
-%   }
+% \begin{function}[updated = 2012-05-08]{\fp_const:Nn, \fp_const:cn}
 %   \begin{syntax}
-%     \cs{fp_set_eq:NN} \meta{fp var1} \meta{fp var2}
+%     \cs{fp_const:Nn} \meta{fp~var} \Arg{floating point expression}
 %   \end{syntax}
-%   Sets the value of \meta{floating point variable1} equal to that of
-%   \meta{floating point variable2}.
+%   Creates a new constant \meta{fp~var} or raises an error if the name
+%   is already taken. The \meta{fp~var} will be set globally equal to
+%   the result of evaluating the \meta{floating point expression}.
 % \end{function}
 %
-% \begin{function}{\fp_zero:N, \fp_zero:c, \fp_gzero:N, \fp_gzero:c}
+% \begin{function}[updated = 2012-05-08]
+%   {\fp_zero:N, \fp_zero:c, \fp_gzero:N, \fp_gzero:c}
 %   \begin{syntax}
-%     \cs{fp_zero:N} \meta{floating point variable}
+%     \cs{fp_zero:N} \meta{fp~var}
 %   \end{syntax}
-%   Sets the \meta{floating point variable} to |+0.000000000e0|.
+%   Sets the \meta{fp~var} to~$+0$.
 % \end{function}
 %
-% \begin{function}[added = 2012-01-07]
+% \begin{function}[updated = 2012-05-08]
 %   {\fp_zero_new:N, \fp_zero_new:c, \fp_gzero_new:N, \fp_gzero_new:c}
 %   \begin{syntax}
-%     \cs{fp_zero_new:N} \meta{floating point variable}
+%     \cs{fp_zero_new:N} \meta{fp~var}
 %   \end{syntax}
-%   Ensures that the \meta{floating point variable} exists globally
+%   Ensures that the \meta{fp~var} exists globally
 %   by applying \cs{fp_new:N} if necessary, then applies
-%   \cs{fp_(g)zero:N} to leave the \meta{floating point variable}
-%   set to zero.
+%   \cs{fp_(g)zero:N} to leave the \meta{fp~var} set to zero.
 % \end{function}
 %
-% \begin{function}{\fp_set:Nn, \fp_set:cn, \fp_gset:Nn, \fp_gset:cn}
+% \section{Setting floating point variables}
+%
+% \begin{function}[updated = 2012-05-08]
+%   {\fp_set:Nn, \fp_set:cn, \fp_gset:Nn, \fp_gset:cn}
 %   \begin{syntax}
-%     \cs{fp_set:Nn} \meta{floating point variable} \Arg{value}
+%     \cs{fp_set:Nn} \meta{fp~var} \Arg{floating point expression}
 %   \end{syntax}
-%   Sets the \meta{floating point variable} variable to \meta{value}.
+%   Sets \meta{fp~var} equal to the result of computing the
+%   \meta{floating point expression}.
 % \end{function}
 %
-% \begin{function}
+% \begin{function}[updated = 2012-05-08]
 %   {
-%     \fp_set_from_dim:Nn,  \fp_set_from_dim:cn,
-%     \fp_gset_from_dim:Nn, \fp_gset_from_dim:cn
+%     \fp_set_eq:NN , \fp_set_eq:cN , \fp_set_eq:Nc , \fp_set_eq:cc ,
+%     \fp_gset_eq:NN, \fp_gset_eq:cN, \fp_gset_eq:Nc, \fp_gset_eq:cc
 %   }
 %   \begin{syntax}
-%     \cs{fp_set_from_dim:Nn} \meta{floating point variable} \Arg{dimexpr}
+%     \cs{fp_set_eq:NN} \meta{fp~var_1} \meta{fp~var_2}
 %   \end{syntax}
-%   Sets the \meta{floating point variable} to the distance represented
-%   by the \meta{dimension expression} in the units points. This means
-%   that distances given in other units are first converted to points
-%   before being assigned to the \meta{floating point variable}.
+%   Sets the floating point variable \meta{fp~var_1} equal to the current
+%   value of \meta{fp~var_2}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\fp_use:N, \fp_use:c}
+% \begin{function}[updated = 2012-05-08]
+%   {\fp_add:Nn, \fp_add:cn, \fp_gadd:Nn, \fp_gadd:cn}
 %   \begin{syntax}
-%     \cs{fp_use:N} \meta{floating point variable}
+%     \cs{fp_add:Nn} \meta{fp~var} \Arg{floating point expression}
 %   \end{syntax}
-%   Inserts the value of the \meta{floating point variable} into the
-%   input stream. The value will be given as a real number without any
-%   exponent part, and will always include a decimal point. For example,
-%   \begin{verbatim}
-%     \fp_new:Nn \test
-%     \fp_set:Nn \test { 1.234 e 5 }
-%     \fp_use:N \test
-%   \end{verbatim}
-%   will insert |12345.00000| into the input stream.
-%   As illustrated, a floating point will always be inserted with ten
-%   significant digits given. Very large and very small values will
-%   include additional zeros for place value.
+%   Adds the result of computing the \meta{floating point expression} to
+%   the \meta{fp~var}.
 % \end{function}
 %
-% \begin{function}{\fp_show:N, \fp_show:c}
+% \begin{function}[updated = 2012-05-08]
+%   {\fp_sub:Nn, \fp_sub:cn, \fp_gsub:Nn, \fp_gsub:cn}
 %   \begin{syntax}
-%     \cs{fp_show:N} \meta{floating point variable}
+%     \cs{fp_sub:Nn} \meta{fp~var} \Arg{floating point expression}
 %   \end{syntax}
-%   Displays the content of the \meta{floating point variable} on the
-%   terminal.
+%   Subtracts the result of computing the \meta{floating point
+%     expression} from the \meta{fp~var}.
 % \end{function}
 %
-% \begin{function}[EXP, pTF, added=2012-03-03]{\fp_if_exist:N, \fp_if_exist:c}
+% \section{Using floating point numbers}
+%
+% \begin{function}[EXP, added = 2012-05-08, updated = 2012-07-08]{\fp_eval:n}
 %   \begin{syntax}
-%     \cs{fp_if_exist_p:N} \meta{fp~var}
-%     \cs{fp_if_exist:NTF} \meta{fp~var} \Arg{true code} \Arg{false code}
+%     \cs{fp_eval:n} \Arg{floating point expression}
 %   \end{syntax}
-%   Tests whether the \meta{fp~var} is currently defined.  This does not
-%   check that the \meta{fp~var} really is a floating point variable.
+%   Evaluates the \meta{floating point expression} and expresses the
+%   result as a decimal number with~$16$ significant figures and no
+%   exponent.  Leading or trailing zeros may be inserted to compensate
+%   for the exponent.  Non-significant trailing zeros are trimmed, and
+%   integers are expressed without a decimal separator.  The values
+%   $\pm\infty$ and \texttt{nan} trigger an \enquote{invalid operation}
+%   exception.  This function is identical to \cs{fp_to_decimal:n}.
 % \end{function}
 %
-% \section{Conversion of floating point values to other formats}
-%
-% It is useful to be able to convert floating point variables to
-% other forms. These functions are expandable, so that the material
-% can be used in a variety of contexts. The \cs{fp_use:N} function
-% should also be consulted in this context, as it will insert the
-% value of the floating point variable as a real number.
-%
-% \begin{function}[rEXP]{\fp_to_dim:N, \fp_to_dim:c}
+% \begin{function}[EXP, added = 2012-05-08, updated = 2012-07-08]
+%   {\fp_to_decimal:N, \fp_to_decimal:c, \fp_to_decimal:n}
 %   \begin{syntax}
-%     \cs{fp_to_dim:N} \meta{floating point variable}
+%     \cs{fp_to_decimal:N} \meta{fp~var}
+%     \cs{fp_to_decimal:n} \Arg{floating point expression}
 %   \end{syntax}
-%   Inserts the value of the \meta{floating point variable}
-%   into the input stream converted into a dimension in points.
+%   Evaluates the \meta{floating point expression} and expresses the
+%   result as a decimal number with $16$ significant figures and no
+%   exponent.  Leading or trailing zeros may be inserted to compensate
+%   for the exponent.  Non-significant trailing zeros are trimmed, and
+%   integers are expressed without a decimal separator.  The values
+%   $\pm\infty$ and \texttt{nan} trigger an \enquote{invalid operation}
+%   exception.
 % \end{function}
 %
-% \begin{function}[rEXP]{\fp_to_int:N, \fp_to_int:c}
+% \begin{function}[EXP, updated = 2012-07-08]
+%   {\fp_to_dim:N, \fp_to_dim:c, \fp_to_dim:n}
 %   \begin{syntax}
-%     \cs{fp_to_int:N} \meta{floating point variable}
+%     \cs{fp_to_dim:N} \meta{fp~var}
+%     \cs{fp_to_dim:n} \Arg{floating point expression}
 %   \end{syntax}
-%   Inserts the integer value of the \meta{floating point variable}
-%   into the input stream. The decimal part of the number will not be
-%   included, but will be used to round the integer.
+%   Evaluates the \meta{floating point expression} and expresses the
+%   result as a dimension (in \texttt{pt}) suitable for use in dimension
+%   expressions.  The output is identical to \cs{fp_to_decimal:n}, with
+%   an additional trailing \texttt{pt}.  In particular, floating point
+%   numbers outside the range $[- 2^{14} + 2^{-17}, 2^{14} - 2^{-17}]$
+%   overflow \TeX{}'s maximum dimension.  The values $\pm\infty$ and
+%   \texttt{nan} trigger an \enquote{invalid operation} exception.
 % \end{function}
 %
-% \begin{function}[rEXP]{\fp_to_tl:N, \fp_to_tl:c}
+% \begin{function}[EXP, updated = 2012-07-08]
+%   {\fp_to_int:N, \fp_to_int:c, \fp_to_int:n}
 %   \begin{syntax}
-%     \cs{fp_to_tl:N} \meta{floating point variable}
+%     \cs{fp_to_int:N} \meta{fp~var}
+%     \cs{fp_to_int:n} \Arg{floating point expression}
 %   \end{syntax}
-%   Inserts a representation of the \meta{floating point variable} into
-%   the input stream as a token list. The representation follows the
-%   conventions of a pocket calculator:
-%   \begin{center}
-%     \ttfamily
-%     \begin{tabular}{r@{.}lr@{.}l}
-%       \toprule
-%         \multicolumn{2}{l}{\rmfamily{Floating point value}} &
-%         \multicolumn{2}{l}{\rmfamily{Representation}} \\
-%       \midrule
-%          1 & 234000000000e0  &  1 & 234    \\
-%         -1 & 234000000000e0  & -1 & 234    \\
-%          1 & 234000000000e3  &  \multicolumn{2}{l}{1234} \\
-%          1 & 234000000000e13 &  \multicolumn{2}{l}{1234e13} \\
-%          1 & 234000000000e-1 & 0 & 1234   \\
-%          1 & 234000000000e-2 & 0 & 01234  \\
-%          1 & 234000000000e-3 & 1 & 234e-3 \\
-%       \bottomrule
-%     \end{tabular}
-%   \end{center}
-%   Notice that trailing zeros are removed in this process, and that
-%   numbers which do not require a decimal part do \emph{not} include
-%   a decimal marker.
+%   Evaluates the \meta{floating point expression}, and rounds the
+%   result to the closest integer, with ties rounded to an even integer.
+%   The result may be outside the range $[- 2^{31} + 1, 2^{31} - 1]$ of
+%   valid \TeX{} integers, triggering \TeX{} errors if used in an
+%   integer expression.  The values $\pm\infty$ and \texttt{nan} trigger
+%   an \enquote{invalid operation} exception.
 % \end{function}
 %
-% \section{Rounding floating point values}
-%
-% The module can round floating point values to either decimal places
-% or significant figures using the usual method in which exact halves
-% are rounded up.
+% \begin{function}[EXP, added = 2012-05-08, updated = 2012-07-08]
+%   {\fp_to_scientific:N, \fp_to_scientific:c, \fp_to_scientific:n}
+%   \begin{syntax}
+%     \cs{fp_to_scientific:N} \meta{fp~var}
+%     \cs{fp_to_scientific:n} \Arg{floating point expression}
+%   \end{syntax}
+%   Evaluates the \meta{floating point expression} and expresses the
+%   result in scientific notation with $16$ significant figures:
+%   \begin{quote}
+%     \meta{optional \texttt{-}}\meta{digit}\texttt{.}\meta{15 digits}\texttt{e}\meta{optional sign}\meta{exponent}
+%   \end{quote}
+%   The leading \meta{digit} is non-zero except in the case of $\pm 0$.
+%   The values $\pm\infty$ and \texttt{nan} trigger an \enquote{invalid
+%     operation} exception.
+% \end{function}
 %
-% \begin{function}
-%   {
-%     \fp_round_figures:Nn,  \fp_round_figures:cn,
-%     \fp_ground_figures:Nn, \fp_ground_figures:cn
-%   }
+% \begin{function}[EXP, updated = 2012-07-08]
+%   {\fp_to_tl:N, \fp_to_tl:c, \fp_to_tl:n}
 %   \begin{syntax}
-%     \cs{fp_round_figures:Nn} \meta{floating point variable} \Arg{target}
+%     \cs{fp_to_tl:N} \meta{fp~var}
+%     \cs{fp_to_tl:n} \Arg{floating point expression}
 %   \end{syntax}
-%   Rounds the \meta{floating point variable} to the \meta{target} number
-%   of significant figures (an integer expression).
+%   Evaluates the \meta{floating point expression} and expresses the
+%   result in (almost) the shortest possible form.  Numbers greater or
+%   equal to $10^{16}$, or less than $10^{-3}$ are expressed in
+%   scientific notation with trailing zeros trimmed (see
+%   \cs{fp_to_scientific:n}).  Numbers in the range $[10^{-3},10^{16})$
+%   are expressed in a decimal notation without exponent, with trailing
+%   zeros trimmed, and no decimal separator for integer values (see
+%   \cs{fp_to_decimal:n}.  The special values $\pm 0$, $\pm \inf$ and
+%   \texttt{nan} are rendered as |0|, |-0|, \texttt{inf}, \texttt{-inf},
+%   and \texttt{nan} respectively.
 % \end{function}
 %
-% \begin{function}
-%   {
-%     \fp_round_places:Nn,  \fp_round_places:cn,
-%     \fp_ground_places:Nn, \fp_ground_places:cn
-%   }
+% \begin{function}[EXP, updated = 2012-07-08]{\fp_use:N, \fp_use:c}
 %   \begin{syntax}
-%     \cs{fp_round_places:Nn} \meta{floating point variable} \Arg{target}
+%     \cs{fp_use:N} \meta{fp~var}
 %   \end{syntax}
-%   Rounds the \meta{floating point variable} to the \meta{target} number
-%   of decimal places (an integer expression).
+%   Inserts the value of the \meta{fp~var} into the input stream as a
+%   decimal number with $16$ significant figures and no exponent.
+%   Leading or trailing zeros may be inserted to compensate for the
+%   exponent.  Non-significant trailing zeros are trimmed.  Integers are
+%   expressed without a decimal separator.  The values $\pm\infty$ and
+%   \texttt{nan} trigger an \enquote{invalid operation} exception.  This
+%   function is identical to \cs{fp_to_decimal:N}.
 % \end{function}
 %
-% \section{Floating-point conditionals}
+% \section{Floating point conditionals}
 %
-% \begin{function}[EXP,pTF]{\fp_if_undefined:N}
+% \begin{function}[EXP, pTF, updated = 2012-05-08]
+%   {\fp_if_exist:N, \fp_if_exist:c}
 %   \begin{syntax}
-%     \cs{fp_if_undefined_p:N} \meta{fixed-point} \\
-%     \cs{fp_if_undefined:NTF} \meta{fixed-point} \Arg{true code} \Arg{false code}
+%     \cs{fp_if_exist_p:N} \meta{fp~var}
+%     \cs{fp_if_exist:NTF} \meta{fp~var} \Arg{true code} \Arg{false code}
 %   \end{syntax}
-%   Tests if \meta{floating point} is undefined (\emph{i.e.}~equal to the
-%   special \cs{c_undefined_fp} variable).
+%   Tests whether the \meta{fp~var} is currently defined.  This does not
+%   check that the \meta{fp~var} really is a floating point variable.
 % \end{function}
 %
-% \begin{function}[EXP,pTF]{\fp_if_zero:N}
+% \begin{function}[EXP, pTF, updated = 2012-05-08]
+%   {\fp_compare:nNn, \fp_compare:n}
 %   \begin{syntax}
-%     \cs{fp_if_zero_p:N} \meta{fixed-point}
-%     \cs{fp_if_zero:NTF} \meta{fixed-point} \Arg{true code} \Arg{false code}
+%     \cs{fp_compare_p:nNn} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2}
+%     \cs{fp_compare:nNnTF} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2} \Arg{true code} \Arg{false code}
+%     \cs{fp_compare_p:n} \{ \meta{fpexpr_1} \meta{relation} \meta{fpexpr_2} \}
+%     \cs{fp_compare:nTF} \{ \meta{fpexpr_1} \meta{relation} \meta{fpexpr_2} \} \Arg{true code} \Arg{false code}
 %   \end{syntax}
-%   Tests if \meta{floating point} is equal to zero (\emph{i.e.}~equal to
-%   the special \cs{c_zero_fp} variable).
+%   Compares the \meta{fpexpr_1} and the \meta{fpexpr_2}, and returns
+%   \texttt{true} if the \meta{relation} is obeyed.  Two floating point
+%   numbers $x$ and $y$ may obey four mutually exclusive relations:
+%   $x<y$, $x=y$, $x>y$, or $x$ and $y$ are not ordered.  The latter
+%   case occurs exactly when one of the operands is \texttt{nan}, and
+%   this relations is denoted by the symbol |?|.  The \texttt{nNn}
+%   functions support the \meta{relations} |<|, |=|, |>|, and |?|.  The
+%   \texttt{n} functions support as a \meta{relation} any combination of
+%   those four symbols, plus an optional leading |!| (which negates the
+%   \meta{relation}), with the restriction that the \meta{relation} may
+%   not start with |?|.  Common choices of \meta{relation} include |>=|
+%   (greater or equal), |!=| (not equal), |!?| (comparable).  Note that
+%   a \texttt{nan} is distinct from any value, even another
+%   \texttt{nan}, hence $x=x$ is not true for a \texttt{nan}. Thus to
+%   test if a value is \texttt{nan}, use
+%   \begin{verbatim}
+%     \fp_compare:nNnTF { <value> } != { <value> }
+%       { } % <value> is nan
+%       { } % <value> is not nan
+%   \end{verbatim}
 % \end{function}
 %
-% \begin{function}[TF]{\fp_compare:nNn}
+% \section{Some useful constants, and scratch variables}
+%
+% \begin{variable}[added = 2012-05-08]{\c_zero_fp, \c_minus_zero_fp}
+%   Zero, with either sign.
+% \end{variable}
+%
+% \begin{variable}[added = 2012-05-08]{\c_inf_fp, \c_minus_inf_fp}
+%   Infinity, with either sign.  These can be input directly in a
+%   floating point expression as \texttt{inf} and \texttt{-inf}.
+% \end{variable}
+%
+% \begin{variable}[updated = 2012-05-08]{\c_e_fp}
+%   The value of the base of the natural logarithm, $\mathrm{e} = \exp(1)$.
+% \end{variable}
+%
+% \begin{variable}[updated = 2012-05-08]{\c_pi_fp}
+%   The value of $\pi$.  This can be input directly in a floating point
+%   expression as \texttt{pi}.  The value is rounded in a slightly odd
+%   way, to ensure for instance that \texttt{sin(pi)} yields an exact $0$.
+% \end{variable}
+%
+% \begin{variable}[added = 2012-05-08]{\c_one_degree_fp}
+%   The value of $1^{\circ}$ in radians.  Multiply an angle given in
+%   degrees by this value to obtain a result in radians, suitable to be
+%   used for trigonometric functions.  Within floating point
+%   expressions, this can be accessed by \texttt{deg}.
+% \end{variable}
+%
+% \begin{variable}{\l_tmpa_fp, \l_tmpb_fp}
+%   Scratch floating points for local assignment. These are never used by
+%   the kernel code, and so are safe for use with any \LaTeX3-defined
+%   function. However, they may be overwritten by other non-kernel
+%   code and so should only be used for short-term storage.
+% \end{variable}
+%
+% \begin{variable}{\g_tmpa_fp, \g_tmpb_fp}
+%   Scratch floating points for global assignment. These are never used by
+%   the kernel code, and so are safe for use with any \LaTeX3-defined
+%   function. However, they may be overwritten by other non-kernel
+%   code and so should only be used for short-term storage.
+% \end{variable}
+%
+% \section{Floating point exceptions}
+% \label{sec:fp-exceptions}
+%^^A todo: redoc
+%
+% \enquote{Exceptions} may occur when performing some floating point
+% operations, such as \texttt{0 / 0}, or \texttt{10 ** 1e9999}.  The
+% \textsc{IEEE} standard defines $5$ types of exceptions.
+% \begin{itemize}
+% \item \emph{Overflow} occurs whenever the result of an operation is
+%   too large to be represented as a normal floating point number.  This
+%   results in $\pm \infty$.
+% \item \emph{Underflow} occurs whenever the result of an operation is
+%   too close to $0$ to be represented as a normal floating point
+%   number.  This results in $\pm 0$.
+% \item \emph{Invalid operation} occurs for operations with no defined
+%   outcome, for instance $0/0$, or $\sin(\infty)$, and almost any
+%   operation involving a \nan{}.  This results in a \nan{}.
+% \item \emph{Division by zero} occurs when dividing a non-zero number
+%   by $0$, or when evaluating \emph{e.g.}, $\ln(0)$ or $\cot(0)$.  This
+%   results in $\pm\infty$.
+% \item \emph{Inexact} occurs whenever the result of a computation is
+%   not exact, in other words, almost always.  This exception is
+%   entirely ignored in \LaTeX3.
+% \end{itemize}
+% To each exception is associated a \enquote{flag}, which can be either
+% \emph{on} or \emph{off}.  By default, when an exception occurs, the
+% corresponding flag is turned on.  The state of the flag can be tested
+% and modified.  The behaviour when an exception occurs can be modified
+% (using \cs{fp_trap:nn}) to either produce an error and turn the flag
+% on, or only turn the flag on, or do nothing at all.
+%
+% \begin{function}[EXP, pTF, added = 2012-05-28]{\fp_if_flag_on:n}
 %   \begin{syntax}
-%     \cs{fp_compare:nNnTF}
-%     ~~\Arg{floating point1} \meta{relation} \Arg{floating point2}
-%     ~~\Arg{true code} \Arg{false code}
+%     \cs{fp_if_flag_on_p:n} \Arg{exception}
+%     \cs{fp_if_flag_on:nTF} \Arg{exception} \Arg{true code} \Arg{false code}
 %   \end{syntax}
-%   This function compared the two \meta{floating point} values, which
-%   may be stored as \texttt{fp} variables, using the \meta{relation}:
-%   \begin{center}
-%     \begin{tabular}{ll}
-%       Equal                 & |=| \\
-%       Greater than          & |>| \\
-%       Less than             & |<| \\
-%     \end{tabular}
-%   \end{center}
-%   The tests treat undefined floating points as
-%   zero as the comparison is intended for real numbers only.
+%   Tests if the flag for the \meta{exception} is on, which normally
+%   means the given \meta{exception} has occurred.
 % \end{function}
 %
-% \begin{function}[TF]{\fp_compare:n}
+% \begin{function}[added = 2012-05-28]{\fp_flag_off:n}
 %   \begin{syntax}
-%     \cs{fp_compare:nTF}
-%     ~~\{ \meta{floating point1} \meta{relation} \meta{floating point2} \}
-%     ~~\Arg{true code} \Arg{false code}
+%     \cs{fp_flag_off:n} \Arg{exception}
 %   \end{syntax}
-%   This function compared the two \meta{floating point} values, which
-%   may be stored as \texttt{fp} variables, using the \meta{relation}:
-%   \begin{center}
-%     \begin{tabular}{ll}
-%       Equal                 & |=| or |==| \\
-%       Greater than          & |>|  \\
-%       Greater than or equal & |>=| \\
-%       Less than             & |<|  \\
-%       Less than or equal    & |<=| \\
-%       Not equal             & |!=| \\
-%     \end{tabular}
-%   \end{center}
-%   The tests treat undefined floating points as
-%   zero as the comparison is intended for real numbers only.
+%   Locally turns off the flag which indicates whether the
+%   \meta{exception} has occurred.
 % \end{function}
 %
-% \section{Unary floating-point operations}
-%
-% The unary operations alter the value stored within an \texttt{fp}
-% variable.
+% \begin{function}[EXP, added = 2012-05-28]{\fp_flag_on:n}
+%   \begin{syntax}
+%     \cs{fp_flag_on:n} \Arg{exception}
+%   \end{syntax}
+%   Locally turns on the flag to indicate (or pretend) that the
+%   \meta{exception} has occurred.  Note that this function is
+%   expandable: it is used internally by \pkg{l3fp} to signal when
+%   exceptions do occur.
+% \end{function}
 %
-% \begin{function}{\fp_abs:N, \fp_abs:c, \fp_gabs:N, \fp_gabs:c}
+% \begin{function}[added = 2012-05-28]{\fp_trap:nn}
 %   \begin{syntax}
-%     \cs{fp_abs:N} \meta{floating point variable}
+%     \cs{fp_trap:nn} \Arg{exception} \Arg{trap type}
 %   \end{syntax}
-%   Converts the \meta{floating point variable} to its absolute value.
+%   All occurrences of the \meta{exception} (\texttt{invalid_operation},
+%   \texttt{division_by_zero}, \texttt{overflow}, or \texttt{underflow})
+%   within the current group are treated as \meta{trap type}, which can
+%   be
+%   \begin{itemize}
+%     \item \texttt{none}: the \meta{exception} will be entirely
+%       ignored, and leave no trace;
+%     \item \texttt{flag}: the \meta{exception} will turn the
+%       corresponding flag on when it occurs;
+%     \item \texttt{error}: additionally, the \meta{exception} will halt
+%       the \TeX{} run and display some information about the current
+%       operation in the terminal.
+%   \end{itemize}
 % \end{function}
 %
-% \begin{function}{\fp_neg:N, \fp_neg:c, \fp_gneg:N, \fp_gneg:c}
+% \section{Floating point expressions}
+%
+% \begin{function}[added = 2012-05-08, updated = 2012-05-27]
+%   {\fp_show:N, \fp_show:c, \fp_show:n}
 %   \begin{syntax}
-%     \cs{fp_neg:N} \meta{floating point variable}
+%     \cs{fp_show:N} \meta{fp~var}
+%     \cs{fp_show:n} \Arg{floating point expression}
 %   \end{syntax}
-%   Reverse the sign of the \meta{floating point variable}.
+%   Evaluates the \meta{floating point expression} and displays the
+%   result in the terminal.
 % \end{function}
 %
-% \section{Floating-point arithmetic}
+% \subsection{Input of floating point numbers} \label{sec:fp-floats}
 %
-% Binary arithmetic operations act on the value stored in an
-% \texttt{fp}, so for example
-% \begin{verbatim}
-%   \fp_set:Nn \l_my_fp { 1.234 }
-%   \fp_sub:Nn \l_my_fp { 5.678 }
-% \end{verbatim}
-%  sets \cs{l_my_fp} to the result of $1.234 - 5.678$
-%  (\emph{i.e.}~$-4.444$).
+%^^A todo: write a grammar
+%^^A todo: clarify what has changed compared to the previous l3fp
+%
+% We support four types of floating point numbers:
+% \begin{itemize}
+%   \item $\pm 0.d_1d_2\ldots{}d_{16} \cdot 10^{n}$, a normal floating
+%     point number, with $d_i\in [0,9]$, $d_1\neq 0$, and $\lvert n\rvert
+%     \leq \ExplSyntaxOn \int_use:N \c__fp_max_exponent_int$;
+%   \item $\pm 0$, zero, with a given sign;
+%   \item $\pm \infty$, infinity, with a given sign;
+%   \item \texttt{nan}, is \enquote{not a number}, and can be either quiet
+%     or signalling (\emph{not yet}: this distinction is currently
+%     unsupported);
+%   \item [\emph{not yet}] subnormal numbers $\pm 0.d_1d_2\ldots{}d_{16}
+%     \cdot 10^{-\ExplSyntaxOn\int_use:N \c__fp_max_exponent_int}$ with
+%     $d_1=0$.
+% \end{itemize}
+% Normal floating point numbers are stored in base $10$, with $16$
+% significant figures.
+%
+% On input, a normal floating point number consists of:
+% \begin{itemize}
+%   \item \meta{sign}: a possibly empty string of |+| and |-| characters;
+%   \item \meta{mantissa}: a non-empty string of digits together with zero
+%     or one dot;
+%   \item \meta{exponent} optionally: the character |e|, followed by a
+%     possibly empty string of |+|~and~|-| tokens, and a non-empty string
+%     of digits.
+% \end{itemize}
+% The sign of the resulting number is |+| if \meta{sign} contains an
+% even number of |-|, and |-| otherwise, hence, an empty \meta{sign}
+% denotes a non-negative input.  The stored mantissa is obtained from
+% \meta{mantissa} by omitting the decimal separator and leading zeros,
+% and rounding to $16$ significant digits, filling with trailing zeros
+% if necessary.  In particular, the value stored is exact if the input
+% \meta{mantissa} has at most $16$ digits.  The stored \meta{exponent}
+% is obtained by combining the input \meta{exponent} ($0$ if absent)
+% with a shift depending on the position of the mantissa and the number
+% of leading zeros.
+%
+% A special case arises if the resulting \meta{exponent} is either
+% too large or too small to be represented. This results either in an
+% overflow (the number is then replaced by $\pm\infty$), or an
+% underflow (resulting in $\pm 0$).
+%
+% The result is thus $\pm 0$ if and only if \meta{mantissa} contains no
+% non-zero digit (\emph{i.e.}, consists only in~|0| characters, and an
+% optional |.| character), or there is an underflow.  Note that a single
+% dot is currently a valid floating point number, equal to~$+0$, but
+% that is not guaranteed to remain the case.
+%
+% Special numbers are input as follows:
+% \begin{itemize}
+%   \item \texttt{inf} represents $+\infty$, and can be preceded by any
+%     \meta{sign}.
+%   \item \texttt{nan} represents a (quiet) non-number. It can be preceded
+%     by any sign, but that will be ignored.
+%   \item Any unrecognisable string will yield a signalling \texttt{nan}.
+% \end{itemize}
+%
+% Note that~|e-1| is not a representation of $10^{-1}$, because it
+% could be mistaken with the difference of \enquote{\texttt{e}} and
+% $1$. This is consistent with several other programming languages.
+% However, in order to avoid confusions, |e-1| is not considered to
+% be this difference either. To input the base of natural logarithms,
+% use \texttt{exp(1)} or \cs{c_e_fp}.
+%
+% \subsection{Precedence of operators}
+% \label{sec:fp-precedence}
+%
+% ^^A List "juxtaposition" somewhere in the list.
 %
-% \begin{function}{\fp_add:Nn, \fp_add:cn, \fp_gadd:Nn, \fp_gadd:cn}
+% We list here all the operations supported in floating point
+% expressions, in order of decreasing precedence: operations listed
+% earlier bind more tightly than operations listed below them.
+% \begin{itemize}
+%   \item Implicit multiplication by juxtaposition (\texttt{2pi}, \emph{etc}).
+%   \item Function calls (\texttt{sin}, \texttt{ln}, \emph{etc}).
+%   \item Binary |**| and |^| (right associative).
+%   \item Unary |+|, |-|, |!|.
+%   \item Binary |*|, |/| and |%|.
+%   \item Binary |+| and |-|.
+%   \item Comparisons |>=|, |!=|, |<?|, \emph{etc}.
+%   \item Logical \texttt{and}, denoted by |&&|.
+%   \item Logical \texttt{or}, denoted by \verb*+||+.
+%   \item Ternary operator |?:| (right associative).
+% \end{itemize}
+% The precedence of operations can be overridden using parentheses.
+% In particular, those precedences imply that
+% \begin{align*}
+%   \mathtt{sin 2pi} & = \sin(2\pi) = 0, \\
+%   \mathtt{2\char`\^2max(3,4)} & = 2^{2 \max(3,4)} = 256.
+% \end{align*}
+% Functions are called on the value of their argument, contrarily to
+% \TeX{} macros.
+%
+% \subsection{Operations} \label{sec:fp-operations}
+%
+% We now present the various operations allowed in floating point
+% expressions.  When used as a truth value, a floating point expression
+% is \texttt{false} if it is $\pm 0$, and \texttt{false} otherwise.
+%
+% The exceptions listed below are mostly not implemented yet. ^^A todo:
+%
+% \begin{function}{?:}
 %   \begin{syntax}
-%     \cs{fp_add:Nn} \meta{floating point} \Arg{value}
+%     \cs{fp_eval:n} \{ \meta{operand_1} |?| \meta{operand_2} |:| \meta{operand_3} \}
 %   \end{syntax}
-%   Adds the \meta{value} to the \meta{floating point}.
+%   The ternary operator |?:| results in \meta{operand_2} if
+%   \meta{operand_1} is true, and \meta{operand_3} if it is false (equal to
+%   $\pm 0$).  All three \meta{operands} are evaluated in all cases.  The
+%   operator is right associative, hence
+%   \begin{verbatim}
+%     \fp_eval:n
+%       {
+%         1 + 3 > 4 ? 1 :
+%         2 + 4 > 5 ? 2 :
+%         3 + 5 > 6 ? 3 : 4
+%       }
+%   \end{verbatim}
+%   first tests whether $1 + 3 > 4$; since this isn't true, the branch
+%   following |:| is taken, and $2 + 4 > 5$ is compared; since this is
+%   true, the branch before |:| is taken, and everything else is
+%   (evaluated then) ignored.  That allows testing for various cases in
+%   a concise manner, with the drawback that all computations are made
+%   in all cases.
 % \end{function}
 %
-% \begin{function}{\fp_sub:Nn, \fp_sub:cn, \fp_gsub:Nn, \fp_gsub:cn}
+% \begingroup \catcode`\|=12
+% \begin{function}{TWO BARS} ^^A To fix
 %   \begin{syntax}
-%     \cs{fp_sub:Nn} \meta{floating point} \Arg{value}
+%     \cs{fp_eval:n} \{ \meta{operand_1} \texttt{||} \meta{operand_2} \}
 %   \end{syntax}
-%   Subtracts the \meta{value} from the \meta{floating point}.
+%   If \meta{operand_1} is true (non-zero), use that value, otherwise the
+%   value of \meta{operand_2}.  Both \meta{operands} are evaluated in all
+%   cases.
 % \end{function}
+% \endgroup
 %
-% \begin{function}{\fp_mul:Nn, \fp_mul:cn, \fp_gmul:Nn, \fp_gmul:cn}
+% \begingroup \catcode`\&=12
+% \begin{function}{&&}
 %   \begin{syntax}
-%     \cs{fp_mul:Nn} \meta{floating point} \Arg{value}
+%     \cs{fp_eval:n} \{ \meta{operand_1} \texttt{&&} \meta{operand_2} \}
 %   \end{syntax}
-%   Multiples the \meta{floating point} by the \meta{value}.
+%   If \meta{operand_1} is false (equal to $\pm 0$), use that value,
+%   otherwise the value of \meta{operand_2}.  Both \meta{operands} are
+%   evaluated in all cases.
 % \end{function}
+% \endgroup
 %
-% \begin{function}{\fp_div:Nn, \fp_div:cn, \fp_gdiv:Nn, \fp_gdiv:cn}
+% \begin{function}{\<, =, >, ?}
 %   \begin{syntax}
-%     \cs{fp_div:Nn} \meta{floating point} \Arg{value}
+%     \cs{fp_eval:n} \{ \meta{operand_1} \meta{comparison} \meta{operand_2} \}
 %   \end{syntax}
-%   Divides the \meta{floating point} by the \meta{value}, making the
-%   assignment within the current \TeX{} group level. If the \meta{value}
-%   is zero, the \meta{floating point} will be set to
-%   \cs{c_undefined_fp}.
+%   The \meta{comparison} consists of a non-empty string of |<|, |=|,
+%   |>|, and |?|, optionally preceeded by |!|.  It may not start with
+%   |?|.  This evaluates to $+1$ if the \meta{comparison} between the
+%   \meta{operand_1} and \meta{operand_2} is true, and $+0$ otherwise.
 % \end{function}
 %
-% \section{Floating-point power operations}
-%
-% \begin{function}{\fp_pow:Nn, \fp_pow:cn, \fp_gpow:Nn, \fp_gpow:cn}
+% \begin{function}{+, -}
 %   \begin{syntax}
-%     \cs{fp_pow:Nn} \meta{floating point} \Arg{value}
+%     \cs{fp_eval:n} \{ \meta{operand_1} |+| \meta{operand_2} \}
+%     \cs{fp_eval:n} \{ \meta{operand_1} |-| \meta{operand_2} \}
 %   \end{syntax}
-%   Raises the \meta{floating point} to the given \meta{value}. If the
-%   \meta{floating point} is negative, then the \meta{value} should be
-%   either a positive real number or a negative integer. If the
-%   \meta{floating point} is positive, then the \meta{value} may be any
-%   real value. Mathematically invalid operations such as $0^{0}$
-%   will give set the \meta{floating point} to  to \cs{c_undefined_fp}.
+%   Computes the sum or the difference of its two \meta{operands}.  The
+%   \enquote{invalid operation} exception occurs for $\infty-\infty$.
+%   \enquote{Inexact}, \enquote{underflow} and \enquote{overflow} occur
+%   when appropriate.
 % \end{function}
 %
-% \section{Exponential and logarithm functions}
-%
-% \begin{function}{\fp_exp:Nn, \fp_exp:cn, \fp_gexp:Nn, \fp_gexp:cn}
+% \begin{function}{*, /}
 %   \begin{syntax}
-%     \cs{fp_exp:Nn} \meta{floating point} \Arg{value}
+%     \cs{fp_eval:n} \{ \meta{operand_1} |*| \meta{operand_2} \}
+%     \cs{fp_eval:n} \{ \meta{operand_1} |/| \meta{operand_2} \}
 %   \end{syntax}
-%   Calculates the exponential of the \meta{value} and assigns this
-%   to the \meta{floating point}.
+%   Computes the product or the ratio of its two \meta{operands}.  The
+%   \enquote{invalid operation} exception occurs for $\infty/\infty$,
+%   $0/0$, or $0*\infty$.  \enquote{Division by zero} occurs when
+%   dividing a finite non-zero number by $\pm 0$.  The
+%   \enquote{inexact}, \enquote{underflow} and \enquote{overflow}
+%   exceptions occur when appropriate.
 % \end{function}
 %
-% \begin{function}{\fp_ln:Nn, \fp_ln:cn, \fp_gln:Nn, \fp_gln:cn}
+% \begin{function}{+, -, !}
 %   \begin{syntax}
-%     \cs{fp_ln:Nn} \meta{floating point} \Arg{value}
+%     \cs{fp_eval:n} \{ |+| \meta{operand} \}
+%     \cs{fp_eval:n} \{ |-| \meta{operand} \}
+%     \cs{fp_eval:n} \{ |!| \meta{operand} \}
 %   \end{syntax}
-%   Calculates the natural logarithm of the \meta{value} and assigns
-%   this to the \meta{floating point}.
+%   The unary |+| does nothing, the unary |-| changes the sign of the
+%   \meta{operand}, and |!| \meta{operand} evaluates to $1$ if
+%   \meta{operand} is false and $0$ otherwise (this is the \texttt{not}
+%   boolean function).
 % \end{function}
 %
-% \section{Trigonometric functions}
-%
-% The trigonometric functions all work in radians. They accept a maximum
-% input value of $100\,000\,000$, as there are issues with range
-% reduction and very large input values.
-%
-% \begin{function}{\fp_sin:Nn, \fp_sin:cn, \fp_gsin:Nn, \fp_gsin:cn}
+% \begingroup\catcode`\^=12
+% \begin{function}{**, ^}
 %   \begin{syntax}
-%     \cs{fp_sin:Nn} \meta{floating point} \Arg{value}
+%     \cs{fp_eval:n} \{ \meta{operand_1} |**| \meta{operand_2} \}
+%     \cs{fp_eval:n} \{ \meta{operand_1} |^| \meta{operand_2} \}
 %   \end{syntax}
-%   Assigns the sine of the \meta{value} to the \meta{floating point}.
-%   The \meta{value} should be given in radians.
+%   Raises \meta{operand_1} to the power \meta{operand_2}.  This operation
+%   is right associative, hence \texttt{2 ** 2 ** 3} equals
+%   $2\sp{2\sp{3}} = 256$.  The \enquote{invalid operation} exception
+%   occurs if \meta{operand_1} is negative or $-0$, \meta{operand_2} is
+%   not an integer, and the result is non-zero.  \enquote{Division by
+%     zero} occurs \emph{not yet}.  The \enquote{inexact},
+%   \enquote{underflow} and \enquote{overflow} exceptions occur when
+%   appropriate.
 % \end{function}
+% \endgroup
 %
-% \begin{function}{\fp_cos:Nn, \fp_cos:cn, \fp_gcos:Nn, \fp_gcos:cn}
+% \begin{function}{abs}
 %   \begin{syntax}
-%     \cs{fp_cos:Nn} \meta{floating point} \Arg{value}
+%     \cs{fp_eval:n} \{ |abs(| \meta{fpexpr} |)| \}
 %   \end{syntax}
-%   Assigns the cosine of the \meta{value} to the \meta{floating point}.
-%   The \meta{value} should be given in radians.
+%   Computes the absolute value of the \meta{fpexpr}.  This function
+%   never raises an exception when \meta{fpexpr} is a number.
 % \end{function}
 %
-% \begin{function}{\fp_tan:Nn, \fp_tan:cn, \fp_gtan:Nn, \fp_gtan:cn}
+% \begin{function}{exp}
 %   \begin{syntax}
-%     \cs{fp_tan:Nn} \meta{floating point} \Arg{value}
+%     \cs{fp_eval:n} \{ |exp(| \meta{fpexpr} |)| \}
 %   \end{syntax}
-%   Assigns the tangent of the \meta{value} to the \meta{floating point}.
-%   The \meta{value} should be given in radians.
+%   Computes the exponential of the \meta{fpexpr}.  The
+%   \enquote{inexact}, \enquote{underflow} and \enquote{overflow}
+%   exceptions occur when appropriate.
 % \end{function}
 %
-% \section{Constant floating point values}
-%
-% \begin{variable}{\c_e_fp}
-%   The value of the base of natural numbers, $\mathrm{e}$.
-% \end{variable}
-%
-% \begin{variable}{\c_one_fp}
-%   A floating point variable with permanent value $1$: used for
-%   speeding up some comparisons.
-% \end{variable}
-%
-% \begin{variable}{\c_pi_fp}
-%   The value of $\pi$.
-% \end{variable}
-%
-% \begin{variable}{\c_undefined_fp}
-%   A special marker floating point variable representing the result of
-%   an operation which does not give a defined result (such as division
-%   by $0$).
-% \end{variable}
-%
-% \begin{variable}{\c_zero_fp}
-%   A permanently zero floating point variable.
-% \end{variable}
-%
-% \section{Notes on the floating point unit}
-%
-% As calculation of the elemental transcendental functions is
-% computationally expensive compared to storage of results, after
-% calculating a trigonometric function, exponent, \emph{etc.}~the module
-% stored the result for reuse. Thus the performance of the module for
-% repeated operations, most probably trigonometric functions, should be
-% much higher than if the values were re-calculated every time they
-% were needed.
-%
-% Anyone with experience of programming floating point calculations will
-% know that this is a complex area. The aim of the unit is to be
-% accurate enough for the likely applications in a typesetting context.
-% The arithmetic operations are therefore intended to provide ten digit
-% accuracy with the last digit accurate to $\pm 1$. The elemental
-% transcendental functions may not provide such high accuracy in every
-% case, although the design aim has been to provide $10$ digit
-% accuracy for cases likely to be relevant in typesetting situations.
-% A good overview of the challenges in this area can be found in
-% J.-M.~Muller, \emph{Elementary functions: algorithms and
-% implementation}, 2nd edition, Birkh{\"{a}}uer Boston, New York, USA,
-% 2006.
-%
-% The internal representation of numbers is tuned to the needs of the
-% underlying \TeX{} system. This means that the format is somewhat
-% different from that used in, for example, computer floating point
-% units. Programming in \TeX{} makes it most convenient to use a
-% radix $10$ system, using \TeX{} \texttt{count} registers for
-% storage and taking advantage where possible of delimited arguments.
-%
-% \end{documentation}
-%
-% \begin{implementation}
-%
-% \section{\pkg{l3fp} Implementation}
-%
-% \TestFiles{m3fp003.lvt}
-%
-%    \begin{macrocode}
-%<*initex|package>
-%    \end{macrocode}
-%
-%    \begin{macrocode}
-%<*package>
-\ProvidesExplPackage
-  {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
-%</package>
-%    \end{macrocode}
-%
-% \subsection{Constants}
-%
-% \begin{variable}{\c_forty_four}
-% \begin{variable}{\c_one_million}
-% \begin{variable}{\c_one_hundred_million}
-% \begin{variable}{\c_five_hundred_million}
-% \begin{variable}{\c_one_thousand_million}
-%   There is some speed to gain by moving numbers into fixed positions.
-%    \begin{macrocode}
-\int_const:Nn \c_forty_four { 44 }
-\int_const:Nn \c_one_million { 1 000 000 }
-\int_const:Nn \c_one_hundred_million { 100 000 000 }
-\int_const:Nn \c_five_hundred_million { 500 000 000 }
-\int_const:Nn \c_one_thousand_million { 1 000 000 000 }
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\c_fp_pi_by_four_decimal_int}
-% \begin{variable}{\c_fp_pi_by_four_extended_int}
-% \begin{variable}{\c_fp_pi_decimal_int}
-% \begin{variable}{\c_fp_pi_extended_int}
-% \begin{variable}{\c_fp_two_pi_decimal_int}
-% \begin{variable}{\c_fp_two_pi_extended_int}
-%   Parts of $\pi$ for trigonometric range reduction, implemented
-%   as \texttt{int} variables for speed.
-%    \begin{macrocode}
-\int_new:N  \c_fp_pi_by_four_decimal_int
-\int_set:Nn \c_fp_pi_by_four_decimal_int { 785 398 158 }
-\int_new:N  \c_fp_pi_by_four_extended_int
-\int_set:Nn \c_fp_pi_by_four_extended_int { 897 448 310 }
-\int_new:N  \c_fp_pi_decimal_int
-\int_set:Nn \c_fp_pi_decimal_int { 141 592 653 }
-\int_new:N  \c_fp_pi_extended_int
-\int_set:Nn \c_fp_pi_extended_int { 589 793 238 }
-\int_new:N  \c_fp_two_pi_decimal_int
-\int_set:Nn \c_fp_two_pi_decimal_int { 283 185 307 }
-\int_new:N  \c_fp_two_pi_extended_int
-\int_set:Nn \c_fp_two_pi_extended_int { 179 586 477 }
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\c_e_fp}
-%   The value $\mathrm{e}$ as a \enquote{machine number}.
-%    \begin{macrocode}
-\tl_const:Nn \c_e_fp { + 2.718281828 e 0 }
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\c_one_fp}
-%   The constant value $1$: used for fast comparisons.
-%    \begin{macrocode}
-\tl_const:Nn \c_one_fp { + 1.000000000 e 0 }
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\c_pi_fp}
-%   The value $\pi$ as a \enquote{machine number}.
-%    \begin{macrocode}
-\tl_const:Nn \c_pi_fp { + 3.141592654 e 0 }
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\c_undefined_fp}
-%   A marker for undefined values.
-%    \begin{macrocode}
-\tl_const:Nn \c_undefined_fp { X 0.000000000 e 0 }
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\c_zero_fp}
-%   The constant zero value.
-%    \begin{macrocode}
-\tl_const:Nn \c_zero_fp { + 0.000000000 e 0 }
-%    \end{macrocode}
-% \end{variable}
-%
-% \subsection{Variables}
-%
-% \begin{variable}{\l_fp_arg_tl}
-%   A token list to store the formalised representation of the input
-%   for transcendental functions.
-%    \begin{macrocode}
-\tl_new:N \l_fp_arg_tl
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_fp_count_int}
-%   A counter for things like the number of divisions possible.
-%    \begin{macrocode}
-\int_new:N \l_fp_count_int
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_fp_div_offset_int}
-%   When carrying out division, an offset is used for the results to
-%   get the decimal part correct.
-%    \begin{macrocode}
-\int_new:N \l_fp_div_offset_int
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_fp_exp_integer_int}
-% \begin{variable}{\l_fp_exp_decimal_int}
-% \begin{variable}{\l_fp_exp_extended_int}
-% \begin{variable}{\l_fp_exp_exponent_int}
-%   Used for the calculation of exponent values.
-%    \begin{macrocode}
-\int_new:N \l_fp_exp_integer_int
-\int_new:N \l_fp_exp_decimal_int
-\int_new:N \l_fp_exp_extended_int
-\int_new:N \l_fp_exp_exponent_int
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_fp_input_a_sign_int}
-% \begin{variable}{\l_fp_input_a_integer_int}
-% \begin{variable}{\l_fp_input_a_decimal_int}
-% \begin{variable}{\l_fp_input_a_exponent_int}
-% \begin{variable}{\l_fp_input_b_sign_int}
-% \begin{variable}{\l_fp_input_b_integer_int}
-% \begin{variable}{\l_fp_input_b_decimal_int}
-% \begin{variable}{\l_fp_input_b_exponent_int}
-%   Storage for the input: two storage areas as there are at most two
-%   inputs.
-%    \begin{macrocode}
-\int_new:N \l_fp_input_a_sign_int
-\int_new:N \l_fp_input_a_integer_int
-\int_new:N \l_fp_input_a_decimal_int
-\int_new:N \l_fp_input_a_exponent_int
-\int_new:N \l_fp_input_b_sign_int
-\int_new:N \l_fp_input_b_integer_int
-\int_new:N \l_fp_input_b_decimal_int
-\int_new:N \l_fp_input_b_exponent_int
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_fp_input_a_extended_int}
-% \begin{variable}{\l_fp_input_b_extended_int}
-%   For internal use, \enquote{extended} floating point numbers are
-%   needed.
-%    \begin{macrocode}
-\int_new:N \l_fp_input_a_extended_int
-\int_new:N \l_fp_input_b_extended_int
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_fp_mul_a_i_int}
-% \begin{variable}{\l_fp_mul_a_ii_int}
-% \begin{variable}{\l_fp_mul_a_iii_int}
-% \begin{variable}{\l_fp_mul_a_iv_int}
-% \begin{variable}{\l_fp_mul_a_v_int}
-% \begin{variable}{\l_fp_mul_a_vi_int}
-% \begin{variable}{\l_fp_mul_b_i_int}
-% \begin{variable}{\l_fp_mul_b_ii_int}
-% \begin{variable}{\l_fp_mul_b_iii_int}
-% \begin{variable}{\l_fp_mul_b_iv_int}
-% \begin{variable}{\l_fp_mul_b_v_int}
-% \begin{variable}{\l_fp_mul_b_vi_int}
-%   Multiplication requires that the decimal part is split into parts
-%   so that there are no overflows.
-%    \begin{macrocode}
-\int_new:N \l_fp_mul_a_i_int
-\int_new:N \l_fp_mul_a_ii_int
-\int_new:N \l_fp_mul_a_iii_int
-\int_new:N \l_fp_mul_a_iv_int
-\int_new:N \l_fp_mul_a_v_int
-\int_new:N \l_fp_mul_a_vi_int
-\int_new:N \l_fp_mul_b_i_int
-\int_new:N \l_fp_mul_b_ii_int
-\int_new:N \l_fp_mul_b_iii_int
-\int_new:N \l_fp_mul_b_iv_int
-\int_new:N \l_fp_mul_b_v_int
-\int_new:N \l_fp_mul_b_vi_int
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_fp_mul_output_int}
-% \begin{variable}{\l_fp_mul_output_tl}
-%   Space for multiplication results.
-%    \begin{macrocode}
-\int_new:N \l_fp_mul_output_int
-\tl_new:N  \l_fp_mul_output_tl
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_fp_output_sign_int}
-% \begin{variable}{\l_fp_output_integer_int}
-% \begin{variable}{\l_fp_output_decimal_int}
-% \begin{variable}{\l_fp_output_exponent_int}
-%   Output is stored in the same way as input.
-%    \begin{macrocode}
-\int_new:N \l_fp_output_sign_int
-\int_new:N \l_fp_output_integer_int
-\int_new:N \l_fp_output_decimal_int
-\int_new:N \l_fp_output_exponent_int
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_fp_output_extended_int}
-%   Again, for calculations an extended part.
-%    \begin{macrocode}
-\int_new:N \l_fp_output_extended_int
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_fp_round_carry_bool}
-%   To indicate that a digit needs to be carried forward.
-%    \begin{macrocode}
-\bool_new:N \l_fp_round_carry_bool
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_fp_round_decimal_tl}
-%   A temporary store when rounding, to build up the decimal part without
-%   needing to do any maths.
-%    \begin{macrocode}
-\tl_new:N \l_fp_round_decimal_tl
-%    \end{macrocode}
-% \end{variable}
+% \begin{function}{ln}
+%   \begin{syntax}
+%     \cs{fp_eval:n} \{ |ln(| \meta{fpexpr} |)| \}
+%   \end{syntax}
+%   Computes the natural logarithm of the \meta{fpexpr}.  Negative
+%   numbers have no (real) logarithm, hence the \enquote{invalid
+%     operation} is raised in that case.  \enquote{Division by zero}
+%   occurs when evaluating the logarithm of $\pm 0$.  The
+%   \enquote{inexact}, \enquote{underflow} and \enquote{overflow}
+%   exceptions occur when appropriate.
+% \end{function}
 %
-% \begin{variable}{\l_fp_round_position_int}
-% \begin{variable}{\l_fp_round_target_int}
-%   Used to check the position for rounding.
-%    \begin{macrocode}
-\int_new:N \l_fp_round_position_int
-\int_new:N \l_fp_round_target_int
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
+% \begin{function}{max, min}
+%   \begin{syntax}
+%     \cs{fp_eval:n} \{ |max(| \meta{fpexpr_1} |,| \meta{fpexpr_2} |,| \ldots{} |)| \}
+%     \cs{fp_eval:n} \{ |min(| \meta{fpexpr_1} |,| \meta{fpexpr_2} |,| \ldots{} |)| \}
+%   \end{syntax}
+%   Evalutes each \meta{fpexpr} and computes the largest (smallest) of
+%   those.  If any of the \meta{fpexpr} is a \nan{}, the result is
+%   \nan{}.
+% \end{function}
 %
-% \begin{variable}{\l_fp_sign_tl}
-%   There are places where the sign needs to be set up \enquote{early},
-%   so that the registers can be re-used.
-%    \begin{macrocode}
-\tl_new:N \l_fp_sign_tl
-%    \end{macrocode}
-% \end{variable}
+% \begin{function}{round, round0, round+, round-}
+%   \begin{syntax}
+%     \cs{fp_eval:n} \{ |round| \meta{option} |(| \meta{fpexpr} |)| \}
+%     \cs{fp_eval:n} \{ |round| \meta{option} |(| \meta{fpexpr_1} , \meta{fpexpr_2} |)| \}
+%   \end{syntax}
+%   Rounds \meta{fpexpr_1} to \meta{fpexpr_2} places (this must be an
+%   integer).  When \meta{fpexpr_2} is missing, it is assumed to be $0$,
+%   \emph{i.e.}, \meta{fpexpr_1} is rounded to an integer.  The
+%   \meta{option} controls the rounding direction:
+%   \begin{itemize}
+%     \item by default, the function rounds to the closest allowed number
+%       (rounding ties to even);
+%     \item with |0|, the function rounds towards $0$, \emph{i.e.}, truncates;
+%     \item with |+|, the function rounds towards $+\infty$;
+%     \item with |-|, the function rounds towards $-\infty$.
+%   \end{itemize}
+% \end{function}
 %
-% \begin{variable}{\l_fp_split_sign_int}
-%   When splitting the input it is fastest to use a fixed name for the
-%   sign part, and to transfer it after the split is complete.
-%    \begin{macrocode}
-\int_new:N \l_fp_split_sign_int
-%    \end{macrocode}
-% \end{variable}
+% \begin{function}{sin, cos, tan, cot}
+%   \begin{syntax}
+%     \cs{fp_eval:n} \{ |sin(| \meta{fpexpr} |)| \}
+%     \cs{fp_eval:n} \{ |cos(| \meta{fpexpr} |)| \}
+%     \cs{fp_eval:n} \{ |tan(| \meta{fpexpr} |)| \}
+%     \cs{fp_eval:n} \{ |cot(| \meta{fpexpr} |)| \}
+%   \end{syntax}
+%   Computes the sine, cosine, tangent or cotangent of the
+%   \meta{fpexpr}.  The trigonometric functions are undefined for an
+%   argument of $\pm\infty$, leading to the \enquote{invalid operation}
+%   exception.  Additionally, evaluating tangent or cotangent at one of
+%   their poles leads to a \enquote{division by zero} exception.  Other
+%   exceptions occur when appropriate.
+% \end{function}
 %
-% \begin{variable}{\l_fp_internal_int}
-%   A scratch \texttt{int}: used only where the value is not carried
-%   forward.
-%    \begin{macrocode}
-\int_new:N \l_fp_internal_int
-%    \end{macrocode}
+% \begin{variable}{inf, nan}
+%   The special values $+\infty$, $-\infty$, and \nan{} are represented
+%   as \texttt{inf}, \texttt{-inf} and \texttt{nan} (see \cs{c_inf_fp},
+%   \cs{c_minus_inf_fp} and \cs{c_nan_fp}).
 % \end{variable}
 %
-% \begin{variable}{\l_fp_internal_tl}
-%   A scratch token list variable for expanding material.
-%    \begin{macrocode}
-\tl_new:N \l_fp_internal_tl
-%    \end{macrocode}
+% \begin{variable}{pi}
+%   The value of $\pi$ (see \cs{c_pi_fp}).
 % \end{variable}
 %
-% \begin{variable}{\l_fp_trig_octant_int}
-%   To track which octant the trigonometric input is in.
-%    \begin{macrocode}
-\int_new:N \l_fp_trig_octant_int
-%    \end{macrocode}
+% \begin{variable}{deg}
+%   The value of $1^{\circ}$ in radians (see \cs{c_one_degree_fp}).
 % \end{variable}
 %
-% \begin{variable}{\l_fp_trig_sign_int}
-% \begin{variable}{\l_fp_trig_decimal_int}
-% \begin{variable}{\l_fp_trig_extended_int}
-%   Used for the calculation of trigonometric values.
-%    \begin{macrocode}
-\int_new:N \l_fp_trig_sign_int
-\int_new:N \l_fp_trig_decimal_int
-\int_new:N \l_fp_trig_extended_int
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
+% \begin{variable}{em, ex, in, pt, pc, cm, mm, dd, cc, nd, nc, bp, sp}
+%   \newcommand{\unit}[1]{\text{\texttt{#1}}}
+%   Those units of measurement are equal to their values in \texttt{pt},
+%   namely
+%   \begin{align*}
+%     1 \unit{in} & = 72.27 \unit{pt} \\
+%     1 \unit{pt} & = 1 \unit{pt} \\
+%     1 \unit{pc} & = 12 \unit{pt} \\
+%     1 \unit{cm} & = \frac{1}{2.54} \unit{in} = 28.45275590551181 \unit{pt} \\
+%     1 \unit{mm} & = \frac{1}{25.4} \unit{in} = 2.845275590551181 \unit{pt} \\
+%     1 \unit{dd} & = 0.376065 \unit{mm} = 1.07000856496063 \unit{pt} \\
+%     1 \unit{cc} & = 12 \unit{dd} = 12.84010277952756 \unit{pt} \\
+%     1 \unit{nd} & = 0.375 \unit{mm} = 1.066978346456693 \unit{pt} \\
+%     1 \unit{nc} & = 12 \unit{nd} = 12.80374015748031 \unit{pt} \\
+%     1 \unit{bp} & = \frac{1}{72} \unit{in} = 1.00375 \unit{pt} \\
+%     1 \unit{sp} & = 2^{-16} \unit{pt} = 1.52587890625e-5 \unit{pt}.
+%   \end{align*}
+%   The values of the (font-dependent) units \texttt{em} and \texttt{ex}
+%   are gathered from \TeX{} when the surrounding floating point
+%   expression is evaluated.
 % \end{variable}
 %
-% \subsection{Parsing numbers}
-%
-% \begin{macro}{\fp_read:N}
-% \begin{macro}[aux]{\fp_read_aux:w}
-%   Reading a stored value is made easier as the format is designed to
-%   match the delimited function. This is always used to read the first
-%   value (register |a|).
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_read:N #1
-  { \exp_after:wN \fp_read_aux:w #1 \q_stop }
-\cs_new_protected:Npn \fp_read_aux:w #1#2 . #3 e #4 \q_stop
-  {
-    \if:w #1 -
-      \l_fp_input_a_sign_int \c_minus_one
-    \else:
-      \l_fp_input_a_sign_int \c_one
-    \fi:
-    \l_fp_input_a_integer_int  #2 \scan_stop:
-    \l_fp_input_a_decimal_int  #3 \scan_stop:
-    \l_fp_input_a_exponent_int #4 \scan_stop:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_split:Nn}
-% \begin{macro}[aux]{\fp_split_sign:}
-% \begin{macro}[aux]{\fp_split_exponent:}
-% \begin{macro}[aux]{\fp_split_aux_i:w}
-% \begin{macro}[aux]{\fp_split_aux_ii:w}
-% \begin{macro}[aux]{\fp_split_aux_iii:w}
-% \begin{macro}[aux]{\fp_split_decimal:w}
-% \begin{macro}[aux]{\fp_split_decimal_aux:w}
-%   The aim here is to use as much of \TeX{}'s mechanism as possible to pick
-%   up the numerical input without any mistakes. In particular, negative
-%   numbers have to be filtered out first in case the integer part is
-%   $0$ (in which case \TeX{} would drop the |-| sign). That process
-%   has to be done in a loop for cases where the sign is repeated.
-%   Finding an exponent is relatively easy, after which the next phase is
-%   to find the integer part, which will terminate with a |.|, and trigger
-%   the decimal-finding code. The later will allow the decimal to be too
-%   long, truncating the result.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_split:Nn #1#2
-  {
-    \tl_set:Nx \l_fp_internal_tl {#2}
-    \tl_set_rescan:Nno \l_fp_internal_tl { \char_set_catcode_ignore:n { 32 } }
-      { \l_fp_internal_tl }
-    \l_fp_split_sign_int \c_one
-    \fp_split_sign:
-    \use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int
-    \exp_after:wN \fp_split_exponent:w \l_fp_internal_tl e e \q_stop #1
-  }
-\cs_new_protected_nopar:Npn \fp_split_sign:
-  {
-    \if_int_compare:w \pdftex_strcmp:D
-      { \exp_after:wN \tl_head:w \l_fp_internal_tl ? \q_stop } { - }
-        = \c_zero
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \exp_after:wN
-            \tl_tail:w \l_fp_internal_tl \prg_do_nothing: \q_stop
-        }
-      \l_fp_split_sign_int -\l_fp_split_sign_int
-      \exp_after:wN \fp_split_sign:
-    \else:
-      \if_int_compare:w \pdftex_strcmp:D
-        { \exp_after:wN \tl_head:w \l_fp_internal_tl ? \q_stop } { + }
-          = \c_zero
-        \tl_set:Nx \l_fp_internal_tl
-          {
-            \exp_after:wN
-              \tl_tail:w \l_fp_internal_tl \prg_do_nothing: \q_stop
-          }
-        \exp_after:wN \exp_after:wN \exp_after:wN \fp_split_sign:
-       \fi:
-    \fi:
-  }
-\cs_new_protected:Npn \fp_split_exponent:w #1 e #2 e #3 \q_stop #4
-  {
-    \use:c { l_fp_input_ #4 _exponent_int }
-      \int_eval:w 0 #2 \scan_stop:
-    \tex_afterassignment:D \fp_split_aux_i:w
-    \use:c { l_fp_input_ #4 _integer_int }
-      \int_eval:w 0 #1 . . \q_stop #4
-  }
-\cs_new_protected:Npn \fp_split_aux_i:w #1 . #2 . #3 \q_stop
-  { \fp_split_aux_ii:w #2 000000000 \q_stop }
-\cs_new_protected:Npn \fp_split_aux_ii:w #1#2#3#4#5#6#7#8#9
-  { \fp_split_aux_iii:w {#1#2#3#4#5#6#7#8#9} }
-\cs_new_protected:Npn \fp_split_aux_iii:w #1#2 \q_stop
-  {
-    \l_fp_internal_int 1 #1 \scan_stop:
-    \exp_after:wN \fp_split_decimal:w
-      \int_use:N \l_fp_internal_int 000000000 \q_stop
-  }
-\cs_new_protected:Npn \fp_split_decimal:w #1#2#3#4#5#6#7#8#9
-  { \fp_split_decimal_aux:w {#2#3#4#5#6#7#8#9} }
-\cs_new_protected:Npn \fp_split_decimal_aux:w #1#2#3 \q_stop #4
-  {
-    \use:c { l_fp_input_ #4 _decimal_int } #1#2 \scan_stop:
-    \if_int_compare:w
-      \int_eval:w
-        \use:c { l_fp_input_ #4 _integer_int } +
-        \use:c { l_fp_input_ #4 _decimal_int }
-      \scan_stop:
-        = \c_zero
-      \use:c { l_fp_input_ #4 _sign_int } \c_one
-    \fi:
-    \if_int_compare:w
-      \use:c { l_fp_input_ #4 _integer_int } < \c_one_thousand_million
-    \else:
-      \exp_after:wN \fp_overflow_msg:
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_standardise:NNNN}
-% \begin{macro}[aux]{\fp_standardise_aux:NNNN}
-% \begin{macro}[aux]{\fp_standardise_aux:}
-% \begin{macro}[aux]{\fp_standardise_aux:w}
-%   The idea here is to shift the input into a known exponent range. This
-%   is done using \TeX{} tokens where possible, as this is faster than
-%   arithmetic.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_standardise:NNNN #1#2#3#4
-  {
-    \if_int_compare:w
-      \int_eval:w #2 + #3 = \c_zero
-      #1 \c_one
-      #4 \c_zero
-      \exp_after:wN \use_none:nnnn
-    \else:
-      \exp_after:wN \fp_standardise_aux:NNNN
-    \fi:
-    #1#2#3#4
-  }
-\cs_new_protected:Npn \fp_standardise_aux:NNNN #1#2#3#4
-  {
-    \cs_set_protected_nopar:Npn \fp_standardise_aux:
-      {
-        \if_int_compare:w #2 = \c_zero
-          \tex_advance:D #3 \c_one_thousand_million
-          \exp_after:wN \fp_standardise_aux:w
-            \int_use:N #3 \q_stop
-           \exp_after:wN \fp_standardise_aux:
-         \fi:
-      }
-    \cs_set_protected:Npn
-      \fp_standardise_aux:w ##1##2##3##4##5##6##7##8##9 \q_stop
-      {
-        #2 ##2 \scan_stop:
-        #3 ##3##4##5##6##7##8##9 0 \scan_stop:
-        \tex_advance:D #4 \c_minus_one
-      }
-    \fp_standardise_aux:
-    \cs_set_protected_nopar:Npn \fp_standardise_aux:
-      {
-        \if_int_compare:w #2 > \c_nine
-          \tex_advance:D #2 \c_one_thousand_million
-          \exp_after:wN \use_i:nn \exp_after:wN
-            \fp_standardise_aux:w \int_use:N #2
-           \exp_after:wN \fp_standardise_aux:
-         \fi:
-      }
-    \cs_set_protected:Npn
-      \fp_standardise_aux:w ##1##2##3##4##5##6##7##8##9
-      {
-        #2 ##1##2##3##4##5##6##7##8 \scan_stop:
-        \tex_advance:D #3 \c_one_thousand_million
-        \tex_divide:D #3 \c_ten
-        \tl_set:Nx \l_fp_internal_tl
-          {
-            ##9
-            \exp_after:wN \use_none:n \int_use:N #3
-          }
-        #3 \l_fp_internal_tl \scan_stop:
-        \tex_advance:D #4 \c_one
-      }
-    \fp_standardise_aux:
-    \if_int_compare:w #4 < \c_one_hundred
-      \if_int_compare:w #4 > -\c_one_hundred
-      \else:
-        #1 \c_one
-        #2 \c_zero
-        #3 \c_zero
-        #4 \c_zero
-      \fi:
-    \else:
-      \exp_after:wN \fp_overflow_msg:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_standardise_aux: { }
-\cs_new_protected_nopar:Npn \fp_standardise_aux:w { }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Internal utilities}
-%
-% \begin{macro}{\fp_level_input_exponents:}
-% \begin{macro}[aux]{\fp_level_input_exponents_a:}
-% \begin{macro}[aux]{\fp_level_input_exponents_a:NNNNNNNNN}
-% \begin{macro}[aux]{\fp_level_input_exponents_b:}
-% \begin{macro}[aux]{\fp_level_input_exponents_b:NNNNNNNNN}
-%   The routines here are similar to those used to standardise the
-%   exponent. However, the aim here is different: the two exponents need
-%   to end up the same.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_level_input_exponents:
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
-      \exp_after:wN \fp_level_input_exponents_a:
-    \else:
-      \exp_after:wN \fp_level_input_exponents_b:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_level_input_exponents_a:
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
-      \tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million
-      \exp_after:wN \use_i:nn \exp_after:wN
-        \fp_level_input_exponents_a:NNNNNNNNN
-          \int_use:N \l_fp_input_b_integer_int
-      \exp_after:wN \fp_level_input_exponents_a:
-    \fi:
-  }
-\cs_new_protected:Npn \fp_level_input_exponents_a:NNNNNNNNN
-  #1#2#3#4#5#6#7#8#9
-  {
-    \l_fp_input_b_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
-    \tex_advance:D \l_fp_input_b_decimal_int \c_one_thousand_million
-    \tex_divide:D \l_fp_input_b_decimal_int \c_ten
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        #9
-        \exp_after:wN \use_none:n
-          \int_use:N \l_fp_input_b_decimal_int
-      }
-    \l_fp_input_b_decimal_int \l_fp_internal_tl \scan_stop:
-    \tex_advance:D \l_fp_input_b_exponent_int \c_one
-  }
-\cs_new_protected_nopar:Npn \fp_level_input_exponents_b:
-  {
-    \if_int_compare:w \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int
-      \tex_advance:D \l_fp_input_a_integer_int \c_one_thousand_million
-      \exp_after:wN \use_i:nn \exp_after:wN
-        \fp_level_input_exponents_b:NNNNNNNNN
-          \int_use:N \l_fp_input_a_integer_int
-      \exp_after:wN \fp_level_input_exponents_b:
-    \fi:
-  }
-\cs_new_protected:Npn \fp_level_input_exponents_b:NNNNNNNNN
-  #1#2#3#4#5#6#7#8#9
-  {
-    \l_fp_input_a_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \tex_divide:D \l_fp_input_a_decimal_int \c_ten
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        #9
-        \exp_after:wN \use_none:n
-          \int_use:N \l_fp_input_a_decimal_int
-      }
-    \l_fp_input_a_decimal_int \l_fp_internal_tl \scan_stop:
-    \tex_advance:D \l_fp_input_a_exponent_int \c_one
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[aux]{\fp_tmp:w}
-%   Used for output of results, cutting down on \cs{exp_after:wN}.
-%   This is just a place holder definition.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_tmp:w #1#2 { }
-%    \end{macrocode}
-% \end{macro}
-%
-% \subsection{Operations for \texttt{fp} variables}
-%
-% The format of \texttt{fp} variables is tightly defined, so that
-% they can be read quickly by the internal code. The format is a single
-% sign token, a single number, the decimal point, nine decimal numbers,
-% an |e| and finally the exponent. This final part may vary in length.
-% When stored, floating points will always be stored with a value in
-% the integer position unless the number is zero.
-%
-% \begin{macro}{\fp_new:N, \fp_new:c}
-% \UnitTested
-%   Fixed-points always have a value, and of course this has to be
-%   initialised globally.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_new:N #1
-  {
-    \tl_new:N #1
-    \tl_gset_eq:NN #1 \c_zero_fp
-  }
-\cs_generate_variant:Nn \fp_new:N { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\fp_const:Nn, \fp_const:cn}
-%   A simple wrapper.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_const:Nn #1#2
-  {
-    \fp_new:N #1
-    \fp_gset:Nn #1 {#2}
-  }
-\cs_generate_variant:Nn \fp_const:Nn { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\fp_zero:N, \fp_zero:c}
-% \UnitTested
-% \begin{macro}{\fp_gzero:N, \fp_gzero:c}
-% \UnitTested
-%   Zeroing fixed-points is pretty obvious.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_zero:N #1
-  { \tl_set_eq:NN #1 \c_zero_fp }
-\cs_new_protected:Npn \fp_gzero:N #1
-  { \tl_gset_eq:NN #1 \c_zero_fp }
-\cs_generate_variant:Nn \fp_zero:N { c }
-\cs_generate_variant:Nn \fp_gzero:N { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}
-%   {\fp_zero_new:N, \fp_zero_new:c, \fp_gzero_new:N, \fp_gzero_new:c}
-%   Create a floating point if needed, otherwise clear it.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_zero_new:N  #1
-  { \fp_if_exist:NTF #1 { \fp_zero:N #1 } { \fp_new:N #1 } }
-\cs_new_protected:Npn \fp_gzero_new:N #1
-  { \fp_if_exist:NTF #1 { \fp_gzero:N #1 } { \fp_new:N #1 } }
-\cs_generate_variant:Nn \fp_zero_new:N  { c }
-\cs_generate_variant:Nn \fp_gzero_new:N { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\fp_set:Nn, \fp_set:cn}
-% \UnitTested
-% \begin{macro}{\fp_gset:Nn, \fp_gset:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_set_aux:NNn}
-%   To trap any input errors, a very simple version of the parser is run
-%   here. This will pick up any invalid characters at this stage, saving
-%   issues later. The splitting approach is the same as the more
-%   advanced function later.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_set:Nn  { \fp_set_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gset:Nn { \fp_set_aux:NNn \tl_gset:Nn }
-\cs_new_protected:Npn \fp_set_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-                -
-              \else:
-                +
-              \fi:
-              \int_use:N \l_fp_input_a_integer_int
-              .
-              \exp_after:wN \use_none:n
-                \int_use:N \l_fp_input_a_decimal_int
-              e
-              \int_use:N \l_fp_input_a_exponent_int
-            }
-        }
-    \fp_tmp:w
-  }
-\cs_generate_variant:Nn \fp_set:Nn  { c }
-\cs_generate_variant:Nn \fp_gset:Nn { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-%
-%
-% \begin{macro}{\fp_set_from_dim:Nn,  \fp_set_from_dim:cn}
-% \UnitTested
-% \begin{macro}{\fp_gset_from_dim:Nn, \fp_gset_from_dim:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_set_from_dim_aux:NNn}
-% \begin{macro}[aux]{\fp_set_from_dim_aux:w}
-% \begin{variable}{\l_fp_internal_dim}
-% \begin{variable}{\l_fp_internal_skip}
-%   Here, dimensions are converted to fixed-points \emph{via} a
-%   temporary variable. This ensures that they always convert as points.
-%   The code is then essentially the same as for \cs{fp_set:Nn}, but with
-%   the dimension passed so that it will be striped of the |pt| on the
-%   way through. The passage through a skip is used to remove any rubber
-%   part.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_set_from_dim:Nn
-  { \fp_set_from_dim_aux:NNn \tl_set:Nx }
-\cs_new_protected_nopar:Npn \fp_gset_from_dim:Nn
-  { \fp_set_from_dim_aux:NNn \tl_gset:Nx }
-\cs_new_protected:Npn \fp_set_from_dim_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \l_fp_internal_skip \etex_glueexpr:D #3 \scan_stop:
-      \l_fp_internal_dim \l_fp_internal_skip
-      \fp_split:Nn a
-        {
-          \exp_after:wN \fp_set_from_dim_aux:w
-            \dim_use:N \l_fp_internal_dim
-        }
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-                -
-              \else:
-                +
-              \fi:
-              \int_use:N \l_fp_input_a_integer_int
-              .
-              \exp_after:wN \use_none:n
-                \int_use:N \l_fp_input_a_decimal_int
-              e
-              \int_use:N \l_fp_input_a_exponent_int
-            }
-        }
-    \fp_tmp:w
-  }
-\cs_set_protected_nopar:Npx \fp_set_from_dim_aux:w
-  {
-    \cs_set:Npn \exp_not:N \fp_set_from_dim_aux:w
-      ##1 \tl_to_str:n { pt } {##1}
-  }
-\fp_set_from_dim_aux:w
-\cs_generate_variant:Nn \fp_set_from_dim:Nn  { c }
-\cs_generate_variant:Nn \fp_gset_from_dim:Nn { c }
-\dim_new:N \l_fp_internal_dim
-\skip_new:N \l_fp_internal_skip
-%    \end{macrocode}
-% \end{variable}
+% \begin{variable}{true, false}
+%   Other names for $1$ and $+0$.
 % \end{variable}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
 %
-% \begin{macro}{\fp_set_eq:NN, \fp_set_eq:cN, \fp_set_eq:Nc, \fp_set_eq:cc}
-% \UnitTested
-% \begin{macro}{\fp_gset_eq:NN, \fp_gset_eq:cN, \fp_gset_eq:Nc, \fp_gset_eq:cc}
-% \UnitTested
-%   Pretty simple, really.
-%    \begin{macrocode}
-\cs_new_eq:NN \fp_set_eq:NN  \tl_set_eq:NN
-\cs_new_eq:NN \fp_set_eq:cN  \tl_set_eq:cN
-\cs_new_eq:NN \fp_set_eq:Nc  \tl_set_eq:Nc
-\cs_new_eq:NN \fp_set_eq:cc  \tl_set_eq:cc
-\cs_new_eq:NN \fp_gset_eq:NN \tl_gset_eq:NN
-\cs_new_eq:NN \fp_gset_eq:cN \tl_gset_eq:cN
-\cs_new_eq:NN \fp_gset_eq:Nc \tl_gset_eq:Nc
-\cs_new_eq:NN \fp_gset_eq:cc \tl_gset_eq:cc
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_show:N, \fp_show:c}
-% \UnitTested
-%   Simple showing of the underlying variable.
-%    \begin{macrocode}
-\cs_new_eq:NN \fp_show:N \tl_show:N
-\cs_new_eq:NN \fp_show:c \tl_show:c
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\fp_use:N, \fp_use:c}
-% \UnitTested
-% \begin{macro}[aux]{\fp_use_aux:w}
-% \begin{macro}[aux]{\fp_use_none:w}
-% \begin{macro}[aux]{\fp_use_small:w}
-% \begin{macro}[aux]{\fp_use_large:w}
-% \begin{macro}[aux]{\fp_use_large_aux_i:w}
-% \begin{macro}[aux]{\fp_use_large_aux_1:w}
-% \begin{macro}[aux]{\fp_use_large_aux_2:w}
-% \begin{macro}[aux]{\fp_use_large_aux_3:w}
-% \begin{macro}[aux]{\fp_use_large_aux_4:w}
-% \begin{macro}[aux]{\fp_use_large_aux_5:w}
-% \begin{macro}[aux]{\fp_use_large_aux_6:w}
-% \begin{macro}[aux]{\fp_use_large_aux_7:w}
-% \begin{macro}[aux]{\fp_use_large_aux_8:w}
-% \begin{macro}[aux]{\fp_use_large_aux_i:w}
-% \begin{macro}[aux]{\fp_use_large_aux_ii:w}
-%   The idea of the \cs{fp_use:N} function to convert the stored
-%   value into something suitable for \TeX{} to use as a number in an
-%   expandable manner. The first step is to deal with the sign, then
-%   work out how big the input is.
-%    \begin{macrocode}
-\cs_new:Npn \fp_use:N #1
-  { \exp_after:wN \fp_use_aux:w #1 \q_stop }
-\cs_generate_variant:Nn \fp_use:N { c }
-\cs_new:Npn \fp_use_aux:w #1#2 e #3 \q_stop
-  {
-    \if:w #1 -
-      -
-    \fi:
-    \if_int_compare:w #3 > \c_zero
-      \exp_after:wN \fp_use_large:w
-    \else:
-      \if_int_compare:w #3 < \c_zero
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \fp_use_small:w
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN \fp_use_none:w
-      \fi:
-    \fi:
-    #2 e #3 \q_stop
-  }
-%    \end{macrocode}
-%   When the exponent is zero, the input is simply returned as output.
-%    \begin{macrocode}
-\cs_new:Npn \fp_use_none:w #1 e #2 \q_stop {#1}
-%    \end{macrocode}
-%   For small numbers (less than $1$) the correct number of zeros
-%   have to be inserted, but the decimal point is easy.
-%    \begin{macrocode}
-\cs_new:Npn \fp_use_small:w #1 . #2 e #3 \q_stop
-  {
-    0 .
-    \prg_replicate:nn { -#3 - 1 } { 0 }
-    #1#2
-  }
-%    \end{macrocode}
-%   Life is more complex for large numbers. The decimal point needs to
-%   be shuffled, with potentially some zero-filling for very large values.
-%    \begin{macrocode}
-\cs_new:Npn \fp_use_large:w #1 . #2 e #3 \q_stop
-  {
-    \if_int_compare:w #3 < \c_ten
-      \exp_after:wN \fp_use_large_aux_i:w
-    \else:
-      \exp_after:wN \fp_use_large_aux_ii:w
-    \fi:
-    #1#2 e #3 \q_stop
-  }
-\cs_new:Npn \fp_use_large_aux_i:w #1#2 e #3 \q_stop
-  {
-    #1
-    \use:c { fp_use_large_aux_ #3 :w } #2 \q_stop
-  }
-\cs_new:cpn { fp_use_large_aux_1:w } #1#2 \q_stop { #1 . #2 }
-\cs_new:cpn { fp_use_large_aux_2:w } #1#2#3 \q_stop
-  { #1#2 . #3 }
-\cs_new:cpn { fp_use_large_aux_3:w } #1#2#3#4 \q_stop
-  { #1#2#3 . #4 }
-\cs_new:cpn { fp_use_large_aux_4:w } #1#2#3#4#5 \q_stop
-  { #1#2#3#4 . #5 }
-\cs_new:cpn { fp_use_large_aux_5:w } #1#2#3#4#5#6 \q_stop
-  { #1#2#3#4#5 . #6 }
-\cs_new:cpn { fp_use_large_aux_6:w } #1#2#3#4#5#6#7 \q_stop
-  { #1#2#3#4#5#6 . #7 }
-\cs_new:cpn { fp_use_large_aux_7:w } #1#2#3#4#5#6#7#8 \q_stop
-  { #1#2#3#4#6#7 . #8 }
-\cs_new:cpn { fp_use_large_aux_8:w } #1#2#3#4#5#6#7#8#9 \q_stop
-  { #1#2#3#4#5#6#7#8 . #9 }
-\cs_new:cpn { fp_use_large_aux_9:w } #1 \q_stop { #1 . }
-\cs_new:Npn \fp_use_large_aux_ii:w #1 e #2 \q_stop
-  {
-    #1
-    \prg_replicate:nn { #2 - 9 } { 0 }
-    .
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[pTF]{\fp_if_exist:N, \fp_if_exist:c}
-%   Copies of the \texttt{cs} functions defined in \pkg{l3basics}.
-%    \begin{macrocode}
-\cs_new_eq:NN \fp_if_exist:NTF \cs_if_exist:NTF
-\cs_new_eq:NN \fp_if_exist:NT  \cs_if_exist:NT
-\cs_new_eq:NN \fp_if_exist:NF  \cs_if_exist:NF
-\cs_new_eq:NN \fp_if_exist_p:N \cs_if_exist_p:N
-\cs_new_eq:NN \fp_if_exist:cTF \cs_if_exist:cTF
-\cs_new_eq:NN \fp_if_exist:cT  \cs_if_exist:cT
-\cs_new_eq:NN \fp_if_exist:cF  \cs_if_exist:cF
-\cs_new_eq:NN \fp_if_exist_p:c \cs_if_exist_p:c
-%    \end{macrocode}
-% \end{macro}
-%
-% \subsection{Transferring to other types}
-%
-% The \cs{fp_use:N} function converts a floating point variable to
-% a form that can be used by \TeX{}. Here, the functions are slightly
-% different, as some information may be discarded.
-%
-% \begin{macro}{\fp_to_dim:N, \fp_to_dim:c}
-%   A very simple wrapper.
-%    \begin{macrocode}
-\cs_new:Npn \fp_to_dim:N #1 { \fp_use:N #1 pt }
-\cs_generate_variant:Nn \fp_to_dim:N { c }
-%    \end{macrocode}
-% \end{macro}
-%
-%
-% \begin{macro}{\fp_to_int:N, \fp_to_int:c}
-% \UnitTested
-% \begin{macro}[aux]{\fp_to_int_aux:w}
-% \begin{macro}[aux]{\fp_to_int_none:w}
-% \begin{macro}[aux]{\fp_to_int_small:w}
-% \begin{macro}[aux]{\fp_to_int_large:w}
-% \begin{macro}[aux]{\fp_to_int_large_aux_i:w}
-% \begin{macro}[aux]{\fp_to_int_large_aux_1:w}
-% \begin{macro}[aux]{\fp_to_int_large_aux_2:w}
-% \begin{macro}[aux]{\fp_to_int_large_aux_3:w}
-% \begin{macro}[aux]{\fp_to_int_large_aux_4:w}
-% \begin{macro}[aux]{\fp_to_int_large_aux_5:w}
-% \begin{macro}[aux]{\fp_to_int_large_aux_6:w}
-% \begin{macro}[aux]{\fp_to_int_large_aux_7:w}
-% \begin{macro}[aux]{\fp_to_int_large_aux_8:w}
-% \begin{macro}[aux]{\fp_to_int_large_aux_i:w}
-% \begin{macro}[aux]{\fp_to_int_large_aux:nnn}
-% \begin{macro}[aux]{\fp_to_int_large_aux_ii:w}
-%   Converting to integers in an expandable manner is very similar to
-%   simply using floating point variables, particularly in the lead-off.
-%    \begin{macrocode}
-\cs_new:Npn \fp_to_int:N #1
-  { \exp_after:wN \fp_to_int_aux:w #1 \q_stop }
-\cs_generate_variant:Nn \fp_to_int:N { c }
-\cs_new:Npn \fp_to_int_aux:w #1#2 e #3 \q_stop
-  {
-    \if:w #1 -
-      -
-    \fi:
-    \if_int_compare:w #3 < \c_zero
-      \exp_after:wN \fp_to_int_small:w
-    \else:
-      \exp_after:wN \fp_to_int_large:w
-    \fi:
-    #2 e #3 \q_stop
-  }
-%    \end{macrocode}
-%   For small numbers, if the decimal part is greater than a half then
-%   there is rounding up to do.
-%    \begin{macrocode}
-\cs_new:Npn \fp_to_int_small:w #1 . #2 e #3 \q_stop
-  {
-    \if_int_compare:w #3 > \c_one
-    \else:
-      \if_int_compare:w #1 < \c_five
-        0
-      \else:
-        1
-      \fi:
-    \fi:
-  }
-%    \end{macrocode}
-% For large numbers, the idea is to split off the part for rounding,
-% do the rounding and fill if needed.
-%    \begin{macrocode}
-\cs_new:Npn \fp_to_int_large:w #1 . #2 e #3 \q_stop
-  {
-    \if_int_compare:w #3 < \c_ten
-      \exp_after:wN \fp_to_int_large_aux_i:w
-    \else:
-      \exp_after:wN \fp_to_int_large_aux_ii:w
-    \fi:
-    #1#2 e #3 \q_stop
-  }
-\cs_new:Npn \fp_to_int_large_aux_i:w #1#2 e #3 \q_stop
-  { \use:c { fp_to_int_large_aux_ #3 :w } #2 \q_stop {#1} }
-\cs_new:cpn { fp_to_int_large_aux_1:w } #1#2 \q_stop
-  { \fp_to_int_large_aux:nnn { #2 0 } {#1} }
-\cs_new:cpn { fp_to_int_large_aux_2:w } #1#2#3 \q_stop
-  { \fp_to_int_large_aux:nnn { #3 00 } {#1#2} }
-\cs_new:cpn { fp_to_int_large_aux_3:w } #1#2#3#4 \q_stop
-  { \fp_to_int_large_aux:nnn { #4 000 } {#1#2#3} }
-\cs_new:cpn { fp_to_int_large_aux_4:w } #1#2#3#4#5 \q_stop
-  { \fp_to_int_large_aux:nnn { #5 0000 } {#1#2#3#4} }
-\cs_new:cpn { fp_to_int_large_aux_5:w } #1#2#3#4#5#6 \q_stop
-  { \fp_to_int_large_aux:nnn { #6 00000 } {#1#2#3#4#5} }
-\cs_new:cpn { fp_to_int_large_aux_6:w } #1#2#3#4#5#6#7 \q_stop
-  { \fp_to_int_large_aux:nnn { #7 000000 } {#1#2#3#4#5#6} }
-\cs_new:cpn { fp_to_int_large_aux_7:w } #1#2#3#4#5#6#7#8 \q_stop
-  { \fp_to_int_large_aux:nnn { #8 0000000 } {#1#2#3#4#5#6#7} }
-\cs_new:cpn { fp_to_int_large_aux_8:w } #1#2#3#4#5#6#7#8#9 \q_stop
-  { \fp_to_int_large_aux:nnn { #9 00000000 } {#1#2#3#4#5#6#7#8} }
-\cs_new:cpn { fp_to_int_large_aux_9:w } #1 \q_stop {#1}
-\cs_new:Npn \fp_to_int_large_aux:nnn #1#2#3
-  {
-    \if_int_compare:w #1 < \c_five_hundred_million
-      #3#2
-    \else:
-      \int_value:w \int_eval:w #3#2 + 1 \int_eval_end:
-    \fi:
-  }
-\cs_new:Npn \fp_to_int_large_aux_ii:w #1 e #2 \q_stop
-  {
-    #1
-    \prg_replicate:nn { #2 - 9 } { 0 }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_to_tl:N, \fp_to_tl:c}
-% \UnitTested
-% \begin{macro}[aux]{\fp_to_tl_aux:w}
-% \begin{macro}[aux]{\fp_to_tl_large:w}
-% \begin{macro}[aux]{\fp_to_tl_large_aux_i:w}
-% \begin{macro}[aux]{\fp_to_tl_large_aux_ii:w}
-% \begin{macro}[aux]{\fp_to_tl_large_0:w}
-% \begin{macro}[aux]{\fp_to_tl_large_1:w}
-% \begin{macro}[aux]{\fp_to_tl_large_2:w}
-% \begin{macro}[aux]{\fp_to_tl_large_3:w}
-% \begin{macro}[aux]{\fp_to_tl_large_4:w}
-% \begin{macro}[aux]{\fp_to_tl_large_5:w}
-% \begin{macro}[aux]{\fp_to_tl_large_6:w}
-% \begin{macro}[aux]{\fp_to_tl_large_7:w}
-% \begin{macro}[aux]{\fp_to_tl_large_8:w}
-% \begin{macro}[aux]{\fp_to_tl_large_8_aux:w}
-% \begin{macro}[aux]{\fp_to_tl_large_9:w}
-% \begin{macro}[aux]{\fp_to_tl_small:w}
-% \begin{macro}[aux]{\fp_to_tl_small_one:w}
-% \begin{macro}[aux]{\fp_to_tl_small_two:w}
-% \begin{macro}[aux]{\fp_to_tl_small_aux:w}
-% \begin{macro}[aux]{\fp_to_tl_large_zeros:NNNNNNNNN}
-% \begin{macro}[aux]{\fp_to_tl_small_zeros:NNNNNNNNN}
-% \begin{macro}[aux]{\fp_use_iix_ix:NNNNNNNNN}
-% \begin{macro}[aux]{\fp_use_ix:NNNNNNNNN}
-% \begin{macro}[aux]{\fp_use_i_to_vii:NNNNNNNNN}
-% \begin{macro}[aux]{\fp_use_i_to_iix:NNNNNNNNN}
-%   Converting to integers in an expandable manner is very similar to
-%   simply using floating point variables, particularly in the lead-off.
-%    \begin{macrocode}
-\cs_new:Npn \fp_to_tl:N #1
-  { \exp_after:wN \fp_to_tl_aux:w #1 \q_stop }
-\cs_generate_variant:Nn \fp_to_tl:N { c }
-\cs_new:Npn \fp_to_tl_aux:w #1#2 e #3 \q_stop
-  {
-    \if:w #1 -
-      -
-    \fi:
-    \if_int_compare:w #3 < \c_zero
-      \exp_after:wN \fp_to_tl_small:w
-    \else:
-      \exp_after:wN \fp_to_tl_large:w
-    \fi:
-    #2 e #3 \q_stop
-  }
-%    \end{macrocode}
-%   For \enquote{large} numbers (exponent $\ge 0$) there are two
-%   cases. For very large exponents ($ \ge 10 $) life is easy: apart
-%   from dropping extra zeros there is no work to do. On the other hand,
-%   for intermediate exponent values the decimal needs to be moved, then
-%   zeros can be dropped.
-%    \begin{macrocode}
-\cs_new:Npn \fp_to_tl_large:w #1 e #2 \q_stop
-  {
-    \if_int_compare:w #2 < \c_ten
-      \exp_after:wN \fp_to_tl_large_aux_i:w
-    \else:
-      \exp_after:wN \fp_to_tl_large_aux_ii:w
-    \fi:
-    #1 e #2 \q_stop
-  }
-\cs_new:Npn \fp_to_tl_large_aux_i:w #1 e #2 \q_stop
-  { \use:c { fp_to_tl_large_ #2 :w } #1 \q_stop }
-\cs_new:Npn \fp_to_tl_large_aux_ii:w #1 . #2 e #3 \q_stop
-  {
-    #1
-    \fp_to_tl_large_zeros:NNNNNNNNN #2
-    e #3
-  }
-\cs_new:cpn { fp_to_tl_large_0:w } #1 . #2 \q_stop
-  {
-    #1
-    \fp_to_tl_large_zeros:NNNNNNNNN #2
-  }
-\cs_new:cpn { fp_to_tl_large_1:w } #1 . #2#3 \q_stop
-  {
-    #1#2
-    \fp_to_tl_large_zeros:NNNNNNNNN #3 0
-  }
-\cs_new:cpn { fp_to_tl_large_2:w } #1 . #2#3#4 \q_stop
-  {
-    #1#2#3
-    \fp_to_tl_large_zeros:NNNNNNNNN #4 00
-  }
-\cs_new:cpn { fp_to_tl_large_3:w } #1 . #2#3#4#5 \q_stop
-  {
-    #1#2#3#4
-    \fp_to_tl_large_zeros:NNNNNNNNN #5 000
-  }
-\cs_new:cpn { fp_to_tl_large_4:w } #1 . #2#3#4#5#6 \q_stop
-  {
-    #1#2#3#4#5
-    \fp_to_tl_large_zeros:NNNNNNNNN #6 0000
-  }
-\cs_new:cpn { fp_to_tl_large_5:w } #1 . #2#3#4#5#6#7 \q_stop
-  {
-    #1#2#3#4#5#6
-    \fp_to_tl_large_zeros:NNNNNNNNN #7 00000
-  }
-\cs_new:cpn { fp_to_tl_large_6:w } #1 . #2#3#4#5#6#7#8 \q_stop
-  {
-    #1#2#3#4#5#6#7
-    \fp_to_tl_large_zeros:NNNNNNNNN #8 000000
-  }
-\cs_new:cpn { fp_to_tl_large_7:w } #1 . #2#3#4#5#6#7#8#9 \q_stop
-  {
-    #1#2#3#4#5#6#7#8
-    \fp_to_tl_large_zeros:NNNNNNNNN #9 0000000
-  }
-\cs_new:cpn { fp_to_tl_large_8:w } #1 .
-  {
-    #1
-    \use:c { fp_to_tl_large_8_aux:w }
-  }
-\cs_new:cpn { fp_to_tl_large_8_aux:w } #1#2#3#4#5#6#7#8#9 \q_stop
-  {
-    #1#2#3#4#5#6#7#8
-    \fp_to_tl_large_zeros:NNNNNNNNN #9 00000000
-  }
-\cs_new:cpn { fp_to_tl_large_9:w } #1 . #2 \q_stop {#1#2}
-%    \end{macrocode}
-%   Dealing with small numbers is a bit more complex as there has to be
-%   rounding. This makes life rather awkward, as there need to be a series
-%   of tests and calculations, as things cannot be stored in an
-%   expandable system.
-%    \begin{macrocode}
-\cs_new:Npn \fp_to_tl_small:w #1 e #2 \q_stop
-  {
-    \if_int_compare:w #2 = \c_minus_one
-      \exp_after:wN \fp_to_tl_small_one:w
-    \else:
-      \if_int_compare:w #2 = -\c_two
-        \exp_after:wN \exp_after:wN \exp_after:wN \fp_to_tl_small_two:w
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN \fp_to_tl_small_aux:w
-      \fi:
-    \fi:
-    #1 e #2 \q_stop
-  }
-\cs_new:Npn \fp_to_tl_small_one:w #1 . #2 e #3 \q_stop
-  {
-    \if_int_compare:w \fp_use_ix:NNNNNNNNN #2 > \c_four
-      \if_int_compare:w
-        \int_eval:w #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
-          < \c_one_thousand_million
-        0.
-        \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN
-          \int_value:w \int_eval:w
-              #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
-            \int_eval_end:
-      \else:
-        1
-      \fi:
-    \else:
-      0. #1
-      \fp_to_tl_small_zeros:NNNNNNNNN #2
-    \fi:
-  }
-\cs_new:Npn \fp_to_tl_small_two:w #1 . #2 e #3 \q_stop
-  {
-    \if_int_compare:w \fp_use_iix_ix:NNNNNNNNN #2 > \c_forty_four
-      \if_int_compare:w
-        \int_eval:w #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
-          < \c_one_thousand_million
-        0.0
-        \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN
-          \int_value:w \int_eval:w
-              #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
-            \int_eval_end:
-      \else:
-        0.1
-      \fi:
-    \else:
-      0.0
-      #1
-      \fp_to_tl_small_zeros:NNNNNNNNN #2
-    \fi:
-  }
-\cs_new:Npn \fp_to_tl_small_aux:w #1 . #2 e #3 \q_stop
-  {
-    #1
-    \fp_to_tl_large_zeros:NNNNNNNNN #2
-    e #3
-  }
-%    \end{macrocode}
-%   Rather than a complex recursion, the tests for finding trailing zeros
-%   are written out long-hand.  The difference between the two is only the
-%   need for a decimal marker.
-%    \begin{macrocode}
-\cs_new:Npn \fp_to_tl_large_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {
-    \if_int_compare:w #9 = \c_zero
-      \if_int_compare:w #8 = \c_zero
-        \if_int_compare:w #7 = \c_zero
-          \if_int_compare:w #6 = \c_zero
-            \if_int_compare:w #5 = \c_zero
-              \if_int_compare:w #4 = \c_zero
-                \if_int_compare:w #3 = \c_zero
-                  \if_int_compare:w #2 = \c_zero
-                    \if_int_compare:w #1 = \c_zero
-                    \else:
-                      . #1
-                    \fi:
-                  \else:
-                    . #1#2
-                  \fi:
-                \else:
-                  . #1#2#3
-                \fi:
-              \else:
-                . #1#2#3#4
-              \fi:
-            \else:
-              . #1#2#3#4#5
-            \fi:
-          \else:
-            . #1#2#3#4#5#6
-          \fi:
-        \else:
-          . #1#2#3#4#5#6#7
-        \fi:
-      \else:
-         . #1#2#3#4#5#6#7#8
-      \fi:
-    \else:
-      . #1#2#3#4#5#6#7#8#9
-    \fi:
-  }
-\cs_new:Npn \fp_to_tl_small_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {
-    \if_int_compare:w #9 = \c_zero
-      \if_int_compare:w #8 = \c_zero
-        \if_int_compare:w #7 = \c_zero
-          \if_int_compare:w #6 = \c_zero
-            \if_int_compare:w #5 = \c_zero
-              \if_int_compare:w #4 = \c_zero
-                \if_int_compare:w #3 = \c_zero
-                  \if_int_compare:w #2 = \c_zero
-                    \if_int_compare:w #1 = \c_zero
-                    \else:
-                      #1
-                    \fi:
-                  \else:
-                    #1#2
-                  \fi:
-                \else:
-                  #1#2#3
-                \fi:
-              \else:
-                #1#2#3#4
-              \fi:
-            \else:
-              #1#2#3#4#5
-            \fi:
-          \else:
-            #1#2#3#4#5#6
-          \fi:
-        \else:
-          #1#2#3#4#5#6#7
-        \fi:
-      \else:
-         #1#2#3#4#5#6#7#8
-      \fi:
-    \else:
-      #1#2#3#4#5#6#7#8#9
-    \fi:
-  }
-%    \end{macrocode}
-%   Some quick \enquote{return a few} functions.
-%    \begin{macrocode}
-\cs_new:Npn \fp_use_iix_ix:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {#8#9}
-\cs_new:Npn \fp_use_ix:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {#9}
-\cs_new:Npn \fp_use_i_to_vii:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {#1#2#3#4#5#6#7}
-\cs_new:Npn \fp_use_i_to_iix:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {#1#2#3#4#5#6#7#8}
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Rounding numbers}
-%
-% The results may well need to be rounded. A couple of related functions
-% to do this for a stored value.
-%
-% \begin{macro}{\fp_round_figures:Nn,  \fp_round_figures:cn}
-% \UnitTested
-% \begin{macro}{\fp_ground_figures:Nn, \fp_ground_figures:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_round_figures_aux:NNn}
-%   Rounding to figures needs only an adjustment to the target by one
-%   (as the target is in decimal places).
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_round_figures:Nn
-  { \fp_round_figures_aux:NNn \tl_set:Nn }
-\cs_generate_variant:Nn \fp_round_figures:Nn { c }
-\cs_new_protected_nopar:Npn \fp_ground_figures:Nn
-  { \fp_round_figures_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_ground_figures:Nn { c }
-\cs_new_protected:Npn \fp_round_figures_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_read:N #2
-      \int_set:Nn \l_fp_round_target_int { #3 - 1 }
-      \if_int_compare:w \l_fp_round_target_int < \c_ten
-        \exp_after:wN \fp_round:
-      \fi:
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-                -
-              \else:
-                +
-              \fi:
-              \int_use:N \l_fp_input_a_integer_int
-              .
-              \exp_after:wN \use_none:n
-                \int_use:N \l_fp_input_a_decimal_int
-              e
-              \int_use:N \l_fp_input_a_exponent_int
-            }
-        }
-    \fp_tmp:w
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_round_places:Nn,  \fp_round_places:cn}
-% \UnitTested
-% \begin{macro}{\fp_ground_places:Nn, \fp_ground_places:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_round_places_aux:NNn}
-%   Rounding to places needs an adjustment for the exponent value, which
-%   will mean that everything should be correct.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_round_places:Nn
-  { \fp_round_places_aux:NNn \tl_set:Nn }
-\cs_generate_variant:Nn \fp_round_places:Nn { c }
-\cs_new_protected_nopar:Npn \fp_ground_places:Nn
-  { \fp_round_places_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_ground_places:Nn { c }
-\cs_new_protected:Npn \fp_round_places_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_read:N #2
-      \int_set:Nn \l_fp_round_target_int
-        { #3 + \l_fp_input_a_exponent_int }
-      \if_int_compare:w \l_fp_round_target_int < \c_ten
-        \exp_after:wN \fp_round:
-      \fi:
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-                -
-              \else:
-                +
-              \fi:
-              \int_use:N \l_fp_input_a_integer_int
-              .
-              \exp_after:wN \use_none:n
-                \int_use:N \l_fp_input_a_decimal_int
-              e
-              \int_use:N \l_fp_input_a_exponent_int
-            }
-        }
-    \fp_tmp:w
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_round:}
-% \begin{macro}[aux]{\fp_round_aux:NNNNNNNNN}
-% \begin{macro}{\fp_round_loop:N}
-%   The rounding approach is the same for decimal places and significant
-%   figures. There are always nine decimal digits to round, so the code
-%   can be written to account for this. The basic logic is simply to
-%   find the rounding, track any carry digit and move along. At the end
-%   of the loop there is a possible shuffle if the integer part has
-%   become $10$.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_round:
-  {
-    \bool_set_false:N \l_fp_round_carry_bool
-    \l_fp_round_position_int \c_eight
-    \tl_clear:N \l_fp_round_decimal_tl
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \exp_after:wN \use_i:nn \exp_after:wN
-      \fp_round_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int
-  }
-\cs_new_protected:Npn \fp_round_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {
-    \fp_round_loop:N #9#8#7#6#5#4#3#2#1
-    \bool_if:NT \l_fp_round_carry_bool
-      { \tex_advance:D \l_fp_input_a_integer_int \c_one }
-    \l_fp_input_a_decimal_int \l_fp_round_decimal_tl \scan_stop:
-    \if_int_compare:w \l_fp_input_a_integer_int < \c_ten
-    \else:
-      \l_fp_input_a_integer_int \c_one
-      \tex_divide:D \l_fp_input_a_decimal_int \c_ten
-      \tex_advance:D \l_fp_input_a_exponent_int \c_one
-    \fi:
-  }
-\cs_new_protected:Npn \fp_round_loop:N #1
-  {
-    \if_int_compare:w \l_fp_round_position_int < \l_fp_round_target_int
-      \bool_if:NTF \l_fp_round_carry_bool
-        { \l_fp_internal_int \int_eval:w #1 + \c_one \scan_stop: }
-        { \l_fp_internal_int \int_eval:w #1 \scan_stop: }
-      \if_int_compare:w \l_fp_internal_int = \c_ten
-        \l_fp_internal_int \c_zero
-      \else:
-        \bool_set_false:N \l_fp_round_carry_bool
-      \fi:
-      \tl_set:Nx \l_fp_round_decimal_tl
-        { \int_use:N \l_fp_internal_int \l_fp_round_decimal_tl }
-    \else:
-      \tl_set:Nx \l_fp_round_decimal_tl { 0 \l_fp_round_decimal_tl }
-      \if_int_compare:w \l_fp_round_position_int = \l_fp_round_target_int
-        \if_int_compare:w #1 > \c_four
-          \bool_set_true:N \l_fp_round_carry_bool
-        \fi:
-      \fi:
-    \fi:
-    \tex_advance:D \l_fp_round_position_int \c_minus_one
-    \if_int_compare:w \l_fp_round_position_int > \c_minus_one
-      \exp_after:wN \fp_round_loop:N
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Unary functions}
-%
-% \begin{macro}{\fp_abs:N,  \fp_abs:c}
-% \UnitTested
-% \begin{macro}{\fp_gabs:N, \fp_gabs:c}
-% \UnitTested
-% \begin{macro}[aux]{\fp_abs_aux:NN}
-%   Setting the absolute value is easy: read the value, ignore the sign,
-%   return the result.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_abs:N  { \fp_abs_aux:NN \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gabs:N { \fp_abs_aux:NN \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_abs:N  { c }
-\cs_generate_variant:Nn \fp_gabs:N { c }
-\cs_new_protected:Npn \fp_abs_aux:NN #1#2
-  {
-    \group_begin:
-      \fp_read:N #2
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              +
-              \int_use:N \l_fp_input_a_integer_int
-              .
-              \exp_after:wN \use_none:n
-                \int_use:N \l_fp_input_a_decimal_int
-              e
-              \int_use:N \l_fp_input_a_exponent_int
-            }
-        }
-    \fp_tmp:w
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_neg:N,  \fp_neg:c}
-% \UnitTested
-% \begin{macro}{\fp_gneg:N, \fp_gneg:c}
-% \UnitTested
-% \begin{macro}[aux]{\fp_neg:NN}
-% Just a bit more complex: read the input, reverse the sign and
-% output the result.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_neg:N  { \fp_neg_aux:NN \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gneg:N { \fp_neg_aux:NN \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_neg:N  { c }
-\cs_generate_variant:Nn \fp_gneg:N { c }
-\cs_new_protected:Npn \fp_neg_aux:NN #1#2
-  {
-    \group_begin:
-      \fp_read:N #2
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-            +
-          \else:
-            -
-          \fi:
-          \int_use:N \l_fp_input_a_integer_int
-          .
-          \exp_after:wN \use_none:n
-            \int_use:N \l_fp_input_a_decimal_int
-          e
-          \int_use:N \l_fp_input_a_exponent_int
-        }
-    \exp_after:wN \group_end: \exp_after:wN
-    #1 \exp_after:wN #2 \exp_after:wN { \l_fp_internal_tl }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Basic arithmetic}
-%
-% \begin{macro}{\fp_add:Nn, \fp_add:cn}
-% \UnitTested
-% \begin{macro}{\fp_gadd:Nn,\fp_gadd:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_add_aux:NNn}
-% \begin{macro}[aux]{\fp_add_core:}
-% \begin{macro}[aux]{\fp_add_sum:}
-% \begin{macro}[aux]{\fp_add_difference:}
-%   The various addition functions are simply different ways to call the
-%   single master function below. This pattern is repeated for the
-%   other arithmetic functions.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_add:Nn  { \fp_add_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gadd:Nn { \fp_add_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_add:Nn   { c }
-\cs_generate_variant:Nn \fp_gadd:Nn  { c }
-%    \end{macrocode}
-% Addition takes place using one of two paths. If the signs of the
-% two parts are the same, they are simply combined. On the other
-% hand, if the signs are different the calculation finds this
-% difference.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_add_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_read:N #2
-      \fp_split:Nn b {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_b_sign_int
-        \l_fp_input_b_integer_int
-        \l_fp_input_b_decimal_int
-        \l_fp_input_b_exponent_int
-      \fp_add_core:
-    \fp_tmp:w #1#2
-  }
-\cs_new_protected_nopar:Npn \fp_add_core:
-  {
-    \fp_level_input_exponents:
-    \if_int_compare:w
-      \int_eval:w
-        \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
-        > \c_zero
-      \exp_after:wN \fp_add_sum:
-    \else:
-      \exp_after:wN \fp_add_difference:
-    \fi:
-    \l_fp_output_exponent_int \l_fp_input_a_exponent_int
-    \fp_standardise:NNNN
-      \l_fp_output_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \cs_set_protected:Npx \fp_tmp:w ##1##2
-      {
-        \group_end:
-        ##1 ##2
-          {
-             \if_int_compare:w \l_fp_output_sign_int < \c_zero
-              -
-            \else:
-              +
-            \fi:
-            \int_use:N \l_fp_output_integer_int
-            .
-            \exp_after:wN \use_none:n
-              \int_value:w \int_eval:w
-                 \l_fp_output_decimal_int + \c_one_thousand_million
-            e
-            \int_use:N \l_fp_output_exponent_int
-          }
-      }
-  }
-%    \end{macrocode}
-%   Finding the sum of two numbers is trivially easy.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_add_sum:
-  {
-    \l_fp_output_sign_int \l_fp_input_a_sign_int
-    \l_fp_output_integer_int
-      \int_eval:w
-        \l_fp_input_a_integer_int + \l_fp_input_b_integer_int
-      \scan_stop:
-    \l_fp_output_decimal_int
-      \int_eval:w
-        \l_fp_input_a_decimal_int + \l_fp_input_b_decimal_int
-      \scan_stop:
-    \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
-    \else:
-      \tex_advance:D \l_fp_output_integer_int \c_one
-      \tex_advance:D \l_fp_output_decimal_int -\c_one_thousand_million
-    \fi:
-  }
-%    \end{macrocode}
-%   When the signs of the two parts of the input are different, the
-%   absolute difference is worked out first. There is then a calculation
-%   to see which way around everything has worked out, so that the final
-%   sign is correct. The difference might also give a zero result with
-%   a negative sign, which is reversed as zero is regarded as positive.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_add_difference:
-  {
-    \l_fp_output_integer_int
-      \int_eval:w
-        \l_fp_input_a_integer_int - \l_fp_input_b_integer_int
-      \scan_stop:
-    \l_fp_output_decimal_int
-      \int_eval:w
-        \l_fp_input_a_decimal_int - \l_fp_input_b_decimal_int
-      \scan_stop:
-    \if_int_compare:w \l_fp_output_decimal_int < \c_zero
-      \tex_advance:D \l_fp_output_integer_int \c_minus_one
-      \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
-    \fi:
-    \if_int_compare:w \l_fp_output_integer_int < \c_zero
-      \l_fp_output_sign_int \l_fp_input_b_sign_int
-      \if_int_compare:w \l_fp_output_decimal_int = \c_zero
-        \l_fp_output_integer_int -\l_fp_output_integer_int
-      \else:
-        \l_fp_output_decimal_int
-          \int_eval:w
-            \c_one_thousand_million - \l_fp_output_decimal_int
-          \scan_stop:
-        \l_fp_output_integer_int
-           \int_eval:w
-             - \l_fp_output_integer_int - \c_one
-           \scan_stop:
-      \fi:
-    \else:
-      \l_fp_output_sign_int \l_fp_input_a_sign_int
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
+% \begin{function}[EXP, added = 2012-05-08]{\dim_to_fp:n}
+%   \begin{syntax}
+%     \cs{dim_to_fp:n} \Arg{dimexpr}
+%   \end{syntax}
+%   Expands to an internal floating point number equal to the value of
+%   the \meta{dimexpr} in \texttt{pt}.
+% \end{function}
 %
-% \begin{macro}{\fp_sub:Nn, \fp_sub:cn}
-% \UnitTested
-% \begin{macro}{\fp_gsub:Nn,\fp_gsub:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_sub_aux:NNn}
-%   Subtraction is essentially the same as addition, but with the sign
-%   of the second component reversed. Thus the core of the two function
-%   groups is the same, with just a little set up here.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_sub:Nn  { \fp_sub_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gsub:Nn { \fp_sub_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_sub:Nn   { c }
-\cs_generate_variant:Nn \fp_gsub:Nn  { c }
-\cs_new_protected:Npn \fp_sub_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_read:N #2
-      \fp_split:Nn b {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_b_sign_int
-        \l_fp_input_b_integer_int
-        \l_fp_input_b_decimal_int
-        \l_fp_input_b_exponent_int
-      \tex_multiply:D \l_fp_input_b_sign_int \c_minus_one
-      \fp_add_core:
-    \fp_tmp:w #1#2
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
+% \begin{function}[EXP, added = 2012-05-14, updated = 2012-07-08]{\fp_abs:n}
+%   \begin{syntax}
+%     \cs{fp_abs:n} \Arg{floating point expression}
+%   \end{syntax}
+%   Evaluates the \meta{floating point expression} as described for
+%   \cs{fp_eval:n} and leaves the absolute value of the result in
+%   the input stream.
+% \end{function}
 %
-% \begin{macro}{\fp_mul:Nn, \fp_mul:cn}
-% \UnitTested
-% \begin{macro}{\fp_gmul:Nn,\fp_gmul:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_mul_aux:NNn}
-% \begin{macro}[aux]{\fp_mul_internal:}
-% \begin{macro}[aux]{\fp_mul_split:NNNN}
-% \begin{macro}[aux]{\fp_mul_split:w}
-% \begin{macro}[aux]{\fp_mul_end_level:}
-% \begin{macro}[aux]{\fp_mul_end_level:NNNNNNNNN}
-%   The pattern is much the same for multiplication.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_mul:Nn  { \fp_mul_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gmul:Nn { \fp_mul_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_mul:Nn  { c }
-\cs_generate_variant:Nn \fp_gmul:Nn { c }
-%    \end{macrocode}
-%   The approach to multiplication is as follows. First, the two numbers
-%   are split into blocks of three digits. These are then multiplied
-%   together to find products for each group of three output digits. This
-%   is al written out in full for speed reasons. Between each block of
-%   three digits in the output, there is a carry step. The very lowest
-%   digits are not calculated, while
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_mul_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_read:N #2
-      \fp_split:Nn b {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_b_sign_int
-        \l_fp_input_b_integer_int
-        \l_fp_input_b_decimal_int
-        \l_fp_input_b_exponent_int
-      \fp_mul_internal:
-      \l_fp_output_exponent_int
-        \int_eval:w
-          \l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int
-        \scan_stop:
-      \fp_standardise:NNNN
-        \l_fp_output_sign_int
-        \l_fp_output_integer_int
-        \l_fp_output_decimal_int
-        \l_fp_output_exponent_int
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              \if_int_compare:w
-                \int_eval:w
-                  \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
-                  < \c_zero
-                \if_int_compare:w
-                  \int_eval:w
-                    \l_fp_output_integer_int + \l_fp_output_decimal_int
-                    = \c_zero
-                  +
-                \else:
-                  -
-                \fi:
-              \else:
-                +
-             \fi:
-              \int_use:N \l_fp_output_integer_int
-              .
-              \exp_after:wN \use_none:n
-                \int_value:w \int_eval:w
-                   \l_fp_output_decimal_int + \c_one_thousand_million
-              e
-              \int_use:N \l_fp_output_exponent_int
-            }
-        }
-    \fp_tmp:w
-  }
-%    \end{macrocode}
-%   Done separately so that the internal use is a bit easier.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_mul_internal:
-  {
-    \fp_mul_split:NNNN \l_fp_input_a_decimal_int
-      \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
-    \fp_mul_split:NNNN \l_fp_input_b_decimal_int
-      \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
-    \l_fp_mul_output_int \c_zero
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_mul_b_i_int
-    \tex_divide:D \l_fp_mul_output_int \c_one_thousand
-    \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_input_b_integer_int
-    \fp_mul_end_level:
-    \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_input_b_integer_int
-    \fp_mul_end_level:
-    \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_input_b_integer_int
-    \fp_mul_end_level:
-    \l_fp_output_decimal_int 0 \l_fp_mul_output_tl \scan_stop:
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_input_b_integer_int
-    \fp_mul_end_level:
-    \l_fp_output_integer_int 0 \l_fp_mul_output_tl \scan_stop:
-  }
-%    \end{macrocode}
-%   The split works by making a $10$ digit number, from which
-%   the first digit can then be dropped using a delimited argument. The
-%   groups of three digits are then assigned to the various parts of
-%   the input: notice that |##9| contains the last two digits of the
-%   smallest part of the input.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_mul_split:NNNN #1#2#3#4
-  {
-    \tex_advance:D #1 \c_one_thousand_million
-    \cs_set_protected:Npn \fp_mul_split_aux:w
-       ##1##2##3##4##5##6##7##8##9 \q_stop {
-        #2 ##2##3##4 \scan_stop:
-        #3 ##5##6##7 \scan_stop:
-        #4 ##8##9    \scan_stop:
-      }
-    \exp_after:wN \fp_mul_split_aux:w \int_use:N #1 \q_stop
-    \tex_advance:D #1 -\c_one_thousand_million
-  }
-\cs_new_protected:Npn \fp_mul_product:NN #1#2
-  {
-    \l_fp_mul_output_int
-      \int_eval:w \l_fp_mul_output_int + #1 * #2 \scan_stop:
-  }
-%    \end{macrocode}
-%   At the end of each output group of three, there is a transfer of
-%   information so that there is no danger of an overflow. This is done by
-%   expansion to keep the number of calculations down.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_mul_end_level:
-  {
-    \tex_advance:D \l_fp_mul_output_int \c_one_thousand_million
-    \exp_after:wN \use_i:nn \exp_after:wN
-      \fp_mul_end_level:NNNNNNNNN \int_use:N \l_fp_mul_output_int
-  }
-\cs_new_protected:Npn \fp_mul_end_level:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {
-    \tl_set:Nx \l_fp_mul_output_tl { #7#8#9 \l_fp_mul_output_tl }
-    \l_fp_mul_output_int #1#2#3#4#5#6 \scan_stop:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
+% ^^A todo
+% ^^A \section{Rounding}
+% ^^A
+% ^^A This explains how to go from a floating point number to a
+% ^^A rounded value for various applications. Perhaps worth coding
+% ^^A functionalities up to what siunitx can do on this matter.
 %
-% \begin{macro}{\fp_div:Nn, \fp_div:cn}
-% \UnitTested
-% \begin{macro}{\fp_gdiv:Nn,\fp_gdiv:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_div_aux:NNn}
-% \begin{macro}{\fp_div_internal:}
-% \begin{macro}[aux]{\fp_div_loop:}
-% \begin{macro}[aux]{\fp_div_divide:}
-% \begin{macro}[aux]{\fp_div_divide_aux:}
-% \begin{macro}[aux]{\fp_div_store:}
-% \begin{macro}[aux]{\fp_div_store_integer:}
-% \begin{macro}[aux]{\fp_div_store_decimal:}
-%   The pattern is much the same for multiplication.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_div:Nn  { \fp_div_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gdiv:Nn { \fp_div_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_div:Nn  { c }
-\cs_generate_variant:Nn \fp_gdiv:Nn { c }
-%    \end{macrocode}
-%   Division proper starts with a couple of tests. If the denominator is
-%   zero then a error is issued. On the other hand, if the numerator is
-%   zero then the result must be $0.0$ and can be given with no
-%   further work.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_div_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_read:N #2
-      \fp_split:Nn b {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_b_sign_int
-        \l_fp_input_b_integer_int
-        \l_fp_input_b_decimal_int
-        \l_fp_input_b_exponent_int
-      \if_int_compare:w
-        \int_eval:w
-          \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
-          = \c_zero
-        \cs_set_protected:Npx \fp_tmp:w ##1##2
-          {
-            \group_end:
-            #1 \exp_not:N #2 { \c_undefined_fp }
-          }
-      \else:
-        \if_int_compare:w
-          \int_eval:w
-            \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-            = \c_zero
-          \cs_set_protected:Npx \fp_tmp:w ##1##2
-            {
-              \group_end:
-              #1 \exp_not:N #2 { \c_zero_fp }
-            }
-        \else:
-          \exp_after:wN \exp_after:wN \exp_after:wN \fp_div_internal:
-        \fi:
-      \fi:
-    \fp_tmp:w #1#2
-  }
-%    \end{macrocode}
-%   The main division algorithm works by finding how many times |b| can
-%   be removed from |a|, storing the result and doing the subtraction.
-%   Input |a| is then multiplied by $10$, and the process is repeated.
-%   The looping ends either when there is nothing left of |a|
-%   (\emph{i.e.}~an exact result) or when the code reaches the ninth
-%   decimal place. Most of the process takes place in the loop function
-%   below.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_div_internal: {
-  \l_fp_output_integer_int \c_zero
-  \l_fp_output_decimal_int \c_zero
-  \cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
-  \l_fp_div_offset_int \c_one_hundred_million
-  \fp_div_loop:
-  \l_fp_output_exponent_int
-    \int_eval:w
-      \l_fp_input_a_exponent_int - \l_fp_input_b_exponent_int
-    \scan_stop:
-  \fp_standardise:NNNN
-    \l_fp_output_sign_int
-    \l_fp_output_integer_int
-    \l_fp_output_decimal_int
-    \l_fp_output_exponent_int
-  \cs_set_protected:Npx \fp_tmp:w ##1##2
-    {
-      \group_end:
-      ##1 ##2
-        {
-          \if_int_compare:w
-            \int_eval:w
-              \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
-              < \c_zero
-            \if_int_compare:w
-              \int_eval:w
-                \l_fp_output_integer_int + \l_fp_output_decimal_int
-                = \c_zero
-              +
-            \else:
-              -
-            \fi:
-          \else:
-            +
-          \fi:
-          \int_use:N \l_fp_output_integer_int
-          .
-          \exp_after:wN \use_none:n
-            \int_value:w \int_eval:w
-               \l_fp_output_decimal_int + \c_one_thousand_million
-             \int_eval_end:
-          e
-          \int_use:N \l_fp_output_exponent_int
-        }
-    }
-}
-%    \end{macrocode}
-%   The main loop implements the approach described above. The storing
-%   function is done as a function so that the integer and decimal parts
-%   can be done separately but rapidly.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_div_loop:
-  {
-    \l_fp_count_int \c_zero
-    \fp_div_divide:
-    \fp_div_store:
-    \tex_multiply:D \l_fp_input_a_integer_int \c_ten
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \exp_after:wN \fp_div_loop_step:w
-      \int_use:N \l_fp_input_a_decimal_int \q_stop
-    \if_int_compare:w
-      \int_eval:w \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-        > \c_zero
-        \if_int_compare:w \l_fp_div_offset_int > \c_zero
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \fp_div_loop:
-        \fi:
-    \fi:
-  }
-%    \end{macrocode}
-%   Checking to see if the numerator can be divides needs quite an
-%   involved check. Either the integer part has to be bigger for the
-%   numerator or, if it is not smaller then the decimal part of the
-%   numerator must not be smaller than that of the denominator. Once
-%   the test is right the rest is much as elsewhere.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_div_divide:
-  {
-    \if_int_compare:w \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
-      \exp_after:wN \fp_div_divide_aux:
-    \else:
-      \if_int_compare:w \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
-      \else:
-        \if_int_compare:w
-          \l_fp_input_a_decimal_int < \l_fp_input_b_decimal_int
-        \else:
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \fp_div_divide_aux:
-        \fi:
-      \fi:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_div_divide_aux:
-  {
-    \tex_advance:D \l_fp_count_int \c_one
-    \tex_advance:D \l_fp_input_a_integer_int -\l_fp_input_b_integer_int
-    \tex_advance:D \l_fp_input_a_decimal_int -\l_fp_input_b_decimal_int
-    \if_int_compare:w \l_fp_input_a_decimal_int < \c_zero
-      \tex_advance:D \l_fp_input_a_integer_int \c_minus_one
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \fi:
-    \fp_div_divide:
-  }
-%    \end{macrocode}
-%   Storing the number of each division is done differently for the
-%   integer and decimal. The integer is easy and a one-off, while the
-%   decimal also needs to account for the position of the digit to store.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_div_store: { }
-\cs_new_protected_nopar:Npn \fp_div_store_integer:
-  {
-    \l_fp_output_integer_int \l_fp_count_int
-    \cs_set_eq:NN \fp_div_store: \fp_div_store_decimal:
-  }
-\cs_new_protected_nopar:Npn \fp_div_store_decimal:
-  {
-    \l_fp_output_decimal_int
-      \int_eval:w
-        \l_fp_output_decimal_int +
-        \l_fp_count_int * \l_fp_div_offset_int
-      \int_eval_end:
-    \tex_divide:D \l_fp_div_offset_int \c_ten
-  }
-\cs_new_protected:Npn \fp_div_loop_step:w #1#2#3#4#5#6#7#8#9 \q_stop
-  {
-    \l_fp_input_a_integer_int
-      \int_eval:w #2 + \l_fp_input_a_integer_int  \int_eval_end:
-    \l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
+% ^^A todo
+% ^^A \section{Floating points}
+% ^^A
+% ^^A Here, there may be a discussion of what floating point numbers
+% ^^A are, and a list of relevant resources (\emph{e.g.}, some of
+% ^^A Kahan's articles), and previous \TeX{} packages.
 %
-% \subsection{Arithmetic for internal use}
+% \section{Disclaimer and roadmap}
 %
-% For the more complex functions, it is only possible to deliver
-% reliable $10$ digit accuracy if the internal calculations are
-% carried out to a higher degree of precision. This is done using a
-% second set of functions so that the `user' versions are not
-% slowed down. These versions are also focussed on the needs of internal
-% calculations. No error checking, sign checking or exponent levelling
-% is done. For addition and subtraction, the arguments are:
+% The package may break down if:
 % \begin{itemize}
-%   \item Integer part of input |a|.
-%   \item Decimal part of input |a|.
-%   \item Additional decimal part of input |a|.
-%   \item Integer part of input |b|.
-%   \item Decimal part of input |b|.
-%   \item Additional decimal part of input |b|.
-%   \item Integer part of output.
-%   \item Decimal part of output.
-%   \item Additional decimal part of output.
+%   \item the escape character is either a digit, or an underscore,
+%   \item the \tn{uccodes} are changed: the test for whether a character
+%     is a letter actually tests if the upper-case code of the character
+%     is between A and Z.
 % \end{itemize}
-% The situation for multiplication and division is a little different as
-% they only deal with the decimal part.
-%
-% \begin{macro}{\fp_add:NNNNNNNNN}
-%   The internal sum is always exactly that: it is always a sum and there
-%   is no sign check.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_add:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {
-    #7 \int_eval:w #1 + #4 \int_eval_end:
-    #8 \int_eval:w #2 + #5 \int_eval_end:
-    #9 \int_eval:w #3 + #6 \int_eval_end:
-    \if_int_compare:w #9 < \c_one_thousand_million
-    \else:
-      \tex_advance:D #8 \c_one
-      \tex_advance:D #9 -\c_one_thousand_million
-    \fi:
-    \if_int_compare:w #8 < \c_one_thousand_million
-    \else:
-      \tex_advance:D #7 \c_one
-      \tex_advance:D #8 -\c_one_thousand_million
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\fp_sub:NNNNNNNNN}
-%   Internal subtraction is needed only when the first number is bigger
-%   than the second, so there is no need to worry about the sign. This is
-%   a good job as there are no arguments left. The flipping flag is
-%   used in the rare case where a sign change is possible.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_sub:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {
-    #7 \int_eval:w #1 - #4 \int_eval_end:
-    #8 \int_eval:w #2 - #5 \int_eval_end:
-    #9 \int_eval:w #3 - #6 \int_eval_end:
-    \if_int_compare:w #9 < \c_zero
-      \tex_advance:D #8 \c_minus_one
-      \tex_advance:D #9 \c_one_thousand_million
-    \fi:
-    \if_int_compare:w #8 < \c_zero
-      \tex_advance:D #7 \c_minus_one
-      \tex_advance:D #8 \c_one_thousand_million
-    \fi:
-    \if_int_compare:w #7 < \c_zero
-      \if_int_compare:w \int_eval:w #8 + #9 = \c_zero
-        #7 -#7
-      \else:
-        \tex_advance:D #7 \c_one
-        #8 \int_eval:w \c_one_thousand_million - #8 \int_eval_end:
-        #9 \int_eval:w \c_one_thousand_million - #9 \int_eval_end:
-      \fi:
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\fp_mul:NNNNNN}
-% Decimal-part only multiplication but with higher accuracy than the
-% user version.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_mul:NNNNNN #1#2#3#4#5#6
-  {
-    \fp_mul_split:NNNN #1
-      \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
-    \fp_mul_split:NNNN #2
-      \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
-    \fp_mul_split:NNNN #3
-      \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
-    \fp_mul_split:NNNN #4
-      \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int
-    \l_fp_mul_output_int \c_zero
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_vi_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_v_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int        \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_v_int         \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_vi_int        \l_fp_mul_b_i_int
-    \tex_divide:D \l_fp_mul_output_int \c_one_thousand
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_v_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_v_int        \l_fp_mul_b_i_int
-    \fp_mul_end_level:
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_i_int
-    \fp_mul_end_level:
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_i_int
-    \fp_mul_end_level:
-    #6 0 \l_fp_mul_output_tl \scan_stop:
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_i_int
-    \fp_mul_end_level:
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_i_int
-    \fp_mul_end_level:
-    \fp_mul_end_level:
-    #5 0 \l_fp_mul_output_tl \scan_stop:
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\fp_mul:NNNNNNNNN}
-%   For internal multiplication where the integer does need to be
-%   retained. This means of course that this code is quite slow, and so
-%   is only used when necessary.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_mul:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {
-    \fp_mul_split:NNNN #2
-      \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
-    \fp_mul_split:NNNN #3
-      \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
-    \fp_mul_split:NNNN #5
-      \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
-    \fp_mul_split:NNNN #6
-      \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int
-    \l_fp_mul_output_int \c_zero
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_vi_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_v_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int        \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_v_int         \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_vi_int        \l_fp_mul_b_i_int
-    \tex_divide:D \l_fp_mul_output_int \c_one_thousand
-    \fp_mul_product:NN #1                       \l_fp_mul_b_vi_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_v_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_v_int        \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_vi_int       #4
-    \fp_mul_end_level:
-    \fp_mul_product:NN #1                       \l_fp_mul_b_v_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_v_int        #4
-    \fp_mul_end_level:
-    \fp_mul_product:NN #1                       \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int       #4
-    \fp_mul_end_level:
-    #9 0 \l_fp_mul_output_tl \scan_stop:
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN #1                       \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      #4
-    \fp_mul_end_level:
-    \fp_mul_product:NN #1                       \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       #4
-    \fp_mul_end_level:
-    \fp_mul_product:NN #1                       \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int        #4
-    \fp_mul_end_level:
-    #8 0 \l_fp_mul_output_tl \scan_stop:
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN #1 #4
-    \fp_mul_end_level:
-    #7 0 \l_fp_mul_output_tl \scan_stop:
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\fp_div_integer:NNNNN}
-%   Here, division is always by an integer, and so it is possible to
-%   use \TeX{}'s native calculations rather than doing it in macros.
-%   The idea here is to divide the decimal part, find any remainder,
-%   then do the real division of the two parts before adding in what
-%   is needed for the remainder.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_div_integer:NNNNN #1#2#3#4#5
-  {
-    \l_fp_internal_int #1
-    \tex_divide:D \l_fp_internal_int #3
-    \l_fp_internal_int \int_eval:w #1 - \l_fp_internal_int * #3 \int_eval_end:
-    #4 #1
-    \tex_divide:D #4 #3
-    #5 #2
-    \tex_divide:D #5 #3
-    \tex_multiply:D \l_fp_internal_int \c_one_thousand
-    \tex_divide:D \l_fp_internal_int #3
-    #5 \int_eval:w #5 + \l_fp_internal_int * \c_one_million \int_eval_end:
-    \if_int_compare:w #5 > \c_one_thousand_million
-      \tex_advance:D #4 \c_one
-      \tex_advance:D #5 -\c_one_thousand_million
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\fp_extended_normalise:}
-% \begin{macro}[aux]{\fp_extended_normalise_aux_i:}
-% \begin{macro}[aux]{\fp_extended_normalise_aux_i:w}
-% \begin{macro}[aux]{\fp_extended_normalise_aux_ii:w}
-% \begin{macro}[aux]{\fp_extended_normalise_aux_ii:}
-% \begin{macro}[aux]{\fp_extended_normalise_aux:NNNNNNNNN}
-%   The \enquote{extended} integers for internal use are mainly used in
-%   fixed-point mode. This comes up in a few places, so a generalised
-%   utility is made available to carry out the change. This function
-%   simply calls the two loops to shift the input to the point of
-%   having a zero exponent.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_extended_normalise:
-  {
-    \fp_extended_normalise_aux_i:
-    \fp_extended_normalise_aux_ii:
-  }
-\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_i:
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int > \c_zero
-      \tex_multiply:D \l_fp_input_a_integer_int \c_ten
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \exp_after:wN \fp_extended_normalise_aux_i:w
-        \int_use:N \l_fp_input_a_decimal_int \q_stop
-       \exp_after:wN \fp_extended_normalise_aux_i:
-     \fi:
-  }
-\cs_new_protected:Npn \fp_extended_normalise_aux_i:w
-  #1#2#3#4#5#6#7#8#9 \q_stop
-  {
-    \l_fp_input_a_integer_int
-      \int_eval:w \l_fp_input_a_integer_int + #2 \scan_stop:
-    \l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
-    \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
-    \exp_after:wN \fp_extended_normalise_aux_ii:w
-      \int_use:N \l_fp_input_a_extended_int \q_stop
-  }
-\cs_new_protected:Npn \fp_extended_normalise_aux_ii:w
-  #1#2#3#4#5#6#7#8#9 \q_stop
-  {
-    \l_fp_input_a_decimal_int
-      \int_eval:w \l_fp_input_a_decimal_int + #2 \scan_stop:
-    \l_fp_input_a_extended_int #3#4#5#6#7#8#9 0 \scan_stop:
-    \tex_advance:D \l_fp_input_a_exponent_int \c_minus_one
-  }
-\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_ii:
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int < \c_zero
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \exp_after:wN \use_i:nn \exp_after:wN
-        \fp_extended_normalise_ii_aux:NNNNNNNNN
-        \int_use:N \l_fp_input_a_decimal_int
-       \exp_after:wN \fp_extended_normalise_aux_ii:
-     \fi:
-  }
-\cs_new_protected:Npn \fp_extended_normalise_ii_aux:NNNNNNNNN
-  #1#2#3#4#5#6#7#8#9
-  {
-    \if_int_compare:w \l_fp_input_a_integer_int = \c_zero
-      \l_fp_input_a_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
-    \else:
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \int_use:N \l_fp_input_a_integer_int
-          #1#2#3#4#5#6#7#8
-        }
-      \l_fp_input_a_integer_int \c_zero
-      \l_fp_input_a_decimal_int \l_fp_internal_tl \scan_stop:
-    \fi:
-    \tex_divide:D \l_fp_input_a_extended_int \c_ten
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        #9
-        \int_use:N \l_fp_input_a_extended_int
-      }
-    \l_fp_input_a_extended_int \l_fp_internal_tl \scan_stop:
-    \tex_advance:D \l_fp_input_a_exponent_int \c_one
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_extended_normalise_output:}
-% \begin{macro}[aux]{\fp_extended_normalise_output_aux_i:NNNNNNNNN}
-% \begin{macro}[aux]{\fp_extended_normalise_output_aux_ii:NNNNNNNNN}
-% \begin{macro}[aux]{\fp_extended_normalise_output_aux:N}
-%   At some stages in working out extended output, it is possible for the
-%   value to need shifting to keep the integer part in range. This only
-%   ever happens such that the integer needs to be made smaller.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_extended_normalise_output:
-  {
-    \if_int_compare:w \l_fp_output_integer_int > \c_nine
-      \tex_advance:D \l_fp_output_integer_int \c_one_thousand_million
-      \exp_after:wN \use_i:nn \exp_after:wN
-        \fp_extended_normalise_output_aux_i:NNNNNNNNN
-        \int_use:N \l_fp_output_integer_int
-      \exp_after:wN \fp_extended_normalise_output:
-    \fi:
-  }
-\cs_new_protected:Npn \fp_extended_normalise_output_aux_i:NNNNNNNNN
-  #1#2#3#4#5#6#7#8#9
-  {
-    \l_fp_output_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
-    \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        #9
-        \exp_after:wN \use_none:n
-        \int_use:N \l_fp_output_decimal_int
-      }
-    \exp_after:wN \fp_extended_normalise_output_aux_ii:NNNNNNNNN
-      \l_fp_internal_tl
-  }
-\cs_new_protected:Npn \fp_extended_normalise_output_aux_ii:NNNNNNNNN
-  #1#2#3#4#5#6#7#8#9
-  {
-    \l_fp_output_decimal_int #1#2#3#4#5#6#7#8#9 \scan_stop:
-    \fp_extended_normalise_output_aux:N
-  }
-\cs_new_protected:Npn \fp_extended_normalise_output_aux:N #1
-  {
-    \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million
-    \tex_divide:D \l_fp_output_extended_int \c_ten
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        #1
-        \exp_after:wN \use_none:n
-          \int_use:N \l_fp_output_extended_int
-      }
-    \l_fp_output_extended_int \l_fp_internal_tl \scan_stop:
-    \tex_advance:D \l_fp_output_exponent_int \c_one
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Trigonometric functions}
-%
-% \begin{macro}{\fp_trig_normalise:}
-% \begin{macro}[aux]{\fp_trig_normalise_aux:}
-% \begin{macro}[aux]{\fp_trig_sub:NNN}
-%   For normalisation, the code essentially switches to fixed-point
-%   arithmetic. There is a shift of the exponent, then repeated
-%   subtractions. The end result is a number in the range
-%   $ -\pi < x \le \pi $.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_trig_normalise:
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int < \c_ten
-      \l_fp_input_a_extended_int \c_zero
-      \fp_extended_normalise:
-      \fp_trig_normalise_aux:
-      \if_int_compare:w \l_fp_input_a_integer_int < \c_zero
-        \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
-      \fi:
-       \exp_after:wN \fp_trig_octant:
-    \else:
-      \l_fp_input_a_sign_int    \c_one
-      \l_fp_output_integer_int  \c_zero
-      \l_fp_output_decimal_int  \c_zero
-      \l_fp_output_exponent_int \c_zero
-      \exp_after:wN \fp_trig_overflow_msg:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_trig_normalise_aux:
-  {
-    \if_int_compare:w \l_fp_input_a_integer_int > \c_three
-      \fp_trig_sub:NNN
-        \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
-      \exp_after:wN \fp_trig_normalise_aux:
-    \else:
-      \if_int_compare:w \l_fp_input_a_integer_int > \c_two
-        \if_int_compare:w \l_fp_input_a_decimal_int > \c_fp_pi_decimal_int
-          \fp_trig_sub:NNN
-            \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \fp_trig_normalise_aux:
-          \fi:
-      \fi:
-    \fi:
-  }
-%    \end{macrocode}
-%   Here, there may be a sign change but there will never be any
-%   variation in the input. So a dedicated function can be used.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_trig_sub:NNN #1#2#3
-  {
-    \l_fp_input_a_integer_int
-      \int_eval:w \l_fp_input_a_integer_int - #1 \int_eval_end:
-    \l_fp_input_a_decimal_int
-      \int_eval:w \l_fp_input_a_decimal_int - #2 \int_eval_end:
-    \l_fp_input_a_extended_int
-      \int_eval:w \l_fp_input_a_extended_int - #3 \int_eval_end:
-    \if_int_compare:w \l_fp_input_a_extended_int < \c_zero
-      \tex_advance:D \l_fp_input_a_decimal_int \c_minus_one
-      \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
-    \fi:
-    \if_int_compare:w \l_fp_input_a_decimal_int < \c_zero
-      \tex_advance:D \l_fp_input_a_integer_int \c_minus_one
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \fi:
-    \if_int_compare:w \l_fp_input_a_integer_int < \c_zero
-      \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
-      \if_int_compare:w
-        \int_eval:w
-          \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
-        = \c_zero
-        \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
-      \else:
-        \l_fp_input_a_integer_int
-           \int_eval:w
-             - \l_fp_input_a_integer_int - \c_one
-           \int_eval_end:
-        \l_fp_input_a_decimal_int
-          \int_eval:w
-            \c_one_thousand_million - \l_fp_input_a_decimal_int
-          \int_eval_end:
-        \l_fp_input_a_extended_int
-          \int_eval:w
-            \c_one_thousand_million - \l_fp_input_a_extended_int
-          \int_eval_end:
-      \fi:
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_trig_octant:}
-% \begin{macro}[aux]
-%   {\fp_trig_octant_aux_i:, \fp_trig_octant_aux_ii:}
-%   Here, the input is further reduced into the range
-%   $ 0 < x \le \pi / 4 $. This is pretty simple: check if
-%   $ \pi / 4 $ can be taken off and if it can do it and loop. The
-%   check at the end is to \enquote{mop up} values which are so close to
-%   $ \pi / 4 $ that they should be treated as such.  The test for
-%   an even octant is needed as the `remainder' needed is from
-%   the nearest $ \pi / 2 $. The check for octant $4$ is needed as an exact
-%   $\pi$ input will otherwise end up in the wrong place!
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_trig_octant:
-  {
-    \l_fp_trig_octant_int \c_one
-    \fp_trig_octant_aux_i:
-    \if_int_compare:w \l_fp_input_a_decimal_int < \c_ten
-      \l_fp_input_a_decimal_int  \c_zero
-      \l_fp_input_a_extended_int \c_zero
-    \fi:
-    \if_int_odd:w \l_fp_trig_octant_int
-    \else:
-      \fp_sub:NNNNNNNNN
-        \c_zero \c_fp_pi_by_four_decimal_int \c_fp_pi_by_four_extended_int
-        \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-          \l_fp_input_a_extended_int
-        \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-          \l_fp_input_a_extended_int
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_trig_octant_aux_i:
-  {
-    \if_int_compare:w \l_fp_trig_octant_int > \c_four
-      \l_fp_trig_octant_int \c_four
-      \l_fp_input_a_decimal_int  \c_fp_pi_by_four_decimal_int
-      \l_fp_input_a_extended_int \c_fp_pi_by_four_extended_int
-    \else:
-      \exp_after:wN \fp_trig_octant_aux_ii:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_trig_octant_aux_ii:
-  {
-    \if_int_compare:w \l_fp_input_a_integer_int > \c_zero
-      \fp_sub:NNNNNNNNN
-        \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-          \l_fp_input_a_extended_int
-        \c_zero \c_fp_pi_by_four_decimal_int \c_fp_pi_by_four_extended_int
-        \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-          \l_fp_input_a_extended_int
-      \tex_advance:D \l_fp_trig_octant_int \c_one
-      \exp_after:wN \fp_trig_octant_aux_i:
-    \else:
-      \if_int_compare:w
-        \l_fp_input_a_decimal_int > \c_fp_pi_by_four_decimal_int
-        \fp_sub:NNNNNNNNN
-          \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-            \l_fp_input_a_extended_int
-          \c_zero \c_fp_pi_by_four_decimal_int
-            \c_fp_pi_by_four_extended_int
-          \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-            \l_fp_input_a_extended_int
-        \tex_advance:D \l_fp_trig_octant_int \c_one
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \fp_trig_octant_aux_i:
-      \fi:
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_sin:Nn, \fp_sin:cn}
-% \UnitTested
-% \begin{macro}{\fp_gsin:Nn,\fp_gsin:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_sin_aux:NNn}
-% \begin{macro}[aux]{\fp_sin_aux_i:}
-% \begin{macro}[aux]{\fp_sin_aux_ii:}
-%   Calculating the sine starts off in the usual way. There is a check
-%   to see if the value has already been worked out before proceeding
-%   further.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_sin:Nn  { \fp_sin_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gsin:Nn { \fp_sin_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_sin:Nn   { c }
-\cs_generate_variant:Nn \fp_gsin:Nn  { c }
-%    \end{macrocode}
-%   The internal routine for sines does a check to see if the value is
-%   already known. This saves a lot of repetition when doing rotations.
-%   For very small values it is best to simply return the input as the
-%   sine: the cut-off is $ 1 \times 10^{-5} $.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_sin_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \tl_set:Nx \l_fp_arg_tl
-        {
-          \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-            -
-          \else:
-            +
-          \fi:
-          \int_use:N \l_fp_input_a_integer_int
-          .
-          \exp_after:wN \use_none:n
-            \int_value:w \int_eval:w
-              \l_fp_input_a_decimal_int + \c_one_thousand_million
-          e
-          \int_use:N \l_fp_input_a_exponent_int
-        }
-      \if_int_compare:w \l_fp_input_a_exponent_int < -\c_five
-        \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2 { \l_fp_arg_tl }
-        }
-      \else:
-        \if_cs_exist:w
-          c_fp_sin ( \l_fp_arg_tl ) _fp
-        \cs_end:
-        \else:
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \fp_sin_aux_i:
-        \fi:
-        \cs_set_protected_nopar:Npx \fp_tmp:w
-          {
-            \group_end:
-            #1 \exp_not:N #2
-              { \use:c { c_fp_sin ( \l_fp_arg_tl ) _fp } }
-          }
-      \fi:
-    \fp_tmp:w
-  }
-%    \end{macrocode}
-%   The internals for sine first normalise the input into an octant, then
-%   choose the correct set up for the Taylor series. The sign for the sine
-%   function is easy, so there is no worry about it. So the only thing to
-%   do is to get the output standardised.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_sin_aux_i:
-  {
-    \fp_trig_normalise:
-    \fp_sin_aux_ii:
-    \if_int_compare:w \l_fp_output_integer_int = \c_one
-      \l_fp_output_exponent_int \c_zero
-    \else:
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-      \l_fp_output_decimal_int \l_fp_output_extended_int
-      \l_fp_output_exponent_int -\c_nine
-    \fi:
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \tl_new:c { c_fp_sin ( \l_fp_arg_tl ) _fp }
-    \tl_gset:cx { c_fp_sin ( \l_fp_arg_tl ) _fp }
-      {
-        \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-          +
-        \else:
-          -
-        \fi:
-        \int_use:N \l_fp_output_integer_int
-        .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_output_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_output_exponent_int
-      }
-  }
-\cs_new_protected_nopar:Npn \fp_sin_aux_ii:
-  {
-    \if_case:w \l_fp_trig_octant_int
-    \or:
-      \exp_after:wN \fp_trig_calc_sin:
-    \or:
-      \exp_after:wN \fp_trig_calc_cos:
-    \or:
-      \exp_after:wN \fp_trig_calc_cos:
-    \or:
-      \exp_after:wN \fp_trig_calc_sin:
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_cos:Nn, \fp_cos:cn}
-% \UnitTested
-% \begin{macro}{\fp_gcos:Nn,\fp_gcos:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_cos_aux:NNn}
-% \begin{macro}[aux]{\fp_cos_aux_i:}
-% \begin{macro}[aux]{\fp_cos_aux_ii:}
-%   Cosine is almost identical, but there is no short cut code here.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_cos:Nn  { \fp_cos_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gcos:Nn { \fp_cos_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_cos:Nn   { c }
-\cs_generate_variant:Nn \fp_gcos:Nn  { c }
-\cs_new_protected:Npn \fp_cos_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \tl_set:Nx \l_fp_arg_tl
-        {
-          \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-            -
-          \else:
-            +
-          \fi:
-          \int_use:N \l_fp_input_a_integer_int
-          .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_input_a_decimal_int + \c_one_thousand_million
-          e
-          \int_use:N \l_fp_input_a_exponent_int
-        }
-      \if_cs_exist:w c_fp_cos ( \l_fp_arg_tl ) _fp \cs_end:
-      \else:
-        \exp_after:wN \fp_cos_aux_i:
-      \fi:
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            { \use:c { c_fp_cos ( \l_fp_arg_tl ) _fp } }
-        }
-    \fp_tmp:w
-  }
-%    \end{macrocode}
-% Almost the same as for sine: just a bit of correction for the sign
-% of the output.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_cos_aux_i:
-  {
-    \fp_trig_normalise:
-    \fp_cos_aux_ii:
-    \if_int_compare:w \l_fp_output_integer_int = \c_one
-      \l_fp_output_exponent_int \c_zero
-    \else:
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-      \l_fp_output_decimal_int \l_fp_output_extended_int
-      \l_fp_output_exponent_int -\c_nine
-    \fi:
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \tl_new:c { c_fp_cos ( \l_fp_arg_tl ) _fp }
-    \tl_gset:cx { c_fp_cos ( \l_fp_arg_tl ) _fp }
-      {
-        \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-          +
-        \else:
-          -
-        \fi:
-        \int_use:N \l_fp_output_integer_int
-        .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_output_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_output_exponent_int
-      }
-  }
-\cs_new_protected_nopar:Npn \fp_cos_aux_ii:
-  {
-    \if_case:w \l_fp_trig_octant_int
-    \or:
-      \exp_after:wN \fp_trig_calc_cos:
-    \or:
-      \exp_after:wN \fp_trig_calc_sin:
-    \or:
-      \exp_after:wN \fp_trig_calc_sin:
-    \or:
-      \exp_after:wN \fp_trig_calc_cos:
-    \fi:
-    \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-      \if_int_compare:w \l_fp_trig_octant_int > \c_two
-        \l_fp_input_a_sign_int \c_minus_one
-      \fi:
-    \else:
-      \if_int_compare:w \l_fp_trig_octant_int > \c_two
-      \else:
-        \l_fp_input_a_sign_int \c_one
-      \fi:
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_trig_calc_cos:}
-% \begin{macro}{\fp_trig_calc_sin:}
-% \begin{macro}[aux]{\fp_trig_calc_Taylor:}
-%   These functions actually do the calculation for sine and cosine.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_trig_calc_cos:
-  {
-    \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
-      \l_fp_output_integer_int \c_one
-      \l_fp_output_decimal_int \c_zero
-    \else:
-      \l_fp_trig_sign_int \c_minus_one
-      \fp_mul:NNNNNN
-        \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-        \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-        \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \fp_div_integer:NNNNN
-        \l_fp_trig_decimal_int \l_fp_trig_extended_int
-        \c_two
-        \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \l_fp_count_int \c_three
-      \if_int_compare:w \l_fp_trig_extended_int = \c_zero
-        \if_int_compare:w \l_fp_trig_decimal_int = \c_zero
-          \l_fp_output_integer_int \c_one
-          \l_fp_output_decimal_int \c_zero
-          \l_fp_output_extended_int \c_zero
-        \else:
-          \l_fp_output_integer_int \c_zero
-          \l_fp_output_decimal_int \c_one_thousand_million
-          \l_fp_output_extended_int \c_zero
-        \fi:
-      \else:
-        \l_fp_output_integer_int \c_zero
-        \l_fp_output_decimal_int 999999999 \scan_stop:
-        \l_fp_output_extended_int \c_one_thousand_million
-      \fi:
-      \tex_advance:D \l_fp_output_extended_int -\l_fp_trig_extended_int
-      \tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int
-      \exp_after:wN \fp_trig_calc_Taylor:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_trig_calc_sin:
-  {
-    \l_fp_output_integer_int \c_zero
-    \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
-      \l_fp_output_decimal_int \c_zero
-    \else:
-      \l_fp_output_decimal_int \l_fp_input_a_decimal_int
-      \l_fp_output_extended_int \l_fp_input_a_extended_int
-      \l_fp_trig_sign_int \c_one
-      \l_fp_trig_decimal_int \l_fp_input_a_decimal_int
-      \l_fp_trig_extended_int \l_fp_input_a_extended_int
-      \l_fp_count_int \c_two
-      \exp_after:wN \fp_trig_calc_Taylor:
-    \fi:
-  }
-%    \end{macrocode}
-%   This implements a Taylor series calculation for the trigonometric
-%   functions. Lots of shuffling about as \TeX\ is not exactly a natural
-%   choice for this sort of thing.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_trig_calc_Taylor:
-  {
-    \l_fp_trig_sign_int -\l_fp_trig_sign_int
-    \fp_mul:NNNNNN
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \fp_mul:NNNNNN
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \fp_div_integer:NNNNN
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \l_fp_count_int
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \tex_advance:D \l_fp_count_int \c_one
-    \fp_div_integer:NNNNN
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \l_fp_count_int
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \tex_advance:D \l_fp_count_int \c_one
-    \if_int_compare:w \l_fp_trig_decimal_int > \c_zero
-      \if_int_compare:w \l_fp_trig_sign_int > \c_zero
-        \tex_advance:D \l_fp_output_decimal_int \l_fp_trig_decimal_int
-        \tex_advance:D \l_fp_output_extended_int
-          \l_fp_trig_extended_int
-        \if_int_compare:w \l_fp_output_extended_int < \c_one_thousand_million
-        \else:
-          \tex_advance:D \l_fp_output_decimal_int \c_one
-          \tex_advance:D \l_fp_output_extended_int
-            -\c_one_thousand_million
-        \fi:
-        \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
-        \else:
-          \tex_advance:D \l_fp_output_integer_int \c_one
-          \tex_advance:D \l_fp_output_decimal_int
-            -\c_one_thousand_million
-        \fi:
-      \else:
-        \tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int
-        \tex_advance:D \l_fp_output_extended_int
-          -\l_fp_input_a_extended_int
-        \if_int_compare:w \l_fp_output_extended_int < \c_zero
-          \tex_advance:D \l_fp_output_decimal_int \c_minus_one
-          \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million
-        \fi:
-        \if_int_compare:w \l_fp_output_decimal_int < \c_zero
-          \tex_advance:D \l_fp_output_integer_int \c_minus_one
-          \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
-        \fi:
-      \fi:
-      \exp_after:wN \fp_trig_calc_Taylor:
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_tan:Nn, \fp_tan:cn}
-% \UnitTested
-% \begin{macro}{\fp_gtan:Nn,\fp_gtan:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_tan_aux:NNn}
-% \begin{macro}[aux]{\fp_tan_aux_i:}
-% \begin{macro}[aux]{\fp_tan_aux_ii:}
-% \begin{macro}[aux]{\fp_tan_aux_iii:}
-% \begin{macro}[aux]{\fp_tan_aux_iv:}
-%   As might be expected, tangents are calculated from the sine and cosine
-%   by division. So there is a bit of set up, the two subsidiary pieces
-%   of work are done and then a division takes place. For small numbers,
-%   the same approach is used as for sines, with the input value simply
-%   returned as is.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_tan:Nn  { \fp_tan_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gtan:Nn { \fp_tan_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_tan:Nn   { c }
-\cs_generate_variant:Nn \fp_gtan:Nn  { c }
-\cs_new_protected:Npn \fp_tan_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \tl_set:Nx \l_fp_arg_tl
-        {
-          \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-            -
-          \else:
-            +
-          \fi:
-          \int_use:N \l_fp_input_a_integer_int
-          .
-          \exp_after:wN \use_none:n
-            \int_value:w \int_eval:w
-              \l_fp_input_a_decimal_int + \c_one_thousand_million
-          e
-          \int_use:N \l_fp_input_a_exponent_int
-        }
-      \if_int_compare:w \l_fp_input_a_exponent_int < -\c_five
-        \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2 { \l_fp_arg_tl }
-        }
-      \else:
-        \if_cs_exist:w
-          c_fp_tan ( \l_fp_arg_tl ) _fp
-        \cs_end:
-        \else:
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \fp_tan_aux_i:
-        \fi:
-        \cs_set_protected_nopar:Npx \fp_tmp:w
-          {
-            \group_end:
-            #1 \exp_not:N #2
-              { \use:c { c_fp_tan ( \l_fp_arg_tl ) _fp } }
-          }
-      \fi:
-    \fp_tmp:w
-  }
-%    \end{macrocode}
-%   The business of the calculation does not check for stored sines or
-%   cosines as there would then be an overhead to reading them back in.
-%   There is also no need to worry about \enquote{small} sine values as
-%   these will have been dealt with earlier. There is a two-step lead off
-%   so that undefined division is not even attempted.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_tan_aux_i:
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int < \c_ten
-      \exp_after:wN \fp_tan_aux_ii:
-    \else:
-      \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
-        \c_zero_fp
-      \exp_after:wN \fp_trig_overflow_msg:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_tan_aux_ii:
-  {
-    \fp_trig_normalise:
-    \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-      \if_int_compare:w \l_fp_trig_octant_int > \c_two
-        \l_fp_output_sign_int \c_minus_one
-      \else:
-        \l_fp_output_sign_int \c_one
-      \fi:
-    \else:
-      \if_int_compare:w \l_fp_trig_octant_int > \c_two
-        \l_fp_output_sign_int \c_one
-      \else:
-        \l_fp_output_sign_int \c_minus_one
-      \fi:
-    \fi:
-    \fp_cos_aux_ii:
-    \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
-      \if_int_compare:w \l_fp_input_a_integer_int = \c_zero
-        \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
-          \c_undefined_fp
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \fp_tan_aux_iii:
-      \fi:
-    \else:
-      \exp_after:wN \fp_tan_aux_iii:
-    \fi:
-  }
-%    \end{macrocode}
-%   The division is done here using the same code as the standard division
-%   unit, shifting the digits in the calculated sine and cosine to
-%   maintain accuracy.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_tan_aux_iii:
-  {
-    \l_fp_input_b_integer_int \l_fp_output_decimal_int
-    \l_fp_input_b_decimal_int \l_fp_output_extended_int
-    \l_fp_input_b_exponent_int -\c_nine
-    \fp_standardise:NNNN
-      \l_fp_input_b_sign_int
-      \l_fp_input_b_integer_int
-      \l_fp_input_b_decimal_int
-      \l_fp_input_b_exponent_int
-    \fp_sin_aux_ii:
-    \l_fp_input_a_integer_int \l_fp_output_decimal_int
-    \l_fp_input_a_decimal_int \l_fp_output_extended_int
-    \l_fp_input_a_exponent_int -\c_nine
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int
-      \l_fp_input_a_decimal_int
-      \l_fp_input_a_exponent_int
-    \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
-      \if_int_compare:w \l_fp_input_a_integer_int = \c_zero
-        \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
-          \c_zero_fp
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN \fp_tan_aux_iv:
-      \fi:
-    \else:
-      \exp_after:wN \fp_tan_aux_iv:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_tan_aux_iv:
-  {
-    \l_fp_output_integer_int \c_zero
-    \l_fp_output_decimal_int \c_zero
-    \cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
-    \l_fp_div_offset_int \c_one_hundred_million
-    \fp_div_loop:
-    \l_fp_output_exponent_int
-      \int_eval:w
-        \l_fp_input_a_exponent_int - \l_fp_input_b_exponent_int
-      \int_eval_end:
-    \fp_standardise:NNNN
-      \l_fp_output_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \tl_new:c { c_fp_tan ( \l_fp_arg_tl ) _fp }
-    \tl_gset:cx { c_fp_tan ( \l_fp_arg_tl ) _fp }
-      {
-        \if_int_compare:w \l_fp_output_sign_int > \c_zero
-          +
-        \else:
-          -
-        \fi:
-        \int_use:N \l_fp_output_integer_int
-        .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_output_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_output_exponent_int
-      }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Exponent and logarithm functions}
-%
-% \begin{variable}{\c_fp_exp_1_tl}
-% \begin{variable}{\c_fp_exp_2_tl}
-% \begin{variable}{\c_fp_exp_3_tl}
-% \begin{variable}{\c_fp_exp_4_tl}
-% \begin{variable}{\c_fp_exp_5_tl}
-% \begin{variable}{\c_fp_exp_6_tl}
-% \begin{variable}{\c_fp_exp_7_tl}
-% \begin{variable}{\c_fp_exp_8_tl}
-% \begin{variable}{\c_fp_exp_9_tl}
-% \begin{variable}{\c_fp_exp_10_tl}
-% \begin{variable}{\c_fp_exp_20_tl}
-% \begin{variable}{\c_fp_exp_30_tl}
-% \begin{variable}{\c_fp_exp_40_tl}
-% \begin{variable}{\c_fp_exp_50_tl}
-% \begin{variable}{\c_fp_exp_60_tl}
-% \begin{variable}{\c_fp_exp_70_tl}
-% \begin{variable}{\c_fp_exp_80_tl}
-% \begin{variable}{\c_fp_exp_90_tl}
-% \begin{variable}{\c_fp_exp_100_tl}
-% \begin{variable}{\c_fp_exp_200_tl}
-%   Calculation of exponentials requires a number of precomputed values:
-%   first the positive integers.
-%    \begin{macrocode}
-\tl_const:cn { c_fp_exp_1_tl }   { { 2 } { 718281828 } { 459045235 } { 0 } }
-\tl_const:cn { c_fp_exp_2_tl }   { { 7 } { 389056098 } { 930650227 } { 0 } }
-\tl_const:cn { c_fp_exp_3_tl }   { { 2 } { 008553692 } { 318766774 } { 1 } }
-\tl_const:cn { c_fp_exp_4_tl }   { { 5 } { 459815003 } { 314423908 } { 1 } }
-\tl_const:cn { c_fp_exp_5_tl }   { { 1 } { 484131591 } { 025766034 } { 2 } }
-\tl_const:cn { c_fp_exp_6_tl }   { { 4 } { 034287934 } { 927351226 } { 2 } }
-\tl_const:cn { c_fp_exp_7_tl }   { { 1 } { 096633158 } { 428458599 } { 3 } }
-\tl_const:cn { c_fp_exp_8_tl }   { { 2 } { 980957987 } { 041728275 } { 3 } }
-\tl_const:cn { c_fp_exp_9_tl }   { { 8 } { 103083927 } { 575384008 } { 3 } }
-\tl_const:cn { c_fp_exp_10_tl }  { { 2 } { 202646579 } { 480671652 } { 4 } }
-\tl_const:cn { c_fp_exp_20_tl }  { { 4 } { 851651954 } { 097902280 } { 8 } }
-\tl_const:cn { c_fp_exp_30_tl }  { { 1 } { 068647458 } { 152446215 } { 13 } }
-\tl_const:cn { c_fp_exp_40_tl }  { { 2 } { 353852668 } { 370199854 } { 17 } }
-\tl_const:cn { c_fp_exp_50_tl }  { { 5 } { 184705528 } { 587072464 } { 21 } }
-\tl_const:cn { c_fp_exp_60_tl }  { { 1 } { 142007389 } { 815684284 } { 26 } }
-\tl_const:cn { c_fp_exp_70_tl }  { { 2 } { 515438670 } { 919167006 } { 30 } }
-\tl_const:cn { c_fp_exp_80_tl }  { { 5 } { 540622384 } { 393510053 } { 34 } }
-\tl_const:cn { c_fp_exp_90_tl }  { { 1 } { 220403294 } { 317840802 } { 39 } }
-\tl_const:cn { c_fp_exp_100_tl } { { 2 } { 688117141 } { 816135448 } { 43 } }
-\tl_const:cn { c_fp_exp_200_tl } { { 7 } { 225973768 } { 125749258 } { 86 } }
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\c_fp_exp_-1_tl}
-% \begin{variable}{\c_fp_exp_-2_tl}
-% \begin{variable}{\c_fp_exp_-3_tl}
-% \begin{variable}{\c_fp_exp_-4_tl}
-% \begin{variable}{\c_fp_exp_-5_tl}
-% \begin{variable}{\c_fp_exp_-6_tl}
-% \begin{variable}{\c_fp_exp_-7_tl}
-% \begin{variable}{\c_fp_exp_-8_tl}
-% \begin{variable}{\c_fp_exp_-9_tl}
-% \begin{variable}{\c_fp_exp_-10_tl}
-% \begin{variable}{\c_fp_exp_-20_tl}
-% \begin{variable}{\c_fp_exp_-30_tl}
-% \begin{variable}{\c_fp_exp_-40_tl}
-% \begin{variable}{\c_fp_exp_-50_tl}
-% \begin{variable}{\c_fp_exp_-60_tl}
-% \begin{variable}{\c_fp_exp_-70_tl}
-% \begin{variable}{\c_fp_exp_-80_tl}
-% \begin{variable}{\c_fp_exp_-90_tl}
-% \begin{variable}{\c_fp_exp_-100_tl}
-% \begin{variable}{\c_fp_exp_-200_tl}
-% Now the negative integers.
-%    \begin{macrocode}
-\tl_const:cn { c_fp_exp_-1_tl }   { { 3 } { 678794411 } { 71442322 }  { -1 } }
-\tl_const:cn { c_fp_exp_-2_tl }   { { 1 } { 353352832 } { 366132692 } { -1 } }
-\tl_const:cn { c_fp_exp_-3_tl }   { { 4 } { 978706836 } { 786394298 } { -2 } }
-\tl_const:cn { c_fp_exp_-4_tl }   { { 1 } { 831563888 } { 873418029 } { -2 } }
-\tl_const:cn { c_fp_exp_-5_tl }   { { 6 } { 737946999 } { 085467097 } { -3 } }
-\tl_const:cn { c_fp_exp_-6_tl }   { { 2 } { 478752176 } { 666358423 } { -3 } }
-\tl_const:cn { c_fp_exp_-7_tl }   { { 9 } { 118819655 } { 545162080 } { -4 } }
-\tl_const:cn { c_fp_exp_-8_tl }   { { 3 } { 354626279 } { 025118388 } { -4 } }
-\tl_const:cn { c_fp_exp_-9_tl }   { { 1 } { 234098040 } { 866795495 } { -4 } }
-\tl_const:cn { c_fp_exp_-10_tl }  { { 4 } { 539992976 } { 248451536 } { -5 } }
-\tl_const:cn { c_fp_exp_-20_tl }  { { 2 } { 061153622 } { 438557828 } { -9 } }
-\tl_const:cn { c_fp_exp_-30_tl }  { { 9 } { 357622968 } { 840174605 } { -14 } }
-\tl_const:cn { c_fp_exp_-40_tl }  { { 4 } { 248354255 } { 291588995 } { -18 } }
-\tl_const:cn { c_fp_exp_-50_tl }  { { 1 } { 928749847 } { 963917783 } { -22 } }
-\tl_const:cn { c_fp_exp_-60_tl }  { { 8 } { 756510762 } { 696520338 } { -27 } }
-\tl_const:cn { c_fp_exp_-70_tl }  { { 3 } { 975449735 } { 908646808 } { -31 } }
-\tl_const:cn { c_fp_exp_-80_tl }  { { 1 } { 804851387 } { 845415172 } { -35 } }
-\tl_const:cn { c_fp_exp_-90_tl }  { { 8 } { 194012623 } { 990515430 } { -40 } }
-\tl_const:cn { c_fp_exp_-100_tl } { { 3 } { 720075976 } { 020835963 } { -44 } }
-\tl_const:cn { c_fp_exp_-200_tl } { { 1 } { 383896526 } { 736737530 } { -87 } }
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{macro}{\fp_exp:Nn, \fp_exp:cn}
-% \UnitTested
-% \begin{macro}{\fp_gexp:Nn,\fp_gexp:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_exp_aux:NNn}
-% \begin{macro}[aux]{\fp_exp_internal:}
-% \begin{macro}[aux]{\fp_exp_aux:}
-% \begin{macro}[aux]{\fp_exp_integer:}
-% \begin{macro}[aux]{\fp_exp_integer_tens:}
-% \begin{macro}[aux]{\fp_exp_integer_units:}
-% \begin{macro}[aux]{\fp_exp_integer_const:n}
-% \begin{macro}[aux]{\fp_exp_integer_const:nnnn}
-% \begin{macro}[aux]{\fp_exp_decimal:}
-% \begin{macro}[aux]{\fp_exp_Taylor:}
-% \begin{macro}[aux]{\fp_exp_const:Nx}
-% \begin{macro}[aux]{\fp_exp_const:cx}
-%   The calculation of an exponent starts off starts in much the same
-%   way as the trigonometric functions: normalise the input, look for
-%   a pre-defined value and if one is not found hand off to the real
-%   workhorse function. The test for a definition of the result is used
-%   so that overflows do not result in any outcome being defined.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_exp:Nn  { \fp_exp_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gexp:Nn { \fp_exp_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_exp:Nn  { c }
-\cs_generate_variant:Nn \fp_gexp:Nn { c }
-\cs_new_protected:Npn \fp_exp_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \l_fp_input_a_extended_int \c_zero
-      \tl_set:Nx \l_fp_arg_tl
-        {
-          \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-            -
-          \else:
-            +
-          \fi:
-          \int_use:N \l_fp_input_a_integer_int
-          .
-          \exp_after:wN \use_none:n
-            \int_value:w \int_eval:w
-               \l_fp_input_a_decimal_int + \c_one_thousand_million
-          e
-          \int_use:N \l_fp_input_a_exponent_int
-        }
-      \if_cs_exist:w c_fp_exp ( \l_fp_arg_tl ) _fp \cs_end:
-      \else:
-        \exp_after:wN \fp_exp_internal:
-      \fi:
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              \if_cs_exist:w c_fp_exp ( \l_fp_arg_tl ) _fp
-                \cs_end:
-                \use:c { c_fp_exp ( \l_fp_arg_tl ) _fp }
-              \else:
-                \c_zero_fp
-              \fi:
-            }
-        }
-    \fp_tmp:w
-  }
-%    \end{macrocode}
-%   The first real step is to convert the input into a fixed-point
-%   representation for further calculation: anything which is dropped
-%   here as too small would not influence the output in any case. There
-%   are a couple of overflow tests: the maximum
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_exp_internal:
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int < \c_three
-      \fp_extended_normalise:
-      \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-        \if_int_compare:w \l_fp_input_a_integer_int < 230 \scan_stop:
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \fp_exp_aux:
-        \else:
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \fp_exp_overflow_msg:
-          \fi:
-      \else:
-        \if_int_compare:w \l_fp_input_a_integer_int < 230 \scan_stop:
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN  \fp_exp_aux:
-        \else:
-          \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
-            { \c_zero_fp }
-        \fi:
-      \fi:
-    \else:
-      \exp_after:wN \fp_exp_overflow_msg:
-    \fi:
-  }
-%    \end{macrocode}
-%   The main algorithm makes use of the fact that
-%   \[
-%     \mathrm{e}^{nmp.q} =
-%       \mathrm{e}^{n}
-%       \mathrm{e}^{m}
-%       \mathrm{e}^{p}
-%       \mathrm{e}^{0.q}
-%   \]
-%   and that there is a Taylor series that can be used to calculate
-%   $ \mathrm{e}^{0.q} $. Thus the approach needed is in three parts.
-%   First, the exponent of the integer part of the input is found
-%   using the pre-calculated constants. Second, the Taylor series is
-%   used to find the exponent for the decimal part of the input. Finally,
-%   the two parts are multiplied together to give the result. As the
-%   normalisation code will already have dealt with any overflowing
-%   values, there are no further checks needed.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_exp_aux:
-  {
-    \if_int_compare:w \l_fp_input_a_integer_int > \c_zero
-      \exp_after:wN \fp_exp_integer:
-    \else:
-      \l_fp_output_integer_int  \c_one
-      \l_fp_output_decimal_int  \c_zero
-      \l_fp_output_extended_int \c_zero
-      \l_fp_output_exponent_int \c_zero
-      \exp_after:wN \fp_exp_decimal:
-    \fi:
-  }
-%    \end{macrocode}
-%   The integer part calculation starts with the hundreds. This is
-%   set up such that very large negative numbers can short-cut the entire
-%   procedure and simply return zero. In other cases, the code either
-%   recovers the exponent of the hundreds value or sets the appropriate
-%   storage to one (so that multiplication works correctly).
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_exp_integer:
-  {
-    \if_int_compare:w \l_fp_input_a_integer_int < \c_one_hundred
-      \l_fp_exp_integer_int  \c_one
-      \l_fp_exp_decimal_int  \c_zero
-      \l_fp_exp_extended_int \c_zero
-      \l_fp_exp_exponent_int \c_zero
-      \exp_after:wN \fp_exp_integer_tens:
-    \else:
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \exp_after:wN \use_i:nnn
-            \int_use:N \l_fp_input_a_integer_int
-        }
-      \l_fp_input_a_integer_int
-        \int_eval:w
-          \l_fp_input_a_integer_int - \l_fp_internal_tl 00
-        \int_eval_end:
-      \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-        \if_int_compare:w \l_fp_output_integer_int > 200 \scan_stop:
-          \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
-            { \c_zero_fp }
-        \else:
-          \fp_exp_integer_const:n { - \l_fp_internal_tl 00 }
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \fp_exp_integer_tens:
-        \fi:
-      \else:
-        \fp_exp_integer_const:n { \l_fp_internal_tl 00 }
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \fp_exp_integer_tens:
-      \fi:
-    \fi:
-  }
-%    \end{macrocode}
-%   The tens and units parts are handled in a similar way, with a
-%   multiplication step to build up the final value. That also includes a
-%   correction step to avoid an overflow of the integer part.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_exp_integer_tens:
-  {
-    \l_fp_output_integer_int  \l_fp_exp_integer_int
-    \l_fp_output_decimal_int  \l_fp_exp_decimal_int
-    \l_fp_output_extended_int \l_fp_exp_extended_int
-    \l_fp_output_exponent_int \l_fp_exp_exponent_int
-    \if_int_compare:w \l_fp_input_a_integer_int > \c_nine
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \exp_after:wN \use_i:nn
-            \int_use:N \l_fp_input_a_integer_int
-        }
-      \l_fp_input_a_integer_int
-        \int_eval:w
-          \l_fp_input_a_integer_int - \l_fp_internal_tl 0
-        \int_eval_end:
-      \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-        \fp_exp_integer_const:n { \l_fp_internal_tl 0 }
-      \else:
-        \fp_exp_integer_const:n { - \l_fp_internal_tl 0 }
-      \fi:
-      \fp_mul:NNNNNNNNN
-        \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-      \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
-      \fp_extended_normalise_output:
-    \fi:
-    \fp_exp_integer_units:
-  }
-\cs_new_protected_nopar:Npn \fp_exp_integer_units:
-  {
-    \if_int_compare:w \l_fp_input_a_integer_int > \c_zero
-      \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-        \fp_exp_integer_const:n { \int_use:N \l_fp_input_a_integer_int }
-      \else:
-        \fp_exp_integer_const:n
-          { - \int_use:N \l_fp_input_a_integer_int }
-      \fi:
-      \fp_mul:NNNNNNNNN
-        \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-      \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
-      \fp_extended_normalise_output:
-    \fi:
-    \fp_exp_decimal:
-  }
-%    \end{macrocode}
-%   Recovery of the stored constant values into the separate registers
-%   is done with a simple expansion then assignment.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_exp_integer_const:n #1
-  {
-    \exp_after:wN \exp_after:wN \exp_after:wN
-      \fp_exp_integer_const:nnnn
-      \cs:w c_fp_exp_ #1 _tl \cs_end:
-  }
-\cs_new_protected:Npn \fp_exp_integer_const:nnnn #1#2#3#4
-  {
-    \l_fp_exp_integer_int  #1 \scan_stop:
-    \l_fp_exp_decimal_int  #2 \scan_stop:
-    \l_fp_exp_extended_int #3 \scan_stop:
-    \l_fp_exp_exponent_int #4 \scan_stop:
-  }
-%    \end{macrocode}
-%   Finding the exponential for the decimal part of the number requires
-%   a Taylor series calculation. The set up is done here with the loop
-%   itself a separate function. Once the decimal part is available this
-%   is multiplied by the integer part already worked out to give
-%   the final result.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_exp_decimal:
-  {
-    \if_int_compare:w \l_fp_input_a_decimal_int > \c_zero
-      \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-        \l_fp_exp_integer_int  \c_one
-        \l_fp_exp_decimal_int  \l_fp_input_a_decimal_int
-        \l_fp_exp_extended_int \l_fp_input_a_extended_int
-      \else:
-        \l_fp_exp_integer_int \c_zero
-        \if_int_compare:w \l_fp_exp_extended_int = \c_zero
-          \l_fp_exp_decimal_int
-            \int_eval:w
-              \c_one_thousand_million - \l_fp_input_a_decimal_int
-            \int_eval_end:
-          \l_fp_exp_extended_int \c_zero
-        \else:
-          \l_fp_exp_decimal_int
-            \int_eval:w
-              999999999 - \l_fp_input_a_decimal_int
-            \scan_stop:
-          \l_fp_exp_extended_int
-            \int_eval:w
-              \c_one_thousand_million - \l_fp_input_a_extended_int
-            \int_eval_end:
-        \fi:
-      \fi:
-      \l_fp_input_b_sign_int     \l_fp_input_a_sign_int
-      \l_fp_input_b_decimal_int  \l_fp_input_a_decimal_int
-      \l_fp_input_b_extended_int \l_fp_input_a_extended_int
-      \l_fp_count_int \c_one
-      \fp_exp_Taylor:
-      \fp_mul:NNNNNNNNN
-        \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-    \fi:
-    \if_int_compare:w \l_fp_output_extended_int < \c_five_hundred_million
-    \else:
-      \tex_advance:D \l_fp_output_decimal_int \c_one
-      \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
-      \else:
-        \l_fp_output_decimal_int \c_zero
-        \tex_advance:D \l_fp_output_integer_int \c_one
-      \fi:
-    \fi:
-    \fp_standardise:NNNN
-      \l_fp_output_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
-      {
-        +
-        \int_use:N \l_fp_output_integer_int
-        .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_output_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_output_exponent_int
-      }
-  }
-%    \end{macrocode}
-%   The Taylor series for $ \exp(x) $ is
-%   \[
-%     1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots
-%   \]
-%   which converges for $ -1 < x < 1 $. The code above sets up
-%   the $ x $ part, leaving the loop to multiply the running
-%   value by $ x / n $ and add it onto the sum. The way that this is
-%   done is that the running total is stored in the \texttt{exp} set of
-%   registers, while the current item is stored as \texttt{input_b}.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_exp_Taylor:
-  {
-    \tex_advance:D \l_fp_count_int \c_one
-    \tex_multiply:D \l_fp_input_b_sign_int \l_fp_input_a_sign_int
-    \fp_mul:NNNNNN
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-      \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-    \fp_div_integer:NNNNN
-      \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-      \l_fp_count_int
-      \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-    \if_int_compare:w
-      \int_eval:w
-        \l_fp_input_b_decimal_int + \l_fp_input_b_extended_int
-        > \c_zero
-      \if_int_compare:w \l_fp_input_b_sign_int > \c_zero
-        \tex_advance:D \l_fp_exp_decimal_int \l_fp_input_b_decimal_int
-        \tex_advance:D \l_fp_exp_extended_int
-          \l_fp_input_b_extended_int
-        \if_int_compare:w \l_fp_exp_extended_int < \c_one_thousand_million
-      \else:
-          \tex_advance:D \l_fp_exp_decimal_int \c_one
-          \tex_advance:D \l_fp_exp_extended_int
-            -\c_one_thousand_million
-        \fi:
-        \if_int_compare:w \l_fp_exp_decimal_int < \c_one_thousand_million
-        \else:
-          \tex_advance:D \l_fp_exp_integer_int \c_one
-          \tex_advance:D \l_fp_exp_decimal_int
-            -\c_one_thousand_million
-        \fi:
-      \else:
-        \tex_advance:D \l_fp_exp_decimal_int -\l_fp_input_b_decimal_int
-        \tex_advance:D \l_fp_exp_extended_int
-          -\l_fp_input_a_extended_int
-        \if_int_compare:w \l_fp_exp_extended_int < \c_zero
-          \tex_advance:D \l_fp_exp_decimal_int \c_minus_one
-          \tex_advance:D \l_fp_exp_extended_int \c_one_thousand_million
-        \fi:
-        \if_int_compare:w \l_fp_exp_decimal_int < \c_zero
-          \tex_advance:D \l_fp_exp_integer_int \c_minus_one
-          \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
-        \fi:
-      \fi:
-      \exp_after:wN \fp_exp_Taylor:
-    \fi:
-  }
-%    \end{macrocode}
-%   This is set up as a function so that the power code can redirect
-%   the effect.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_exp_const:Nx #1#2
-  {
-    \tl_new:N #1
-    \tl_gset:Nx #1 {#2}
-  }
-\cs_generate_variant:Nn \fp_exp_const:Nx { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{variable}{\c_fp_ln_10_1_tl}
-% \begin{variable}{\c_fp_ln_10_2_tl}
-% \begin{variable}{\c_fp_ln_10_3_tl}
-% \begin{variable}{\c_fp_ln_10_4_tl}
-% \begin{variable}{\c_fp_ln_10_5_tl}
-% \begin{variable}{\c_fp_ln_10_6_tl}
-% \begin{variable}{\c_fp_ln_10_7_tl}
-% \begin{variable}{\c_fp_ln_10_8_tl}
-% \begin{variable}{\c_fp_ln_10_9_tl}
-%   Constants for working out logarithms: first those for the powers of
-%   ten.
-%    \begin{macrocode}
-\tl_const:cn { c_fp_ln_10_1_tl } { { 2 } { 302585092 } { 994045684 } { 0 } }
-\tl_const:cn { c_fp_ln_10_2_tl } { { 4 } { 605170185 } { 988091368 } { 0 } }
-\tl_const:cn { c_fp_ln_10_3_tl } { { 6 } { 907755278 } { 982137052 } { 0 } }
-\tl_const:cn { c_fp_ln_10_4_tl } { { 9 } { 210340371 } { 976182736 } { 0 } }
-\tl_const:cn { c_fp_ln_10_5_tl } { { 1 } { 151292546 } { 497022842 } { 1 } }
-\tl_const:cn { c_fp_ln_10_6_tl } { { 1 } { 381551055 } { 796427410 } { 1 } }
-\tl_const:cn { c_fp_ln_10_7_tl } { { 1 } { 611809565 } { 095831979 } { 1 } }
-\tl_const:cn { c_fp_ln_10_8_tl } { { 1 } { 842068074 } { 395226547 } { 1 } }
-\tl_const:cn { c_fp_ln_10_9_tl } { { 2 } { 072326583 } { 694641116 } { 1 } }
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%^^A 0.69...309 4.
-% \begin{variable}{\c_fp_ln_2_1_tl }
-% \begin{variable}{\c_fp_ln_2_2_tl }
-% \begin{variable}{\c_fp_ln_2_3_tl }
-% The smaller set for powers of two.
-%    \begin{macrocode}
-\tl_const:cn { c_fp_ln_2_1_tl } { { 0 } { 693147180 } { 559945309 } { 0 } }
-\tl_const:cn { c_fp_ln_2_2_tl } { { 1 } { 386294361 } { 119890618 } { 0 } }
-\tl_const:cn { c_fp_ln_2_3_tl } { { 2 } { 079441541 } { 679835928 } { 0 } }
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{macro}{\fp_ln:Nn, \fp_ln:cn}
-% \UnitTested
-% \begin{macro}{\fp_gln:Nn,\fp_gln:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_ln_aux:NNn}
-% \begin{macro}[aux]{\fp_ln_aux:}
-% \begin{macro}[aux]{\fp_ln_exponent:}
-% \begin{macro}[aux]{\fp_ln_internal:}
-% \begin{macro}[aux]{\fp_ln_exponent_tens:}
-% \begin{macro}[aux]{\fp_ln_exponent_units:}
-% \begin{macro}[aux]{\fp_ln_normalise:}
-% \begin{macro}[aux]{\fp_ln_nornalise_aux:NNNNNNNNN}
-% \begin{macro}[aux]{\fp_ln_mantissa:}
-% \begin{macro}[aux]{\fp_ln_mantissa_aux:}
-% \begin{macro}[aux]{\fp_ln_mantissa_divide_two:}
-% \begin{macro}[aux]{\fp_ln_integer_const:nn}
-% \begin{macro}[aux]{\fp_ln_Taylor:}
-% \begin{macro}[aux]{\fp_ln_fixed:}
-% \begin{macro}[aux]{\fp_ln_fixed_aux:NNNNNNNNN}
-% \begin{macro}[aux]{\fp_ln_Taylor_aux:}
-%   The approach for logarithms is again based on a mix of tables and
-%   Taylor series. Here, the initial validation is a bit easier and so it
-%   is set up earlier, meaning less need to escape later on.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_ln:Nn  { \fp_ln_aux:NNn \tl_set:Nn  }
-\cs_new_protected_nopar:Npn \fp_gln:Nn { \fp_ln_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_ln:Nn  { c }
-\cs_generate_variant:Nn \fp_gln:Nn { c }
-\cs_new_protected:Npn \fp_ln_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-        \if_int_compare:w
-          \int_eval:w
-            \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-            > \c_zero
-          \exp_after:wN \exp_after:wN \exp_after:wN \fp_ln_aux:
-        \else:
-          \cs_set_protected:Npx \fp_tmp:w ##1##2
-            {
-              \group_end:
-              ##1 \exp_not:N ##2 { \c_zero_fp }
-            }
-          \exp_after:wN \exp_after:wN \exp_after:wN \fp_ln_error_msg:
-        \fi:
-      \else:
-        \cs_set_protected:Npx \fp_tmp:w ##1##2
-          {
-            \group_end:
-            ##1 \exp_not:N ##2 { \c_zero_fp }
-          }
-        \exp_after:wN \fp_ln_error_msg:
-      \fi:
-    \fp_tmp:w #1 #2
-  }
-%    \end{macrocode}
-%   As the input at this stage meets the validity criteria above, the
-%   argument can now be saved for further processing. There is no need
-%   to look at the sign of the input as it must be positive. The function
-%   here simply sets up to either do the full calculation or recover
-%   the stored value, as appropriate.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_ln_aux:
-  {
-    \tl_set:Nx \l_fp_arg_tl
-      {
-        +
-        \int_use:N \l_fp_input_a_integer_int
-        .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_input_a_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_input_a_exponent_int
-      }
-    \if_cs_exist:w c_fp_ln ( \l_fp_arg_tl ) _fp \cs_end:
-    \else:
-      \exp_after:wN \fp_ln_exponent:
-    \fi:
-    \cs_set_protected:Npx \fp_tmp:w ##1##2
-      {
-        \group_end:
-        ##1 \exp_not:N ##2
-          { \use:c { c_fp_ln ( \l_fp_arg_tl ) _fp } }
-      }
-  }
-%    \end{macrocode}
-%   The main algorithm here uses the fact the logarithm can be divided
-%   up, first taking out the powers of ten, then powers of two and finally
-%   using a Taylor series for the remainder.
-%   \[
-%     \ln ( 10^{n} \times 2^{m} \times x )
-%       = \ln ( 10^{n} ) + \ln ( 2^{m} ) + \ln ( x )
-%   \]
-%   The second point to remember is that
-%   \[
-%     \ln ( x^{-1} ) = - \ln ( x )
-%   \]
-%   which means that for the powers of $ 10 $ and $ 2 $ constants
-%   are only needed for positive powers.
-%
-%   The first step is to set up the sign for the output functions and
-%   work out the powers of ten in the exponent. First the larger powers
-%   are sorted out. The values for the constants are the same as those
-%   for the smaller ones, just with a shift in the exponent.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_ln_exponent:
-  {
-    \fp_ln_internal:
-    \if_int_compare:w \l_fp_output_extended_int < \c_five_hundred_million
-    \else:
-      \tex_advance:D \l_fp_output_decimal_int \c_one
-      \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
-      \else:
-        \l_fp_output_decimal_int \c_zero
-        \tex_advance:D \l_fp_output_integer_int \c_one
-      \fi:
-    \fi:
-    \fp_standardise:NNNN
-      \l_fp_output_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \tl_const:cx { c_fp_ln ( \l_fp_arg_tl ) _fp }
-      {
-        \if_int_compare:w \l_fp_output_sign_int > \c_zero
-          +
-        \else:
-          -
-        \fi:
-        \int_use:N \l_fp_output_integer_int
-        .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_output_decimal_int + \c_one_thousand_million
-           \scan_stop:
-        e
-        \int_use:N \l_fp_output_exponent_int
-      }
-  }
-\cs_new_protected_nopar:Npn \fp_ln_internal:
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int < \c_zero
-      \l_fp_input_a_exponent_int -\l_fp_input_a_exponent_int
-      \l_fp_output_sign_int \c_minus_one
-    \else:
-      \l_fp_output_sign_int \c_one
-    \fi:
-    \if_int_compare:w \l_fp_input_a_exponent_int > \c_nine
-      \exp_after:wN \fp_ln_exponent_tens:NN
-        \int_use:N \l_fp_input_a_exponent_int
-    \else:
-      \l_fp_output_integer_int  \c_zero
-      \l_fp_output_decimal_int  \c_zero
-      \l_fp_output_extended_int \c_zero
-      \l_fp_output_exponent_int \c_zero
-    \fi:
-    \fp_ln_exponent_units:
-  }
-\cs_new_protected:Npn \fp_ln_exponent_tens:NN #1 #2
-  {
-    \l_fp_input_a_exponent_int #2 \scan_stop:
-    \fp_ln_const:nn { 10 } { #1 }
-    \tex_advance:D \l_fp_exp_exponent_int \c_one
-    \l_fp_output_integer_int  \l_fp_exp_integer_int
-    \l_fp_output_decimal_int  \l_fp_exp_decimal_int
-    \l_fp_output_extended_int \l_fp_exp_extended_int
-    \l_fp_output_exponent_int \l_fp_exp_exponent_int
-  }
-%    \end{macrocode}
-%   Next the smaller powers of ten, which will need to be combined
-%   with the above: always an additive process.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_ln_exponent_units:
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int > \c_zero
-      \fp_ln_const:nn { 10 } { \int_use:N \l_fp_input_a_exponent_int }
-      \fp_ln_normalise:
-      \fp_add:NNNNNNNNN
-        \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-    \fi:
-    \fp_ln_mantissa:
-  }
-%    \end{macrocode}
-%   The smaller table-based parts may need to be exponent shifted so that
-%   they stay in line with the larger parts. This is similar to the
-%   approach in other places, but here there is a need to watch the
-%   extended part of the number. The only case where the new exponent is
-%   larger than the old is if there was no previous part. Then simply set
-%   the exponent.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_ln_normalise:
-  {
-    \if_int_compare:w \l_fp_exp_exponent_int < \l_fp_output_exponent_int
-      \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
-      \exp_after:wN \use_i:nn \exp_after:wN
-        \fp_ln_normalise_aux:NNNNNNNNN
-        \int_use:N \l_fp_exp_decimal_int
-       \exp_after:wN \fp_ln_normalise:
-    \else:
-      \l_fp_output_exponent_int \l_fp_exp_exponent_int
-    \fi:
-  }
-\cs_new_protected:Npn \fp_ln_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {
-    \if_int_compare:w \l_fp_exp_integer_int = \c_zero
-      \l_fp_exp_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
-    \else:
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \int_use:N \l_fp_exp_integer_int
-          #1#2#3#4#5#6#7#8
-        }
-      \l_fp_exp_integer_int \c_zero
-      \l_fp_exp_decimal_int \l_fp_internal_tl \scan_stop:
-    \fi:
-    \tex_divide:D \l_fp_exp_extended_int \c_ten
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        #9
-        \int_use:N \l_fp_exp_extended_int
-      }
-    \l_fp_exp_extended_int \l_fp_internal_tl \scan_stop:
-    \tex_advance:D \l_fp_exp_exponent_int \c_one
-  }
-%    \end{macrocode}
-%   The next phase is to decompose the mantissa by division by two to
-%   leave a value which is in the range $ 1 \le x < 2 $. The sum of the
-%   two powers needs to take account of the sign of the output: if it
-%   is negative then the result gets \emph{smaller} as the mantissa gets
-%   \emph{bigger}.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_ln_mantissa:
-  {
-    \l_fp_count_int \c_zero
-    \l_fp_input_a_extended_int \c_zero
-    \fp_ln_mantissa_aux:
-    \if_int_compare:w \l_fp_count_int > \c_zero
-      \fp_ln_const:nn { 2 } { \int_use:N \l_fp_count_int }
-      \fp_ln_normalise:
-      \if_int_compare:w \l_fp_output_sign_int > \c_zero
-        \exp_after:wN \fp_add:NNNNNNNNN
-      \else:
-        \exp_after:wN \fp_sub:NNNNNNNNN
-      \fi:
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-      \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-    \fi:
-    \if_int_compare:w
-      \int_eval:w
-        \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int > \c_one
-      \exp_after:wN \fp_ln_Taylor:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_ln_mantissa_aux:
-  {
-    \if_int_compare:w \l_fp_input_a_integer_int > \c_one
-      \tex_advance:D \l_fp_count_int \c_one
-      \fp_ln_mantissa_divide_two:
-      \exp_after:wN \fp_ln_mantissa_aux:
-    \fi:
-  }
-%    \end{macrocode}
-%   A fast one-shot division by two.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_ln_mantissa_divide_two:
-  {
-    \if_int_odd:w \l_fp_input_a_decimal_int
-      \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
-    \fi:
-    \if_int_odd:w \l_fp_input_a_integer_int
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \fi:
-    \tex_divide:D \l_fp_input_a_integer_int  \c_two
-    \tex_divide:D \l_fp_input_a_decimal_int  \c_two
-    \tex_divide:D \l_fp_input_a_extended_int \c_two
-  }
-%    \end{macrocode}
-%   Recovering constants makes use of the same auxiliary code as for
-%   exponents.
-%    \begin{macrocode}
-\cs_new_protected:Npn \fp_ln_const:nn #1#2
-  {
-    \exp_after:wN \exp_after:wN \exp_after:wN
-      \fp_exp_integer_const:nnnn
-      \cs:w c_fp_ln_ #1 _ #2 _tl \cs_end:
-  }
-%    \end{macrocode}
-%   The Taylor series for the logarithm function is best implemented using
-%   the identity
-%   \[
-%     \ln(x) = \ln\left( \frac{y + 1}{y - 1} \right)
-%   \]
-%   with
-%   \[
-%     y = \frac{x - 1}{x + 1}
-%   \]
-%   This leads to the series
-%   \[
-%     \ln(x)
-%       = 2y
-%         \left(
-%           1 + y^{2}
-%             \left(
-%               \frac{1}{3} + y^{2}
-%                 \left(
-%                   \frac{1}{5} + y^{2}
-%                     \left(
-%                       \frac{1}{7} + y^{2}
-%                         \left(
-%                           \frac{1}{9} + \cdots
-%                         \right)
-%                     \right)
-%                 \right)
-%             \right)
-%         \right)
-%   \]
-%   This expansion has the advantage that a lot of the work can be
-%   loaded up early by finding $ y^{2} $ before the loop itself starts.
-%   (In practice, the implementation does the multiplication by two at the
-%   end of the loop, and expands out the brackets as this is an overall
-%   more efficient approach.)
-%
-%   At the implementation level, the code starts by calculating $ y $
-%   and storing that in input \texttt{a} (which is no longer needed
-%   for other purposes). That is done using the full division system
-%   avoiding the parsing step. The value is then switched to a fixed-point
-%   representation. There is then some shuffling to get all of the working
-%   space set up. At this stage, a lot of registers are in use and so
-%   the Taylor series is calculated within a group so that the
-%   \texttt{output} variables can be used to hold the result. The value
-%   of $ y^{2} $ is held in input \texttt{b} (there are a few
-%   assignments saved by choosing this over \texttt{a}), while input
-%   \texttt{a} is used for the \enquote{loop value}.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_ln_Taylor:
-  {
-    \group_begin:
-      \l_fp_input_a_integer_int \c_zero
-      \l_fp_input_a_exponent_int \c_zero
-      \l_fp_input_b_integer_int \c_two
-      \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
-      \l_fp_input_b_exponent_int \c_zero
-      \fp_div_internal:
-      \fp_ln_fixed:
-      \l_fp_input_a_integer_int  \l_fp_output_integer_int
-      \l_fp_input_a_decimal_int  \l_fp_output_decimal_int
-      \l_fp_input_a_extended_int \c_zero
-      \l_fp_input_a_exponent_int \l_fp_output_exponent_int
-      \l_fp_output_decimal_int \c_zero %^^A Bug?
-      \l_fp_output_decimal_int  \l_fp_input_a_decimal_int
-      \l_fp_output_extended_int \l_fp_input_a_extended_int
-      \fp_mul:NNNNNN
-        \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-        \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-        \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-      \l_fp_count_int \c_one
-      \fp_ln_Taylor_aux:
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          \l_fp_exp_integer_int \c_zero
-          \exp_not:N \l_fp_exp_decimal_int
-            \int_use:N \l_fp_output_decimal_int \scan_stop:
-          \exp_not:N \l_fp_exp_extended_int
-            \int_use:N \l_fp_output_extended_int \scan_stop:
-          \exp_not:N \l_fp_exp_exponent_int
-            \int_use:N \l_fp_output_exponent_int \scan_stop:
-        }
-    \fp_tmp:w
-%    \end{macrocode}
-%   After the loop part of the Taylor series, the factor of $ 2 $ needs
-%   to be included. The total for the result can then be constructed.
-%    \begin{macrocode}
-    \tex_advance:D \l_fp_exp_decimal_int \l_fp_exp_decimal_int
-    \if_int_compare:w \l_fp_exp_extended_int < \c_five_hundred_million
-    \else:
-      \tex_advance:D \l_fp_exp_extended_int -\c_five_hundred_million
-      \tex_advance:D \l_fp_exp_decimal_int \c_one
-    \fi:
-    \tex_advance:D \l_fp_exp_extended_int \l_fp_exp_extended_int
-    \fp_ln_normalise:
-    \if_int_compare:w \l_fp_output_sign_int > \c_zero
-      \exp_after:wN \fp_add:NNNNNNNNN
-    \else:
-      \exp_after:wN \fp_sub:NNNNNNNNN
-    \fi:
-    \l_fp_output_integer_int \l_fp_output_decimal_int
-      \l_fp_output_extended_int
-    \c_zero \l_fp_exp_decimal_int \l_fp_exp_extended_int
-    \l_fp_output_integer_int \l_fp_output_decimal_int
-      \l_fp_output_extended_int
-  }
-%    \end{macrocode}
-% The usual shifts to move to fixed-point working. This is done using
-% the \texttt{output} registers as this saves a reassignment here.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_ln_fixed:
-  {
-    \if_int_compare:w \l_fp_output_exponent_int < \c_zero
-      \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
-      \exp_after:wN \use_i:nn \exp_after:wN
-        \fp_ln_fixed_aux:NNNNNNNNN
-        \int_use:N \l_fp_output_decimal_int
-       \exp_after:wN \fp_ln_fixed:
-     \fi:
-  }
-\cs_new_protected:Npn \fp_ln_fixed_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {
-    \if_int_compare:w \l_fp_output_integer_int = \c_zero
-      \l_fp_output_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
-    \else:
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \int_use:N \l_fp_output_integer_int
-          #1#2#3#4#5#6#7#8
-        }
-      \l_fp_output_integer_int \c_zero
-      \l_fp_output_decimal_int \l_fp_internal_tl \scan_stop:
-    \fi:
-    \tex_advance:D \l_fp_output_exponent_int \c_one
-  }
-%    \end{macrocode}
-%   The main loop for the Taylor series: unlike some of the other similar
-%   functions, the result here is not the final value and is therefore
-%   subject to further manipulation outside of the loop.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_ln_Taylor_aux:
-  {
-    \tex_advance:D \l_fp_count_int \c_two
-    \fp_mul:NNNNNN
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-    \if_int_compare:w
-      \int_eval:w
-        \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
-        > \c_zero
-      \fp_div_integer:NNNNN
-        \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-        \l_fp_count_int
-        \l_fp_exp_decimal_int \l_fp_exp_extended_int
-        \tex_advance:D \l_fp_output_decimal_int \l_fp_exp_decimal_int
-        \tex_advance:D \l_fp_output_extended_int \l_fp_exp_extended_int
-        \if_int_compare:w \l_fp_output_extended_int < \c_one_thousand_million
-        \else:
-          \tex_advance:D \l_fp_output_decimal_int \c_one
-          \tex_advance:D \l_fp_output_extended_int
-            -\c_one_thousand_million
-        \fi:
-        \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
-        \else:
-          \tex_advance:D \l_fp_output_integer_int \c_one
-          \tex_advance:D \l_fp_output_decimal_int
-            -\c_one_thousand_million
-        \fi:
-      \exp_after:wN \fp_ln_Taylor_aux:
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\fp_pow:Nn, \fp_pow:cn}
-% \UnitTested
-% \begin{macro}{\fp_gpow:Nn,\fp_gpow:cn}
-% \UnitTested
-% \begin{macro}[aux]{\fp_pow_aux:NNn}
-% \begin{macro}[aux]{\fp_pow_aux_i:}
-% \begin{macro}[aux]{\fp_pow_positive:}
-% \begin{macro}[aux]{\fp_pow_negative:}
-% \begin{macro}[aux]{\fp_pow_aux_ii:}
-% \begin{macro}[aux]{\fp_pow_aux_iii:}
-% \begin{macro}[aux]{\fp_pow_aux_iv:}
-%   The approach used for working out powers is to first filter out the
-%   various special cases and then do most of the work using the
-%   logarithm and exponent functions. The two storage areas are used
-%   in the reverse of the `natural' logic as this avoids some
-%   re-assignment in the sanity checking code.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_pow:Nn  { \fp_pow_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gpow:Nn { \fp_pow_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_pow:Nn  { c }
-\cs_generate_variant:Nn \fp_gpow:Nn { c }
-\cs_new_protected:Npn \fp_pow_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_read:N #2
-      \l_fp_input_b_sign_int     \l_fp_input_a_sign_int
-      \l_fp_input_b_integer_int  \l_fp_input_a_integer_int
-      \l_fp_input_b_decimal_int  \l_fp_input_a_decimal_int
-      \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \if_int_compare:w
-        \int_eval:w
-          \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
-          = \c_zero
-         \if_int_compare:w
-           \int_eval:w
-             \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-             = \c_zero
-             \cs_set_protected:Npx \fp_tmp:w ##1##2
-               {
-                 \group_end:
-                 ##1 ##2 { \c_undefined_fp }
-               }
-           \else:
-             \cs_set_protected:Npx \fp_tmp:w ##1##2
-               {
-                 \group_end:
-                 ##1 ##2 { \c_zero_fp }
-               }
-          \fi:
-       \else:
-         \if_int_compare:w
-           \int_eval:w
-             \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-             = \c_zero
-             \cs_set_protected:Npx \fp_tmp:w ##1##2
-               {
-                 \group_end:
-                 ##1 ##2 { \c_one_fp }
-               }
-           \else:
-             \exp_after:wN \exp_after:wN \exp_after:wN
-               \fp_pow_aux_i:
-          \fi:
-       \fi:
-    \fp_tmp:w #1 #2
-}
-%    \end{macrocode}
-%   Simply using the logarithm function directly will fail when negative
-%   numbers are raised to integer powers, which is a mathematically valid
-%   operation. So there are some more tests to make, after forcing the
-%   power into an integer and decimal parts, if necessary.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_pow_aux_i:
-  {
-    \if_int_compare:w \l_fp_input_b_sign_int > \c_zero
-      \tl_set:Nn \l_fp_sign_tl { + }
-      \exp_after:wN \fp_pow_aux_ii:
-    \else:
-      \l_fp_input_a_extended_int \c_zero
-      \if_int_compare:w \l_fp_input_a_exponent_int < \c_ten
-        \group_begin:
-        \fp_extended_normalise:
-        \if_int_compare:w
-          \int_eval:w
-            \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
-            = \c_zero
-           \group_end:
-          \tl_set:Nn \l_fp_sign_tl { - }
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \fp_pow_aux_ii:
-        \else:
-          \group_end:
-          \cs_set_protected:Npx \fp_tmp:w ##1##2
-            {
-              \group_end:
-              ##1 ##2 { \c_undefined_fp }
-           }
-        \fi:
-      \else:
-        \cs_set_protected:Npx \fp_tmp:w ##1##2
-          {
-            \group_end:
-            ##1 ##2 { \c_undefined_fp }
-         }
-      \fi:
-    \fi:
-  }
-%    \end{macrocode}
-%   The approach used here for powers works well in most cases but gives
-%   poorer results for negative integer powers, which often have exact
-%   values.  So there is some filtering to do. For negative powers where
-%   the power is small, an alternative approach is used in which the
-%   positive value is worked out and the reciprocal is then taken. The
-%   filtering is unfortunately rather long.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_pow_aux_ii:
-  {
-    \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-      \exp_after:wN \fp_pow_aux_iv:
-    \else:
-      \if_int_compare:w \l_fp_input_a_exponent_int < \c_ten
-        \group_begin:
-        \l_fp_input_a_extended_int \c_zero
-        \fp_extended_normalise:
-        \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
-          \if_int_compare:w \l_fp_input_a_integer_int > \c_ten
-            \group_end:
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-              \fp_pow_aux_iv:
-          \else:
-            \group_end:
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-              \exp_after:wN \fp_pow_aux_iii:
-          \fi:
-        \else:
-          \group_end:
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-              \exp_after:wN \fp_pow_aux_iv:
-        \fi:
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \fp_pow_aux_iv:
-      \fi:
-    \fi:
-    \cs_set_protected:Npx \fp_tmp:w ##1##2
-      {
-        \group_end:
-        ##1 ##2
-          {
-            \l_fp_sign_tl
-            \int_use:N \l_fp_output_integer_int
-            .
-            \exp_after:wN \use_none:n
-              \int_value:w \int_eval:w
-                 \l_fp_output_decimal_int + \c_one_thousand_million
-            e
-            \int_use:N \l_fp_output_exponent_int
-          }
-      }
-  }
-%    \end{macrocode}
-%   For the small negative integer powers, the calculation is done for
-%   the positive power and the reciprocal is then taken.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_pow_aux_iii:
-  {
-    \l_fp_input_a_sign_int \c_one
-    \fp_pow_aux_iv:
-    \l_fp_input_a_integer_int  \c_one
-    \l_fp_input_a_decimal_int  \c_zero
-    \l_fp_input_a_exponent_int \c_zero
-    \l_fp_input_b_integer_int  \l_fp_output_integer_int
-    \l_fp_input_b_decimal_int  \l_fp_output_decimal_int
-    \l_fp_input_b_exponent_int \l_fp_output_exponent_int
-    \fp_div_internal:
-  }
-%    \end{macrocode}
-%   The business end of the code starts by finding the logarithm of the
-%   given base. There is a bit of a shuffle so that this does not have
-%   to be re-parsed and so that the output ends up in the correct place.
-%   There is also a need to enable using the short-cut for a
-%   pre-calculated result. The internal part of the multiplication
-%   function can then be used to do the second part of the calculation
-%   directly. There is some more set up before doing the exponential:
-%   the idea here is to deactivate some internals so that everything works
-%   smoothly.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \fp_pow_aux_iv:
-  {
-    \group_begin:
-      \l_fp_input_a_integer_int  \l_fp_input_b_integer_int
-      \l_fp_input_a_decimal_int  \l_fp_input_b_decimal_int
-      \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int
-      \fp_ln_internal:
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          \exp_not:N \l_fp_input_b_sign_int
-            \int_use:N \l_fp_output_sign_int \scan_stop:
-          \exp_not:N \l_fp_input_b_integer_int
-            \int_use:N \l_fp_output_integer_int \scan_stop:
-          \exp_not:N \l_fp_input_b_decimal_int
-            \int_use:N \l_fp_output_decimal_int \scan_stop:
-          \exp_not:N \l_fp_input_b_extended_int
-            \int_use:N \l_fp_output_extended_int \scan_stop:
-          \exp_not:N \l_fp_input_b_exponent_int
-            \int_use:N \l_fp_output_exponent_int \scan_stop:
-        }
-    \fp_tmp:w
-    \l_fp_input_a_extended_int  \c_zero
-    \fp_mul:NNNNNNNNN
-      \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-        \l_fp_input_a_extended_int
-      \l_fp_input_b_integer_int \l_fp_input_b_decimal_int
-        \l_fp_input_b_extended_int
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-    \l_fp_output_exponent_int
-      \int_eval:w
-        \l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int
-      \scan_stop:
-    \fp_extended_normalise_output:
-    \tex_multiply:D \l_fp_input_a_sign_int \l_fp_input_b_sign_int
-    \l_fp_input_a_integer_int  \l_fp_output_integer_int
-    \l_fp_input_a_decimal_int  \l_fp_output_decimal_int
-    \l_fp_input_a_extended_int \l_fp_output_extended_int
-    \l_fp_input_a_exponent_int \l_fp_output_exponent_int
-    \l_fp_output_integer_int  \c_zero
-    \l_fp_output_decimal_int  \c_zero
-    \l_fp_output_extended_int \c_zero
-    \l_fp_output_exponent_int \c_zero
-    \cs_set_eq:NN \fp_exp_const:Nx \use_none:nn
-    \fp_exp_internal:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
 %
-% \subsection{Tests for special values}
-%
-% \begin{macro}[pTF]{\fp_if_undefined:N}
-% \UnitTested
-%   Testing for an undefined value is easy.
-%    \begin{macrocode}
-\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF }
-  {
-    \if_meaning:w #1 \c_undefined_fp
-      \prg_return_true:
-    \else:
-      \prg_return_false:
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[pTF]{\fp_if_zero:N}
-% \UnitTested
-%   Testing for a zero fixed-point is also easy.
-%    \begin{macrocode}
-\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF }
-  {
-    \if_meaning:w #1 \c_zero_fp
-      \prg_return_true:
-    \else:
-      \prg_return_false:
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \subsection{Floating-point conditionals}
-%
-% \begin{macro}[TF]{\fp_compare:nNn}
-% \begin{macro}[TF]{\fp_compare:NNN}
-% \UnitTested
-% \begin{macro}[aux]{\fp_compare_aux:N}
-% \begin{macro}[aux]{\fp_compare_=:}
-% \begin{macro}[aux]{\fp_compare_<:}
-% \begin{macro}[aux]{\fp_compare_<_aux:}
-% \begin{macro}[aux]{\fp_compare_absolute_a>b:}
-% \begin{macro}[aux]{\fp_compare_absolute_a<b:}
-% \begin{macro}[aux]{\fp_compare_>:}
-%   The idea for the comparisons is to provide two versions: slower and
-%   faster. The lead off for both is the same: get the two numbers
-%   read and then look for a function to handle the comparison.
-%    \begin{macrocode}
-\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3 { T , F , TF }
-  {
-    \group_begin:
-      \fp_split:Nn a {#1}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \fp_split:Nn b {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_b_sign_int
-        \l_fp_input_b_integer_int
-        \l_fp_input_b_decimal_int
-        \l_fp_input_b_exponent_int
-      \fp_compare_aux:N #2
-  }
-\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3 { T , F , TF }
-  {
-    \group_begin:
-      \fp_read:N #3
-      \l_fp_input_b_sign_int     \l_fp_input_a_sign_int
-      \l_fp_input_b_integer_int  \l_fp_input_a_integer_int
-      \l_fp_input_b_decimal_int  \l_fp_input_a_decimal_int
-      \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int
-      \fp_read:N #1
-      \fp_compare_aux:N #2
-  }
-\cs_new_protected:Npn \fp_compare_aux:N #1
-  {
-    \cs_if_exist:cTF { fp_compare_#1: }
-      { \use:c { fp_compare_#1: } }
-      {
-        \group_end:
-        \prg_return_false:
-      }
-  }
-%    \end{macrocode}
-%   For equality, the test is pretty easy as things are either equal or
-%   they are not.
-%    \begin{macrocode}
-\cs_new_protected_nopar:cpn { fp_compare_=: }
-  {
-    \if_int_compare:w \l_fp_input_a_sign_int = \l_fp_input_b_sign_int
-      \if_int_compare:w \l_fp_input_a_integer_int = \l_fp_input_b_integer_int
-        \if_int_compare:w \l_fp_input_a_decimal_int = \l_fp_input_b_decimal_int
-          \if_int_compare:w
-            \l_fp_input_a_exponent_int = \l_fp_input_b_exponent_int
-            \group_end:
-            \prg_return_true:
-          \else:
-            \group_end:
-            \prg_return_false:
-          \fi:
-        \else:
-          \group_end:
-          \prg_return_false:
-        \fi:
-      \else:
-        \group_end:
-        \prg_return_false:
-      \fi:
-    \else:
-      \group_end:
-      \prg_return_false:
-    \fi:
-  }
-%    \end{macrocode}
-%   Comparing two values is quite complex. First, there is a filter step
-%   to check if one or other of the given values is zero. If it is then
-%   the result is relatively easy to determine.
-%    \begin{macrocode}
-\cs_new_protected_nopar:cpn { fp_compare_>: }
-  {
-    \if_int_compare:w \int_eval:w
-      \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-      = \c_zero
-      \if_int_compare:w \int_eval:w
-        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
-        = \c_zero
-        \group_end:
-        \prg_return_false:
-      \else:
-        \if_int_compare:w \l_fp_input_b_sign_int > \c_zero
-          \group_end:
-          \prg_return_false:
-        \else:
-          \group_end:
-          \prg_return_true:
-        \fi:
-      \fi:
-    \else:
-      \if_int_compare:w \int_eval:w
-        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
-        = \c_zero
-        \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-          \group_end:
-          \prg_return_true:
-        \else:
-          \group_end:
-          \prg_return_false:
-        \fi:
-      \else:
-        \use:c { fp_compare_>_aux: }
-      \fi:
-    \fi:
-  }
-%    \end{macrocode}
-%   Next, check the sign of the input: this again may give an obvious
-%   result. If both signs are the same, then hand off to comparing the
-%   absolute values.
-%    \begin{macrocode}
-\cs_new_protected_nopar:cpn { fp_compare_>_aux: }
-  {
-    \if_int_compare:w \l_fp_input_a_sign_int > \l_fp_input_b_sign_int
-      \group_end:
-      \prg_return_true:
-    \else:
-      \if_int_compare:w \l_fp_input_a_sign_int < \l_fp_input_b_sign_int
-        \group_end:
-        \prg_return_false:
-      \else:
-        \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-          \use:c { fp_compare_absolute_a>b: }
-        \else:
-          \use:c { fp_compare_absolute_a<b: }
-        \fi:
-      \fi:
-    \fi:
-  }
-%    \end{macrocode}
-%   Rather long runs of checks, as there is the need to go through each
-%   layer of the input and do the comparison. There is also the need to
-%   avoid messing up with equal inputs at each stage.
-%    \begin{macrocode}
-\cs_new_protected_nopar:cpn { fp_compare_absolute_a>b: }
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
-      \group_end:
-      \prg_return_true:
-    \else:
-      \if_int_compare:w \l_fp_input_a_exponent_int < \l_fp_input_b_exponent_int
-        \group_end:
-        \prg_return_false:
-      \else:
-        \if_int_compare:w \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
-          \group_end:
-          \prg_return_true:
-        \else:
-          \if_int_compare:w
-            \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
-            \group_end:
-            \prg_return_false:
-          \else:
-            \if_int_compare:w
-              \l_fp_input_a_decimal_int > \l_fp_input_b_decimal_int
-              \group_end:
-              \prg_return_true:
-            \else:
-              \group_end:
-              \prg_return_false:
-            \fi:
-          \fi:
-        \fi:
-      \fi:
-    \fi:
-  }
-\cs_new_protected_nopar:cpn { fp_compare_absolute_a<b: }
-  {
-    \if_int_compare:w \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int
-      \group_end:
-      \prg_return_true:
-    \else:
-      \if_int_compare:w \l_fp_input_b_exponent_int < \l_fp_input_a_exponent_int
-        \group_end:
-        \prg_return_false:
-      \else:
-        \if_int_compare:w \l_fp_input_b_integer_int > \l_fp_input_a_integer_int
-          \group_end:
-          \prg_return_true:
-        \else:
-          \if_int_compare:w
-            \l_fp_input_b_integer_int < \l_fp_input_a_integer_int
-            \group_end:
-            \prg_return_false:
-          \else:
-            \if_int_compare:w
-              \l_fp_input_b_decimal_int > \l_fp_input_a_decimal_int
-              \group_end:
-              \prg_return_true:
-            \else:
-              \group_end:
-              \prg_return_false:
-            \fi:
-          \fi:
-        \fi:
-      \fi:
-    \fi:
-  }
-%    \end{macrocode}
-%   This is just a case of reversing the two input values and then
-%   running the tests already defined.
-%    \begin{macrocode}
-\cs_new_protected_nopar:cpn { fp_compare_<: }
-  {
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        \int_set:Nn \exp_not:N \l_fp_input_a_sign_int
-          { \int_use:N \l_fp_input_b_sign_int }
-        \int_set:Nn \exp_not:N \l_fp_input_a_integer_int
-          { \int_use:N \l_fp_input_b_integer_int }
-        \int_set:Nn \exp_not:N \l_fp_input_a_decimal_int
-          { \int_use:N \l_fp_input_b_decimal_int }
-        \int_set:Nn \exp_not:N \l_fp_input_a_exponent_int
-          { \int_use:N \l_fp_input_b_exponent_int }
-        \int_set:Nn \exp_not:N \l_fp_input_b_sign_int
-          { \int_use:N \l_fp_input_a_sign_int }
-        \int_set:Nn \exp_not:N \l_fp_input_b_integer_int
-          { \int_use:N \l_fp_input_a_integer_int }
-        \int_set:Nn \exp_not:N \l_fp_input_b_decimal_int
-          { \int_use:N \l_fp_input_a_decimal_int }
-        \int_set:Nn \exp_not:N \l_fp_input_b_exponent_int
-          { \int_use:N \l_fp_input_a_exponent_int }
-      }
-    \l_fp_internal_tl
-    \use:c { fp_compare_>: }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
+% The following need to be done. I'll try to time-order the items.
+% \begin{itemize}
+%   \item Decide what exponent range to consider.
+%   \item Change the internal representation of fp, by replacing braced
+%     groups of $4$ digits by delimited arguments.
+%   \item Modulo and remainder, and rounding functions |quantize|,
+%     |quantize0|, |quantize+|, |quantize-|, |quantize=|, |round=|.
+%     Should the modulo also be provided as (catcode 12) |%|?
+%   \item \cs{fp_format:nn} \Arg{fpexpr} \Arg{format}, but what should
+%     \meta{format} be?  More general pretty printing?
+%   \item Add |and|, |or|, |xor|?  Perhaps under the names \texttt{all},
+%     \texttt{any}, and \texttt{xor}?
+%   \item Add \texttt{csc} and \texttt{sec}.
+%   \item Add $\log(x,b)$ for logarithm of $x$ in base $b$.
+%   \item \texttt{hypot} (Euclidean length) and $\atan(x,y) = \atan(x/y)$,
+%     also called \texttt{atan2} in other math packages.
+%     Cartesian-to-polar transform.  Other inverse trigonometric functions
+%     \texttt{acos}, \texttt{asin}, \texttt{atan} (one and two arguments).
+%     Also \texttt{asec}, \texttt{acsc}?
+%   \item Hyperbolic functions \texttt{cosh}, \texttt{sinh}, \texttt{tanh}.
+%   \item Inverse hyperbolics.
+%   \item Base conversion, input such as \texttt{0xAB.CDEF}.
+%   \item Random numbers (pgfmath provides |rnd|, |rand|, |random|), with
+%     seed reset at every \cs{fp_set:Nn}.
+%   \item Factorial (not with |!|), gamma function.
+%   \item Improve coefficients of \texttt{sin}, \texttt{cos} and
+%     \texttt{tan}.
+%   \item Treat upper and lower case letters identically in
+%     identifiers, and ignore underscores.
+%   \item Parse $-3<-2<-1$ as it should, not $(-3<-2)<-1$.
+%   \item Add an |array(1,2,3)| and |i=complex(0,1)|.
+%   \item Provide an experimental |map| function?  Perhaps easier to
+%     implement if it is a single character, |@sin(1,2)|?
+%   \item Provide \cs{fp_if_nan:nTF}?
+% \end{itemize}
+% \pkg{Pgfmath} also provides box-measurements (depth, height, width), but
+% boxes are not possible expandably.
 %
-% \begin{macro}[TF]{\fp_compare:n}
-% \begin{macro}[aux]
-%   {
-%     \fp_compare_aux_i:w,  \fp_compare_aux_ii:w, \fp_compare_aux_iii:w,
-%     \fp_compare_aux_iv:w, \fp_compare_aux_v:w,  \fp_compare_aux_vi:w,
-%     \fp_compare_aux_vii:w
-%   }
-%   As \TeX{} cannot help out here, a daisy-chain of delimited functions
-%   are used. This is very much a first-generation approach: revision will
-%   be needed if these functions are really useful.
-%    \begin{macrocode}
-\prg_new_protected_conditional:Npnn \fp_compare:n #1 { T , F , TF }
-  {
-    \group_begin:
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \group_end:
-          \fp_compare_aux_i:w #1 \exp_not:n { == \q_nil == \q_stop }
-        }
-     \l_fp_internal_tl
-  }
-\cs_new_protected:Npn \fp_compare_aux_i:w #1 == #2 == #3 \q_stop
-  {
-    \quark_if_nil:nTF {#2}
-      { \fp_compare_aux_ii:w #1 != \q_nil != \q_stop }
-      { \fp_compare:nNnTF {#1} = {#2} \prg_return_true: \prg_return_false: }
-  }
-\cs_new_protected:Npn \fp_compare_aux_ii:w #1 != #2 != #3 \q_stop
-  {
-    \quark_if_nil:nTF {#2}
-      { \fp_compare_aux_iii:w #1 <= \q_nil <= \q_stop }
-      { \fp_compare:nNnTF {#1} = {#2} \prg_return_false: \prg_return_true: }
-  }
-\cs_new_protected:Npn \fp_compare_aux_iii:w #1 <= #2 <= #3 \q_stop
-  {
-    \quark_if_nil:nTF {#2}
-      { \fp_compare_aux_iv:w #1 >= \q_nil >= \q_stop }
-      { \fp_compare:nNnTF {#1} > {#2} \prg_return_false: \prg_return_true: }
-  }
-\cs_new_protected:Npn \fp_compare_aux_iv:w #1 >= #2 >= #3 \q_stop
-  {
-    \quark_if_nil:nTF {#2}
-      { \fp_compare_aux_v:w #1 = \q_nil  \q_stop }
-      { \fp_compare:nNnTF {#1} < {#2} \prg_return_false: \prg_return_true: }
-  }
-\cs_new_protected:Npn \fp_compare_aux_v:w #1 = #2 = #3 \q_stop
-  {
-    \quark_if_nil:nTF {#2}
-      { \fp_compare_aux_vi:w #1 < \q_nil < \q_stop }
-      { \fp_compare:nNnTF {#1} = {#2} \prg_return_true: \prg_return_false: }
-  }
-\cs_new_protected:Npn \fp_compare_aux_vi:w #1 < #2 < #3 \q_stop
-  {
-    \quark_if_nil:nTF {#2}
-      { \fp_compare_aux_vii:w #1 > \q_nil > \q_stop }
-      { \fp_compare:nNnTF {#1} < {#2} \prg_return_true: \prg_return_false: }
-  }
-\cs_new_protected:Npn \fp_compare_aux_vii:w #1 > #2 > #3 \q_stop
-  {
-    \quark_if_nil:nTF {#2}
-      { \prg_return_false: }
-      { \fp_compare:nNnTF {#1} > {#2} \prg_return_true: \prg_return_false: }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
+% Bugs. (Exclamation points mark important bugs.)
+% \begin{itemize}
+%   \item[!] \cs{fp_eval:n} |{nan}| mustn't produce an error.
+%   \item $1-10^{-16}$ should not give $1$.
+%   \item When rounding towards $-\infty$, |\dim_to_fp:n {0pt}| should
+%     return $-0$, not $+0$.
+%   \item \texttt{0e9999999999} gives a \TeX{} \enquote{number too
+%       large} error.
+%   \item \texttt{tan} and \texttt{cot} give very slightly wrong results
+%     for arguments near $10^{-8}$.
+%   \item[!] Multiplying $0$ with $\infty$ doesn't trigger an invalid
+%     operation error.
+%   \item Conversion to integers with \cs{fp_to_int:n} does not check
+%     for overflow.
+%   \item Subnormals are not implemented.
+% \end{itemize}
 %
-% \subsection{Messages}
+% \end{documentation}
 %
-% \begin{macro}{\fp_overflow_msg:}
-% A generic overflow message, used whenever there is a possible
-% overflow.
-%    \begin{macrocode}
-\msg_kernel_new:nnnn { fpu } { overflow }
-  { Number~too~big. }
-  {
-    The~input~given~is~too~big~for~the~LaTeX~floating~point~unit. \\
-    Further~errors~may~well~occur!
-  }
-\cs_new_protected_nopar:Npn \fp_overflow_msg:
-  { \msg_kernel_error:nn { fpu } { overflow } }
-%    \end{macrocode}
-% \end{macro}
+% \begin{implementation}
 %
-% \begin{macro}{\fp_exp_overflow_msg:}
-% A slightly more helpful message for exponent overflows.
-%    \begin{macrocode}
-\msg_kernel_new:nnnn { fpu } { exponent-overflow }
-  { Number~too~big~for~exponent~unit. }
-  {
-    The~exponent~of~the~input~given~is~too~big~for~the~floating~point~
-    unit:~the~maximum~input~value~for~an~exponent~is~230.
-  }
-\cs_new_protected_nopar:Npn \fp_exp_overflow_msg:
-  { \msg_kernel_error:nn { fpu } { exponent-overflow } }
-%    \end{macrocode}
-% \end{macro}
+% \section{\pkg{l3fp} implementation}
 %
-% \begin{macro}{\fp_ln_error_msg:}
-% Logarithms are only valid for positive number
 %    \begin{macrocode}
-\msg_kernel_new:nnnn { fpu } { logarithm-input-error }
-  { Invalid~input~to~ln~function. }
-  { Logarithms~can~only~be~calculated~for~positive~numbers. }
-\cs_new_protected_nopar:Npn \fp_ln_error_msg: {
-  \msg_kernel_error:nn { fpu } { logarithm-input-error }
-}
+%<*package>
 %    \end{macrocode}
-% \end{macro}
 %
-% \begin{macro}{\fp_trig_overflow_msg:}
-% A slightly more helpful message for trigonometric overflows.
 %    \begin{macrocode}
-\msg_kernel_new:nnnn { fpu } { trigonometric-overflow }
-  { Number~too~big~for~trigonometry~unit. }
-  {
-    The~trigonometry~code~can~only~work~with~numbers~smaller~
-    than~1000000000.
-  }
-\cs_new_protected_nopar:Npn \fp_trig_overflow_msg:
-  { \msg_kernel_error:nn { fpu } { trigonometric-overflow } }
+\ProvidesExplPackage
+  {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
+\__expl_package_check:
 %    \end{macrocode}
-% \end{macro}
 %
 %    \begin{macrocode}
-%</initex|package>
+%</package>
 %    \end{macrocode}
 %
 % \end{implementation}
 %
-%\PrintIndex
+% \PrintIndex
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3int.dtx b/Master/texmf-dist/source/latex/l3kernel/l3int.dtx
index fdae7fa1046..a12b22a45fb 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3int.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3int.dtx
@@ -35,8 +35,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3int.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental integers}
+\GetIdInfo$Id: l3int.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Integers}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -73,7 +73,7 @@
 % \texttt{+}, \texttt{-}, \texttt{/} and \texttt{*} and
 % parentheses can be used within such expressions to carry
 % arithmetic operations. This module carries out these functions
-% on \emph{integer expressions} (\enquote{\texttt{int expr}}).
+% on \emph{integer expressions} (\enquote{\texttt{intexpr}}).
 %
 % \section{Integer expressions}
 %
@@ -99,7 +99,7 @@
 %   both evaluate to \( -6 \). The  \Arg{integer expression} may
 %   contain the operators \texttt{+}, \texttt{-}, \texttt{*} and
 %   \texttt{/}, along with parenthesis \texttt{(} and \texttt{)}.
-%   After two expansions, \cs{int_eval:n} yields a
+%   After two expansions, \cs{int_eval:n} yields an
 %   \meta{integer denotation} which is left in the input stream. This is
 %   \emph{not} an \meta{internal integer}, and therefore requires
 %   suitable termination if used in a \TeX{}-style integer assignment.
@@ -124,7 +124,7 @@
 %   second, rounding any remainder. Ties are rounded away from zero.
 %   Note that this is identical to using
 %   |/| directly in an \meta{integer expression}. The result is left in
-%   the input stream as a \meta{integer denotation} after two expansions.
+%   the input stream as an \meta{integer denotation} after two expansions.
 % \end{function}
 %
 % \begin{function}[EXP, updated = 2012-02-09]{\int_div_truncate:nn}
@@ -134,7 +134,7 @@
 %   Evaluates the two \meta{integer expressions} as described earlier,
 %   then calculates the result of dividing the first value by the
 %   second, truncating any remainder. Note that division using |/|
-%   rounds the result. The result is left in the input stream as a
+%   rounds the result. The result is left in the input stream as an
 %   \meta{integer denotation} after two expansions.
 % \end{function}
 %
@@ -202,10 +202,10 @@
 %     \int_gset_eq:NN, \int_gset_eq:cN, \int_gset_eq:Nc, \int_gset_eq:cc
 %   }
 %   \begin{syntax}
-%     \cs{int_set_eq:NN} \meta{integer1} \meta{integer2}
+%     \cs{int_set_eq:NN} \meta{integer_1} \meta{integer_2}
 %   \end{syntax}
-%   Sets the content of \meta{integer1} equal to that of
-%   \meta{integer2}.
+%   Sets the content of \meta{integer_1} equal to that of
+%   \meta{integer_2}.
 % \end{function}
 %
 % \begin{function}[EXP, pTF, added=2012-03-03]
@@ -268,9 +268,9 @@
 %   \begin{syntax}
 %     \cs{int_use:N} \meta{integer}
 %   \end{syntax}
-%   Recovers the content of a \meta{integer} and places it directly
+%   Recovers the content of an \meta{integer} and places it directly
 %   in the input stream. An error will be raised if the variable does
-%   not exist or if it is invalid. Can be omitted in places where a
+%   not exist or if it is invalid. Can be omitted in places where an
 %   \meta{integer} is required (such as in the first and third arguments
 %   of \cs{int_compare:nNnTF}).
 %   \begin{texnote}
@@ -302,9 +302,9 @@
 %
 % \begin{function}[EXP,pTF]{\int_compare:n}
 %   \begin{syntax}
-%     \cs{int_compare_p:n} \{ \meta{intexpr1} \meta{relation} \meta{intexpr2} \} \\
+%     \cs{int_compare_p:n} \{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \\
 %     \cs{int_compare:nTF}
-%     ~~\{ \meta{intexpr1} \meta{relation} \meta{intexpr2} \}
+%     ~~\{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \}
 %     ~~\Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   This function first evaluates each of the \meta{integer expressions}
@@ -322,6 +322,36 @@
 %   \end{center}
 % \end{function}
 %
+% \begin{function}[added = 2012-06-03, EXP]{\int_case:nnn}
+%   \begin{syntax}
+%     \cs{int_case:nnn} \Arg{test integer expression} \\
+%     ~~|{| \\
+%     ~~~~\Arg{intexpr case_1} \Arg{code case_1} \\
+%     ~~~~\Arg{intexpr case_2} \Arg{code case_2} \\
+%     ~~~~\ldots \\
+%     ~~~~\Arg{intexpr case_n} \Arg{code case_n} \\
+%     ~~|}| \\
+%     ~~\Arg{else code}
+%   \end{syntax}
+%   This function evaluates the \meta{test integer expression} and
+%   compares this in turn to each of the
+%   \meta{integer expression cases}. If the two are equal then the
+%   associated \meta{code} is left in the input stream. If none of
+%   the tests are \texttt{true} then the \texttt{else code} will be
+%   left in the input stream. For example
+%   \begin{verbatim}
+%     \int_case:nnn
+%       { 2 * 5 }
+%       {
+%         { 5 }       { Small }
+%         { 4 + 6 }   { Medium }
+%         { -2 * 10 } { Negative }
+%       }
+%       { No idea! }
+%    \end{verbatim}
+%    will leave \enquote{\texttt{Medium}} in the input stream.
+% \end{function}
+%
 % \begin{function}[EXP,pTF]{\int_if_even:n, \int_if_odd:n}
 %   \begin{syntax}
 %     \cs{int_if_odd_p:n} \Arg{integer expression}
@@ -390,7 +420,7 @@
 % \begin{function}[rEXP]{\int_do_while:nn}
 %   \begin{syntax}
 %      \cs{int_do_while:nn}
-%      ~~\{ \meta{intexpr1} \meta{relation} \meta{intexpr2} \} \Arg{code}
+%      ~~\{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \Arg{code}
 %   \end{syntax}
 %   Evaluates the relationship between the two \meta{integer expressions}
 %   as described for \cs{int_compare:nTF}, and then places the
@@ -403,7 +433,7 @@
 % \begin{function}[rEXP]{\int_do_until:nn}
 %   \begin{syntax}
 %      \cs{int_do_until:nn}
-%      ~~\{ \meta{intexpr1} \meta{relation} \meta{intexpr2} \} \Arg{code}
+%      ~~\{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \Arg{code}
 %   \end{syntax}
 %   Evaluates the relationship between the two \meta{integer expressions}
 %   as described for \cs{int_compare:nTF}, and then places the
@@ -416,7 +446,7 @@
 % \begin{function}[rEXP]{\int_until_do:nn}
 %   \begin{syntax}
 %      \cs{int_until_do:nn}
-%      ~~\{ \meta{intexpr1} \meta{relation} \meta{intexpr2} \} \Arg{code}
+%      ~~\{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \Arg{code}
 %   \end{syntax}
 %   Places the \meta{code} in the input stream for \TeX\ to process, and
 %   then evaluates the relationship between the two
@@ -429,7 +459,7 @@
 % \begin{function}[rEXP]{\int_while_do:nn}
 %   \begin{syntax}
 %      \cs{int_while_do:nn} \
-%      ~~\{ \meta{intexpr1} \meta{relation} \meta{intexpr2} \} \Arg{code}
+%      ~~\{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \Arg{code}
 %   \end{syntax}
 %   Places the \meta{code} in the input stream for \TeX{} to process, and
 %   then evaluates the relationship between the two
@@ -439,6 +469,59 @@
 %   \meta{relation} is \texttt{false}.
 % \end{function}
 %
+% \section{Integer step functions}
+%
+% \begin{function}[added = 2012-06-04, updated = 2012-06-29, rEXP]
+%   {\int_step_function:nnnN}
+%   \begin{syntax}
+%     \cs{int_step_function:nnnN} \Arg{initial value} \Arg{step} \Arg{final value} \meta{function}
+%   \end{syntax}
+%   This function first evaluates the \meta{initial value}, \meta{step}
+%   and \meta{final value}, all of which should be integer expressions.
+%   The \meta{function} is then placed in front of each \meta{value}
+%   from the \meta{initial value} to the \meta{final value} in turn
+%   (using \meta{step} between each \meta{value}). Thus \meta{function}
+%   should absorb one numerical argument. For example
+%   \begin{verbatim}
+%     \cs_set:Npn \my_func:n #1 { [I~saw~#1] \quad }
+%     \int_step_function:nnnN { 1 } { 1 } { 5 } \my_func:n
+%   \end{verbatim}
+%   would print
+%   \begin{quote}
+%     [I saw 1] \quad
+%     [I saw 2] \quad
+%     [I saw 3] \quad
+%     [I saw 4] \quad
+%     [I saw 5] \quad
+%   \end{quote}
+% \end{function}
+%
+% \begin{function}[added = 2012-06-04, updated = 2012-06-29]
+%   {\int_step_inline:nnnn}
+%   \begin{syntax}
+%     \cs{int_step_inline:nnnn} \Arg{initial value} \Arg{step} \Arg{final value} \Arg{code}
+%   \end{syntax}
+%   This function first evaluates the \meta{initial value}, \meta{step}
+%   and \meta{final value}, all of which should be integer expressions.
+%   The \meta{code} is then placed in front of each \meta{value}
+%   from the \meta{initial value} to the \meta{final value} in turn
+%   (using \meta{step} between each \meta{value}). Thus the \meta{code}
+%   should define a function of one argument (|#1|).
+% \end{function}
+%
+% \begin{function}[added = 2012-06-04, updated = 2012-06-29]
+%   {\int_step_variable:nnnNn}
+%   \begin{syntax}
+%     \cs{int_step_variable:nnnNn} \\
+%     ~~\Arg{initial value} \Arg{step} \Arg{final value} \meta{tl~var} \Arg{code}
+%   \end{syntax}
+%   This function first evaluates the \meta{initial value}, \meta{step}
+%   and \meta{final value}, all of which should be integer expressions.
+%   The \meta{code} is inserted into the input stream, with the
+%   \meta{tl~var} defined as the current \meta{value}. Thus the
+%   \meta{code} should make use of the \meta{tl~var}.
+% \end{function}
+%
 % \section{Formatting integers}
 %
 % Integers can be placed into the output stream with formatting. These
@@ -626,7 +709,7 @@
 %   Displays the value of the \meta{integer} on the terminal.
 % \end{function}
 %
-% \begin{function}[added = 2011-11-22]{\int_show:n}
+% \begin{function}[added = 2011-11-22, updated = 2012-05-27]{\int_show:n}
 %   \begin{syntax}
 %     \cs{int_show:n} \meta{integer expression}
 %   \end{syntax}
@@ -678,7 +761,7 @@
 %
 % \section{Scratch integers}
 %
-% \begin{variable}{\l_tmpa_int, \l_tmpb_int, \l_tmpc_int}
+% \begin{variable}{\l_tmpa_int, \l_tmpb_int}
 %   Scratch integer for local assignment. These are never used by
 %   the kernel code, and so are safe for use with any \LaTeX3-defined
 %   function. However, they may be overwritten by other non-kernel
@@ -692,57 +775,11 @@
 %   code and so should only be used for short-term storage.
 % \end{variable}
 %
-% \section{Internal functions}
-%
-% \begin{function}[EXP]{\int_get_digits:n}
-%   \begin{syntax}
-%     \cs{int_get_digits:n} \meta{value}
-%   \end{syntax}
-%     Parses the \meta{value} to leave the absolute \meta{value}
-%     in the input stream. This may therefore be used
-%     to remove multiple sign tokens from the \meta{value}
-%     (which may be symbolic).
-% \end{function}
-%
-% \begin{function}[rEXP]{\int_get_sign:n}
-%   \begin{syntax}
-%     \cs{int_get_sign:n} \meta{value}
-%   \end{syntax}
-%     Parses the \meta{value} to leave a single sign token
-%     (either |+| or |-|) in the input stream. This may therefore be used
-%     to sanitise sign tokens from the \meta{value} (which may be symbolic).
-% \end{function}
-%
-% \begin{function}[updated = 2011-09-17, EXP]{\int_to_letter:n}
-%   \begin{syntax}
-%     \cs{int_to_letter:n} \meta{integer value}
-%   \end{syntax}
-%   For \meta{integer values} from $0$ to $9$, leaves the \meta{value}
-%   in the input stream unchanged. For \meta{integer values} from
-%   $10$ to $35$, leaves the appropriate upper case letter (from the
-%   standard English alphabet) in the input stream: for example,
-%   $10$ is converted to |A|, $11$ to |B|, \emph{etc.}
-% \end{function}
+% \section{Primitive conditionals}
 %
-% \begin{function}[EXP]{\int_to_roman:w}
+% \begin{function}[EXP]{\if_int_compare:w}
 %   \begin{syntax}
-%     \cs{int_to_roman:w} \meta{integer} \meta{space} \textit{or} \meta{non-expandable token}
-%   \end{syntax}
-%   Converts \meta{integer} to it lower case Roman representation. Expansion
-%   ends when a space or non-expandable token is found.
-%   Note that this function produces a string of letters with category code
-%   $12$ and that protected functions \emph{are} expanded by this
-%   process. Negative \meta{integer} values result in no output, although
-%   the function does not terminate expansion until a suitable endpoint
-%   is found in the same way as for positive numbers.
-%   \begin{texnote}
-%     This is the \TeX{} primitive \tn{romannumeral} renamed.
-%   \end{texnote}
-% \end{function}
-%
-% \begin{function}[EXP]{\if_num:w, \if_int_compare:w}
-%   \begin{syntax}
-%     \cs{if_num:w} \meta{integer1} \meta{relation} \meta{integer2}
+%     \cs{if_int_compare:w} \meta{integer_1} \meta{relation} \meta{integer_2}
 %     ~~\meta{true code}
 %     \cs{else:}
 %     ~~\meta{false code}
@@ -758,15 +795,15 @@
 %
 % \begin{function}[EXP]{\if_case:w, \or:}
 %   \begin{syntax}
-%     \cs{if_case:w} \meta{integer} \meta{case0}
-%     ~~\cs{or:} \meta{case1}
+%     \cs{if_case:w} \meta{integer} \meta{case_0}
+%     ~~\cs{or:} \meta{case_1}
 %     ~~\cs{or:} |...|
 %     ~~\cs{else:} \meta{default}
 %     \cs{fi:}
 %   \end{syntax}
 %   Selects a case to execute based on the value of the \meta{integer}. The
-%   first case (\meta{case0}) is executed if \meta{integer} is $0$, the second
-%   (\meta{case1}) if the \meta{integer} is $1$, \emph{etc.} The
+%   first case (\meta{case_0}) is executed if \meta{integer} is $0$, the second
+%   (\meta{case_1}) if the \meta{integer} is $1$, \emph{etc.} The
 %   \meta{integer} may be a literal, a constant or an integer
 %   expression (\emph{e.g.}~using \cs{int_eval:n}).
 %   \begin{texnote}
@@ -774,10 +811,44 @@
 %   \end{texnote}
 % \end{function}
 %
-% \begin{function}[EXP]{\int_value:w}
+% \begin{function}[EXP]{\if_int_odd:w}
+%   \begin{syntax}
+%     \cs{if_int_odd:w} \meta{tokens}  \meta{optional space}
+%     ~~\meta{true code}
+%     \cs{else:}
+%     ~~\meta{true code}
+%     \cs{fi:}
+%   \end{syntax}
+%   Expands \meta{tokens} until a non-numeric token or a space is found, and
+%   tests whether the resulting \meta{integer} is odd. If so, \meta{true code}
+%   is executed. The \cs{else:} branch is optional.
+%   \begin{texnote}
+%     This is the \TeX{} primitive \tn{ifodd}.
+%   \end{texnote}
+% \end{function}
+%
+% \section{Internal functions}
+%
+% \begin{function}[EXP]{\__int_to_roman:w}
+%   \begin{syntax}
+%     \cs{__int_to_roman:w} \meta{integer} \meta{space} \textit{or} \meta{non-expandable token}
+%   \end{syntax}
+%   Converts \meta{integer} to it lower case Roman representation. Expansion
+%   ends when a space or non-expandable token is found.
+%   Note that this function produces a string of letters with category code
+%   $12$ and that protected functions \emph{are} expanded by this
+%   process. Negative \meta{integer} values result in no output, although
+%   the function does not terminate expansion until a suitable endpoint
+%   is found in the same way as for positive numbers.
+%   \begin{texnote}
+%     This is the \TeX{} primitive \tn{romannumeral} renamed.
+%   \end{texnote}
+% \end{function}
+%
+% \begin{function}[EXP]{\__int_value:w}
 %   \begin{syntax}
-%     \cs{int_value:w} \meta{integer}
-%     \cs{int_value:w} \meta{tokens} \meta{optional space}
+%     \cs{__int_value:w} \meta{integer}
+%     \cs{__int_value:w} \meta{tokens} \meta{optional space}
 %   \end{syntax}
 %   Expands \meta{tokens} until an \meta{integer} is formed. One space may be
 %   gobbled in the process.
@@ -786,35 +857,29 @@
 %   \end{texnote}
 % \end{function}
 %
-% \begin{function}[EXP]{\int_eval:w, \int_eval_end:}
+% \begin{function}[EXP]{\__int_eval:w, \__int_eval_end:}
 %   \begin{syntax}
-%     \cs{int_eval:w} \meta{intexpr} \cs{int_eval_end:}
+%     \cs{__int_eval:w} \meta{intexpr} \cs{__int_eval_end:}
 %   \end{syntax}
 %   Evaluates \meta{integer expression} as described for \cs{int_eval:n}.
 %   The evaluation stops when an unexpandable token which is not a valid
-%   part of an integer is read or when \cs{int_eval_end:} is
+%   part of an integer is read or when \cs{__int_eval_end:} is
 %   reached. The latter is gobbled by the scanner mechanism:
-%   \cs{int_eval_end:} itself is unexpandable but used correctly
+%   \cs{__int_eval_end:} itself is unexpandable but used correctly
 %   the entire construct is expandable.
 %   \begin{texnote}
 %     This is the \eTeX{} primitive \tn{numexpr}.
 %   \end{texnote}
 % \end{function}
 %
-% \begin{function}[EXP]{\if_int_odd:w}
+% \begin{function}{\__prg_compare_error:, \__prg_compare_error:Nw}
 %   \begin{syntax}
-%     \cs{if_int_odd:w} \meta{tokens}  \meta{optional space}
-%     ~~\meta{true code}
-%     \cs{else:}
-%     ~~\meta{true code}
-%     \cs{fi:}
+%     \cs{__prg_compare_error:}
+%     \cs{__prg_compare_error:Nw} \meta{token}
 %   \end{syntax}
-%   Expands \meta{tokens} until a non-numeric token or a space is found, and
-%   tests whether the resulting \meta{integer} is odd. If so, \meta{true code}
-%   is executed. The \cs{else:} branch is optional.
-%   \begin{texnote}
-%     This is the \TeX{} primitive \tn{ifodd}.
-%   \end{texnote}
+%   These are used within \cs{int_compare:n(TF)}, \cs{dim_compare:n(TF)}
+%   and so on to recover correctly if the \texttt{n}-type argument does not
+%   contain a properly-formed relation.
 % \end{function}
 %
 % \end{documentation}
@@ -827,58 +892,59 @@
 %<*initex|package>
 %    \end{macrocode}
 %
+%    \begin{macrocode}
+%<@@=int>
+%    \end{macrocode}
+%
 % \TestFiles{m3int001,m3int002,m3int03}
 %
 %    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
-% \begin{macro}{\int_to_roman:w}
+% \begin{macro}{\@@_to_roman:w}
 % \begin{macro}{\if_int_compare:w}
 %   Done in \pkg{l3basics}.
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\int_value:w}
-% \begin{macro}{\int_eval:w}
-% \begin{macro}{\int_eval_end:}
-% \begin{macro}{\if_num:w}
+% \begin{macro}{\@@_value:w}
+% \begin{macro}{\@@_eval:w}
+% \begin{macro}{\@@_eval_end:}
 % \begin{macro}{\if_int_odd:w}
 % \begin{macro}{\if_case:w}
 %   Here are the remaining primitives for number comparisons and
 %   expressions.
 %    \begin{macrocode}
-\cs_new_eq:NN \int_value:w   \tex_number:D
-\cs_new_eq:NN \int_eval:w    \etex_numexpr:D
-\cs_new_eq:NN \int_eval_end: \tex_relax:D
-\cs_new_eq:NN \if_num:w      \tex_ifnum:D
-\cs_new_eq:NN \if_int_odd:w  \tex_ifodd:D
-\cs_new_eq:NN \if_case:w     \tex_ifcase:D
+\cs_new_eq:NN \@@_value:w      \tex_number:D
+\cs_new_eq:NN \@@_eval:w       \etex_numexpr:D
+\cs_new_eq:NN \@@_eval_end:    \tex_relax:D
+\cs_new_eq:NN \if_int_odd:w     \tex_ifodd:D
+\cs_new_eq:NN \if_case:w        \tex_ifcase:D
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 % \end{macro}
 % \end{macro}
 % \end{macro}
-% \end{macro}
 %
 % \subsection{Integer expressions}
 %
 % \begin{macro}{\int_eval:n}
-%   Wrapper for \cs{int_eval:w}. Can be used in an integer expression
+%   Wrapper for \cs{@@_eval:w}. Can be used in an integer expression
 %   or directly in the input stream. In format mode, there is already
 %   a definition in \pkg{l3alloc} for bookstrapping, which is therefore
 %   corrected to the \enquote{real} version here.
 %    \begin{macrocode}
 %<*initex>
-\cs_set:Npn \int_eval:n #1 { \int_value:w \int_eval:w #1 \int_eval_end: }
+\cs_set:Npn \int_eval:n #1 { \@@_value:w \@@_eval:w #1 \@@_eval_end: }
 %</initex>
 %<*package>
-\cs_new:Npn \int_eval:n #1 { \int_value:w \int_eval:w #1 \int_eval_end: }
+\cs_new:Npn \int_eval:n #1 { \@@_value:w \@@_eval:w #1 \@@_eval_end: }
 %</package>
 %    \end{macrocode}
 % \end{macro}
@@ -893,33 +959,33 @@
 %    \begin{macrocode}
 \cs_new:Npn \int_abs:n #1
   {
-    \int_value:w
-      \if_int_compare:w \int_eval:w #1 < \c_zero
+    \@@_value:w
+      \if_int_compare:w \@@_eval:w #1 < \c_zero
         -
       \fi:
-    \int_eval:w #1 \int_eval_end:
+    \@@_eval:w #1 \@@_eval_end:
   }
 \cs_new:Npn \int_max:nn #1#2
   {
-    \int_value:w \int_eval:w
+    \@@_value:w \@@_eval:w
       \if_int_compare:w
-        \int_eval:w #1 > \int_eval:w #2 \int_eval_end:
+        \@@_eval:w #1 > \@@_eval:w #2 \@@_eval_end:
         #1
       \else:
         #2
       \fi:
-    \int_eval_end:
+    \@@_eval_end:
   }
 \cs_new:Npn \int_min:nn #1#2
   {
-    \int_value:w \int_eval:w
+    \@@_value:w \@@_eval:w
       \if_int_compare:w
-        \int_eval:w #1 < \int_eval:w #2 \int_eval_end:
+        \@@_eval:w #1 < \@@_eval:w #2 \@@_eval_end:
         #1
       \else:
         #2
       \fi:
-    \int_eval_end:
+    \@@_eval_end:
   }
 %    \end{macrocode}
 % \end{macro}
@@ -932,12 +998,12 @@
 % \UnitTested
 % \begin{macro}[EXP]{\int_mod:nn}
 % \UnitTested
-% \begin{macro}[aux, EXP]{\int_div_truncate_aux:NwNw}
-%   As \cs{int_eval:w} rounds the result of a division we also provide a
+% \begin{macro}[aux, EXP]{\@@_div_truncate:NwNw}
+%   As \cs{@@_eval:w} rounds the result of a division we also provide a
 %   version that truncates the result. We use an auxiliary to make sure
 %   numerator and denominator are only evaluated once: this comes in
 %   handy when those are more expressions are expensive to evaluate
-%   (\emph{e.g.}, \cs{tl_length:n}). If the numerator |#1#2| is $0$,
+%   (\emph{e.g.}, \cs{tl_count:n}). If the numerator |#1#2| is $0$,
 %   then we divide $0$ by the denominator (this ensures that $0/0$ is
 %   correctly reported as an error). Otherwise, shift the numerator
 %   |#1#2| towards $0$ by $(\left\vert\texttt{\#3\#4}\right\vert-1)/2$, which we
@@ -948,13 +1014,13 @@
 %    \begin{macrocode}
 \cs_new:Npn \int_div_truncate:nn #1#2
   {
-    \int_use:N \int_eval:w
-      \exp_after:wN \int_div_truncate_aux:NwNw
-      \int_use:N \int_eval:w #1 \exp_after:wN ;
-      \int_use:N \int_eval:w #2 ;
-    \int_eval_end:
+    \int_use:N \@@_eval:w
+      \exp_after:wN \@@_div_truncate:NwNw
+      \int_use:N \@@_eval:w #1 \exp_after:wN ;
+      \int_use:N \@@_eval:w #2 ;
+    \@@_eval_end:
   }
-\cs_new:Npn \int_div_truncate_aux:NwNw #1#2; #3#4;
+\cs_new:Npn \@@_div_truncate:NwNw #1#2; #3#4;
   {
     \if_meaning:w 0 #1
       \c_zero
@@ -976,9 +1042,9 @@
 %    \begin{macrocode}
 \cs_new:Npn \int_mod:nn #1#2
   {
-    \int_value:w \int_eval:w
+    \@@_value:w \@@_eval:w
       #1 - \int_div_truncate:nn {#1} {#2} * ( #2 )
-    \int_eval_end:
+    \@@_eval_end:
   }
 %    \end{macrocode}
 % \end{macro}
@@ -996,7 +1062,7 @@
 %<*package>
 \cs_new_protected:Npn \int_new:N #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \newcount #1
   }
 %</package>
@@ -1005,8 +1071,8 @@
 % \end{macro}
 %
 % \begin{macro}{\int_const:Nn, \int_const:cn}
-% \begin{macro}[aux]{\int_constdef:Nw}
-% \begin{variable}{\c_max_const_int}
+% \begin{macro}[aux]{\@@_constdef:Nw}
+% \begin{variable}{\c__max_constdef_int}
 % \UnitTested
 %   As stated, most constants can be defined as \tn{chardef} or
 %   \tn{mathchardef} but that's engine dependent. As a result, there is some
@@ -1016,15 +1082,15 @@
   {
     \int_compare:nNnTF {#2} > \c_minus_one
       {
-        \int_compare:nNnTF {#2} > \c_max_const_int
+        \int_compare:nNnTF {#2} > \c__max_constdef_int
           {
             \int_new:N #1
             \int_gset:Nn #1 {#2}
           }
           {
-            \chk_if_free_cs:N #1
-            \tex_global:D \int_constdef:Nw #1 =
-              \int_eval:w #2 \int_eval_end:
+            \__chk_if_free_cs:N #1
+            \tex_global:D \@@_constdef:Nw #1 =
+              \@@_eval:w #2 \@@_eval_end:
           }
       }
       {
@@ -1035,12 +1101,12 @@
 \cs_generate_variant:Nn \int_const:Nn { c }
 \pdftex_if_engine:TF
   {
-    \cs_new_eq:NN \int_constdef:Nw \tex_mathchardef:D
-    \tex_mathchardef:D \c_max_const_int 32 767 ~
+    \cs_new_eq:NN \@@_constdef:Nw \tex_mathchardef:D
+    \tex_mathchardef:D \c__max_constdef_int 32 767 ~
   }
   {
-    \cs_new_eq:NN \int_constdef:Nw \tex_chardef:D
-    \tex_chardef:D \c_max_const_int 1 114 111 ~
+    \cs_new_eq:NN \@@_constdef:Nw \tex_chardef:D
+    \tex_chardef:D \c__max_constdef_int 1 114 111 ~
   }
 %    \end{macrocode}
 % \end{variable}
@@ -1119,9 +1185,9 @@
 %    Adding and subtracting to and from a counter \ldots
 %    \begin{macrocode}
 \cs_new_protected:Npn \int_add:Nn #1#2
-  { \tex_advance:D #1 by \int_eval:w #2 \int_eval_end: }
+  { \tex_advance:D #1 by \@@_eval:w #2 \@@_eval_end: }
 \cs_new_protected:Npn \int_sub:Nn #1#2
-  { \tex_advance:D #1 by - \int_eval:w #2 \int_eval_end: }
+  { \tex_advance:D #1 by - \@@_eval:w #2 \@@_eval_end: }
 \cs_new_protected_nopar:Npn \int_gadd:Nn
   { \tex_global:D \int_add:Nn }
 \cs_new_protected_nopar:Npn \int_gsub:Nn
@@ -1174,7 +1240,7 @@
 %   code seen with token list variables.
 %    \begin{macrocode}
 \cs_new_protected:Npn \int_set:Nn #1#2
-  { #1 ~ \int_eval:w #2\int_eval_end: }
+  { #1 ~ \@@_eval:w #2\@@_eval_end: }
 \cs_new_protected_nopar:Npn \int_gset:Nn { \tex_global:D \int_set:Nn }
 \cs_generate_variant:Nn \int_set:Nn  { c }
 \cs_generate_variant:Nn \int_gset:Nn { c }
@@ -1195,30 +1261,30 @@
 %
 % \subsection{Integer expression conditionals}
 %
-% \begin{macro}[aux, EXP]{\kernel_compare_error:, \kernel_compare_error:NNw}
+% \begin{macro}[aux, EXP]{\__prg_compare_error:, \__prg_compare_error:NNw}
 %   Those functions are used for comparison tests which use a simple
 %   syntax where only one set of braces is required and additional
 %   operators such as |!=| and |>=| are supported.  The tests first
 %   evaluate their left-hand side, with a trailing
-%   \cs{kernel_compare_error:}. This marker is normally not expanded,
+%   \cs{__prg_compare_error:}. This marker is normally not expanded,
 %   but if the relation symbol is missing from the test's argument, then
 %   the marker inserts |=| (and itself) after triggering the relevant
 %   \TeX{} error.  If the first token which appears after evaluating and
 %   removing the left-hand side is not a known relation symbol, then a
-%   judiciously placed \cs{kernel_compare_error:Nw} gets expanded,
+%   judiciously placed \cs{__prg_compare_error:Nw} gets expanded,
 %   cleaning up the end of the test and telling the user what the
 %   problem was.
 %    \begin{macrocode}
-\cs_new_protected_nopar:Npn \kernel_compare_error:
+\cs_new_protected_nopar:Npn \__prg_compare_error:
   {
-    \if_num:w \c_zero \c_zero \fi:
+    \if_int_compare:w \c_zero \c_zero \fi:
     =
-    \kernel_compare_error:
+    \__prg_compare_error:
   }
-\cs_new:Npn \kernel_compare_error:Nw
+\cs_new:Npn \__prg_compare_error:Nw
     #1#2 \prg_return_true: \else: \prg_return_false: \fi:
   {
-    \msg_expandable_kernel_error:nnn
+    \__msg_kernel_expandable_error:nnn
       { kernel } { unknown-comparison } {#1}
     \prg_return_false:
   }
@@ -1226,31 +1292,31 @@
 % \end{macro}
 %
 % \begin{macro}[pTF, EXP]{\int_compare:n}
-% \begin{macro}[aux, EXP]{\int_compare_aux:Nw, \int_compare_aux:NNw}
+% \begin{macro}[aux, EXP]{\@@_compare_aux:Nw, \@@_compare_aux:NNw}
 % \begin{macro}[aux, EXP]
 %   {
-%     \int_compare_=:NNw,
-%     \int_compare_<:NNw,
-%     \int_compare_>:NNw,
-%     \int_compare_==:NNw,
-%     \int_compare_!=:NNw,
-%     \int_compare_<=:NNw,
-%     \int_compare_>=:NNw
+%     \@@_compare_=:NNw,
+%     \@@_compare_<:NNw,
+%     \@@_compare_>:NNw,
+%     \@@_compare_==:NNw,
+%     \@@_compare_!=:NNw,
+%     \@@_compare_<=:NNw,
+%     \@@_compare_>=:NNw
 %   }
 %   Comparison tests using a simple syntax where only one set of braces
 %   is required and additional operators such as |!=| and |>=| are
 %   supported.  We can start evaluating from the left using
-%   \cs{int_eval:w}, and we know that since the relation symbols |<|,
+%   \cs{@@_eval:w}, and we know that since the relation symbols |<|,
 %   |>|, |=| and |!| are not allowed in such expressions, they will
 %   terminate the expression.  Therefore, we first let \TeX{} evaluate
 %   this left hand side of the (in)equality.  We also insert at that
-%   stage the end of the test: \cs{int_eval_end:} will end the
+%   stage the end of the test: \cs{@@_eval_end:} will end the
 %   evaluation of the right-hand side.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \int_compare:n #1 { p , T , F , TF }
   {
-    \exp_after:wN \int_compare_aux:Nw \int_use:N \int_eval:w #1
-        \kernel_compare_error: \int_eval_end:
+    \exp_after:wN \@@_compare_aux:Nw \int_use:N \@@_eval:w #1
+        \__prg_compare_error: \@@_eval_end:
       \prg_return_true:
     \else:
       \prg_return_false:
@@ -1258,47 +1324,47 @@
   }
 %    \end{macrocode}
 %   We have just evaluated the left-hand side.  To access the relation
-%   symbol, we remove the number by applying \cs{int_to_roman:w}, after
+%   symbol, we remove the number by applying \cs{@@_to_roman:w}, after
 %   making sure that the argument becomes non-positive: its roman
-%   numeral representation is then empty.  The \cs{int_compare_aux:NNw}
+%   numeral representation is then empty.  The \cs{@@_compare_aux:NNw}
 %   auxiliary then probes the first two tokens to determine the relation
 %   symbol, building a control sequence from it.  All the extended forms
 %   have an extra |=| hence the test for that as a second token.  If the
 %   relation symbol is unknown, then the control sequence is turned by
-%   \TeX{} into \cs{scan_stop:}, and \cs{kernel_compare_error:Nw}
+%   \TeX{} into \cs{scan_stop:}, and \cs{__prg_compare_error:Nw}
 %   raises an error.
 %    \begin{macrocode}
-\cs_new:Npn \int_compare_aux:Nw #1#2 \kernel_compare_error:
+\cs_new:Npn \@@_compare_aux:Nw #1#2 \__prg_compare_error:
   {
-    \exp_after:wN \int_compare_aux:NNw
-      \int_to_roman:w - 0 #2 ?? \q_mark
+    \exp_after:wN \@@_compare_aux:NNw
+      \@@_to_roman:w - 0 #2 ?? \q_mark
     #1#2
   }
-\cs_new:Npn \int_compare_aux:NNw #1#2#3 \q_mark
+\cs_new:Npn \@@_compare_aux:NNw #1#2#3 \q_mark
   {
-    \use:c { int_compare_  #1  \if_meaning:w = #2 =  \fi: :NNw }
-      \kernel_compare_error:Nw #1
+    \use:c { @@_compare_  #1  \if_meaning:w = #2 =  \fi: :NNw }
+      \__prg_compare_error:Nw #1
   }
 %    \end{macrocode}
 %   The actual comparisons are then simple function calls, using the
 %   relation as delimiter for a delimited argument and discarding
-%   \cs{kernel_compare_error:Nw} \meta{token} responsible for error
+%   \cs{__prg_compare_error:Nw} \meta{token} responsible for error
 %   detection.
 %    \begin{macrocode}
-\cs_new:cpn { int_compare_=:NNw } #1#2#3 =
-  { \if_int_compare:w #3 = \int_eval:w }
-\cs_new:cpn { int_compare_<:NNw } #1#2#3 <
-  { \if_int_compare:w #3 < \int_eval:w }
-\cs_new:cpn { int_compare_>:NNw } #1#2#3 >
-  { \if_int_compare:w #3 > \int_eval:w }
-\cs_new:cpn { int_compare_==:NNw } #1#2#3 ==
-  { \if_int_compare:w #3 = \int_eval:w }
-\cs_new:cpn { int_compare_!=:NNw } #1#2#3 !=
-  { \reverse_if:N \if_int_compare:w #3 = \int_eval:w }
-\cs_new:cpn { int_compare_<=:NNw } #1#2#3 <=
-  { \reverse_if:N \if_int_compare:w #3 > \int_eval:w }
-\cs_new:cpn { int_compare_>=:NNw } #1#2#3 >=
-  { \reverse_if:N \if_int_compare:w #3 < \int_eval:w }
+\cs_new:cpn { @@_compare_=:NNw } #1#2#3 =
+  { \if_int_compare:w #3 = \@@_eval:w }
+\cs_new:cpn { @@_compare_<:NNw } #1#2#3 <
+  { \if_int_compare:w #3 < \@@_eval:w }
+\cs_new:cpn { @@_compare_>:NNw } #1#2#3 >
+  { \if_int_compare:w #3 > \@@_eval:w }
+\cs_new:cpn { @@_compare_==:NNw } #1#2#3 ==
+  { \if_int_compare:w #3 = \@@_eval:w }
+\cs_new:cpn { @@_compare_!=:NNw } #1#2#3 !=
+  { \reverse_if:N \if_int_compare:w #3 = \@@_eval:w }
+\cs_new:cpn { @@_compare_<=:NNw } #1#2#3 <=
+  { \reverse_if:N \if_int_compare:w #3 > \@@_eval:w }
+\cs_new:cpn { @@_compare_>=:NNw } #1#2#3 >=
+  { \reverse_if:N \if_int_compare:w #3 < \@@_eval:w }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1308,9 +1374,9 @@
 % \UnitTested
 % More efficient but less natural in typing.
 %    \begin{macrocode}
-\prg_new_conditional:Npnn \int_compare:nNn #1#2#3 { p , T , F , TF}
+\prg_new_conditional:Npnn \int_compare:nNn #1#2#3 { p , T , F , TF }
   {
-    \if_int_compare:w \int_eval:w #1 #2 \int_eval:w #3 \int_eval_end:
+    \if_int_compare:w \@@_eval:w #1 #2 \@@_eval:w #3 \@@_eval_end:
       \prg_return_true:
     \else:
       \prg_return_false:
@@ -1319,6 +1385,35 @@
 %    \end{macrocode}
 % \end{macro}
 %
+% \begin{macro}{\int_case:nnn}
+% \begin{macro}[aux]{\@@_case:nnn}
+% \begin{macro}[aux]{\@@_case:nw, \@@_case_end:nw}
+%   For integer cases, the first task to fully expand the check
+%   condition. After that, a loop is started to compare each possible
+%   value and stop if the test is true. The tested value is put at the
+%   end to ensure that there is necessarily a match, which will fire the
+%   \enquote{else} pathway. The leading \tn{romannumeral} triggers an
+%   expansion which is then stopped in \cs{@@_case_end:nw}.
+%    \begin{macrocode}
+\cs_new:Npn \int_case:nnn #1
+  {
+    \tex_romannumeral:D
+    \exp_args:Nf \@@_case:nnn { \int_eval:n {#1} }
+  }
+\cs_new:Npn \@@_case:nnn #1#2#3
+  { \@@_case:nw {#1} #2 {#1} {#3} \q_recursion_stop }
+\cs_new:Npn \@@_case:nw #1#2#3
+  {
+    \int_compare:nNnTF {#1} = {#2}
+      { \@@_case_end:nw {#3} }
+      { \@@_case:nw {#1} }
+  }
+\cs_new_eq:NN \@@_case_end:nw \__prg_case_end:nw
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
 % \begin{macro}[pTF]{\int_if_odd:n}
 % \UnitTested
 % \begin{macro}[pTF]{\int_if_even:n}
@@ -1327,7 +1422,7 @@
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \int_if_odd:n #1 { p , T , F , TF}
   {
-    \if_int_odd:w \int_eval:w #1 \int_eval_end:
+    \if_int_odd:w \@@_eval:w #1 \@@_eval_end:
       \prg_return_true:
     \else:
       \prg_return_false:
@@ -1335,7 +1430,7 @@
   }
 \prg_new_conditional:Npnn \int_if_even:n #1 { p , T , F , TF}
   {
-    \if_int_odd:w \int_eval:w #1 \int_eval_end:
+    \if_int_odd:w \@@_eval:w #1 \@@_eval_end:
       \prg_return_false:
     \else:
       \prg_return_true:
@@ -1437,6 +1532,86 @@
 % \end{macro}
 % \end{macro}
 %
+% \subsection{Integer step functions}
+%
+% \begin{macro}{\int_step_function:nnnN}
+% \begin{macro}[aux]{\@@_step:NnnnN}
+%   Repeating a function by steps first needs a check on the direction
+%   of the steps. After that, do the function for the start value
+%   then step and loop around. It would be more symmetrical to test
+%   for a step size of zero before checking the sign, but we optimize
+%   for the most frequent case (positive step).
+%    \begin{macrocode}
+\cs_new:Npn \int_step_function:nnnN #1#2#3#4
+  {
+    \int_compare:nNnTF {#2} > \c_zero
+      { \exp_args:NNf \@@_step:NnnnN > }
+      {
+        \int_compare:nNnTF {#2} = \c_zero
+          {
+            \__msg_kernel_expandable_error:nnn { kernel } { zero-step } {#4}
+            \use_none:nnnn
+          }
+          { \exp_args:NNf \@@_step:NnnnN < }
+      }
+      { \int_eval:n {#1} } {#2} {#3} #4
+  }
+\cs_new:Npn \@@_step:NnnnN #1#2#3#4#5
+  {
+    \int_compare:nNnF {#2} #1 {#4}
+      {
+        #5 {#2}
+        \exp_args:NNf \@@_step:NnnnN
+          #1 { \int_eval:n { #2 + #3 } } {#3} {#4} #5
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\int_step_inline:nnnn}
+% \begin{macro}{\int_step_variable:nnnNn}
+% \UnitTested
+% \begin{macro}[aux]{\@@_step:NNnnnn}
+%   The approach here is to build a function, with a global integer
+%   required to make the nesting safe (as seen in other in line
+%   functions), and map that function using \cs{int_step_function:nnnN}.
+%   We put a \cs{__prg_break_point:Nn} so that \texttt{map_break}
+%   functions from other modules correctly decrement \cs{g__prg_map_int}
+%   before looking for their own break point.  The first argument is
+%   \cs{scan_stop:}, so no breaking function will recognize this break
+%   point as its own.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \int_step_inline:nnnn
+  {
+    \int_gincr:N \g__prg_map_int
+    \exp_args:NNc \@@_step:NNnnnn
+      \cs_gset_nopar:Npn
+      { __prg_map_ \int_use:N \g__prg_map_int :w }
+  }
+\cs_new_protected:Npn \int_step_variable:nnnNn #1#2#3#4#5
+  {
+    \int_gincr:N \g__prg_map_int
+    \exp_args:NNc \@@_step:NNnnnn
+      \cs_gset_nopar:Npx
+      { __prg_map_ \int_use:N \g__prg_map_int :w }
+      {#1}{#2}{#3}
+      {
+        \tl_set:Nn \exp_not:N #4 {##1}
+        \exp_not:n {#5}
+      }
+  }
+\cs_new_protected:Npn \@@_step:NNnnnn #1#2#3#4#5#6
+  {
+    #1 #2 ##1 {#6}
+    \int_step_function:nnnN {#3} {#4} {#5} #2
+    \__prg_break_point:Nn \scan_stop: { \int_gdecr:N \g__prg_map_int }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
 % \subsection{Formatting integers}
 %
 % \begin{macro}{\int_to_arabic:n}
@@ -1449,6 +1624,7 @@
 %
 % \begin{macro}{\int_to_symbols:nnn}
 % \UnitTested
+% \begin{macro}[aux]{\@@_to_symbols:nnnn}
 %   For conversion of integers to arbitrary symbols the method is in
 %   general as follows. The input number (|#1|) is compared to the total
 %   number of symbols available at each place (|#2|). If the input is larger
@@ -1463,17 +1639,17 @@
   {
     \int_compare:nNnTF {#1} > {#2}
       {
-        \exp_args:NNo \exp_args:No \int_to_symbols_aux:nnnn
+        \exp_args:NNo \exp_args:No \@@_to_symbols:nnnn
           {
-            \prg_case_int:nnn
+            \int_case:nnn
               { 1 + \int_mod:nn { #1 - 1 } {#2} }
               {#3} { }
           }
           {#1} {#2} {#3}
       }
-      { \prg_case_int:nnn {#1} {#3} { } }
+      { \int_case:nnn {#1} {#3} { } }
   }
-\cs_new:Npn \int_to_symbols_aux:nnnn #1#2#3#4
+\cs_new:Npn \@@_to_symbols:nnnn #1#2#3#4
   {
     \exp_args:Nf \int_to_symbols:nnn
       { \int_div_truncate:nn { #2 - 1 } {#3} } {#3} {#4}
@@ -1481,6 +1657,7 @@
   }
 %    \end{macrocode}
 % \end{macro}
+% \end{macro}
 %
 % \begin{macro}{\int_to_alph:n,\int_to_Alph:n}
 % \UnitTested
@@ -1556,9 +1733,9 @@
 %
 % \begin{macro}{\int_to_base:nn}
 % \UnitTested
-% \begin{macro}[aux]{\int_to_base_aux_i:nn,
-%     \int_to_base_aux_ii:nnN,\int_to_base_aux_iii:nnnN}
-% \begin{macro}[int]{\int_to_letter:n}
+% \begin{macro}[aux]{\@@_to_base:nn,
+%     \@@_to_base:nnN,\@@_to_base:nnnN}
+% \begin{macro}[aux]{\@@_to_letter:n}
 % \UnitTested
 %   Converting from base ten (|#1|) to a second base (|#2|) starts with
 %   computing |#1|: if it is a complicated calculation, we shouldn't
@@ -1567,12 +1744,12 @@
 %   function.
 %    \begin{macrocode}
 \cs_new:Npn \int_to_base:nn #1
-  { \exp_args:Nf \int_to_base_aux_i:nn { \int_eval:n {#1} } }
-\cs_new:Npn \int_to_base_aux_i:nn #1#2
+  { \exp_args:Nf \@@_to_base:nn { \int_eval:n {#1} } }
+\cs_new:Npn \@@_to_base:nn #1#2
   {
     \int_compare:nNnTF {#1} < \c_zero
-      { \exp_args:No \int_to_base_aux_ii:nnN { \use_none:n #1 } {#2} - }
-      { \int_to_base_aux_ii:nnN {#1} {#2} \c_empty_tl }
+      { \exp_args:No \@@_to_base:nnN { \use_none:n #1 } {#2} - }
+      { \@@_to_base:nnN {#1} {#2} \c_empty_tl }
   }
 %    \end{macrocode}
 %   Here, the idea is to provide a recursive system to deal with the
@@ -1585,21 +1762,21 @@
 %   modulus is converted to a symbol and put on the right,
 %   and the remainder is carried forward to the next round.
 %    \begin{macrocode}
-\cs_new:Npn \int_to_base_aux_ii:nnN #1#2#3
+\cs_new:Npn \@@_to_base:nnN #1#2#3
   {
     \int_compare:nNnTF {#1} < {#2}
-      { \exp_last_unbraced:Nf #3 { \int_to_letter:n {#1} } }
+      { \exp_last_unbraced:Nf #3 { \@@_to_letter:n {#1} } }
       {
-        \exp_args:Nf \int_to_base_aux_iii:nnnN
-          { \int_to_letter:n { \int_mod:nn {#1} {#2} } }
+        \exp_args:Nf \@@_to_base:nnnN
+          { \@@_to_letter:n { \int_mod:nn {#1} {#2} } }
           {#1}
           {#2}
           #3
       }
   }
-\cs_new:Npn \int_to_base_aux_iii:nnnN #1#2#3#4
+\cs_new:Npn \@@_to_base:nnnN #1#2#3#4
   {
-    \exp_args:Nf \int_to_base_aux_ii:nnN
+    \exp_args:Nf \@@_to_base:nnN
       { \int_div_truncate:nn {#2} {#3} }
       {#3}
       #4
@@ -1607,7 +1784,7 @@
   }
 %    \end{macrocode}
 %   Convert to a letter only if necessary, otherwise simply return the
-%   value unchanged. It would be cleaner to use \cs{prg_case_int:nnn},
+%   value unchanged. It would be cleaner to use \cs{int_case:nnn},
 %   but in our case, the cases are contiguous, so it is forty times faster
 %   to use the \cs{if_case:w} primitive. The first \cs{exp_after:wN}
 %   expands the conditional, jumping to the correct case, the second one
@@ -1615,10 +1792,10 @@
 %   Since |#1| might be an expression, and not directly a single digit,
 %   we need to evaluate it properly, and expand the trailing \cs{fi:}.
 %    \begin{macrocode}
-\cs_new:Npn \int_to_letter:n #1
+\cs_new:Npn \@@_to_letter:n #1
   {
     \exp_after:wN \exp_after:wN
-    \if_case:w \int_eval:w #1 - \c_ten \int_eval_end:
+    \if_case:w \@@_eval:w #1 - \c_ten \@@_eval_end:
          A
     \or: B
     \or: C
@@ -1645,7 +1822,7 @@
     \or: X
     \or: Y
     \or: Z
-    \else: \int_value:w \int_eval:w #1 \exp_after:wN \int_eval_end:
+    \else: \@@_value:w \@@_eval:w #1 \exp_after:wN \@@_eval_end:
     \fi:
   }
 %    \end{macrocode}
@@ -1668,17 +1845,17 @@
 %
 % \begin{macro}{\int_to_roman:n, \int_to_Roman:n}
 % \UnitTested
-% \begin{macro}[aux]{\int_to_roman_aux:N, \int_to_roman_aux:N}
+% \begin{macro}[aux]{\@@_to_roman:N, \@@_to_roman:N}
 % \begin{macro}[aux]
 %   {
-%     \int_to_roman_i:w, \int_to_roman_v:w, \int_to_roman_x:w,
-%     \int_to_roman_l:w, \int_to_roman_c:w, \int_to_roman_d:w,
-%     \int_to_roman_m:w, \int_to_roman_Q:w,
-%     \int_to_Roman_i:w, \int_to_Roman_v:w, \int_to_Roman_x:w,
-%     \int_to_Roman_l:w, \int_to_Roman_c:w, \int_to_Roman_d:w,
-%     \int_to_Roman_m:w, \int_to_Roman_Q:w,
+%     \@@_to_roman_i:w, \@@_to_roman_v:w, \@@_to_roman_x:w,
+%     \@@_to_roman_l:w, \@@_to_roman_c:w, \@@_to_roman_d:w,
+%     \@@_to_roman_m:w, \@@_to_roman_Q:w,
+%     \@@_to_Roman_i:w, \@@_to_Roman_v:w, \@@_to_Roman_x:w,
+%     \@@_to_Roman_l:w, \@@_to_Roman_c:w, \@@_to_Roman_d:w,
+%     \@@_to_Roman_m:w, \@@_to_Roman_Q:w,
 %   }
-% The \cs{int_to_roman:w} primitive creates tokens of category
+% The \cs{@@_to_roman:w} primitive creates tokens of category
 % code $12$ (other). Usually, what is actually wanted is letters.
 % The approach here is to convert the output of the primitive into
 % letters using appropriate control sequence names. That keeps
@@ -1687,40 +1864,40 @@
 %    \begin{macrocode}
 \cs_new:Npn \int_to_roman:n #1
   {
-    \exp_after:wN \int_to_roman_aux:N
-      \int_to_roman:w \int_eval:n {#1} Q
+    \exp_after:wN \@@_to_roman:N
+      \@@_to_roman:w \int_eval:n {#1} Q
   }
-\cs_new:Npn \int_to_roman_aux:N #1
+\cs_new:Npn \@@_to_roman:N #1
   {
-    \use:c { int_to_roman_ #1 :w }
-    \int_to_roman_aux:N
+    \use:c { @@_to_roman_ #1 :w }
+    \@@_to_roman:N
   }
 \cs_new:Npn \int_to_Roman:n #1
   {
-    \exp_after:wN \int_to_Roman_aux:N
-      \int_to_roman:w \int_eval:n {#1} Q
+    \exp_after:wN \@@_to_Roman_aux:N
+      \@@_to_roman:w \int_eval:n {#1} Q
   }
-\cs_new:Npn \int_to_Roman_aux:N #1
+\cs_new:Npn \@@_to_Roman_aux:N #1
   {
-    \use:c { int_to_Roman_ #1 :w }
-    \int_to_Roman_aux:N
+    \use:c { @@_to_Roman_ #1 :w }
+    \@@_to_Roman_aux:N
   }
-\cs_new_nopar:Npn \int_to_roman_i:w { i }
-\cs_new_nopar:Npn \int_to_roman_v:w { v }
-\cs_new_nopar:Npn \int_to_roman_x:w { x }
-\cs_new_nopar:Npn \int_to_roman_l:w { l }
-\cs_new_nopar:Npn \int_to_roman_c:w { c }
-\cs_new_nopar:Npn \int_to_roman_d:w { d }
-\cs_new_nopar:Npn \int_to_roman_m:w { m }
-\cs_new_nopar:Npn \int_to_roman_Q:w #1 { }
-\cs_new_nopar:Npn \int_to_Roman_i:w { I }
-\cs_new_nopar:Npn \int_to_Roman_v:w { V }
-\cs_new_nopar:Npn \int_to_Roman_x:w { X }
-\cs_new_nopar:Npn \int_to_Roman_l:w { L }
-\cs_new_nopar:Npn \int_to_Roman_c:w { C }
-\cs_new_nopar:Npn \int_to_Roman_d:w { D }
-\cs_new_nopar:Npn \int_to_Roman_m:w { M }
-\cs_new:Npn \int_to_Roman_Q:w #1 { }
+\cs_new_nopar:Npn \@@_to_roman_i:w { i }
+\cs_new_nopar:Npn \@@_to_roman_v:w { v }
+\cs_new_nopar:Npn \@@_to_roman_x:w { x }
+\cs_new_nopar:Npn \@@_to_roman_l:w { l }
+\cs_new_nopar:Npn \@@_to_roman_c:w { c }
+\cs_new_nopar:Npn \@@_to_roman_d:w { d }
+\cs_new_nopar:Npn \@@_to_roman_m:w { m }
+\cs_new_nopar:Npn \@@_to_roman_Q:w #1 { }
+\cs_new_nopar:Npn \@@_to_Roman_i:w { I }
+\cs_new_nopar:Npn \@@_to_Roman_v:w { V }
+\cs_new_nopar:Npn \@@_to_Roman_x:w { X }
+\cs_new_nopar:Npn \@@_to_Roman_l:w { L }
+\cs_new_nopar:Npn \@@_to_Roman_c:w { C }
+\cs_new_nopar:Npn \@@_to_Roman_d:w { D }
+\cs_new_nopar:Npn \@@_to_Roman_m:w { M }
+\cs_new:Npn \@@_to_Roman_Q:w #1 { }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1728,54 +1905,54 @@
 %
 % \subsection{Converting from other formats to integers}
 %
-% \begin{macro}[int]{\int_get_sign:n}
-% \begin{macro}[int]{\int_get_digits:n}
+% \begin{macro}[int]{\@@_get_sign:n}
+% \begin{macro}[int]{\@@_get_digits:n}
 % \begin{macro}[aux]
-%   {\int_get_sign_and_digits_aux:nNNN, \int_get_sign_and_digits_aux:oNNN}
+%   {\@@_get_sign_and_digits:nNNN, \@@_get_sign_and_digits:oNNN}
 %   Finding a number and its sign requires dealing with an arbitrary
 %   list of |+| and |-| symbols. This is done by working through token
 %   by token until there is something else at the start of the input.
 %   The sign of the input is tracked by the first Boolean used by the
 %   auxiliary function.
 %    \begin{macrocode}
-\cs_new:Npn \int_get_sign:n #1
+\cs_new:Npn \@@_get_sign:n #1
   {
-    \int_get_sign_and_digits_aux:nNNN {#1}
+    \@@_get_sign_and_digits:nNNN {#1}
       \c_true_bool \c_true_bool \c_false_bool
   }
-\cs_new:Npn \int_get_digits:n #1
+\cs_new:Npn \@@_get_digits:n #1
   {
-    \int_get_sign_and_digits_aux:nNNN {#1}
+    \@@_get_sign_and_digits:nNNN {#1}
       \c_true_bool \c_false_bool \c_true_bool
   }
 %    \end{macrocode}
 %   The auxiliary loops through, finding sign tokens and removing them.
 %   The sign itself is carried through as a flag.
 %    \begin{macrocode}
-\cs_new:Npn \int_get_sign_and_digits_aux:nNNN #1#2#3#4
+\cs_new:Npn \@@_get_sign_and_digits:nNNN #1#2#3#4
   {
     \exp_args:Nf \tl_if_head_eq_charcode:nNTF {#1} -
       {
         \bool_if:NTF #2
           {
-            \int_get_sign_and_digits_aux:oNNN
+            \@@_get_sign_and_digits:oNNN
               { \use_none:n #1 } \c_false_bool #3#4
           }
           {
-            \int_get_sign_and_digits_aux:oNNN
+            \@@_get_sign_and_digits:oNNN
               { \use_none:n #1 } \c_true_bool #3#4
           }
       }
       {
         \exp_args:Nf \tl_if_head_eq_charcode:nNTF {#1} +
-          { \int_get_sign_and_digits_aux:oNNN { \use_none:n #1 } #2#3#4 }
+          { \@@_get_sign_and_digits:oNNN { \use_none:n #1 } #2#3#4 }
           {
             \bool_if:NT #3 { \bool_if:NF #2 - }
             \bool_if:NT #4 {#1}
           }
       }
   }
-\cs_generate_variant:Nn \int_get_sign_and_digits_aux:nNNN { o }
+\cs_generate_variant:Nn \@@_get_sign_and_digits:nNNN { o }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1783,9 +1960,9 @@
 %
 % \begin{macro}{\int_from_alph:n}
 % \UnitTested
-% \begin{macro}[aux]{\int_from_alph_aux:n}
-% \begin{macro}[aux]{\int_from_alph_aux:nN}
-% \begin{macro}[aux]{\int_from_alph_aux:N}
+% \begin{macro}[aux]{\@@_from_alph:n}
+% \begin{macro}[aux]{\@@_from_alph:nN}
+% \begin{macro}[aux]{\@@_from_alph:N}
 %   The aim here is to iterate through the input, converting one letter at
 %   a time to a number. The same approach is also used for base
 %   conversion, but this needs a different final auxiliary.
@@ -1794,22 +1971,22 @@
   {
     \int_eval:n
       {
-        \int_get_sign:n {#1}
-        \exp_args:Nf \int_from_alph_aux:n { \int_get_digits:n {#1} }
+        \@@_get_sign:n {#1}
+        \exp_args:Nf \@@_from_alph:n { \@@_get_digits:n {#1} }
       }
   }
-\cs_new:Npn \int_from_alph_aux:n #1
-  { \int_from_alph_aux:nN { 0 } #1 \q_nil }
-\cs_new:Npn \int_from_alph_aux:nN #1#2
+\cs_new:Npn \@@_from_alph:n #1
+  { \@@_from_alph:nN { 0 } #1 \q_nil }
+\cs_new:Npn \@@_from_alph:nN #1#2
   {
     \quark_if_nil:NTF #2
       {#1}
       {
-        \exp_args:Nf \int_from_alph_aux:nN
-          { \int_eval:n { #1 * 26 + \int_from_alph_aux:N #2 } }
+        \exp_args:Nf \@@_from_alph:nN
+          { \int_eval:n { #1 * 26 + \@@_from_alph:N #2 } }
       }
   }
-\cs_new:Npn \int_from_alph_aux:N #1
+\cs_new:Npn \@@_from_alph:N #1
   { \int_eval:n { `#1 - \int_compare:nNnTF { `#1 } < { 91 } { 64 } { 96 } } }
 %    \end{macrocode}
 % \end{macro}
@@ -1819,9 +1996,9 @@
 %
 % \begin{macro}{\int_from_base:nn}
 % \UnitTested
-% \begin{macro}[aux]{\int_from_base_aux:nn}
-% \begin{macro}[aux]{\int_from_base_aux:nnN}
-% \begin{macro}[aux]{\int_from_base_aux:N}
+% \begin{macro}[aux]{\@@_from_base:nn}
+% \begin{macro}[aux]{\@@_from_base:nnN}
+% \begin{macro}[aux]{\@@_from_base:N}
 %   Conversion to base ten means stripping off the sign then iterating
 %   through the input one token at a time. The total number is then added
 %   up as the code loops.
@@ -1830,20 +2007,20 @@
   {
     \int_eval:n
       {
-        \int_get_sign:n {#1}
-        \exp_args:Nf \int_from_base_aux:nn
-          { \int_get_digits:n {#1} } {#2}
+        \@@_get_sign:n {#1}
+        \exp_args:Nf \@@_from_base:nn
+          { \@@_get_digits:n {#1} } {#2}
       }
   }
-\cs_new:Npn \int_from_base_aux:nn #1#2
-  { \int_from_base_aux:nnN { 0 } { #2 } #1 \q_nil }
-\cs_new:Npn \int_from_base_aux:nnN #1#2#3
+\cs_new:Npn \@@_from_base:nn #1#2
+  { \@@_from_base:nnN { 0 } { #2 } #1 \q_nil }
+\cs_new:Npn \@@_from_base:nnN #1#2#3
   {
     \quark_if_nil:NTF #3
       {#1}
       {
-        \exp_args:Nf \int_from_base_aux:nnN
-          { \int_eval:n { #1 * #2 + \int_from_base_aux:N #3 } }
+        \exp_args:Nf \@@_from_base:nnN
+          { \int_eval:n { #1 * #2 + \@@_from_base:N #3 } }
           {#2}
       }
   }
@@ -1852,7 +2029,7 @@
 %   them into the appropriate number, hence the two-part nature of the
 %   function.
 %    \begin{macrocode}
-\cs_new:Npn \int_from_base_aux:N #1
+\cs_new:Npn \@@_from_base:N #1
   {
     \int_compare:nNnTF { `#1 } < { 58 }
       {#1}
@@ -1882,40 +2059,40 @@
 %
 % \begin{variable}
 %   {
-%     \c_int_from_roman_i_int, \c_int_from_roman_v_int,
-%     \c_int_from_roman_x_int, \c_int_from_roman_l_int,
-%     \c_int_from_roman_c_int, \c_int_from_roman_d_int,
-%     \c_int_from_roman_m_int,
-%     \c_int_from_roman_I_int, \c_int_from_roman_V_int,
-%     \c_int_from_roman_X_int, \c_int_from_roman_L_int,
-%     \c_int_from_roman_C_int, \c_int_from_roman_D_int,
-%     \c_int_from_roman_M_int
+%     \c_@@_from_roman_i_int, \c_@@_from_roman_v_int,
+%     \c_@@_from_roman_x_int, \c_@@_from_roman_l_int,
+%     \c_@@_from_roman_c_int, \c_@@_from_roman_d_int,
+%     \c_@@_from_roman_m_int,
+%     \c_@@_from_roman_I_int, \c_@@_from_roman_V_int,
+%     \c_@@_from_roman_X_int, \c_@@_from_roman_L_int,
+%     \c_@@_from_roman_C_int, \c_@@_from_roman_D_int,
+%     \c_@@_from_roman_M_int
 %  }
 % Constants used to convert from Roman numerals to integers.
 %    \begin{macrocode}
-\int_const:cn { c_int_from_roman_i_int } { 1 }
-\int_const:cn { c_int_from_roman_v_int } { 5 }
-\int_const:cn { c_int_from_roman_x_int } { 10 }
-\int_const:cn { c_int_from_roman_l_int } { 50 }
-\int_const:cn { c_int_from_roman_c_int } { 100 }
-\int_const:cn { c_int_from_roman_d_int } { 500 }
-\int_const:cn { c_int_from_roman_m_int } { 1000 }
-\int_const:cn { c_int_from_roman_I_int } { 1 }
-\int_const:cn { c_int_from_roman_V_int } { 5 }
-\int_const:cn { c_int_from_roman_X_int } { 10 }
-\int_const:cn { c_int_from_roman_L_int } { 50 }
-\int_const:cn { c_int_from_roman_C_int } { 100 }
-\int_const:cn { c_int_from_roman_D_int } { 500 }
-\int_const:cn { c_int_from_roman_M_int } { 1000 }
+\int_const:cn { c_@@_from_roman_i_int } { 1 }
+\int_const:cn { c_@@_from_roman_v_int } { 5 }
+\int_const:cn { c_@@_from_roman_x_int } { 10 }
+\int_const:cn { c_@@_from_roman_l_int } { 50 }
+\int_const:cn { c_@@_from_roman_c_int } { 100 }
+\int_const:cn { c_@@_from_roman_d_int } { 500 }
+\int_const:cn { c_@@_from_roman_m_int } { 1000 }
+\int_const:cn { c_@@_from_roman_I_int } { 1 }
+\int_const:cn { c_@@_from_roman_V_int } { 5 }
+\int_const:cn { c_@@_from_roman_X_int } { 10 }
+\int_const:cn { c_@@_from_roman_L_int } { 50 }
+\int_const:cn { c_@@_from_roman_C_int } { 100 }
+\int_const:cn { c_@@_from_roman_D_int } { 500 }
+\int_const:cn { c_@@_from_roman_M_int } { 1000 }
 %    \end{macrocode}
 % \end{variable}
 %
 % \begin{macro}{\int_from_roman:n}
 % \UnitTested
 % \TestMissing{boundary cases / wrong input?}
-% \begin{macro}[aux]{\int_from_roman_aux:NN}
-% \begin{macro}[aux]{\int_from_roman_end:w}
-% \begin{macro}[aux]{\int_from_roman_clean_up:w}
+% \begin{macro}[aux]{\@@_from_roman:NN}
+% \begin{macro}[aux]{\@@_from_roman_end:w}
+% \begin{macro}[aux]{\@@_from_roman_clean_up:w}
 %   The method here is to iterate through the input, finding the
 %   appropriate value for each letter and building up a sum. This is
 %   then evaluated by \TeX{}.
@@ -1924,48 +2101,48 @@
   {
     \tl_if_blank:nF {#1}
       {
-        \exp_after:wN \int_from_roman_end:w
-          \int_value:w \int_eval:w
-            \int_from_roman_aux:NN #1 Q \q_stop
+        \exp_after:wN \@@_from_roman_end:w
+          \@@_value:w \@@_eval:w
+            \@@_from_roman:NN #1 Q \q_stop
       }
   }
-\cs_new:Npn \int_from_roman_aux:NN #1#2
+\cs_new:Npn \@@_from_roman:NN #1#2
   {
     \str_if_eq:nnTF {#1} { Q }
       {#1#2}
       {
         \str_if_eq:nnTF {#2} { Q }
           {
-            \int_if_exist:cF { c_int_from_roman_ #1 _int }
-              { \int_from_roman_clean_up:w }
+            \int_if_exist:cF { c_@@_from_roman_ #1 _int }
+              { \@@_from_roman_clean_up:w }
             +
-            \use:c { c_int_from_roman_ #1 _int }
+            \use:c { c_@@_from_roman_ #1 _int }
             #2
           }
           {
-            \int_if_exist:cF { c_int_from_roman_ #1 _int }
-              { \int_from_roman_clean_up:w }
-            \int_if_exist:cF { c_int_from_roman_ #2 _int }
-              { \int_from_roman_clean_up:w }
+            \int_if_exist:cF { c_@@_from_roman_ #1 _int }
+              { \@@_from_roman_clean_up:w }
+            \int_if_exist:cF { c_@@_from_roman_ #2 _int }
+              { \@@_from_roman_clean_up:w }
             \int_compare:nNnTF
-              { \use:c { c_int_from_roman_ #1 _int } }
+              { \use:c { c_@@_from_roman_ #1 _int } }
               <
-              { \use:c { c_int_from_roman_ #2 _int  } }
+              { \use:c { c_@@_from_roman_ #2 _int  } }
               {
-                + \use:c { c_int_from_roman_ #2 _int }
-                - \use:c { c_int_from_roman_ #1 _int }
-                \int_from_roman_aux:NN
+                + \use:c { c_@@_from_roman_ #2 _int }
+                - \use:c { c_@@_from_roman_ #1 _int }
+                \@@_from_roman:NN
               }
               {
-                + \use:c { c_int_from_roman_ #1 _int }
-                \int_from_roman_aux:NN #2
+                + \use:c { c_@@_from_roman_ #1 _int }
+                \@@_from_roman:NN #2
               }
           }
       }
   }
-\cs_new:Npn \int_from_roman_end:w #1 Q #2 \q_stop
+\cs_new:Npn \@@_from_roman_end:w #1 Q #2 \q_stop
   { \tl_if_empty:nTF {#2} {#1} {#2} }
-\cs_new:Npn \int_from_roman_clean_up:w #1 Q { + 0 Q -1 }
+\cs_new:Npn \@@_from_roman_clean_up:w #1 Q { + 0 Q -1 }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1977,16 +2154,19 @@
 % \begin{macro}{\int_show:N,\int_show:c}
 % \UnitTested
 %    \begin{macrocode}
-\cs_new_eq:NN \int_show:N \kernel_register_show:N
-\cs_new_eq:NN \int_show:c \kernel_register_show:c
+\cs_new_eq:NN \int_show:N \__kernel_register_show:N
+\cs_new_eq:NN \int_show:c \__kernel_register_show:c
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}{\int_show:n}
 % \UnitTested
+%   We don't use the \TeX{} primitive \tn{showthe} to show integer
+%   expressions: this gives a more unified output, since the closing
+%   brace is read by the integer expression in all cases.
 %    \begin{macrocode}
 \cs_new_protected:Npn \int_show:n #1
-  { \tex_showthe:D \int_eval:w #1 \int_eval_end: }
+  { \etex_showtokens:D \exp_after:wN { \int_use:N \@@_eval:w #1 } }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2064,14 +2244,13 @@
 %
 % \subsection{Scratch integers}
 %
-% \begin{variable}{\l_tmpa_int, \l_tmpb_int, \l_tmpc_int}
+% \begin{variable}{\l_tmpa_int, \l_tmpb_int}
 % \begin{variable}{\g_tmpa_int, \g_tmpb_int}
-%    We provide three local and two global scratch counters, maybe we
+%    We provide two local and two global scratch counters, maybe we
 %    need more or less.
 %    \begin{macrocode}
 \int_new:N \l_tmpa_int
 \int_new:N \l_tmpb_int
-\int_new:N \l_tmpc_int
 \int_new:N \g_tmpa_int
 \int_new:N \g_tmpb_int
 %    \end{macrocode}
@@ -2147,6 +2326,35 @@
 % \end{macro}
 % \end{macro}
 %
+% \begin{macro}{\if_num:w}
+%   Deprecated 2012-05-30 for removal after 2012-11-30.
+%    \begin{macrocode}
+\cs_new_eq:NN \if_num:w \if_int_compare:w
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{variable}{\l_tmpc_int}
+%   Deprecated 2012-07-04 for removal after 2012-12-31.
+%    \begin{macrocode}
+\int_new:N \l_tmpc_int
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}{\int_eval:w, \int_eval_end:}
+%   Deprecated 2012-07-13 for removal after 2012-12-31.
+%    \begin{macrocode}
+\cs_new_eq:NN \int_eval:w    \@@_eval:w
+\cs_new_eq:NN \int_eval_end: \@@_eval_end:
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\int_value:w}
+%   Deprecated 2012-07-14 for removal after 2012-12-31.
+%    \begin{macrocode}
+\cs_new_eq:NN \int_value:w \@@_value:w
+%    \end{macrocode}
+% \end{macro}
+%
 %    \begin{macrocode}
 %</initex|package>
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3keys.dtx b/Master/texmf-dist/source/latex/l3kernel/l3keys.dtx
index e0becb45696..7e3cc783af2 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3keys.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3keys.dtx
@@ -1,6 +1,6 @@
 % \iffalse meta-comment
 %
-%% File: l3keys.dtx Copyright (C) 2006-2011 The LaTeX3 Project
+%% File: l3keys.dtx Copyright (C) 2006-2012 The LaTeX3 Project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3keys.dtx 3487 2012-03-03 19:36:51Z bruno $
+\GetIdInfo$Id: l3keys.dtx 3986 2012-07-15 19:23:51Z joseph $
   {L3 Experimental key-value interfaces}
 %</driver|package>
 %<*driver>
@@ -170,27 +170,18 @@
 % arbitrary \meta{key}, which when used may be supplied with a
 % \meta{value}. All key \emph{definitions} are local.
 %
-% \begin{function}{.bool_set:N}
+% \begin{function}{.bool_set:N, .bool_gset:N}
 %   \begin{syntax}
 %     \meta{key} .bool_set:N = \meta{boolean}
 %   \end{syntax}
 %   Defines \meta{key} to set \meta{boolean} to \meta{value} (which
 %   must be either \texttt{true} or \texttt{false}).  If the variable
 %   does not exist, it will be created at the point that the key is
-%   set up. The \meta{boolean} will be assigned locally.
+%   set up. 
 % \end{function}
 %
-% \begin{function}{.bool_gset:N}
-%   \begin{syntax}
-%     \meta{key} .bool_gset:N = \meta{boolean}
-%   \end{syntax}
-%   Defines \meta{key} to set \meta{boolean} to \meta{value} (which
-%   must be either \texttt{true} or \texttt{false}).  If the variable
-%   does not exist, it will be created at the point that the key is
-%   set up. The \meta{boolean} will be assigned globally.
-% \end{function}
-%
-% \begin{function}[added = 2011-08-28]{.bool_set_inverse:N}
+% \begin{function}[added = 2011-08-28]
+%   {.bool_set_inverse:N, .bool_gset_inverse:N}
 %   \begin{syntax}
 %     \meta{key} .bool_set_inverse:N = \meta{boolean}
 %   \end{syntax}
@@ -198,22 +189,7 @@
 %   inverse of \meta{value} (which  must be either \texttt{true} or
 %   \texttt{false}).
 %   If the \meta{boolean} does not exist, it will be created at the point
-%   that the key is set up. The \meta{boolean} will be assigned locally.
-%
-%   \textbf{This property is experimental.}
-% \end{function}
-%
-% \begin{function}{.bool_gset_inverse:N}
-%   \begin{syntax}
-%     \meta{key} .bool_gset_inverse:N = \meta{boolean}
-%   \end{syntax}
-%   Defines \meta{key} to set \meta{boolean} to the logical
-%   inverse of \meta{value} (which  must be either \texttt{true} or
-%   \texttt{false}).
-%   If the \meta{boolean} does not exist, it will be created at the point
-%   that the key is set up. The \meta{boolean} will be assigned globally.
-%
-%   \textbf{This property is experimental.}
+%   that the key is set up.
 % \end{function}
 %
 % \begin{function}{.choice:}
@@ -233,10 +209,8 @@
 %   which are implemented using the \meta{code}. Inside \meta{code},
 %   \cs{l_keys_choice_tl} will be the name of the choice made, and
 %   \cs{l_keys_choice_int} will be the position of the choice in the list
-%   of \meta{choices} (indexed from $0$).
+%   of \meta{choices} (indexed from~$1$).
 %   Choices are discussed in detail in section~\ref{sec:choice}.
-%
-%   \textbf{This property is experimental.}
 % \end{function}
 %
 % \begin{function}{.choice_code:n, .choice_code:x}
@@ -251,21 +225,12 @@
 %   detail in section~\ref{sec:choice}.
 % \end{function}
 %
-% \begin{function}[added=2011/09/11]{.clist_set:N, .clist_set:c}
+% \begin{function}[added=2011/09/11]
+%   {.clist_set:N, .clist_set:c, .clist_gset:N, .clist_gset:c}
 %   \begin{syntax}
 %     \meta{key} .clist_set:N = \meta{comma list variable}
 %   \end{syntax}
-%   Defines \meta{key} to locally set \meta{comma list variable} to \meta{value}.
-%   Spaces around commas and empty items will be stripped.
-%   If the variable does not exist, it
-%   will be created at the point that the key is set up.
-% \end{function}
-%
-% \begin{function}[added=2011/09/11]{.clist_gset:N, .clist_gset:c}
-%   \begin{syntax}
-%     \meta{key} .clist_gset:N = \meta{comma list variable}
-%   \end{syntax}
-%   Defines \meta{key} to globally set \meta{comma list variable} to \meta{value}.
+%   Defines \meta{key} to set \meta{comma list variable} to \meta{value}.
 %   Spaces around commas and empty items will be stripped.
 %   If the variable does not exist, it
 %   will be created at the point that the key is set up.
@@ -304,44 +269,22 @@
 %   \end{verbatim}
 % \end{function}
 %
-% \begin{function}{.dim_set:N, .dim_set:c}
+% \begin{function}{.dim_set:N, .dim_set:c, .dim_gset:N, .dim_gset:c}
 %   \begin{syntax}
 %     \meta{key} .dim_set:N = \meta{dimension}
 %   \end{syntax}
 %   Defines \meta{key} to set \meta{dimension} to \meta{value} (which
 %   must a dimension expression).  If the variable does not exist, it
-%   will be created at the point that the key is set up. The
-%   \meta{dimension} will be assigned locally.
-% \end{function}
-%
-% \begin{function}{.dim_gset:N, .dim_gset:c}
-%   \begin{syntax}
-%     \meta{key} .dim_gset:N = \meta{dimension}
-%   \end{syntax}
-%   Defines \meta{key} to set \meta{dimension} to \meta{value} (which
-%   must a dimension expression).  If the variable does not exist, it
-%   will be created at the point that the key is set up. The
-%   \meta{dimension} will be assigned globally.
+%   will be created at the point that the key is set up. 
 % \end{function}
 %
-% \begin{function}{.fp_set:N, .fp_set:c}
+% \begin{function}{.fp_set:N, .fp_set:c, .fp_gset:N, .fp_gset:c}
 %   \begin{syntax}
 %     \meta{key} .fp_set:N = \meta{floating point}
 %   \end{syntax}
 %   Defines \meta{key} to set \meta{floating point} to \meta{value}
 %   (which must a floating point number).  If the variable does not exist,
-%   it will be created at the point that the key is set up. The
-%   \meta{integer} will be assigned locally.
-% \end{function}
-%
-% \begin{function}{.fp_gset:N, .fp_gset:c}
-%   \begin{syntax}
-%     \meta{key} .fp_gset:N = \meta{floating point}
-%   \end{syntax}
-%   Defines \meta{key} to set \meta{floating-point} to \meta{value}
-%   (which must a floating point number).  If the variable does not exist,
-%   it will be created at the point that the key is set up. The
-%   \meta{integer} will be assigned globally.
+%   it will be created at the point that the key is set up.
 % \end{function}
 %
 % \begin{function}{.generate_choices:n}
@@ -355,25 +298,24 @@
 %   \texttt{.choice_code:n} (or \texttt{.choice_code:x}). Choices are
 %   discussed in detail in section~\ref{sec:choice}.
 % \end{function}
-%
-% \begin{function}{.int_set:N, .int_set:c}
+% 
+% \begin{function}[added = 2012-06-02]{.initial:n, .initial:V}
 %   \begin{syntax}
-%     \meta{key} .int_set:N = \meta{integer}
+%     \meta{key} .initial:n = \meta{value}
 %   \end{syntax}
-%   Defines \meta{key} to set \meta{integer} to \meta{value} (which
-%   must be an integer expression).  If the variable does not exist, it
-%   will be created at the point that the key is set up. The
-%   \meta{integer} will be assigned locally.
+%   Initialises the \meta{key} with the \meta{value}, equivalent to
+%   \begin{quote}
+%     \cs{keys_set:nn} \marg{module} \{ \meta{key} = \meta{value} \}
+%   \end{quote}
 % \end{function}
 %
-% \begin{function}{.int_gset:N, .int_gset:c}
+% \begin{function}{.int_set:N, .int_set:c, .int_gset:N, .int_gset:c}
 %   \begin{syntax}
-%     \meta{key} .int_gset:N = \meta{integer}
+%     \meta{key} .int_set:N = \meta{integer}
 %   \end{syntax}
 %   Defines \meta{key} to set \meta{integer} to \meta{value} (which
 %   must be an integer expression).  If the variable does not exist, it
-%   will be created at the point that the key is set up. The
-%   \meta{integer} will be assigned globally.
+%   will be created at the point that the key is set up.
 % \end{function}
 %
 % \begin{function}{.meta:n, .meta:x}
@@ -397,81 +339,47 @@
 %   \textbf{This property is experimental.}
 % \end{function}
 %
-% \begin{function}[added = 2011-08-21]{.multichoice:nn}
+% \begin{function}[added = 2011-08-21]{.multichoices:nn}
 %   \begin{syntax}
-%     \meta{key} .multichoice:nn \meta{choices} \meta{code}
+%     \meta{key} .multichoices:nn \meta{choices} \meta{code}
 %   \end{syntax}
 %   Sets \meta{key} to act as a multiple choice key, and defines a series
 %   \meta{choices}
 %   which are implemented using the \meta{code}. Inside \meta{code},
 %   \cs{l_keys_choice_tl} will be the name of the choice made, and
 %   \cs{l_keys_choice_int} will be the position of the choice in the list
-%   of \meta{choices} (indexed from $0$).
+%   of \meta{choices} (indexed from~$1$).
 %   Choices are discussed in detail in section~\ref{sec:choice}.
 %
 %   \textbf{This property is experimental.}
 % \end{function}
 %
-% \begin{function}{.skip_set:N, .skip_set:c}
+% \begin{function}{.skip_set:N, .skip_set:c, .skip_gset:N, .skip_gset:c}
 %   \begin{syntax}
 %     \meta{key} .skip_set:N = \meta{skip}
 %   \end{syntax}
 %   Defines \meta{key} to set \meta{skip} to \meta{value} (which
 %   must be a skip expression). If the variable does not exist, it
-%   will be created at the point that the key is set up. The
-%   \meta{skip} will be assigned locally.
-% \end{function}
-%
-% \begin{function}{.skip_gset:N, .skip_gset:c}
-%   \begin{syntax}
-%     \meta{key} .skip_gset:N = \meta{skip}
-%   \end{syntax}
-%   Defines \meta{key} to set \meta{skip} to \meta{value} (which
-%   must be a skip expression). If the variable does not exist, it
-%   will be created at the point that the key is set up. The
-%   \meta{skip} will be assigned globally.
+%   will be created at the point that the key is set up.
 % \end{function}
 %
-% \begin{function}{.tl_set:N, .tl_set:c}
+% \begin{function}{.tl_set:N, .tl_set:c, .tl_gset:N, .tl_gset:c}
 %   \begin{syntax}
 %     \meta{key} .tl_set:N = \meta{token list variable}
 %   \end{syntax}
 %   Defines \meta{key} to set \meta{token list variable} to \meta{value}.
 %   If the variable does not exist, it will be created at the point that
-%   the key is set up. The \meta{token list variable} will be assigned
-%   locally.
-% \end{function}
-%
-% \begin{function}{.tl_gset:N, .tl_gset:c}
-%   \begin{syntax}
-%     \meta{key} .tl_gset:N = \meta{token list variable}
-%   \end{syntax}
-%   Defines \meta{key} to set \meta{token list variable} to \meta{value}.
-%   If the variable does not exist, it will be created at the point that
-%   the key is set up. The \meta{token list variable} will be assigned
-%   globally.
+%   the key is set up.
 % \end{function}
 %
-% \begin{function}{.tl_set_x:N, .tl_set_x:c}
+% \begin{function}{.tl_set_x:N, .tl_set_x:c, .tl_gset_x:N, .tl_gset_x:c}
 %   \begin{syntax}
 %     \meta{key} .tl_set_x:N = \meta{token list variable}
 %   \end{syntax}
 %   Defines \meta{key} to set \meta{token list variable} to \meta{value},
 %   which will be subjected to an \texttt{x}-type expansion
 %   (\emph{i.e.}~using \cs{tl_set:Nx}). If the variable does not exist,
-%   it will be created at the point that the key is set up. The
-%   \meta{token list variable} will be assigned locally.
-% \end{function}
-%
-% \begin{function}{.tl_gset_x:N, .tl_gset_x:c}
-%   \begin{syntax}
-%     \meta{key} .tl_gset_x:N = \meta{token list variable}
-%   \end{syntax}
-%   Defines \meta{key} to set \meta{token list variable} to \meta{value},
-%   which will be subjected to an \texttt{x}-type expansion
-%   (\emph{i.e.}~using \cs{tl_set:Nx}). If the variable does not exist,
-%   it will be created at the point that the key is set up. The
-%   \meta{token list variable} will be assigned globally.
+%   it will be created at the point that the key is set up.
 % \end{function}
 %
 % \begin{function}{.value_forbidden:}
@@ -552,9 +460,7 @@
 %     }
 % \end{verbatim}
 % Following common computing practice, \cs{l_keys_choice_int} is
-% indexed from $0$ (as an offset), so that the value of
-% \cs{l_keys_choice_int} for the first choice in a list will be
-% zero.
+% indexed from~$1$.
 %
 % The same approach is also implemented by the \emph{experimental}
 % property \texttt{.choices:nn}. This combines the functionality of
@@ -691,9 +597,6 @@
 %
 % \section{Setting known keys only}
 %
-% The functionality described in this section is experimental and may be
-% altered or removed, depending on feedback.
-%
 % \begin{function}[added = 2011-08-23]
 %   {
 %     \keys_set_known:nnN, \keys_set_known:nVN,
@@ -720,7 +623,7 @@
 %   has been defined for \meta{key}.
 % \end{function}
 %
-% \begin{function}[added = 2011-08-21,EXP,pTF]{\keys_if_choice_exist:nn}
+% \begin{function}[added = 2011-08-21,EXP,pTF]{\keys_if_choice_exist:nnn}
 %   \begin{syntax}
 %     \cs{keys_if_choice_exist_p:nnn} \meta{module} \meta{key} \meta{choice} \\
 %     \cs{keys_if_choice_exist:nnnTF} \meta{module} \meta{key} \meta{choice} \Arg{true code} \Arg{false code}
@@ -782,15 +685,15 @@
 %
 % \begin{function}[updated = 2011-09-08]{\keyval_parse:NNn}
 %   \begin{syntax}
-%     \cs{keyval_parse:NNn} \meta{function1} \meta{function2} \Arg{key--value list}
+%     \cs{keyval_parse:NNn} \meta{function_1} \meta{function_2} \Arg{key--value list}
 %   \end{syntax}
 %   Parses the \meta{key--value list} into a series of \meta{keys} and
 %   associated \meta{values}, or keys alone (if no \meta{value} was
-%   given).  \meta{function1} should take one argument, while
-%   \meta{function2} should absorb two arguments. After
+%   given).  \meta{function_1} should take one argument, while
+%   \meta{function_2} should absorb two arguments. After
 %   \cs{keyval_parse:NNn} has parsed the \meta{key--value list},
-%   \meta{function1} will be used to process keys given with no value
-%   and \meta{function2} will be used to process keys given with a
+%   \meta{function_1} will be used to process keys given with no value
+%   and \meta{function_2} will be used to process keys given with a
 %   value. The order of the \meta{keys} in the \meta{key--value list}
 %   will be preserved. Thus
 %   \begin{verbatim}
@@ -825,41 +728,43 @@
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
 % \subsection{Low-level interface}
+% 
+%<@@=keyval>
 %
 % For historical reasons this code uses the `keyval' module prefix.
 %
-% \begin{variable}{\g_keyval_level_int}
+% \begin{variable}{\g_@@_level_int}
 %   For nesting purposes an integer is needed for the current level.
 %    \begin{macrocode}
-\int_new:N \g_keyval_level_int
+\int_new:N \g_@@_level_int
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_keyval_key_tl, \l_keyval_value_tl}
+% \begin{variable}{\l_@@_key_tl, \l_@@_value_tl}
 %   The current key name and value.
 %    \begin{macrocode}
-\tl_new:N \l_keyval_key_tl
-\tl_new:N \l_keyval_value_tl
+\tl_new:N \l_@@_key_tl
+\tl_new:N \l_@@_value_tl
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_keyval_sanitise_tl}
-% \begin{variable}{\l_keyval_parse_tl}
+% \begin{variable}{\l_@@_sanitise_tl}
+% \begin{variable}{\l_@@_parse_tl}
 %   Token list variables for dealing with awkward category codes in the
 %   input.
 %    \begin{macrocode}
-\tl_new:N \l_keyval_sanitise_tl
-\tl_new:N \l_keyval_parse_tl
+\tl_new:N \l_@@_sanitise_tl
+\tl_new:N \l_@@_parse_tl
 %    \end{macrocode}
 %\end{variable}
 %\end{variable}
 %
-% \begin{macro}{\keyval_parse:n}
+% \begin{macro}{\@@_parse:n}
 %   The parsing function first deals with the category codes for
 %   |=| and |,|, so that there are no odd events. The input is then
 %   handed off to the element by element system.
@@ -872,49 +777,49 @@
 \tl_to_lowercase:n
   {
     \group_end:
-    \cs_new_protected:Npn \keyval_parse:n #1
+    \cs_new_protected:Npn \@@_parse:n #1
       {
         \group_begin:
-          \tl_clear:N \l_keyval_sanitise_tl
-          \tl_set:Nn \l_keyval_sanitise_tl {#1}
-          \tl_replace_all:Nnn \l_keyval_sanitise_tl { = } { 8 }
-          \tl_replace_all:Nnn \l_keyval_sanitise_tl { , } { 9 }
-          \tl_clear:N \l_keyval_parse_tl
-          \exp_after:wN \keyval_parse_elt:w \exp_after:wN
-            \q_no_value \l_keyval_sanitise_tl 9 \q_nil 9
+          \tl_clear:N \l_@@_sanitise_tl
+          \tl_set:Nn \l_@@_sanitise_tl {#1}
+          \tl_replace_all:Nnn \l_@@_sanitise_tl { = } { 8 }
+          \tl_replace_all:Nnn \l_@@_sanitise_tl { , } { 9 }
+          \tl_clear:N \l_@@_parse_tl
+          \exp_after:wN \@@_parse_elt:w \exp_after:wN
+            \q_no_value \l_@@_sanitise_tl 9 \q_nil 9
         \exp_after:wN \group_end:
-        \l_keyval_parse_tl
+        \l_@@_parse_tl
       }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\keyval_parse_elt:w}
+% \begin{macro}{\@@_parse_elt:w}
 %   Each item to be parsed will have \cs{q_no_value} added to the front.
 %   Hence the blank test here can always be used to find a totally
 %   empty argument. If this is the case, the system loops round. If there
 %   is something to parse, there is a check for the \cs{q_nil} marker
 %   and if not a hand-off.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keyval_parse_elt:w #1 ,
+\cs_new_protected:Npn \@@_parse_elt:w #1 ,
   {
     \tl_if_blank:oTF { \use_none:n #1 }
-      { \keyval_parse_elt:w \q_no_value }
+      { \@@_parse_elt:w \q_no_value }
       {
         \quark_if_nil:oF { \use_ii:nn #1 }
           {
-            \keyval_split_key_value:w #1 = = \q_stop
-            \keyval_parse_elt:w \q_no_value
+            \@@_split_key_value:w #1 = = \q_stop
+            \@@_parse_elt:w \q_no_value
           }
       }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\keyval_split_key_value:w}
-% \begin{macro}[aux]{\keyval_split_key_value_aux:wTF}
+% \begin{macro}{\@@_split_key_value:w}
+% \begin{macro}[aux]{\@@_split_key_value:wTF}
 %   The key and value are handled separately. First the key is grabbed and
-%   saved as \cs{l_keyval_key_tl}. Then a check is need to see if there is
+%   saved as \cs{l_@@_key_tl}. Then a check is need to see if there is
 %   a value at all: if not then the key name is simply added to the output.
 %   If there is a value then there is a check to ensure that there was
 %   only one |=| in the input (remembering some extra ones are around at
@@ -922,84 +827,84 @@
 %   hand-off to find the value: the \cs{q_nil} is there to prevent loss
 %   of braces.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keyval_split_key_value:w #1 = #2 \q_stop
+\cs_new_protected:Npn \@@_split_key_value:w #1 = #2 \q_stop
   {
-    \keyval_split_key:w #1 \q_stop
+    \@@_split_key:w #1 \q_stop
     \str_if_eq:nnTF {#2} { = }
       {
-        \tl_put_right:Nx \l_keyval_parse_tl
+        \tl_put_right:Nx \l_@@_parse_tl
           {
             \exp_not:c
-              { keyval_key_no_value_elt_ \int_use:N \g_keyval_level_int :n }
-              { \exp_not:o \l_keyval_key_tl }
+              { @@_key_no_value_elt_ \int_use:N \g_@@_level_int :n }
+              { \exp_not:o \l_@@_key_tl }
           }
       }
       {
-        \keyval_split_key_value_aux:wTF #2 \q_no_value \q_stop
-          { \keyval_split_value:w \q_nil #2 }
-          { \msg_kernel_error:nn { keyval } { misplaced-equals-sign } }
+        \@@_split_key_value:wTF #2 \q_no_value \q_stop
+          { \@@_split_value:w \q_nil #2 }
+          { \__msg_kernel_error:nn { kernel } { misplaced-equals-sign } }
       }
   }
-\cs_new:Npn \keyval_split_key_value_aux:wTF #1 = #2#3 \q_stop
+\cs_new:Npn \@@_split_key_value:wTF #1 = #2#3 \q_stop
   { \tl_if_head_eq_meaning:nNTF {#3} \q_no_value }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\keyval_split_key:w}
+% \begin{macro}{\@@_split_key:w}
 %   The aim here is to remove spaces and also exactly one set of braces.
 %   There is also a quark to remove, hence the \cs{use_none:n} appearing before
 %   application of \cs{tl_trim_spaces:n}.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keyval_split_key:w #1 \q_stop
+\cs_new_protected:Npn \@@_split_key:w #1 \q_stop
   {
-    \tl_set:Nx \l_keyval_key_tl
+    \tl_set:Nx \l_@@_key_tl
       { \exp_after:wN \tl_trim_spaces:n \exp_after:wN { \use_none:n #1 } }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\keyval_split_value:w}
+% \begin{macro}{\@@_split_value:w}
 %   Here the value has to be separated from the equals signs and the
 %   leading \cs{q_nil} added in to keep the brace levels. Fist the
 %   processing function can be added to the output list. If there is no
-%   value, setting \cs{l_keyval_value_tl} with three groups removed will
+%   value, setting \cs{l_@@_value_tl} with three groups removed will
 %   leave nothing at all, and so an empty group can be added to the
 %   parsed list. On the other hand, if the value is entirely contained
-%   within a set of braces then \cs{l_keyval_value_tl} will contain
+%   within a set of braces then \cs{l_@@_value_tl} will contain
 %   \cs{q_nil} only. In that case, strip off the leading quark using
 %   \cs{use_ii:nnn}, which also deals with any spaces.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keyval_split_value:w #1 = =
+\cs_new_protected:Npn \@@_split_value:w #1 = =
   {
-    \tl_put_right:Nx \l_keyval_parse_tl
+    \tl_put_right:Nx \l_@@_parse_tl
       {
         \exp_not:c
-          { keyval_key_value_elt_ \int_use:N \g_keyval_level_int :nn }
-          { \exp_not:o \l_keyval_key_tl }
+          { @@_key_value_elt_ \int_use:N \g_@@_level_int :nn }
+          { \exp_not:o \l_@@_key_tl }
       }
-    \tl_set:Nx \l_keyval_value_tl
+    \tl_set:Nx \l_@@_value_tl
       { \exp_not:o { \use_none:nnn #1 \q_nil \q_nil } }
-    \tl_if_empty:NTF \l_keyval_value_tl
-      { \tl_put_right:Nn \l_keyval_parse_tl { { } } }
+    \tl_if_empty:NTF \l_@@_value_tl
+      { \tl_put_right:Nn \l_@@_parse_tl { { } } }
       {
-        \quark_if_nil:NTF \l_keyval_value_tl
+        \quark_if_nil:NTF \l_@@_value_tl
           {
-            \tl_put_right:Nx \l_keyval_parse_tl
+            \tl_put_right:Nx \l_@@_parse_tl
               { { \exp_not:o { \use_ii:nnn #1 \q_nil } } }
           }
-          { \keyval_split_value_aux:w #1 \q_stop }
+          { \@@_split_value_aux:w #1 \q_stop }
       }
   }
 %    \end{macrocode}
 %   A similar idea to the key code: remove the spaces from each end and
 %   deal with one set of braces.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keyval_split_value_aux:w \q_nil #1 \q_stop
+\cs_new_protected:Npn \@@_split_value_aux:w \q_nil #1 \q_stop
   {
-    \tl_set:Nx \l_keyval_value_tl { \tl_trim_spaces:n {#1} }
-    \tl_put_right:Nx \l_keyval_parse_tl
-      { { \exp_not:o \l_keyval_value_tl } }
+    \tl_set:Nx \l_@@_value_tl { \tl_trim_spaces:n {#1} }
+    \tl_put_right:Nx \l_@@_parse_tl
+      { { \exp_not:o \l_@@_value_tl } }
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1010,20 +915,20 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \keyval_parse:NNn #1#2#3
   {
-    \int_gincr:N \g_keyval_level_int
+    \int_gincr:N \g_@@_level_int
     \cs_gset_eq:cN
-      { keyval_key_no_value_elt_ \int_use:N \g_keyval_level_int :n } #1
+      { @@_key_no_value_elt_ \int_use:N \g_@@_level_int :n } #1
     \cs_gset_eq:cN
-      { keyval_key_value_elt_ \int_use:N \g_keyval_level_int :nn }   #2
-    \keyval_parse:n {#3}
-    \int_gdecr:N \g_keyval_level_int
+      { @@_key_value_elt_ \int_use:N \g_@@_level_int :nn }   #2
+    \@@_parse:n {#3}
+    \int_gdecr:N \g_@@_level_int
   }
 %    \end{macrocode}
 % \end{macro}
 %
 % One message for the low level parsing system.
 %    \begin{macrocode}
-\msg_kernel_new:nnnn { keyval } { misplaced-equals-sign }
+\__msg_kernel_new:nnnn { kernel } { misplaced-equals-sign }
   { Misplaced~equals~sign~in~key-value~input~\msg_line_number: }
   {
     LaTeX~is~attempting~to~parse~some~key-value~input~but~found~
@@ -1032,36 +937,40 @@
 %    \end{macrocode}
 %
 % \subsection{Constants and variables}
+% 
+%    \begin{macrocode}
+%<@@=keys>
+%    \end{macrocode}
 %
-% \begin{variable}{\c_keys_code_root_tl, \c_keys_vars_root_tl}
+% \begin{variable}{\c_@@_code_root_tl, \c_@@_vars_root_tl}
 %   The prefixes for the code and variables of the keys themselves.
 %    \begin{macrocode}
-\tl_const:Nn \c_keys_code_root_tl { key~code~>~ }
-\tl_const:Nn \c_keys_vars_root_tl { key~var~>~ }
+\tl_const:Nn \c_@@_code_root_tl { key~code~>~ }
+\tl_const:Nn \c_@@_vars_root_tl { key~var~>~ }
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\c_keys_props_root_tl}
+% \begin{variable}{\c_@@_props_root_tl}
 %   The prefix for storing properties.
 %    \begin{macrocode}
-\tl_const:Nn \c_keys_props_root_tl { key~prop~>~ }
+\tl_const:Nn \c_@@_props_root_tl { key~prop~>~ }
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\c_keys_value_forbidden_tl, \c_keys_value_required_tl}
+% \begin{variable}{\c_@@_value_forbidden_tl, \c_@@_value_required_tl}
 %   Two marker token lists.
 %    \begin{macrocode}
-\tl_const:Nn \c_keys_value_forbidden_tl { forbidden }
-\tl_const:Nn \c_keys_value_required_tl  { required }
+\tl_const:Nn \c_@@_value_forbidden_tl { forbidden }
+\tl_const:Nn \c_@@_value_required_tl  { required }
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_keys_choice_int, \l_keys_choices_tl}
+% \begin{variable}{\l_keys_choice_int, \l_keys_choice_tl}
 %   Publicly accessible data on which choice is being used when several
 %   are generated as a set.
 %    \begin{macrocode}
 \int_new:N \l_keys_choice_int
-\tl_new:N \l_keys_choices_tl
+\tl_new:N \l_keys_choice_tl
 %    \end{macrocode}
 % \end{variable}
 %
@@ -1072,18 +981,18 @@
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_keys_module_tl}
+% \begin{variable}{\l_@@_module_tl}
 %   The module for an entire set of keys.
 %    \begin{macrocode}
-\tl_new:N \l_keys_module_tl
+\tl_new:N \l_@@_module_tl
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_keys_no_value_bool}
+% \begin{variable}{\l_@@_no_value_bool}
 %   A marker is needed internally to show if only a key or a key plus a
 %   value was seen: this is recorded here.
 %    \begin{macrocode}
-\bool_new:N \l_keys_no_value_bool
+\bool_new:N \l_@@_no_value_bool
 %    \end{macrocode}
 % \end{variable}
 %
@@ -1095,18 +1004,18 @@
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_keys_property_tl}
+% \begin{variable}{\l_@@_property_tl}
 %   The \enquote{property} begin set for a key at definition time is
 %   stored here.
 %    \begin{macrocode}
-\tl_new:N \l_keys_property_tl
+\tl_new:N \l_@@_property_tl
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_keys_unknown_clist}
+% \begin{variable}{\l_@@_unknown_clist}
 %   Used when setting only known keys to store those left over.
 %    \begin{macrocode}
-\tl_new:N \l_keys_unknown_clist
+\tl_new:N \l_@@_unknown_clist
 %    \end{macrocode}
 % \end{variable}
 %
@@ -1120,51 +1029,51 @@
 % \subsection{The key defining mechanism}
 %
 % \begin{macro}{\keys_define:nn}
-% \begin{macro}[aux]{\keys_define_aux:nnn, \keys_define_aux:onn}
+% \begin{macro}[aux]{\@@_define:nnn, \@@_define:onn}
 %   The public function for definitions is just a wrapper for the lower
 %   level mechanism, more or less. The outer function is designed to
 %   keep a track of the current module, to allow safe nesting. The module is set
 %   removing any leading |/| (which is not needed here).
 %    \begin{macrocode}
 \cs_new_protected:Npn \keys_define:nn
-  { \keys_define_aux:onn \l_keys_module_tl }
-\cs_new_protected:Npn \keys_define_aux:nnn #1#2#3
+  { \@@_define:onn \l_@@_module_tl }
+\cs_new_protected:Npn \@@_define:nnn #1#2#3
   {
-    \tl_set:Nx \l_keys_module_tl { \tl_to_str:n {#2} }
-    \keyval_parse:NNn \keys_define_elt:n \keys_define_elt:nn {#3}
-    \tl_set:Nn \l_keys_module_tl {#1}
+    \tl_set:Nx \l_@@_module_tl { \tl_to_str:n {#2} }
+    \keyval_parse:NNn \@@_define_elt:n \@@_define_elt:nn {#3}
+    \tl_set:Nn \l_@@_module_tl {#1}
   }
-\cs_generate_variant:Nn \keys_define_aux:nnn { o }
+\cs_generate_variant:Nn \@@_define:nnn { o }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_define_elt:n}
-% \begin{macro}[int]{\keys_define_elt:nn}
-% \begin{macro}[aux]{\keys_define_elt_aux:nn}
+% \begin{macro}[int]{\@@_define_elt:n}
+% \begin{macro}[int]{\@@_define_elt:nn}
+% \begin{macro}[aux]{\@@_define_elt_aux:nn}
 %   The outer functions here record whether a value was given and then
 %   converge on a common internal mechanism. There is first a search for
 %   a property in the current key name, then a check to make sure it is
 %   known before the code hands off to the next step.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_define_elt:n #1
+\cs_new_protected:Npn \@@_define_elt:n #1
   {
-    \bool_set_true:N \l_keys_no_value_bool
-    \keys_define_elt_aux:nn {#1} { }
+    \bool_set_true:N \l_@@_no_value_bool
+    \@@_define_elt_aux:nn {#1} { }
   }
-\cs_new_protected:Npn \keys_define_elt:nn #1#2
+\cs_new_protected:Npn \@@_define_elt:nn #1#2
   {
-    \bool_set_false:N \l_keys_no_value_bool
-    \keys_define_elt_aux:nn {#1} {#2}
+    \bool_set_false:N \l_@@_no_value_bool
+    \@@_define_elt_aux:nn {#1} {#2}
   }
-\cs_new_protected:Npn \keys_define_elt_aux:nn #1#2
+\cs_new_protected:Npn \@@_define_elt_aux:nn #1#2
   {
-    \keys_property_find:n {#1}
-    \cs_if_exist:cTF { \c_keys_props_root_tl \l_keys_property_tl }
-      { \keys_define_key:n {#2} }
+    \@@_property_find:n {#1}
+    \cs_if_exist:cTF { \c_@@_props_root_tl \l_@@_property_tl }
+      { \@@_define_key:n {#2} }
       {
-        \msg_kernel_error:nnxx { keys } { property-unknown }
-          { \l_keys_property_tl } { \l_keys_path_tl }
+        \__msg_kernel_error:nnxx { kernel } { property-unknown }
+          { \l_@@_property_tl } { \l_keys_path_tl }
       }
   }
 %    \end{macrocode}
@@ -1172,57 +1081,57 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_property_find:n}
-% \begin{macro}[aux]{\keys_property_find_aux:w}
+% \begin{macro}[int]{\@@_property_find:n}
+% \begin{macro}[aux]{\@@_property_find:w}
 %   Searching for a property means finding the last |.| in the input,
 %   and storing the text before and after it. Everything is turned into
 %   strings, so there is no problem using an \texttt{x}-type expansion.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_property_find:n #1
+\cs_new_protected:Npn \@@_property_find:n #1
   {
-    \tl_set:Nx \l_keys_path_tl { \l_keys_module_tl / }
+    \tl_set:Nx \l_keys_path_tl { \l_@@_module_tl / }
     \tl_if_in:nnTF {#1} { . }
-      { \keys_property_find_aux:w #1 \q_stop }
-      { \msg_kernel_error:nnx { keys } { key-no-property } {#1} }
+      { \@@_property_find:w #1 \q_stop }
+      { \__msg_kernel_error:nnx { kernel } { key-no-property } {#1} }
   }
-\cs_new_protected:Npn \keys_property_find_aux:w #1 . #2 \q_stop
+\cs_new_protected:Npn \@@_property_find:w #1 . #2 \q_stop
   {
     \tl_set:Nx \l_keys_path_tl { \l_keys_path_tl \tl_to_str:n {#1} }
     \tl_if_in:nnTF {#2} { . }
       {
         \tl_set:Nx \l_keys_path_tl { \l_keys_path_tl . }
-        \keys_property_find_aux:w #2 \q_stop
+        \@@_property_find:w #2 \q_stop
       }
-      { \tl_set:Nn \l_keys_property_tl { . #2 } }
+      { \tl_set:Nn \l_@@_property_tl { . #2 } }
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_define_key:n}
-% \begin{macro}[aux]{\keys_define_key_aux:w}
+% \begin{macro}[int]{\@@_define_key:n}
+% \begin{macro}[aux]{\@@_define_key:w}
 %   Two possible cases. If there is a value for the key, then just use
 %   the function. If not, then a check to make sure there is no need for
 %   a value with the property. If there should be one then complain,
 %   otherwise execute it. There is no need to check for a |:| as if it
 %   is missing the earlier tests will have failed.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_define_key:n #1
+\cs_new_protected:Npn \@@_define_key:n #1
   {
-    \bool_if:NTF \l_keys_no_value_bool
+    \bool_if:NTF \l_@@_no_value_bool
       {
-        \exp_after:wN \keys_define_key_aux:w
-          \l_keys_property_tl \q_stop
-          { \use:c { \c_keys_props_root_tl \l_keys_property_tl } }
+        \exp_after:wN \@@_define_key:w
+          \l_@@_property_tl \q_stop
+          { \use:c { \c_@@_props_root_tl \l_@@_property_tl } }
           {
-            \msg_kernel_error:nnxx { keys }
-              { property-requires-value } { \l_keys_property_tl }
+            \__msg_kernel_error:nnxx { kernel }
+              { property-requires-value } { \l_@@_property_tl }
               { \l_keys_path_tl }
             }
       }
-      { \use:c { \c_keys_props_root_tl \l_keys_property_tl } {#1} }
+      { \use:c { \c_@@_props_root_tl \l_@@_property_tl } {#1} }
   }
-\cs_new_protected:Npn \keys_define_key_aux:w #1 : #2 \q_stop
+\cs_new_protected:Npn \@@_define_key:w #1 : #2 \q_stop
   { \tl_if_empty:nTF {#2} }
 %    \end{macrocode}
 % \end{macro}
@@ -1230,226 +1139,246 @@
 %
 % \subsection{Turning properties into actions}
 %
-% \begin{macro}[int]{\keys_bool_set:NN}
+% \begin{macro}[int]{\@@_bool_set:NN}
 %   Boolean keys are really just choices, but all done by hand. The
 %   second argument here is the scope: either empty or \texttt{g} for
 %   global.
 %    \begin{macrocode}
-\cs_new:Npn \keys_bool_set:NN #1#2
+\cs_new:Npn \@@_bool_set:NN #1#2
   {
     \bool_if_exist:NF #1 { \bool_new:N #1 }
-    \keys_choice_make:
-    \keys_cmd_set:nx { \l_keys_path_tl / true }
+    \@@_choice_make:
+    \@@_cmd_set:nx { \l_keys_path_tl / true }
       { \exp_not:c { bool_ #2 set_true:N } \exp_not:N #1 }
-    \keys_cmd_set:nx { \l_keys_path_tl / false }
+    \@@_cmd_set:nx { \l_keys_path_tl / false }
       { \exp_not:c { bool_ #2 set_false:N } \exp_not:N #1 }
-    \keys_cmd_set:nn { \l_keys_path_tl / unknown }
+    \@@_cmd_set:nn { \l_keys_path_tl / unknown }
       {
-        \msg_kernel_error:nnx { keys } { boolean-values-only }
+        \__msg_kernel_error:nnx { kernel } { boolean-values-only }
           { \l_keys_key_tl }
       }
-    \keys_default_set:n { true }
+    \@@_default_set:n { true }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_bool_set_inverse:NN}
+% \begin{macro}[int]{\@@_bool_set_inverse:NN}
 %   Inverse boolean setting is much the same.
 %    \begin{macrocode}
-\cs_new:Npn \keys_bool_set_inverse:NN #1#2
+\cs_new:Npn \@@_bool_set_inverse:NN #1#2
   {
     \bool_if_exist:NF #1 { \bool_new:N #1 }
-    \keys_choice_make:
-    \keys_cmd_set:nx { \l_keys_path_tl / true }
+    \@@_choice_make:
+    \@@_cmd_set:nx { \l_keys_path_tl / true }
       { \exp_not:c { bool_ #2 set_false:N } \exp_not:N #1 }
-    \keys_cmd_set:nx { \l_keys_path_tl / false }
+    \@@_cmd_set:nx { \l_keys_path_tl / false }
       { \exp_not:c { bool_ #2 set_true:N } \exp_not:N #1 }
-    \keys_cmd_set:nn { \l_keys_path_tl / unknown }
+    \@@_cmd_set:nn { \l_keys_path_tl / unknown }
       {
-        \msg_kernel_error:nnx { keys } { boolean-values-only }
+        \__msg_kernel_error:nnx { kernel } { boolean-values-only }
           { \l_keys_key_tl }
       }
-    \keys_default_set:n { true }
+    \@@_default_set:n { true }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_choice_make:}
+% \begin{macro}[int]{\@@_choice_make:}
 %   To make a choice from a key, two steps: set the code, and set the
 %   unknown key.
 %    \begin{macrocode}
-\cs_new_protected_nopar:Npn \keys_choice_make:
+\cs_new_protected_nopar:Npn \@@_choice_make:
   {
-    \keys_cmd_set:nn { \l_keys_path_tl }
-      { \keys_choice_find:n {##1} }
-    \keys_cmd_set:nn { \l_keys_path_tl / unknown }
+    \@@_cmd_set:nn { \l_keys_path_tl }
+      { \@@_choice_find:n {##1} }
+    \@@_cmd_set:nn { \l_keys_path_tl / unknown }
       {
-        \msg_kernel_error:nnxx { keys } { choice-unknown }
+        \__msg_kernel_error:nnxx { kernel } { key-choice-unknown }
           { \l_keys_path_tl } {##1}
       }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_choices_make:nn}
+% \begin{macro}[int]{\@@_choices_make:nn}
 %   Auto-generating choices means setting up the root key as a choice, then
 %   defining each choice in turn.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_choices_make:nn #1#2
+\cs_new_protected:Npn \@@_choices_make:nn #1#2
   {
-    \keys_choice_make:
+    \@@_choice_make:
     \int_zero:N \l_keys_choice_int
     \clist_map_inline:nn {#1}
       {
-        \keys_cmd_set:nx { \l_keys_path_tl / ##1 }
+        \int_incr:N \l_keys_choice_int
+        \@@_cmd_set:nx { \l_keys_path_tl / ##1 }
           {
             \tl_set:Nn \exp_not:N \l_keys_choice_tl {##1}
             \int_set:Nn \exp_not:N \l_keys_choice_int
               { \int_use:N \l_keys_choice_int }
             \exp_not:n {#2}
           }
-        \int_incr:N \l_keys_choice_int
       }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_choices_generate:n}
-% \begin{macro}[aux]{\keys_choices_generate_aux:n}
+% \begin{macro}[int]{\@@_choices_generate:n}
+% \begin{macro}[aux]{\@@_choices_generate_aux:n}
 %   Creating multiple-choices means setting up the \enquote{indicator}
 %   code, then applying whatever the user wanted.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_choices_generate:n #1
+\cs_new_protected:Npn \@@_choices_generate:n #1
   {
     \cs_if_exist:cTF
-      { \c_keys_vars_root_tl \l_keys_path_tl .choice~code }
+      { \c_@@_vars_root_tl \l_keys_path_tl .choice~code }
       {
-        \keys_choice_make:
+        \@@_choice_make:
         \int_zero:N \l_keys_choice_int
-        \clist_map_function:nN {#1} \keys_choices_generate_aux:n
+        \clist_map_function:nN {#1} \@@_choices_generate_aux:n
       }
       {
-        \msg_kernel_error:nnx { keys }
+        \__msg_kernel_error:nnx { kernel }
           { generate-choices-before-code } { \l_keys_path_tl }
       }
   }
-\cs_new_protected:Npn \keys_choices_generate_aux:n #1
+\cs_new_protected:Npn \@@_choices_generate_aux:n #1
   {
-    \keys_cmd_set:nx { \l_keys_path_tl / #1 }
+    \int_incr:N \l_keys_choice_int
+    \@@_cmd_set:nx { \l_keys_path_tl / #1 }
       {
         \tl_set:Nn \exp_not:N \l_keys_choice_tl {#1}
         \int_set:Nn \exp_not:N \l_keys_choice_int
           { \int_use:N \l_keys_choice_int }
         \exp_not:v
-          { \c_keys_vars_root_tl \l_keys_path_tl .choice~code }
+          { \c_@@_vars_root_tl \l_keys_path_tl .choice~code }
       }
-    \int_incr:N \l_keys_choice_int
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_choice_code_store:x}
+% \begin{macro}[int]{\@@_choice_code_store:n, \@@_choice_code_store:x}
 %   The code for making multiple choices is stored in a token list.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_choice_code_store:x #1
+\cs_new_protected:Npn \@@_choice_code_store:n #1
   {
     \cs_if_exist:cF
-      { \c_keys_vars_root_tl \l_keys_path_tl .choice~code }
+      { \c_@@_vars_root_tl \l_keys_path_tl .choice~code }
       {
         \tl_new:c
-          { \c_keys_vars_root_tl \l_keys_path_tl .choice~code }
+          { \c_@@_vars_root_tl \l_keys_path_tl .choice~code }
       }
-    \tl_set:cx { \c_keys_vars_root_tl \l_keys_path_tl .choice~code }
+    \tl_set:cn { \c_@@_vars_root_tl \l_keys_path_tl .choice~code }
       {#1}
   }
+\cs_generate_variant:Nn \@@_choice_code_store:n { x }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_cmd_set:nn, \keys_cmd_set:nx}
-% \begin{macro}[aux]{\keys_cmd_set_aux:n}
+% \begin{macro}[int]{\@@_cmd_set:nn, \@@_cmd_set:nx, \@@_cmd_set:Vo}
+% \begin{macro}[aux]{\@@_cmd_set:n}
 %   Creating a new command means tidying up the properties and then making
 %   the internal function which actually does the work.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_cmd_set:nn #1#2
+\cs_new_protected:Npn \@@_cmd_set:nn #1#2
   {
-    \keys_cmd_set_aux:n {#1}
-    \cs_set:cpn { \c_keys_code_root_tl #1 } ##1 {#2}
+    \@@_cmd_set:n {#1}
+    \cs_set:cpn { \c_@@_code_root_tl #1 } ##1 {#2}
   }
-\cs_new_protected:Npn \keys_cmd_set:nx #1#2
+\cs_new_protected:Npn \@@_cmd_set:nx #1#2
   {
-    \keys_cmd_set_aux:n {#1}
-    \cs_set:cpx { \c_keys_code_root_tl #1 } ##1 {#2}
+    \@@_cmd_set:n {#1}
+    \cs_set:cpx { \c_@@_code_root_tl #1 } ##1 {#2}
   }
-\cs_new_protected:Npn \keys_cmd_set_aux:n #1
+\cs_generate_variant:Nn \@@_cmd_set:nn { Vo }
+\cs_new_protected:Npn \@@_cmd_set:n #1
   {
-    \tl_clear_new:c { \c_keys_vars_root_tl #1 .default }
-    \tl_set:cn { \c_keys_vars_root_tl #1 .default } { \q_no_value }
-    \tl_clear_new:c { \c_keys_vars_root_tl #1 .req }
+    \tl_clear_new:c { \c_@@_vars_root_tl #1 .default }
+    \tl_set:cn { \c_@@_vars_root_tl #1 .default } { \q_no_value }
+    \tl_clear_new:c { \c_@@_vars_root_tl #1 .req }
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_default_set:n, \keys_default_set:V}
+% \begin{macro}[int]{\@@_default_set:n, \@@_default_set:V}
 %   Setting a default value is easy.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_default_set:n #1
-  { \tl_set:cn { \c_keys_vars_root_tl \l_keys_path_tl .default } {#1} }
-\cs_generate_variant:Nn \keys_default_set:n { V }
+\cs_new_protected:Npn \@@_default_set:n #1
+  { \tl_set:cn { \c_@@_vars_root_tl \l_keys_path_tl .default } {#1} }
+\cs_generate_variant:Nn \@@_default_set:n { V }
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}[aux]{\@@_initialise:n, \@@_initialise:V}
+% \begin{macro}[aux, EXP]{\@@_initialise:wn}
+%   A set up for initialisation from which the key system requires that
+%   the path is split up into a module and a key name. At this stage,
+%   \cs{l_keys_path_tl} will contain \texttt{/} so a split is easy to do.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_initialise:n #1
+  {
+    \use:x
+      { \exp_after:wN \@@_initialise:wn \l_keys_path_tl \q_stop {#1} }  
+  }
+\cs_generate_variant:Nn \@@_initialise:n { V }
+\cs_new:Npn \@@_initialise:wn #1 / #2 \q_stop #3
+  { \keys_set:nn {#1} { #2 = \exp_not:n { {#3} } } }
 %    \end{macrocode}
 % \end{macro}
+% \end{macro}
 %
-% \begin{macro}{\keys_meta_make:n, \keys_meta_make:x}
+% \begin{macro}{\@@_meta_make:n, \@@_meta_make:x}
 %   To create a meta-key, simply set up to pass data through.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_meta_make:n #1
+\cs_new_protected:Npn \@@_meta_make:n #1
   {
-    \exp_args:NNo \keys_cmd_set:nn \l_keys_path_tl
-      { \exp_after:wN \keys_set:nn \exp_after:wN { \l_keys_module_tl } {#1} }
+    \@@_cmd_set:Vo \l_keys_path_tl
+      { \exp_after:wN \keys_set:nn \exp_after:wN { \l_@@_module_tl } {#1} }
   }
-\cs_new_protected:Npn \keys_meta_make:x #1
+\cs_new_protected:Npn \@@_meta_make:x #1
   {
-    \keys_cmd_set:nx { \l_keys_path_tl }
-      { \exp_not:N \keys_set:nn { \l_keys_module_tl } {#1} }
+    \@@_cmd_set:nx { \l_keys_path_tl }
+      { \exp_not:N \keys_set:nn { \l_@@_module_tl } {#1} }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_multichoice_find:n}
-% \begin{macro}[int]{\keys_multichoice_make:}
-% \begin{macro}[int]{\keys_multichoices_make:nn}
+% \begin{macro}[int]{\@@_multichoice_find:n}
+% \begin{macro}[int]{\@@_multichoice_make:}
+% \begin{macro}[int]{\@@_multichoices_make:nn}
 %   Choices where several values can be selected are very similar to normal
 %   exclusive choices. There is just a slight change in implementation to
 %   map across a comma-separated list. This then requires that the appropriate
 %   set up takes place elsewhere.
 %    \begin{macrocode}
-\cs_new:Npn \keys_multichoice_find:n #1
-  { \clist_map_function:nN {#1} \keys_choice_find:n }
-\cs_new_protected_nopar:Npn \keys_multichoice_make:
+\cs_new:Npn \@@_multichoice_find:n #1
+  { \clist_map_function:nN {#1} \@@_choice_find:n }
+\cs_new_protected_nopar:Npn \@@_multichoice_make:
   {
-    \keys_cmd_set:nn { \l_keys_path_tl }
-      { \keys_multichoice_find:n {##1} }
-    \keys_cmd_set:nn { \l_keys_path_tl / unknown }
+    \@@_cmd_set:nn { \l_keys_path_tl }
+      { \@@_multichoice_find:n {##1} }
+    \@@_cmd_set:nn { \l_keys_path_tl / unknown }
       {
-        \msg_kernel_error:nnxx { keys } { choice-unknown }
+        \__msg_kernel_error:nnxx { kernel } { key-choice-unknown }
           { \l_keys_path_tl } {##1}
       }
   }
-\cs_new_protected:Npn \keys_multichoices_make:nn #1#2
+\cs_new_protected:Npn \@@_multichoices_make:nn #1#2
   {
-    \keys_multichoice_make:
+    \@@_multichoice_make:
     \int_zero:N \l_keys_choice_int
     \clist_map_inline:nn {#1}
       {
-        \keys_cmd_set:nx { \l_keys_path_tl / ##1 }
+        \int_incr:N \l_keys_choice_int
+        \@@_cmd_set:nx { \l_keys_path_tl / ##1 }
           {
             \tl_set:Nn \exp_not:N \l_keys_choice_tl {##1}
             \int_set:Nn \exp_not:N \l_keys_choice_int
               { \int_use:N \l_keys_choice_int }
             \exp_not:n {#2}
           }
-        \int_incr:N \l_keys_choice_int
       }
   }
 %    \end{macrocode}
@@ -1457,36 +1386,36 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_value_requirement:n}
+% \begin{macro}[int]{\@@_value_requirement:n}
 %   Values can be required or forbidden by having the appropriate marker
 %   set.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_value_requirement:n #1
+\cs_new_protected:Npn \@@_value_requirement:n #1
   {
     \tl_set_eq:cc
-      { \c_keys_vars_root_tl \l_keys_path_tl .req }
-      { c_keys_value_ #1 _tl }
+      { \c_@@_vars_root_tl \l_keys_path_tl .req }
+      { c_@@_value_ #1 _tl }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_variable_set:NnNN, \keys_variable_set:cnNN}
-% \begin{macro}[int]{\keys_variable_set:NnN, \keys_variable_set:cnN}
+% \begin{macro}[int]{\@@_variable_set:NnNN, \@@_variable_set:cnNN}
+% \begin{macro}[int]{\@@_variable_set:NnN, \@@_variable_set:cnN}
 %   Setting a variable takes the type and scope separately so that
 %   it is easy to make a new variable if needed. The three-argument
 %   version is set up so that the use of |{ }| as an \texttt{N}-type
 %   variable is only done once!
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_variable_set:NnNN #1#2#3#4
+\cs_new_protected:Npn \@@_variable_set:NnNN #1#2#3#4
   {
     \use:c { #2_if_exist:NF } #1 { \use:c { #2 _new:N } #1 }
-    \keys_cmd_set:nx { \l_keys_path_tl }
+    \@@_cmd_set:nx { \l_keys_path_tl }
       { \exp_not:c { #2 _ #3 set:N #4 } \exp_not:N #1 {##1} }
   }
-\cs_new_protected:Npn \keys_variable_set:NnN #1#2#3
-  { \keys_variable_set:NnNN #1 {#2} { } #3 }
-\cs_generate_variant:Nn \keys_variable_set:NnNN { c }
-\cs_generate_variant:Nn \keys_variable_set:NnN  { c }
+\cs_new_protected:Npn \@@_variable_set:NnN #1#2#3
+  { \@@_variable_set:NnNN #1 {#2} { } #3 }
+\cs_generate_variant:Nn \@@_variable_set:NnNN { c }
+\cs_generate_variant:Nn \@@_variable_set:NnN  { c }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1500,10 +1429,10 @@
 % \begin{macro}{.bool_gset:N}
 %   One function for this.
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .bool_set:N } #1
-  { \keys_bool_set:NN #1 { } }
-\cs_new_protected:cpn { \c_keys_props_root_tl .bool_gset:N } #1
-  { \keys_bool_set:NN #1 g }
+\cs_new_protected:cpn { \c_@@_props_root_tl .bool_set:N } #1
+  { \@@_bool_set:NN #1 { } }
+\cs_new_protected:cpn { \c_@@_props_root_tl .bool_gset:N } #1
+  { \@@_bool_set:NN #1 g }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1512,10 +1441,10 @@
 % \begin{macro}{.bool_gset_inverse:N}
 %   One function for this.
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .bool_set_inverse:N } #1
-  { \keys_bool_set_inverse:NN #1 { } }
-\cs_new_protected:cpn { \c_keys_props_root_tl .bool_gset_inverse:N } #1
-  { \keys_bool_set_inverse:NN #1 g }
+\cs_new_protected:cpn { \c_@@_props_root_tl .bool_set_inverse:N } #1
+  { \@@_bool_set_inverse:NN #1 { } }
+\cs_new_protected:cpn { \c_@@_props_root_tl .bool_gset_inverse:N } #1
+  { \@@_bool_set_inverse:NN #1 g }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1524,8 +1453,8 @@
 %   Making a choice is handled internally, as it is also needed by
 %  \texttt{.generate_choices:n}.
 %    \begin{macrocode}
-\cs_new_protected_nopar:cpn { \c_keys_props_root_tl .choice: }
-  { \keys_choice_make: }
+\cs_new_protected_nopar:cpn { \c_@@_props_root_tl .choice: }
+  { \@@_choice_make: }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1534,8 +1463,8 @@
 %   Here, |#1| will consist of two separate
 %   arguments, hence the slightly odd-looking implementation.
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .choices:nn } #1
-  { \keys_choices_make:nn #1 }
+\cs_new_protected:cpn { \c_@@_props_root_tl .choices:nn } #1
+  { \@@_choices_make:nn #1 }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1543,35 +1472,34 @@
 %   Creating code is simply a case of passing through to the underlying
 %   \texttt{set} function.
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .code:n } #1
-  { \keys_cmd_set:nn { \l_keys_path_tl } {#1} }
-\cs_new_protected:cpn { \c_keys_props_root_tl .code:x } #1
-  { \keys_cmd_set:nx { \l_keys_path_tl } {#1} }
+\cs_new_protected:cpn { \c_@@_props_root_tl .code:n } #1
+  { \@@_cmd_set:nn { \l_keys_path_tl } {#1} }
+\cs_new_protected:cpn { \c_@@_props_root_tl .code:x } #1
+  { \@@_cmd_set:nx { \l_keys_path_tl } {#1} }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}{.choice_code:n, .choice_code:x}
-%   Storing the code for choices, using \cs{exp_not:n} to avoid needing
-%   two internal functions.
+%   Storing the code for choices
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .choice_code:n } #1
-  { \keys_choice_code_store:x { \exp_not:n {#1} } }
-\cs_new_protected:cpn { \c_keys_props_root_tl .choice_code:x } #1
-  { \keys_choice_code_store:x {#1} }
+\cs_new_protected:cpn { \c_@@_props_root_tl .choice_code:n } #1
+  { \@@_choice_code_store:n {#1} }
+\cs_new_protected:cpn { \c_@@_props_root_tl .choice_code:x } #1
+  { \@@_choice_code_store:x {#1} }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}{.clist_set:N, .clist_set:c}
 % \begin{macro}{.clist_gset:N, .clist_gset:c}
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .clist_set:N } #1
-  { \keys_variable_set:NnN #1 { clist } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .clist_set:c } #1
-  { \keys_variable_set:cnN {#1} { clist } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .clist_gset:N } #1
-  { \keys_variable_set:NnNN #1 { clist } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .clist_gset:c } #1
-  { \keys_variable_set:cnNN {#1} { clist } g n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .clist_set:N } #1
+  { \@@_variable_set:NnN #1 { clist } n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .clist_set:c } #1
+  { \@@_variable_set:cnN {#1} { clist } n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .clist_gset:N } #1
+  { \@@_variable_set:NnNN #1 { clist } g n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .clist_gset:c } #1
+  { \@@_variable_set:cnNN {#1} { clist } g n }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1579,10 +1507,10 @@
 % \begin{macro}{.default:n, .default:V}
 %   Expansion is left to the internal functions.
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .default:n } #1
-  { \keys_default_set:n {#1} }
-\cs_new_protected:cpn { \c_keys_props_root_tl .default:V } #1
-  { \keys_default_set:V #1 }
+\cs_new_protected:cpn { \c_@@_props_root_tl .default:n } #1
+  { \@@_default_set:n {#1} }
+\cs_new_protected:cpn { \c_@@_props_root_tl .default:V } #1
+  { \@@_default_set:V #1 }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1590,14 +1518,14 @@
 % \begin{macro}{.dim_gset:N, .dim_gset:c}
 % Setting a variable is very easy: just pass the data along.
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .dim_set:N } #1
-  { \keys_variable_set:NnN #1 { dim } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .dim_set:c } #1
-  { \keys_variable_set:cnN {#1} { dim } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .dim_gset:N } #1
-  { \keys_variable_set:NnNN #1 { dim } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .dim_gset:c } #1
-  { \keys_variable_set:cnNN {#1} { dim } g n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .dim_set:N } #1
+  { \@@_variable_set:NnN #1 { dim } n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .dim_set:c } #1
+  { \@@_variable_set:cnN {#1} { dim } n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .dim_gset:N } #1
+  { \@@_variable_set:NnNN #1 { dim } g n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .dim_gset:c } #1
+  { \@@_variable_set:cnNN {#1} { dim } g n }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1606,14 +1534,14 @@
 % \begin{macro}{.fp_gset:N, .fp_gset:c}
 %   Setting a variable is very easy: just pass the data along.
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .fp_set:N } #1
-  { \keys_variable_set:NnN #1 { fp } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .fp_set:c } #1
-  { \keys_variable_set:cnN {#1} { fp } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .fp_gset:N } #1
-  { \keys_variable_set:NnNN #1 { fp } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .fp_gset:c } #1
-  { \keys_variable_set:cnNN {#1} { fp } g n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .fp_set:N } #1
+  { \@@_variable_set:NnN #1 { fp } n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .fp_set:c } #1
+  { \@@_variable_set:cnN {#1} { fp } n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .fp_gset:N } #1
+  { \@@_variable_set:NnNN #1 { fp } g n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .fp_gset:c } #1
+  { \@@_variable_set:cnNN {#1} { fp } g n }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1621,8 +1549,18 @@
 % \begin{macro}{.generate_choices:n}
 %   Making choices is easy.
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .generate_choices:n } #1
-  { \keys_choices_generate:n {#1} }
+\cs_new_protected:cpn { \c_@@_props_root_tl .generate_choices:n } #1
+  { \@@_choices_generate:n {#1} }
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{.initial:n, .initial:V}
+%   The standard hand-off approach.
+%    \begin{macrocode}
+\cs_new_protected:cpn { \c_@@_props_root_tl .initial:n } #1
+  { \@@_initialise:n {#1} }
+\cs_new_protected:cpn { \c_@@_props_root_tl .initial:V } #1
+  { \@@_initialise:V #1 }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1630,14 +1568,14 @@
 % \begin{macro}{.int_gset:N, .int_gset:c}
 %   Setting a variable is very easy: just pass the data along.
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .int_set:N } #1
-  { \keys_variable_set:NnN #1 { int } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .int_set:c } #1
-  { \keys_variable_set:cnN {#1} { int } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .int_gset:N } #1
-  { \keys_variable_set:NnNN #1 { int } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .int_gset:c } #1
-  { \keys_variable_set:cnNN {#1} { int } g n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .int_set:N } #1
+  { \@@_variable_set:NnN #1 { int } n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .int_set:c } #1
+  { \@@_variable_set:cnN {#1} { int } n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .int_gset:N } #1
+  { \@@_variable_set:NnNN #1 { int } g n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .int_gset:c } #1
+  { \@@_variable_set:cnNN {#1} { int } g n }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1645,10 +1583,10 @@
 %\begin{macro}{.meta:n, .meta:x}
 % Making a meta is handled internally.
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .meta:n } #1
-  { \keys_meta_make:n {#1} }
-\cs_new_protected:cpn { \c_keys_props_root_tl .meta:x } #1
-  { \keys_meta_make:x {#1} }
+\cs_new_protected:cpn { \c_@@_props_root_tl .meta:n } #1
+  { \@@_meta_make:n {#1} }
+\cs_new_protected:cpn { \c_@@_props_root_tl .meta:x } #1
+  { \@@_meta_make:x {#1} }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1657,10 +1595,10 @@
 %   The same idea as \texttt{.choice:} and \texttt{.choices:nn}, but
 %   where more than one choice is allowed.
 %    \begin{macrocode}
-\cs_new_protected_nopar:cpn { \c_keys_props_root_tl .multichoice: }
-  { \keys_multichoice_make: }
-\cs_new_protected:cpn { \c_keys_props_root_tl .multichoices:nn } #1
-  { \keys_multichoices_make:nn #1 }
+\cs_new_protected_nopar:cpn { \c_@@_props_root_tl .multichoice: }
+  { \@@_multichoice_make: }
+\cs_new_protected:cpn { \c_@@_props_root_tl .multichoices:nn } #1
+  { \@@_multichoices_make:nn #1 }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1669,14 +1607,14 @@
 % \begin{macro}{.skip_gset:N, .skip_gset:c}
 %   Setting a variable is very easy: just pass the data along.
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .skip_set:N } #1
-  { \keys_variable_set:NnN #1 { skip } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .skip_set:c } #1
-  { \keys_variable_set:cnN {#1} { skip } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .skip_gset:N } #1
-  { \keys_variable_set:NnNN #1 { skip } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .skip_gset:c } #1
-  { \keys_variable_set:cnNN {#1} { skip } g n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .skip_set:N } #1
+  { \@@_variable_set:NnN #1 { skip } n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .skip_set:c } #1
+  { \@@_variable_set:cnN {#1} { skip } n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .skip_gset:N } #1
+  { \@@_variable_set:NnNN #1 { skip } g n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .skip_gset:c } #1
+  { \@@_variable_set:cnNN {#1} { skip } g n }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1688,22 +1626,22 @@
 % \begin{macro}{.tl_gset_x:N, .tl_gset_x:c}
 %   Setting a variable is very easy: just pass the data along.
 %    \begin{macrocode}
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_set:N } #1
-   { \keys_variable_set:NnN #1 { tl } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_set:c } #1
-  { \keys_variable_set:cnN {#1} { tl } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_set_x:N } #1
-  { \keys_variable_set:NnN #1 { tl } x }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_set_x:c } #1
-  { \keys_variable_set:cnN {#1} { tl } x }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_gset:N } #1
-  { \keys_variable_set:NnNN #1 { tl } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_gset:c } #1
-  { \keys_variable_set:cnNN {#1} { tl } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_gset_x:N } #1
-  { \keys_variable_set:NnNN #1 { tl } g x }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_gset_x:c } #1
-  { \keys_variable_set:cnNN {#1} { tl } g x }
+\cs_new_protected:cpn { \c_@@_props_root_tl .tl_set:N } #1
+   { \@@_variable_set:NnN #1 { tl } n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .tl_set:c } #1
+  { \@@_variable_set:cnN {#1} { tl } n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .tl_set_x:N } #1
+  { \@@_variable_set:NnN #1 { tl } x }
+\cs_new_protected:cpn { \c_@@_props_root_tl .tl_set_x:c } #1
+  { \@@_variable_set:cnN {#1} { tl } x }
+\cs_new_protected:cpn { \c_@@_props_root_tl .tl_gset:N } #1
+  { \@@_variable_set:NnNN #1 { tl } g n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .tl_gset:c } #1
+  { \@@_variable_set:cnNN {#1} { tl } g n }
+\cs_new_protected:cpn { \c_@@_props_root_tl .tl_gset_x:N } #1
+  { \@@_variable_set:NnNN #1 { tl } g x }
+\cs_new_protected:cpn { \c_@@_props_root_tl .tl_gset_x:c } #1
+  { \@@_variable_set:cnNN {#1} { tl } g x }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1714,10 +1652,10 @@
 % \begin{macro}{.value_required:}
 %   These are very similar, so both call the same function.
 %    \begin{macrocode}
-\cs_new_protected_nopar:cpn { \c_keys_props_root_tl .value_forbidden: }
-  { \keys_value_requirement:n { forbidden } }
-\cs_new_protected_nopar:cpn { \c_keys_props_root_tl .value_required: }
-  { \keys_value_requirement:n { required } }
+\cs_new_protected_nopar:cpn { \c_@@_props_root_tl .value_forbidden: }
+  { \@@_value_requirement:n { forbidden } }
+\cs_new_protected_nopar:cpn { \c_@@_props_root_tl .value_required: }
+  { \@@_value_requirement:n { required } }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1725,19 +1663,19 @@
 % \subsection{Setting keys}
 %
 % \begin{macro}{\keys_set:nn, \keys_set:nV, \keys_set:nv, \keys_set:no}
-% \begin{macro}[aux]{\keys_set_aux:nnn, \keys_set_aux:onn}
+% \begin{macro}[aux]{\@@_set:nnn, \@@_set:onn}
 %   A simple wrapper again.
 %    \begin{macrocode}
 \cs_new_protected:Npn \keys_set:nn
-  { \keys_set_aux:onn { \l_keys_module_tl } }
-\cs_new_protected:Npn \keys_set_aux:nnn #1#2#3
+  { \@@_set:onn { \l_@@_module_tl } }
+\cs_new_protected:Npn \@@_set:nnn #1#2#3
   {
-    \tl_set:Nx \l_keys_module_tl { \tl_to_str:n {#2} }
-    \keyval_parse:NNn \keys_set_elt:n \keys_set_elt:nn {#3}
-    \tl_set:Nn \l_keys_module_tl {#1}
+    \tl_set:Nx \l_@@_module_tl { \tl_to_str:n {#2} }
+    \keyval_parse:NNn \@@_set_elt:n \@@_set_elt:nn {#3}
+    \tl_set:Nn \l_@@_module_tl {#1}
   }
 \cs_generate_variant:Nn \keys_set:nn { nV , nv , no }
-\cs_generate_variant:Nn \keys_set_aux:nnn { o }
+\cs_generate_variant:Nn \@@_set:nnn { o }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1747,89 +1685,89 @@
 %     \keys_set_known:nnN, \keys_set_known:nVN,
 %     \keys_set_known:nvN, \keys_set_known:noN
 %   }
-% \begin{macro}[aux]{\keys_set_known_aux:nnnN, \keys_set_known_aux:onnN}
+% \begin{macro}[aux]{\@@_set_known:nnnN, \@@_set_known:onnN}
 %    \begin{macrocode}
 \cs_new_protected:Npn \keys_set_known:nnN
-  { \keys_set_known_aux:onnN { \l_keys_module_tl } }
-\cs_new_protected:Npn \keys_set_known_aux:nnnN #1#2#3#4
+  { \@@_set_known:onnN { \l_@@_module_tl } }
+\cs_new_protected:Npn \@@_set_known:nnnN #1#2#3#4
   {
-    \tl_set:Nx \l_keys_module_tl { \tl_to_str:n {#2} }
-    \clist_clear:N \l_keys_unknown_clist
-    \cs_set_eq:NN \keys_execute_unknown: \keys_execute_unknown_alt:
-    \keyval_parse:NNn \keys_set_elt:n \keys_set_elt:nn {#3}
-    \cs_set_eq:NN \keys_execute_unknown: \keys_execute_unknown_std:
-    \tl_set:Nn \l_keys_module_tl {#1}
-    \clist_set_eq:NN #4 \l_keys_unknown_clist
+    \tl_set:Nx \l_@@_module_tl { \tl_to_str:n {#2} }
+    \clist_clear:N \l_@@_unknown_clist
+    \cs_set_eq:NN \@@_execute_unknown: \@@_execute_unknown_alt:
+    \keyval_parse:NNn \@@_set_elt:n \@@_set_elt:nn {#3}
+    \cs_set_eq:NN \@@_execute_unknown: \@@_execute_unknown_std:
+    \tl_set:Nn \l_@@_module_tl {#1}
+    \clist_set_eq:NN #4 \l_@@_unknown_clist
   }
 \cs_generate_variant:Nn \keys_set_known:nnN { nV , nv , no }
-\cs_generate_variant:Nn \keys_set_known_aux:nnnN { o }
+\cs_generate_variant:Nn \@@_set_known:nnnN { o }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_set_elt:n, \keys_set_elt:nn}
-% \begin{macro}[aux]{\keys_set_elt_aux:nn}
+% \begin{macro}[int]{\@@_set_elt:n, \@@_set_elt:nn}
+% \begin{macro}[aux]{\@@_set_elt_aux:nn}
 %   A shared system once again. First, set the current path and add a
 %   default if needed. There are then checks to see if the a value is
 %   required or forbidden. If everything passes, move on to execute the
 %   code.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_set_elt:n #1
+\cs_new_protected:Npn \@@_set_elt:n #1
   {
-    \bool_set_true:N \l_keys_no_value_bool
-    \keys_set_elt_aux:nn {#1} { }
+    \bool_set_true:N \l_@@_no_value_bool
+    \@@_set_elt_aux:nn {#1} { }
   }
-\cs_new_protected:Npn \keys_set_elt:nn #1#2
+\cs_new_protected:Npn \@@_set_elt:nn #1#2
   {
-    \bool_set_false:N \l_keys_no_value_bool
-    \keys_set_elt_aux:nn {#1} {#2}
+    \bool_set_false:N \l_@@_no_value_bool
+    \@@_set_elt_aux:nn {#1} {#2}
   }
-\cs_new_protected:Npn \keys_set_elt_aux:nn #1#2
+\cs_new_protected:Npn \@@_set_elt_aux:nn #1#2
   {
     \tl_set:Nx \l_keys_key_tl { \tl_to_str:n {#1} }
-    \tl_set:Nx \l_keys_path_tl { \l_keys_module_tl / \l_keys_key_tl }
-    \keys_value_or_default:n {#2}
+    \tl_set:Nx \l_keys_path_tl { \l_@@_module_tl / \l_keys_key_tl }
+    \@@_value_or_default:n {#2}
     \bool_if:nTF
       {
-        \keys_if_value_p:n { required } &&
-        \l_keys_no_value_bool
+        \@@_if_value_p:n { required } &&
+        \l_@@_no_value_bool
       }
       {
-        \msg_kernel_error:nnx { keys } { value-required }
+        \__msg_kernel_error:nnx { kernel } { value-required }
           { \l_keys_path_tl }
       }
       {
         \bool_if:nTF
           {
-              \keys_if_value_p:n { forbidden } &&
-            ! \l_keys_no_value_bool
+              \@@_if_value_p:n { forbidden } &&
+            ! \l_@@_no_value_bool
           }
           {
-            \msg_kernel_error:nnxx { keys } { value-forbidden }
+            \__msg_kernel_error:nnxx { kernel } { value-forbidden }
               { \l_keys_path_tl } { \l_keys_value_tl }
           }
-          { \keys_execute: }
+          { \@@_execute: }
       }
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_value_or_default:n}
+% \begin{macro}[int]{\@@_value_or_default:n}
 %   If a value is given, return it as |#1|, otherwise send a default if
 %   available.
 %    \begin{macrocode}
-\cs_new_protected:Npn \keys_value_or_default:n #1
+\cs_new_protected:Npn \@@_value_or_default:n #1
   {
     \tl_set:Nn \l_keys_value_tl {#1}
-    \bool_if:NT \l_keys_no_value_bool
+    \bool_if:NT \l_@@_no_value_bool
       {
-        \quark_if_no_value:cF { \c_keys_vars_root_tl \l_keys_path_tl .default }
+        \quark_if_no_value:cF { \c_@@_vars_root_tl \l_keys_path_tl .default }
           {
-            \cs_if_exist:cT { \c_keys_vars_root_tl \l_keys_path_tl .default }
+            \cs_if_exist:cT { \c_@@_vars_root_tl \l_keys_path_tl .default }
               {
                 \tl_set_eq:Nc \l_keys_value_tl
-                  { \c_keys_vars_root_tl \l_keys_path_tl .default }
+                  { \c_@@_vars_root_tl \l_keys_path_tl .default }
               }
           }
       }
@@ -1837,57 +1775,57 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_if_value_p:n}
+% \begin{macro}[int]{\@@_if_value_p:n}
 %   To test if a value is required or forbidden. A simple check for
 %   the existence of the appropriate marker.
 %    \begin{macrocode}
-\prg_new_conditional:Npnn \keys_if_value:n #1 { p }
+\prg_new_conditional:Npnn \@@_if_value:n #1 { p }
   {
-    \tl_if_eq:ccTF { c_keys_value_ #1 _tl }
-      { \c_keys_vars_root_tl \l_keys_path_tl .req }
+    \tl_if_eq:ccTF { c_@@_value_ #1 _tl }
+      { \c_@@_vars_root_tl \l_keys_path_tl .req }
       { \prg_return_true: }
       { \prg_return_false: }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_execute:}
+% \begin{macro}[int]{\@@_execute:}
 % \begin{macro}[aux]
 %   {
-%     \keys_execute_unknown:,
-%     \keys_execute_unknown_std:,
-%     \keys_execute_unknown_alt:
+%     \@@_execute_unknown:,
+%     \@@_execute_unknown_std:,
+%     \@@_execute_unknown_alt:
 %   }
-% \begin{macro}[aux]{\keys_execute:nn}
+% \begin{macro}[aux]{\@@_execute:nn}
 %   Actually executing a key is done in two parts. First, look for the
 %   key itself, then look for the \texttt{unknown} key with the same
 %   path. If both of these fail, complain.
 %    \begin{macrocode}
-\cs_new_nopar:Npn \keys_execute:
-  { \keys_execute:nn { \l_keys_path_tl } { \keys_execute_unknown: } }
-\cs_new_nopar:Npn \keys_execute_unknown:
+\cs_new_nopar:Npn \@@_execute:
+  { \@@_execute:nn { \l_keys_path_tl } { \@@_execute_unknown: } }
+\cs_new_nopar:Npn \@@_execute_unknown:
   {
-    \keys_execute:nn { \l_keys_module_tl / unknown }
+    \@@_execute:nn { \l_@@_module_tl / unknown }
       {
-        \msg_kernel_error:nnxx { keys } { key-unknown }
-          { \l_keys_path_tl } { \l_keys_module_tl }
+        \__msg_kernel_error:nnxx { kernel } { key-unknown }
+          { \l_keys_path_tl } { \l_@@_module_tl }
       }
   }
-\cs_new_eq:NN \keys_execute_unknown_std: \keys_execute_unknown:
-\cs_new_nopar:Npn \keys_execute_unknown_alt:
+\cs_new_eq:NN \@@_execute_unknown_std: \@@_execute_unknown:
+\cs_new_nopar:Npn \@@_execute_unknown_alt:
   {
-    \clist_put_right:Nx \l_keys_unknown_clist
+    \clist_put_right:Nx \l_@@_unknown_clist
       {
         \exp_not:o \l_keys_key_tl
-        \bool_if:NF \l_keys_no_value_bool
+        \bool_if:NF \l_@@_no_value_bool
           { = { \exp_not:o \l_keys_value_tl } }
       }
   }
-\cs_new:Npn \keys_execute:nn #1#2
+\cs_new:Npn \@@_execute:nn #1#2
   {
-    \cs_if_exist:cTF { \c_keys_code_root_tl #1 }
+    \cs_if_exist:cTF { \c_@@_code_root_tl #1 }
       {
-        \exp_args:Nc \exp_args:No { \c_keys_code_root_tl #1 }
+        \exp_args:Nc \exp_args:No { \c_@@_code_root_tl #1 }
           \l_keys_value_tl
       }
       {#2}
@@ -1897,15 +1835,15 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int]{\keys_choice_find:n}
+% \begin{macro}[int]{\@@_choice_find:n}
 %   Executing a choice has two parts. First, try the choice given, then
 %   if that fails call the unknown key. That will exist, as it is created
 %   when a choice is first made. So there is no need for any escape code.
 %    \begin{macrocode}
-\cs_new:Npn \keys_choice_find:n #1
+\cs_new:Npn \@@_choice_find:n #1
   {
-    \keys_execute:nn { \l_keys_path_tl / \tl_to_str:n {#1} }
-      { \keys_execute:nn { \l_keys_path_tl / unknown } { } }
+    \@@_execute:nn { \l_keys_path_tl / \tl_to_str:n {#1} }
+      { \@@_execute:nn { \l_keys_path_tl / unknown } { } }
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1917,7 +1855,7 @@
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \keys_if_exist:nn #1#2 { p , T , F , TF }
   {
-    \cs_if_exist:cTF { \c_keys_code_root_tl #1 / #2 }
+    \cs_if_exist:cTF { \c_@@_code_root_tl #1 / #2 }
       { \prg_return_true: }
       { \prg_return_false: }
   }
@@ -1929,7 +1867,7 @@
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \keys_if_choice_exist:nnn #1#2#3 { p , T , F , TF }
   {
-    \cs_if_exist:cTF { \c_keys_code_root_tl #1 / #2 / #3 }
+    \cs_if_exist:cTF { \c_@@_code_root_tl #1 / #2 / #3 }
       { \prg_return_true: }
       { \prg_return_false: }
   }
@@ -1940,7 +1878,7 @@
 %   Showing a key is just a question of using the correct name.
 %    \begin{macrocode}
 \cs_new:Npn \keys_show:nn #1#2
-  { \cs_show:c { \c_keys_code_root_tl #1 / \tl_to_str:n {#2} } }
+  { \cs_show:c { \c_@@_code_root_tl #1 / \tl_to_str:n {#2} } }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1948,23 +1886,23 @@
 %
 % For when there is a need to complain.
 %    \begin{macrocode}
-\msg_kernel_new:nnnn { keys } { boolean-values-only }
+\__msg_kernel_new:nnnn { kernel } { boolean-values-only }
   { Key~'#1'~accepts~boolean~values~only. }
   { The~key~'#1'~only~accepts~the~values~'true'~and~'false'. }
-\msg_kernel_new:nnnn { keys } { choice-unknown }
+\__msg_kernel_new:nnnn { kernel } { choice-unknown }
   { Choice~'#2'~unknown~for~key~'#1'. }
   {
     The~key~'#1'~takes~a~limited~number~of~values.\\
     The~input~given,~'#2',~is~not~on~the~list~accepted.
   }
-\msg_kernel_new:nnnn { keys } { generate-choices-before-code }
+\__msg_kernel_new:nnnn { kernel } { generate-choices-before-code }
   { No~code~available~to~generate~choices~for~key~'#1'. }
   {
     \c_msg_coding_error_text_tl
     Before~using~.generate_choices:n~the~code~should~be~defined~
     with~'.choice_code:n'~or~'.choice_code:x'.
   }
-\msg_kernel_new:nnnn { keys } { key-no-property }
+\__msg_kernel_new:nnnn { kernel } { key-no-property }
   { No~property~given~in~definition~of~key~'#1'. }
   {
     \c_msg_coding_error_text_tl
@@ -1973,39 +1911,33 @@
     ~ ~ #1 .<property> \\
     LaTeX~did~not~find~a~'.'~to~indicate~the~start~of~a~property.
   }
-\msg_kernel_new:nnnn { keys } { key-unknown }
+\__msg_kernel_new:nnnn { kernel } { key-unknown }
   { The~key~'#1'~is~unknown~and~is~being~ignored. }
   {
     The~module~'#2'~does~not~have~a~key~called~#1'.\\
     Check~that~you~have~spelled~the~key~name~correctly.
   }
-\msg_kernel_new:nnnn { keys } { option-unknown }
-  { Unknown~option~'#1'~for~package~#2. }
-  {
-    LaTeX~has~been~asked~to~set~an~option~called~'#1'~
-    but~the~#2~package~has~not~created~an~option~with~this~name.
-  }
-\msg_kernel_new:nnnn { keys } { property-requires-value }
+\__msg_kernel_new:nnnn { kernel } { property-requires-value }
   { The~property~'#1'~requires~a~value. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~was~asked~to~set~property~'#2'~for~key~'#1'.\\
     No~value~was~given~for~the~property,~and~one~is~required.
   }
-\msg_kernel_new:nnnn { keys } { property-unknown }
+\__msg_kernel_new:nnnn { kernel } { property-unknown }
   { The~key~property~'#1'~is~unknown. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~has~been~asked~to~set~the~property~'#1'~for~key~'#2':~
     this~property~is~not~defined.
   }
-\msg_kernel_new:nnnn { keys } { value-forbidden }
+\__msg_kernel_new:nnnn { kernel } { value-forbidden }
   { The~key~'#1'~does~not~taken~a~value. }
   {
     The~key~'#1'~should~be~given~without~a~value.\\
     LaTeX~will~ignore~the~given~value~'#2'.
   }
-\msg_kernel_new:nnnn { keys } { value-required }
+\__msg_kernel_new:nnnn { kernel } { value-required }
   { The~key~'#1'~requires~a~value. }
   {
     The~key~'#1'~must~have~a~value.\\
@@ -2031,6 +1963,12 @@
 % \end{macro}
 % \end{macro}
 % \end{macro}
+% 
+% Internal material for removal by 2012-12-31.
+% 
+%    \begin{macrocode}
+\cs_new_eq:NN \c_keys_code_root_tl \c__keys_code_root_tl
+%    \end{macrocode}
 %
 %    \begin{macrocode}
 %</initex|package>
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3luatex.dtx b/Master/texmf-dist/source/latex/l3kernel/l3luatex.dtx
index 212c953b2aa..5fbaea8cbd6 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3luatex.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3luatex.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3luatex.dtx 3355 2012-02-09 07:18:22Z joseph $
+\GetIdInfo$Id: l3luatex.dtx 3986 2012-07-15 19:23:51Z joseph $
   {L3 Experimental LuaTeX-specific functions}
 %</driver|package>
 %<*driver>
@@ -158,7 +158,7 @@
 %     \cs{cctab_gset:Nn} \meta{category code table} \Arg{category code set up}
 %   \end{syntax}
 %   Sets the \meta{category code table} to apply the category codes
-%   which apply when the prevailing regime is modified by the
+%   which apply when the prevailing r{\'e}gime is modified by the
 %   \meta{category code set up}. Thus within a standard code block
 %   the starting point will be the code applied by \cs{c_code_cctab}.
 %   The assignment of the table is global: the underlying primitive does
@@ -226,27 +226,17 @@
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
-% An error message.
-%    \begin{macrocode}
-\msg_kernel_new:nnnn { luatex } { bad-engine }
-  { LuaTeX~engine~not~in~use!~Ignoring~#1. }
-  {
-    The~feature~you~are~using~is~only~available~
-    with~the~LuaTeX~engine.~LaTeX3~ignored~`#1#2'.
-  }
-%    \end{macrocode}
-%
 % \begin{macro}{\lua_now:n, \lua_now:x}
 % \begin{macro}{\lua_shipout_x:n, \lua_shipout_x:x}
 % \begin{macro}{\lua_shipout:n, \lua_shipout:x}
 %   When \LuaTeX{} is in use, this is all a question of primitives with new
 %   names. On the other hand, for \pdfTeX{} and \XeTeX{} the argument should
 %   be removed from the input stream before issuing an error. This is
-%   expandable, using \cs{msg_expandable_kernel_error:nnn}
+%   expandable, using \cs{__msg_kernel_expandable_error:nnn}
 %   as done for \texttt{V}-type expansion in \pkg{l3expan}.
 %    \begin{macrocode}
 \luatex_if_engine:TF
@@ -257,13 +247,13 @@
   {
     \cs_new:Npn \lua_now:x #1
       {
-        \msg_expandable_kernel_error:nnn
-          { luatex } { bad-engine } { \lua_now:x }
+        \__msg_kernel_expandable_error:nnn
+          { kernel } { bad-engine } { \lua_now:x }
       }
     \cs_new_protected:Npn \lua_shipout_x:n #1
       {
-        \msg_expandable_kernel_error:nnn
-          { luatex } { bad-engine } { \lua_shipout_x:n }
+        \__msg_kernel_expandable_error:nnn
+          { kernel } { bad-engine } { \lua_shipout_x:n }
       }
   }
 \cs_new:Npn \lua_now:n #1
@@ -279,17 +269,21 @@
 %
 % \subsection{Category code tables}
 %
-% \begin{variable}{\g_cctab_allocate_int}
-% \begin{variable}{\g_cctab_stack_int}
-% \begin{variable}{\g_cctab_stack_seq}
+%    \begin{macrocode}
+%<@@=cctab>
+%    \end{macrocode}
+%
+% \begin{variable}{\g_@@_allocate_int}
+% \begin{variable}{\g_@@_stack_int}
+% \begin{variable}{\g_@@_stack_seq}
 %   To allocate category code tables, both the read-only and stack
 %   tables need to be followed. There is also a sequence stack for the
 %   dynamic tables themselves.
 %    \begin{macrocode}
-\int_new:N  \g_cctab_allocate_int
-\int_set:Nn \g_cctab_allocate_int { \c_minus_one }
-\int_new:N \g_cctab_stack_int
-\seq_new:N \g_cctab_stack_seq
+\int_new:N  \g_@@_allocate_int
+\int_set:Nn \g_@@_allocate_int { \c_minus_one }
+\int_new:N \g_@@_stack_int
+\seq_new:N \g_@@_stack_seq
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
@@ -306,21 +300,21 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \cctab_new:N #1
   {
-    \chk_if_free_cs:N #1
-    \int_gadd:Nn \g_cctab_allocate_int { \c_two }
+    \__chk_if_free_cs:N #1
+    \int_gadd:Nn \g_@@_allocate_int { \c_two }
     \int_compare:nNnTF
-      \g_cctab_allocate_int <  { \c_max_register_int + \c_one }
+      \g_@@_allocate_int <  { \c_max_register_int + \c_one }
        {
-         \tex_global:D \tex_chardef:D #1 \g_cctab_allocate_int
+         \tex_global:D \tex_chardef:D #1 \g_@@_allocate_int
          \luatex_initcatcodetable:D #1
        }
-       { \msg_kernel_fatal:nnx { kernel } { out-of-registers } { cctab } }
+       { \__msg_kernel_fatal:nnx { kernel } { out-of-registers } { cctab } }
   }
 \luatex_if_engine:F
   {
     \cs_set_protected:Npn \cctab_new:N #1
       {
-        \msg_kernel_error:nnx { luatex } { bad-engine }
+        \__msg_kernel_error:nnx { kernel } { bad-engine }
           { \exp_not:N \cctab_new:N }
       }
   }
@@ -329,7 +323,7 @@
   {
     \cs_set_protected:Npn \cctab_new:N #1
       {
-        \chk_if_free_cs:N #1
+        \__chk_if_free_cs:N #1
         \newcatcodetable #1
         \luatex_initcatcodetable:D #1
       }
@@ -340,39 +334,39 @@
 %
 % \begin{macro}{\cctab_begin:N}
 % \begin{macro}{\cctab_end:}
-% \begin{variable}{\l_cctab_internal_tl}
+% \begin{variable}{\l_@@_internal_tl}
 %   The aim here is to ensure that the saved tables are read-only. This is
 %   done by using a stack of tables which are not read only, and actually
 %   having them as \enquote{in use} copies.
 %    \begin{macrocode}
 \cs_new_protected:Npn \cctab_begin:N #1
   {
-    \seq_gpush:Nx \g_cctab_stack_seq { \tex_the:D \luatex_catcodetable:D }
+    \seq_gpush:Nx \g_@@_stack_seq { \tex_the:D \luatex_catcodetable:D }
     \luatex_catcodetable:D #1
-    \int_gadd:Nn \g_cctab_stack_int { \c_two }
-    \int_compare:nNnT \g_cctab_stack_int > \c_max_register_int
-      { \msg_kernel_fatal:nn { code } { cctab-stack-full } }
-    \luatex_savecatcodetable:D \g_cctab_stack_int
-    \luatex_catcodetable:D \g_cctab_stack_int
+    \int_gadd:Nn \g_@@_stack_int { \c_two }
+    \int_compare:nNnT \g_@@_stack_int > \c_max_register_int
+      { \__msg_kernel_fatal:nn { kernel } { cctab-stack-full } }
+    \luatex_savecatcodetable:D \g_@@_stack_int
+    \luatex_catcodetable:D \g_@@_stack_int
   }
 \cs_new_protected_nopar:Npn \cctab_end:
   {
-    \int_gsub:Nn \g_cctab_stack_int { \c_two }
-    \seq_if_empty:NTF \g_cctab_stack_seq
-      { \tl_set:Nn \l_cctab_internal_tl { 0 } }
-      { \seq_gpop:NN \g_cctab_stack_seq \l_cctab_internal_tl }
-    \luatex_catcodetable:D \l_cctab_internal_tl \scan_stop:
+    \int_gsub:Nn \g_@@_stack_int { \c_two }
+    \seq_if_empty:NTF \g_@@_stack_seq
+      { \tl_set:Nn \l_@@_internal_tl { 0 } }
+      { \seq_gpop:NN \g_@@_stack_seq \l_@@_internal_tl }
+    \luatex_catcodetable:D \l_@@_internal_tl \scan_stop:
   }
 \luatex_if_engine:F
   {
     \cs_set_protected:Npn \cctab_begin:N #1
       {
-        \msg_kernel_error:nnxx { luatex } { bad-engine }
+        \__msg_kernel_error:nnxx { kernel } { bad-engine }
           { \exp_not:N \cctab_begin:N } {#1}
       }
     \cs_set_protected_nopar:Npn \cctab_end:
       {
-        \msg_kernel_error:nnx { luatex } { bad-engine }
+        \__msg_kernel_error:nnx { kernel } { bad-engine }
           { \exp_not:N \cctab_end: }
       }
   }
@@ -383,7 +377,7 @@
     \cs_set_protected_nopar:Npn \cctab_end: { \EndCatcodeRegime }
   }
 %</package>
-\tl_new:N \l_cctab_internal_tl
+\tl_new:N \l_@@_internal_tl
 %    \end{macrocode}
 % \end{variable}
 % \end{macro}
@@ -405,7 +399,7 @@
   {
     \cs_set_protected:Npn \cctab_gset:Nn #1#2
       {
-        \msg_kernel_error:nnxx { luatex } { bad-engine }
+        \__msg_kernel_error:nnxx { kernel } { bad-engine }
           { \exp_not:N \cctab_gset:Nn } { #1 {#2} }
       }
   }
@@ -454,12 +448,12 @@
       }
     \cctab_gset:Nn \c_other_cctab
       {
-        \prg_stepwise_inline:nnnn { 0 } { 1 } { 127 }
+        \int_step_inline:nnnn { 0 } { 1 } { 127 }
           { \char_set_catcode_other:n {#1} }
       }
     \cctab_gset:Nn \c_str_cctab
       {
-        \prg_stepwise_inline:nnnn { 0 } { 1 } { 127 }
+        \int_step_inline:nnnn { 0 } { 1 } { 127 }
           { \char_set_catcode_other:n {#1} }
         \char_set_catcode_space:n { 32 }
       }
@@ -471,6 +465,23 @@
 % \end{variable}
 % \end{variable}
 % \end{variable}
+% 
+% \subsection{Messages}
+% 
+%    \begin{macrocode}
+\__msg_kernel_new:nnnn { kernel } { bad-engine }
+  { LuaTeX~engine~not~in~use!~Ignoring~#1. }
+  {
+    The~feature~you~are~using~is~only~available~
+    with~the~LuaTeX~engine.~LaTeX3~ignored~`#1#2'.
+  }
+\__msg_kernel_new:nnnn { kernel } { cctab-stack-full }
+  { The~category~code~table~stack~is~exhausted. }
+  {
+    LaTeX~has~been~asked~to~switch~to~a~new~category~code~table,~
+    but~there~is~no~more~space~to~do~this!
+  }
+%    \end{macrocode}
 %
 % \subsection{Deprecated functions}
 %
@@ -478,7 +489,9 @@
 %
 % \begin{variable}{\c_string_cctab}
 %    \begin{macrocode}
+%<*deprecated>
 \cs_new_eq:NN \c_string_cctab \c_str_cctab
+%</deprecated>
 %    \end{macrocode}
 % \end{variable}
 %
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3msg.dtx b/Master/texmf-dist/source/latex/l3kernel/l3msg.dtx
index 89362b7e7d4..a545ab5e126 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3msg.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3msg.dtx
@@ -35,8 +35,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3msg.dtx 3568 2012-04-23 13:23:58Z joseph $
-  {L3 Experimental messages}
+\GetIdInfo$Id: l3msg.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Messages}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -91,12 +91,7 @@
 %
 % \section{Creating new messages}
 %
-% ^^A Wrong: "\msg_new:nnnn" is (as it should) global.
-% ^^A However, redirections are indeed local.
-% All messages have to be created before they can be used. All message
-% setting is local, with the general assumption that messages will
-% be managed as part of module set up outside of any \TeX{} grouping.
-%
+% All messages have to be created before they can be used.
 % The text of messages will automatically by wrapped to the length
 % available in the console. As a result, formatting is only needed
 % where it will help to show meaning. In particular, |\\| may be
@@ -124,9 +119,8 @@
 %   \meta{more text} if the user requests it. If no \meta{more text} is
 %   available then a standard text is given instead. Within \meta{text}
 %   and \meta{more text} four parameters (|#1| to |#4|) can be used:
-%   these will be supplied at the time the message is used. The
-%   parameters will be expanded when the message is used. An error will
-%   be raised if the \meta{message} already exists.
+%   these will be supplied at the time the message is
+%   used. An error will be raised if the \meta{message} already exists.
 % \end{function}
 %
 % \begin{function}{\msg_set:nnnn, \msg_set:nnn, \msg_gset:nnnn, \msg_gset:nnn}
@@ -138,11 +132,10 @@
 %   \meta{more text} if the user requests it. If no \meta{more text} is
 %   available then a standard text is given instead. Within \meta{text}
 %   and \meta{more text} four parameters (|#1| to |#4|) can be used:
-%   these will be supplied at the time the message is used. The
-%   parameters will be expanded when the message is used.
+%   these will be supplied at the time the message is used.
 % \end{function}
 %
-% \begin{function}[EXP,pTF, added=2012-03-03]{\msg_if_exist:nn}
+% \begin{function}[EXP, pTF, added = 2012-03-03]{\msg_if_exist:nn}
 %   \begin{syntax}
 %     \cs{msg_if_exist_p:nn} \Arg{module} \Arg{message}
 %     \cs{msg_if_exist:nnTF} \Arg{module} \Arg{message} \Arg{true code} \Arg{false code}
@@ -169,33 +162,15 @@
 %   Prints the current line number when a message is given.
 % \end{function}
 %
-% \begin{variable}{\c_msg_return_text_tl}
-%  Standard text to indicate that the user should try pressing
-%  \meta{return} to continue. The standard definition reads:
-%  \begin{verbatim}
-%    Try typing <return> to proceed.
-%
-%    If that doesn't work, type X <return> to quit.
-%  \end{verbatim}
-% \end{variable}
-%
-% \begin{variable}{\c_msg_trouble_text_tl}
-%  Standard text to indicate that the more errors are likely and
-%  that aborting the run is advised. The standard definition reads:
-%  \begin{verbatim}
-%    More errors will almost certainly follow:
-%    the LaTeX run should be aborted.
-%  \end{verbatim}
-% \end{variable}
-%
 % \begin{function}[EXP]{\msg_fatal_text:n}
 %   \begin{syntax}
 %     \cs{msg_fatal_text:n} \Arg{module}
 %   \end{syntax}
-%   Produces the standard text:
-%   \begin{verbatim}
-%     Fatal <module> error
-%   \end{verbatim}
+%   Produces the standard text
+%   \begin{quote}
+%     \ttfamily
+%     Fatal \meta{module} error
+%   \end{quote}
 %   This function can be redefined to alter the language in which the
 %   message is given, using |#1| as the name of the \meta{module} to
 %   be included.
@@ -205,10 +180,11 @@
 %   \begin{syntax}
 %     \cs{msg_critical_text:n} \Arg{module}
 %   \end{syntax}
-%   Produces the standard text:
-%   \begin{verbatim}
-%     Critical <module> error
-%   \end{verbatim}
+%   Produces the standard text
+%   \begin{quote}
+%     \ttfamily
+%     Critical \meta{module} error
+%   \end{quote}
 %   This function can be redefined to alter the language in which the
 %   message is given, using |#1| as the name of the \meta{module} to
 %   be included.
@@ -218,10 +194,11 @@
 %   \begin{syntax}
 %     \cs{msg_error_text:n} \Arg{module}
 %   \end{syntax}
-%   Produces the standard text:
-%   \begin{verbatim}
-%     <module> error
-%   \end{verbatim}
+%   Produces the standard text
+%   \begin{quote}
+%     \ttfamily
+%     \meta{module} error
+%   \end{quote}
 %   This function can be redefined to alter the language in which the
 %   message is given, using |#1| as the name of the \meta{module} to
 %   be included.
@@ -231,10 +208,11 @@
 %   \begin{syntax}
 %     \cs{msg_warning_text:n} \Arg{module}
 %   \end{syntax}
-%   Produces the standard text:
-%   \begin{verbatim}
-%     <module> warning
-%   \end{verbatim}
+%   Produces the standard text
+%   \begin{quote}
+%     \ttfamily
+%     \meta{module} warning
+%   \end{quote}
 %   This function can be redefined to alter the language in which the
 %   message is given, using |#1| as the name of the \meta{module} to
 %   be included.
@@ -245,161 +223,184 @@
 %     \cs{msg_info_text:n} \Arg{module}
 %   \end{syntax}
 %   Produces the standard text:
-%   \begin{verbatim}
-%     <module> info
-%   \end{verbatim}
+%   \begin{quote}
+%     \ttfamily
+%     \meta{module} info
+%   \end{quote}
 %   This function can be redefined to alter the language in which the
 %   message is given, using |#1| as the name of the \meta{module} to
 %   be included.
 % \end{function}
-%
-% \section{Issuing messages}
-%
-% Messages behave differently depending on the message class. A number
-% of standard message classes are supplied, but more can be
-% created.
-%
-% When issuing messages, any arguments passed should use
-% \cs{tl_to_str:n} or \cs{token_to_str:N} to prevent unwanted expansion
-% of the material.
-%
-% \begin{function}[updated = 2012-04-12]{\msg_class_set:nn}
+% 
+% \begin{function}[EXP]{\msg_see_documentation_text:n}
 %   \begin{syntax}
-%     \cs{msg_class_set:nn} \Arg{class} \Arg{code}
+%     \cs{msg_see_documentation_text:n} \Arg{module}
 %   \end{syntax}
-%   Sets a \meta{class} to output a message, using \meta{code}
-%   to process the message text. The \meta{class} should be a text
-%   value, while the \meta{code} may be any arbitrary material.
-%   The \meta{code} will receive~$6$ arguments: the module
-%   name (|#1|), the message name (|#2|) and the four arguments
-%   taken by the message text (|#3| to |#6|).
-%   ^^A Add an example?  An application could be that an IDE redirects
-%   ^^A classes from 'error' to 'IDEerror', 'warning' to 'IDEwarning',
-%   ^^A etc, and defines 'IDEerror' and 'IDEwarning' to produce messages
-%   ^^A which are simpler to parse.
+%   Produces the standard text
+%   \begin{quote}
+%     \ttfamily
+%     
+%     See the \meta{module} documentation for further information.
+%   \end{quote}
+%   This function can be redefined to alter the language in which the
+%   message is given, using |#1| as the name of the \meta{module} to
+%   be included.
 % \end{function}
 %
-% The kernel defines several common message classes. The following
-% describes the standard behaviour of each class if no redirection of
-% the class or message is active. In all cases, the message may be
-% issued supplying~$0$ to~$4$ arguments. The code will
-% ensure that there an no errors if the number of arguments supplied
-% here does not match the number in the definition of the message
-% (although of course the sense of the message may be impaired).
+% \section{Issuing messages}
+%
+% Messages behave differently depending on the message class. In all cases,
+% the message may be issued supplying~$0$ to~$4$ arguments.  If the number of
+% arguments supplied here does not match the number in the definition of the
+% message, extra arguments will be ignored, or empty arguments added (of
+% course the sense of the message may be impaired). The four arguments will
+% be converted to strings before being added to the message text: the
+% \texttt{x}-type variants should be used to expand material.
 %
-% \begin{function}
+% \begin{function}[updated = 2012-06-29]
 %   {
+%     \msg_fatal:nnnnnn ,
+%     \msg_fatal:nnnnn  ,
+%     \msg_fatal:nnnn   ,
+%     \msg_fatal:nnn    ,
+%     \msg_fatal:nn     ,
 %     \msg_fatal:nnxxxx ,
 %     \msg_fatal:nnxxx  ,
 %     \msg_fatal:nnxx   ,
-%     \msg_fatal:nnx    ,
-%     \msg_fatal:nn
+%     \msg_fatal:nnx
 %   }
 %   \begin{syntax}
-%     \cs{msg_fatal:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%     \cs{msg_fatal:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
 %   \end{syntax}
 %   Issues \meta{module} error \meta{message}, passing \meta{arg one} to
 %   \meta{arg four} to the text-creating functions. After issuing a
 %   fatal error the \TeX{} run will halt.
 % \end{function}
 %
-% \begin{function}
+% \begin{function}[updated = 2012-06-29]
 %   {
+%     \msg_critical:nnnnnn ,
+%     \msg_critical:nnnnn  ,
+%     \msg_critical:nnnn   ,
+%     \msg_critical:nnn    ,
+%     \msg_critical:nn     ,
 %     \msg_critical:nnxxxx ,
 %     \msg_critical:nnxxx  ,
 %     \msg_critical:nnxx   ,
-%     \msg_critical:nnx    ,
-%     \msg_critical:nn
+%     \msg_critical:nnx
 %   }
 %   \begin{syntax}
-%     \cs{msg_critical:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%     \cs{msg_critical:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
 %   \end{syntax}
 %   Issues \meta{module} error \meta{message}, passing \meta{arg one} to
-%   \meta{arg four} to the text-creating functions. After issuing the
-%   message reading the current input file will stop. This may halt
-%   the \TeX{} run (if the current file is the main file) or
-%   may abort reading a sub-file.
+%   \meta{arg four} to the text-creating functions.  After issuing a
+%   critical error, \TeX{} will stop reading the current input file.
+%   This may halt the \TeX{} run (if the current file is the main file)
+%   or may abort reading a sub-file.
+%   \begin{texnote}
+%     The \TeX{} \tn{endinput} primitive is used to exit the file.  In
+%     particular, the rest of the current line remains in the input
+%     stream. ^^A Can we fix that?
+%   \end{texnote}
 % \end{function}
-% ^^A Perhaps add detection that we are in the main file to really do
-% ^^A '\tex_end:D' in that case?
 %
-% \begin{function}
+% \begin{function}[updated = 2012-06-29]
 %   {
+%     \msg_error:nnnnnn ,
+%     \msg_error:nnnnn  ,
+%     \msg_error:nnnn   ,
+%     \msg_error:nnn    ,
+%     \msg_error:nn     ,
 %     \msg_error:nnxxxx ,
 %     \msg_error:nnxxx  ,
 %     \msg_error:nnxx   ,
-%     \msg_error:nnx    ,
-%     \msg_error:nn
+%     \msg_error:nnx
 %   }
 %   \begin{syntax}
-%     \cs{msg_error:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%     \cs{msg_error:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
 %   \end{syntax}
 %   Issues \meta{module} error \meta{message}, passing \meta{arg one} to
-%   \meta{arg four} to the text-creating functions. The error will
-%   stop processing and issue the text at the terminal. After user input,
-%   the run will continue.
+%   \meta{arg four} to the text-creating functions.  The error will
+%   interrupt processing and issue the text at the terminal.  After user
+%   input, the run will continue.
 % \end{function}
 %
-%  \begin{function}
-%    {
-%      \msg_warning:nnxxxx ,
-%      \msg_warning:nnxxx  ,
-%      \msg_warning:nnxx   ,
-%      \msg_warning:nnx    ,
-%      \msg_warning:nn
-%    }
-%    \begin{syntax}
-%      \cs{msg_warning:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
-%    \end{syntax}
-%    Issues \meta{module} warning \meta{message}, passing \meta{arg one} to
-%    \meta{arg four} to the text-creating functions. The warning text
-%    will be added to the log file, but the \TeX{} run will not be
-%    interrupted.
-%  \end{function}
+% \begin{function}[updated = 2012-06-29]
+%   {
+%     \msg_warning:nnnnnn ,
+%     \msg_warning:nnnnn  ,
+%     \msg_warning:nnnn   ,
+%     \msg_warning:nnn    ,
+%     \msg_warning:nn     ,
+%     \msg_warning:nnxxxx ,
+%     \msg_warning:nnxxx  ,
+%     \msg_warning:nnxx   ,
+%     \msg_warning:nnx
+%   }
+%   \begin{syntax}
+%     \cs{msg_warning:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%   \end{syntax}
+%   Issues \meta{module} warning \meta{message}, passing \meta{arg one}
+%   to \meta{arg four} to the text-creating functions. The warning text
+%   will be added to the log file and the terminal, but the \TeX{} run
+%   will not be interrupted.
+% \end{function}
 %
-% \begin{function}
+% \begin{function}[updated = 2012-06-29]
 %   {
+%     \msg_info:nnnnnn ,
+%     \msg_info:nnnnn  ,
+%     \msg_info:nnnn   ,
+%     \msg_info:nnn    ,
+%     \msg_info:nn     ,
 %     \msg_info:nnxxxx ,
 %     \msg_info:nnxxx  ,
 %     \msg_info:nnxx   ,
-%     \msg_info:nnx    ,
-%     \msg_info:nn
+%     \msg_info:nnx
 %   }
 %   \begin{syntax}
-%     \cs{msg_info:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%     \cs{msg_info:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
 %   \end{syntax}
 %   Issues \meta{module} information \meta{message}, passing
 %   \meta{arg one} to \meta{arg four} to the text-creating functions.
 %   The information text will be added to the log file.
 % \end{function}
 %
-% \begin{function}
+% \begin{function}[updated = 2012-07-14]
 %   {
+%     \msg_log:nnnnnn ,
+%     \msg_log:nnnnn  ,
+%     \msg_log:nnnn   ,
+%     \msg_log:nnn    ,
+%     \msg_log:nn     ,
 %     \msg_log:nnxxxx ,
 %     \msg_log:nnxxx  ,
 %     \msg_log:nnxx   ,
-%     \msg_log:nnx    ,
-%     \msg_log:nn
+%     \msg_log:nnx
 %   }
 %   \begin{syntax}
-%     \cs{msg_log:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%     \cs{msg_log:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
 %   \end{syntax}
 %   Issues \meta{module} information \meta{message}, passing
 %   \meta{arg one} to \meta{arg four} to the text-creating functions.
 %   The information text will be added to the log file: the output
-%   is briefer than \cs{msg_info:nnxxxx}.
+%   is briefer than \cs{msg_info:nnnnnn}.
 % \end{function}
 %
-% \begin{function}
+% \begin{function}[updated = 2012-06-29]
 %   {
+%     \msg_none:nnnnnn ,
+%     \msg_none:nnnnn  ,
+%     \msg_none:nnnn   ,
+%     \msg_none:nnn    ,
+%     \msg_none:nn     ,
 %     \msg_none:nnxxxx ,
 %     \msg_none:nnxxx  ,
 %     \msg_none:nnxx   ,
-%     \msg_none:nnx    ,
-%     \msg_none:nn
+%     \msg_none:nnx
 %   }
 %   \begin{syntax}
-%     \cs{msg_none:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%     \cs{msg_none:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
 %   \end{syntax}
 %   Does nothing: used as a message class to prevent any output at
 %   all (see the discussion of message redirection).
@@ -434,18 +435,23 @@
 % it is possible to select out an individual message for special treatment
 % even if the entire class is already redirected.
 %
-% \begin{function}[updated = 2012-04-12]{\msg_redirect_class:nn}
+% Multiple redirections are possible.  Redirections can be cancelled by
+% providing an empty argument for the target class.  Redirection to a
+% missing class will raise errors immediately.  Infinite loops are
+% prevented by eliminating the redirection starting from the target of
+% the redirection that caused the loop to appear.  Namely, if
+% redirections are requested as $A \to B$, $B \to C$ and $C \to A$ in
+% this order, then the $A \to B$ redirection is cancelled.
+%
+% \begin{function}[updated = 2012-04-27]{\msg_redirect_class:nn}
 %   \begin{syntax}
 %     \cs{msg_redirect_class:nn} \Arg{class one} \Arg{class two}
 %   \end{syntax}
 %   Changes the behaviour of messages of \meta{class one} so that they
-%   are processed using the code for those of \meta{class two}. Multiple
-%   redirections are possible. Redirection to a missing class or
-%   infinite loops will raise errors when the messages are used,
-%   rather than at the point of redirection.
+%   are processed using the code for those of \meta{class two}.
 % \end{function}
 %
-% \begin{function}[updated = 2012-04-12]{\msg_redirect_module:nnn}
+% \begin{function}[updated = 2012-04-27]{\msg_redirect_module:nnn}
 %   \begin{syntax}
 %     \cs{msg_redirect_module:nnn} \Arg{module} \Arg{class one} \Arg{class two}
 %   \end{syntax}
@@ -460,14 +466,14 @@
 %   \end{verbatim}
 % \end{function}
 %
-% \begin{function}[updated = 2012-04-12]{\msg_redirect_name:nnn}
+% \begin{function}[updated = 2012-04-27]{\msg_redirect_name:nnn}
 %   \begin{syntax}
 %     \cs{msg_redirect_name:nnn} \Arg{module} \Arg{message} \Arg{class}
 %   \end{syntax}
-%   Redirects a specific \meta{message} from a specific \meta{module}
-%   to act as a member of \meta{class} of messages. This function can
-%   be used to make a selected message \enquote{silent} without
-%   changing global parameters:
+%   Redirects a specific \meta{message} from a specific \meta{module} to
+%   act as a member of \meta{class} of messages.  No further redirection
+%   is performed.  This function can be used to make a selected message
+%   \enquote{silent} without changing global parameters:
 %   \begin{verbatim}
 %     \msg_redirect_name:nnn { module } { annoying-message } { none }
 %   \end{verbatim}
@@ -479,18 +485,9 @@
 % higher-level system. However, there are occasions where direct
 % access to these functions is desirable.
 %
-% \begin{function}[EXP]{\msg_newline:, \msg_two_newlines:}
-%   \begin{syntax}
-%     \cs{msg_newline:}
-%   \end{syntax}
-%   Forces a new line in a message. This is a low-level function, which
-%   will not include any additional printing information in the message:
-%   contrast with |\\| in messages. The |two| version adds two lines.
-% \end{function}
-%
-% \begin{function}{\msg_interrupt:xxx}
+% \begin{function}[added = 2012-06-28]{\msg_interrupt:nnn}
 %   \begin{syntax}
-%     \cs{msg_interrupt:xxx} \Arg{first line} \Arg{text} \Arg{extra text}
+%     \cs{msg_interrupt:nnn} \Arg{first line} \Arg{text} \Arg{extra text}
 %   \end{syntax}
 %   Interrupts the \TeX{} run, issuing a formatted message comprising
 %   \meta{first line} and \meta{text} laid out in the format
@@ -511,13 +508,15 @@
 %     |  <extra text>
 %     |...............................................
 %   \end{verbatim}
-%   where the \meta{extra text} will be wrapped to fit within the current
-%   line length.
+%   where the \meta{extra text} will be wrapped within the current
+%   line length. Wrapping of both \meta{text} and \meta{more text} takes place
+%   using \cs{iow_wrap:nnnN}; the documentation for the latter should be
+%   consulted for full details.
 % \end{function}
 %
-% \begin{function}{\msg_log:x}
+% \begin{function}[added = 2012-06-28]{\msg_log:n}
 %   \begin{syntax}
-%     \cs{msg_log:x} \Arg{text}
+%     \cs{msg_log:n} \Arg{text}
 %   \end{syntax}
 %   Writes to the log file with the \meta{text} laid out in the format
 %   \begin{verbatim}
@@ -526,12 +525,13 @@
 %     .................................................
 %   \end{verbatim}
 %   where the \meta{text} will be wrapped to fit within the current
-%   line length.
+%   line length.  Wrapping takes place using \cs{iow_wrap:nnnN}; the
+%   documentation for the latter should be consulted for full details.
 % \end{function}
 %
-% \begin{function}{\msg_term:x}
+% \begin{function}[added = 2012-06-28]{\msg_term:n}
 %   \begin{syntax}
-%     \cs{msg_term:x} \Arg{text}
+%     \cs{msg_term:n} \Arg{text}
 %   \end{syntax}
 %   Writes to the terminal and log file with the \meta{text} laid out in the
 %   format
@@ -541,7 +541,8 @@
 %     *************************************************
 %   \end{verbatim}
 %   where the \meta{text} will be wrapped to fit within the current
-%   line length.
+%   line length. Wrapping takes place using \cs{iow_wrap:nnnN}; the
+%   documentation for the latter should be consulted for full details.
 % \end{function}
 %
 % \section{Kernel-specific functions}
@@ -551,59 +552,65 @@
 % and also ensures that serious errors can be handled properly.
 %
 % \begin{function}[updated = 2011-08-16]
-%   {\msg_kernel_new:nnnn, \msg_kernel_new:nnn}
+%   {\__msg_kernel_new:nnnn, \__msg_kernel_new:nnn}
 %   \begin{syntax}
-%     \cs{msg_kernel_new:nnnn} \Arg{module} \Arg{message} \Arg{text} \Arg{more text}
+%     \cs{__msg_kernel_new:nnnn} \Arg{module} \Arg{message} \Arg{text} \Arg{more text}
 %   \end{syntax}
 %   Creates a kernel \meta{message} for a given \meta{module}.
 %   The message will be defined to first give \meta{text} and then
 %   \meta{more text} if the user requests it. If no \meta{more text} is
 %   available then a standard text is given instead. Within \meta{text}
 %   and \meta{more text} four parameters (|#1| to |#4|) can be used:
-%   these will be supplied at the time the message is used. The
-%   parameters will be expanded when the message is used. An error will
-%   be raised if the \meta{message} already exists.
+%   these will be supplied and expanded at the time the message is used.
+%   An error will be raised if the \meta{message} already exists.
 % \end{function}
 %
-% \begin{function}{\msg_kernel_set:nnnn, \msg_kernel_set:nnn}
+% \begin{function}{\__msg_kernel_set:nnnn, \__msg_kernel_set:nnn}
 %   \begin{syntax}
-%     \cs{msg_kernel_set:nnnn} \Arg{module} \Arg{message} \Arg{text} \Arg{more text}
+%     \cs{__msg_kernel_set:nnnn} \Arg{module} \Arg{message} \Arg{text} \Arg{more text}
 %   \end{syntax}
 %   Sets up the text for a kernel \meta{message} for a given \meta{module}.
 %   The message will be defined to first give \meta{text} and then
 %   \meta{more text} if the user requests it. If no \meta{more text} is
 %   available then a standard text is given instead. Within \meta{text}
 %   and \meta{more text} four parameters (|#1| to |#4|) can be used:
-%   these will be supplied at the time the message is used. The
-%   parameters will be expanded when the message is used.
+%   these will be supplied and expanded at the time the message is used.
 % \end{function}
 %
-% \begin{function}
+% \begin{function}[updated = 2012-06-29]
 %   {
-%     \msg_kernel_fatal:nnxxxx ,
-%     \msg_kernel_fatal:nnxxx  ,
-%     \msg_kernel_fatal:nnxx   ,
-%     \msg_kernel_fatal:nnx    ,
-%     \msg_kernel_fatal:nn
+%     \__msg_kernel_fatal:nnnnnn ,
+%     \__msg_kernel_fatal:nnnnn  ,
+%     \__msg_kernel_fatal:nnnn   ,
+%     \__msg_kernel_fatal:nnn    ,
+%     \__msg_kernel_fatal:nn     ,
+%     \__msg_kernel_fatal:nnxxxx ,
+%     \__msg_kernel_fatal:nnxxx  ,
+%     \__msg_kernel_fatal:nnxx   ,
+%     \__msg_kernel_fatal:nnx
 %   }
 %   \begin{syntax}
-%     \cs{msg_kernel_fatal:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%     \cs{__msg_kernel_fatal:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
 %   \end{syntax}
 %   Issues kernel \meta{module} error \meta{message}, passing \meta{arg one}
 %   to \meta{arg four} to the text-creating functions. After issuing a
 %   fatal error the \TeX{} run will halt. Cannot be redirected.
 % \end{function}
 %
-% \begin{function}
+% \begin{function}[updated = 2012-06-29]
 %   {
-%     \msg_kernel_error:nnxxxx ,
-%     \msg_kernel_error:nnxxx  ,
-%     \msg_kernel_error:nnxx   ,
-%     \msg_kernel_error:nnx    ,
-%     \msg_kernel_error:nn
+%     \__msg_kernel_error:nnnnnn ,
+%     \__msg_kernel_error:nnnnn  ,
+%     \__msg_kernel_error:nnnn   ,
+%     \__msg_kernel_error:nnn    ,
+%     \__msg_kernel_error:nn     ,
+%     \__msg_kernel_error:nnxxxx ,
+%     \__msg_kernel_error:nnxxx  ,
+%     \__msg_kernel_error:nnxx   ,
+%     \__msg_kernel_error:nnx
 %   }
 %   \begin{syntax}
-%     \cs{msg_kernel_error:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%     \cs{__msg_kernel_error:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
 %   \end{syntax}
 %   Issues kernel \meta{module} error \meta{message}, passing \meta{arg one}
 %   to
@@ -612,34 +619,42 @@
 %   the run will continue. Cannot be redirected.
 % \end{function}
 %
-%  \begin{function}
-%    {
-%      \msg_kernel_warning:nnxxxx ,
-%      \msg_kernel_warning:nnxxx  ,
-%      \msg_kernel_warning:nnxx   ,
-%      \msg_kernel_warning:nnx    ,
-%      \msg_kernel_warning:nn
-%    }
-%    \begin{syntax}
-%      \cs{msg_kernel_warning:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
-%    \end{syntax}
-%    Issues kernel \meta{module} warning \meta{message}, passing
-%    \meta{arg one} to
-%    \meta{arg four} to the text-creating functions. The warning text
-%    will be added to the log file, but the \TeX{} run will not be
-%    interrupted.
-%  \end{function}
+% \begin{function}[updated = 2012-06-29]
+%   {
+%     \__msg_kernel_warning:nnnnnn ,
+%     \__msg_kernel_warning:nnnnn  ,
+%     \__msg_kernel_warning:nnnn   ,
+%     \__msg_kernel_warning:nnn    ,
+%     \__msg_kernel_warning:nn     ,
+%     \__msg_kernel_warning:nnxxxx ,
+%     \__msg_kernel_warning:nnxxx  ,
+%     \__msg_kernel_warning:nnxx   ,
+%     \__msg_kernel_warning:nnx
+%   }
+%   \begin{syntax}
+%     \cs{__msg_kernel_warning:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%   \end{syntax}
+%   Issues kernel \meta{module} warning \meta{message}, passing
+%   \meta{arg one} to
+%   \meta{arg four} to the text-creating functions. The warning text
+%   will be added to the log file, but the \TeX{} run will not be
+%   interrupted.
+% \end{function}
 %
-% \begin{function}
+% \begin{function}[updated = 2012-06-29]
 %   {
-%     \msg_kernel_info:nnxxxx ,
-%     \msg_kernel_info:nnxxx  ,
-%     \msg_kernel_info:nnxx   ,
-%     \msg_kernel_info:nnx    ,
-%     \msg_kernel_info:nn
+%     \__msg_kernel_info:nnnnnn ,
+%     \__msg_kernel_info:nnnnn  ,
+%     \__msg_kernel_info:nnnn   ,
+%     \__msg_kernel_info:nnn    ,
+%     \__msg_kernel_info:nn     ,
+%     \__msg_kernel_info:nnxxxx ,
+%     \__msg_kernel_info:nnxxx  ,
+%     \__msg_kernel_info:nnxx   ,
+%     \__msg_kernel_info:nnx
 %   }
 %   \begin{syntax}
-%     \cs{msg_kernel_info:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%     \cs{__msg_kernel_info:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
 %   \end{syntax}
 %   Issues kernel \meta{module} information \meta{message}, passing
 %   \meta{arg one} to \meta{arg four} to the text-creating functions.
@@ -658,14 +673,14 @@
 %
 % \begin{function}[EXP, added = 2011-11-23]
 %   {
-%     \msg_expandable_kernel_error:nnnnnn,
-%     \msg_expandable_kernel_error:nnnnn,
-%     \msg_expandable_kernel_error:nnnn,
-%     \msg_expandable_kernel_error:nnn,
-%     \msg_expandable_kernel_error:nn
+%     \__msg_kernel_expandable_error:nnnnnn,
+%     \__msg_kernel_expandable_error:nnnnn,
+%     \__msg_kernel_expandable_error:nnnn,
+%     \__msg_kernel_expandable_error:nnn,
+%     \__msg_kernel_expandable_error:nn
 %   }
 %   \begin{syntax}
-%     \cs{msg_expandable_kernel_error:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%     \cs{__msg_kernel_expandable_error:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
 %   \end{syntax}
 %   Issues an error, passing \meta{arg one} to \meta{arg four}
 %   to the text-creating functions. The resulting string must
@@ -673,9 +688,9 @@
 % \end{function}
 %
 % \begin{function}[EXP, added = 2011-08-11, updated = 2011-08-13]
-%   {\msg_expandable_error:n}
+%   {\__msg_expandable_error:n}
 %   \begin{syntax}
-%     \cs{msg_expandable_error:n} \Arg{error message}
+%     \cs{__msg_expandable_error:n} \Arg{error message}
 %   \end{syntax}
 %   Issues an \enquote{Undefined error} message from \TeX{} itself,
 %   and prints the \meta{error message}. The \meta{error message}
@@ -692,30 +707,53 @@
 %
 % The following functions are used in several kernel modules.
 %
-% \begin{function}{\msg_aux_use:nn, \msg_aux_use:nnxxxx}
+% \begin{function}
+%   {
+%     \__msg_term:nnnnnn,
+%     \__msg_term:nnnnnV,
+%     \__msg_term:nnnnn,
+%     \__msg_term:nnn  ,
+%     \__msg_term:nn
+%   }
 %   \begin{syntax}
-%     \cs{msg_aux_use:nnxxxx} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
+%     \cs{__msg_term:nnnnnn} \Arg{module} \Arg{message} \Arg{arg one} \Arg{arg two} \Arg{arg three} \Arg{arg four}
 %   \end{syntax}
-%   Prints the \meta{message} from \meta{module} in the terminal,
-%   without formatting.
+%   Prints the \meta{message} from \meta{module} in the terminal without
+%   formatting. Used in messages which print complex variable contents
+%   completely.
 % \end{function}
-%
-% \begin{function}{\msg_aux_show:x}
+% 
+% \begin{function}{\__msg_show_variable:Nnn, \__msg_show_variable:Nnx}
 %   \begin{syntax}
-%     \cs{msg_aux_show:x} \Arg{formatted string}
+%     \cs{__msg_show_variable:Nnn} \meta{variable} \Arg{type} \Arg{formatted content}
+%   \end{syntax}
+%   Displays the \meta{formatted content} of the \meta{variable} of \meta{type}
+%   in the terminal. The \meta{formatted content} will typically be generated
+%   by \texttt{x}-type expansion using the \cs{__msg_show_variable:Nnx} variant:
+%   the nature of the formatting is dependent on the calling module.
+% \end{function}
+% 
+% \begin{function}{\__msg_show_variable:n, \__msg_show_variable:x}
+%   \begin{syntax}
+%     \cs{__msg_show_variable:n} \Arg{formatted string}
 %   \end{syntax}
 %   Shows the \meta{formatted string} on the terminal.  After expansion,
 %   unless it is empty, the \meta{formatted string} must contain |>|,
 %   and the part of \meta{formatted string} before the first |>| is
 %   removed. Failure to do so causes low-level \TeX{} errors.
 % \end{function}
-%
-% \begin{function}{\msg_aux_show:Nnx}
+% 
+% \begin{function}
+%   {\__msg_show_item:n, \__msg_show_item:nn, \__msg_show_item_unbraced:nn}
 %   \begin{syntax}
-%     \cs{msg_aux_show:Nnx} \meta{variable} \Arg{module} \Arg{token list}
+%     \cs{__msg_show_item:n}  \meta{item}
+%     \cs{__msg_show_item:nn} \meta{item-key} \meta{item-value}
 %   \end{syntax}
-%   Auxiliary common to \pkg{l3clist}, \pkg{l3prop} and \pkg{seq},
-%   which displays an appropriate message and the contents of the variable.
+%   Auxiliary functions used within the argument of
+%   \cs{__msg_show_variable:Nnx} to format variable items correctly for
+%   display. The \cs{__msg_show_item:n} version is used for simple lists,
+%   the \cs{__msg_show_item:nn} and \cs{__msg_show_item_ubraced:nn} versions
+%   for key--value like data structures.
 % \end{function}
 %
 % \end{documentation}
@@ -727,19 +765,23 @@
 %    \begin{macrocode}
 %<*initex|package>
 %    \end{macrocode}
+%    
+%    \begin{macrocode}
+%<@@=msg>
+%    \end{macrocode}
 %
 %    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
-% \begin{variable}{\l_msg_internal_tl}
+% \begin{variable}{\l_@@_internal_tl}
 %   A general scratch for the module.
 %    \begin{macrocode}
-\tl_new:N \l_msg_internal_tl
+\tl_new:N \l_@@_internal_tl
 %    \end{macrocode}
 % \end{variable}
 %
@@ -749,11 +791,11 @@
 % the code here. First, a mechanism for creating message text.
 % This is pretty simple, as there is not actually a lot to do.
 %
-% \begin{variable}{\c_msg_text_prefix_tl, \c_msg_more_text_prefix_tl}
+% \begin{variable}{\c_@@_text_prefix_tl, \c_@@_more_text_prefix_tl}
 %   Locations for the text of messages.
 %    \begin{macrocode}
-\tl_const:Nn \c_msg_text_prefix_tl      { msg~text~>~ }
-\tl_const:Nn \c_msg_more_text_prefix_tl { msg~extra~text~>~ }
+\tl_const:Nn \c_@@_text_prefix_tl      { msg~text~>~ }
+\tl_const:Nn \c_@@_more_text_prefix_tl { msg~extra~text~>~ }
 %    \end{macrocode}
 % \end{variable}
 %
@@ -763,37 +805,37 @@
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \msg_if_exist:nn #1#2 { p , T , F , TF }
   {
-    \cs_if_exist:cTF { \c_msg_text_prefix_tl #1 / #2 }
+    \cs_if_exist:cTF { \c_@@_text_prefix_tl #1 / #2 }
       { \prg_return_true: } { \prg_return_false: }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]{\chk_if_free_msg:nn}
-%   This auxiliary is similar to \cs{chk_if_free_cs:N}, and is used when
+% \begin{macro}[aux]{\__chk_if_free_msg:nn}
+%   This auxiliary is similar to \cs{__chk_if_free_cs:N}, and is used when
 %   defining messages with \cs{msg_new:nnnn}. It could be inlined in
 %   \cs{msg_new:nnnn}, but the experimental \pkg{l3trace} module needs
 %   to disable this check when reloading a package with the extra
 %   tracing information.
 %    \begin{macrocode}
-\cs_new_protected:Npn \chk_if_free_msg:nn #1#2
+\cs_new_protected:Npn \__chk_if_free_msg:nn #1#2
   {
     \msg_if_exist:nnT {#1} {#2}
       {
-        \msg_kernel_error:nnxx { msg } { message-already-defined }
+        \@@_kernel_error:nnxx { kernel } { message-already-defined }
           {#1} {#2}
       }
   }
 %<*package>
 \tex_ifodd:D \l@expl@log@functions@bool
-  \cs_gset_protected:Npn \chk_if_free_msg:nn #1#2
+  \cs_gset_protected:Npn \__chk_if_free_msg:nn #1#2
     {
       \msg_if_exist:nnT {#1} {#2}
         {
-          \msg_kernel_error:nnxx { msg } { message-already-defined }
+          \@@_kernel_error:nnxx { kernel } { message-already-defined }
             {#1} {#2}
         }
-      \iow_log:x { Defining~message~#1/#2~ \msg_line_context: }
+      \iow_log:x { Defining~message~ #1 / #2 ~\msg_line_context: }
     }
 \fi:
 %</package>
@@ -808,25 +850,25 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \msg_new:nnnn #1#2
   {
-    \chk_if_free_msg:nn {#1} {#2}
+    \__chk_if_free_msg:nn {#1} {#2}
     \msg_gset:nnnn {#1} {#2}
   }
 \cs_new_protected:Npn \msg_new:nnn #1#2#3
   { \msg_new:nnnn {#1} {#2} {#3} { } }
 \cs_new_protected:Npn \msg_set:nnnn #1#2#3#4
   {
-    \cs_set:cpn { \c_msg_text_prefix_tl #1 / #2 }
+    \cs_set:cpn { \c_@@_text_prefix_tl #1 / #2 }
       ##1##2##3##4 {#3}
-    \cs_set:cpn { \c_msg_more_text_prefix_tl #1 / #2 }
+    \cs_set:cpn { \c_@@_more_text_prefix_tl #1 / #2 }
       ##1##2##3##4 {#4}
   }
 \cs_new_protected:Npn \msg_set:nnn #1#2#3
   { \msg_set:nnnn {#1} {#2} {#3} { } }
 \cs_new_protected:Npn \msg_gset:nnnn #1#2#3#4
   {
-    \cs_gset:cpn { \c_msg_text_prefix_tl #1 / #2 }
+    \cs_gset:cpn { \c_@@_text_prefix_tl #1 / #2 }
       ##1##2##3##4 {#3}
-    \cs_gset:cpn { \c_msg_more_text_prefix_tl #1 / #2 }
+    \cs_gset:cpn { \c_@@_more_text_prefix_tl #1 / #2 }
       ##1##2##3##4 {#4}
   }
 \cs_new_protected:Npn \msg_gset:nnn #1#2#3
@@ -887,15 +929,7 @@
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{macro}{\msg_newline:, \msg_two_newlines:}
-%   New lines are printed in the same way as for low-level file writing.
-%    \begin{macrocode}
-\cs_new_nopar:Npn \msg_newline: { ^^J }
-\cs_new_nopar:Npn \msg_two_newlines: { ^^J ^^J }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\msg_line_number, \msg_line_context:}
+% \begin{macro}{\msg_line_number:, \msg_line_context:}
 %   For writing the line number nicely. \cs{msg_line_context:} was set up
 %   earlier, so this is not \texttt{new}.
 %    \begin{macrocode}
@@ -911,7 +945,7 @@
 %
 % \subsection{Showing messages: low level mechanism}
 %
-% \begin{macro}{\msg_interrupt:xxx}
+% \begin{macro}{\msg_interrupt:nnn}
 %   The low-level interruption macro is rather opaque, unfortunately.
 %   Depending on the availability of more information there is a choice
 %   of how to set up the further help.  We feed the extra help text and
@@ -919,36 +953,36 @@
 %   must first setup \TeX{}'s \tn{errhelp} register before issuing an
 %   \tn{errmessage}.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_interrupt:xxx #1#2#3
+\cs_new_protected:Npn \msg_interrupt:nnn #1#2#3
   {
     \tl_if_empty:nTF {#3}
       {
-        \msg_interrupt_wrap:xx { \\ \c_msg_no_info_text_tl }
+        \@@_interrupt_wrap:nn { \\ \c_msg_no_info_text_tl }
           {#1 \\\\ #2 \\\\ \c_msg_continue_text_tl }
       }
       {
-        \msg_interrupt_wrap:xx { \\ #3 }
+        \@@_interrupt_wrap:nn { \\ #3 }
           {#1 \\\\ #2 \\\\ \c_msg_help_text_tl }
       }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]{\msg_interrupt_wrap:xx}
-% \begin{macro}[aux]{\msg_interrupt_more_text:n}
+% \begin{macro}[aux]{\@@_interrupt_wrap:nn}
+% \begin{macro}[aux]{\@@_interrupt_more_text:n}
 %   First setup \TeX{}'s \tn{errhelp} register with the extra help |#1|,
 %   then build a nice-looking error message with |#2|.  Everything is
 %   done using \texttt{x}-type expansion as the new line markers are
 %   different for the two type of text and need to be correctly set up.
-%   The auxiliary \cs{msg_interrupt_more_text:n} recieves its argument
+%   The auxiliary \cs{@@_interrupt_more_text:n} receives its argument
 %   as a line-wrapped string, which is thus unaffected by expansion.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_interrupt_wrap:xx #1#2
+\cs_new_protected:Npn \@@_interrupt_wrap:nn #1#2
   {
-    \iow_wrap:xnnnN {#1} { | ~ } { 2 } { } \msg_interrupt_more_text:n
-    \iow_wrap:xnnnN {#2} { ! ~ } { 2 } { } \msg_interrupt_text:n
+    \iow_wrap:nnnN {#1} { | ~ } { } \@@_interrupt_more_text:n
+    \iow_wrap:nnnN {#2} { ! ~ } { } \@@_interrupt_text:n
   }
-\cs_new_protected:Npn \msg_interrupt_more_text:n #1
+\cs_new_protected:Npn \@@_interrupt_more_text:n #1
   {
     \exp_args:Nx \tex_errhelp:D
       {
@@ -961,17 +995,16 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[aux]{\msg_interrupt_text:n}
-% \begin{variable}{\c_msg_hide_tl<dots>}
+% \begin{macro}[aux]{\@@_interrupt_text:n}
 %   The business end of the process starts by producing some visual
 %   separation of the message from the main part of the log.  The error
 %   message needs to be printed with everything made
 %   \enquote{invisible}: \TeX{}'s own information involves the macro in
 %   which \tn{errmessage} is called, and the end of the argument of the
 %   \tn{errmessage}, including the closing brace.  We use an active |!|
-%   to call the \tn{errmessage} primitive, and end its argument with an
-%   odd \cs{c_msg_hide_tl<dots>} which fills the output with dots.  The
-%   trailing closing brace is turned into a space to hide it as well.
+%   to call the \tn{errmessage} primitive, and end its argument with
+%   \cs{use_none:n} \Arg{dots} which fills the output with dots.  Two
+%   trailing closing braces are turned into spaces to hide them as well.
 %   The group in which we alter the definition of the active |!| is
 %   closed before producing the message: this ensures that tokens
 %   inserted by typing |I| in the command-line will bee inserted after
@@ -982,13 +1015,10 @@
   \char_set_lccode:nn {`\}} {`\ }
   \char_set_lccode:nn {`\&} {`\!}
   \char_set_catcode_active:N \&
-  \char_set_catcode_letter:N \.
-  \tl_new:N
-    \c_msg_hide_tl............................................
 \tl_to_lowercase:n
   {
     \group_end:
-    \cs_new_protected:Npn \msg_interrupt_text:n #1
+    \cs_new_protected:Npn \@@_interrupt_text:n #1
       {
         \iow_term:x
           {
@@ -1003,7 +1033,8 @@
               \tex_errmessage:D
                 {
                   #1
-                  \c_msg_hide_tl............................................
+                  \use_none:n
+                    { ............................................ }
                 }
             }
           \exp_after:wN
@@ -1012,27 +1043,24 @@
       }
   }
 %    \end{macrocode}
-% \end{variable}
 % \end{macro}
 %
-% \begin{macro}{\msg_log:x}
-% \begin{macro}{\msg_term:x}
+% \begin{macro}{\msg_log:n}
+% \begin{macro}{\msg_term:n}
 %   Printing to the log or terminal without a stop is rather easier.
 %   A bit of simple visual work sets things off nicely.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_log:x #1
+\cs_new_protected:Npn \msg_log:n #1
   {
-    \iow_log:x { ................................................. }
-    \iow_wrap:xnnnN { . ~ #1} { . ~ } { 2 } { }
-      \iow_log:x
-    \iow_log:x { ................................................. }
+    \iow_log:n { ................................................. }
+    \iow_wrap:nnnN { . ~ #1} { . ~ } { } \iow_log:n
+    \iow_log:n { ................................................. }
   }
-\cs_new_protected:Npn \msg_term:x #1
+\cs_new_protected:Npn \msg_term:n #1
   {
-    \iow_term:x { ************************************************* }
-    \iow_wrap:xnnnN { * ~ #1} { * ~ } { 2 } { }
-      \iow_term:x
-    \iow_term:x { ************************************************* }
+    \iow_term:n { ************************************************* }
+    \iow_wrap:nnnN { * ~ #1} { * ~ } { } \iow_term:n
+    \iow_term:n { ************************************************* }
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1041,8 +1069,12 @@
 % \subsection{Displaying messages}
 %
 % \LaTeX{} is handling error messages and so the \TeX{} ones are disabled.
+% This is already done by the \LaTeXe{} kernel, so to avoid messing up any
+% deliberate change by a user this is only set in format mode.
 %    \begin{macrocode}
-\int_gset:Nn \tex_errorcontextlines:D { -1 }
+%<*initex>
+\int_gset_eq:NN \tex_errorcontextlines:D \c_minus_one
+%</initex>
 %    \end{macrocode}
 %
 % \begin{macro}
@@ -1054,7 +1086,7 @@
 %     \msg_info_text:n
 %   }
 %   A function for issuing messages: both the text and order could
-%   in principal vary.
+%   in principle vary.
 %    \begin{macrocode}
 \cs_new:Npn \msg_fatal_text:n #1 { Fatal~#1~error }
 \cs_new:Npn \msg_critical_text:n #1 { Critical~#1~error }
@@ -1065,591 +1097,637 @@
 % \end{macro}
 %
 % \begin{macro}{\msg_see_documentation_text:n}
-%   Contextual footer information.
+%   Contextual footer information.  The \LaTeX{} module only comprises
+%   \LaTeX3 code, so we refer to the \LaTeX3 documentation rather than
+%   simply \enquote{\LaTeX{}}.
 %    \begin{macrocode}
 \cs_new:Npn \msg_see_documentation_text:n #1
-  { \\ \\ See~the~#1~documentation~for~further~information. }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\msg_class_set:nn}
-%  Setting up a message class does two tasks. Any existing redirection
-%  is cleared, and the various message functions are created
-%  to simply use the code stored for the message.
-%    \begin{macrocode}
-\cs_new_protected:Npn \msg_class_set:nn #1#2
   {
-    \prop_clear_new:c { l_msg_redirect_ #1 _prop }
-    \cs_set_protected:cpn { msg_ #1 :nnxxxx } ##1##2##3##4##5##6
-      { \msg_use:nnnnxxxx {#1} {#2} {##1} {##2} {##3} {##4} {##5} {##6} }
-    \cs_set_protected:cpx { msg_ #1 :nnxxx } ##1##2##3##4##5
-      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} {##5} { } }
-    \cs_set_protected:cpx { msg_ #1 :nnxx } ##1##2##3##4
-      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} { } { } }
-    \cs_set_protected:cpx { msg_ #1 :nnx } ##1##2##3
-      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} { } { } { } }
-    \cs_set_protected:cpx { msg_ #1 :nn } ##1##2
-      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} { } { } { } { } }
+    \\ \\ See~the~
+    \str_if_eq:nnTF {#1} { LaTeX } { LaTeX3 } {#1} ~
+    documentation~for~further~information.
   }
 %    \end{macrocode}
 % \end{macro}
-%
-% \begin{macro}[pTF]{\msg_if_more_text:N, \msg_if_more_text:c}
-% \begin{macro}[aux]{\msg_no_more_text:xxxx}
-%   A test to see if any more text is available, using a
-%   permanently-empty text function.
-%   ^^A It would be more efficient to not define the more-text when absent.
+% 
+% \begin{macro}{\@@_class_new:nn}
 %    \begin{macrocode}
-\prg_new_conditional:Npnn \msg_if_more_text:N #1 { p , T , F , TF }
-  {
-    \cs_if_eq:NNTF #1 \msg_no_more_text:xxxx
-      { \prg_return_false:  }
-      { \prg_return_true: }
-  }
-\cs_new:Npn \msg_no_more_text:xxxx #1#2#3#4 { }
-\cs_generate_variant:Nn \msg_if_more_text_p:N { c }
-\cs_generate_variant:Nn \msg_if_more_text:NT  { c }
-\cs_generate_variant:Nn \msg_if_more_text:NF  { c }
-\cs_generate_variant:Nn \msg_if_more_text:NTF { c }
+\group_begin:
+  \cs_set_protected:Npn \@@_class_new:nn #1#2
+    {
+      \prop_new:c { l_@@_redirect_ #1 _prop }
+      \cs_new_protected:cpn { @@_ #1 _code:nnnnnn } ##1##2##3##4##5##6 {#2}
+      \cs_new_protected:cpn { msg_ #1 :nnnnnn } ##1##2##3##4##5##6
+        {
+          \@@_use:nnnnnnn {#1} {##1} {##2}
+            { \tl_to_str:n {##3} } { \tl_to_str:n {##4} }
+            { \tl_to_str:n {##5} } { \tl_to_str:n {##6} }
+        }
+      \cs_new_protected:cpx { msg_ #1 :nnnnn } ##1##2##3##4##5
+        { \exp_not:c { msg_ #1 :nnnnnn } {##1} {##2} {##3} {##4} {##5} { } }
+      \cs_new_protected:cpx { msg_ #1 :nnnn } ##1##2##3##4
+        { \exp_not:c { msg_ #1 :nnnnnn } {##1} {##2} {##3} {##4} { } { } }
+      \cs_new_protected:cpx { msg_ #1 :nnn } ##1##2##3
+        { \exp_not:c { msg_ #1 :nnnnnn } {##1} {##2} {##3} { } { } { } }
+      \cs_new_protected:cpx { msg_ #1 :nn } ##1##2
+        { \exp_not:c { msg_ #1 :nnnnnn } {##1} {##2} { } { } { } { } }
+      \cs_new_protected:cpn { msg_ #1 :nnxxxx } ##1##2##3##4##5##6
+        {
+          \use:x
+            {
+              \@@_use:nnnnnnn 
+                { \exp_not:n {#1} } { \exp_not:n {##1} } { \exp_not:n {##2} }
+                {##3} {##4} {##5} {##6}
+            }
+        }
+      \cs_new_protected:cpx { msg_ #1 :nnxxx } ##1##2##3##4##5
+        { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} {##5} { } }
+      \cs_new_protected:cpx { msg_ #1 :nnxx } ##1##2##3##4
+        { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} { } { } }
+      \cs_new_protected:cpx { msg_ #1 :nnx } ##1##2##3
+        { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} { } { } { } }
+    }
 %    \end{macrocode}
 % \end{macro}
-% \end{macro}
 %
 % \begin{macro}
-%  {
-%    \msg_fatal:nnxxxx ,
-%    \msg_fatal:nnxxx  ,
-%    \msg_fatal:nnxx   ,
-%    \msg_fatal:nnx    ,
-%    \msg_fatal:nn
-%  }
+%   {
+%     \msg_fatal:nnnnnn ,
+%     \msg_fatal:nnnnn  ,
+%     \msg_fatal:nnnn   ,
+%     \msg_fatal:nnn    ,
+%     \msg_fatal:nn     ,
+%     \msg_fatal:nnxxxx ,
+%     \msg_fatal:nnxxx  ,
+%     \msg_fatal:nnxx   ,
+%     \msg_fatal:nnx
+%   }
 %   For fatal errors, after the error message \TeX{} bails out.
 %    \begin{macrocode}
-\msg_class_set:nn { fatal }
-  {
-    \msg_interrupt:xxx
-      { \msg_fatal_text:n {#1} : ~ "#2" }
-      {
-        \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
-        \msg_see_documentation_text:n {#1}
-      }
-      { \c_msg_fatal_text_tl }
-    \tex_end:D
-  }
+  \@@_class_new:nn { fatal }
+    {
+      \msg_interrupt:nnn
+        { \msg_fatal_text:n {#1} : ~ "#2" }
+        {
+          \use:c { \c_@@_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
+          \msg_see_documentation_text:n {#1}
+        }
+        { \c_msg_fatal_text_tl }
+      \tex_end:D
+    }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}
 %   {
+%     \msg_critical:nnnnnn ,
+%     \msg_critical:nnnnn  ,
+%     \msg_critical:nnnn   ,
+%     \msg_critical:nnn    ,
+%     \msg_critical:nn     ,
 %     \msg_critical:nnxxxx ,
 %     \msg_critical:nnxxx  ,
 %     \msg_critical:nnxx   ,
-%     \msg_critical:nnx    ,
-%     \msg_critical:nn
-%  }
+%     \msg_critical:nnx
+%   }
 %   Not quite so bad: just end the current file.
 %    \begin{macrocode}
-\msg_class_set:nn { critical }
-  {
-    \msg_interrupt:xxx
-      { \msg_critical_text:n {#1} : ~ "#2" }
-      {
-        \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
-        \msg_see_documentation_text:n {#1}
-      }
-      { \c_msg_critical_text_tl }
-    \tex_endinput:D
-  }
+  \@@_class_new:nn { critical }
+    {
+      \msg_interrupt:nnn
+        { \msg_critical_text:n {#1} : ~ "#2" }
+        {
+          \use:c { \c_@@_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
+          \msg_see_documentation_text:n {#1}
+        }
+        { \c_msg_critical_text_tl }
+      \tex_endinput:D
+    }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}
 %   {
+%     \msg_error:nnnnnn ,
+%     \msg_error:nnnnn  ,
+%     \msg_error:nnnn   ,
+%     \msg_error:nnn    ,
+%     \msg_error:nn     ,
 %     \msg_error:nnxxxx ,
 %     \msg_error:nnxxx  ,
 %     \msg_error:nnxx   ,
-%     \msg_error:nnx    ,
-%     \msg_error:nn
+%     \msg_error:nnx
 %   }
-%   For an error, the interrupt routine is called, then any recovery code
-%   is tried.
+% \begin{macro}[aux]{\@@_error:cnnnnn, \@@_no_more_text:nnnn}
+%   For an error, the interrupt routine is called.  We check if there is
+%   a \enquote{more text} by comparing that control sequence with a
+%   permanently empty text.
 %    \begin{macrocode}
-\msg_class_set:nn { error }
-  {
-    \msg_if_more_text:cTF { \c_msg_more_text_prefix_tl #1 / #2 }
-      {
-        \msg_interrupt:xxx
-          { \msg_error_text:n {#1} : ~ "#2" }
-          {
-            \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
-            \msg_see_documentation_text:n {#1}
-          }
-          { \use:c { \c_msg_more_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6} }
-     }
-     {
-        \msg_interrupt:xxx
-          { \msg_error_text:n {#1} : ~ "#2" }
-          {
-            \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
-            \msg_see_documentation_text:n {#1}
-          }
-          { }
-     }
-  }
+  \@@_class_new:nn { error }
+    {
+      \@@_error:cnnnnn
+        { \c_@@_more_text_prefix_tl #1 / #2 }
+        {#3} {#4} {#5} {#6}
+        {
+          \msg_interrupt:nnn
+            { \msg_error_text:n {#1} : ~ "#2" }
+            {
+              \use:c { \c_@@_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
+              \msg_see_documentation_text:n {#1}
+            }
+       }
+    }
+  \cs_new_protected:Npn \@@_error:cnnnnn #1#2#3#4#5#6
+    {
+      \cs_if_eq:cNTF {#1} \@@_no_more_text:nnnn
+        { #6 { } }
+        { #6 { \use:c {#1} {#2} {#3} {#4} {#5} } }
+    }
+  \cs_new:Npn \@@_no_more_text:nnnn #1#2#3#4 { }
 %    \end{macrocode}
 % \end{macro}
+% \end{macro}
 %
 % \begin{macro}
 %   {
+%     \msg_warning:nnnnnn ,
+%     \msg_warning:nnnnn  ,
+%     \msg_warning:nnnn   ,
+%     \msg_warning:nnn    ,
+%     \msg_warning:nn     ,
 %     \msg_warning:nnxxxx ,
 %     \msg_warning:nnxxx  ,
 %     \msg_warning:nnxx   ,
-%     \msg_warning:nnx    ,
-%     \msg_warning:nn
+%     \msg_warning:nnx
 %   }
 %   Warnings are printed to the terminal.
 %    \begin{macrocode}
-\msg_class_set:nn { warning }
-  {
-    \msg_term:x
-      {
-        \msg_warning_text:n {#1} : ~ "#2" \\ \\
-        \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
-      }
-  }
+  \@@_class_new:nn { warning }
+    {
+      \msg_term:n
+        {
+          \msg_warning_text:n {#1} : ~ "#2" \\ \\
+          \use:c { \c_@@_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
+        }
+    }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}
 %   {
+%     \msg_info:nnnnnn ,
+%     \msg_info:nnnnn  ,
+%     \msg_info:nnnn   ,
+%     \msg_info:nnn    ,
+%     \msg_info:nn     ,
 %     \msg_info:nnxxxx ,
 %     \msg_info:nnxxx  ,
 %     \msg_info:nnxx   ,
-%     \msg_info:nnx    ,
-%     \msg_info:nn
+%     \msg_info:nnx
 %   }
 %   Information only goes into the log.
 %    \begin{macrocode}
-\msg_class_set:nn { info }
-  {
-    \msg_log:x
-      {
-        \msg_info_text:n {#1} : ~ "#2" \\ \\
-        \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
-      }
-  }
+  \@@_class_new:nn { info }
+    {
+      \msg_log:n
+        {
+          \msg_info_text:n {#1} : ~ "#2" \\ \\
+          \use:c { \c_@@_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
+        }
+    }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}
 %   {
+%     \msg_log:nnnnnn ,
+%     \msg_log:nnnnn  ,
+%     \msg_log:nnnn   ,
+%     \msg_log:nnn    ,
+%     \msg_log:nn     ,
 %     \msg_log:nnxxxx ,
 %     \msg_log:nnxxx  ,
 %     \msg_log:nnxx   ,
-%     \msg_log:nnx    ,
-%     \msg_log:nn
+%     \msg_log:nnx
 %   }
 %   \enquote{Log} data is very similar to information, but with no extras
 %   added.
 %    \begin{macrocode}
-\msg_class_set:nn { log }
-  {
-    \msg_log:x
-      { \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6} }
-  }
+  \@@_class_new:nn { log }
+    {
+      \iow_wrap:nnnN
+        { \use:c { \c_@@_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6} }
+        { } { } \iow_log:n
+    }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}
 %   {
+%     \msg_none:nnnnnn ,
+%     \msg_none:nnnnn  ,
+%     \msg_none:nnnn   ,
+%     \msg_none:nnn    ,
+%     \msg_none:nn     ,
 %     \msg_none:nnxxxx ,
 %     \msg_none:nnxxx  ,
 %     \msg_none:nnxx   ,
-%     \msg_none:nnx    ,
-%     \msg_none:nn
+%     \msg_none:nnx
 %   }
 %   The \texttt{none} message type is needed so that input can be gobbled.
 %    \begin{macrocode}
-\msg_class_set:nn { none } { }
+  \@@_class_new:nn { none } { }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{variable}{\l_msg_class_tl, \l_msg_current_class_tl}
+% End the group to eliminate \cs{@@_class_new:nn}.
+%    \begin{macrocode}
+\group_end:
+%    \end{macrocode}
+% 
+% \begin{macro}[aux]{\@@_class_chk_exist:nT}
+%   Checking that a message class exists.  We build this from
+%   \cs{cs_if_free:cTF} rather than \cs{cs_if_exist:cTF} because that
+%   avoids reading the second argument earlier than necessary.
+%    \begin{macrocode}
+\cs_new:Npn \@@_class_chk_exist:nT #1
+  {
+    \cs_if_free:cTF { @@_ #1 _code:nnnnnn }
+      { \@@_kernel_error:nnx { kernel } { message-class-unknown } {#1} }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{variable}{\l_@@_class_tl, \l_@@_current_class_tl}
 %   Support variables needed for the redirection system.
 %    \begin{macrocode}
-\tl_new:N \l_msg_class_tl
-\tl_new:N \l_msg_current_class_tl
+\tl_new:N \l_@@_class_tl
+\tl_new:N \l_@@_current_class_tl
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_msg_redirect_classes_prop, \l_msg_redirect_names_prop}
-%   For filtering messages, a list of all messages and of those which have
-%   to be modified is required.
+% \begin{variable}{\l_@@_redirect_prop}
+%   For redirection of individually-named messages
 %    \begin{macrocode}
-\prop_new:N \l_msg_redirect_classes_prop
-\prop_new:N \l_msg_redirect_names_prop
+\prop_new:N \l_@@_redirect_prop
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_msg_redirect_prop}
-%   For redirection of individually-named messages
+% \begin{variable}{\l_@@_hierarchy_seq}
+%   During redirection, split the message name into a sequence with
+%   items |{/module/submodule}|, |{/module}|, and |{}|.
 %    \begin{macrocode}
-\prop_new:N \l_msg_redirect_prop
+\seq_new:N \l_@@_hierarchy_seq
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_msg_use_direct_bool}
-%   Used to force redirection when a name is given directly.
+% \begin{variable}{\l_@@_class_loop_seq}
+%   Classes encountered when following redirections to check for loops.
 %    \begin{macrocode}
-\bool_new:N \l_msg_use_direct_bool
+\seq_new:N \l_@@_class_loop_seq
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{macro}[int]{\msg_use:nnnnxxxx}
-% \begin{macro}[aux]{\msg_use_code:, \msg_use_or_change_class:}
-% \begin{macro}[aux]{\msg_use_aux_i:nn, \msg_use_aux_ii:nn}
-% \begin{macro}[aux]{\msg_use_aux_iii:w}
-% \begin{macro}[aux]{\msg_use_aux_iv:w}
-% \begin{macro}[aux]{\msg_use_aux_v:}
-%   Actually using a message is a multi-step process. First, some safety
-%   checks on the message and class requested. The code and arguments are
-%   then stored to avoid passing them around.
+% \begin{macro}[int]{\@@_use:nnnnnnn}
+% \begin{macro}[aux]
+%   {
+%     \@@_use_redirect_name:n  , \@@_use_hierarchy:nwwN ,
+%     \@@_use_redirect_module:n, \@@_use_code:
+%   }
+%   Actually using a message is a multi-step process.  First, some
+%   safety checks on the message and class requested.  The code and
+%   arguments are then stored to avoid passing them around.  The
+%   assignment to \cs{@@_use_code:} is similar to \cs{tl_set:Nn}.
+%   The message is eventually produced with whatever \cs{l_@@_class_tl}
+%   is when \cs{@@_use_code:} is called.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_use:nnnnxxxx #1#2#3#4#5#6#7#8
+\cs_new_protected:Npn \@@_use:nnnnnnn #1#2#3#4#5#6#7
   {
-    \msg_if_exist:nnTF {#3} {#4}
+    \msg_if_exist:nnTF {#2} {#3}
       {
-        \cs_if_exist:cTF { msg_ #1 :nnxxxx }
+        \@@_class_chk_exist:nT {#1}
           {
-            \tl_set:Nn \l_msg_current_class_tl {#1}
-            \cs_set_protected_nopar:Npx \msg_use_code: { \exp_not:n {#2} }
-            \cs_set_protected_nopar:Npn \msg_use_or_change_class:
+            \tl_set:Nn \l_@@_current_class_tl {#1}
+            \cs_set_protected_nopar:Npx \@@_use_code:
               {
-                \tl_if_eq:NNTF \l_msg_current_class_tl \l_msg_class_tl
-                  { \msg_use_code: }
+                \exp_not:n
                   {
-                    \use:c { msg_ \l_msg_class_tl :nnxxxx }
-                      {#3} {#4} {#5} {#6} {#7} {#8}
+                    \use:c { @@_ \l_@@_class_tl _code:nnnnnn }
+                      {#2} {#3} {#4} {#5} {#6} {#7}
                   }
               }
-            \bool_if:NTF \l_msg_use_direct_bool
-              {
-                \bool_set_false:N \l_msg_use_direct_bool
-                \msg_use_code:
-              }
-              { \msg_use_aux_i:nn {#3} {#4} }
+            \@@_use_redirect_name:n { #2 / #3 }
           }
-          { \msg_kernel_error:nnx { msg } { message-class-unknown } {#1} }
       }
-      { \msg_kernel_error:nnxx { msg } { message-unknown } {#3} {#4} }
+      { \@@_kernel_error:nnxx { kernel } { message-unknown } {#2} {#3} }
   }
-\cs_new_protected_nopar:Npn \msg_use_code: { }
-\cs_new_protected_nopar:Npn \msg_use_or_change_class: { }
+\cs_new_protected_nopar:Npn \@@_use_code: { }
 %    \end{macrocode}
-%   The first check is for a individual message redirection. If this applies
-%   then no further redirection is attempted.
+%   The first check is for a individual message redirection. If this
+%   applies then no further redirection is attempted.  Otherwise, split
+%   the message name into \texttt{module/submodule/message} (with an
+%   arbitrary number of slashes), and store |{/module/submodule}|,
+%   |{/module}| and |{}| into \cs{l_@@_hierarchy_seq}.  We will then
+%   map through this sequence, applying the most specific redirection.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_use_aux_i:nn #1#2
+\cs_new_protected:Npn \@@_use_redirect_name:n #1
   {
-    \prop_get:NnNTF \l_msg_redirect_prop { #1 / #2 } \l_msg_class_tl
+    \prop_get:NnNTF \l_@@_redirect_prop { / #1 } \l_@@_class_tl
+      { \@@_use_code: }
       {
-        \bool_set_true:N \l_msg_use_direct_bool
-        \msg_use_or_change_class:
+        \seq_clear:N \l_@@_hierarchy_seq
+        \@@_use_hierarchy:nwwN { }
+          #1 \q_mark \@@_use_hierarchy:nwwN
+          /  \q_mark \use_none_delimit_by_q_stop:w
+          \q_stop
+        \@@_use_redirect_module:n { }
       }
-      { \msg_use_aux_ii:nn {#1} {#2} }
   }
-%    \end{macrocode}
-%   Next check if there is a redirection by module or by submodule.
-%    \begin{macrocode}
-\cs_new_protected:Npn \msg_use_aux_ii:nn #1#2
+\cs_new_protected:Npn \@@_use_hierarchy:nwwN #1#2 / #3 \q_mark #4
   {
-    \prop_get:coNTF { l_msg_redirect_ \l_msg_current_class_tl _ prop }
-      { \msg_use_aux_iii:w #1 / #2 / \q_stop } \l_msg_class_tl
-      { \msg_use_or_change_class: }
-      {
-        \prop_get:coNTF { l_msg_redirect_ \l_msg_current_class_tl _ prop }
-          { \msg_use_aux_iv:w #1 / #2 \q_stop } \l_msg_class_tl
-        { \msg_use_or_change_class: }
-        { \msg_use_aux_v: }
-      }
+    \seq_put_left:Nn \l_@@_hierarchy_seq {#1}
+    #4 { #1 / #2 } #3 \q_mark #4
   }
-\cs_new:Npn \msg_use_aux_iii:w  #1 / #2 / #3 \q_stop { #1 / #2 }
-\cs_new:Npn \msg_use_aux_iv:w #1 / #2 \q_stop { #1 }
 %    \end{macrocode}
-%   Finally test for redirection of an entire class.
+%   At this point, the items of \cs{l_@@_hierarchy_seq} are the
+%   various levels at which we should look for a redirection.
+%   Redirections which are less specific than the argument of
+%   \cs{@@_use_redirect_module:n} are not attempted.  This argument is
+%   empty for a class redirection, \texttt{/module} for a module
+%   redirection, \emph{etc.}  Loop through the sequence to find the most
+%   specific redirection, with module |##1|.  The loop is interrupted
+%   after testing for a redirection for |##1| equal to the argument |#1|
+%   (least specific redirection allowed).  When a redirection is found,
+%   break the mapping, then if the redirection targets the same class,
+%   output the code with that class, and otherwise set the target as the
+%   new current class, and search for further redirections.  Those
+%   redirections should be at least as specific as |##1|.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_use_aux_v:
+\cs_new_protected:Npn \@@_use_redirect_module:n #1
   {
-    \prop_get:cnNF { l_msg_redirect_ \l_msg_current_class_tl _ prop }
-      { * } \l_msg_class_tl
-      { \tl_set_eq:NN \l_msg_class_tl \l_msg_current_class_tl }
-    \msg_use_or_change_class:
+    \seq_map_inline:Nn \l_@@_hierarchy_seq
+      {
+        \prop_get:cnNTF { l_@@_redirect_ \l_@@_current_class_tl _prop }
+          {##1} \l_@@_class_tl
+          {
+            \seq_map_break:n
+              {
+                \tl_if_eq:NNTF \l_@@_current_class_tl \l_@@_class_tl
+                  { \@@_use_code: }
+                  {
+                    \tl_set_eq:NN \l_@@_current_class_tl \l_@@_class_tl
+                    \@@_use_redirect_module:n {##1}
+                  }
+              }
+          }
+          {
+            \str_if_eq:nnT {##1} {#1}
+              {
+                \tl_set_eq:NN \l_@@_class_tl \l_@@_current_class_tl
+                \seq_map_break:n { \@@_use_code: }
+              }
+          }
+      }
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
 %
-% \begin{macro}{\msg_redirect_class:nn}
-% \begin{macro}[aux]{\msg_redirect_class_aux:nnn, \msg_redirect_class_aux:nVn}
-%   Converts class one into class two.
+% \begin{macro}{\msg_redirect_name:nnn}
+%   Named message will always use the given class even if that class is
+%   redirected further.  An empty target class cancels any existing
+%   redirection for that message.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_redirect_class:nn #1#2
-  {
-    \cs_if_exist:cTF { msg_ #1 :nnxxxx }
-      {
-        \cs_if_exist:cTF { msg_ #2 :nnxxxx }
-          {
-            \tl_set:Nn \l_msg_current_class_tl {#1}
-            \msg_redirect_class_aux:nnn {#1} {#2} {#2}
-          }
-          { \msg_kernel_error:nnx { msg } { message-class-unknown } {#2} }
-      }
-      { \msg_kernel_error:nnx { msg } { message-class-unknown } {#1} }
-  }
-\cs_new_protected:Npn \msg_redirect_class_aux:nnn #1#2#3
+\cs_new_protected:Npn \msg_redirect_name:nnn #1#2#3
   {
-    \prop_get:cnNTF { l_msg_redirect_ #2 _prop } { * } \l_msg_class_tl
+    \tl_if_empty:nTF {#3}
+      { \prop_remove:Nn \l_@@_redirect_prop { / #1 / #2 } }
       {
-        \tl_if_eq:NNTF \l_msg_class_tl \l_msg_current_class_tl
-          { \msg_kernel_error:nnxx { msg } { message-loop } {#1} {#3} }
-          { \msg_redirect_class_aux:nVn {#1} \l_msg_class_tl {#3} }
+        \@@_class_chk_exist:nT {#3}
+          { \prop_put:Nnn \l_@@_redirect_prop { / #1 / #2 } {#3} }
       }
-      { \prop_put:cnn { l_msg_redirect_ #1 _prop } { * } {#3} }
   }
-\cs_generate_variant:Nn \msg_redirect_class_aux:nnn { nV }
 %    \end{macrocode}
 % \end{macro}
-% \end{macro}
 %
-% \begin{macro}{\msg_redirect_module:nnn}
-% \begin{macro}[aux]
-%   {\msg_redirect_module_aux:nnnn, \msg_redirect_module_aux:nnVn}
-%   For when all messages of a class should be altered for a given module.
+% \begin{macro}{\msg_redirect_class:nn, \msg_redirect_module:nnn}
+% \begin{macro}[aux]{\@@_redirect:nnn, \@@_redirect_loop_chk:nnn}
+% \begin{macro}[aux]{\@@_redirect_loop_list:n}
+%   If the target class is empty, eliminate the corresponding
+%   redirection.  Otherwise, add the redirection.  We must then check
+%   for a loop: as an initialization, we start by storing the initial
+%   class in \cs{l_@@_current_class_tl}.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_redirect_module:nnn #1#2#3
+\cs_new_protected_nopar:Npn \msg_redirect_class:nn
+  { \@@_redirect:nnn { } }
+\cs_new_protected:Npn \msg_redirect_module:nnn #1
+  { \@@_redirect:nnn { / #1 } }
+\cs_new_protected:Npn \@@_redirect:nnn #1#2#3
   {
-    \cs_if_exist:cTF { msg_ #2 :nnxxxx }
+    \@@_class_chk_exist:nT {#2}
       {
-        \cs_if_exist:cTF { msg_ #3 :nnxxxx }
+        \tl_if_empty:nTF {#3}
+          { \prop_remove:cn { l_@@_redirect_ #2 _prop } {#1} }
           {
-            \tl_set:Nn \l_msg_current_class_tl {#1}
-            \msg_redirect_module_aux:nnnn {#1} {#2} {#3} {#3}
+            \@@_class_chk_exist:nT {#3}
+              {
+                \prop_put:cnn { l_@@_redirect_ #2 _prop } {#1} {#3}
+                \tl_set:Nn \l_@@_current_class_tl {#2}
+                \seq_clear:N \l_@@_class_loop_seq
+                \@@_redirect_loop_chk:nnn {#2} {#3} {#1}
+              }
           }
-          { \msg_kernel_error:nnx { msg } { message-class-unknown } {#3} }
       }
-      { \msg_kernel_error:nnx { msg } { message-class-unknown } {#2} }
   }
-\cs_new_protected:Npn \msg_redirect_module_aux:nnnn #1#2#3#4
+%    \end{macrocode}
+%   Since multiple redirections can only happen with increasing
+%   specificity, a loop requires that all steps are of the same
+%   specificity.  The new redirection can thus only create a loop with
+%   other redirections for the exact same module, |#1|, and not
+%   submodules.  After some initialization above, follow redirections
+%   with \cs{l_@@_class_tl}, and keep track in
+%   \cs{l_@@_class_loop_seq} of the various classes encountered.  A
+%   redirection from a class to itself, or the absence of redirection
+%   both mean that there is no loop.  A redirection to the initial class
+%   marks a loop.  To break it, we must decide which redirection to
+%   cancel.  The user most likely wants the newly added redirection to
+%   hold with no further redirection.  We thus remove the redirection
+%   starting from |#2|, target of the new redirection.  Note that no
+%   message is emitted by any of the underlying functions: otherwise we
+%   may get an infinite loop because of a message from the message
+%   system itself.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_redirect_loop_chk:nnn #1#2#3
   {
-    \prop_get:cnNTF { l_msg_redirect_ #3 _prop } {#1} \l_msg_class_tl
+    \seq_put_right:Nn \l_@@_class_loop_seq {#1}
+    \prop_get:cnNT { l_@@_redirect_ #1 _prop } {#3} \l_@@_class_tl
       {
-        \tl_if_eq:NNTF \l_msg_class_tl \l_msg_current_class_tl
-          { \msg_kernel_error:nnxx { msg } { message-loop } {#2} {#4} }
-          { \msg_redirect_moduel_aux:nVn {#1} {#2} \l_msg_class_tl {#4} }
+        \str_if_eq_x:nnF { \l_@@_class_tl } {#1}
+          {
+            \tl_if_eq:NNTF \l_@@_class_tl \l_@@_current_class_tl
+              {
+                \prop_put:cnn { l_@@_redirect_ #2 _prop } {#3} {#2}
+                \@@_kernel_warning:nnxxxx { kernel } { message-redirect-loop }
+                  { \seq_item:Nn \l_@@_class_loop_seq { \c_one } }
+                  { \seq_item:Nn \l_@@_class_loop_seq { \c_two } }
+                  {#3}
+                  {
+                    \seq_map_function:NN \l_@@_class_loop_seq
+                      \@@_redirect_loop_list:n
+                    { \seq_item:Nn \l_@@_class_loop_seq { \c_one } }
+                  }
+              }
+              { \@@_redirect_loop_chk:onn \l_@@_class_tl {#2} {#3} }
+          }
       }
-      { \prop_put:cnn { l_msg_redirect_ #2 _prop } {#1} {#4} }
   }
-\cs_generate_variant:Nn \msg_redirect_module_aux:nnnn { nnV }
+\cs_generate_variant:Nn \@@_redirect_loop_chk:nnn { o }
+\cs_new:Npn \@@_redirect_loop_list:n #1 { {#1} ~ => ~ }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
-%
-% \begin{macro}{\msg_redirect_name:nnn}
-%   Named message will always use the given class even if that class is
-%   redirected further.
-%    \begin{macrocode}
-\cs_new_protected:Npn \msg_redirect_name:nnn #1#2#3
-  {
-    \cs_if_exist:cTF { msg_ #3 :nnxxxx }
-      { \prop_put:Nnn \l_msg_redirect_prop { #1 / #2 } {#3} }
-      { \msg_kernel_error:nnx { msg } { message-class-unknown } {#3} }
-  }
-%    \end{macrocode}
 % \end{macro}
 %
 % \subsection{Kernel-specific functions}
 %
-% \begin{macro}{\msg_kernel_new:nnnn}
-% \begin{macro}{\msg_kernel_new:nnn}
-% \begin{macro}{\msg_kernel_set:nnnn}
-% \begin{macro}{\msg_kernel_set:nnn}
+% \begin{macro}{\@@_kernel_new:nnnn, \@@_kernel_new:nnn}
+% \begin{macro}{\@@_kernel_set:nnnn, \@@_kernel_set:nnn}
 %   The kernel needs some messages of its own. These are created using
 %   pre-built functions. Two functions are provided: one more general
 %   and one which only has the short text part.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_kernel_new:nnnn #1#2
+\cs_new_protected:Npn \@@_kernel_new:nnnn #1#2
   { \msg_new:nnnn { LaTeX } { #1 / #2 } }
-\cs_new_protected:Npn \msg_kernel_new:nnn #1#2
+\cs_new_protected:Npn \@@_kernel_new:nnn #1#2
   { \msg_new:nnn { LaTeX } { #1 / #2 } }
-\cs_new_protected:Npn \msg_kernel_set:nnnn #1#2
+\cs_new_protected:Npn \@@_kernel_set:nnnn #1#2
   { \msg_set:nnnn { LaTeX } { #1 / #2 } }
-\cs_new_protected:Npn \msg_kernel_set:nnn #1#2
+\cs_new_protected:Npn \@@_kernel_set:nnn #1#2
   { \msg_set:nnn { LaTeX } { #1 / #2 } }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
-% \end{macro}
-% \end{macro}
 %
-% \begin{macro}{\msg_kernel_fatal:nnxxxx}
-% \begin{macro}{\msg_kernel_fatal:nnxxx}
-% \begin{macro}{\msg_kernel_fatal:nnxx}
-% \begin{macro}{\msg_kernel_fatal:nnx}
-% \begin{macro}{\msg_kernel_fatal:nn}
-%   Fatal kernel errors cannot be re-defined.
+% \begin{macro}[aux]{\@@_kernel_class_new:nn}
+% \begin{macro}[aux]{\@@_kernel_class_new_aux:nn}
+%   All the functions for kernel messages come in variants ranging
+%   from~$0$ to~$4$ arguments.  Those with less than~$4$ arguments are
+%   defined in terms of the $4$-argument variant, in a way very similar
+%   to \cs{msg_class_set:nn}.  This auxiliary is destroyed at the end of
+%   the group.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_kernel_fatal:nnxxxx #1#2#3#4#5#6
-  {
-    \msg_interrupt:xxx
-      { \msg_fatal_text:n { LaTeX } : ~ "#1 / #2" }
-      {
-        \use:c { \c_msg_text_prefix_tl LaTeX / #1 / #2 }
-          {#3} {#4} {#5} {#6}
-        \msg_see_documentation_text:n { LaTeX3 }
-      }
-      { \c_msg_fatal_text_tl }
-    \tex_end:D
-  }
-\cs_new_protected:Npn \msg_kernel_fatal:nnxxx #1#2#3#4#5
-  {\msg_kernel_fatal:nnxxxx {#1} {#2} {#3} {#4} {#5} { } }
-\cs_new_protected:Npn \msg_kernel_fatal:nnxx #1#2#3#4
-  { \msg_kernel_fatal:nnxxxx {#1} {#2} {#3} {#4} { } { } }
-\cs_new_protected:Npn \msg_kernel_fatal:nnx #1#2#3
-  { \msg_kernel_fatal:nnxxxx {#1} {#2} {#3} { } { } { } }
-\cs_new_protected:Npn \msg_kernel_fatal:nn #1#2
-  { \msg_kernel_fatal:nnxxxx {#1} {#2} { } { } { } { } }
+\group_begin:
+  \cs_set_protected:Npn \@@_kernel_class_new:nn #1
+    { \@@_kernel_class_new_aux:nn { kernel_ #1 } }
+  \cs_set_protected:Npn \@@_kernel_class_new_aux:nn #1#2
+    {
+      \cs_new_protected:cpn { @@_ #1 :nnnnnn } ##1##2 {#2}
+      \cs_new_protected:cpx { @@_ #1 :nnnnn } ##1##2##3##4##5
+        { \exp_not:c { @@_ #1 :nnnnnn } {##1} {##2} {##3} {##4} {##5} { } }
+      \cs_new_protected:cpx { @@_ #1 :nnnn } ##1##2##3##4
+        { \exp_not:c { @@_ #1 :nnnnnn } {##1} {##2} {##3} {##4} { } { } }
+      \cs_new_protected:cpx { @@_ #1 :nnn } ##1##2##3
+        { \exp_not:c { @@_ #1 :nnnnnn } {##1} {##2} {##3} { } { } { } }
+      \cs_new_protected:cpx { @@_ #1 :nn } ##1##2
+        { \exp_not:c { @@_ #1 :nnnnnn } {##1} {##2} { } { } { } { } }
+      \cs_new_protected:cpx { @@_ #1 :nnxxxx } ##1##2##3##4##5##6
+        {
+          \use:x
+            {
+              \exp_not:c { @@_ #1 :nnnnnn }
+                { \exp_not:N \exp_not:n {##1} }
+                { \exp_not:N \exp_not:n {##2} }
+                {##3} {##4} {##5} {##6}
+            }
+        }
+      \cs_new_protected:cpx { @@_ #1 :nnxxx } ##1##2##3##4##5
+        { \exp_not:c { @@_ #1 :nnxxxx } {##1} {##2} {##3} {##4} {##5} { } }
+      \cs_new_protected:cpx { @@_ #1 :nnxx } ##1##2##3##4
+        { \exp_not:c { @@_ #1 :nnxxxx } {##1} {##2} {##3} {##4} { } { } }
+      \cs_new_protected:cpx { @@_ #1 :nnx } ##1##2##3
+        { \exp_not:c { @@_ #1 :nnxxxx } {##1} {##2} {##3} { } { } { } }
+    }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
 %
-% \begin{macro}{\msg_kernel_error:nnxxxx}
-% \begin{macro}{\msg_kernel_error:nnxxx}
-% \begin{macro}{\msg_kernel_error:nnxx}
-% \begin{macro}{\msg_kernel_error:nnx}
-% \begin{macro}{\msg_kernel_error:nn}
-%   Neither can kernel errors.
+% \begin{macro}
+%   {
+%     \@@_kernel_fatal:nnnnnn ,
+%     \@@_kernel_fatal:nnnnn  ,
+%     \@@_kernel_fatal:nnnn   ,
+%     \@@_kernel_fatal:nnn    ,
+%     \@@_kernel_fatal:nn     ,
+%     \@@_kernel_fatal:nnxxxx ,
+%     \@@_kernel_fatal:nnxxx  ,
+%     \@@_kernel_fatal:nnxx   ,
+%     \@@_kernel_fatal:nnx    ,
+%     \@@_kernel_error:nnnnnn ,
+%     \@@_kernel_error:nnnnn  ,
+%     \@@_kernel_error:nnnn   ,
+%     \@@_kernel_error:nnn    ,
+%     \@@_kernel_error:nn     ,
+%     \@@_kernel_error:nnxxxx ,
+%     \@@_kernel_error:nnxxx  ,
+%     \@@_kernel_error:nnxx   ,
+%     \@@_kernel_error:nnx
+%   }
+%   Neither fatal kernel errors nor kernel errors can be redirected.  We
+%   directly use the code for (non-kernel) fatal errors and errors,
+%   adding the \enquote{\LaTeX{}} module name.  Three functions are
+%   already defined by \pkg{l3basics}; we need to undefine them to avoid
+%   errors.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_kernel_error:nnxxxx #1#2#3#4#5#6
-  {
-    \msg_if_more_text:cTF { \c_msg_more_text_prefix_tl LaTeX / #1 / #2 }
-      {
-        \msg_interrupt:xxx
-          { \msg_error_text:n { LaTeX } : ~ " #1 / #2 " }
-          {
-            \use:c { \c_msg_text_prefix_tl LaTeX / #1 / #2 }
-              {#3} {#4} {#5} {#6}
-            \msg_see_documentation_text:n { LaTeX3 }
-          }
-          {
-            \use:c { \c_msg_more_text_prefix_tl LaTeX / #1 / #2 }
-              {#3} {#4} {#5} {#6}
-          }
-      }
-      {
-        \msg_interrupt:xxx
-          { \msg_error_text:n { LaTeX } : ~ " #1 / #2 " }
-          {
-            \use:c { \c_msg_text_prefix_tl LaTeX / #1 / #2 }
-              {#3} {#4} {#5} {#6}
-            \msg_see_documentation_text:n { LaTeX3 }
-          }
-          { }
-      }
-  }
-\cs_new_protected:Npn \msg_kernel_error:nnxxx #1#2#3#4#5
-  {\msg_kernel_error:nnxxxx {#1} {#2} {#3} {#4} {#5} { } }
-\cs_gset_protected:Npn \msg_kernel_error:nnxx #1#2#3#4
-  { \msg_kernel_error:nnxxxx {#1} {#2} {#3} {#4} { } { } }
-\cs_gset_protected:Npn \msg_kernel_error:nnx #1#2#3
-  { \msg_kernel_error:nnxxxx {#1} {#2} {#3} { } { } { } }
-\cs_gset_protected:Npn \msg_kernel_error:nn #1#2
-  { \msg_kernel_error:nnxxxx {#1} {#2} { } { } { } { } }
+  \@@_kernel_class_new:nn { fatal }
+    { \@@_fatal_code:nnnnnn { LaTeX } { #1 / #2 } }
+  \cs_undefine:N \@@_kernel_error:nnxx
+  \cs_undefine:N \@@_kernel_error:nnx
+  \cs_undefine:N \@@_kernel_error:nn
+  \@@_kernel_class_new:nn { error }
+    { \@@_error_code:nnnnnn { LaTeX } { #1 / #2 } }
 %    \end{macrocode}
 % \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
 %
-% \begin{macro}{\msg_kernel_warning:nnxxxx}
-% \begin{macro}{\msg_kernel_warning:nnxxx}
-% \begin{macro}{\msg_kernel_warning:nnxx}
-% \begin{macro}{\msg_kernel_warning:nnx}
-% \begin{macro}{\msg_kernel_warning:nn}
-% \begin{macro}{\msg_kernel_info:nnxxxx}
-% \begin{macro}{\msg_kernel_info:nnxxx}
-% \begin{macro}{\msg_kernel_info:nnxx}
-% \begin{macro}{\msg_kernel_info:nnx}
-% \begin{macro}{\msg_kernel_info:nn}
-%   Kernel messages which can be redirected.
+% \begin{macro}
+%   {
+%     \@@_kernel_warning:nnnnnn ,
+%     \@@_kernel_warning:nnnnn  ,
+%     \@@_kernel_warning:nnnn   ,
+%     \@@_kernel_warning:nnn    ,
+%     \@@_kernel_warning:nn     ,
+%     \@@_kernel_warning:nnxxxx ,
+%     \@@_kernel_warning:nnxxx  ,
+%     \@@_kernel_warning:nnxx   ,
+%     \@@_kernel_warning:nnx    ,
+%     \@@_kernel_info:nnnnnn    ,
+%     \@@_kernel_info:nnnnn     ,
+%     \@@_kernel_info:nnnn      ,
+%     \@@_kernel_info:nnn       ,
+%     \@@_kernel_info:nn        ,
+%     \@@_kernel_info:nnxxxx    ,
+%     \@@_kernel_info:nnxxx     ,
+%     \@@_kernel_info:nnxx      ,
+%     \@@_kernel_info:nnx
+%   }
+%   Kernel messages which can be redirected simply use the machinery for
+%   normal messages, with the module name \enquote{\LaTeX{}}.
 %    \begin{macrocode}
-\prop_new:N \l_msg_redirect_kernel_warning_prop
-\cs_new_protected:Npn \msg_kernel_warning:nnxxxx #1#2#3#4#5#6
-  {
-    \msg_use:nnnnxxxx { warning }
-      {
-        \msg_term:x
-          {
-            \msg_warning_text:n { LaTeX } : ~ " #1 / #2 " \\ \\
-            \use:c { \c_msg_text_prefix_tl LaTeX / #1 / #2 }
-              {#3} {#4} {#5} {#6}
-          }
-      }
-      { LaTeX } { #1 / #2 } {#3} {#4} {#5} {#6}
-  }
-\cs_new_protected:Npn \msg_kernel_warning:nnxxx #1#2#3#4#5
-  { \msg_kernel_warning:nnxxxx {#1} {#2} {#3} {#4} {#5} { } }
-\cs_new_protected:Npn \msg_kernel_warning:nnxx #1#2#3#4
-  { \msg_kernel_warning:nnxxxx {#1} {#2} {#3} {#4} { } { } }
-\cs_new_protected:Npn \msg_kernel_warning:nnx #1#2#3
-  { \msg_kernel_warning:nnxxxx {#1} {#2} {#3} { } { } { } }
-\cs_new_protected:Npn \msg_kernel_warning:nn #1#2
-  { \msg_kernel_warning:nnxxxx {#1} {#2} { } { } { } { } }
-\prop_new:N \l_msg_redirect_kernel_info_prop
-\cs_new_protected:Npn \msg_kernel_info:nnxxxx #1#2#3#4#5#6
-  {
-    \msg_use:nnnnxxxx { info }
-      {
-        \msg_log:x
-          {
-            \msg_info_text:n { LaTeX } : ~ " #1 / #2 " \\ \\
-            \use:c { \c_msg_text_prefix_tl LaTeX / #1 / #2 }
-              {#3} {#4} {#5} {#6}
-          }
-      }
-      { LaTeX } { #1 / #2 } {#3} {#4} {#5} {#6}
-  }
-\cs_new_protected:Npn \msg_kernel_info:nnxxx #1#2#3#4#5
-  { \msg_kernel_info:nnxxxx {#1} {#2} {#3} {#4} {#5} { } }
-\cs_new_protected:Npn \msg_kernel_info:nnxx #1#2#3#4
-  { \msg_kernel_info:nnxxxx {#1} {#2} {#3} {#4} { } { } }
-\cs_new_protected:Npn \msg_kernel_info:nnx #1#2#3
-  { \msg_kernel_info:nnxxxx {#1} {#2} {#3} { } { } { } }
-\cs_new_protected:Npn \msg_kernel_info:nn #1#2
-  { \msg_kernel_info:nnxxxx {#1} {#2} { } { } { } { } }
+  \@@_kernel_class_new:nn { warning }
+    { \msg_warning:nnxxxx { LaTeX } { #1 / #2 } }
+  \@@_kernel_class_new:nn { info }
+    { \msg_info:nnxxxx { LaTeX } { #1 / #2 } }
 %    \end{macrocode}
 % \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
+%
+% End the group to eliminate \cs{@@_kernel_class_new:nn}.
+%    \begin{macrocode}
+\group_end:
+%    \end{macrocode}
 %
 % Error messages needed to actually implement the message system
 % itself.
 %    \begin{macrocode}
-\msg_kernel_new:nnnn { msg } { message-already-defined }
+\@@_kernel_new:nnnn { kernel } { message-already-defined }
   { Message~'#2'~for~module~'#1'~already~defined. }
   {
     \c_msg_coding_error_text_tl
@@ -1657,41 +1735,45 @@
     by~the~module~'#1':~this~message~already~exists.
     \c_msg_return_text_tl
   }
-\msg_kernel_new:nnnn { msg } { message-unknown }
+\@@_kernel_new:nnnn { kernel } { message-unknown }
   { Unknown~message~'#2'~for~module~'#1'. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~was~asked~to~display~a~message~called~'#2'\\
-    by~the~module~'#1'~module:~this~message~does~not~exist.
+    by~the~module~'#1':~this~message~does~not~exist.
     \c_msg_return_text_tl
   }
-\msg_kernel_new:nnnn { msg } { message-class-unknown }
+\@@_kernel_new:nnnn { kernel } { message-class-unknown }
   { Unknown~message~class~'#1'. }
   {
     LaTeX~has~been~asked~to~redirect~messages~to~a~class~'#1':\\
     this~was~never~defined.
     \c_msg_return_text_tl
   }
-\msg_kernel_new:nnnn { msg } { redirect-loop }
-  { Message~redirection~loop~for~message~class~'#1'. }
+\@@_kernel_new:nnnn { kernel } { message-redirect-loop }
+  { 
+    Message~redirection~loop~caused~by~ {#1} ~=>~ {#2}
+    \tl_if_empty:nF {#3} { ~for~module~' \use_none:n #3 ' } .
+  }
   {
-    LaTeX~has~been~asked~to~redirect~messages~in~an~infinite~loop.\\
-    The~original~message~here~has~been~lost.
-    \c_msg_return_text_tl
+    Adding~the~message~redirection~ {#1} ~=>~ {#2}
+    \tl_if_empty:nF {#3} { ~for~the~module~' \use_none:n #3 ' } ~
+    created~an~infinite~loop\\\\
+    \iow_indent:n { #4 \\\\ }
   }
 %    \end{macrocode}
 %
 % Messages for earlier kernel modules.
 %    \begin{macrocode}
-\msg_kernel_new:nnnn { kernel } { bad-number-of-arguments }
+\@@_kernel_new:nnnn { kernel } { bad-number-of-arguments }
   { Function~'#1'~cannot~be~defined~with~#2~arguments. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~has~been~asked~to~define~a~function~'#1'~with~
-    #2~arguments. \\
+    #2~arguments.~
     TeX~allows~between~0~and~9~arguments~for~a~single~function.
   }
-\msg_kernel_new:nnnn { kernel } { command-already-defined }
+\@@_kernel_new:nnnn { kernel } { command-already-defined }
   { Control~sequence~#1~already~defined. }
   {
     \c_msg_coding_error_text_tl
@@ -1700,102 +1782,123 @@
     The~current~meaning~is:\\
     \ \ #2
   }
-\msg_kernel_new:nnnn { kernel } { command-not-defined }
+\@@_kernel_new:nnnn { kernel } { command-not-defined }
   { Control~sequence~#1~undefined. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~has~been~asked~to~use~a~command~#1,~but~this~has~not~
     been~defined~yet.
   }
-\msg_kernel_new:nnnn { kernel } { out-of-registers }
+\@@_kernel_new:nnnn { kernel } { empty-search-pattern }
+  { Empty~search~pattern. }
+  {
+    \c_msg_coding_error_text_tl
+    LaTeX~has~been~asked~to~replace~an~empty~pattern~by~'#1':~that~
+    would~lead~to~an~infinite~loop!
+  }
+\@@_kernel_new:nnnn { kernel } { out-of-registers }
   { No~room~for~a~new~#1. }
   {
     TeX~only~supports~\int_use:N \c_max_register_int \
     of~each~type.~All~the~#1~registers~have~been~used.~
     This~run~will~be~aborted~now.
   }
-\msg_kernel_new:nnnn { kernel } { variable-not-defined }
-  { Variable~#1~undefined. }
+\@@_kernel_new:nnnn { kernel } { missing-colon }
+  { Function~'#1'~contains~no~':'. }
   {
     \c_msg_coding_error_text_tl
-    LaTeX~has~been~asked~to~show~a~variable~#1,~but~this~has~not~
-    been~defined~yet.
+    Code-level~functions~must~contain~':'~to~separate~the~
+    argument~specification~from~the~function~name.~This~is~
+    needed~when~defining~conditionals~or~when~building~a~
+    parameter~text~from~the~number~of~arguments~of~the~function.
   }
-\msg_kernel_new:nnnn { seq } { empty-sequence }
-  { Empty~sequence~#1. }
+\@@_kernel_new:nnnn { kernel } { protected-predicate }
+  { Predicate~'#1'~must~be~expandable. }
   {
     \c_msg_coding_error_text_tl
-    LaTeX~has~been~asked~to~recover~an~entry~from~a~sequence~that~
-    has~no~content:~that~cannot~happen!
+    LaTeX~has~been~asked~to~define~'#1'~as~a~protected~predicate.~
+    Only~expandable~tests~can~have~a~predicate~version.
   }
-\msg_kernel_new:nnnn { tl } { empty-search-pattern }
-  { Empty~search~pattern. }
+\@@_kernel_new:nnnn { kernel } { conditional-form-unknown }
+  { Conditional~form~'#1'~for~function~'#2'~unknown. }
   {
     \c_msg_coding_error_text_tl
-    LaTeX~has~been~asked~to~replace~an~empty~pattern~by~'#1':~that~%
-    would~lead~to~an~infinite~loop!
+    LaTeX~has~been~asked~to~define~the~conditional~form~'#1'~of~
+    the~function~'#2',~but~only~'TF',~'T',~'F',~and~'p'~forms~exist.
   }
-\msg_kernel_new:nnnn { scan } { already-defined }
+\@@_kernel_new:nnnn { kernel } { scanmark-already-defined }
   { Scan~mark~#1~already~defined. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~has~been~asked~to~create~a~new~scan~mark~'#1'~
     but~this~name~has~already~been~used~for~a~scan~mark.
   }
+\@@_kernel_new:nnnn { kernel } { variable-not-defined }
+  { Variable~#1~undefined. }
+  {
+    \c_msg_coding_error_text_tl
+    LaTeX~has~been~asked~to~show~a~variable~#1,~but~this~has~not~
+    been~defined~yet.
+  }
+\@@_kernel_new:nnnn { kernel } { variant-too-long }
+  { Variant~form~'#1'~longer~than~base~signature~of~'#2'. }
+  {
+    \c_msg_coding_error_text_tl
+    LaTeX~has~been~asked~to~create~a~variant~of~the~function~'#2'~
+    with~a~signature~starting~with~'#1',~but~that~is~longer~than~
+    the~signature~(part~after~the~colon)~of~'#2'.
+  }
 %    \end{macrocode}
 %
 % Some errors only appear in expandable settings,
 % hence don't need a \enquote{more-text} argument.
 %    \begin{macrocode}
-\msg_kernel_new:nnn { seq } { misused }
-  { A~sequence~was~misused. }
-\msg_kernel_new:nnn { kernel } { bad-var }
+\@@_kernel_new:nnn { kernel } { bad-variable }
   { Erroneous~variable~#1 used! }
-\msg_kernel_new:nnn { prg } { zero-step }
-  { Zero~step~size~for~stepwise~function~#1. }
-\msg_kernel_new:nnn { prg } { replicate-neg }
+\@@_kernel_new:nnn { kernel } { misused-sequence }
+  { A~sequence~was~misused. }
+\@@_kernel_new:nnn { kernel } { negative-replication }
   { Negative~argument~for~\prg_replicate:nn. }
-\msg_kernel_new:nnn { kernel } { unknown-comparison }
+\@@_kernel_new:nnn { kernel } { unknown-comparison }
   { Relation~symbol~'#1'~unknown:~use~=,~<,~>,~==,~!=,~<=,~>=. }
+\@@_kernel_new:nnn { kernel } { zero-step }
+  { Zero~step~size~for~step~function~#1. }
 %    \end{macrocode}
 %
 % Messages used by the \enquote{\texttt{show}} functions.
 %    \begin{macrocode}
-\msg_kernel_new:nnn { seq } { show }
+\@@_kernel_new:nnn { kernel } { show-clist }
   {
-    The~sequence~\token_to_str:N #1~
-    \seq_if_empty:NTF #1
+    The~comma~list~
+    \str_if_eq:nnF {#1} { \l__clist_internal_clist } { \token_to_str:N #1~}
+    \clist_if_empty:NTF #1
       { is~empty }
       { contains~the~items~(without~outer~braces): }
   }
-\msg_kernel_new:nnn { prop } { show }
+\@@_kernel_new:nnn { kernel } { show-prop }
   {
     The~property~list~\token_to_str:N #1~
     \prop_if_empty:NTF #1
       { is~empty }
       { contains~the~pairs~(without~outer~braces): }
   }
-\msg_kernel_new:nnn { clist } { show }
+\@@_kernel_new:nnn { kernel } { show-seq }
   {
-    The~comma~list~
-    \str_if_eq:nnF {#1} { \l_clist_internal_clist } { \token_to_str:N #1~}
-    \clist_if_empty:NTF #1
+    The~sequence~\token_to_str:N #1~
+    \seq_if_empty:NTF #1
       { is~empty }
       { contains~the~items~(without~outer~braces): }
   }
-\msg_kernel_new:nnn { ior } { show-no-stream }
-  { No~input~streams~are~open }
-\msg_kernel_new:nnn { ior } { show-open-streams }
-  { The~following~input~streams~are~in~use: }
-\msg_kernel_new:nnn { iow } { show-no-stream }
-  { No~output~streams~are~open }
-\msg_kernel_new:nnn { iow } { show-open-streams }
-  { The~following~output~streams~are~in~use: }
+\@@_kernel_new:nnn { kernel } { show-no-stream }
+  { No~ #1 ~streams~are~open }
+\@@_kernel_new:nnn { kernel } { show-open-streams }
+  { The~following~ #1 ~streams~are~in~use: }
 %    \end{macrocode}
 %
 % \subsection{Expandable errors}
 %
-% \begin{macro}[int]{\msg_expandable_error:n}
+% \begin{macro}[int]{\@@_expandable_error:n}
+% \begin{macro}[aux]{\@@_expandable_error:w}
 %   In expansion only context, we cannot use the normal means of
 %   reporting errors. Instead, we feed \TeX{} an undefined control
 %   sequence, \cs{LaTeX3 error:}. It is thus interrupted, and shows
@@ -1806,7 +1909,7 @@
 %   \end{verbatim}
 %   In other words, \TeX{} is processing the argument of \cs{use:n},
 %   which is \cs{LaTeX3 error:} \meta{error message}.
-%   Then \cs{msg_expandable_error_aux:w} cleans up. In fact, there
+%   Then \cs{@@_expandable_error:w} cleans up. In fact, there
 %   is an extra subtlety: if the user inserts tokens for error recovery,
 %   they should be kept. Thus we also use an odd space character
 %   (with category code $7$) and keep tokens until that space character,
@@ -1816,70 +1919,71 @@
 %    \begin{macrocode}
 \group_begin:
 \char_set_catcode_math_superscript:N \^
-\char_set_lccode:nn {`^} {`\ }
-\char_set_lccode:nn {`L} {`L}
-\char_set_lccode:nn {`T} {`T}
-\char_set_lccode:nn {`X} {`X}
+\char_set_lccode:nn { `^ } { `\  }
+\char_set_lccode:nn { `L } { `L }
+\char_set_lccode:nn { `T } { `T }
+\char_set_lccode:nn { `X } { `X }
 \tl_to_lowercase:n
   {
-    \cs_new:Npx \msg_expandable_error:n #1
+    \cs_new:Npx \@@_expandable_error:n #1
       {
         \exp_not:n
           {
             \tex_romannumeral:D
             \exp_after:wN \exp_after:wN
-            \exp_after:wN \msg_expandable_error_aux:w
+            \exp_after:wN \@@_expandable_error:w
             \exp_after:wN \exp_after:wN
             \exp_after:wN \c_zero
           }
         \exp_not:N \use:n { \exp_not:c { LaTeX3~error: } ^ #1 } ^
       }
-    \cs_new:Npn \msg_expandable_error_aux:w #1 ^ #2 ^ { #1 }
+    \cs_new:Npn \@@_expandable_error:w #1 ^ #2 ^ { #1 }
   }
 \group_end:
 %    \end{macrocode}
 % \end{macro}
+% \end{macro}
 %
 % \begin{macro}
 %   {
-%     \msg_expandable_kernel_error:nnnnnn,
-%     \msg_expandable_kernel_error:nnnnn,
-%     \msg_expandable_kernel_error:nnnn,
-%     \msg_expandable_kernel_error:nnn,
-%     \msg_expandable_kernel_error:nn
+%     \@@_kernel_expandable_error:nnnnnn,
+%     \@@_kernel_expandable_error:nnnnn,
+%     \@@_kernel_expandable_error:nnnn,
+%     \@@_kernel_expandable_error:nnn,
+%     \@@_kernel_expandable_error:nn
 %   }
 %   The command built from the csname
-%   |\c_msg_text_prefix_tl LaTeX / #1 / #2|
+%   |\c_@@_text_prefix_tl LaTeX / #1 / #2|
 %   takes four arguments and builds the error text, which is fed to
-%   \cs{msg_expandable_error:n}.
+%   \cs{@@_expandable_error:n}.
 %    \begin{macrocode}
-\cs_new:Npn \msg_expandable_kernel_error:nnnnnn #1#2#3#4#5#6
+\cs_new:Npn \@@_kernel_expandable_error:nnnnnn #1#2#3#4#5#6
   {
-    \exp_args:Nf \msg_expandable_error:n
+    \exp_args:Nf \@@_expandable_error:n
       {
         \exp_args:NNc \exp_after:wN \exp_stop_f:
-          { \c_msg_text_prefix_tl LaTeX / #1 / #2 }
+          { \c_@@_text_prefix_tl LaTeX / #1 / #2 }
           {#3} {#4} {#5} {#6}
       }
   }
-\cs_new:Npn \msg_expandable_kernel_error:nnnnn #1#2#3#4#5
+\cs_new:Npn \@@_kernel_expandable_error:nnnnn #1#2#3#4#5
   {
-    \msg_expandable_kernel_error:nnnnnn
+    \@@_kernel_expandable_error:nnnnnn
       {#1} {#2} {#3} {#4} {#5} { }
   }
-\cs_new:Npn \msg_expandable_kernel_error:nnnn #1#2#3#4
+\cs_new:Npn \@@_kernel_expandable_error:nnnn #1#2#3#4
   {
-    \msg_expandable_kernel_error:nnnnnn
+    \@@_kernel_expandable_error:nnnnnn
       {#1} {#2} {#3} {#4} { } { }
   }
-\cs_new:Npn \msg_expandable_kernel_error:nnn #1#2#3
+\cs_new:Npn \@@_kernel_expandable_error:nnn #1#2#3
   {
-    \msg_expandable_kernel_error:nnnnnn
+    \@@_kernel_expandable_error:nnnnnn
       {#1} {#2} {#3} { } { } { }
   }
-\cs_new:Npn \msg_expandable_kernel_error:nn #1#2
+\cs_new:Npn \@@_kernel_expandable_error:nn #1#2
   {
-    \msg_expandable_kernel_error:nnnnnn
+    \@@_kernel_expandable_error:nnnnnn
       {#1} {#2} { } { } { } { }
   }
 %    \end{macrocode}
@@ -1888,93 +1992,103 @@
 % \subsection{Showing variables}
 %
 % Functions defined in this section are used for diagnostic functions
-% in \pkg{l3clist}, \pkg{l3io}, \pkg{l3prop}, \pkg{l3seq}, \pkg{xtemplate}
-%
-% \begin{macro}[aux]{\msg_aux_use:nn}
-% \begin{macro}[aux]{\msg_aux_use:nnxxxx}
-%   Print the text of a message to the terminal, without formatting.
+% in \pkg{l3clist}, \pkg{l3file}, \pkg{l3prop}, \pkg{l3seq}, \pkg{xtemplate}
+%
+% \begin{macro}[int]
+%   {\@@_term:nnnnnn, \@@_term:nnnnnV}
+% \begin{macro}[int]{\@@_term:nnnnn}
+% \begin{macro}[int]{\@@_term:nnn}
+% \begin{macro}[int]{\@@_term:nn}
+%   Print the text of a message to the terminal without formatting:
+%   short cuts around \cs{iow_wrap:nnnN}.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_aux_use:nn #1#2
-  { \msg_aux_use:nnxxxx {#1} {#2} { } { } { } { } }
-\cs_new_protected:Npn \msg_aux_use:nnxxxx #1#2#3#4#5#6
-  {
-    \iow_wrap:xnnnN
-      {
-        \use:c { \c_msg_text_prefix_tl #1 / #2 }
-          {#3} {#4} {#5} {#6}
-      }
-      { } \c_zero { } \iow_term:x
-  }
+\cs_new_protected:Npn \@@_term:nnnnnn #1#2#3#4#5#6
+  {
+    \iow_wrap:nnnN
+      { \use:c { \c_@@_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6} }
+      { } { } \iow_term:n
+  }
+\cs_generate_variant:Nn \@@_term:nnnnnn { nnnnnV }
+\cs_new_protected:Npn \@@_term:nnnnn #1#2#3#4#5
+  { \@@_term:nnnnnn {#1} {#2} {#3} {#4} {#5} { } }
+\cs_new_protected:Npn \@@_term:nnn #1#2#3
+  { \@@_term:nnnnnn {#1} {#2} {#3} { } { } { } }
+\cs_new_protected:Npn \@@_term:nn #1#2
+  { \@@_term:nnnnnn {#1} {#2} { } { } { } { } }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
+% \end{macro}
+% \end{macro}
 %
-% \begin{macro}[int]{\msg_aux_show:Nnx}
-% \begin{macro}[aux]{\msg_aux_show:x}
-% \begin{macro}[aux,EXP]{\msg_aux_show:w}
-%   The arguments of \cs{msg_aux_show:Nnx} are
+% \begin{macro}[int]{\@@_show_variable:Nnn, \@@_show_variable:Nnn}
+% \begin{macro}[int]{\@@_show_variable:n, \@@_show_variable:x}
+% \begin{macro}[aux,EXP]{\@@_show_variable:w}
+%   The arguments of \cs{@@_show_variable:Nnn} are
 %   \begin{itemize}
-%   \item The \meta{variable} to be shown.
-%   \item The \texttt{TF} emptyness conditional for that type of variables.
-%   \item The type of the variable.
-%   \item A mapping of the form \cs{seq_map_function:NN} \meta{variable}
-%     \cs{msg_aux_show:n}, which produces the formatted string.
+%     \item The \meta{variable} to be shown.
+%     \item The \texttt{TF} emptiness conditional for that type of variables.
+%     \item The type of the variable.
+%     \item A mapping of the form \cs{seq_map_function:NN} \meta{variable}
+%       \cs{@@_show_item:n}, which produces the formatted string.
 %   \end{itemize}
 %   We remove a new line and \verb*|> | from the first item using
 %   a \texttt{w}-type auxiliary, and the fact that \texttt{f}-expansion
 %   removes a space. To avoid a low-level \TeX{} error if there is
 %   an empty argument, a simple test is used to keep the output
-%   \enquote{clean}. The odd \cs{exp_after:wN} and trailing
-%   \cs{prg_do_nothing:} improve the output slightly.
+%   \enquote{clean}. The odd \cs{exp_after:wN} which expands the closing
+%   brace improves the output slightly.
 %    \begin{macrocode}
-\cs_new_protected:Npn \msg_aux_show:Nnx #1#2#3
+\cs_new_protected:Npn \@@_show_variable:Nnn #1#2#3
   {
     \cs_if_exist:NTF #1
       {
-        \msg_aux_use:nnxxxx { LaTeX / #2 } { show } {#1} { } { } { }
-        \msg_aux_show:x {#3}
+        \@@_term:nnn { LaTeX / kernel } { show- #2 } {#1}
+        \@@_show_variable:x {#3}
       }
       {
-        \msg_kernel_error:nnx { kernel } { variable-not-defined }
+        \@@_kernel_error:nnx { kernel } { variable-not-defined }
           { \token_to_str:N #1 }
       }
   }
-\cs_new_protected:Npn \msg_aux_show:x #1
+\cs_generate_variant:Nn \@@_show_variable:Nnn { Nnx }
+\cs_new_protected:Npn \@@_show_variable:n #1
   {
-    \tl_set:Nx \l_msg_internal_tl {#1}
-    \tl_if_empty:NT \l_msg_internal_tl
-      { \tl_set:Nx \l_msg_internal_tl { > } }
-    \exp_args:Nf \etex_showtokens:D
+    \tl_set:Nn \l_@@_internal_tl {#1}
+    \tl_if_empty:NTF \l_@@_internal_tl
+      { \etex_showtokens:D \exp_after:wN { } }
       {
-        \exp_after:wN \exp_after:wN
-        \exp_after:wN \msg_aux_show:w
-        \exp_after:wN \l_msg_internal_tl
-        \exp_after:wN
+        \exp_args:Nf \etex_showtokens:D
+          {
+            \exp_after:wN \exp_after:wN
+            \exp_after:wN \@@_show_variable:w
+            \exp_after:wN \l_@@_internal_tl
+          }
       }
-    \prg_do_nothing:
   }
-\cs_new:Npn \msg_aux_show:w #1 > { }
+\cs_generate_variant:Nn \@@_show_variable:n { x }
+\cs_new:Npn \@@_show_variable:w #1 > { }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[aux,EXP]{\msg_aux_show:n}
-% \begin{macro}[aux,EXP]{\msg_aux_show:nn}
-% \begin{macro}[aux,EXP]{\msg_aux_show_unbraced:nn}
+% \begin{macro}[int,EXP]{\@@_show_item:n}
+% \begin{macro}[int,EXP]{\@@_show_item:nn}
+% \begin{macro}[int,EXP]{\@@_show_item_unbraced:nn}
 %   Each item in the variable is formatted using one of
 %   the following functions.
 %    \begin{macrocode}
-\cs_new:Npn \msg_aux_show:n #1
+\cs_new:Npn \@@_show_item:n #1
   {
     \iow_newline: > \c_space_tl \c_space_tl { \exp_not:n {#1} }
   }
-\cs_new:Npn \msg_aux_show:nn #1#2
+\cs_new:Npn \@@_show_item:nn #1#2
   {
     \iow_newline: > \c_space_tl \c_space_tl { \exp_not:n {#1} }
     \c_space_tl \c_space_tl => \c_space_tl \c_space_tl { \exp_not:n {#2} }
   }
-\cs_new:Npn \msg_aux_show_unbraced:nn #1#2
+\cs_new:Npn \@@_show_item_unbraced:nn #1#2
   {
     \iow_newline: > \c_space_tl \c_space_tl \exp_not:n {#1}
     \c_space_tl \c_space_tl => \c_space_tl \c_space_tl \exp_not:n {#2}
@@ -2042,22 +2156,22 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\msg_kernel_bug:x}
-% \begin{variable}{\c_msg_kernel_bug_text_tl, \c_msg_kernel_bug_more_text_tl}
+% \begin{macro}{\@@_kernel_bug:x}
+% \begin{variable}{\c_@@_kernel_bug_text_tl, \c_@@_kernel_bug_more_text_tl}
 %    \begin{macrocode}
 %<*deprecated>
-\cs_set_protected:Npn \msg_kernel_bug:x #1
+\cs_set_protected:Npn \@@_kernel_bug:x #1
   {
-    \msg_interrupt:xxx { \c_msg_kernel_bug_text_tl }
+    \msg_interrupt:nnn { \c_@@_kernel_bug_text_tl }
       {
         #1
        \msg_see_documentation_text:n { LaTeX3 }
       }
-      { \c_msg_kernel_bug_more_text_tl }
+      { \c_@@_kernel_bug_more_text_tl }
   }
-\tl_const:Nn \c_msg_kernel_bug_text_tl
+\tl_const:Nn \c_@@_kernel_bug_text_tl
   { This~is~a~LaTeX~bug:~check~coding! }
-\tl_const:Nn \c_msg_kernel_bug_more_text_tl
+\tl_const:Nn \c_@@_kernel_bug_more_text_tl
   {
     There~is~a~coding~bug~somewhere~around~here. \\
     This~probably~needs~examining~by~an~expert.
@@ -2067,6 +2181,55 @@
 %    \end{macrocode}
 % \end{variable}
 % \end{macro}
+% 
+% Deprecated on 2012-06-28, for removal by 2012-12-31.
+%
+% \begin{macro}{\msg_newline:, \msg_two_newlines:}
+%   New lines are printed in the same way as for low-level file writing.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \msg_newline: { ^^J }
+\cs_new_nopar:Npn \msg_two_newlines: { ^^J ^^J }
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\msg_log:x, \msg_term:x}
+% \begin{macro}{\msg_interrupt:xxx}
+%   These were all misnamed.
+%    \begin{macrocode}
+\cs_generate_variant:Nn \msg_log:n { x }
+\cs_generate_variant:Nn \msg_term:n { x }
+\cs_generate_variant:Nn \msg_interrupt:nnn { xxx }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% 
+% Deprecated on 2012-06-29, for removal by 2012-12-31.
+% 
+% \begin{macro}{\msg_class_set:nn}
+%   Setting up a message class does two tasks. Any existing redirection
+%   is cleared, and the various message functions are created
+%   to simply use the code stored for the message.
+%    \begin{macrocode}
+\cs_new_protected:Npn \msg_class_set:nn #1#2
+  {
+    \cs_if_exist:cTF { @@_ #1 _code:nnnnnn }
+      \cs_set_protected:cpn
+      \cs_new_protected:cpn
+        { @@_ #1 _code:nnnnnn } ##1##2##3##4##5##6 {#2}
+    \prop_clear_new:c { l_@@_redirect_ #1 _prop }
+    \cs_set_protected_nopar:cpn { msg_ #1 :nnxxxx }
+      { \@@_use:nnnnnnn {#1} }
+    \cs_set_protected:cpx { msg_ #1 :nnxxx } ##1##2##3##4##5
+      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} {##5} { } }
+    \cs_set_protected:cpx { msg_ #1 :nnxx } ##1##2##3##4
+      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} { } { } }
+    \cs_set_protected:cpx { msg_ #1 :nnx } ##1##2##3
+      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} { } { } { } }
+    \cs_set_protected:cpx { msg_ #1 :nn } ##1##2
+      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} { } { } { } { } }
+  }
+%    \end{macrocode}
+% \end{macro}
 %
 %    \begin{macrocode}
 %</initex|package>
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3names.dtx b/Master/texmf-dist/source/latex/l3kernel/l3names.dtx
index 13d403f4633..a77f3103063 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3names.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3names.dtx
@@ -1,6 +1,6 @@
 % \iffalse meta-comment
 %
-%% File: l3names.dtx Copyright (C) 1990-2011 The LaTeX3 project
+%% File: l3names.dtx Copyright (C) 1990-2012 The LaTeX3 project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -34,9 +34,9 @@
 %% -----------------------------------------------------------------------
 %
 %<*package>
-\RequirePackage{l3bootstrap}[2011-12-29]
-\GetIdInfo$Id: l3names.dtx 3494 2012-03-04 09:58:29Z joseph $
-  {L3 Experimental namespace for primitives}
+\RequirePackage{l3bootstrap}[2012/07/15]
+\GetIdInfo$Id: l3names.dtx 3990 2012-07-16 07:46:03Z joseph $
+  {L3 Namespace for primitives}
 %</package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -73,7 +73,7 @@
 % performs the following tasks:
 % \begin{itemize}
 %   \item defines new names for all \TeX{} primitives;
-%   \item switches to the category code regime for programming;
+%   \item switches to the category code r{\'e}gime for programming;
 %   \item provides support settings for building the code as a \TeX{} format.
 % \end{itemize}
 %
@@ -111,12 +111,12 @@
 %
 % The code here simply renames all of the primitives to new, internal,
 % names. In format mode, it also deletes all of the existing names (although
-% some od come back later).
+% some do come back later).
 %
 % \begin{macro}{\tex_undefined:D}
-% This function does not exist at all, but is the name used by the
-% plain \TeX{} format for an undefined function. So it should
-% be marked here as \enquote{taken}.
+%   This function does not exist at all, but is the name used by the
+%   plain \TeX{} format for an undefined function. So it should
+%   be marked here as \enquote{taken}.
 % \end{macro}
 %
 % The \tn{let} primitive is renamed by hand first as it is essential for
@@ -127,17 +127,17 @@
 \let \tex_let:D    \let
 %    \end{macrocode}
 %
-% Everything is inside a (rather long) group, which kees \cs{name_primitve:NN}
-% trapped.
+% Everything is inside a (rather long) group, which keeps
+% \cs{__expl_primitive:NN} trapped.
 %    \begin{macrocode}
 \begingroup
 %    \end{macrocode}
 %
-% \begin{macro}[aux]{\name_primitive:NN}
+% \begin{macro}[aux]{\__expl_primitive:NN}
 %   A temporary function to actually do the renaming. This also allows the
 %   original names to be removed in format mode.
 %    \begin{macrocode}
-  \long \def \name_primitive:NN #1#2
+  \long \def \__expl_primitive:NN #1#2
     {
       \tex_global:D \tex_let:D #2 #1
 %<*initex>
@@ -153,406 +153,406 @@
 % These are given modified new names, so that they may be entered
 % without catcode tricks.
 %    \begin{macrocode}
-  \name_primitive:NN \                      \tex_space:D
-  \name_primitive:NN \/                     \tex_italiccor:D
-  \name_primitive:NN \-                     \tex_hyphen:D
+  \__expl_primitive:NN \                      \tex_space:D
+  \__expl_primitive:NN \/                     \tex_italiccorrection:D
+  \__expl_primitive:NN \-                     \tex_hyphen:D
 %    \end{macrocode}
 %
 % Now all the other primitives.
 %    \begin{macrocode}
-  \name_primitive:NN \let                   \tex_let:D
-  \name_primitive:NN \def                   \tex_def:D
-  \name_primitive:NN \edef                  \tex_edef:D
-  \name_primitive:NN \gdef                  \tex_gdef:D
-  \name_primitive:NN \xdef                  \tex_xdef:D
-  \name_primitive:NN \chardef               \tex_chardef:D
-  \name_primitive:NN \countdef              \tex_countdef:D
-  \name_primitive:NN \dimendef              \tex_dimendef:D
-  \name_primitive:NN \skipdef               \tex_skipdef:D
-  \name_primitive:NN \muskipdef             \tex_muskipdef:D
-  \name_primitive:NN \mathchardef           \tex_mathchardef:D
-  \name_primitive:NN \toksdef               \tex_toksdef:D
-  \name_primitive:NN \futurelet             \tex_futurelet:D
-  \name_primitive:NN \advance               \tex_advance:D
-  \name_primitive:NN \divide                \tex_divide:D
-  \name_primitive:NN \multiply              \tex_multiply:D
-  \name_primitive:NN \font                  \tex_font:D
-  \name_primitive:NN \fam                   \tex_fam:D
-  \name_primitive:NN \global                \tex_global:D
-  \name_primitive:NN \long                  \tex_long:D
-  \name_primitive:NN \outer                 \tex_outer:D
-  \name_primitive:NN \setlanguage           \tex_setlanguage:D
-  \name_primitive:NN \globaldefs            \tex_globaldefs:D
-  \name_primitive:NN \afterassignment       \tex_afterassignment:D
-  \name_primitive:NN \aftergroup            \tex_aftergroup:D
-  \name_primitive:NN \expandafter           \tex_expandafter:D
-  \name_primitive:NN \noexpand              \tex_noexpand:D
-  \name_primitive:NN \begingroup            \tex_begingroup:D
-  \name_primitive:NN \endgroup              \tex_endgroup:D
-  \name_primitive:NN \halign                \tex_halign:D
-  \name_primitive:NN \valign                \tex_valign:D
-  \name_primitive:NN \cr                    \tex_cr:D
-  \name_primitive:NN \crcr                  \tex_crcr:D
-  \name_primitive:NN \noalign               \tex_noalign:D
-  \name_primitive:NN \omit                  \tex_omit:D
-  \name_primitive:NN \span                  \tex_span:D
-  \name_primitive:NN \tabskip               \tex_tabskip:D
-  \name_primitive:NN \everycr               \tex_everycr:D
-  \name_primitive:NN \if                    \tex_if:D
-  \name_primitive:NN \ifcase                \tex_ifcase:D
-  \name_primitive:NN \ifcat                 \tex_ifcat:D
-  \name_primitive:NN \ifnum                 \tex_ifnum:D
-  \name_primitive:NN \ifodd                 \tex_ifodd:D
-  \name_primitive:NN \ifdim                 \tex_ifdim:D
-  \name_primitive:NN \ifeof                 \tex_ifeof:D
-  \name_primitive:NN \ifhbox                \tex_ifhbox:D
-  \name_primitive:NN \ifvbox                \tex_ifvbox:D
-  \name_primitive:NN \ifvoid                \tex_ifvoid:D
-  \name_primitive:NN \ifx                   \tex_ifx:D
-  \name_primitive:NN \iffalse               \tex_iffalse:D
-  \name_primitive:NN \iftrue                \tex_iftrue:D
-  \name_primitive:NN \ifhmode               \tex_ifhmode:D
-  \name_primitive:NN \ifmmode               \tex_ifmmode:D
-  \name_primitive:NN \ifvmode               \tex_ifvmode:D
-  \name_primitive:NN \ifinner               \tex_ifinner:D
-  \name_primitive:NN \else                  \tex_else:D
-  \name_primitive:NN \fi                    \tex_fi:D
-  \name_primitive:NN \or                    \tex_or:D
-  \name_primitive:NN \immediate             \tex_immediate:D
-  \name_primitive:NN \closeout              \tex_closeout:D
-  \name_primitive:NN \openin                \tex_openin:D
-  \name_primitive:NN \openout               \tex_openout:D
-  \name_primitive:NN \read                  \tex_read:D
-  \name_primitive:NN \write                 \tex_write:D
-  \name_primitive:NN \closein               \tex_closein:D
-  \name_primitive:NN \newlinechar           \tex_newlinechar:D
-  \name_primitive:NN \input                 \tex_input:D
-  \name_primitive:NN \endinput              \tex_endinput:D
-  \name_primitive:NN \inputlineno           \tex_inputlineno:D
-  \name_primitive:NN \errmessage            \tex_errmessage:D
-  \name_primitive:NN \message               \tex_message:D
-  \name_primitive:NN \show                  \tex_show:D
-  \name_primitive:NN \showthe               \tex_showthe:D
-  \name_primitive:NN \showbox               \tex_showbox:D
-  \name_primitive:NN \showlists             \tex_showlists:D
-  \name_primitive:NN \errhelp               \tex_errhelp:D
-  \name_primitive:NN \errorcontextlines     \tex_errorcontextlines:D
-  \name_primitive:NN \tracingcommands       \tex_tracingcommands:D
-  \name_primitive:NN \tracinglostchars      \tex_tracinglostchars:D
-  \name_primitive:NN \tracingmacros         \tex_tracingmacros:D
-  \name_primitive:NN \tracingonline         \tex_tracingonline:D
-  \name_primitive:NN \tracingoutput         \tex_tracingoutput:D
-  \name_primitive:NN \tracingpages          \tex_tracingpages:D
-  \name_primitive:NN \tracingparagraphs     \tex_tracingparagraphs:D
-  \name_primitive:NN \tracingrestores       \tex_tracingrestores:D
-  \name_primitive:NN \tracingstats          \tex_tracingstats:D
-  \name_primitive:NN \pausing               \tex_pausing:D
-  \name_primitive:NN \showboxbreadth        \tex_showboxbreadth:D
-  \name_primitive:NN \showboxdepth          \tex_showboxdepth:D
-  \name_primitive:NN \batchmode             \tex_batchmode:D
-  \name_primitive:NN \errorstopmode         \tex_errorstopmode:D
-  \name_primitive:NN \nonstopmode           \tex_nonstopmode:D
-  \name_primitive:NN \scrollmode            \tex_scrollmode:D
-  \name_primitive:NN \end                   \tex_end:D
-  \name_primitive:NN \csname                \tex_csname:D
-  \name_primitive:NN \endcsname             \tex_endcsname:D
-  \name_primitive:NN \ignorespaces          \tex_ignorespaces:D
-  \name_primitive:NN \relax                 \tex_relax:D
-  \name_primitive:NN \the                   \tex_the:D
-  \name_primitive:NN \mag                   \tex_mag:D
-  \name_primitive:NN \language              \tex_language:D
-  \name_primitive:NN \mark                  \tex_mark:D
-  \name_primitive:NN \topmark               \tex_topmark:D
-  \name_primitive:NN \firstmark             \tex_firstmark:D
-  \name_primitive:NN \botmark               \tex_botmark:D
-  \name_primitive:NN \splitfirstmark        \tex_splitfirstmark:D
-  \name_primitive:NN \splitbotmark          \tex_splitbotmark:D
-  \name_primitive:NN \fontname              \tex_fontname:D
-  \name_primitive:NN \escapechar            \tex_escapechar:D
-  \name_primitive:NN \endlinechar           \tex_endlinechar:D
-  \name_primitive:NN \mathchoice            \tex_mathchoice:D
-  \name_primitive:NN \delimiter             \tex_delimiter:D
-  \name_primitive:NN \mathaccent            \tex_mathaccent:D
-  \name_primitive:NN \mathchar              \tex_mathchar:D
-  \name_primitive:NN \mskip                 \tex_mskip:D
-  \name_primitive:NN \radical               \tex_radical:D
-  \name_primitive:NN \vcenter               \tex_vcenter:D
-  \name_primitive:NN \mkern                 \tex_mkern:D
-  \name_primitive:NN \above                 \tex_above:D
-  \name_primitive:NN \abovewithdelims       \tex_abovewithdelims:D
-  \name_primitive:NN \atop                  \tex_atop:D
-  \name_primitive:NN \atopwithdelims        \tex_atopwithdelims:D
-  \name_primitive:NN \over                  \tex_over:D
-  \name_primitive:NN \overwithdelims        \tex_overwithdelims:D
-  \name_primitive:NN \displaystyle          \tex_displaystyle:D
-  \name_primitive:NN \textstyle             \tex_textstyle:D
-  \name_primitive:NN \scriptstyle           \tex_scriptstyle:D
-  \name_primitive:NN \scriptscriptstyle     \tex_scriptscriptstyle:D
-  \name_primitive:NN \nonscript             \tex_nonscript:D
-  \name_primitive:NN \eqno                  \tex_eqno:D
-  \name_primitive:NN \leqno                 \tex_leqno:D
-  \name_primitive:NN \abovedisplayshortskip \tex_abovedisplayshortskip:D
-  \name_primitive:NN \abovedisplayskip      \tex_abovedisplayskip:D
-  \name_primitive:NN \belowdisplayshortskip \tex_belowdisplayshortskip:D
-  \name_primitive:NN \belowdisplayskip      \tex_belowdisplayskip:D
-  \name_primitive:NN \displaywidowpenalty   \tex_displaywidowpenalty:D
-  \name_primitive:NN \displayindent         \tex_displayindent:D
-  \name_primitive:NN \displaywidth          \tex_displaywidth:D
-  \name_primitive:NN \everydisplay          \tex_everydisplay:D
-  \name_primitive:NN \predisplaysize        \tex_predisplaysize:D
-  \name_primitive:NN \predisplaypenalty     \tex_predisplaypenalty:D
-  \name_primitive:NN \postdisplaypenalty    \tex_postdisplaypenalty:D
-  \name_primitive:NN \mathbin               \tex_mathbin:D
-  \name_primitive:NN \mathclose             \tex_mathclose:D
-  \name_primitive:NN \mathinner             \tex_mathinner:D
-  \name_primitive:NN \mathop                \tex_mathop:D
-  \name_primitive:NN \displaylimits         \tex_displaylimits:D
-  \name_primitive:NN \limits                \tex_limits:D
-  \name_primitive:NN \nolimits              \tex_nolimits:D
-  \name_primitive:NN \mathopen              \tex_mathopen:D
-  \name_primitive:NN \mathord               \tex_mathord:D
-  \name_primitive:NN \mathpunct             \tex_mathpunct:D
-  \name_primitive:NN \mathrel               \tex_mathrel:D
-  \name_primitive:NN \overline              \tex_overline:D
-  \name_primitive:NN \underline             \tex_underline:D
-  \name_primitive:NN \left                  \tex_left:D
-  \name_primitive:NN \right                 \tex_right:D
-  \name_primitive:NN \binoppenalty          \tex_binoppenalty:D
-  \name_primitive:NN \relpenalty            \tex_relpenalty:D
-  \name_primitive:NN \delimitershortfall    \tex_delimitershortfall:D
-  \name_primitive:NN \delimiterfactor       \tex_delimiterfactor:D
-  \name_primitive:NN \nulldelimiterspace    \tex_nulldelimiterspace:D
-  \name_primitive:NN \everymath             \tex_everymath:D
-  \name_primitive:NN \mathsurround          \tex_mathsurround:D
-  \name_primitive:NN \medmuskip             \tex_medmuskip:D
-  \name_primitive:NN \thinmuskip            \tex_thinmuskip:D
-  \name_primitive:NN \thickmuskip           \tex_thickmuskip:D
-  \name_primitive:NN \scriptspace           \tex_scriptspace:D
-  \name_primitive:NN \noboundary            \tex_noboundary:D
-  \name_primitive:NN \accent                \tex_accent:D
-  \name_primitive:NN \char                  \tex_char:D
-  \name_primitive:NN \discretionary         \tex_discretionary:D
-  \name_primitive:NN \hfil                  \tex_hfil:D
-  \name_primitive:NN \hfilneg               \tex_hfilneg:D
-  \name_primitive:NN \hfill                 \tex_hfill:D
-  \name_primitive:NN \hskip                 \tex_hskip:D
-  \name_primitive:NN \hss                   \tex_hss:D
-  \name_primitive:NN \vfil                  \tex_vfil:D
-  \name_primitive:NN \vfilneg               \tex_vfilneg:D
-  \name_primitive:NN \vfill                 \tex_vfill:D
-  \name_primitive:NN \vskip                 \tex_vskip:D
-  \name_primitive:NN \vss                   \tex_vss:D
-  \name_primitive:NN \unskip                \tex_unskip:D
-  \name_primitive:NN \kern                  \tex_kern:D
-  \name_primitive:NN \unkern                \tex_unkern:D
-  \name_primitive:NN \hrule                 \tex_hrule:D
-  \name_primitive:NN \vrule                 \tex_vrule:D
-  \name_primitive:NN \leaders               \tex_leaders:D
-  \name_primitive:NN \cleaders              \tex_cleaders:D
-  \name_primitive:NN \xleaders              \tex_xleaders:D
-  \name_primitive:NN \lastkern              \tex_lastkern:D
-  \name_primitive:NN \lastskip              \tex_lastskip:D
-  \name_primitive:NN \indent                \tex_indent:D
-  \name_primitive:NN \par                   \tex_par:D
-  \name_primitive:NN \noindent              \tex_noindent:D
-  \name_primitive:NN \vadjust               \tex_vadjust:D
-  \name_primitive:NN \baselineskip          \tex_baselineskip:D
-  \name_primitive:NN \lineskip              \tex_lineskip:D
-  \name_primitive:NN \lineskiplimit         \tex_lineskiplimit:D
-  \name_primitive:NN \clubpenalty           \tex_clubpenalty:D
-  \name_primitive:NN \widowpenalty          \tex_widowpenalty:D
-  \name_primitive:NN \exhyphenpenalty       \tex_exhyphenpenalty:D
-  \name_primitive:NN \hyphenpenalty         \tex_hyphenpenalty:D
-  \name_primitive:NN \linepenalty           \tex_linepenalty:D
-  \name_primitive:NN \doublehyphendemerits  \tex_doublehyphendemerits:D
-  \name_primitive:NN \finalhyphendemerits   \tex_finalhyphendemerits:D
-  \name_primitive:NN \adjdemerits           \tex_adjdemerits:D
-  \name_primitive:NN \hangafter             \tex_hangafter:D
-  \name_primitive:NN \hangindent            \tex_hangindent:D
-  \name_primitive:NN \parshape              \tex_parshape:D
-  \name_primitive:NN \hsize                 \tex_hsize:D
-  \name_primitive:NN \lefthyphenmin         \tex_lefthyphenmin:D
-  \name_primitive:NN \righthyphenmin        \tex_righthyphenmin:D
-  \name_primitive:NN \leftskip              \tex_leftskip:D
-  \name_primitive:NN \rightskip             \tex_rightskip:D
-  \name_primitive:NN \looseness             \tex_looseness:D
-  \name_primitive:NN \parskip               \tex_parskip:D
-  \name_primitive:NN \parindent             \tex_parindent:D
-  \name_primitive:NN \uchyph                \tex_uchyph:D
-  \name_primitive:NN \emergencystretch      \tex_emergencystretch:D
-  \name_primitive:NN \pretolerance          \tex_pretolerance:D
-  \name_primitive:NN \tolerance             \tex_tolerance:D
-  \name_primitive:NN \spaceskip             \tex_spaceskip:D
-  \name_primitive:NN \xspaceskip            \tex_xspaceskip:D
-  \name_primitive:NN \parfillskip           \tex_parfillskip:D
-  \name_primitive:NN \everypar              \tex_everypar:D
-  \name_primitive:NN \prevgraf              \tex_prevgraf:D
-  \name_primitive:NN \spacefactor           \tex_spacefactor:D
-  \name_primitive:NN \shipout               \tex_shipout:D
-  \name_primitive:NN \vsize                 \tex_vsize:D
-  \name_primitive:NN \interlinepenalty      \tex_interlinepenalty:D
-  \name_primitive:NN \brokenpenalty         \tex_brokenpenalty:D
-  \name_primitive:NN \topskip               \tex_topskip:D
-  \name_primitive:NN \maxdeadcycles         \tex_maxdeadcycles:D
-  \name_primitive:NN \maxdepth              \tex_maxdepth:D
-  \name_primitive:NN \output                \tex_output:D
-  \name_primitive:NN \deadcycles            \tex_deadcycles:D
-  \name_primitive:NN \pagedepth             \tex_pagedepth:D
-  \name_primitive:NN \pagestretch           \tex_pagestretch:D
-  \name_primitive:NN \pagefilstretch        \tex_pagefilstretch:D
-  \name_primitive:NN \pagefillstretch       \tex_pagefillstretch:D
-  \name_primitive:NN \pagefilllstretch      \tex_pagefilllstretch:D
-  \name_primitive:NN \pageshrink            \tex_pageshrink:D
-  \name_primitive:NN \pagegoal              \tex_pagegoal:D
-  \name_primitive:NN \pagetotal             \tex_pagetotal:D
-  \name_primitive:NN \outputpenalty         \tex_outputpenalty:D
-  \name_primitive:NN \hoffset               \tex_hoffset:D
-  \name_primitive:NN \voffset               \tex_voffset:D
-  \name_primitive:NN \insert                \tex_insert:D
-  \name_primitive:NN \holdinginserts        \tex_holdinginserts:D
-  \name_primitive:NN \floatingpenalty       \tex_floatingpenalty:D
-  \name_primitive:NN \insertpenalties       \tex_insertpenalties:D
-  \name_primitive:NN \lower                 \tex_lower:D
-  \name_primitive:NN \moveleft              \tex_moveleft:D
-  \name_primitive:NN \moveright             \tex_moveright:D
-  \name_primitive:NN \raise                 \tex_raise:D
-  \name_primitive:NN \copy                  \tex_copy:D
-  \name_primitive:NN \lastbox               \tex_lastbox:D
-  \name_primitive:NN \vsplit                \tex_vsplit:D
-  \name_primitive:NN \unhbox                \tex_unhbox:D
-  \name_primitive:NN \unhcopy               \tex_unhcopy:D
-  \name_primitive:NN \unvbox                \tex_unvbox:D
-  \name_primitive:NN \unvcopy               \tex_unvcopy:D
-  \name_primitive:NN \setbox                \tex_setbox:D
-  \name_primitive:NN \hbox                  \tex_hbox:D
-  \name_primitive:NN \vbox                  \tex_vbox:D
-  \name_primitive:NN \vtop                  \tex_vtop:D
-  \name_primitive:NN \prevdepth             \tex_prevdepth:D
-  \name_primitive:NN \badness               \tex_badness:D
-  \name_primitive:NN \hbadness              \tex_hbadness:D
-  \name_primitive:NN \vbadness              \tex_vbadness:D
-  \name_primitive:NN \hfuzz                 \tex_hfuzz:D
-  \name_primitive:NN \vfuzz                 \tex_vfuzz:D
-  \name_primitive:NN \overfullrule          \tex_overfullrule:D
-  \name_primitive:NN \boxmaxdepth           \tex_boxmaxdepth:D
-  \name_primitive:NN \splitmaxdepth         \tex_splitmaxdepth:D
-  \name_primitive:NN \splittopskip          \tex_splittopskip:D
-  \name_primitive:NN \everyhbox             \tex_everyhbox:D
-  \name_primitive:NN \everyvbox             \tex_everyvbox:D
-  \name_primitive:NN \nullfont              \tex_nullfont:D
-  \name_primitive:NN \textfont              \tex_textfont:D
-  \name_primitive:NN \scriptfont            \tex_scriptfont:D
-  \name_primitive:NN \scriptscriptfont      \tex_scriptscriptfont:D
-  \name_primitive:NN \fontdimen             \tex_fontdimen:D
-  \name_primitive:NN \hyphenchar            \tex_hyphenchar:D
-  \name_primitive:NN \skewchar              \tex_skewchar:D
-  \name_primitive:NN \defaulthyphenchar     \tex_defaulthyphenchar:D
-  \name_primitive:NN \defaultskewchar       \tex_defaultskewchar:D
-  \name_primitive:NN \number                \tex_number:D
-  \name_primitive:NN \romannumeral          \tex_romannumeral:D
-  \name_primitive:NN \string                \tex_string:D
-  \name_primitive:NN \lowercase             \tex_lowercase:D
-  \name_primitive:NN \uppercase             \tex_uppercase:D
-  \name_primitive:NN \meaning               \tex_meaning:D
-  \name_primitive:NN \penalty               \tex_penalty:D
-  \name_primitive:NN \unpenalty             \tex_unpenalty:D
-  \name_primitive:NN \lastpenalty           \tex_lastpenalty:D
-  \name_primitive:NN \special               \tex_special:D
-  \name_primitive:NN \dump                  \tex_dump:D
-  \name_primitive:NN \patterns              \tex_patterns:D
-  \name_primitive:NN \hyphenation           \tex_hyphenation:D
-  \name_primitive:NN \time                  \tex_time:D
-  \name_primitive:NN \day                   \tex_day:D
-  \name_primitive:NN \month                 \tex_month:D
-  \name_primitive:NN \year                  \tex_year:D
-  \name_primitive:NN \jobname               \tex_jobname:D
-  \name_primitive:NN \everyjob              \tex_everyjob:D
-  \name_primitive:NN \count                 \tex_count:D
-  \name_primitive:NN \dimen                 \tex_dimen:D
-  \name_primitive:NN \skip                  \tex_skip:D
-  \name_primitive:NN \toks                  \tex_toks:D
-  \name_primitive:NN \muskip                \tex_muskip:D
-  \name_primitive:NN \box                   \tex_box:D
-  \name_primitive:NN \wd                    \tex_wd:D
-  \name_primitive:NN \ht                    \tex_ht:D
-  \name_primitive:NN \dp                    \tex_dp:D
-  \name_primitive:NN \catcode               \tex_catcode:D
-  \name_primitive:NN \delcode               \tex_delcode:D
-  \name_primitive:NN \sfcode                \tex_sfcode:D
-  \name_primitive:NN \lccode                \tex_lccode:D
-  \name_primitive:NN \uccode                \tex_uccode:D
-  \name_primitive:NN \mathcode              \tex_mathcode:D
+  \__expl_primitive:NN \let                   \tex_let:D
+  \__expl_primitive:NN \def                   \tex_def:D
+  \__expl_primitive:NN \edef                  \tex_edef:D
+  \__expl_primitive:NN \gdef                  \tex_gdef:D
+  \__expl_primitive:NN \xdef                  \tex_xdef:D
+  \__expl_primitive:NN \chardef               \tex_chardef:D
+  \__expl_primitive:NN \countdef              \tex_countdef:D
+  \__expl_primitive:NN \dimendef              \tex_dimendef:D
+  \__expl_primitive:NN \skipdef               \tex_skipdef:D
+  \__expl_primitive:NN \muskipdef             \tex_muskipdef:D
+  \__expl_primitive:NN \mathchardef           \tex_mathchardef:D
+  \__expl_primitive:NN \toksdef               \tex_toksdef:D
+  \__expl_primitive:NN \futurelet             \tex_futurelet:D
+  \__expl_primitive:NN \advance               \tex_advance:D
+  \__expl_primitive:NN \divide                \tex_divide:D
+  \__expl_primitive:NN \multiply              \tex_multiply:D
+  \__expl_primitive:NN \font                  \tex_font:D
+  \__expl_primitive:NN \fam                   \tex_fam:D
+  \__expl_primitive:NN \global                \tex_global:D
+  \__expl_primitive:NN \long                  \tex_long:D
+  \__expl_primitive:NN \outer                 \tex_outer:D
+  \__expl_primitive:NN \setlanguage           \tex_setlanguage:D
+  \__expl_primitive:NN \globaldefs            \tex_globaldefs:D
+  \__expl_primitive:NN \afterassignment       \tex_afterassignment:D
+  \__expl_primitive:NN \aftergroup            \tex_aftergroup:D
+  \__expl_primitive:NN \expandafter           \tex_expandafter:D
+  \__expl_primitive:NN \noexpand              \tex_noexpand:D
+  \__expl_primitive:NN \begingroup            \tex_begingroup:D
+  \__expl_primitive:NN \endgroup              \tex_endgroup:D
+  \__expl_primitive:NN \halign                \tex_halign:D
+  \__expl_primitive:NN \valign                \tex_valign:D
+  \__expl_primitive:NN \cr                    \tex_cr:D
+  \__expl_primitive:NN \crcr                  \tex_crcr:D
+  \__expl_primitive:NN \noalign               \tex_noalign:D
+  \__expl_primitive:NN \omit                  \tex_omit:D
+  \__expl_primitive:NN \span                  \tex_span:D
+  \__expl_primitive:NN \tabskip               \tex_tabskip:D
+  \__expl_primitive:NN \everycr               \tex_everycr:D
+  \__expl_primitive:NN \if                    \tex_if:D
+  \__expl_primitive:NN \ifcase                \tex_ifcase:D
+  \__expl_primitive:NN \ifcat                 \tex_ifcat:D
+  \__expl_primitive:NN \ifnum                 \tex_ifnum:D
+  \__expl_primitive:NN \ifodd                 \tex_ifodd:D
+  \__expl_primitive:NN \ifdim                 \tex_ifdim:D
+  \__expl_primitive:NN \ifeof                 \tex_ifeof:D
+  \__expl_primitive:NN \ifhbox                \tex_ifhbox:D
+  \__expl_primitive:NN \ifvbox                \tex_ifvbox:D
+  \__expl_primitive:NN \ifvoid                \tex_ifvoid:D
+  \__expl_primitive:NN \ifx                   \tex_ifx:D
+  \__expl_primitive:NN \iffalse               \tex_iffalse:D
+  \__expl_primitive:NN \iftrue                \tex_iftrue:D
+  \__expl_primitive:NN \ifhmode               \tex_ifhmode:D
+  \__expl_primitive:NN \ifmmode               \tex_ifmmode:D
+  \__expl_primitive:NN \ifvmode               \tex_ifvmode:D
+  \__expl_primitive:NN \ifinner               \tex_ifinner:D
+  \__expl_primitive:NN \else                  \tex_else:D
+  \__expl_primitive:NN \fi                    \tex_fi:D
+  \__expl_primitive:NN \or                    \tex_or:D
+  \__expl_primitive:NN \immediate             \tex_immediate:D
+  \__expl_primitive:NN \closeout              \tex_closeout:D
+  \__expl_primitive:NN \openin                \tex_openin:D
+  \__expl_primitive:NN \openout               \tex_openout:D
+  \__expl_primitive:NN \read                  \tex_read:D
+  \__expl_primitive:NN \write                 \tex_write:D
+  \__expl_primitive:NN \closein               \tex_closein:D
+  \__expl_primitive:NN \newlinechar           \tex_newlinechar:D
+  \__expl_primitive:NN \input                 \tex_input:D
+  \__expl_primitive:NN \endinput              \tex_endinput:D
+  \__expl_primitive:NN \inputlineno           \tex_inputlineno:D
+  \__expl_primitive:NN \errmessage            \tex_errmessage:D
+  \__expl_primitive:NN \message               \tex_message:D
+  \__expl_primitive:NN \show                  \tex_show:D
+  \__expl_primitive:NN \showthe               \tex_showthe:D
+  \__expl_primitive:NN \showbox               \tex_showbox:D
+  \__expl_primitive:NN \showlists             \tex_showlists:D
+  \__expl_primitive:NN \errhelp               \tex_errhelp:D
+  \__expl_primitive:NN \errorcontextlines     \tex_errorcontextlines:D
+  \__expl_primitive:NN \tracingcommands       \tex_tracingcommands:D
+  \__expl_primitive:NN \tracinglostchars      \tex_tracinglostchars:D
+  \__expl_primitive:NN \tracingmacros         \tex_tracingmacros:D
+  \__expl_primitive:NN \tracingonline         \tex_tracingonline:D
+  \__expl_primitive:NN \tracingoutput         \tex_tracingoutput:D
+  \__expl_primitive:NN \tracingpages          \tex_tracingpages:D
+  \__expl_primitive:NN \tracingparagraphs     \tex_tracingparagraphs:D
+  \__expl_primitive:NN \tracingrestores       \tex_tracingrestores:D
+  \__expl_primitive:NN \tracingstats          \tex_tracingstats:D
+  \__expl_primitive:NN \pausing               \tex_pausing:D
+  \__expl_primitive:NN \showboxbreadth        \tex_showboxbreadth:D
+  \__expl_primitive:NN \showboxdepth          \tex_showboxdepth:D
+  \__expl_primitive:NN \batchmode             \tex_batchmode:D
+  \__expl_primitive:NN \errorstopmode         \tex_errorstopmode:D
+  \__expl_primitive:NN \nonstopmode           \tex_nonstopmode:D
+  \__expl_primitive:NN \scrollmode            \tex_scrollmode:D
+  \__expl_primitive:NN \end                   \tex_end:D
+  \__expl_primitive:NN \csname                \tex_csname:D
+  \__expl_primitive:NN \endcsname             \tex_endcsname:D
+  \__expl_primitive:NN \ignorespaces          \tex_ignorespaces:D
+  \__expl_primitive:NN \relax                 \tex_relax:D
+  \__expl_primitive:NN \the                   \tex_the:D
+  \__expl_primitive:NN \mag                   \tex_mag:D
+  \__expl_primitive:NN \language              \tex_language:D
+  \__expl_primitive:NN \mark                  \tex_mark:D
+  \__expl_primitive:NN \topmark               \tex_topmark:D
+  \__expl_primitive:NN \firstmark             \tex_firstmark:D
+  \__expl_primitive:NN \botmark               \tex_botmark:D
+  \__expl_primitive:NN \splitfirstmark        \tex_splitfirstmark:D
+  \__expl_primitive:NN \splitbotmark          \tex_splitbotmark:D
+  \__expl_primitive:NN \fontname              \tex_fontname:D
+  \__expl_primitive:NN \escapechar            \tex_escapechar:D
+  \__expl_primitive:NN \endlinechar           \tex_endlinechar:D
+  \__expl_primitive:NN \mathchoice            \tex_mathchoice:D
+  \__expl_primitive:NN \delimiter             \tex_delimiter:D
+  \__expl_primitive:NN \mathaccent            \tex_mathaccent:D
+  \__expl_primitive:NN \mathchar              \tex_mathchar:D
+  \__expl_primitive:NN \mskip                 \tex_mskip:D
+  \__expl_primitive:NN \radical               \tex_radical:D
+  \__expl_primitive:NN \vcenter               \tex_vcenter:D
+  \__expl_primitive:NN \mkern                 \tex_mkern:D
+  \__expl_primitive:NN \above                 \tex_above:D
+  \__expl_primitive:NN \abovewithdelims       \tex_abovewithdelims:D
+  \__expl_primitive:NN \atop                  \tex_atop:D
+  \__expl_primitive:NN \atopwithdelims        \tex_atopwithdelims:D
+  \__expl_primitive:NN \over                  \tex_over:D
+  \__expl_primitive:NN \overwithdelims        \tex_overwithdelims:D
+  \__expl_primitive:NN \displaystyle          \tex_displaystyle:D
+  \__expl_primitive:NN \textstyle             \tex_textstyle:D
+  \__expl_primitive:NN \scriptstyle           \tex_scriptstyle:D
+  \__expl_primitive:NN \scriptscriptstyle     \tex_scriptscriptstyle:D
+  \__expl_primitive:NN \nonscript             \tex_nonscript:D
+  \__expl_primitive:NN \eqno                  \tex_eqno:D
+  \__expl_primitive:NN \leqno                 \tex_leqno:D
+  \__expl_primitive:NN \abovedisplayshortskip \tex_abovedisplayshortskip:D
+  \__expl_primitive:NN \abovedisplayskip      \tex_abovedisplayskip:D
+  \__expl_primitive:NN \belowdisplayshortskip \tex_belowdisplayshortskip:D
+  \__expl_primitive:NN \belowdisplayskip      \tex_belowdisplayskip:D
+  \__expl_primitive:NN \displaywidowpenalty   \tex_displaywidowpenalty:D
+  \__expl_primitive:NN \displayindent         \tex_displayindent:D
+  \__expl_primitive:NN \displaywidth          \tex_displaywidth:D
+  \__expl_primitive:NN \everydisplay          \tex_everydisplay:D
+  \__expl_primitive:NN \predisplaysize        \tex_predisplaysize:D
+  \__expl_primitive:NN \predisplaypenalty     \tex_predisplaypenalty:D
+  \__expl_primitive:NN \postdisplaypenalty    \tex_postdisplaypenalty:D
+  \__expl_primitive:NN \mathbin               \tex_mathbin:D
+  \__expl_primitive:NN \mathclose             \tex_mathclose:D
+  \__expl_primitive:NN \mathinner             \tex_mathinner:D
+  \__expl_primitive:NN \mathop                \tex_mathop:D
+  \__expl_primitive:NN \displaylimits         \tex_displaylimits:D
+  \__expl_primitive:NN \limits                \tex_limits:D
+  \__expl_primitive:NN \nolimits              \tex_nolimits:D
+  \__expl_primitive:NN \mathopen              \tex_mathopen:D
+  \__expl_primitive:NN \mathord               \tex_mathord:D
+  \__expl_primitive:NN \mathpunct             \tex_mathpunct:D
+  \__expl_primitive:NN \mathrel               \tex_mathrel:D
+  \__expl_primitive:NN \overline              \tex_overline:D
+  \__expl_primitive:NN \underline             \tex_underline:D
+  \__expl_primitive:NN \left                  \tex_left:D
+  \__expl_primitive:NN \right                 \tex_right:D
+  \__expl_primitive:NN \binoppenalty          \tex_binoppenalty:D
+  \__expl_primitive:NN \relpenalty            \tex_relpenalty:D
+  \__expl_primitive:NN \delimitershortfall    \tex_delimitershortfall:D
+  \__expl_primitive:NN \delimiterfactor       \tex_delimiterfactor:D
+  \__expl_primitive:NN \nulldelimiterspace    \tex_nulldelimiterspace:D
+  \__expl_primitive:NN \everymath             \tex_everymath:D
+  \__expl_primitive:NN \mathsurround          \tex_mathsurround:D
+  \__expl_primitive:NN \medmuskip             \tex_medmuskip:D
+  \__expl_primitive:NN \thinmuskip            \tex_thinmuskip:D
+  \__expl_primitive:NN \thickmuskip           \tex_thickmuskip:D
+  \__expl_primitive:NN \scriptspace           \tex_scriptspace:D
+  \__expl_primitive:NN \noboundary            \tex_noboundary:D
+  \__expl_primitive:NN \accent                \tex_accent:D
+  \__expl_primitive:NN \char                  \tex_char:D
+  \__expl_primitive:NN \discretionary         \tex_discretionary:D
+  \__expl_primitive:NN \hfil                  \tex_hfil:D
+  \__expl_primitive:NN \hfilneg               \tex_hfilneg:D
+  \__expl_primitive:NN \hfill                 \tex_hfill:D
+  \__expl_primitive:NN \hskip                 \tex_hskip:D
+  \__expl_primitive:NN \hss                   \tex_hss:D
+  \__expl_primitive:NN \vfil                  \tex_vfil:D
+  \__expl_primitive:NN \vfilneg               \tex_vfilneg:D
+  \__expl_primitive:NN \vfill                 \tex_vfill:D
+  \__expl_primitive:NN \vskip                 \tex_vskip:D
+  \__expl_primitive:NN \vss                   \tex_vss:D
+  \__expl_primitive:NN \unskip                \tex_unskip:D
+  \__expl_primitive:NN \kern                  \tex_kern:D
+  \__expl_primitive:NN \unkern                \tex_unkern:D
+  \__expl_primitive:NN \hrule                 \tex_hrule:D
+  \__expl_primitive:NN \vrule                 \tex_vrule:D
+  \__expl_primitive:NN \leaders               \tex_leaders:D
+  \__expl_primitive:NN \cleaders              \tex_cleaders:D
+  \__expl_primitive:NN \xleaders              \tex_xleaders:D
+  \__expl_primitive:NN \lastkern              \tex_lastkern:D
+  \__expl_primitive:NN \lastskip              \tex_lastskip:D
+  \__expl_primitive:NN \indent                \tex_indent:D
+  \__expl_primitive:NN \par                   \tex_par:D
+  \__expl_primitive:NN \noindent              \tex_noindent:D
+  \__expl_primitive:NN \vadjust               \tex_vadjust:D
+  \__expl_primitive:NN \baselineskip          \tex_baselineskip:D
+  \__expl_primitive:NN \lineskip              \tex_lineskip:D
+  \__expl_primitive:NN \lineskiplimit         \tex_lineskiplimit:D
+  \__expl_primitive:NN \clubpenalty           \tex_clubpenalty:D
+  \__expl_primitive:NN \widowpenalty          \tex_widowpenalty:D
+  \__expl_primitive:NN \exhyphenpenalty       \tex_exhyphenpenalty:D
+  \__expl_primitive:NN \hyphenpenalty         \tex_hyphenpenalty:D
+  \__expl_primitive:NN \linepenalty           \tex_linepenalty:D
+  \__expl_primitive:NN \doublehyphendemerits  \tex_doublehyphendemerits:D
+  \__expl_primitive:NN \finalhyphendemerits   \tex_finalhyphendemerits:D
+  \__expl_primitive:NN \adjdemerits           \tex_adjdemerits:D
+  \__expl_primitive:NN \hangafter             \tex_hangafter:D
+  \__expl_primitive:NN \hangindent            \tex_hangindent:D
+  \__expl_primitive:NN \parshape              \tex_parshape:D
+  \__expl_primitive:NN \hsize                 \tex_hsize:D
+  \__expl_primitive:NN \lefthyphenmin         \tex_lefthyphenmin:D
+  \__expl_primitive:NN \righthyphenmin        \tex_righthyphenmin:D
+  \__expl_primitive:NN \leftskip              \tex_leftskip:D
+  \__expl_primitive:NN \rightskip             \tex_rightskip:D
+  \__expl_primitive:NN \looseness             \tex_looseness:D
+  \__expl_primitive:NN \parskip               \tex_parskip:D
+  \__expl_primitive:NN \parindent             \tex_parindent:D
+  \__expl_primitive:NN \uchyph                \tex_uchyph:D
+  \__expl_primitive:NN \emergencystretch      \tex_emergencystretch:D
+  \__expl_primitive:NN \pretolerance          \tex_pretolerance:D
+  \__expl_primitive:NN \tolerance             \tex_tolerance:D
+  \__expl_primitive:NN \spaceskip             \tex_spaceskip:D
+  \__expl_primitive:NN \xspaceskip            \tex_xspaceskip:D
+  \__expl_primitive:NN \parfillskip           \tex_parfillskip:D
+  \__expl_primitive:NN \everypar              \tex_everypar:D
+  \__expl_primitive:NN \prevgraf              \tex_prevgraf:D
+  \__expl_primitive:NN \spacefactor           \tex_spacefactor:D
+  \__expl_primitive:NN \shipout               \tex_shipout:D
+  \__expl_primitive:NN \vsize                 \tex_vsize:D
+  \__expl_primitive:NN \interlinepenalty      \tex_interlinepenalty:D
+  \__expl_primitive:NN \brokenpenalty         \tex_brokenpenalty:D
+  \__expl_primitive:NN \topskip               \tex_topskip:D
+  \__expl_primitive:NN \maxdeadcycles         \tex_maxdeadcycles:D
+  \__expl_primitive:NN \maxdepth              \tex_maxdepth:D
+  \__expl_primitive:NN \output                \tex_output:D
+  \__expl_primitive:NN \deadcycles            \tex_deadcycles:D
+  \__expl_primitive:NN \pagedepth             \tex_pagedepth:D
+  \__expl_primitive:NN \pagestretch           \tex_pagestretch:D
+  \__expl_primitive:NN \pagefilstretch        \tex_pagefilstretch:D
+  \__expl_primitive:NN \pagefillstretch       \tex_pagefillstretch:D
+  \__expl_primitive:NN \pagefilllstretch      \tex_pagefilllstretch:D
+  \__expl_primitive:NN \pageshrink            \tex_pageshrink:D
+  \__expl_primitive:NN \pagegoal              \tex_pagegoal:D
+  \__expl_primitive:NN \pagetotal             \tex_pagetotal:D
+  \__expl_primitive:NN \outputpenalty         \tex_outputpenalty:D
+  \__expl_primitive:NN \hoffset               \tex_hoffset:D
+  \__expl_primitive:NN \voffset               \tex_voffset:D
+  \__expl_primitive:NN \insert                \tex_insert:D
+  \__expl_primitive:NN \holdinginserts        \tex_holdinginserts:D
+  \__expl_primitive:NN \floatingpenalty       \tex_floatingpenalty:D
+  \__expl_primitive:NN \insertpenalties       \tex_insertpenalties:D
+  \__expl_primitive:NN \lower                 \tex_lower:D
+  \__expl_primitive:NN \moveleft              \tex_moveleft:D
+  \__expl_primitive:NN \moveright             \tex_moveright:D
+  \__expl_primitive:NN \raise                 \tex_raise:D
+  \__expl_primitive:NN \copy                  \tex_copy:D
+  \__expl_primitive:NN \lastbox               \tex_lastbox:D
+  \__expl_primitive:NN \vsplit                \tex_vsplit:D
+  \__expl_primitive:NN \unhbox                \tex_unhbox:D
+  \__expl_primitive:NN \unhcopy               \tex_unhcopy:D
+  \__expl_primitive:NN \unvbox                \tex_unvbox:D
+  \__expl_primitive:NN \unvcopy               \tex_unvcopy:D
+  \__expl_primitive:NN \setbox                \tex_setbox:D
+  \__expl_primitive:NN \hbox                  \tex_hbox:D
+  \__expl_primitive:NN \vbox                  \tex_vbox:D
+  \__expl_primitive:NN \vtop                  \tex_vtop:D
+  \__expl_primitive:NN \prevdepth             \tex_prevdepth:D
+  \__expl_primitive:NN \badness               \tex_badness:D
+  \__expl_primitive:NN \hbadness              \tex_hbadness:D
+  \__expl_primitive:NN \vbadness              \tex_vbadness:D
+  \__expl_primitive:NN \hfuzz                 \tex_hfuzz:D
+  \__expl_primitive:NN \vfuzz                 \tex_vfuzz:D
+  \__expl_primitive:NN \overfullrule          \tex_overfullrule:D
+  \__expl_primitive:NN \boxmaxdepth           \tex_boxmaxdepth:D
+  \__expl_primitive:NN \splitmaxdepth         \tex_splitmaxdepth:D
+  \__expl_primitive:NN \splittopskip          \tex_splittopskip:D
+  \__expl_primitive:NN \everyhbox             \tex_everyhbox:D
+  \__expl_primitive:NN \everyvbox             \tex_everyvbox:D
+  \__expl_primitive:NN \nullfont              \tex_nullfont:D
+  \__expl_primitive:NN \textfont              \tex_textfont:D
+  \__expl_primitive:NN \scriptfont            \tex_scriptfont:D
+  \__expl_primitive:NN \scriptscriptfont      \tex_scriptscriptfont:D
+  \__expl_primitive:NN \fontdimen             \tex_fontdimen:D
+  \__expl_primitive:NN \hyphenchar            \tex_hyphenchar:D
+  \__expl_primitive:NN \skewchar              \tex_skewchar:D
+  \__expl_primitive:NN \defaulthyphenchar     \tex_defaulthyphenchar:D
+  \__expl_primitive:NN \defaultskewchar       \tex_defaultskewchar:D
+  \__expl_primitive:NN \number                \tex_number:D
+  \__expl_primitive:NN \romannumeral          \tex_romannumeral:D
+  \__expl_primitive:NN \string                \tex_string:D
+  \__expl_primitive:NN \lowercase             \tex_lowercase:D
+  \__expl_primitive:NN \uppercase             \tex_uppercase:D
+  \__expl_primitive:NN \meaning               \tex_meaning:D
+  \__expl_primitive:NN \penalty               \tex_penalty:D
+  \__expl_primitive:NN \unpenalty             \tex_unpenalty:D
+  \__expl_primitive:NN \lastpenalty           \tex_lastpenalty:D
+  \__expl_primitive:NN \special               \tex_special:D
+  \__expl_primitive:NN \dump                  \tex_dump:D
+  \__expl_primitive:NN \patterns              \tex_patterns:D
+  \__expl_primitive:NN \hyphenation           \tex_hyphenation:D
+  \__expl_primitive:NN \time                  \tex_time:D
+  \__expl_primitive:NN \day                   \tex_day:D
+  \__expl_primitive:NN \month                 \tex_month:D
+  \__expl_primitive:NN \year                  \tex_year:D
+  \__expl_primitive:NN \jobname               \tex_jobname:D
+  \__expl_primitive:NN \everyjob              \tex_everyjob:D
+  \__expl_primitive:NN \count                 \tex_count:D
+  \__expl_primitive:NN \dimen                 \tex_dimen:D
+  \__expl_primitive:NN \skip                  \tex_skip:D
+  \__expl_primitive:NN \toks                  \tex_toks:D
+  \__expl_primitive:NN \muskip                \tex_muskip:D
+  \__expl_primitive:NN \box                   \tex_box:D
+  \__expl_primitive:NN \wd                    \tex_wd:D
+  \__expl_primitive:NN \ht                    \tex_ht:D
+  \__expl_primitive:NN \dp                    \tex_dp:D
+  \__expl_primitive:NN \catcode               \tex_catcode:D
+  \__expl_primitive:NN \delcode               \tex_delcode:D
+  \__expl_primitive:NN \sfcode                \tex_sfcode:D
+  \__expl_primitive:NN \lccode                \tex_lccode:D
+  \__expl_primitive:NN \uccode                \tex_uccode:D
+  \__expl_primitive:NN \mathcode              \tex_mathcode:D
 %    \end{macrocode}
 % Since \LaTeX3 requires at least the \eTeX{} extensions,
 % we also rename the additional primitives. These are all
 % given the prefix |\etex_|.
 %    \begin{macrocode}
-  \name_primitive:NN \ifdefined             \etex_ifdefined:D
-  \name_primitive:NN \ifcsname              \etex_ifcsname:D
-  \name_primitive:NN \unless                \etex_unless:D
-  \name_primitive:NN \eTeXversion           \etex_eTeXversion:D
-  \name_primitive:NN \eTeXrevision          \etex_eTeXrevision:D
-  \name_primitive:NN \marks                 \etex_marks:D
-  \name_primitive:NN \topmarks              \etex_topmarks:D
-  \name_primitive:NN \firstmarks            \etex_firstmarks:D
-  \name_primitive:NN \botmarks              \etex_botmarks:D
-  \name_primitive:NN \splitfirstmarks       \etex_splitfirstmarks:D
-  \name_primitive:NN \splitbotmarks         \etex_splitbotmarks:D
-  \name_primitive:NN \unexpanded            \etex_unexpanded:D
-  \name_primitive:NN \detokenize            \etex_detokenize:D
-  \name_primitive:NN \scantokens            \etex_scantokens:D
-  \name_primitive:NN \showtokens            \etex_showtokens:D
-  \name_primitive:NN \readline              \etex_readline:D
-  \name_primitive:NN \tracingassigns        \etex_tracingassigns:D
-  \name_primitive:NN \tracingscantokens     \etex_tracingscantokens:D
-  \name_primitive:NN \tracingnesting        \etex_tracingnesting:D
-  \name_primitive:NN \tracingifs            \etex_tracingifs:D
-  \name_primitive:NN \currentiflevel        \etex_currentiflevel:D
-  \name_primitive:NN \currentifbranch       \etex_currentifbranch:D
-  \name_primitive:NN \currentiftype         \etex_currentiftype:D
-  \name_primitive:NN \tracinggroups         \etex_tracinggroups:D
-  \name_primitive:NN \currentgrouplevel     \etex_currentgrouplevel:D
-  \name_primitive:NN \currentgrouptype      \etex_currentgrouptype:D
-  \name_primitive:NN \showgroups            \etex_showgroups:D
-  \name_primitive:NN \showifs               \etex_showifs:D
-  \name_primitive:NN \interactionmode       \etex_interactionmode:D
-  \name_primitive:NN \lastnodetype          \etex_lastnodetype:D
-  \name_primitive:NN \iffontchar            \etex_iffontchar:D
-  \name_primitive:NN \fontcharht            \etex_fontcharht:D
-  \name_primitive:NN \fontchardp            \etex_fontchardp:D
-  \name_primitive:NN \fontcharwd            \etex_fontcharwd:D
-  \name_primitive:NN \fontcharic            \etex_fontcharic:D
-  \name_primitive:NN \parshapeindent        \etex_parshapeindent:D
-  \name_primitive:NN \parshapelength        \etex_parshapelength:D
-  \name_primitive:NN \parshapedimen         \etex_parshapedimen:D
-  \name_primitive:NN \numexpr               \etex_numexpr:D
-  \name_primitive:NN \dimexpr               \etex_dimexpr:D
-  \name_primitive:NN \glueexpr              \etex_glueexpr:D
-  \name_primitive:NN \muexpr                \etex_muexpr:D
-  \name_primitive:NN \gluestretch           \etex_gluestretch:D
-  \name_primitive:NN \glueshrink            \etex_glueshrink:D
-  \name_primitive:NN \gluestretchorder      \etex_gluestretchorder:D
-  \name_primitive:NN \glueshrinkorder       \etex_glueshrinkorder:D
-  \name_primitive:NN \gluetomu              \etex_gluetomu:D
-  \name_primitive:NN \mutoglue              \etex_mutoglue:D
-  \name_primitive:NN \lastlinefit           \etex_lastlinefit:D
-  \name_primitive:NN \interlinepenalties    \etex_interlinepenalties:D
-  \name_primitive:NN \clubpenalties         \etex_clubpenalties:D
-  \name_primitive:NN \widowpenalties        \etex_widowpenalties:D
-  \name_primitive:NN \displaywidowpenalties \etex_displaywidowpenalties:D
-  \name_primitive:NN \middle                \etex_middle:D
-  \name_primitive:NN \savinghyphcodes       \etex_savinghyphcodes:D
-  \name_primitive:NN \savingvdiscards       \etex_savingvdiscards:D
-  \name_primitive:NN \pagediscards          \etex_pagediscards:D
-  \name_primitive:NN \splitdiscards         \etex_splitdiscards:D
-  \name_primitive:NN \TeXXeTstate           \etex_TeXXeTstate:D
-  \name_primitive:NN \beginL                \etex_beginL:D
-  \name_primitive:NN \endL                  \etex_endL:D
-  \name_primitive:NN \beginR                \etex_beginR:D
-  \name_primitive:NN \endR                  \etex_endR:D
-  \name_primitive:NN \predisplaydirection   \etex_predisplaydirection:D
-  \name_primitive:NN \everyeof              \etex_everyeof:D
-  \name_primitive:NN \protected             \etex_protected:D
+  \__expl_primitive:NN \ifdefined             \etex_ifdefined:D
+  \__expl_primitive:NN \ifcsname              \etex_ifcsname:D
+  \__expl_primitive:NN \unless                \etex_unless:D
+  \__expl_primitive:NN \eTeXversion           \etex_eTeXversion:D
+  \__expl_primitive:NN \eTeXrevision          \etex_eTeXrevision:D
+  \__expl_primitive:NN \marks                 \etex_marks:D
+  \__expl_primitive:NN \topmarks              \etex_topmarks:D
+  \__expl_primitive:NN \firstmarks            \etex_firstmarks:D
+  \__expl_primitive:NN \botmarks              \etex_botmarks:D
+  \__expl_primitive:NN \splitfirstmarks       \etex_splitfirstmarks:D
+  \__expl_primitive:NN \splitbotmarks         \etex_splitbotmarks:D
+  \__expl_primitive:NN \unexpanded            \etex_unexpanded:D
+  \__expl_primitive:NN \detokenize            \etex_detokenize:D
+  \__expl_primitive:NN \scantokens            \etex_scantokens:D
+  \__expl_primitive:NN \showtokens            \etex_showtokens:D
+  \__expl_primitive:NN \readline              \etex_readline:D
+  \__expl_primitive:NN \tracingassigns        \etex_tracingassigns:D
+  \__expl_primitive:NN \tracingscantokens     \etex_tracingscantokens:D
+  \__expl_primitive:NN \tracingnesting        \etex_tracingnesting:D
+  \__expl_primitive:NN \tracingifs            \etex_tracingifs:D
+  \__expl_primitive:NN \currentiflevel        \etex_currentiflevel:D
+  \__expl_primitive:NN \currentifbranch       \etex_currentifbranch:D
+  \__expl_primitive:NN \currentiftype         \etex_currentiftype:D
+  \__expl_primitive:NN \tracinggroups         \etex_tracinggroups:D
+  \__expl_primitive:NN \currentgrouplevel     \etex_currentgrouplevel:D
+  \__expl_primitive:NN \currentgrouptype      \etex_currentgrouptype:D
+  \__expl_primitive:NN \showgroups            \etex_showgroups:D
+  \__expl_primitive:NN \showifs               \etex_showifs:D
+  \__expl_primitive:NN \interactionmode       \etex_interactionmode:D
+  \__expl_primitive:NN \lastnodetype          \etex_lastnodetype:D
+  \__expl_primitive:NN \iffontchar            \etex_iffontchar:D
+  \__expl_primitive:NN \fontcharht            \etex_fontcharht:D
+  \__expl_primitive:NN \fontchardp            \etex_fontchardp:D
+  \__expl_primitive:NN \fontcharwd            \etex_fontcharwd:D
+  \__expl_primitive:NN \fontcharic            \etex_fontcharic:D
+  \__expl_primitive:NN \parshapeindent        \etex_parshapeindent:D
+  \__expl_primitive:NN \parshapelength        \etex_parshapelength:D
+  \__expl_primitive:NN \parshapedimen         \etex_parshapedimen:D
+  \__expl_primitive:NN \numexpr               \etex_numexpr:D
+  \__expl_primitive:NN \dimexpr               \etex_dimexpr:D
+  \__expl_primitive:NN \glueexpr              \etex_glueexpr:D
+  \__expl_primitive:NN \muexpr                \etex_muexpr:D
+  \__expl_primitive:NN \gluestretch           \etex_gluestretch:D
+  \__expl_primitive:NN \glueshrink            \etex_glueshrink:D
+  \__expl_primitive:NN \gluestretchorder      \etex_gluestretchorder:D
+  \__expl_primitive:NN \glueshrinkorder       \etex_glueshrinkorder:D
+  \__expl_primitive:NN \gluetomu              \etex_gluetomu:D
+  \__expl_primitive:NN \mutoglue              \etex_mutoglue:D
+  \__expl_primitive:NN \lastlinefit           \etex_lastlinefit:D
+  \__expl_primitive:NN \interlinepenalties    \etex_interlinepenalties:D
+  \__expl_primitive:NN \clubpenalties         \etex_clubpenalties:D
+  \__expl_primitive:NN \widowpenalties        \etex_widowpenalties:D
+  \__expl_primitive:NN \displaywidowpenalties \etex_displaywidowpenalties:D
+  \__expl_primitive:NN \middle                \etex_middle:D
+  \__expl_primitive:NN \savinghyphcodes       \etex_savinghyphcodes:D
+  \__expl_primitive:NN \savingvdiscards       \etex_savingvdiscards:D
+  \__expl_primitive:NN \pagediscards          \etex_pagediscards:D
+  \__expl_primitive:NN \splitdiscards         \etex_splitdiscards:D
+  \__expl_primitive:NN \TeXXeTstate           \etex_TeXXeTstate:D
+  \__expl_primitive:NN \beginL                \etex_beginL:D
+  \__expl_primitive:NN \endL                  \etex_endL:D
+  \__expl_primitive:NN \beginR                \etex_beginR:D
+  \__expl_primitive:NN \endR                  \etex_endR:D
+  \__expl_primitive:NN \predisplaydirection   \etex_predisplaydirection:D
+  \__expl_primitive:NN \everyeof              \etex_everyeof:D
+  \__expl_primitive:NN \protected             \etex_protected:D
 %    \end{macrocode}
 % The newer primitives are more complex: there are an awful lot of them,
 % and we don't use them all at the moment. So the following is selective.
@@ -561,43 +561,43 @@
 % there are a lot of \pdfTeX{} primitives that start \cs{pdf\ldots} but
 % are not related to PDF output. These ones related to PDF output.
 %    \begin{macrocode}
-  \name_primitive:NN \pdfcreationdate       \pdftex_pdfcreationdate:D
-  \name_primitive:NN \pdfcolorstack         \pdftex_pdfcolorstack:D
-  \name_primitive:NN \pdfcompresslevel      \pdftex_pdfcompresslevel:D
-  \name_primitive:NN \pdfdecimaldigits      \pdftex_pdfdecimaldigits:D
-  \name_primitive:NN \pdfhorigin            \pdftex_pdfhorigin:D
-  \name_primitive:NN \pdfinfo               \pdftex_pdfinfo:D
-  \name_primitive:NN \pdflastxform          \pdftex_pdflastxform:D
-  \name_primitive:NN \pdfliteral            \pdftex_pdfliteral:D
-  \name_primitive:NN \pdfminorversion       \pdftex_pdfminorversion:D
-  \name_primitive:NN \pdfobjcompresslevel   \pdftex_pdfobjcompresslevel:D
-  \name_primitive:NN \pdfoutput             \pdftex_pdfoutput:D
-  \name_primitive:NN \pdfrefxform           \pdftex_pdfrefxform:D
-  \name_primitive:NN \pdfrestore            \pdftex_pdfrestore:D
-  \name_primitive:NN \pdfsave               \pdftex_pdfsave:D
-  \name_primitive:NN \pdfsetmatrix          \pdftex_pdfsetmatrix:D
-  \name_primitive:NN \pdfpkresolution       \pdftex_pdfpkresolution:D
-  \name_primitive:NN \pdftexrevision        \pdftex_pdftextrevision:D
-  \name_primitive:NN \pdfvorigin            \pdftex_pdfvorigin:D
-  \name_primitive:NN \pdfxform              \pdftex_pdfxform:D
+  \__expl_primitive:NN \pdfcreationdate       \pdftex_pdfcreationdate:D
+  \__expl_primitive:NN \pdfcolorstack         \pdftex_pdfcolorstack:D
+  \__expl_primitive:NN \pdfcompresslevel      \pdftex_pdfcompresslevel:D
+  \__expl_primitive:NN \pdfdecimaldigits      \pdftex_pdfdecimaldigits:D
+  \__expl_primitive:NN \pdfhorigin            \pdftex_pdfhorigin:D
+  \__expl_primitive:NN \pdfinfo               \pdftex_pdfinfo:D
+  \__expl_primitive:NN \pdflastxform          \pdftex_pdflastxform:D
+  \__expl_primitive:NN \pdfliteral            \pdftex_pdfliteral:D
+  \__expl_primitive:NN \pdfminorversion       \pdftex_pdfminorversion:D
+  \__expl_primitive:NN \pdfobjcompresslevel   \pdftex_pdfobjcompresslevel:D
+  \__expl_primitive:NN \pdfoutput             \pdftex_pdfoutput:D
+  \__expl_primitive:NN \pdfrefxform           \pdftex_pdfrefxform:D
+  \__expl_primitive:NN \pdfrestore            \pdftex_pdfrestore:D
+  \__expl_primitive:NN \pdfsave               \pdftex_pdfsave:D
+  \__expl_primitive:NN \pdfsetmatrix          \pdftex_pdfsetmatrix:D
+  \__expl_primitive:NN \pdfpkresolution       \pdftex_pdfpkresolution:D
+  \__expl_primitive:NN \pdftexrevision        \pdftex_pdftextrevision:D
+  \__expl_primitive:NN \pdfvorigin            \pdftex_pdfvorigin:D
+  \__expl_primitive:NN \pdfxform              \pdftex_pdfxform:D
 %    \end{macrocode}
 % While these are not.
 %    \begin{macrocode}
-  \name_primitive:NN \pdfstrcmp             \pdftex_strcmp:D
+  \__expl_primitive:NN \pdfstrcmp             \pdftex_strcmp:D
 %    \end{macrocode}
 % \XeTeX{}-specific primitives. Note that \XeTeX{}'s \tn{strcmp} is
 % handled earlier and is \enquote{rolled up} into \tn{pdfstrcmp}.
 %    \begin{macrocode}
-  \name_primitive:NN \XeTeXversion          \xetex_XeTeXversion:D
+  \__expl_primitive:NN \XeTeXversion          \xetex_XeTeXversion:D
 %    \end{macrocode}
 % Primitives from \LuaTeX{}.
 %    \begin{macrocode}
-  \name_primitive:NN \catcodetable          \luatex_catcodetable:D
-  \name_primitive:NN \directlua             \luatex_directlua:D
-  \name_primitive:NN \initcatcodetable      \luatex_initcatcodetable:D
-  \name_primitive:NN \latelua               \luatex_latelua:D
-  \name_primitive:NN \luatexversion         \luatex_luatexversion:D
-  \name_primitive:NN \savecatcodetable      \luatex_savecatcodetable:D
+  \__expl_primitive:NN \catcodetable          \luatex_catcodetable:D
+  \__expl_primitive:NN \directlua             \luatex_directlua:D
+  \__expl_primitive:NN \initcatcodetable      \luatex_initcatcodetable:D
+  \__expl_primitive:NN \latelua               \luatex_latelua:D
+  \__expl_primitive:NN \luatexversion         \luatex_luatexversion:D
+  \__expl_primitive:NN \savecatcodetable      \luatex_savecatcodetable:D
 %    \end{macrocode}
 % The job is done: close the group (using the primitive renamed!).
 %    \begin{macrocode}
@@ -612,7 +612,7 @@
 \tex_let:D \tex_everymath:D         \frozen@everymath
 \tex_let:D \tex_hyphen:D            \@@hyph
 \tex_let:D \tex_input:D             \@@input
-\tex_let:D \tex_italic_correction:D \@@italiccorr
+\tex_let:D \tex_italiccorrection:D  \@@italiccorr
 \tex_let:D \tex_underline:D         \@@underline
 %    \end{macrocode}
 % That is also true for the \pkg{luatex} package for \LaTeXe{}.
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3prg.dtx b/Master/texmf-dist/source/latex/l3kernel/l3prg.dtx
index 88f53e59759..6d4fb15351d 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3prg.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3prg.dtx
@@ -1,6 +1,6 @@
 % \iffalse meta-comment
 %
-%% File: l3prg.dtx Copyright (C) 2005-2011 The LaTeX3 Project
+%% File: l3prg.dtx Copyright (C) 2005-2012 The LaTeX3 Project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -35,8 +35,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3prg.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental control structures}
+\GetIdInfo$Id: l3prg.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Control structures}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -78,13 +78,13 @@
 % \LaTeX3 has two forms of conditional flow processing based
 % on these states. The firs form is predicate functions that turn the
 % returned state into a boolean \meta{true} or \meta{false}. For
-% example, the function |\cs_if_free_p:N| checks whether the control
+% example, the function \cs{cs_if_free_p:N} checks whether the control
 % sequence given as its argument is free and then returns the boolean
 % \meta{true} or \meta{false} values to be used in testing with
-% |\if_predicate:w| or in functions to be described below.  The second form
+% \cs{if_predicate:w} or in functions to be described below.  The second form
 % is the kind of functions choosing a particular argument from the
 % input stream based on the result of the testing as in
-% |\cs_if_free:NTF| which also takes one argument (the |N|) and then
+% \cs{cs_if_free:NTF} which also takes one argument (the |N|) and then
 % executes either \texttt{true} or \texttt{false} depending on the
 % result. Important to note here is that the arguments are executed
 % after exiting the underlying |\if...\fi:| structure.
@@ -182,13 +182,13 @@
 % This defines the function |\foo_if_bar_p:NN|, |\foo_if_bar:NNTF| and
 % |\foo_if_bar:NNT| but not |\foo_if_bar:NNF| (because |F| is missing
 % from the \meta{conditions} list). The return statements take care of
-% resolving the remaining |\else:| and |\fi:| before returning the
+% resolving the remaining \cs{else:} and \cs{fi:} before returning the
 % state. There must be a return statement for each branch, failing to do
 % so will result in an error if that branch is executed.
 %
 % \begin{function}{\prg_new_eq_conditional:NNn, \prg_set_eq_conditional:NNn}
 %   \begin{syntax}
-%     \cs{prg_new_eq_conditional:NNn} \cs{\meta{name1}:\meta{arg spec1}} \cs{\meta{name2}:\meta{arg spec2}} \Arg{conditions}
+%     \cs{prg_new_eq_conditional:NNn} \cs{\meta{name_1}:\meta{arg spec_1}} \cs{\meta{name_2}:\meta{arg spec_2}} \Arg{conditions}
 %   \end{syntax}
 %   These functions copies a family of conditionals. The \texttt{new} version
 %   will check for existing definitions (\emph{cf.}~\cs{cs_new:Npn}) whereas
@@ -214,12 +214,12 @@
 % connected to conditional processing as sometimes you want to
 % execute some code depending on the value of a switch
 % (\emph{e.g.},~draft/final) and other times you perhaps want to use it as a
-% predicate function in an |\if_predicate:w| test. The problem of the
-% primitive |\if_false:| and |\if_true:| tokens is that it is not
+% predicate function in an \cs{if_predicate:w} test. The problem of the
+% primitive \cs{if_false:} and \cs{if_true:} tokens is that it is not
 % always safe to pass them around as they may interfere with scanning
 % for termination of primitive conditional processing. Therefore, we
-% employ two canonical booleans: |\c_true_bool| or
-% |\c_false_bool|. Besides preventing problems as described above, it
+% employ two canonical booleans: \cs{c_true_bool} or
+% \cs{c_false_bool}. Besides preventing problems as described above, it
 % also allows us to implement a simple boolean parser supporting the
 % logical operations And, Or, Not, \emph{etc.}\ which can then be used on
 % both the boolean type and predicate functions.
@@ -265,12 +265,12 @@
 %     \bool_gset_eq:NN, \bool_gset_eq:cN, \bool_gset_eq:Nc, \bool_gset_eq:cc
 %   }
 %   \begin{syntax}
-%     \cs{bool_set_eq:NN} \meta{boolean1} \meta{boolean2}
+%     \cs{bool_set_eq:NN} \meta{boolean_1} \meta{boolean_2}
 %   \end{syntax}
-%   Sets the content of \meta{boolean1} equal to that of \meta{boolean2}.
+%   Sets the content of \meta{boolean_1} equal to that of \meta{boolean_2}.
 % \end{function}
 %
-% \begin{function}
+% \begin{function}[updated = 2012-07-08]
 %   {\bool_set:Nn, \bool_set:cn, \bool_gset:Nn, \bool_gset:cn}
 %   \begin{syntax}
 %     \cs{bool_set:Nn} \meta{boolean} \Arg{boolexpr}
@@ -296,7 +296,7 @@
 %   Displays the logical truth of the \meta{boolean} on the terminal.
 % \end{function}
 %
-% \begin{function}[added = 2012-02-09]{\bool_show:n}
+% \begin{function}[added = 2012-02-09, updated = 2012-07-08]{\bool_show:n}
 %   \begin{syntax}
 %     \cs{bool_show:n} \Arg{boolean expression}
 %   \end{syntax}
@@ -314,14 +314,14 @@
 %   check that the \meta{boolean} really is a boolean variable.
 % \end{function}
 %
-% \begin{variable}{\l_tmpa_bool}
+% \begin{variable}{\l_tmpa_bool, \l_tmpb_bool}
 %   A scratch boolean for local assignment. It is never used by
 %   the kernel code, and so is safe for use with any \LaTeX3-defined
 %   function. However, it may be overwritten by other non-kernel
 %   code and so should only be used for short-term storage.
 % \end{variable}
 %
-% \begin{variable}{\g_tmpa_bool}
+% \begin{variable}{\g_tmpa_bool, \g_tmpb_bool}
 %   A scratch boolean for global assignment. It is never used by
 %   the kernel code, and so is safe for use with any \LaTeX3-defined
 %   function. However, it may be overwritten by other non-kernel
@@ -337,7 +337,8 @@
 % A boolean expression is an expression which given input in the form
 % of predicate functions and boolean variables, return boolean
 % \meta{true} or \meta{false}. It supports the logical operations And,
-% Or and Not as the well-known infix operators |&&|, \verb"||" and |!|. In
+% Or and Not as the well-known infix operators |&&|, \verb"||" and |!|
+% with their usual precedences. In
 % addition to this, parentheses can be used to isolate
 % sub-expressions. For example,
 % \begin{verbatim}
@@ -354,7 +355,7 @@
 % be changed any more, the remaining tests within the current group
 % are skipped.
 %
-% \begin{function}[EXP,pTF]{\bool_if:n}
+% \begin{function}[EXP, pTF, updated = 2012-07-08]{\bool_if:n}
 %   \begin{syntax}
 %     \cs{bool_if_p:n} \Arg{boolean expression}
 %     \cs{bool_if:nTF} \Arg{boolean expression} \Arg{true code} \Arg{false code}
@@ -367,7 +368,7 @@
 %   |!| (\enquote{Not}) and parentheses. Minimal evaluation is used
 %   in the processing, so that once a result is defined there is
 %   not further expansion of the tests. For example
-%  \begin{verbatim}
+%   \begin{verbatim}
 %     \bool_if_p:n
 %       {
 %        \int_compare_p:nNn { 1 } = { 1 }
@@ -378,17 +379,15 @@
 %          \int_compare_p:nNn { 1 } = { \error } % is skipped
 %        )
 %        &&
-%        ! ( \int_compare_p:nNn { 2 } = { 4 } )
+%        ! \int_compare_p:nNn { 2 } = { 4 }
 %     }
 %   \end{verbatim}
 %   will be \texttt{true} and will not evaluate
 %   |\int_compare_p:nNn { 1 } = { \error }|. The logical Not applies to
-%   the next single predicate or group. As shown above, this means that
-%   any predicates requiring an argument have to be given within
-%   parentheses.
+%   the next predicate or group.
 % \end{function}
 %
-% \begin{function}[EXP]{\bool_not_p:n}
+% \begin{function}[EXP, updated = 2012-07-08]{\bool_not_p:n}
 %   \begin{syntax}
 %      \cs{bool_not_p:n} \Arg{boolean expression}
 %   \end{syntax}
@@ -396,9 +395,9 @@
 %   expression.
 % \end{function}
 %
-% \begin{function}[EXP]{\bool_xor_p:nn}
+% \begin{function}[EXP, updated = 2012-07-08]{\bool_xor_p:nn}
 %   \begin{syntax}
-%     \cs{bool_xor_p:nn} \Arg{boolexpr_1} \Arg{boolexpr_1}
+%     \cs{bool_xor_p:nn} \Arg{boolexpr_1} \Arg{boolexpr_2}
 %   \end{syntax}
 %   Implements an \enquote{exclusive or} operation between two boolean
 %   expressions. There is no infix operation for this logical
@@ -431,7 +430,7 @@
 %   until the \meta{boolean} is \texttt{false}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\bool_until_do:nn}
+% \begin{function}[rEXP, updated = 2012-07-08]{\bool_until_do:nn}
 %   \begin{syntax}
 %     \cs{bool_until_do:nn} \Arg{boolean expression} \Arg{code}
 %   \end{syntax}
@@ -443,7 +442,7 @@
 %   then loop until the \meta{boolean expression} is \texttt{true}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\bool_while_do:nn}
+% \begin{function}[rEXP, updated = 2012-07-08]{\bool_while_do:nn}
 %   \begin{syntax}
 %     \cs{bool_while_do:nn} \Arg{boolean expression} \Arg{code}
 %   \end{syntax}
@@ -455,109 +454,6 @@
 %   then loop until the \meta{boolean expression} is \texttt{false}.
 % \end{function}
 %
-% \section{Switching by case}
-%
-% For cases where a number of cases need to be considered a family of
-% case-selecting functions are available.
-%
-% \begin{function}[updated = 2011-09-17, EXP]{\prg_case_int:nnn}
-%   \begin{syntax}
-%     \cs{prg_case_int:nnn} \Arg{test integer expression} \\
-%     ~~|{| \\
-%     ~~~~\Arg{intexpr case1} \Arg{code case1} \\
-%     ~~~~\Arg{intexpr case2} \Arg{code case2} \\
-%     ~~~~\ldots \\
-%     ~~~~\Arg{intexpr case$\sb{n}$} \Arg{code case$\sb{n}$} \\
-%     ~~|}| \\
-%     ~~\Arg{else case}
-%   \end{syntax}
-%   This function evaluates the \meta{test integer expression} and
-%   compares this in turn to each of the
-%   \meta{integer expression cases}. If the two are equal then the
-%   associated \meta{code} is left in the input stream. If none of
-%   the tests are \texttt{true} then the \texttt{else code} will be
-%   left in the input stream.
-% \end{function}
-%
-% As an example of \cs{prg_case_int:nnn}:
-%   \begin{verbatim}
-%     \prg_case_int:nnn
-%       { 2 * 5 }
-%       {
-%         { 5 }       { Small }
-%         { 4 + 6 }   { Medium }
-%         { -2 * 10 } { Negative }
-%       }
-%       { No idea! }
-%    \end{verbatim}
-%   will leave \enquote{\texttt{Medium}} in the input stream.
-%
-% \begin{function}[updated = 2011-07-06, EXP]{\prg_case_dim:nnn}
-%   \begin{syntax}
-%     \cs{prg_case_dim:nnn} \Arg{test dimension expression} \\
-%     ~~|{| \\
-%     ~~~~\Arg{dimexpr case1} \Arg{code case1} \\
-%     ~~~~\Arg{dimexpr case2} \Arg{code case2} \\
-%     ~~~~\ldots \\
-%     ~~~~\Arg{dimexpr case$\sb{n}$} \Arg{code case$\sb{n}$} \\
-%     ~~|}| \\
-%     ~~\Arg{else case}
-%   \end{syntax}
-%   This function evaluates the \meta{test dimension expression} and
-%   compares this in turn to each of the
-%   \meta{dimension expression cases}. If the two are equal then the
-%   associated \meta{code} is left in the input stream. If none of
-%   the tests are \texttt{true} then the \texttt{else code} will be
-%   left in the input stream.
-% \end{function}
-%
-% \begin{function}[updated = 2011-09-17, EXP]
-%   {\prg_case_str:nnn, \prg_case_str:onn, \prg_case_str:xxn}
-%   \begin{syntax}
-%     \cs{prg_case_str:nnn} \Arg{test string} \\
-%     ~~|{| \\
-%     ~~~~\Arg{string case1} \Arg{code case1} \\
-%     ~~~~\Arg{string case2} \Arg{code case2} \\
-%     ~~~~\ldots \\
-%     ~~~~\Arg{string case$\sb{n}$} \Arg{code case$\sb{n}$} \\
-%     ~~|}| \\
-%     ~~\Arg{else case}
-%   \end{syntax}
-%   This function compares the \meta{test string} in turn with each
-%   of the \meta{string cases}. If the two are equal (as described for
-%   \cs{str_if_eq:nnTF} then the
-%   associated \meta{code} is left in the input stream. If none of
-%   the tests are \texttt{true} then the \texttt{else code} will be
-%   left in the input stream. The |xx| variant fully expands
-%   \meta{strings} before comparing them, but does not expand the
-%   corresponding \meta{code}. It is fully expandable, in the same way
-%   as the underlying \cs{str_if_eq:xxTF} test.
-%^^A The \meta{test string} is expanded in each comparison, and must
-%^^A always yield the same result: in particular, random numbers should
-%^^A not be used within this string.
-% \end{function}
-%
-% \begin{function}[updated = 2011-09-17, EXP]
-%   {\prg_case_tl:Nnn, \prg_case_tl:cnn}
-%   \begin{syntax}
-%     \cs{prg_case_tl:Nnn} \meta{test token list variable} \\
-%     ~~"{" \\
-%     ~~~~\meta{token list variable case1} \Arg{code case1} \\
-%     ~~~~\meta{token list variable case2} \Arg{code case2} \\
-%     ~~~~\ldots \\
-%     ~~~~\meta{token list variable case$\sb{n}$} \Arg{code case$\sb{n}$} \\
-%     ~~"}" \\
-%     ~~\Arg{else case}
-%   \end{syntax}
-%   This function compares the \meta{test token list variable} in turn
-%   with each of the \meta{token list variable cases}. If the two
-%   are equal (as described for
-%   \cs{tl_if_eq:nnTF}
-%   then the associated \meta{code} is left in the input
-%   stream. If none of the tests are \texttt{true} then the
-%   \texttt{else code} will be left in the input stream.
-% \end{function}
-%
 % \section{Producing $n$ copies}
 %
 % \begin{function}[updated = 2011-07-04, EXP]{\prg_replicate:nn}
@@ -570,54 +466,6 @@
 %   nesting. It yields its result after two expansion steps.
 % \end{function}
 %
-% \begin{function}[updated = 2011-09-06,rEXP]{\prg_stepwise_function:nnnN}
-%   \begin{syntax}
-%     \cs{prg_stepwise_function:nnnN} \Arg{initial value} \Arg{step} \Arg{final value} \meta{function}
-%   \end{syntax}
-%   This function first evaluates the \meta{initial value}, \meta{step}
-%   and \meta{final value}, all of which should be integer expressions.
-%   The \meta{function} is then placed in front of each \meta{value}
-%   from the \meta{initial value} to the \meta{final value} in turn
-%   (using \meta{step} between each \meta{value}). Thus \meta{function}
-%   should absorb one numerical argument. For example
-%   \begin{verbatim}
-%     \cs_set:Npn \my_func:n #1 { [I~saw~#1] \quad }
-%     \prg_stepwise_function:nnnN { 1 } { 1 } { 5 } \my_func:n
-%   \end{verbatim}
-%   would print
-%   \begin{quote}
-%     [I saw 1] \quad
-%     [I saw 2] \quad
-%     [I saw 3] \quad
-%     [I saw 4] \quad
-%     [I saw 5] \quad
-%   \end{quote}
-% \end{function}
-%
-% \begin{function}[updated = 2011-09-06]{\prg_stepwise_inline:nnnn}
-%   \begin{syntax}
-%     \cs{prg_stepwise_inline:nnnn} \Arg{initial value} \Arg{step} \Arg{final value} \Arg{code}
-%   \end{syntax}
-%   This function first evaluates the \meta{initial value}, \meta{step}
-%   and \meta{final value}, all of which should be integer expressions.
-%   The \meta{code} is then placed in front of each \meta{value}
-%   from the \meta{initial value} to the \meta{final value} in turn
-%   (using \meta{step} between each \meta{value}). Thus the \meta{code}
-%   should define a function of one argument (|#1|).
-% \end{function}
-%
-% \begin{function}[updated = 2011-09-06]{\prg_stepwise_variable:nnnNn}
-%   \begin{syntax}
-%     \cs{prg_stepwise_variable:nnnNn} \\
-%     ~~\Arg{initial value} \Arg{step} \Arg{final value} \meta{tl~var} \Arg{code}
-%   \end{syntax}
-%   This function first evaluates the \meta{initial value}, \meta{step}
-%   and \meta{final value}, all of which should be integer expressions.
-%   The \meta{code} is inserted into the input stream, with the
-%   \meta{tl~var} defined as the current \meta{value}. Thus the
-%   \meta{code} should make use of the \meta{tl~var}.
-% \end{function}
-%
 % \section{Detecting \TeX{}'s mode}
 %
 % \begin{function}[EXP,pTF]{\mode_if_horizontal:}
@@ -651,6 +499,26 @@
 %   Detects if \TeX{} is currently in vertical mode.
 % \end{function}
 %
+% \section{Primitive conditionals}
+%
+% \begin{function}[EXP]{\if_predicate:w}
+%   \begin{syntax}
+%     "\if_predicate:w" <predicate> <true code> "\else:" <false code> "\fi:"
+%   \end{syntax}
+%   This function takes a predicate function and
+%   branches according to the result.  (In practice this function would also
+%   accept a single boolean variable in place of the <predicate> but to make the
+%   coding clearer this should be done through "\if_bool:N".)
+% \end{function}
+%
+% \begin{function}[EXP]{\if_bool:N}
+%   \begin{syntax}
+%     "\if_bool:N" <boolean> <true code> "\else:" <false code> "\fi:"
+%   \end{syntax}
+%   This function takes a boolean variable and
+%   branches according to the result.
+% \end{function}
+%
 % \section{Internal programming functions}
 %
 % \begin{function}[updated = 2011-08-11, EXP]
@@ -692,61 +560,70 @@
 %   \end{texnote}
 % \end{function}
 %
-% \begin{function}[EXP]{\prg_variable_get_scope:N}
+% \begin{function}[EXP]{\__prg_variable_get_scope:N}
 %   \begin{syntax}
-%     \cs{prg_variable_get_scope:N} \meta{variable}
+%     \cs{__prg_variable_get_scope:N} \meta{variable}
 %   \end{syntax}
 %   Returns the scope (\texttt{g} for global, blank otherwise) for the
 %   \meta{variable}.
 % \end{function}
 %
-% \begin{function}[EXP]{\prg_variable_get_type:N}
+% \begin{function}[EXP]{\__prg_variable_get_type:N}
 %   \begin{syntax}
-%     \cs{prg_variable_get_type:N} \meta{variable}
+%     \cs{__prg_variable_get_type:N} \meta{variable}
 %   \end{syntax}
 %   Returns the type of \meta{variable} (\texttt{tl}, \texttt{int},
 %   \emph{etc.})
 % \end{function}
 %
-% \begin{function}[EXP]{\if_predicate:w}
+% \begin{function}[EXP]{\__prg_break_point:Nn}
 %   \begin{syntax}
-%     "\if_predicate:w" <predicate> <true code> "\else:" <false code> "\fi:"
+%     \cs{__prg_break_point:Nn} \cs{\meta{type}_map_break:} \meta{tokens}
 %   \end{syntax}
-%   This function takes a predicate function and
-%   branches according to the result.  (In practice this function would also
-%   accept a single boolean variable in place of the <predicate> but to make the
-%   coding clearer this should be done through "\if_bool:N".)
+%   Used to mark the end of a recursion or mapping: the functions
+%   \cs{\meta{type}_map_break:} and \cs{\meta{type}_map_break:n} use
+%   this to break out of the loop. After the loop ends, the
+%   \meta{tokens} are inserted into the input stream. This occurs even
+%   if the the break functions are \emph{not} applied:
+%   \cs{__prg_break_point:Nn} is functionally-equivalent in these cases
+%   to \cs{use_ii:nn}.
 % \end{function}
 %
-% \begin{function}[EXP]{\if_bool:N}
+% \begin{function}[EXP]{\__prg_map_break:Nn}
 %   \begin{syntax}
-%     "\if_bool:N" <boolean> <true code> "\else:" <false code> "\fi:"
+%     \cs{__prg_map_break:Nn} \cs{\meta{type}_map_break:} \Arg{user code}
+%     \ldots{}
+%     \cs{__prg_break_point:Nn} \cs{\meta{type}_map_break:} \Arg{ending code}
 %   \end{syntax}
-%   This function takes a boolean variable and
-%   branches according to the result.
+%   Breaks a recursion in mapping contexts, inserting in the input
+%   stream the \meta{user code} after the \meta{ending code} for the
+%   loop.  The function breaks loops, inserting their \meta{ending
+%     code}, until reaching a loop with the same \meta{type} as its
+%   first argument.  This \cs{\meta{type}_map_break:} argument is simply
+%   used as a recognizable marker for the \meta{type}.
 % \end{function}
 %
-% \begin{function}[EXP]{\prg_break_point:n}
-%   \begin{syntax}
-%     \cs{prg_break_point:n} \meta{tokens}
-%   \end{syntax}
-%   Used to mark the end of a recursion or mapping: the functions
-%   \cs{prg_map_break:} and \cs{prg_map_break:n} use this to break out
-%   of the loop. After the loop ends, the \meta{tokens} are inserted into
-%   the input stream. This occurs even if the the break functions are
-%   \emph{not} applied: \cs{prg_break_point:n} is functionally-equivalent
-%   in these cases to \cs{use:n}.
+% \begin{variable}{\g__prg_map_int}
+%   This integer is used by non-expandable mapping functions to track
+%   the level of nesting in force.  The functions \cs{__prg_map_1:w},
+%   \cs{__prg_map_2:w}, \emph{etc.}, labelled by \cs{g__prg_map_int}
+%   hold functions to be mapped over various list datatypes in inline
+%   and variable mappings.
+% \end{variable}
+%
+% \begin{function}[EXP]{\__prg_break_point:}
+%   This copy of \cs{prg_do_nothing:} is used to mark the end of a fast
+%   short-term recursions: the function \cs{__prg_break:n} uses this to
+%   break out of the loop.
 % \end{function}
 %
-% \begin{function}[EXP]{\prg_map_break:, \prg_map_break:n}
+% \begin{function}[EXP]{\__prg_break:, \__prg_break:n}
 %   \begin{syntax}
-%     \cs{prg_map_break:n} \Arg{user code}
-%     \ldots{}
-%     \cs{prg_break_point:n} \Arg{ending code}
+%     \cs{__prg_break:n} \Arg{tokens} \ldots{} \cs{__prg_break_point:}
 %   \end{syntax}
-%   Breaks a recursion in mapping contexts, inserting
-%   in the input stream the \meta{user code} after the
-%   \meta{ending code} for the loop.
+%   Breaks a recursion which has no \meta{ending code} and which is not
+%   a user-breakable mapping (see for instance \cs{prop_get:Nn}), and
+%   inserts \meta{tokens} in the input stream.
 % \end{function}
 %
 % \end{documentation}
@@ -765,7 +642,7 @@
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
@@ -815,6 +692,10 @@
 %
 % \subsection{The boolean data type}
 %
+%    \begin{macrocode}
+%<@@=bool>
+%    \end{macrocode}
+%
 % \begin{macro}{\bool_new:N, \bool_new:c}
 % \UnitTested
 %   Boolean variables have to be initiated when they are created. Other
@@ -874,7 +755,7 @@
 % \begin{macro}{\bool_set:Nn,\bool_set:cn}
 % \begin{macro}{\bool_gset:Nn,\bool_gset:cn}
 %   This function evaluates a boolean expression and assigns the first
-%   argument the meaning |\c_true_bool| or |\c_false_bool|.
+%   argument the meaning \cs{c_true_bool} or \cs{c_false_bool}.
 %    \begin{macrocode}
 \cs_new_protected:Npn \bool_set:Nn #1#2
   { \tex_chardef:D #1 = \bool_if_p:n {#2} }
@@ -884,6 +765,7 @@
 \cs_generate_variant:Nn \bool_gset:Nn { c }
 %    \end{macrocode}
 % \end{macro}
+% \end{macro}
 %
 % \begin{macro}[pTF]{\bool_if:N, \bool_if:c}
 % \UnitTested
@@ -904,11 +786,10 @@
 \cs_generate_variant:Nn \bool_if:NTF { c }
 %    \end{macrocode}
 % \end{macro}
-% \end{macro}
 %
 % \begin{macro}{\bool_show:N, \bool_show:c, \bool_show:n}
 %   Show the truth value of the boolean, as \texttt{true} or
-%   \texttt{false}. We use \cs{msg_aux_show:x} to get a better output;
+%   \texttt{false}. We use \cs{__msg_show_variable:x} to get a better output;
 %   this function requires its argument to start with |>|.
 %    \begin{macrocode}
 \cs_new_protected:Npn \bool_show:N #1
@@ -916,25 +797,27 @@
     \bool_if_exist:NTF #1
       { \bool_show:n {#1} }
       {
-        \msg_kernel_error:nnx { kernel } { variable-not-defined }
+        \__msg_kernel_error:nnx { kernel } { variable-not-defined }
           { \token_to_str:N #1 }
       }
   }
 \cs_new_protected:Npn \bool_show:n #1
   {
     \bool_if:nTF {#1}
-      { \msg_aux_show:x { > true } }
-      { \msg_aux_show:x { > false } }
+      { \__msg_show_variable:x { > true } }
+      { \__msg_show_variable:x { > false } }
   }
 \cs_generate_variant:Nn \bool_show:N { c }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{variable}{\l_tmpa_bool, \g_tmpa_bool}
+% \begin{variable}{\l_tmpa_bool, \l_tmpb_bool, \g_tmpa_bool, \g_tmpb_bool}
 %    A few booleans just if you need them.
 %    \begin{macrocode}
 \bool_new:N \l_tmpa_bool
+\bool_new:N \l_tmpb_bool
 \bool_new:N \g_tmpa_bool
+\bool_new:N \g_tmpb_bool
 %    \end{macrocode}
 % \end{variable}
 %
@@ -956,36 +839,12 @@
 %
 % \begin{macro}[pTF]{\bool_if:n}
 % \UnitTested
-% \begin{macro}[aux]{\bool_get_next:N}
-% \begin{macro}[aux]{\bool_cleanup:N}
-% \begin{macro}[aux]{\bool_choose:NN}
-% \begin{macro}[aux]
-%   {
-%     bool_!:w,
-%     \bool_Not:w,
-%     \bool_Not:w,
-%     \bool_(:w,
-%     \bool_p:w,
-%     \bool_8_1:w,
-%     \bool_I_1:w,
-%     \bool_8_0:w,
-%     \bool_I_0:w,
-%     \bool_)_0:w,
-%     \bool_)_1:w,
-%     \bool_S_0:w,
-%     \bool_S_1:w
-% }
-% \begin{macro}[aux]
-%   {
-%     \bool_eval_skip_to_end:Nw, \bool_eval_skip_to_end_aux:Nw,
-%     \bool_eval_skip_to_end_aux_ii:Nw
-%  }
-%   Evaluating the truth value of a list of predicates is done using
-%   an input syntax somewhat similar to the one found in other
-%   programming languages with |(| and |)| for grouping, |!| for
-%   logical \enquote{Not}, |&&| for logical \enquote{And} and \verb"||"
-%   for logical \enquote{Or}. We shall use the terms Not, And, Or, Open and
-%   Close for  these operations.
+%   Evaluating the truth value of a list of predicates is done using an
+%   input syntax somewhat similar to the one found in other programming
+%   languages with |(| and |)| for grouping, |!| for logical
+%   \enquote{Not}, |&&| for logical \enquote{And} and \verb"||" for
+%   logical \enquote{Or}.  We shall use the terms Not, And, Or, Open and
+%   Close for these operations.
 %
 %   Any expression is terminated by a Close operation. Evaluation
 %   happens from left to right in the following manner using a GetNext
@@ -993,16 +852,18 @@
 %   \begin{itemize}
 %     \item If an Open is seen, start evaluating a new expression using
 %       the Eval function and call GetNext again.
-%     \item If a Not is seen, insert a negating function (if-even in
-%       this case) and call GetNext.
-%     \item If none of the above, start evaluating a new expression by
-%       reinserting the token found (this is supposed to be a predicate
-%       function) in front of Eval.
+%     \item If a Not is seen, remove the |!| and call a GetNotNext
+%       function, which eventually reverses the logic compared to
+%       GetNext.
+%     \item If none of the above, reinsert the token found (this is
+%       supposed to be a predicate function) in front of an Eval
+%       function, which evaluates it to the boolean value \meta{true} or
+%       \meta{false}.
 %   \end{itemize}
 %   The Eval function then contains a post-processing operation which
-%   grabs the instruction following the predicate. This is either And,
-%   Or or Close. In each case the truth value is used to determine
-%   where to go next. The following situations can arise:
+%   grabs the instruction following the predicate.  This is either And,
+%   Or or Close.  In each case the truth value is used to determine
+%   where to go next.  The following situations can arise:
 %   \begin{description}
 %     \item[\meta{true}And] Current truth value is true, logical And
 %       seen, continue with GetNext to examine truth value of next
@@ -1021,8 +882,8 @@
 %     \item[\meta{false}Close] Current truth value is false, Close
 %       seen, return \meta{false}.
 %   \end{description}
-%   We introduce an additional Stop operation with the following
-%   semantics:
+%   We introduce an additional Stop operation with the same
+%   semantics as the Close operation.
 %   \begin{description}
 %     \item[\meta{true}Stop] Current truth value is true, return
 %       \meta{true}.
@@ -1030,17 +891,6 @@
 %       \meta{false}.
 %   \end{description}
 %   The reasons for this follow below.
-%
-%   Now for how these works in practice. The canonical true and false
-%   values have numerical values $1$ and $0$ respectively. We evaluate
-%   this using the primitive |\int_value:w:D| operation. First we
-%   issue a |\group_align_safe_begin:| as we are using |&&| as syntax
-%   shorthand for the And operation and we need to hide it for \TeX{}.
-%   We also need to finish this special group before finally
-%   returning a |\c_true_bool| or |\c_false_bool| as there might
-%   otherwise be something left in front in the input stream. For
-%   this we call the Stop operation, denoted simply by a |S|
-%   following the last Close operation.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \bool_if:n #1 { T , F , TF }
   {
@@ -1050,178 +900,195 @@
       \prg_return_false:
     \fi:
   }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\bool_if_p:n}
+% \begin{macro}[EXP, aux]
+%   {
+%     \@@_if_left_parentheses:wwwn ,
+%     \@@_if_right_parentheses:wwwn ,
+%     \@@_if_or:wwwn
+%   }
+%   First issue a \cs{group_align_safe_begin:} as we are using |&&|
+%   as syntax shorthand for the And operation and we need to hide it for
+%   \TeX{}.  This will be closed at the end of the expression parsing
+%   (see |S| below).
+%
+%   Minimal (\enquote{short-circuit}) evaluation of boolean expressions
+%   requires skipping to the end of the current parenthesized group when
+%   \meta{true}\verb"||" is seen, but to the next \verb"||" or closing
+%   parenthesis when \meta{false}|&&| is seen.  To avoid having separate
+%   functions for the two cases, we transform the boolean expression by
+%   doubling each parenthesis and adding parenthesis around each
+%   \verb"||".  This ensures that |&&| will bind tighter than \verb"||".
+%
+%   The replacement is done in three passes, for left and right
+%   parentheses and for \verb"||".  At each pass, the part of the
+%   expression that has been transformed is stored before \cs{q_nil},
+%   the rest lies until the first \cs{q_mark}, followed by an empty
+%   brace group.  A trailing marker ensures that the auxiliaries'
+%   delimited arguments will not run-away.  As long as the delimiter
+%   matches inside the expression, material is moved before \cs{q_nil}
+%   and we continue.  Afterwards, the trailing marker is taken as a
+%   delimiter, |#4| is the next auxiliary, immediately followed by a new
+%   \cs{q_nil} delimiter, which indicates that nothing has been treated
+%   at this pass.  The last step calls \cs{@@_if_parse:NNNww} which
+%   cleans up and triggers the evaluation of the expression itself.
+%    \begin{macrocode}
 \cs_new:Npn \bool_if_p:n #1
   {
     \group_align_safe_begin:
-    \bool_get_next:N ( #1 ) S
+    \@@_if_left_parentheses:wwwn \q_nil
+      #1 \q_mark { }
+      (  \q_mark { \@@_if_right_parentheses:wwwn \q_nil }
+      )  \q_mark { \@@_if_or:wwwn \q_nil }
+      || \q_mark \@@_if_parse:NNNww
+    \q_stop
   }
+\cs_new:Npn \@@_if_left_parentheses:wwwn #1 \q_nil #2 ( #3 \q_mark #4
+  { #4 \@@_if_left_parentheses:wwwn #1 #2 (( \q_nil #3 \q_mark {#4} }
+\cs_new:Npn \@@_if_right_parentheses:wwwn #1 \q_nil #2 ) #3 \q_mark #4
+  { #4 \@@_if_right_parentheses:wwwn #1 #2 )) \q_nil #3 \q_mark {#4} }
+\cs_new:Npn \@@_if_or:wwwn #1 \q_nil #2 || #3 \q_mark #4
+  { #4 \@@_if_or:wwwn #1 #2 )||( \q_nil #3 \q_mark {#4} }
 %    \end{macrocode}
-%   The GetNext operation. We make it a switch: If not a |!| or |(|, we
-%   assume it is a predicate.
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP, aux]{\@@_if_parse:NNNww}
+%   After removing extra tokens from the transformation phase, start
+%   evaluating.  At the end, we will need to finish the special
+%   \texttt{align_safe} group before finally
+%   returning a \cs{c_true_bool} or \cs{c_false_bool} as there might
+%   otherwise be something left in front in the input stream. For this
+%   we call the Stop operation, denoted simply by a |S| following the
+%   last Close operation.
 %    \begin{macrocode}
-\cs_new:Npn \bool_get_next:N #1
+\cs_new:Npn \@@_if_parse:NNNww #1#2#3#4 \q_mark #5 \q_stop
   {
-    \use:c
-      {
-        bool_
-        \if_meaning:w !#1 ! \else: \if_meaning:w (#1 ( \else: p \fi: \fi:
-        :w
-      }
-      #1
+    \__bool_get_next:NN \use_i:nn (( #4 )) S
   }
 %    \end{macrocode}
-%   This variant gets called when a Not has just been entered.
-%   It (eventually) results in a reversal of the logic of the directly
-%   following material.
+% \end{macro}
+%
+% \begin{macro}[aux]{\@@_get_next:NN}
+%   The GetNext operation.  This is a switch: if what follows is neither
+%   |!| nor |(|, we assume it is a predicate.  The first argument is
+%   \cs{use_ii:nn} if the logic must eventually be reversed (after a
+%   |!|), otherwise it is \cs{use_i:nn}.  This function eventually
+%   expand to the truth value \cs{c_true_bool} or \cs{c_false_bool} of
+%   the expression which follows until the next unmatched closing
+%   parenthesis.
 %    \begin{macrocode}
-\cs_new:Npn \bool_get_not_next:N #1
+\cs_new:Npn \@@_get_next:NN #1#2
   {
     \use:c
       {
-      bool_not_
-      \if_meaning:w !#1 ! \else: \if_meaning:w (#1 ( \else: p \fi: \fi:
-      :w
+        @@_
+        \if_meaning:w !#2 ! \else: \if_meaning:w (#2 ( \else: p \fi: \fi:
+        :Nw
       }
-        #1
-  }
-%    \end{macrocode}
-%   We need these later on to nullify the unity operation |!!|.
-%    \begin{macrocode}
-\cs_new:Npn \bool_get_next:NN #1#2 { \bool_get_next:N #2 }
-\cs_new:Npn \bool_get_not_next:NN #1#2 { \bool_get_not_next:N #2 }
-%    \end{macrocode}
-%   The Not operation. Discard the token read and reverse the truth
-%   value of the next expression if there
-%   are brackets; otherwise
-%   if we're coming up to a |!| then we don't need to reverse anything
-%   (but we then want to continue scanning ahead in case some fool has written
-%   |!!(...)|);
-%   otherwise we have a boolean that we can reverse here and now.
-%    \begin{macrocode}
-\cs_new:cpn { bool_!:w } #1#2
-  {
-    \if_meaning:w ( #2
-      \exp_after:wN \bool_Not:w
-    \else:
-      \if_meaning:w ! #2
-        \exp_after:wN \exp_after:wN \exp_after:wN \bool_get_next:NN
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN \bool_Not:N
-      \fi:
-    \fi:
-    #2
-  }
-%    \end{macrocode}
-%   Variant called when already inside a Not.
-%   Essentially the opposite of the above.
-%    \begin{macrocode}
-\cs_new:cpn { bool_not_!:w } #1#2
-  {
-    \if_meaning:w ( #2
-      \exp_after:wN \bool_not_Not:w
-    \else:
-      \if_meaning:w ! #2
-        \exp_after:wN \exp_after:wN \exp_after:wN \bool_get_not_next:NN
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN \bool_not_Not:N
-      \fi:
-    \fi:
-    #2
+      #1 #2
   }
 %    \end{macrocode}
-%   These occur when processing |!(...)|. The idea is to use a variant
-%   of |\bool_get_next:N| that finishes its parsing with a logic reversal.
-%   Of course, the double logic reversal gets us back to where we started.
+% \end{macro}
+%
+% \begin{macro}[aux]{\@@_!:Nw}
+%   The Not operation reverses the logic: discard the |!| token and call
+%   the GetNext operation with its first argument reversed.
 %    \begin{macrocode}
-\cs_new:Npn \bool_Not:w { \exp_after:wN \int_value:w \bool_get_not_next:N }
-\cs_new:Npn \bool_not_Not:w { \exp_after:wN \int_value:w \bool_get_next:N }
+\cs_new:cpn { @@_!:Nw } #1#2
+  { \exp_after:wN \@@_get_next:NN #1 \use_ii:nn \use_i:nn }
 %    \end{macrocode}
-%   These occur when processing |!<bool>| and can be evaluated directly.
+% \end{macro}
+%
+% \begin{macro}[aux]{\@@_(:Nw}
+%   The Open operation starts a sub-expression after discarding the
+%   token.  This is done by calling GetNext, with a post-processing step
+%   which looks for And, Or or Close afterwards.
 %    \begin{macrocode}
-\cs_new:Npn \bool_Not:N #1
+\cs_new:cpn { @@_(:Nw } #1#2
   {
-    \exp_after:wN \bool_p:w
-    \if_meaning:w #1 \c_true_bool
-      \c_false_bool
-    \else:
-      \c_true_bool
-    \fi:
+    \exp_after:wN \@@_choose:NNN \exp_after:wN #1
+    \__int_value:w \@@_get_next:NN \use_i:nn
   }
-\cs_new:Npn \bool_not_Not:N #1
-  {
-    \exp_after:wN \bool_p:w
-    \if_meaning:w #1 \c_true_bool
-      \c_true_bool
-    \else:
-      \c_false_bool
-    \fi:
-  }
-%    \end{macrocode}
-%   The Open operation. Discard the token read and start a
-%   sub-expression.
-%   |\bool_get_next:N| continues building up the logical expressions as usual;
-%   |\bool_not_cleanup:N| is what reverses the logic if we're inside |!(...)|.
-%    \begin{macrocode}
-\cs_new:cpn { bool_(:w } #1
-  { \exp_after:wN  \bool_cleanup:N \int_value:w \bool_get_next:N }
-\cs_new:cpn { bool_not_(:w } #1
-  { \exp_after:wN  \bool_not_cleanup:N \int_value:w \bool_get_next:N }
 %    \end{macrocode}
-%   Otherwise just evaluate the predicate and look for And, Or or Close
-%   afterwards.
+% \end{macro}
+%
+% \begin{macro}[aux]{\@@_p:Nw}
+%   If what follows GetNext is neither |!| nor |(|, evaluate the
+%   predicate using the primitive \cs{__int_value:w}.  The canonical
+%   true and false values have numerical values $1$ and $0$
+%   respectively.  Look for And, Or or Close afterwards.
 %    \begin{macrocode}
-\cs_new:cpn { bool_p:w } { \exp_after:wN \bool_cleanup:N \int_value:w  }
-\cs_new:cpn { bool_not_p:w } {\exp_after:wN \bool_not_cleanup:N \int_value:w }
+\cs_new:cpn { @@_p:Nw } #1
+  { \exp_after:wN \@@_choose:NNN \exp_after:wN #1 \__int_value:w }
 %    \end{macrocode}
-%   This cleanup function can be omitted once predicates return their
-%   true/false booleans outside the conditionals.
+% \end{macro}
+%
+% \begin{macro}[aux]{\@@_choose:NNN}
+%   Branching the eight-way switch.  The arguments are 1: \cs{use_i:nn}
+%   or \cs{use_ii:nn}, 2: $0$ or $1$ encoding the current truth value,
+%   3: the next operation, And, Or, Close or Stop.  If |#1| is
+%   \cs{use_ii:nn}, the logic of |#2| must be reversed.
 %    \begin{macrocode}
-\cs_new:Npn \bool_cleanup:N #1
+\cs_new:Npn \@@_choose:NNN #1#2#3
   {
-    \exp_after:wN \bool_choose:NN \exp_after:wN #1
-    \int_to_roman:w - `\q
-  }
-\cs_new:Npn \bool_not_cleanup:N #1
-  {
-    \exp_after:wN \bool_not_choose:NN \exp_after:wN #1
-    \int_to_roman:w - `\q
+    \use:c
+      {
+        @@_ #3 _
+        #1 #2 { \if_meaning:w 0 #2 1 \else: 0 \fi: }
+        :w
+      }
   }
 %    \end{macrocode}
-%   Branching the six way switch.
-%   Reversals should be reasonably straightforward.
-%    \begin{macrocode}
-\cs_new:Npn \bool_choose:NN #1#2 { \use:c { bool_ #2 _ #1 :w } }
-\cs_new:Npn \bool_not_choose:NN #1#2 { \use:c { bool_not_ #2 _ #1 :w } }
-%    \end{macrocode}
-%   Continues scanning. Must remove the second "&" or \verb"|".
-%    \begin{macrocode}
-\cs_new_nopar:cpn { bool_&_1:w } & { \bool_get_next:N }
-\cs_new_nopar:cpn { bool_|_0:w } | { \bool_get_next:N }
-\cs_new_nopar:cpn { bool_not_&_0:w } & { \bool_get_next:N }
-\cs_new_nopar:cpn { bool_not_|_1:w } | { \bool_get_next:N }
-%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux]
+%   {
+%     \@@_)_0:w,
+%     \@@_)_1:w,
+%     \@@_S_0:w,
+%     \@@_S_1:w,
+%   }
 %   Closing a group is just about returning the result. The Stop
 %   operation is similar except it closes the special alignment group
 %   before returning the boolean.
 %    \begin{macrocode}
-\cs_new_nopar:cpn { bool_)_0:w } { \c_false_bool }
-\cs_new_nopar:cpn { bool_)_1:w } { \c_true_bool }
-\cs_new_nopar:cpn { bool_not_)_0:w } { \c_true_bool }
-\cs_new_nopar:cpn { bool_not_)_1:w } { \c_false_bool }
-\cs_new_nopar:cpn { bool_S_0:w } { \group_align_safe_end: \c_false_bool }
-\cs_new_nopar:cpn { bool_S_1:w } { \group_align_safe_end: \c_true_bool }
+\cs_new_nopar:cpn { @@_)_0:w } { \c_false_bool }
+\cs_new_nopar:cpn { @@_)_1:w } { \c_true_bool }
+\cs_new_nopar:cpn { @@_S_0:w } { \group_align_safe_end: \c_false_bool }
+\cs_new_nopar:cpn { @@_S_1:w } { \group_align_safe_end: \c_true_bool }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux]+\@@_&_1:w+
+% \begin{macro}[aux]+\@@_|_0:w+
+%   Two cases where we simply continue scanning.  We must remove the
+%   second "&" or \verb"|".
+%    \begin{macrocode}
+\cs_new_nopar:cpn { @@_&_1:w } & { \@@_get_next:NN \use_i:nn }
+\cs_new_nopar:cpn { @@_|_0:w } | { \@@_get_next:NN \use_i:nn }
 %    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[aux]+\@@_&_0:w+
+% \begin{macro}[aux]+\@@_|_1:w+
+% \begin{macro}[aux]
+%   {
+%     \@@_eval_skip_to_end:Nw,
+%     \@@_eval_skip_to_end_ii:Nw,
+%     \@@_eval_skip_to_end_iii:Nw
+%   }
 %   When the truth value has already been decided, we have to throw away
 %   the remainder of the current group as we are doing minimal
 %   evaluation. This is slightly tricky as there are no braces so we
 %   have to play match the |()| manually.
 %    \begin{macrocode}
-\cs_new_nopar:cpn { bool_&_0:w } & { \bool_eval_skip_to_end:Nw \c_false_bool }
-\cs_new_nopar:cpn { bool_|_1:w } | { \bool_eval_skip_to_end:Nw \c_true_bool }
-\cs_new_nopar:cpn { bool_not_&_1:w } &
-  { \bool_eval_skip_to_end:Nw \c_false_bool }
-\cs_new_nopar:cpn { bool_not_|_0:w } |
-  { \bool_eval_skip_to_end:Nw \c_true_bool }
+\cs_new_nopar:cpn { @@_&_0:w } & { \@@_eval_skip_to_end:Nw \c_false_bool }
+\cs_new_nopar:cpn { @@_|_1:w } | { \@@_eval_skip_to_end:Nw \c_true_bool }
 %    \end{macrocode}
 %   There is always at least one |)| waiting, namely the outer
 %   one. However, we are facing the problem that there may be more than
@@ -1275,9 +1142,9 @@
 %   finally close the group nicely.
 %    \begin{macrocode}
 %% (
-\cs_new:Npn \bool_eval_skip_to_end:Nw #1#2 )
+\cs_new:Npn \@@_eval_skip_to_end:Nw #1#2 )
   {
-    \bool_eval_skip_to_end_aux:Nw #1#2 ( % )
+    \@@_eval_skip_to_end_ii:Nw #1#2 ( % )
     \q_no_value \q_stop
     {#2}
   }
@@ -1286,31 +1153,29 @@
 %   the boolean |#1|.  If there is, we need to grab a |()| pair and then
 %   recurse
 %    \begin{macrocode}
-\cs_new:Npn \bool_eval_skip_to_end_aux:Nw #1#2 ( #3#4 \q_stop #5 % )
+\cs_new:Npn \@@_eval_skip_to_end_ii:Nw #1#2 ( #3#4 \q_stop #5 % )
   {
     \quark_if_no_value:NTF #3
     {#1}
-    { \bool_eval_skip_to_end_aux_ii:Nw #1 #5 }
+    { \@@_eval_skip_to_end_iii:Nw #1 #5 }
   }
 %    \end{macrocode}
 %   Keep the boolean, throw away anything up to the |(| as it is
 %   irrelevant, remove a |()| pair but remember to reinsert |#3| as it may
 %   contain |(| tokens!
 %    \begin{macrocode}
-\cs_new:Npn \bool_eval_skip_to_end_aux_ii:Nw #1#2 ( #3 )
+\cs_new:Npn \@@_eval_skip_to_end_iii:Nw #1#2 ( #3 )
   { % (
-    \bool_eval_skip_to_end:Nw #1#3 )
+    \@@_eval_skip_to_end:Nw #1#3 )
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 % \end{macro}
-% \end{macro}
-% \end{macro}
 %
 % \begin{macro}{\bool_not_p:n}
 % \UnitTested
-%   The Not variant just reverses the outcome of |\bool_if_p:n|. Can
+%   The Not variant just reverses the outcome of \cs{bool_if_p:n}. Can
 %   be optimized but this is nice and simple and according to the
 %   implementation plan. Not even particularly useful to have it when
 %   the infix notation is easier to use.
@@ -1410,156 +1275,42 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \subsection{Switching by case}
-%
-% A family of functions to select one case of a number: the same ideas
-% are used for a number of different situations.
-%
-% \begin{macro}[aux]{\prg_case_end:nw}
-%   In all cases the end statement is the same. Here, |#1| will be the
-%   code needed, |#2| the other cases to throw away, including the
-%   \enquote{else} case. The \cs{c_zero} marker stops the expansion of
-%   \tn{romannumeral} which begins each \cs{prg_case_...} function.
-%    \begin{macrocode}
-\cs_new:Npn \prg_case_end:nw #1 #2 \q_recursion_stop { \c_zero #1 }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\prg_case_int:nnn}
-% \UnitTested
-% \begin{macro}[aux]{\prg_case_int_aux:nnn,\prg_case_int_aux:nw}
-%   For integer cases, the first task to fully expand the check
-%   condition. After that, a loop is started to compare each possible
-%   value and stop if the test is true. The tested value is put at the
-%   end to ensure that there is necessarily a match, which will fire the
-%   \enquote{else} pathway. The leading \tn{romannumeral} triggers an
-%   expansion which is then stopped in \cs{prg_case_end:nw}.
-%    \begin{macrocode}
-\cs_new:Npn \prg_case_int:nnn #1
-  {
-    \tex_romannumeral:D
-    \exp_args:Nf \prg_case_int_aux:nnn { \int_eval:n {#1} }
-  }
-\cs_new:Npn \prg_case_int_aux:nnn #1 #2 #3
-  { \prg_case_int_aux:nw {#1} #2 {#1} {#3} \q_recursion_stop }
-\cs_new:Npn \prg_case_int_aux:nw #1#2#3
-  {
-    \int_compare:nNnTF {#1} = {#2}
-      { \prg_case_end:nw {#3} }
-      { \prg_case_int_aux:nw {#1} }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\prg_case_dim:nnn}
-% \UnitTested
-% \begin{macro}[aux]{\prg_case_dim_aux:nnn,\prg_case_dim_aux:nw}
-%   The dimension function is the same, just a change of calculation
-%   method.
-%    \begin{macrocode}
-\cs_new:Npn \prg_case_dim:nnn #1
-  {
-    \tex_romannumeral:D
-    \exp_args:Nf \prg_case_dim_aux:nnn { \dim_eval:n {#1} }
-  }
-\cs_new:Npn \prg_case_dim_aux:nnn #1 #2 #3
-  { \prg_case_dim_aux:nw {#1} #2 {#1} {#3} \q_recursion_stop }
-\cs_new:Npn \prg_case_dim_aux:nw #1#2#3
-  {
-    \dim_compare:nNnTF {#1} = {#2}
-      { \prg_case_end:nw {#3} }
-      { \prg_case_dim_aux:nw {#1} }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\prg_case_str:nnn, \prg_case_str:onn, \prg_case_str:xxn}
-% \UnitTested
-% \begin{macro}[aux]{\prg_case_str_aux:nw, \prg_case_str_x_aux:nw}
-%   No calculations for strings, otherwise no surprises.
-%    \begin{macrocode}
-\cs_new:Npn \prg_case_str:nnn #1#2#3
-  {
-    \tex_romannumeral:D
-    \prg_case_str_aux:nw {#1} #2 {#1} {#3} \q_recursion_stop
-  }
-\cs_new:Npn \prg_case_str_aux:nw #1#2#3
-  {
-    \str_if_eq:nnTF {#1} {#2}
-      { \prg_case_end:nw {#3} }
-      { \prg_case_str_aux:nw {#1} }
-  }
-\cs_generate_variant:Nn \prg_case_str:nnn { o }
-\cs_new:Npn \prg_case_str:xxn #1#2#3
-  {
-    \tex_romannumeral:D
-    \prg_case_str_x_aux:nw {#1} #2 {#1} {#3} \q_recursion_stop
-  }
-\cs_new:Npn \prg_case_str_x_aux:nw #1#2#3
-  {
-    \str_if_eq:xxTF {#1} {#2}
-      { \prg_case_end:nw {#3} }
-      { \prg_case_str_x_aux:nw {#1} }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
+% \subsection{Producing $n$ copies}
 %
-% \begin{macro}{\prg_case_tl:Nnn, \prg_case_tl:cnn}
-% \UnitTested
-% \begin{macro}[aux]{\prg_case_tl_aux:Nw}
-%   Similar again, but this time with some variants.
 %    \begin{macrocode}
-\cs_new:Npn \prg_case_tl:Nnn #1#2#3
-  {
-    \tex_romannumeral:D
-    \prg_case_tl_aux:Nw #1 #2 #1 {#3} \q_recursion_stop
-  }
-\cs_new:Npn \prg_case_tl_aux:Nw #1#2#3
-  {
-    \tl_if_eq:NNTF #1 #2
-      { \prg_case_end:nw {#3} }
-      { \prg_case_tl_aux:Nw #1 }
-  }
-\cs_generate_variant:Nn \prg_case_tl:Nnn { c }
+%<@@=prg>
 %    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Producing $n$ copies}
 %
 % \begin{macro}{\prg_replicate:nn}
 % \UnitTested
-% \begin{macro}[aux]{\prg_replicate_aux:N, \prg_replicate_first_aux:N}
-% \begin{macro}[aux]{\prg_replicate_}
+% \begin{macro}[aux]{\@@_replicate:N, \@@_replicate_first:N}
+% \begin{macro}[aux]{\@@_replicate_}
 % \begin{macro}[aux]
 %   {
-%     \prg_replicate_0:n,
-%     \prg_replicate_1:n,
-%     \prg_replicate_2:n,
-%     \prg_replicate_3:n,
-%     \prg_replicate_4:n,
-%     \prg_replicate_5:n,
-%     \prg_replicate_6:n,
-%     \prg_replicate_7:n,
-%     \prg_replicate_8:n,
-%     \prg_replicate_9:n
+%     \@@_replicate_0:n,
+%     \@@_replicate_1:n,
+%     \@@_replicate_2:n,
+%     \@@_replicate_3:n,
+%     \@@_replicate_4:n,
+%     \@@_replicate_5:n,
+%     \@@_replicate_6:n,
+%     \@@_replicate_7:n,
+%     \@@_replicate_8:n,
+%     \@@_replicate_9:n
 %   }
 % \begin{macro}[aux]
 %   {
-%     \prg_replicate_first_-:n,
-%     \prg_replicate_first_0:n,
-%     \prg_replicate_first_1:n,
-%     \prg_replicate_first_2:n,
-%     \prg_replicate_first_3:n,
-%     \prg_replicate_first_4:n,
-%     \prg_replicate_first_5:n,
-%     \prg_replicate_first_6:n,
-%     \prg_replicate_first_7:n,
-%     \prg_replicate_first_8:n,
-%     \prg_replicate_first_9:n
+%     \@@_replicate_first_-:n,
+%     \@@_replicate_first_0:n,
+%     \@@_replicate_first_1:n,
+%     \@@_replicate_first_2:n,
+%     \@@_replicate_first_3:n,
+%     \@@_replicate_first_4:n,
+%     \@@_replicate_first_5:n,
+%     \@@_replicate_first_6:n,
+%     \@@_replicate_first_7:n,
+%     \@@_replicate_first_8:n,
+%     \@@_replicate_first_9:n
 %   }
 %   This function uses a cascading csname technique by David Kastrup
 %   (who else :-)
@@ -1577,7 +1328,7 @@
 %   to avoid the last function to insert say, $100$ copies of the original
 %   argument just to gobble them again we define separate functions to
 %   be inserted first. These functions also close the expansion of
-%   \cs{int_to_roman:w}, which ensures that \cs{prg_replicate:nn} only
+%   \cs{__int_to_roman:w}, which ensures that \cs{prg_replicate:nn} only
 %   requires two steps of expansion.
 %
 %   This function has one flaw though: Since it constantly passes down
@@ -1587,144 +1338,67 @@
 %   necessary, it is possible to write
 %   |\prg_replicate:nn{1000}{\prg_replicate:nn{1000}{|\meta{code}|}}|. An
 %   alternative approach is to create a string of |m|'s with
-%   \cs{int_to_roman:w} which can be done with just four macros but that
+%   \cs{__int_to_roman:w} which can be done with just four macros but that
 %   method has its own problems since it can exhaust the string
 %   pool. Also, it is considerably slower than what we use here so the
 %   few extra csnames are well spent I would say.
 %    \begin{macrocode}
 \cs_new:Npn \prg_replicate:nn #1
   {
-    \int_to_roman:w
-      \exp_after:wN \prg_replicate_first_aux:N
-        \int_value:w \int_eval:w #1 \int_eval_end:
+    \__int_to_roman:w
+      \exp_after:wN \@@_replicate_first:N
+        \__int_value:w \__int_eval:w #1 \__int_eval_end:
       \cs_end:
   }
-\cs_new:Npn \prg_replicate_aux:N #1
-  { \cs:w prg_replicate_#1 :n \prg_replicate_aux:N }
-\cs_new:Npn \prg_replicate_first_aux:N #1
-  { \cs:w prg_replicate_first_ #1 :n \prg_replicate_aux:N }
+\cs_new:Npn \@@_replicate:N #1
+  { \cs:w @@_replicate_#1 :n \@@_replicate:N }
+\cs_new:Npn \@@_replicate_first:N #1
+  { \cs:w @@_replicate_first_ #1 :n \@@_replicate:N }
 %    \end{macrocode}
-% Then comes all the functions that do the hard work of inserting all
-% the copies.
+%   Then comes all the functions that do the hard work of inserting all
+%   the copies.  The first function takes |:n| as a parameter.
 %    \begin{macrocode}
-\cs_new:Npn \prg_replicate_ :n #1 { \cs_end: }
-\cs_new:cpn { prg_replicate_0:n } #1 { \cs_end: {#1#1#1#1#1#1#1#1#1#1} }
-\cs_new:cpn { prg_replicate_1:n } #1 { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1 }
-\cs_new:cpn { prg_replicate_2:n } #1 { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1 }
-\cs_new:cpn { prg_replicate_3:n } #1
+\cs_new:Npn \@@_replicate_ :n #1 { \cs_end: }
+\cs_new:cpn { @@_replicate_0:n } #1 { \cs_end: {#1#1#1#1#1#1#1#1#1#1} }
+\cs_new:cpn { @@_replicate_1:n } #1 { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1 }
+\cs_new:cpn { @@_replicate_2:n } #1 { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1 }
+\cs_new:cpn { @@_replicate_3:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1 }
-\cs_new:cpn { prg_replicate_4:n } #1
+\cs_new:cpn { @@_replicate_4:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1#1 }
-\cs_new:cpn { prg_replicate_5:n } #1
+\cs_new:cpn { @@_replicate_5:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_6:n } #1
+\cs_new:cpn { @@_replicate_6:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_7:n } #1
+\cs_new:cpn { @@_replicate_7:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_8:n } #1
+\cs_new:cpn { @@_replicate_8:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_9:n } #1
+\cs_new:cpn { @@_replicate_9:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1#1#1#1#1#1#1 }
 %    \end{macrocode}
 %    Users shouldn't ask for something to be replicated once or even
 %    not at all but\dots
 %    \begin{macrocode}
-\cs_new:cpn { prg_replicate_first_-:n } #1
-  { \c_zero \msg_expandable_kernel_error:nn { prg } { replicate-neg } }
-\cs_new:cpn { prg_replicate_first_0:n } #1 { \c_zero }
-\cs_new:cpn { prg_replicate_first_1:n } #1 { \c_zero #1 }
-\cs_new:cpn { prg_replicate_first_2:n } #1 { \c_zero #1#1 }
-\cs_new:cpn { prg_replicate_first_3:n } #1 { \c_zero #1#1#1 }
-\cs_new:cpn { prg_replicate_first_4:n } #1 { \c_zero #1#1#1#1 }
-\cs_new:cpn { prg_replicate_first_5:n } #1 { \c_zero #1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_first_6:n } #1 { \c_zero #1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_first_7:n } #1 { \c_zero #1#1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_first_8:n } #1 { \c_zero #1#1#1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_first_9:n } #1 { \c_zero #1#1#1#1#1#1#1#1#1 }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\prg_stepwise_function:nnnN}
-% \begin{macro}[aux]{\prg_stepwise_aux:nnnN}
-% \begin{macro}[aux]{\prg_stepwise_aux:NnnnN}
-%   Repeating a function by steps first needs a check on the direction
-%   of the steps. After that, do the function for the start value
-%   then step and loop around. It would be more symmetrical to test
-%   for a step size of zero before checking the sign, but we optimize
-%   for the most frequent case (positive step).
-%    \begin{macrocode}
-\cs_new:Npn \prg_stepwise_function:nnnN #1#2#3#4
+\cs_new:cpn { @@_replicate_first_-:n } #1
   {
-    \prg_stepwise_aux:nnnN {#1} {#2} {#3} #4
-    \prg_break_point:n { }
-  }
-\cs_new:Npn \prg_stepwise_aux:nnnN #1#2#3#4
-  {
-    \int_compare:nNnTF {#2} > \c_zero
-      { \exp_args:NNf \prg_stepwise_aux:NnnnN > }
-      {
-        \int_compare:nNnTF {#2} = \c_zero
-          {
-            \msg_expandable_kernel_error:nnn { prg } { zero-step } {#4}
-            \prg_map_break:
-          }
-          { \exp_args:NNf \prg_stepwise_aux:NnnnN < }
-      }
-      { \int_eval:n {#1} } {#2} {#3} #4
-  }
-\cs_new:Npn \prg_stepwise_aux:NnnnN #1#2#3#4#5
-  {
-    \int_compare:nNnF {#2} #1 {#4}
-      {
-        #5 {#2}
-        \exp_args:NNf \prg_stepwise_aux:NnnnN
-          #1 { \int_eval:n { #2 + #3 } } {#3} {#4} #5
-      }
+    \c_zero
+    \__msg_kernel_expandable_error:nn { kernel } { negative-replication }
   }
+\cs_new:cpn { @@_replicate_first_0:n } #1 { \c_zero }
+\cs_new:cpn { @@_replicate_first_1:n } #1 { \c_zero #1 }
+\cs_new:cpn { @@_replicate_first_2:n } #1 { \c_zero #1#1 }
+\cs_new:cpn { @@_replicate_first_3:n } #1 { \c_zero #1#1#1 }
+\cs_new:cpn { @@_replicate_first_4:n } #1 { \c_zero #1#1#1#1 }
+\cs_new:cpn { @@_replicate_first_5:n } #1 { \c_zero #1#1#1#1#1 }
+\cs_new:cpn { @@_replicate_first_6:n } #1 { \c_zero #1#1#1#1#1#1 }
+\cs_new:cpn { @@_replicate_first_7:n } #1 { \c_zero #1#1#1#1#1#1#1 }
+\cs_new:cpn { @@_replicate_first_8:n } #1 { \c_zero #1#1#1#1#1#1#1#1 }
+\cs_new:cpn { @@_replicate_first_9:n } #1 { \c_zero #1#1#1#1#1#1#1#1#1 }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 % \end{macro}
-%
-% \begin{macro}{\prg_stepwise_inline:nnnn}
-% \begin{macro}{\prg_stepwise_variable:nnnNn}
-% \UnitTested
-% \begin{macro}[aux]{\prg_stepwise_aux:NNnnnn}
-%   The approach here is to build a function, with a global integer required
-%   to make the nesting safe (as seen in other in line functions),
-%   and map that function using \cs{prg_stepwise_function:nnnN}.
-%    \begin{macrocode}
-\cs_new_protected:Npn \prg_stepwise_inline:nnnn
-  {
-    \exp_args:NNc \prg_stepwise_aux:NNnnnn
-      \cs_gset_nopar:Npn
-      { g_prg_stepwise_ \int_use:N \g_prg_map_int :n }
-  }
-\cs_new_protected:Npn \prg_stepwise_variable:nnnNn #1#2#3#4#5
-  {
-    \exp_args:NNc \prg_stepwise_aux:NNnnnn
-      \cs_gset_nopar:Npx
-      { g_prg_stepwise_ \int_use:N \g_prg_map_int :n }
-      {#1}{#2}{#3}
-      {
-        \tl_set:Nn \exp_not:N #4 {##1}
-        \exp_not:n {#5}
-      }
-  }
-\cs_new_protected:Npn \prg_stepwise_aux:NNnnnn #1#2#3#4#5#6
-  {
-    #1 #2 ##1 {#6}
-    \int_gincr:N \g_prg_map_int
-    \prg_stepwise_aux:nnnN {#3} {#4} {#5} #2
-    \prg_break_point:n { \int_gdecr:N \g_prg_map_int }
-  }
-%    \end{macrocode}
-% \end{macro}
 % \end{macro}
 % \end{macro}
 %
@@ -1735,7 +1409,7 @@
 %   For testing vertical mode. Strikes me here on the bus with David,
 %   that as long as we are just talking about returning true and
 %   false states, we can just use the primitive conditionals for this
-%   and gobbling the |\c_zero| in the input stream. However this
+%   and gobbling the \cs{c_zero} in the input stream. However this
 %   requires knowledge of the implementation so we keep things nice
 %   and clean and use the return statements.
 %    \begin{macrocode}
@@ -1779,13 +1453,13 @@
 %   \TeX{}'s alignment structures present many problems. As Knuth says
 %   himself in \emph{\TeX : The Program}: \enquote{It's sort of a miracle
 %   whenever \tn{halign} or \tn{valign} work, [\ldots]} One problem relates
-%   to commands that internally issues a |\cr| but also peek ahead for
+%   to commands that internally issues a \tn{cr} but also peek ahead for
 %   the next character for use in, say, an optional argument. If the
 %   next token happens to be a |&| with category code~4 we will get some
 %   sort of weird error message because the underlying
 %   \tn{futurelet} will store the token at the end of the alignment
 %   template. This could be a |&|$_4$ giving a message like
-%   |! Misplaced \cr.| or even worse: it could be the |\endtemplate|
+%   |! Misplaced \cr.| or even worse: it could be the \tn{endtemplate}
 %   token causing even more trouble! To solve this we have to open a
 %   special group so that \TeX{} still thinks it's on safe ground but at
 %   the same time we don't want to introduce any brace group that may
@@ -1805,11 +1479,11 @@
 %
 % \begin{macro}[int]{\scan_align_safe_stop:}
 %   When \TeX{} is in the beginning of an align cell (right after the
-%   |\cr|) it is in a somewhat strange mode as it is looking ahead to
+%   \tn{cr}) it is in a somewhat strange mode as it is looking ahead to
 %   find an \tn{omit} or \tn{noalign} and hasn't looked at the
 %   preamble yet. Thus an \tn{ifmmode} test will always fail unless
-%   we insert |\scan_stop:| to stop \TeX{}'s scanning ahead. On the other
-%   hand we don't want to insert a |\scan_stop:| every time as that will
+%   we insert \cs{scan_stop:} to stop \TeX{}'s scanning ahead. On the other
+%   hand we don't want to insert a \cs{scan_stop:} every time as that will
 %   destroy kerning between letters\footnote{Unless we enforce an extra
 %   pass with an appropriate value of \tn{pretolerance}.}
 %   Unfortunately there is no way to detect if we're in the beginning of
@@ -1817,7 +1491,7 @@
 %   on column number, \emph{etc.} However we \emph{can} detect if we're in an
 %   alignment cell by checking the current group type and we can also
 %   check if the previous node was a character or ligature. What is done
-%   here is that |\scan_stop:| is only inserted if an only
+%   here is that \cs{scan_stop:} is only inserted if an only
 %   if a)~we're in the outer part of an alignment cell and b)~the last node
 %   \emph{wasn't} a char node or a ligature node. Thus an older definition
 %   here was
@@ -1842,47 +1516,51 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int]{\prg_variable_get_scope:N}
-% \begin{macro}[aux]{\prg_variable_get_scope_aux:w}
-% \begin{macro}[int]{\prg_variable_get_type:N}
-% \begin{macro}[aux]{\prg_variable_get_type:w}
+%    \begin{macrocode}
+%<@@=prg>
+%    \end{macrocode}
+%
+% \begin{macro}[int]{\@@_variable_get_scope:N}
+% \begin{macro}[aux]{\@@_variable_get_scope:w}
+% \begin{macro}[int]{\@@_variable_get_type:N}
+% \begin{macro}[aux]{\@@_variable_get_type:w}
 %   Expandable functions to find the type of a variable, and to
 %   return \texttt{g} if the variable is global. The trick for
-%   \cs{prg_variable_get_scope:N} is the same as that in
-%   \cs{cs_split_function:NN}, but it can be simplified as the
+%   \cs{@@_variable_get_scope:N} is the same as that in
+%   \cs{__cs_split_function:NN}, but it can be simplified as the
 %   requirements here are less complex.
 %    \begin{macrocode}
 \group_begin:
-  \tex_lccode:D `\& = `\g \scan_stop:
-  \tex_catcode:D `\& = \c_twelve
+  \tex_lccode:D `* = `g \scan_stop:
+  \tex_catcode:D `* = \c_twelve
 \tl_to_lowercase:n
   {
     \group_end:
-    \cs_new:Npn \prg_variable_get_scope:N #1
+    \cs_new:Npn \@@_variable_get_scope:N #1
       {
         \exp_after:wN \exp_after:wN
-        \exp_after:wN \prg_variable_get_scope_aux:w
+        \exp_after:wN \@@_variable_get_scope:w
           \cs_to_str:N #1 \exp_stop_f: \q_stop
       }
-    \cs_new:Npn \prg_variable_get_scope_aux:w #1#2 \q_stop
-      { \token_if_eq_meaning:NNT & #1 { g } }
+    \cs_new:Npn \@@_variable_get_scope:w #1#2 \q_stop
+      { \token_if_eq_meaning:NNT * #1 { g } }
   }
 \group_begin:
-  \tex_lccode:D `\& = `\_ \scan_stop:
-  \tex_catcode:D `\& = \c_twelve
+  \tex_lccode:D `* = `_ \scan_stop:
+  \tex_catcode:D `* = \c_twelve
 \tl_to_lowercase:n
   {
     \group_end:
-    \cs_new:Npn \prg_variable_get_type:N #1
+    \cs_new:Npn \@@_variable_get_type:N #1
       {
-        \exp_after:wN \prg_variable_get_type_aux:w
-          \token_to_str:N #1 & a \q_stop
+        \exp_after:wN \@@_variable_get_type:w
+          \token_to_str:N #1 * a \q_stop
       }
-    \cs_new:Npn \prg_variable_get_type_aux:w #1 & #2#3 \q_stop
+    \cs_new:Npn \@@_variable_get_type:w #1 * #2#3 \q_stop
       {
         \token_if_eq_meaning:NNTF a #2
           {#1}
-          { \prg_variable_get_type_aux:w #2#3 \q_stop }
+          { \@@_variable_get_type:w #2#3 \q_stop }
       }
   }
 %    \end{macrocode}
@@ -1891,20 +1569,32 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{variable}{\g_prg_map_int}
+% \begin{variable}{\g_@@_map_int}
 %   A nesting counter for mapping.
 %    \begin{macrocode}
-\int_new:N \g_prg_map_int
+\int_new:N \g_@@_map_int
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{macro}{\prg_break_point:n}
-% \begin{macro}{\prg_map_break:}
-% \begin{macro}{\prg_map_break:n}
-%   These are all defined in \pkg{l3basics}, as they are needed
+% \begin{macro}{\@@_break_point:Nn}
+% \begin{macro}{\@@_map_break:Nn}
+%   These are defined in \pkg{l3basics}, as they are needed
 %   \enquote{early}. This is just a reminder that that is the case!
 % \end{macro}
 % \end{macro}
+%
+% \begin{macro}{\@@_break_point:}
+% \begin{macro}{\@@_break:, \@@_break:n}
+%   Very simple analogs of \cs{@@_break_point:Nn} and
+%   \cs{@@_map_break:Nn}, for use in fast short-term recursions which
+%   are not mappings, do not need to support nesting, and in which
+%   nothing has to be done at the end of the loop.
+%    \begin{macrocode}
+\cs_new_eq:NN \@@_break_point: \prg_do_nothing:
+\cs_new:Npn \@@_break: #1 \@@_break_point: { }
+\cs_new:Npn \@@_break:n #1#2 \@@_break_point: {#1}
+%    \end{macrocode}
+% \end{macro}
 % \end{macro}
 %
 % \subsection{Deprecated functions}
@@ -1939,6 +1629,7 @@
 %   by Bernd Raichle. Firstly we define the function for parsing the
 %   initial list and then the braced list afterwards.
 %    \begin{macrocode}
+%<*deprecated>
 \cs_new_protected:Npn \prg_define_quicksort:nnn #1#2#3 {
   \cs_set:cpx{#1_quicksort:n}##1{
     \exp_not:c{#1_quicksort_start_partition:w} ##1
@@ -1956,9 +1647,11 @@
     \exp_not:N \quark_if_nil:nT {##1}\exp_not:N \use_none_delimit_by_q_stop:w
     \exp_not:c{#1_quicksort_do_partition_i_braced:nnnn} {##1}{}{}
   }
+%</deprecated>
 %    \end{macrocode}
 % Now for doing the partitions.
 %    \begin{macrocode}
+%<*deprecated>
   \cs_set:cpx {#1_quicksort_do_partition_i:nnnw} ##1##2##3 #2 ##4 #3 {
     \exp_not:N \quark_if_nil:nTF {##4} \exp_not:c {#1_do_quicksort_braced:nnnnw}
     {
@@ -1995,10 +1688,12 @@
     }
     {##1}{##2}{##3}{##4}
   }
+%</deprecated>
 %    \end{macrocode}
 % This part of the code handles the two branches in each
 % sorting. Again we will also have to do it braced.
 %    \begin{macrocode}
+%<*deprecated>
   \cs_set:cpx {#1_quicksort_partition_less_i:nnnn} ##1##2##3##4{
     \exp_not:c{#1_quicksort_do_partition_i:nnnw}{##1}{##2}{{##4}##3}}
   \cs_set:cpx {#1_quicksort_partition_less_ii:nnnn} ##1##2##3##4{
@@ -2015,15 +1710,18 @@
     \exp_not:c{#1_quicksort_do_partition_i_braced:nnnn}{##1}{{##4}##2}{##3}}
   \cs_set:cpx {#1_quicksort_partition_greater_ii_braced:nnnn} ##1##2##3##4{
     \exp_not:c{#1_quicksort_do_partition_ii_braced:nnnn}{##1}{##2{##4}}{##3}}
+%</deprecated>
 %    \end{macrocode}
 % Finally, the big kahuna! This is where the sub-lists are sorted.
 %    \begin{macrocode}
+%<*deprecated>
   \cs_set:cpx {#1_do_quicksort_braced:nnnnw} ##1##2##3##4\q_stop {
     \exp_not:c{#1_quicksort_braced:n}{##2}
     \exp_not:c{#1_quicksort_function:n}{##1}
     \exp_not:c{#1_quicksort_braced:n}{##3}
   }
 }
+%</deprecated>
 %    \end{macrocode}
 % \end{macro}
 %
@@ -2032,15 +1730,19 @@
 %   |\prg_quicksort_compare:nnTF| to compare items, and places the
 %   function |\prg_quicksort_function:n| in front of each of them.
 %    \begin{macrocode}
+%<*deprecated>
 \prg_define_quicksort:nnn {prg}{}{}
+%</deprecated>
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}{\prg_quicksort_function:n}
 % \begin{macro}{\prg_quicksort_compare:nnTF}
 %    \begin{macrocode}
+%<*deprecated>
 \cs_set:Npn \prg_quicksort_function:n {\ERROR}
 \cs_set:Npn \prg_quicksort_compare:nnTF {\ERROR}
+%</deprecated>
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -2061,6 +1763,38 @@
 % \end{macro}
 % \end{macro}
 %
+% Deprecated 2012-06-03 for removal after 2012-12-31.
+%
+% \begin{macro}[EXP]
+%   {
+%     \prg_case_int:nnn, \prg_case_str:nnn, \prg_case_str:onn,
+%     \prg_case_str:xxn, \prg_case_tl:Nnn, \prg_case_tl:cnn
+%   }
+%   Moved to more sensible modules.
+%    \begin{macrocode}
+\cs_new_eq:NN \prg_case_int:nnn \int_case:nnn
+\cs_new_eq:NN \prg_case_str:nnn \str_case:nnn
+\cs_new_eq:NN \prg_case_str:onn \str_case:onn
+\cs_new_eq:NN \prg_case_str:xxn \str_case_x:nnn
+\cs_new_eq:NN \prg_case_tl:Nnn  \tl_case:Nnn
+\cs_new_eq:NN \prg_case_tl:cnn  \tl_case:cnn
+%    \end{macrocode}
+% \end{macro}
+%
+% Deprecated 2012-06-04 for removal after 2012-12-31.
+%
+% \begin{macro}
+%   {
+%     \prg_stepwise_function:nnnN, \prg_stepwise_inline:nnnn,
+%     \prg_stepwise_variable:nnnNn
+%   }
+%    \begin{macrocode}
+\cs_new_eq:NN \prg_stepwise_function:nnnN  \int_step_function:nnnN
+\cs_new_eq:NN \prg_stepwise_inline:nnnn    \int_step_inline:nnnn
+\cs_new_eq:NN \prg_stepwise_variable:nnnNn \int_step_variable:nnnNn
+%    \end{macrocode}
+% \end{macro}
+%
 %    \begin{macrocode}
 %</initex|package>
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3prop.dtx b/Master/texmf-dist/source/latex/l3kernel/l3prop.dtx
index b90ff41e63a..e20e2aa5d26 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3prop.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3prop.dtx
@@ -35,8 +35,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3prop.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental property lists}
+\GetIdInfo$Id: l3prop.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Property lists}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -90,7 +90,7 @@
 %     \cs{prop_new:N} \meta{property list}
 %   \end{syntax}
 %   Creates a new \meta{property list} or raises an error if the name is
-%   already taken. The declaration is global. The \meta{property lists} will
+%   already taken. The declaration is global. The \meta{property list} will
 %   initially contain no entries.
 % \end{function}
 %
@@ -121,15 +121,15 @@
 %     \prop_gset_eq:NN, \prop_gset_eq:cN, \prop_gset_eq:Nc, \prop_gset_eq:cc
 %   }
 %   \begin{syntax}
-%     \cs{prop_set_eq:NN} \meta{property list1} \meta{property list2}
+%     \cs{prop_set_eq:NN} \meta{property list_1} \meta{property list_2}
 %   \end{syntax}
-%   Sets the content of \meta{property list1} equal to that of
-%   \meta{property list2}.
+%   Sets the content of \meta{property list_1} equal to that of
+%   \meta{property list_2}.
 % \end{function}
 %
 % \section{Adding entries to property lists}
 %
-% \begin{function}
+% \begin{function}[updated = 2012-07-09]
 %   {
 %     \prop_put:Nnn,  \prop_put:NnV,  \prop_put:Nno,  \prop_put:Nnx,
 %     \prop_put:NVn,  \prop_put:NVV,  \prop_put:Non,  \prop_put:Noo,
@@ -198,7 +198,7 @@
 %   \meta{property list} then the \meta{token list variable} will
 %   contain the special marker \cs{q_no_value}. The \meta{key} and
 %   \meta{value} are then deleted from the property list. Both
-%   assignments are local.
+%   assignments are local.  See also \cs{prop_pop:NnNTF}.
 % \end{function}
 %
 % \begin{function}[updated = 2011-08-18]
@@ -213,29 +213,29 @@
 %   contain the special marker \cs{q_no_value}. The \meta{key} and
 %   \meta{value} are then deleted from the property list.
 %   The \meta{property list} is modified globally, while the assignment of
-%   the \meta{token list variable} is local.
+%   the \meta{token list variable} is local.  See also \cs{prop_gpop:NnNTF}.
 % \end{function}
-%%
+%
 % \section{Modifying property lists}
 %
-% \begin{function}
+% \begin{function}[added = 2012-05-12]
 %   {
-%     \prop_del:Nn,  \prop_del:NV,  \prop_del:cn,  \prop_del:cV,
-%     \prop_gdel:Nn, \prop_gdel:NV, \prop_gdel:cn, \prop_gdel:cV
+%     \prop_remove:Nn,  \prop_remove:NV,  \prop_remove:cn,  \prop_remove:cV,
+%     \prop_gremove:Nn, \prop_gremove:NV, \prop_gremove:cn, \prop_gremove:cV
 %   }
 %   \begin{syntax}
-%     \cs{prop_del:Nn} \meta{property list} \Arg{key}
+%     \cs{prop_remove:Nn} \meta{property list} \Arg{key}
 %   \end{syntax}
-%   Deletes the entry listed under \meta{key} from the
-%   \meta{property list} which may be accessed. If the \meta{key} is
+%   Removes the entry listed under \meta{key} from the
+%   \meta{property list}.  If the \meta{key} is
 %   not found in the \meta{property list} no change occurs,
 %   \emph{i.e}~there is no need to test for the existence of a key before
-%   deleting it. The deletion is restricted to the current \TeX{} group.
+%   deleting it.
 % \end{function}
 %
 % \section{Property list conditionals}
 %
-% \begin{function}[EXP, pTF, added=2012-03-03]
+% \begin{function}[EXP, pTF, added = 2012-03-03]
 %   {\prop_if_exist:N, \prop_if_exist:c}
 %   \begin{syntax}
 %     \cs{prop_if_exist_p:N} \meta{property list}
@@ -278,7 +278,7 @@
 % or absence of a key in a property list. They offer increased readability
 % and performance over separate testing and recovery phases.
 %
-% \begin{function}[updated = 2011-08-28, TF]
+% \begin{function}[updated = 2012-05-19, TF]
 %   {
 %     \prop_get:NnN, \prop_get:NVN, \prop_get:NoN,
 %     \prop_get:cnN, \prop_get:cVN, \prop_get:coN
@@ -288,21 +288,24 @@
 %     ~~\Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   If the \meta{key} is not present in the \meta{property list}, leaves
-%   the \meta{false code} in the input stream and leaves the
-%   \meta{token list variable} unchanged. If the \meta{key} is present in
-%   the \meta{property list}, stores the corresponding \meta{value}
-%   in the \meta{token list variable} without removing it from the
-%   \meta{property list}. The \meta{token list variable} is assigned locally.
+%   the \meta{false code} in the input stream.  The value of the
+%   \meta{token list variable} is not defined in this case and should
+%   not be relied upon.  If the \meta{key} is present in the
+%   \meta{property list}, stores the corresponding \meta{value} in the
+%   \meta{token list variable} without removing it from the
+%   \meta{property list}, then leaves the \meta{true code} in the input
+%   stream.  The \meta{token list variable} is assigned locally.
 % \end{function}
 %
-% \begin{function}[added = 2011-08-18,TF]{\prop_pop:NnN, \prop_pop:cnN}
+% \begin{function}[TF, added = 2011-08-18, updated = 2012-05-19]
+%   {\prop_pop:NnN, \prop_pop:cnN}
 %   \begin{syntax}
-%     \cs{prop_pop:NnNTF} \meta{property list} \Arg{key} \meta{token list variable} \\
-%     ~~\Arg{true code} \Arg{false code}
+%     \cs{prop_pop:NnNTF} \meta{property list} \Arg{key} \meta{token list variable} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   If the \meta{key} is not present in the \meta{property list}, leaves
-%   the \meta{false code} in the input stream and leaves the
-%   \meta{token list variable} unchanged. If the \meta{key} is present in
+%   the \meta{false code} in the input stream.  The value of the
+%   \meta{token list variable} is not defined in this case and should
+%   not be relied upon.  If the \meta{key} is present in
 %   the \meta{property list}, pops the corresponding \meta{value}
 %   in the \meta{token list variable}, \emph{i.e.}~removes the item from
 %   the \meta{property list}.
@@ -310,9 +313,26 @@
 %   are assigned locally.
 % \end{function}
 %
+% \begin{function}[TF, added = 2011-08-18, updated = 2012-05-19]
+%   {\prop_gpop:NnN, \prop_gpop:cnN}
+%   \begin{syntax}
+%     \cs{prop_gpop:NnNTF} \meta{property list} \Arg{key} \meta{token list variable} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   If the \meta{key} is not present in the \meta{property list}, leaves
+%   the \meta{false code} in the input stream.  The value of the
+%   \meta{token list variable} is not defined in this case and should
+%   not be relied upon.  If the \meta{key} is present in
+%   the \meta{property list}, pops the corresponding \meta{value}
+%   in the \meta{token list variable}, \emph{i.e.}~removes the item from
+%   the \meta{property list}.
+%   The \meta{property list} is modified globally, while the
+%   \meta{token list variable} is assigned locally.
+% \end{function}
+%
 % \section{Mapping to property lists}
 %
-% \begin{function}[rEXP]{\prop_map_function:NN, \prop_map_function:cN}
+% \begin{function}[updated = 2012-06-29, rEXP]
+%   {\prop_map_function:NN, \prop_map_function:cN}
 %   \begin{syntax}
 %     \cs{prop_map_function:NN} \meta{property list} \meta{function}
 %   \end{syntax}
@@ -323,7 +343,8 @@
 %   should not be relied upon.
 % \end{function}
 %
-% \begin{function}{\prop_map_inline:Nn, \prop_map_inline:cn}
+% \begin{function}[updated = 2012-06-29]
+%   {\prop_map_inline:Nn, \prop_map_inline:cn}
 %   \begin{syntax}
 %     \cs{prop_map_inline:Nn} \meta{property list} \Arg{inline function}
 %   \end{syntax}
@@ -335,7 +356,7 @@
 %   should not be relied upon.
 % \end{function}
 %
-% \begin{function}[rEXP]{\prop_map_break:}
+% \begin{function}[updated = 2012-06-29, rEXP]{\prop_map_break:}
 %   \begin{syntax}
 %     \cs{prop_map_break:}
 %   \end{syntax}
@@ -356,7 +377,7 @@
 %   level \TeX{} errors.
 % \end{function}
 %
-% \begin{function}[rEXP]{\prop_map_break:n}
+% \begin{function}[updated = 2012-06-29, rEXP]{\prop_map_break:n}
 %   \begin{syntax}
 %     \cs{prop_map_break:n} \Arg{tokens}
 %   \end{syntax}
@@ -387,103 +408,45 @@
 %   Displays the entries in the \meta{property list} in the terminal.
 % \end{function}
 %
-% \section{Experimental property list functions}
+% \section{Scratch property lists}
 %
-% This section contains functions which may or may not be retained, depending
-% on how useful they are found to be.
+% \begin{variable}[added = 2012-06-23]{\l_tmpa_prop, \l_tmpb_prop}
+%   Scratch property lists for local assignment. These are never used by
+%   the kernel code, and so are safe for use with any \LaTeX3-defined
+%   function. However, they may be overwritten by other non-kernel
+%   code and so should only be used for short-term storage.
+% \end{variable}
 %
-% \begin{function}[added = 2011-08-18,TF]{\prop_gpop:NnN, \prop_gpop:cnN}
-%   \begin{syntax}
-%     \cs{prop_gpop:NnNTF} \meta{property list} \Arg{key} \meta{token list variable} \\
-%     ~~\Arg{true code} \Arg{false code}
-%   \end{syntax}
-%   If the \meta{key} is not present in the \meta{property list}, leaves
-%   the \meta{false code} in the input stream and leaves the
-%   \meta{token list variable} unchanged. If the \meta{key} is present in
-%   the \meta{property list}, pops the corresponding \meta{value}
-%   in the \meta{token list variable}, \emph{i.e.}~removes the item from
-%   the \meta{property list}.
-%   The \meta{property list} is modified globally, while the
-%   \meta{token list variable} is assigned locally.
-% \end{function}
+% \begin{variable}[added = 2012-06-23]{\g_tmpa_prop, \g_tmpb_prop}
+%   Scratch property lists for global assignment. These are never used by
+%   the kernel code, and so are safe for use with any \LaTeX3-defined
+%   function. However, they may be overwritten by other non-kernel
+%   code and so should only be used for short-term storage.
+% \end{variable}
 %
-% \begin{function}[added = 2011-08-18,rEXP]
-%   {\prop_map_tokens:Nn, \prop_map_tokens:cn}
-%   \begin{syntax}
-%     \cs{prop_map_tokens:Nn} \meta{property list} \Arg{code}
-%   \end{syntax}
-%   Analogue of \cs{prop_map_function:NN} which maps several tokens
-%   instead of a single function.  The \meta{code} receives each
-%   key--value pair in the \meta{property list} as two trailing brace
-%   groups. For instance,
-%   \begin{verbatim}
-%     \prop_map_tokens:Nn \l_my_prop { \str_if_eq:nnT { mykey } }
-%   \end{verbatim}
-%   will expand to the value corresponding to \texttt{mykey}: for each
-%   pair in \cs{l_my_prop} the function \cs{str_if_eq:nnT} receives
-%   \texttt{mykey}, the \meta{key} and the \meta{value} as its three
-%   arguments.  For that specific task, \cs{prop_get:Nn} is faster.
-% \end{function}
+% \section{Constants}
 %
-% \begin{function}[updated = 2012-01-08,EXP]{\prop_get:Nn, \prop_get:cn}
-%   \begin{syntax}
-%     \cs{prop_get:Nn} \meta{property list} \Arg{key}
-%   \end{syntax}
-%   Expands to the \meta{value} corresponding to the \meta{key} in
-%   the \meta{property list}. If the \meta{key} is missing, this has
-%   an empty expansion.
-%   \begin{texnote}
-%     This function is slower than the non-expandable analogue
-%     \cs{prop_get:NnN}.
-%     The result is returned within the \tn{unexpanded}
-%     primitive (\cs{exp_not:n}), which means that the \meta{value}
-%     will not expand further when appearing in an x-type
-%     argument expansion.
-%   \end{texnote}
-% \end{function}
+% \begin{variable}{\c_empty_prop}
+%   A permanently-empty property list used for internal comparisons.
+% \end{variable}
 %
 % \section{Internal property list functions}
 %
-% \begin{function}{\q_prop}
+% \begin{variable}{\q__prop}
 %   The internal token used to separate out property list entries, separating
 %   both the \meta{key} from the \meta{value} and also one entry from another.
-% \end{function}
-%
-% \begin{function}{\c_empty_prop}
-%   A permanently-empty property list used for internal comparisons.
-% \end{function}
-%
-% \begin{function}{\prop_split:Nnn}
-%   \begin{syntax}
-%     \cs{prop_split:Nnn} \meta{property list} \Arg{key} \Arg{code}
-%   \end{syntax}
-%   Splits the \meta{property list} at the \meta{key}, giving three
-%   groups: the \meta{extract} of \meta{property list} before the
-%   \meta{key}, the \meta{value} associated with the \meta{key} and the
-%   \meta{extract} of the \meta{property list} after the \meta{value}.
-%   The first \meta{extract} retains the internal structure of a property
-%   list. The second is only missing the leading separator \cs{q_prop}.
-%   This ensures that the concatenation of the two \meta{extracts} is a
-%   property list.
-%   If the \meta{key} is not present in the \meta{property list} then
-%   the second group will contain the marker \cs{q_no_value} and the third
-%   is empty.
-%   Once the split has occurred, the \meta{code} is inserted followed by the
-%   three groups: thus the \meta{code} should properly absorb three
-%   arguments.
-%   The \meta{key} comparison takes place as described for \cs{str_if_eq:nn}.
-% \end{function}
+% \end{variable}
 %
-% \begin{function}{\prop_split:NnTF}
+% \begin{function}{\__prop_split:NnTF}
 %   \begin{syntax}
-%     \cs{prop_split:NnTF} \meta{property list} \Arg{key} \Arg{true code} \Arg{false code}
+%     \cs{__prop_split:NnTF} \meta{property list} \Arg{key} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   Splits the \meta{property list} at the \meta{key}, giving three
 %   groups: the \meta{extract} of \meta{property list} before the
 %   \meta{key}, the \meta{value} associated with the \meta{key} and the
 %   \meta{extract} of the \meta{property list} after the \meta{value}.
 %   The first \meta{extract} retains the internal structure of a property
-%   list. The second is only missing the leading separator \cs{q_prop}.
+%   list. The second is only missing the leading separator \cs{q__prop}.
 %   This ensures that the concatenation of the two \meta{extracts} is a
 %   property list.
 %   If the \meta{key} is present in the \meta{property list} then the
@@ -501,44 +464,51 @@
 %
 % \section{\pkg{l3prop} implementation}
 %
-% \TestFiles{m3prop001}
+% \TestFiles{m3prop001, m3prop002, m3prop003, m3prop004, m3show001}
 %
 %    \begin{macrocode}
 %<*initex|package>
 %    \end{macrocode}
 %
 %    \begin{macrocode}
+%<@@=prop>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
 % A property list is a macro whose top-level expansion is for the form
-% \enquote{\cs{q_prop} \meta{key$_0$} \cs{q_prop} \Arg{value$_0$} \cs{q_prop}
-% \ldots \cs{q_prop} \meta{key$_{n-1}$} \cs{q_prop} \Arg{value$_{n-1}$}
-% \cs{q_prop}}.
-% The trailing \cs{q_prop} is always present for performance reasons: this
-% means that empty property lists are not actually empty.
-%
-% \begin{macro}[int]{\q_prop}
+% \begin{quote}
+%   \cs{q_@@} \meta{key_1} \cs{q_@@} \Arg{value_1} \\
+%   \ldots{} \\
+%   \cs{q_@@} \meta{key_n} \cs{q_@@} \Arg{value_n} \\
+%   \cs{q_@@}
+% \end{quote}
+% where the trailing \cs{q_@@} is always present for performance
+% reasons: this means that empty property lists are not actually empty.
+%
+% \begin{macro}[int]{\q_@@}
 %   A private quark is used as a marker between entries.
 %    \begin{macrocode}
-\quark_new:N \q_prop
+\quark_new:N \q_@@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{variable}{\c_empty_prop}
-%   An empty prop contains exactly one \cs{q_prop}.
+% \begin{variable}[tested = m3prop004]{\c_empty_prop}
+%   An empty prop contains exactly one \cs{q_@@}.
 %    \begin{macrocode}
-\tl_const:Nn \c_empty_prop { \q_prop }
+\tl_const:Nn \c_empty_prop { \q_@@ }
 %    \end{macrocode}
 % \end{variable}
 %
 % \subsection{Allocation and initialisation}
 %
-% \begin{macro}{\prop_new:N,\prop_new:c}
+% \begin{macro}[tested = m3prop001]{\prop_new:N,\prop_new:c}
 %   Internally, property lists are token lists, but an empty prop
 %   is not an empty tl, so we need to do things by hand.
 %    \begin{macrocode}
@@ -547,20 +517,20 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\prop_clear:N, \prop_clear:c}
-% \begin{macro}{\prop_gclear:N, \prop_gclear:c}
+% \begin{macro}[tested = m3prop001]{\prop_clear:N, \prop_clear:c}
+% \begin{macro}[tested = m3prop001]{\prop_gclear:N, \prop_gclear:c}
 %   The same idea for  clearing
 %    \begin{macrocode}
 \cs_new_protected:Npn \prop_clear:N #1  { \cs_set_eq:NN   #1  \c_empty_prop }
-\cs_new_protected:Npn \prop_clear:c #1  { \cs_set_eq:cN  {#1} \c_empty_prop }
+\cs_generate_variant:Nn \prop_clear:N { c }
 \cs_new_protected:Npn \prop_gclear:N #1 { \cs_gset_eq:NN  #1  \c_empty_prop }
-\cs_new_protected:Npn \prop_gclear:c #1 { \cs_gset_eq:cN {#1} \c_empty_prop }
+\cs_generate_variant:Nn \prop_gclear:N { c }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\prop_clear_new:N, \prop_clear_new:c}
-% \begin{macro}{\prop_gclear_new:N, \prop_gclear_new:c}
+% \begin{macro}[tested = m3prop001]{\prop_clear_new:N, \prop_clear_new:c}
+% \begin{macro}[tested = m3prop001]{\prop_gclear_new:N, \prop_gclear_new:c}
 %   Once again a simple copy from the token list functions.
 %    \begin{macrocode}
 \cs_new_protected:Npn \prop_clear_new:N #1
@@ -573,9 +543,9 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}
+% \begin{macro}[tested = m3prop001]
 %   {\prop_set_eq:NN, \prop_set_eq:cN, \prop_set_eq:Nc, \prop_set_eq:cc}
-% \begin{macro}
+% \begin{macro}[tested = m3prop001]
 %   {\prop_gset_eq:NN, \prop_gset_eq:cN, \prop_gset_eq:Nc, \prop_gset_eq:cc}
 %   Once again, these are simply copies from the token list functions.
 %    \begin{macrocode}
@@ -591,116 +561,109 @@
 % \end{macro}
 % \end{macro}
 %
+% \begin{variable}[tested = m3prop004]{\l_tmpa_prop, \l_tmpb_prop}
+% \begin{variable}[tested = m3prop004]{\g_tmpa_prop, \g_tmpb_prop}
+%   We can now initialize the scratch variables.
+%    \begin{macrocode}
+\prop_new:N \l_tmpa_prop
+\prop_new:N \l_tmpb_prop
+\prop_new:N \g_tmpa_prop
+\prop_new:N \g_tmpb_prop
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+%
 % \subsection{Accessing data in property lists}
 %
-% \begin{macro}[int]{\prop_split:NnTF}
-% \begin{macro}[aux]{\prop_split_aux:NnTF}
-% \begin{macro}[aux]{\prop_split_aux:nnnn}
-% \begin{macro}[aux]{\prop_split_aux:w}
+% \begin{macro}[int]{\@@_split:NnTF}
+% \begin{macro}[aux]{\@@_split_aux:NnTF}
+% \begin{macro}[aux]{\@@_split_aux:nnnn}
+% \begin{macro}[aux]{\@@_split_aux:w}
 %   This function is used by most of the module, and hence must be fast.
 %   The aim here is to split a property list at a given key into the part
 %   before the key--value pair, the value associated with the key and the part
 %   after the key--value pair. To do this, the key is first detokenized (to
 %   avoid repeatedly doing this), then a delimited function is constructed to
-%   match the key. It will match \cs{q_prop} \meta{detokenized key} \cs{q_prop}
-%   \marg{value} \meta{extra argument}, effectively separating an
-%   \meta{extract1} before the key in the property list and an \meta{extract2}
+%   match the key. It will match \cs{q_@@} \meta{detokenized key} \cs{q_@@}
+%   \Arg{value} \meta{extra argument}, effectively separating an
+%   \meta{extract_1} before the key in the property list and an \meta{extract_2}
 %   after the key.
 %
 %   If the key is present in the property list, then \meta{extra argument}
-%   is simply \cs{q_prop}, and \cs{prop_split_aux:nnnn} will gobble this
+%   is simply \cs{q_@@}, and \cs{@@_split_aux:nnnn} will gobble this
 %   and the false branch (|#4|), leaving the correct code on the input
 %   stream. More precisely, it leaves the user code (true branch), followed
 %   by three groups, \Arg{extract_1} \Arg{value} \Arg{extract_2}.
-%   In order for \meta{extract1}\meta{extract2} to be a well-formed
-%   property list, \meta{extract1} has a leading and trailing \cs{q_prop},
-%   retaining exactly the structure of a property list, while \meta{extract2}
-%   omits the leading \cs{q_prop}.
-%
-%   If the key is not there, then \meta{extra argument} is
-%   |? \use_ii:nn { }|, and |\prop_split_aux:nnnn ? \use_ii:nn { }| removes
-%   the three brace groups that just follow. Then \cs{use_ii:nn} removes
-%   the true branch, leaving the false branch, with no trailing material.
+%   In order for \meta{extract_1}\meta{extract_2} to be a well-formed
+%   property list, \meta{extract_1} has a leading and trailing \cs{q_@@},
+%   retaining exactly the structure of a property list, while \meta{extract_2}
+%   omits the leading \cs{q_@@}.
+%
+%   If the key is not there, then \meta{extra argument} is |?|
+%   \cs{use_ii:nn} |{ }|, and \cs{@@_split_aux:nnnn} |?| \cs{use_ii:nn}
+%   |{ }| removes the three brace groups that just follow.  Then
+%   \cs{use_ii:nn} removes the true branch, leaving the false branch,
+%   with no trailing material.
 %    \begin{macrocode}
-\cs_new_protected:Npn \prop_split:NnTF #1#2
-  { \exp_args:NNo \prop_split_aux:NnTF #1 { \tl_to_str:n {#2} } }
-\cs_new_protected:Npn \prop_split_aux:NnTF #1#2
+\cs_new_protected:Npn \@@_split:NnTF #1#2
+  { \exp_args:NNo \@@_split_aux:NnTF #1 { \tl_to_str:n {#2} } }
+\cs_new_protected:Npn \@@_split_aux:NnTF #1#2
   {
-    \cs_set_protected:Npn \prop_split_aux:w
-      ##1 \q_prop #2 \q_prop ##2 ##3 ##4 \q_mark ##5 \q_stop
-      { \prop_split_aux:nnnn ##3 { {##1 \q_prop } {##2} {##4} } }
-    \exp_after:wN \prop_split_aux:w #1 \q_mark
-         \q_prop #2 \q_prop { } { ? \use_ii:nn { } } \q_mark \q_stop
+    \cs_set_protected:Npn \@@_split_aux:w
+      ##1 \q_@@ #2 \q_@@ ##2 ##3 ##4 \q_mark ##5 \q_stop
+      { \@@_split_aux:nnnn ##3 { {##1 \q_@@ } {##2} {##4} } }
+    \exp_after:wN \@@_split_aux:w #1 \q_mark
+         \q_@@ #2 \q_@@ { } { ? \use_ii:nn { } } \q_mark \q_stop
   }
-\cs_new:Npn \prop_split_aux:nnnn #1#2#3#4 { #3 #2 }
-\cs_new_protected:Npn \prop_split_aux:w { }
+\cs_new:Npn \@@_split_aux:nnnn #1#2#3#4 { #3 #2 }
+\cs_new_protected:Npn \@@_split_aux:w { }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int]{\prop_split:Nnn}
-%   The goal here is to provide a common interface for both true and false
-%   branches of \cs{prop_split:NnTF}. In both cases, the code given by the
-%   user will be placed in front of three brace groups, \Arg{extract_1}
-%   \Arg{value} \Arg{extract_2}.
-%   If the key was missing from the property list, then \meta{extract1}
-%   is the full property list, \meta{value} is \cs{q_no_value}, and
-%   \meta{extract2} is empty.
-%   Otherwise, \meta{extract1} is the part of the property list before the
-%   \meta{key}, and has the structure of a property list, \meta{value} is
-%   the value corresponding to the \meta{key}, and \meta{extract2} (the part
-%   after the \meta{key}) is missing the leading \cs{q_prop}.
-%    \begin{macrocode}
-\cs_new_protected:Npn \prop_split:Nnn #1#2#3
-  {
-    \prop_split:NnTF #1 {#2}
-    {#3}
-    { \exp_args:Nno \use:n {#3} {#1} { \q_no_value } { } }
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\prop_del:Nn, \prop_del:NV, \prop_del:cn, \prop_del:cV}
-% \begin{macro}{\prop_gdel:Nn, \prop_gdel:NV, \prop_gdel:cn, \prop_gdel:cV}
-% \begin{macro}[aux]{\prop_del_aux:NNnnn}
+% \begin{macro}[tested = m3prop002]
+%   {\prop_remove:Nn, \prop_remove:NV, \prop_remove:cn, \prop_remove:cV}
+% \begin{macro}[tested = m3prop002]
+%   {\prop_gremove:Nn, \prop_gremove:NV, \prop_gremove:cn, \prop_gremove:cV}
+% \begin{macro}[aux]{\@@_remove:NNnnn}
 %   Deleting from a property starts by splitting the list.
 %   If the key is present in the property list, the returned value is ignored.
 %   If the key is missing, nothing happens.
 %    \begin{macrocode}
-\cs_new_protected:Npn \prop_del:Nn #1#2
-  { \prop_split:NnTF #1 {#2} { \prop_del_aux:NNnnn \tl_set:Nn #1 } { } }
-\cs_new_protected:Npn \prop_gdel:Nn #1#2
-  { \prop_split:NnTF #1 {#2} { \prop_del_aux:NNnnn \tl_gset:Nn #1 } { } }
-\cs_new_protected:Npn \prop_del_aux:NNnnn #1#2#3#4#5
+\cs_new_protected:Npn \prop_remove:Nn #1#2
+  { \@@_split:NnTF #1 {#2} { \@@_remove:NNnnn \tl_set:Nn #1 } { } }
+\cs_new_protected:Npn \prop_gremove:Nn #1#2
+  { \@@_split:NnTF #1 {#2} { \@@_remove:NNnnn \tl_gset:Nn #1 } { } }
+\cs_new_protected:Npn \@@_remove:NNnnn #1#2#3#4#5
   { #1 #2 { #3 #5 } }
-\cs_generate_variant:Nn \prop_del:Nn  {     NV }
-\cs_generate_variant:Nn \prop_del:Nn  { c , cV }
-\cs_generate_variant:Nn \prop_gdel:Nn {     NV }
-\cs_generate_variant:Nn \prop_gdel:Nn { c , cV }
+\cs_generate_variant:Nn \prop_remove:Nn  {     NV }
+\cs_generate_variant:Nn \prop_remove:Nn  { c , cV }
+\cs_generate_variant:Nn \prop_gremove:Nn {     NV }
+\cs_generate_variant:Nn \prop_gremove:Nn { c , cV }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}
+% \begin{macro}[tested = m3prop002]
 %   {
 %     \prop_get:NnN, \prop_get:NVN, \prop_get:NoN,
-%     \prop_get:cnN, \prop_get:cVN, \prop_get:NoN
+%     \prop_get:cnN, \prop_get:cVN, \prop_get:coN
 %   }
-% \begin{macro}[aux]{\prop_get_aux:Nnnn}
+% \begin{macro}[aux]{\@@_get:Nnnn}
 %   Getting an item from a list is very easy: after splitting,
 %   if the key is in the property list, just set the token list variable
 %   to the return value, otherwise to \cs{q_no_value}.
 %    \begin{macrocode}
 \cs_new_protected:Npn \prop_get:NnN #1#2#3
   {
-    \prop_split:NnTF #1 {#2}
-      { \prop_get_aux:Nnnn #3 }
+    \@@_split:NnTF #1 {#2}
+      { \@@_get:Nnnn #3 }
       { \tl_set:Nn #3 { \q_no_value } }
   }
-\cs_new_protected:Npn \prop_get_aux:Nnnn #1#2#3#4
+\cs_new_protected:Npn \@@_get:Nnnn #1#2#3#4
   { \tl_set:Nn #1 {#3} }
 \cs_generate_variant:Nn \prop_get:NnN {     NV , No }
 \cs_generate_variant:Nn \prop_get:NnN { c , cV , co }
@@ -708,9 +671,11 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\prop_pop:NnN, \prop_pop:NoN, \prop_pop:cnN, \prop_pop:coN}
-% \begin{macro}{\prop_gpop:NnN, \prop_gpop:NoN, \prop_gpop:cnN, \prop_gpop:coN}
-% \begin{macro}[aux]{\prop_pop_aux:NNNnnn}
+% \begin{macro}[tested = m3prop002]
+%   {\prop_pop:NnN, \prop_pop:NoN, \prop_pop:cnN, \prop_pop:coN}
+% \begin{macro}[tested = m3prop002]
+%   {\prop_gpop:NnN, \prop_gpop:NoN, \prop_gpop:cnN, \prop_gpop:coN}
+% \begin{macro}[aux]{\@@_pop:NNNnnn}
 %   Popping a value also starts by doing the split.
 %   If the key is present, save the value in the token list and update the
 %   property list as when deleting.
@@ -718,17 +683,17 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \prop_pop:NnN #1#2#3
   {
-    \prop_split:NnTF #1 {#2}
-      { \prop_pop_aux:NNNnnn \tl_set:Nn #1 #3 }
+    \@@_split:NnTF #1 {#2}
+      { \@@_pop:NNNnnn \tl_set:Nn #1 #3 }
       { \tl_set:Nn #3 { \q_no_value } }
   }
 \cs_new_protected:Npn \prop_gpop:NnN #1#2#3
   {
-    \prop_split:NnTF #1 {#2}
-      { \prop_pop_aux:NNNnnn \tl_gset:Nn #1 #3 }
+    \@@_split:NnTF #1 {#2}
+      { \@@_pop:NNNnnn \tl_gset:Nn #1 #3 }
       { \tl_set:Nn #3 { \q_no_value } }
   }
-\cs_new_protected:Npn \prop_pop_aux:NNNnnn #1#2#3#4#5#6
+\cs_new_protected:Npn \@@_pop:NNNnnn #1#2#3#4#5#6
   {
     \tl_set:Nn #3 {#5}
     #1 #2 { #4 #6 }
@@ -742,38 +707,82 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}
+% \begin{macro}[TF, tested = m3prop004]
+%   {\prop_pop:NnN, \prop_pop:cnN, \prop_gpop:NnN, \prop_gpop:cnN}
+% \begin{macro}[aux]{\@@_pop_true:NNNnnn}
+%   Popping an item from a property list, keeping track of whether
+%   the key was present or not, is implemented as a conditional.
+%   If the key was missing, neither the property list, nor the token
+%   list are altered. Otherwise, \cs{prg_return_true:} is used after
+%   the assignments.
+%    \begin{macrocode}
+\prg_new_protected_conditional:Npnn \prop_pop:NnN #1#2#3 { T , F , TF }
+  {
+    \@@_split:NnTF #1 {#2}
+      { \@@_pop_true:NNNnnn \tl_set:Nn #1 #3 }
+      { \prg_return_false: }
+  }
+\prg_new_protected_conditional:Npnn \prop_gpop:NnN #1#2#3 { T , F , TF }
+  {
+    \@@_split:NnTF #1 {#2}
+      { \@@_pop_true:NNNnnn \tl_gset:Nn #1 #3 }
+      { \prg_return_false: }
+  }
+\cs_new_protected:Npn \@@_pop_true:NNNnnn #1#2#3#4#5#6
+  {
+    \tl_set:Nn #3 {#5}
+    #1 #2 { #4 #6 }
+    \prg_return_true:
+  }
+\cs_generate_variant:Nn \prop_pop:NnNT   { c }
+\cs_generate_variant:Nn \prop_pop:NnNF   { c }
+\cs_generate_variant:Nn \prop_pop:NnNTF  { c }
+\cs_generate_variant:Nn \prop_gpop:NnNT  { c }
+\cs_generate_variant:Nn \prop_gpop:NnNF  { c }
+\cs_generate_variant:Nn \prop_gpop:NnNTF { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[tested = m3prop002]
 %   {
 %     \prop_put:Nnn, \prop_put:NnV, \prop_put:Nno, \prop_put:Nnx,
 %     \prop_put:NVn, \prop_put:NVV, \prop_put:Non, \prop_put:Noo,
 %     \prop_put:cnn, \prop_put:cnV, \prop_put:cno, \prop_put:cnx,
 %     \prop_put:cVn, \prop_put:cVV, \prop_put:con, \prop_put:coo
 %   }
-% \begin{macro}
+% \begin{macro}[tested = m3prop002]
 %   {
 %     \prop_gput:Nnn, \prop_gput:NnV, \prop_gput:Nno, \prop_gput:Nnx,
 %     \prop_gput:NVn, \prop_gput:NVV, \prop_gput:Non, \prop_gput:Noo,
 %     \prop_gput:cnn, \prop_gput:cnV, \prop_gput:cno, \prop_gput:cnx,
 %     \prop_gput:cVn, \prop_gput:cVV, \prop_gput:con, \prop_gput:coo
 %   }
-% \begin{macro}[aux]{\prop_put_aux:NNnnnnn}
-%   Putting a key--value pair in a property list starts by splitting
-%   to remove any existing value. The property list is then
-%   reconstructed with the two remaining parts |#5| and |#7| first,
-%   followed by the new or updated entry.
+% \begin{macro}[aux]{\@@_put:NNNnn, \@@_put:NNnnnnn}
+%   Putting a key--value pair in a property list starts by splitting to
+%   remove any existing value.  If the \meta{key} was absent, append the
+%   new key--value pair.  Otherwise, the property list is reconstructed
+%   from the two remaining parts |#5| and |#7|, and the updated entry.
+%   The updated entry is placed at the same spot as the original
+%   \meta{key} in the property list, preserving the order of entries.
 %    \begin{macrocode}
-\cs_new_protected:Npn \prop_put:Nnn { \prop_put_aux:NNnn \tl_set:Nx }
-\cs_new_protected:Npn \prop_gput:Nnn { \prop_put_aux:NNnn \tl_gset:Nx }
-\cs_new_protected:Npn \prop_put_aux:NNnn #1#2#3#4
+\cs_new_protected:Npn \prop_put:Nnn
+  { \@@_put:NNNnn \tl_set:Nx \tl_put_right:Nx }
+\cs_new_protected:Npn \prop_gput:Nnn
+  { \@@_put:NNNnn \tl_gset:Nx \tl_gput_right:Nx }
+\cs_new_protected:Npn \@@_put:NNNnn #1#2#3#4#5
   {
-    \prop_split:Nnn #2 {#3} { \prop_put_aux:NNnnnnn #1 #2 {#3} {#4} }
+    \@@_split:NnTF #3 {#4}
+      { \@@_put:NNnnnnn #1 #3 {#4} {#5} }
+      { #2 #3 { \tl_to_str:n {#4} \exp_not:n { \q_@@ {#5} \q_@@ } } }
   }
-\cs_new_protected:Npn \prop_put_aux:NNnnnnn #1#2#3#4#5#6#7
+\cs_new_protected:Npn \@@_put:NNnnnnn #1#2#3#4#5#6#7
   {
     #1 #2
       {
-        \exp_not:n { #5 #7 }
-        \tl_to_str:n {#3} \exp_not:n { \q_prop {#4} \q_prop }
+        \exp_not:n {#5}
+        \tl_to_str:n {#3} \exp_not:n { \q_@@ {#4} \q_@@ }
+        \exp_not:n {#7}
       }
   }
 \cs_generate_variant:Nn \prop_put:Nnn
@@ -789,24 +798,27 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\prop_put_if_new:Nnn, \prop_put_if_new:cnn}
-% \begin{macro}{\prop_gput_if_new:Nnn, \prop_gput_if_new:cnn}
+% \begin{macro}[tested = m3prop002]
+%   {\prop_put_if_new:Nnn, \prop_put_if_new:cnn}
+% \begin{macro}[tested = m3prop002]
+%   {\prop_gput_if_new:Nnn, \prop_gput_if_new:cnn}
+% \begin{macro}[aux]{\@@_put_if_new:NNnn}
 %   Adding conditionally also splits. If the key is already present,
-%   the three brace groups given by \cs{prop_split:NnTF} are removed.
+%   the three brace groups given by \cs{@@_split:NnTF} are removed.
 %   If the key is new, then the value is added, being careful to
 %   convert the key to a string using \cs{tl_to_str:n}.
 %    \begin{macrocode}
 \cs_new_protected_nopar:Npn \prop_put_if_new:Nnn
-  { \prop_put_if_new_aux:NNnn \tl_put_right:Nx }
+  { \@@_put_if_new:NNnn \tl_put_right:Nx }
 \cs_new_protected_nopar:Npn \prop_gput_if_new:Nnn
-  { \prop_put_if_new_aux:NNnn \tl_gput_right:Nx }
-\cs_new_protected:Npn \prop_put_if_new_aux:NNnn #1#2#3#4
+  { \@@_put_if_new:NNnn \tl_gput_right:Nx }
+\cs_new_protected:Npn \@@_put_if_new:NNnn #1#2#3#4
   {
-    \prop_split:NnTF #2 {#3}
+    \@@_split:NnTF #2 {#3}
       { \use_none:nnn }
       {
         #1 #2
-          { \tl_to_str:n {#3} \exp_not:n { \q_prop {#4} \q_prop } }
+          { \tl_to_str:n {#3} \exp_not:n { \q_@@ {#4} \q_@@ } }
       }
   }
 \cs_generate_variant:Nn \prop_put_if_new:Nnn  { c }
@@ -814,10 +826,11 @@
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
+% \end{macro}
 %
 % \subsection{Property list conditionals}
 %
-% \begin{macro}[pTF]{\prop_if_exist:N, \prop_if_exist:c}
+% \begin{macro}[pTF, tested = m3prop004]{\prop_if_exist:N, \prop_if_exist:c}
 %   Copies of the \texttt{cs} functions defined in \pkg{l3basics}.
 %    \begin{macrocode}
 \cs_new_eq:NN \prop_if_exist:NTF \cs_if_exist:NTF
@@ -831,7 +844,7 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[pTF]{\prop_if_empty:N, \prop_if_empty:c}
+% \begin{macro}[pTF, tested = m3prop003]{\prop_if_empty:N, \prop_if_empty:c}
 %   The test here uses \cs{c_empty_prop} as it is not really empty!
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \prop_if_empty:N #1 { p, T , F , TF }
@@ -849,19 +862,19 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[pTF]
+% \begin{macro}[pTF, tested = m3prop003]
 %   {
 %     \prop_if_in:Nn, \prop_if_in:NV, \prop_if_in:No,
 %     \prop_if_in:cn, \prop_if_in:cV, \prop_if_in:co
 %   }
-% \begin{macro}[aux]{\prop_if_in_aux:nwn,\prop_if_in_aux:N}
+% \begin{macro}[aux]{\@@_if_in:nwn,\@@_if_in:N}
 %   Testing expandably if a key is in a property list
 %   requires to go through the key--value pairs one by one.
 %   This is rather slow, and a faster test would be
 %   \begin{verbatim}
 %     \prg_new_protected_conditional:Npnn \prop_if_in:Nn #1 #2
 %       {
-%         \prop_split:NnTF #1 {#2}
+%         \@@_split:NnTF #1 {#2}
 %           {
 %             \prg_return_true:
 %             \use_none:nnn
@@ -869,15 +882,15 @@
 %         { \prg_return_false: }
 %       }
 %   \end{verbatim}
-%   but \cs{prop_split:NnTF} is non-expandable.
+%   but \cs{@@_split:NnTF} is non-expandable.
 %
-%   Instead, the key is compared to each key in turn using \cs{str_if_eq:xx},
+%   Instead, the key is compared to each key in turn using \cs{str_if_eq_x:nn},
 %   which is expandable. To terminate the mapping, we add the key that
 %   is search for at the end of the property list. This second
 %   \cs{tl_to_str:n} is not expanded at the start, but only when included
-%   in the \cs{str_if_eq:xx}. It cannot make the breaking mechanism choke,
+%   in the \cs{str_if_eq_x:nn}. It cannot make the breaking mechanism choke,
 %   because the arbitrary token list material is enclosed in braces.
-%   When ending, we test the next token: it is either \cs{q_prop}
+%   When ending, we test the next token: it is either \cs{q_@@}
 %   or \cs{q_recursion_tail} in the case of a missing key.
 %   Here, \cs{prop_map_function:NN} is not sufficient for the mapping,
 %   since it can only map a single token, and cannot carry the key that
@@ -885,26 +898,26 @@
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \prop_if_in:Nn #1#2 { p , T , F , TF }
   {
-    \exp_last_unbraced:Noo \prop_if_in_aux:nwn
+    \exp_last_unbraced:Noo \@@_if_in:nwn
       { \tl_to_str:n {#2} } #1
-      \tl_to_str:n {#2} \q_prop { }
-    \q_recursion_tail
-    \prg_break_point:n { }
+      \tl_to_str:n {#2} \q_@@ { }
+    \q_recursion_tail % could be any cs != \q_@@
+    \__prg_break_point:
   }
-\cs_new:Npn \prop_if_in_aux:nwn #1 \q_prop #2 \q_prop #3
+\cs_new:Npn \@@_if_in:nwn #1 \q_@@ #2 \q_@@ #3
   {
-    \str_if_eq:xxTF {#1} {#2}
-      { \prop_if_in_aux:N }
-      { \prop_if_in_aux:nwn {#1} }
+    \str_if_eq_x:nnTF {#1} {#2}
+      { \@@_if_in:N }
+      { \@@_if_in:nwn {#1} }
   }
-\cs_new:Npn \prop_if_in_aux:N #1
+\cs_new:Npn \@@_if_in:N #1
   {
-    \if_meaning:w \q_prop #1
+    \if_meaning:w \q_@@ #1
       \prg_return_true:
     \else:
       \prg_return_false:
     \fi:
-    \prop_map_break:
+    \__prg_break:
   }
 \cs_generate_variant:Nn \prop_if_in_p:Nn {     NV , No }
 \cs_generate_variant:Nn \prop_if_in_p:Nn { c , cV , co }
@@ -920,23 +933,23 @@
 %
 % \subsection{Recovering values from property lists with branching}
 %
-% \begin{macro}[TF]
+% \begin{macro}[TF, tested = m3prop004]
 %   {
 %     \prop_get:NnN, \prop_get:NVN, \prop_get:NoN,
 %     \prop_get:cnN, \prop_get:cVN, \prop_get:coN
 %   }
-% \begin{macro}[aux]{\prop_get_aux_true:Nnnn}
+% \begin{macro}[aux]{\@@_get_true:Nnnn}
 %   Getting the value corresponding to a key, keeping track of whether
 %   the key was present or not, is implemented as a conditional (with
 %   side effects). If the key was absent, the token list is not altered.
 %    \begin{macrocode}
 \prg_new_protected_conditional:Npnn \prop_get:NnN #1#2#3 { T , F , TF }
   {
-    \prop_split:NnTF #1 {#2}
-      { \prop_get_aux_true:Nnnn #3 }
+    \@@_split:NnTF #1 {#2}
+      { \@@_get_true:Nnnn #3 }
       { \prg_return_false: }
   }
-\cs_new_protected:Npn \prop_get_aux_true:Nnnn #1#2#3#4
+\cs_new_protected:Npn \@@_get_true:Nnnn #1#2#3#4
   {
     \tl_set:Nn #1 {#3}
     \prg_return_true:
@@ -953,29 +966,27 @@
 %
 % \subsection{Mapping to property lists}
 %
-% \begin{macro}
+% \begin{macro}[tested = m3prop003]
 %   {
 %     \prop_map_function:NN, \prop_map_function:Nc,
 %     \prop_map_function:cN, \prop_map_function:cc
 %   }
-% \begin{macro}[aux]{\prop_map_function_aux:Nwn}
-%   The fastest way to do a recursion here is to use an
+% \begin{macro}[aux]{\@@_map_function:Nwn}
+%   The fastest way to do a recursion here would be to use an
 %   \cs{if_meaning:w} test: the keys are strings, and thus
 %   cannot match the marker \cs{q_recursion_tail}.
 %    \begin{macrocode}
 \cs_new:Npn \prop_map_function:NN #1#2
   {
-    \exp_last_unbraced:NNo \prop_map_function_aux:Nwn #2
-      #1 \q_recursion_tail \q_prop { }
-    \prg_break_point:n { }
+    \exp_last_unbraced:NNo \@@_map_function:Nwn #2
+      #1 \q_recursion_tail \q_@@ { }
+    \__prg_break_point:Nn \prop_map_break: { }
   }
-\cs_new:Npn \prop_map_function_aux:Nwn #1 \q_prop #2 \q_prop #3
+\cs_new:Npn \@@_map_function:Nwn #1 \q_@@ #2 \q_@@ #3
   {
-    \if_meaning:w \q_recursion_tail #2
-      \exp_after:wN \prop_map_break:
-    \fi:
+    \__quark_if_recursion_tail_break:nN {#2} \prop_map_break:
     #1 {#2} {#3}
-    \prop_map_function_aux:Nwn #1
+    \@@_map_function:Nwn #1
   }
 \cs_generate_variant:Nn \prop_map_function:NN {     Nc }
 \cs_generate_variant:Nn \prop_map_function:NN { c , cc }
@@ -983,145 +994,53 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\prop_map_inline:Nn, \prop_map_inline:cn}
+% \begin{macro}[tested = m3prop003]{\prop_map_inline:Nn, \prop_map_inline:cn}
 %   Mapping in line requires a nesting level counter.
 %    \begin{macrocode}
 \cs_new_protected:Npn \prop_map_inline:Nn #1#2
   {
-    \int_gincr:N \g_prg_map_int
-    \cs_gset:cpn { prop_map_inline_ \int_use:N \g_prg_map_int :nn }
-      ##1##2 {#2}
-    \exp_last_unbraced:Nco \prop_map_function_aux:Nwn
-      { prop_map_inline_ \int_use:N \g_prg_map_int :nn }
+    \int_gincr:N \g__prg_map_int
+    \cs_gset:cpn { __prg_map_ \int_use:N \g__prg_map_int :w } ##1##2 {#2}
+    \exp_last_unbraced:Nco \@@_map_function:Nwn
+      { __prg_map_ \int_use:N \g__prg_map_int :w }
       #1
-      \q_recursion_tail \q_prop { }
-    \prg_break_point:n { \int_gdecr:N \g_prg_map_int }
+      \q_recursion_tail \q_@@ { }
+    \__prg_break_point:Nn \prop_map_break: { \int_gdecr:N \g__prg_map_int }
   }
 \cs_generate_variant:Nn \prop_map_inline:Nn { c }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\prop_map_break:}
-% \begin{macro}{\prop_map_break:n}
-%   The break statements are simply copies.
+% \begin{macro}[tested = m3prop003]{\prop_map_break:}
+% \begin{macro}[tested = m3prop003]{\prop_map_break:n}
+%   The break statements are based on the general \cs{__prg_map_break:Nn}.
 %    \begin{macrocode}
-\cs_new_eq:NN \prop_map_break:  \prg_map_break:
-\cs_new_eq:NN \prop_map_break:n \prg_map_break:n
+\cs_new_nopar:Npn \prop_map_break:
+  { \__prg_map_break:Nn \prop_map_break: { } }
+\cs_new_nopar:Npn \prop_map_break:n
+  { \__prg_map_break:Nn \prop_map_break: }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
 % \subsection{Viewing property lists}
 %
-% \begin{macro}{\prop_show:N, \prop_show:c}
-%   Apply the general \cs{msg_aux_show:Nnx}. Contrarily
-%   to sequences and comma lists, we use \cs{msg_aux_show:nn}
+% \begin{macro}[tested = m3show001]{\prop_show:N, \prop_show:c}
+%   Apply the general \cs{__msg_show_variable:Nnn}. Contrarily
+%   to sequences and comma lists, we use \cs{__msg_show_item:nn}
 %   to format both the key and the value for each pair.
 %    \begin{macrocode}
 \cs_new_protected:Npn \prop_show:N #1
   {
-    \msg_aux_show:Nnx
+    \__msg_show_variable:Nnn
       #1
       { prop }
-      { \prop_map_function:NN #1 \msg_aux_show:nn }
+      { \prop_map_function:NN #1 \__msg_show_item:nn }
   }
 \cs_generate_variant:Nn \prop_show:N { c }
 %    \end{macrocode}
 % \end{macro}
 %
-% \subsection{Experimental functions}
-%
-% \begin{macro}[TF]
-%   {\prop_pop:NnN, \prop_pop:cnN, \prop_gpop:cnN, \prop_gpop:cnN}
-% \begin{macro}[aux]{\prop_pop_aux_true:NNNnnn}
-%   Popping an item from a property list, keeping track of whether
-%   the key was present or not, is implemented as a conditional.
-%   If the key was missing, neither the property list, nor the token
-%   list are altered. Otherwise, \cs{prg_return_true:} is used after
-%   the assignments.
-%    \begin{macrocode}
-\prg_new_protected_conditional:Npnn \prop_pop:NnN #1#2#3 { T , F , TF }
-  {
-    \prop_split:NnTF #1 {#2}
-      { \prop_pop_aux_true:NNNnnn \tl_set:Nn #1 #3 }
-      { \prg_return_false: }
-  }
-\prg_new_protected_conditional:Npnn \prop_gpop:NnN #1#2#3 { T , F , TF }
-  {
-    \prop_split:NnTF #1 {#2}
-      { \prop_pop_aux_true:NNNnnn \tl_gset:Nn #1 #3 }
-      { \prg_return_false: }
-  }
-\cs_new_protected:Npn \prop_pop_aux_true:NNNnnn #1#2#3#4#5#6
-  {
-    \tl_set:Nn #3 {#5}
-    #1 #2 { #4 #6 }
-    \prg_return_true:
-  }
-\cs_generate_variant:Nn \prop_pop:NnNT   { c }
-\cs_generate_variant:Nn \prop_pop:NnNF   { c }
-\cs_generate_variant:Nn \prop_pop:NnNTF  { c }
-\cs_generate_variant:Nn \prop_gpop:NnNT  { c }
-\cs_generate_variant:Nn \prop_gpop:NnNF  { c }
-\cs_generate_variant:Nn \prop_gpop:NnNTF { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[rEXP]{\prop_map_tokens:Nn, \prop_map_tokens:cn}
-% \begin{macro}[aux]{\prop_map_tokens_aux:nwn}
-%   The mapping grabs one key--value pair at a time, and stops when
-%   reaching the marker key \cs{q_recursion_tail}, which
-%   cannot appear in normal keys since those are strings. The odd
-%   construction |\use:n {#1}| allows |#1| to contain any token.
-%    \begin{macrocode}
-\cs_new:Npn \prop_map_tokens:Nn #1#2
-  {
-    \exp_last_unbraced:Nno \prop_map_tokens_aux:nwn {#2} #1
-    \q_recursion_tail \q_prop { }
-    \prg_break_point:n { }
-  }
-\cs_new:Npn \prop_map_tokens_aux:nwn #1 \q_prop #2 \q_prop #3
-  {
-    \if_meaning:w \q_recursion_tail #2
-       \exp_after:wN \prop_map_break:
-    \fi:
-    \use:n {#1} {#2} {#3}
-    \prop_map_tokens_aux:nwn {#1}
-  }
-\cs_generate_variant:Nn \prop_map_tokens:Nn { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[EXP]{\prop_get:Nn, \prop_get:cn}
-% \begin{macro}[aux]{\prop_get_Nn_aux:nwn}
-%   Getting the value corresponding to a key in a property list in an
-%   expandable fashion is a simple instance of mapping some tokens.
-%   Map the function \cs{prop_get_aux:nnn} which takes as its three
-%   arguments the \meta{key} that we are looking for, the current
-%   \meta{key} and the current \meta{value}. If the \meta{keys} match,
-%   the \meta{value} is returned. If none of the keys match, this expands
-%   to nothing.
-%    \begin{macrocode}
-\cs_new:Npn \prop_get:Nn #1#2
-  {
-    \exp_last_unbraced:Noo \prop_get_Nn_aux:nwn
-      { \tl_to_str:n {#2} } #1
-      \tl_to_str:n {#2} \q_prop { }
-    \prg_break_point:n { }
-  }
-\cs_new:Npn \prop_get_Nn_aux:nwn #1 \q_prop #2 \q_prop #3
-  {
-    \str_if_eq:xxTF {#1} {#2}
-      { \prg_map_break:n { \exp_not:n {#3} } }
-      { \prop_get_Nn_aux:nwn {#1} }
-  }
-\cs_generate_variant:Nn \prop_get:Nn { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
 % \subsection{Deprecated interfaces}
 %
 % Deprecated on 2011-05-27, for removal by 2011-08-31.
@@ -1142,10 +1061,12 @@
 %   the necessary code for the transition is provided directly.
 %    \begin{macrocode}
 %<*deprecated>
+\tl_new:N \l_@@_internal_tl
 \cs_new_protected:Npn \prop_gget:NnN #1#2#3
-  { \prop_split:Nnn #1 {#2} { \prop_gget_aux:Nnnn #3 } }
-\cs_new_protected:Npn \prop_gget_aux:Nnnn #1#2#3#4
-  { \tl_gset:Nn #1 {#3} }
+  {
+    \prop_get:NnN #1 {#2} \l_@@_internal_tl
+    \tl_gset_eq:NN #3 \l_@@_internal_tl
+  }
 \cs_generate_variant:Nn \prop_gget:NnN {     NV }
 \cs_generate_variant:Nn \prop_gget:NnN { c , cV }
 %</deprecated>
@@ -1195,6 +1116,23 @@
 %    \end{macrocode}
 % \end{macro}
 %
+% Deprecated on 2012-05-12, for removal by 2012-11-30.
+%
+% \begin{macro}{\prop_del:Nn, \prop_del:NV, \prop_del:cn, \prop_del:cV}
+% \begin{macro}{\prop_gdel:Nn, \prop_gdel:NV, \prop_gdel:cn, \prop_gdel:cV}
+%    \begin{macrocode}
+\cs_new_eq:NN \prop_del:Nn \prop_remove:Nn
+\cs_new_eq:NN \prop_del:NV \prop_remove:NV
+\cs_new_eq:NN \prop_del:cn \prop_remove:cn
+\cs_new_eq:NN \prop_del:cV \prop_remove:cV
+\cs_new_eq:NN \prop_gdel:Nn \prop_gremove:Nn
+\cs_new_eq:NN \prop_gdel:NV \prop_gremove:NV
+\cs_new_eq:NN \prop_gdel:cn \prop_gremove:cn
+\cs_new_eq:NN \prop_gdel:cV \prop_gremove:cV
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
 %    \begin{macrocode}
 %</initex|package>
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3quark.dtx b/Master/texmf-dist/source/latex/l3kernel/l3quark.dtx
index 3cb65a59b33..b85b03440df 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3quark.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3quark.dtx
@@ -35,8 +35,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3quark.dtx 3384 2012-02-12 13:13:11Z will $
-  {L3 Experimental quarks}
+\GetIdInfo$Id: l3quark.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Quarks}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -71,8 +71,9 @@
 %
 % Two special types of constants in \LaTeX3 are \enquote{quarks} and
 % \enquote{scan marks}. By convention all constants of type quark
-% start out with |\q_|, and scan marks start with |\s_|.
-% \emph{Scan marks are an experimental feature.}
+% start out with |\q_|, and scan marks start with |\s_|. Scan marks are
+% for internal use by the kernel: they are not intended for more general
+% use.
 %
 % \subsection{Quarks}
 %
@@ -114,22 +115,6 @@
 % An example of the quark testing functions and their use in recursion
 % can be seen in the implementation of \cs{clist_map_function:NN}.
 %
-%
-% \subsection{Scan marks}
-%
-% Scan marks are control sequences set equal to \cs{scan_stop:},
-% hence will never expand in an expansion context and will be (largely)
-% invisible if they are encountered in a typesetting context.
-%
-% Like quarks, they can be used as delimiters in weird functions
-% and are often safer to use for this purpose.
-% Since they are harmless when executed by \TeX{} in non-expandable
-% contexts, they can be used to mark the end of a set of instructions.
-% This allows to skip to that point if the end of the instructions
-% should not be performed (see \pkg{l3regex}).
-%
-%^^A todo: talk about the use of scan marks in galley and fp.
-%
 % \section{Defining quarks}
 %
 % \begin{function}{\quark_new:N}
@@ -279,63 +264,81 @@
 %   ended.
 % \end{function}
 %
+% \section{Clearing quarks away}
+%
+% \begin{function}{\use_none_delimit_by_q_recursion_stop:w}
+%   \begin{syntax}
+%     \cs{use_none_delimit_by_q_recursion_stop:w} \meta{tokens} \cs{q_recursion_stop}
+%   \end{syntax}
+%   Used to prematurely terminate a recursion using \cs{q_recursion_stop}
+%   as the end marker, removing any remaining \meta{tokens} from the
+%   input stream.
+% \end{function}
+%
+% \begin{function}{\use_i_delimit_by_q_recursion_stop:nw}
+%   \begin{syntax}
+%     \cs{use_i_delimit_by_q_recursion_stop:nw} \Arg{insertion}
+%     ~~\meta{tokens} \cs{q_recursion_stop}
+%   \end{syntax}
+%   Used to prematurely terminate a recursion using \cs{q_recursion_stop}
+%   as the end marker, removing any remaining \meta{tokens} from the
+%   input stream. The \meta{insertion} is then made into the input
+%   stream after the end of the recursion.
+% \end{function}
+%
+% \section{Internal quark functions}
+%
 % \begin{function}
 %   {
-%     \quark_if_recursion_tail_break:N,
-%     \quark_if_recursion_tail_break:n
+%     \__quark_if_recursion_tail_break:NN,
+%     \__quark_if_recursion_tail_break:nN
 %   }
 %   \begin{syntax}
-%     \cs{quark_if_recursion_tail_break:n} \Arg{token list}
+%     \cs{__quark_if_recursion_tail_break:nN} \Arg{token list} \cs{\meta{type}_map_break:}
 %   \end{syntax}
-%   Tests if \meta{token list} contains only \cs{q_recursion_tail},
-%   and if so terminates the recursion using \cs{prg_map_break:}.
-%   The recursion end should be marked by \cs{prg_break_point:n}.
+%   Tests if \meta{token list} contains only \cs{q_recursion_tail}, and
+%   if so terminates the recursion using \cs{\meta{type}_map_break:}.
+%   The recursion end should be marked by \cs{prg_break_point:Nn}
+%   \cs{\meta{type}_map_break:}.
 % \end{function}
 %
 % \section{Scan marks}
 %
-% \begin{function}{\scan_new:N}
+% Scan marks are control sequences set equal to \cs{scan_stop:},
+% hence will never expand in an expansion context and will be (largely)
+% invisible if they are encountered in a typesetting context.
+%
+% Like quarks, they can be used as delimiters in weird functions
+% and are often safer to use for this purpose.
+% Since they are harmless when executed by \TeX{} in non-expandable
+% contexts, they can be used to mark the end of a set of instructions.
+% This allows to skip to that point if the end of the instructions
+% should not be performed (see \pkg{l3regex}).
+% 
+% The scan marks system is only for internal use by the kernel team in
+% a small number of very specific places. These functions should not be
+% used more generally.
+%
+% \begin{function}{\__scan_new:N}
 %   \begin{syntax}
-%     \cs{scan_new:N} \meta{scan mark}
+%     \cs{__scan_new:N} \meta{scan mark}
 %   \end{syntax}
 %   Creates a new \meta{scan mark} which is set equal to \cs{scan_stop:}.
 %   The \meta{scan mark} will be defined globally, and an error message
 %   will be raised if the name was already taken by another scan mark.
 % \end{function}
 %
-% \begin{variable}{\s_stop}
+% \begin{variable}{\s__stop}
 %   Used at the end of a set of instructions, as a marker
-%   that can be jumped to using \cs{use_none_delimit_by_s_stop:w}.
+%   that can be jumped to using \cs{__use_none_delimit_by_s__stop:w}.
 % \end{variable}
 %
-% \begin{function}{\use_none_delimit_by_s_stop:w}
+% \begin{function}{\__use_none_delimit_by_s__stop:w}
 %   \begin{syntax}
-%     \cs{use_none_delimit_by_s_stop:w} \meta{tokens} \cs{s_stop}
+%     \cs{__use_none_delimit_by_s__stop:w} \meta{tokens} \cs{s__stop}
 %   \end{syntax}
-%   Removes the \meta{tokens} and \cs{s_stop} from the input stream.
-%   This leads to a low-level \TeX{} error if \cs{s_stop} is absent.
-% \end{function}
-%
-% \section{Internal quark functions}
-%
-% \begin{function}{\use_none_delimit_by_q_recursion_stop:w}
-%   \begin{syntax}
-%     \cs{use_none_delimit_by_q_recursion_stop:w} \meta{tokens} \cs{q_recursion_stop}
-%   \end{syntax}
-%   Used to prematurely terminate a recursion using \cs{q_recursion_stop}
-%   as the end marker, removing any remaining \meta{tokens} from the
-%   input stream.
-% \end{function}
-%
-% \begin{function}{\use_i_delimit_by_q_recursion_stop:nw}
-%   \begin{syntax}
-%     \cs{use_i_delimit_by_q_recursion_stop:nw} \Arg{insertion}
-%     ~~\meta{tokens} \cs{q_recursion_stop}
-%   \end{syntax}
-%   Used to prematurely terminate a recursion using \cs{q_recursion_stop}
-%   as the end marker, removing any remaining \meta{tokens} from the
-%   input stream. The \meta{insertion} is then made into the input
-%   stream after the end of the recursion.
+%   Removes the \meta{tokens} and \cs{s__stop} from the input stream.
+%   This leads to a low-level \TeX{} error if \cs{s__stop} is absent.
 % \end{function}
 %
 % \end{documentation}
@@ -354,7 +357,7 @@
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
@@ -453,22 +456,22 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\quark_if_recursion_tail_break:N}
-% \begin{macro}{\quark_if_recursion_tail_break:n}
+% \begin{macro}{\__quark_if_recursion_tail_break:NN}
+% \begin{macro}{\__quark_if_recursion_tail_break:nN}
 %   Analogs of the \cs{quark_if_recursion_tail_stop\ldots{}} functions.
-%   Break the mapping using \cs{prg_map_break:}.
+%   Break the mapping using |#2|.
 %    \begin{macrocode}
-\cs_new:Npn \quark_if_recursion_tail_break:N #1
+\cs_new:Npn \__quark_if_recursion_tail_break:NN #1#2
   {
     \if_meaning:w \q_recursion_tail #1
-      \exp_after:wN \prg_map_break:
+      \exp_after:wN #2
     \fi:
   }
-\cs_new:Npn \quark_if_recursion_tail_break:n #1
+\cs_new:Npn \__quark_if_recursion_tail_break:nN #1#2
   {
     \if_int_compare:w \pdftex_strcmp:D
       { \exp_not:N \q_recursion_tail } { \exp_not:n {#1} } = \c_zero
-      \exp_after:wN \prg_map_break:
+      \exp_after:wN #2
     \fi:
   }
 %    \end{macrocode}
@@ -477,7 +480,7 @@
 %
 % \begin{macro}[pTF]{\quark_if_nil:N}
 % \UnitTested
-% \begin{macro}[pTF]{\quark_if_no_value:N., \quark_if_no_value:c}
+% \begin{macro}[pTF]{\quark_if_no_value:N, \quark_if_no_value:c}
 % \UnitTested
 %   Here we test if we found a special quark as the first argument.
 %   We better start with \cs{q_no_value} as the first argument since
@@ -541,59 +544,77 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{variable}{\q_tl_act_mark,\q_tl_act_stop}
+% \begin{variable}{\q__tl_act_mark, \q__tl_act_stop}
 %   These private quarks are needed by \pkg{l3tl}, but that is loaded
 %   before the quark module, hence their definition is deferred.
 %    \begin{macrocode}
-\quark_new:N \q_tl_act_mark
-\quark_new:N \q_tl_act_stop
+\quark_new:N \q__tl_act_mark
+\quark_new:N \q__tl_act_stop
 %    \end{macrocode}
 % \end{variable}
 %
 % \subsection{Scan marks}
+% 
+%    \begin{macrocode}
+%<@@=scan>
+%    \end{macrocode}
 %
-% \begin{variable}{\g_scan_marks_tl}
+% \begin{variable}{\g_@@_marks_tl}
 % \UnitTested
 %   The list of all scan marks currently declared.
 %    \begin{macrocode}
-\tl_new:N \g_scan_marks_tl
+\tl_new:N \g_@@_marks_tl
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{macro}{\scan_new:N}
+% \begin{macro}[int]{\@@_new:N}
 % \UnitTested
 %   Check whether the variable is already a scan mark,
 %   then declare it to be equal to \cs{scan_stop:} globally.
 %    \begin{macrocode}
-\cs_new_protected:Npn \scan_new:N #1
+\cs_new_protected:Npn \@@_new:N #1
   {
-    \tl_if_in:NnTF \g_scan_marks_tl { #1 }
+    \tl_if_in:NnTF \g_@@_marks_tl { #1 }
       {
-        \msg_kernel_error:nnx { scan } { already-defined }
+        \__msg_kernel_error:nnx { kernel } { scanmark-already-defined }
           { \token_to_str:N #1 }
       }
       {
-        \tl_gput_right:Nn \g_scan_marks_tl {#1}
+        \tl_gput_right:Nn \g_@@_marks_tl {#1}
         \cs_new_eq:NN #1 \scan_stop:
       }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{variable}{\s_stop}
+% \begin{variable}{\s__stop}
 % \UnitTested
 %   We only declare one scan mark here, more can be defined
 %   by specific modules.
 %    \begin{macrocode}
-\scan_new:N \s_stop
+\@@_new:N \s__stop
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{macro}{\use_none_delimit_by_s_stop:w}
+% \begin{macro}[int]{\__use_none_delimit_by_s__stop:w}
 % \UnitTested
 %   Similar to \cs{use_none_delimit_by_q_stop:w}.
 %    \begin{macrocode}
-\cs_new:Npn \use_none_delimit_by_s_stop:w #1 \s_stop { }
+\cs_new:Npn \__use_none_delimit_by_s__stop:w #1 \s__stop { }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Deprecated quark functions}
+%
+% \begin{macro}
+%   {\quark_if_recursion_tail_break:N, \quark_if_recursion_tail_break:n}
+%   It's not clear what breaking function we should be using here, so
+%   I'm picking one somewhat arbitrarily.
+%    \begin{macrocode}
+\cs_new:Npn \quark_if_recursion_tail_break:N #1
+  { \__quark_if_recursion_tail_break:NN #1 \prg_break: }
+\cs_new:Npn \quark_if_recursion_tail_break:n #1
+  { \__quark_if_recursion_tail_break:nN {#1} \prg_break: }
 %    \end{macrocode}
 % \end{macro}
 %
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3seq.dtx b/Master/texmf-dist/source/latex/l3kernel/l3seq.dtx
index d8dd80c75ed..d4a3688a068 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3seq.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3seq.dtx
@@ -35,8 +35,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3seq.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental sequences and stacks}
+\GetIdInfo$Id: l3seq.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Sequences and stacks}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -109,14 +109,17 @@
 %     \seq_gset_eq:NN, \seq_gset_eq:cN, \seq_gset_eq:Nc, \seq_gset_eq:cc
 %   }
 %   \begin{syntax}
-%     \cs{seq_set_eq:NN} \meta{sequence1} \meta{sequence2}
+%     \cs{seq_set_eq:NN} \meta{sequence_1} \meta{sequence_2}
 %   \end{syntax}
-%   Sets the content of \meta{sequence1} equal to that of
-%   \meta{sequence2}.
+%   Sets the content of \meta{sequence_1} equal to that of
+%   \meta{sequence_2}.
 % \end{function}
 %
-% \begin{function}[added = 2011-08-15, updated = 2011-12-07]
-%   {\seq_set_split:Nnn, \seq_gset_split:Nnn}
+% \begin{function}[added = 2011-08-15, updated = 2012-07-02]
+%   {
+%     \seq_set_split:Nnn , \seq_set_split:NnV ,
+%     \seq_gset_split:Nnn, \seq_gset_split:NnV
+%   }
 %   \begin{syntax}
 %     \cs{seq_set_split:Nnn} \meta{sequence} \Arg{delimiter} \Arg{token list}
 %   \end{syntax}
@@ -137,11 +140,11 @@
 % \begin{function}
 %   {\seq_concat:NNN, \seq_concat:ccc, \seq_gconcat:NNN, \seq_gconcat:ccc}
 %   \begin{syntax}
-%     \cs{seq_concat:NNN} \meta{sequence1} \meta{sequence2} \meta{sequence3}
+%     \cs{seq_concat:NNN} \meta{sequence_1} \meta{sequence_2} \meta{sequence_3}
 %   \end{syntax}
-%   Concatenates the content of \meta{sequence2} and \meta{sequence3}
-%   together and saves the result in \meta{sequence1}. The items in
-%   \meta{sequence2} will be placed at the left side of the new sequence.
+%   Concatenates the content of \meta{sequence_2} and \meta{sequence_3}
+%   together and saves the result in \meta{sequence_1}. The items in
+%   \meta{sequence_2} will be placed at the left side of the new sequence.
 % \end{function}
 %
 % \begin{function}[EXP, pTF, added=2012-03-03]
@@ -197,27 +200,29 @@
 % \meta{token list variable} used with \cs{tl_set:Nn} and \emph{never}
 % \cs{tl_gset:Nn}.
 %
-% \begin{function}{\seq_get_left:NN, \seq_get_left:cN}
+% \begin{function}[updated = 2012-05-14]{\seq_get_left:NN, \seq_get_left:cN}
 %   \begin{syntax}
 %     \cs{seq_get_left:NN} \meta{sequence} \meta{token list variable}
 %   \end{syntax}
 %   Stores the left-most item from a \meta{sequence} in the
 %   \meta{token list variable} without removing it from the
 %   \meta{sequence}. The \meta{token list variable} is assigned locally.
-%   If \meta{sequence} is empty an error will be raised.
+%   If \meta{sequence} is empty the \meta{token list variable} will
+%   contain the special marker \cs{q_no_value}.
 % \end{function}
 %
-% \begin{function}{\seq_get_right:NN, \seq_get_right:cN}
+% \begin{function}[updated = 2012-05-19]{\seq_get_right:NN, \seq_get_right:cN}
 %   \begin{syntax}
 %     \cs{seq_get_right:NN} \meta{sequence} \meta{token list variable}
 %   \end{syntax}
 %   Stores the right-most item from a \meta{sequence} in the
 %   \meta{token list variable} without removing it from the
 %   \meta{sequence}. The \meta{token list variable} is assigned locally.
-%   If \meta{sequence} is empty an error will be raised.
+%   If \meta{sequence} is empty the \meta{token list variable} will
+%   contain the special marker \cs{q_no_value}.
 % \end{function}
 %
-% \begin{function}{\seq_pop_left:NN, \seq_pop_left:cN}
+% \begin{function}[updated = 2012-05-14]{\seq_pop_left:NN, \seq_pop_left:cN}
 %   \begin{syntax}
 %     \cs{seq_pop_left:NN} \meta{sequence} \meta{token list variable}
 %   \end{syntax}
@@ -225,10 +230,11 @@
 %   \meta{token list variable}, \emph{i.e.}~removes the item from the
 %   sequence and stores it in the \meta{token list variable}.
 %   Both of the variables are assigned locally. If \meta{sequence} is
-%   empty an error will be raised.
+%   empty the \meta{token list variable} will
+%   contain the special marker \cs{q_no_value}.
 % \end{function}
 %
-% \begin{function}{\seq_gpop_left:NN, \seq_gpop_left:cN}
+% \begin{function}[updated = 2012-05-14]{\seq_gpop_left:NN, \seq_gpop_left:cN}
 %   \begin{syntax}
 %     \cs{seq_gpop_left:NN} \meta{sequence} \meta{token list variable}
 %   \end{syntax}
@@ -237,10 +243,11 @@
 %   sequence and stores it in the \meta{token list variable}.
 %   The \meta{sequence} is modified globally, while the assignment of
 %   the \meta{token list variable} is local.
-%   If \meta{sequence} is  empty an error will be raised.
+%   If \meta{sequence} is empty the \meta{token list variable} will
+%   contain the special marker \cs{q_no_value}.
 % \end{function}
 %
-% \begin{function}{\seq_pop_right:NN, \seq_pop_right:cN}
+% \begin{function}[updated = 2012-05-19]{\seq_pop_right:NN, \seq_pop_right:cN}
 %   \begin{syntax}
 %     \cs{seq_pop_right:NN} \meta{sequence} \meta{token list variable}
 %   \end{syntax}
@@ -248,10 +255,11 @@
 %   \meta{token list variable}, \emph{i.e.}~removes the item from the
 %   sequence and stores it in in the \meta{token list variable}.
 %   Both of the variables are assigned locally. If \meta{sequence} is
-%   empty an error will be raised.
+%   empty the \meta{token list variable} will
+%   contain the special marker \cs{q_no_value}.
 % \end{function}
 %
-% \begin{function}{\seq_gpop_right:NN, \seq_gpop_right:cN}
+% \begin{function}[updated = 2012-05-19]{\seq_gpop_right:NN, \seq_gpop_right:cN}
 %   \begin{syntax}
 %     \cs{seq_gpop_right:NN} \meta{sequence} \meta{token list variable}
 %   \end{syntax}
@@ -260,7 +268,104 @@
 %   sequence and stores it in the \meta{token list variable}.
 %   The \meta{sequence} is modified globally, while the assignment of
 %   the \meta{token list variable} is local.
-%   If \meta{sequence} is  empty an error will be raised.
+%   If \meta{sequence} is empty the \meta{token list variable} will
+%   contain the special marker \cs{q_no_value}.
+% \end{function}
+%
+% \section{Recovering values from sequences with branching}
+%
+% The functions in this section combine tests for non-empty sequences
+% with recovery of an item from the sequence. They offer increased readability
+% and performance over separate testing and recovery phases.
+%
+% \begin{function}[TF, added = 2012-05-14, updated = 2012-05-19]
+%   {\seq_get_left:NN, \seq_get_left:cN}
+%   \begin{syntax}
+%     \cs{seq_get_left:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   If the \meta{sequence} is empty, leaves the \meta{false code} in the
+%   input stream.  The value of the \meta{token list variable} is
+%   not defined in this case and should not be relied upon.  If the
+%   \meta{sequence} is non-empty, stores the left-most item from a
+%   \meta{sequence}
+%   in the \meta{token list variable} without removing it from a
+%   \meta{sequence}.
+%   The \meta{token list variable} is assigned locally.
+% \end{function}
+%
+% \begin{function}[TF, added = 2012-05-19]
+%   {\seq_get_right:NN, \seq_get_right:cN}
+%   \begin{syntax}
+%     \cs{seq_get_right:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   If the \meta{sequence} is empty, leaves the \meta{false code} in the
+%   input stream.  The value of the \meta{token list variable} is
+%   not defined in this case and should not be relied upon.  If the
+%   \meta{sequence} is non-empty, stores the right-most item from a
+%   \meta{sequence}
+%   in the \meta{token list variable} without removing it from a
+%   \meta{sequence}.
+%   The \meta{token list variable} is assigned locally.
+% \end{function}
+%
+% \begin{function}[TF, added = 2012-05-14, updated = 2012-05-19]
+%   {\seq_pop_left:NN, \seq_pop_left:cN}
+%   \begin{syntax}
+%     \cs{seq_pop_left:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   If the \meta{sequence} is empty, leaves the \meta{false code} in the
+%   input stream.  The value of the \meta{token list variable} is
+%   not defined in this case and should not be relied upon.  If the
+%   \meta{sequence} is non-empty, pops the left-most item from a
+%   \meta{sequence}
+%   in the \meta{token list variable}, \emph{i.e.}~removes the item from a
+%   \meta{sequence}.
+%   Both the \meta{sequence} and the \meta{token list variable} are assigned
+%   locally.
+% \end{function}
+%
+% \begin{function}[TF, added = 2012-05-14, updated = 2012-05-19]
+%   {\seq_gpop_left:NN, \seq_gpop_left:cN}
+%   \begin{syntax}
+%     \cs{seq_gpop_left:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   If the \meta{sequence} is empty, leaves the \meta{false code} in the
+%   input stream.  The value of the \meta{token list variable} is
+%   not defined in this case and should not be relied upon.  If the
+%   \meta{sequence} is non-empty, pops the left-most item from a \meta{sequence}
+%   in the \meta{token list variable}, \emph{i.e.}~removes the item from a
+%   \meta{sequence}.
+%   The \meta{sequence} is modified globally, while the \meta{token list variable}
+%   is assigned locally.
+% \end{function}
+%
+% \begin{function}[TF, added = 2012-05-19]
+%   {\seq_pop_right:NN, \seq_pop_right:cN}
+%   \begin{syntax}
+%     \cs{seq_pop_right:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   If the \meta{sequence} is empty, leaves the \meta{false code} in the
+%   input stream.  The value of the \meta{token list variable} is
+%   not defined in this case and should not be relied upon.  If the
+%   \meta{sequence} is non-empty, pops the right-most item from a \meta{sequence}
+%   in the \meta{token list variable}, \emph{i.e.}~removes the item from a
+%   \meta{sequence}.
+%   Both the \meta{sequence} and the \meta{token list variable} are assigned
+%   locally.
+% \end{function}
+%
+% \begin{function}[TF, added = 2012-05-19]
+%   {\seq_gpop_right:NN, \seq_gpop_right:cN}
+%   \begin{syntax}
+%     \cs{seq_gpop_right:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   If the \meta{sequence} is empty, leaves the \meta{false code} in the
+%   input stream.  The value of the \meta{token list variable} is
+%   not defined in this case and should not be relied upon.  If the
+%   \meta{sequence} is non-empty, pops the right-most item from a \meta{sequence}
+%   in the \meta{token list variable}, \emph{i.e.}~removes the item from a
+%   \meta{sequence}. The \meta{sequence} is modified globally, while the
+%   \meta{token list variable} is assigned locally.
 % \end{function}
 %
 % \section{Modifying sequences}
@@ -324,7 +429,8 @@
 %
 % \section{Mapping to sequences}
 %
-% \begin{function}[rEXP]{\seq_map_function:NN, \seq_map_function:cN}
+% \begin{function}[rEXP, updated = 2012-06-29]
+%   {\seq_map_function:NN, \seq_map_function:cN}
 %   \begin{syntax}
 %     \cs{seq_map_function:NN} \meta{sequence} \meta{function}
 %   \end{syntax}
@@ -336,7 +442,8 @@
 %   One mapping may be nested inside another.
 % \end{function}
 %
-% \begin{function}{\seq_map_inline:Nn, \seq_map_inline:cn}
+% \begin{function}[updated = 2012-06-29]
+%   {\seq_map_inline:Nn, \seq_map_inline:cn}
 %   \begin{syntax}
 %     \cs{seq_map_inline:Nn} \meta{sequence} \Arg{inline function}
 %   \end{syntax}
@@ -347,10 +454,11 @@
 %   are returned from left to right.
 % \end{function}
 %
-% \begin{function}{
-%   \seq_map_variable:NNn, \seq_map_variable:Ncn,
-%   \seq_map_variable:cNn, \seq_map_variable:ccn
-% }
+% \begin{function}[updated = 2012-06-29]
+%   {
+%     \seq_map_variable:NNn, \seq_map_variable:Ncn,
+%     \seq_map_variable:cNn, \seq_map_variable:ccn
+%   }
 %   \begin{syntax}
 %     \cs{seq_map_variable:NNn} \meta{sequence} \meta{tl~var.} \Arg{function using tl~var.}
 %   \end{syntax}
@@ -362,7 +470,7 @@
 %   are returned from left to right.
 % \end{function}
 %
-% \begin{function}[rEXP]{\seq_map_break:}
+% \begin{function}[rEXP, updated = 2012-06-29]{\seq_map_break:}
 %   \begin{syntax}
 %     \cs{seq_map_break:}
 %   \end{syntax}
@@ -383,13 +491,13 @@
 %   level \TeX{} errors.
 %   \begin{texnote}
 %     When the mapping is broken, additional tokens may be inserted by the
-%     internal macro \cs{prg_break_point:n} before further items are taken
+%     internal macro \cs{__prg_break_point:Nn} before further items are taken
 %     from the input stream. This will depend on the design of the mapping
 %     function.
 %   \end{texnote}
 % \end{function}
 %
-% \begin{function}[rEXP]{\seq_map_break:n}
+% \begin{function}[rEXP, updated = 2012-06-29]{\seq_map_break:n}
 %   \begin{syntax}
 %     \cs{seq_map_break:n} \Arg{tokens}
 %   \end{syntax}
@@ -411,12 +519,22 @@
 %   level \TeX{} errors.
 %   \begin{texnote}
 %     When the mapping is broken, additional tokens may be inserted by the
-%     internal macro \cs{prg_break_point:n} before the \meta{tokens} are
+%     internal macro \cs{__prg_break_point:Nn} before the \meta{tokens} are
 %     inserted into the input stream.
 %     This will depend on the design of the mapping function.
 %   \end{texnote}
 % \end{function}
 %
+% \begin{function}[EXP, added = 2012-07-13]{\seq_count:N, \seq_count:c}
+%   \begin{syntax}
+%     \cs{seq_count:N} \meta{sequence}
+%   \end{syntax}
+%   Leaves the number of items in the \meta{sequence} in the input
+%   stream as an \meta{integer denotation}. The total number of items
+%   in a \meta{sequence} will include those which are empty and duplicates,
+%   \emph{i.e.}~every item in a \meta{sequence} is unique.
+% \end{function}
+%
 % \section{Sequences as stacks}
 %
 % Sequences can be used as stacks, where data is pushed to and popped
@@ -426,322 +544,147 @@
 % in the previous section: a sequence should either be used as an
 % ordered data type or as a stack, but not in both ways.
 %
-% \begin{function}{\seq_get:NN, \seq_get:cN}
+% \begin{function}[updated = 2012-05-14]{\seq_get:NN, \seq_get:cN}
 %   \begin{syntax}
 %     \cs{seq_get:NN} \meta{sequence} \meta{token list variable}
 %   \end{syntax}
 %   Reads the top item from a \meta{sequence} into the
 %   \meta{token list variable} without removing it from the
 %   \meta{sequence}. The \meta{token list variable} is assigned locally.
-%   If \meta{sequence} is empty an error will be raised.
+%   If \meta{sequence} is empty the \meta{token list variable} will
+%   contain the special marker \cs{q_no_value}.
 % \end{function}
 %
-% \begin{function}{\seq_pop:NN, \seq_pop:cN}
+% \begin{function}[updated = 2012-05-14]{\seq_pop:NN, \seq_pop:cN}
 %   \begin{syntax}
 %     \cs{seq_pop:NN} \meta{sequence} \meta{token list variable}
 %   \end{syntax}
 %   Pops the top item from a \meta{sequence} into the
 %   \meta{token list variable}. Both of the variables are assigned
-%   locally. If \meta{sequence} is empty an error will be raised.
+%   locally. If \meta{sequence} is empty the \meta{token list variable} will
+%   contain the special marker \cs{q_no_value}.
 % \end{function}
 %
-% \begin{function}{\seq_gpop:NN, \seq_gpop:cN}
+% \begin{function}[updated = 2012-05-14]{\seq_gpop:NN, \seq_gpop:cN}
 %   \begin{syntax}
 %     \cs{seq_gpop:NN} \meta{sequence} \meta{token list variable}
 %   \end{syntax}
 %   Pops the top item from a \meta{sequence} into the
 %   \meta{token list variable}. The \meta{sequence} is modified globally,
 %   while the \meta{token list variable} is assigned locally. If
-%   \meta{sequence} is empty an error will be raised.
-% \end{function}
-%
-% \begin{function}
-%   {
-%     \seq_push:Nn, \seq_push:NV, \seq_push:Nv, \seq_push:No, \seq_push:Nx,
-%     \seq_push:cn, \seq_push:cV, \seq_push:cv, \seq_push:co, \seq_push:cx,
-%     \seq_gpush:Nn, \seq_gpush:NV, \seq_gpush:Nv,
-%     \seq_gpush:No, \seq_gpush:Nx,
-%     \seq_gpush:cn, \seq_gpush:cV, \seq_gpush:cv,
-%     \seq_gpush:co, \seq_gpush:cx
-%   }
-%   \begin{syntax}
-%     \cs{seq_push:Nn} \meta{sequence} \Arg{item}
-%   \end{syntax}
-%   Adds the \Arg{item} to the top of the \meta{sequence}.
-% \end{function}
-%
-% \section{Viewing sequences}
-%
-% \begin{function}{\seq_show:N, \seq_show:c}
-%   \begin{syntax}
-%     \cs{seq_show:N} \meta{sequence}
-%   \end{syntax}
-%   Displays the entries in the \meta{sequence} in the terminal.
-% \end{function}
-%
-% \section{Experimental sequence functions}
-%
-% This section contains functions which may or may not be retained, depending
-% on how useful they are found to be.
-%
-% \begin{function}[TF]{\seq_get_left:NN, \seq_get_left:cN}
-%   \begin{syntax}
-%     \cs{seq_get_left:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
-%   \end{syntax}
-%   If the \meta{sequence} is empty, leaves the \meta{false code} in the
-%   input stream and leaves the \meta{token list variable} unchanged. If the
-%   \meta{sequence} is non-empty, stores the left-most item from a
-%   \meta{sequence}
-%   in the \meta{token list variable} without removing it from a
-%   \meta{sequence}.
-%   The \meta{token list variable} is assigned locally.
-% \end{function}
-%
-% \begin{function}[TF]{\seq_get_right:NN, \seq_get_right:cN}
-%   \begin{syntax}
-%     \cs{seq_get_right:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
-%   \end{syntax}
-%   If the \meta{sequence} is empty, leaves the \meta{false code} in the
-%   input stream and leaves the \meta{token list variable} unchanged. If the
-%   \meta{sequence} is non-empty, stores the right-most item from a
-%   \meta{sequence}
-%   in the \meta{token list variable} without removing it from a
-%   \meta{sequence}.
-%   The \meta{token list variable} is assigned locally.
-% \end{function}
-%
-% \begin{function}[TF]{\seq_pop_left:NN, \seq_pop_left:cN}
-%   \begin{syntax}
-%     \cs{seq_pop_left:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
-%   \end{syntax}
-%   If the \meta{sequence} is empty, leaves the \meta{false code} in the
-%   input stream and leaves the \meta{token list variable} unchanged. If the
-%   \meta{sequence} is non-empty, pops the left-most item from a
-%   \meta{sequence}
-%   in the \meta{token list variable}, \emph{i.e.}~removes the item from a
-%   \meta{sequence}.
-%   Both the \meta{sequence} and the \meta{token list variable} are assigned
-%   locally.
+%   \meta{sequence} is empty the \meta{token list variable} will
+%   contain the special marker \cs{q_no_value}.
 % \end{function}
 %
-% \begin{function}[TF]{\seq_gpop_left:NN, \seq_gpop_left:cN}
+% \begin{function}[TF, added = 2012-05-14, updated = 2012-05-19]{\seq_get:NN, \seq_get:cN}
 %   \begin{syntax}
-%     \cs{seq_gpop_left:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
+%     \cs{seq_get:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   If the \meta{sequence} is empty, leaves the \meta{false code} in the
-%   input stream and leaves the \meta{token list variable} unchanged. If the
-%   \meta{sequence} is non-empty, pops the left-most item from a \meta{sequence}
-%   in the \meta{token list variable}, \emph{i.e.}~removes the item from a
-%   \meta{sequence}.
-%   The \meta{sequence} is modified globally, while the \meta{token list variable}
-%   is assigned locally.
+%   input stream.  The value of the \meta{token list variable} is
+%   not defined in this case and should not be relied upon.  If the
+%   \meta{sequence} is non-empty, stores the top item from a
+%   \meta{sequence} in the \meta{token list variable} without removing it from
+%   the \meta{sequence}. The \meta{token list variable} is assigned locally.
 % \end{function}
 %
-% \begin{function}[TF]{\seq_pop_right:NN, \seq_pop_right:cN}
+% \begin{function}[TF, added = 2012-05-14, updated = 2012-05-19]{\seq_pop:NN, \seq_pop:cN}
 %   \begin{syntax}
-%     \cs{seq_pop_right:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
+%     \cs{seq_pop:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   If the \meta{sequence} is empty, leaves the \meta{false code} in the
-%   input stream and leaves the \meta{token list variable} unchanged. If the
-%   \meta{sequence} is non-empty, pops the right-most item from a \meta{sequence}
-%   in the \meta{token list variable}, \emph{i.e.}~removes the item from a
-%   \meta{sequence}.
-%   Both the \meta{sequence} and the \meta{token list variable} are assigned
-%   locally.
+%   input stream.  The value of the \meta{token list variable} is
+%   not defined in this case and should not be relied upon.  If the
+%   \meta{sequence} is non-empty, pops the top item from the
+%   \meta{sequence} in the \meta{token list variable}, \emph{i.e.}~removes the
+%   item from the \meta{sequence}. Both the \meta{sequence} and the
+%   \meta{token list variable} are assigned locally.
 % \end{function}
 %
-% \begin{function}[TF]{\seq_gpop_right:NN, \seq_gpop_right:cN}
+% \begin{function}[TF, added = 2012-05-14, updated = 2012-05-19]{\seq_gpop:NN, \seq_gpop:cN}
 %   \begin{syntax}
-%     \cs{seq_gpop_right:NNTF} \meta{sequence} \meta{token list variable}
-%     ~~\Arg{true code} \Arg{false code}
+%     \cs{seq_gpop:NNTF} \meta{sequence} \meta{token list variable} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   If the \meta{sequence} is empty, leaves the \meta{false code} in the
-%   input stream and leaves the \meta{token list variable} unchanged. If the
-%   \meta{sequence} is non-empty, pops the right-most item from a \meta{sequence}
-%   in the \meta{token list variable}, \emph{i.e.}~removes the item from a
-%   \meta{sequence}.
-%   The \meta{sequence} is modified globally, while the \meta{token list variable}
-%   is assigned locally.
-% \end{function}
-%
-% \begin{function}[EXP]{\seq_length:N, \seq_length:c}
-%   \begin{syntax}
-%     \cs{seq_length:N} \meta{sequence}
-%   \end{syntax}
-%   Leaves the number of items in the \meta{sequence} in the input
-%   stream as an \meta{integer denotation}. The total number of items
-%   in a \meta{sequence} will include those which are empty and duplicates,
-%   \emph{i.e.}~every item in a \meta{sequence} is unique.
-% \end{function}
-%
-% \begin{function}[EXP, updated = 2012-01-08]{\seq_item:Nn, \seq_item:cn}
-%   \begin{syntax}
-%     \cs{seq_item:Nn} \meta{sequence} \Arg{integer expression}
-%   \end{syntax}
-%   Indexing items in the \meta{sequence} from $0$ at the top (left), this
-%   function will evaluate the \meta{integer expression} and leave the
-%   appropriate item from the sequence in the input stream. If the
-%   \meta{integer expression} is negative, indexing occurs from the
-%   bottom (right) of the sequence. When the \meta{integer expression}
-%   is larger than the number of items in the \meta{sequence} (as
-%   calculated by \cs{seq_length:N}) then the function will expand to
-%   nothing.
-%   \begin{texnote}
-%     The result is returned within the \tn{unexpanded}
-%     primitive (\cs{exp_not:n}), which means that the \meta{item}
-%     will not expand further when appearing in an x-type
-%     argument expansion.
-%   \end{texnote}
-% \end{function}
-%
-% \begin{function}[rEXP]{\seq_use:N, \seq_use:c}
-%   \begin{syntax}
-%     \cs{seq_use:N} \meta{sequence}
-%   \end{syntax}
-%   Places each \meta{item} in the \meta{sequence} in turn in the input stream.
-%   This occurs in an expandable fashion, and is implemented as a mapping.
-%   This means that the process may be prematurely terminated using
-%   \cs{seq_map_break:} or \cs{seq_map_break:n}. The \meta{items} in the
-%   \meta{sequence} will be used from left (top) to right (bottom).
-% \end{function}
-%
-% \begin{function}[rEXP]
-%   {
-%     \seq_mapthread_function:NNN, \seq_mapthread_function:NcN,
-%     \seq_mapthread_function:cNN, \seq_mapthread_function:ccN
-%   }
-%   \begin{syntax}
-%     \cs{seq_mapthread_function:NNN} \meta{seq1} \meta{seq2} \meta{function}
-%   \end{syntax}
-%   Applies \meta{function} to every pair of items
-%   \meta{seq1-item}--\meta{seq2-item} from the two sequences, returning
-%   items from both sequences from left to right.   The \meta{function} will
-%   receive two \texttt{n}-type arguments for each iteration. The  mapping
-%   will terminate when
-%   the end of either sequence is reached (\emph{i.e.}~whichever sequence has
-%   fewer items determines how many iterations
-%   occur).
+%   input stream.  The value of the \meta{token list variable} is
+%   not defined in this case and should not be relied upon.  If the
+%   \meta{sequence} is non-empty, pops the top item from the \meta{sequence}
+%   in the \meta{token list variable}, \emph{i.e.}~removes the item from the
+%   \meta{sequence}. The \meta{sequence} is modified globally, while the
+%   \meta{token list variable} is assigned locally.
 % \end{function}
 %
 % \begin{function}
 %   {
-%     \seq_set_from_clist:NN,  \seq_set_from_clist:cN,
-%     \seq_set_from_clist:Nc,  \seq_set_from_clist:cc,
-%     \seq_set_from_clist:Nn,  \seq_set_from_clist:cn,
-%     \seq_gset_from_clist:NN, \seq_gset_from_clist:cN,
-%     \seq_gset_from_clist:Nc, \seq_gset_from_clist:cc,
-%     \seq_gset_from_clist:Nn, \seq_gset_from_clist:cn
+%     \seq_push:Nn, \seq_push:NV, \seq_push:Nv, \seq_push:No, \seq_push:Nx,
+%     \seq_push:cn, \seq_push:cV, \seq_push:cv, \seq_push:co, \seq_push:cx,
+%     \seq_gpush:Nn, \seq_gpush:NV, \seq_gpush:Nv,
+%     \seq_gpush:No, \seq_gpush:Nx,
+%     \seq_gpush:cn, \seq_gpush:cV, \seq_gpush:cv,
+%     \seq_gpush:co, \seq_gpush:cx
 %   }
 %   \begin{syntax}
-%     \cs{seq_set_from_clist:NN} \meta{sequence} \meta{comma-list}
+%     \cs{seq_push:Nn} \meta{sequence} \Arg{item}
 %   \end{syntax}
-%   Sets the \meta{sequence} within the current \TeX{} group to be equal
-%   to the content of the \meta{comma-list}.
+%   Adds the \Arg{item} to the top of the \meta{sequence}.
 % \end{function}
 %
-% \begin{function}[added = 2011-11-22, updated = 2011-11-24]
-%     {\seq_reverse:N, \seq_greverse:N}
-%   \begin{syntax}
-%     \cs{seq_reverse:N} \meta{sequence}
-%   \end{syntax}
-%   Reverses the order of items in the \meta{sequence}, and
-%   assigns the result to \meta{sequence}, locally or globally
-%   according to the variant chosen.
-% \end{function}
+% \section{Constant and scratch sequences}
 %
-% \begin{function}[added = 2011-12-22]
-%   {\seq_set_filter:NNn, \seq_gset_filter:NNn}
-%   \begin{syntax}
-%     \cs{seq_set_filter:NNn} \meta{sequence1} \meta{sequence2} \Arg{inline boolexpr}
-%   \end{syntax}
-%   Evaluates the \meta{inline boolexpr} for every \meta{item} stored
-%   within the \meta{sequence2}. The \meta{inline boolexpr} will
-%   receive the \meta{item} as |#1|. The sequence of all \meta{items}
-%   for which the \meta{inline boolexpr} evaluated to \texttt{true}
-%   is assigned to \meta{sequence1}.
-%   \begin{texnote}
-%     Contrarily to other mapping functions, \cs{seq_map_break:} cannot
-%     be used in this function, and will lead to low-level \TeX{} errors.
-%   \end{texnote}
-% \end{function}
+% \begin{variable}[added = 2012-07-02]{\c_empty_seq}
+%   Constant that is always empty.
+% \end{variable}
 %
-% \begin{function}[added = 2011-12-22]
-%   {\seq_set_map:NNn, \seq_gset_map:NNn}
-%   \begin{syntax}
-%     \cs{seq_set_map:NNn} \meta{sequence1} \meta{sequence2} \Arg{inline function}
-%   \end{syntax}
-%   Applies \meta{inline function} to every \meta{item} stored
-%   within the \meta{sequence2}. The \meta{inline function} should
-%   consist of code which will receive the \meta{item} as |#1|.
-%   The sequence resulting from \texttt{x}-expanding
-%   \meta{inline function} applied to each \meta{item}
-%   is assigned to \meta{sequence1}. As such, the code
-%   in \meta{inline function} should be expandable.
-%   \begin{texnote}
-%     Contrarily to other mapping functions, \cs{seq_map_break:} cannot
-%     be used in this function, and will lead to low-level \TeX{} errors.
-%   \end{texnote}
-% \end{function}
+% \begin{variable}[added = 2012-04-26]{\l_tmpa_seq, \l_tmpb_seq}
+%   Scratch sequences for local assignment. These are never used by
+%   the kernel code, and so are safe for use with any \LaTeX3-defined
+%   function. However, they may be overwritten by other non-kernel
+%   code and so should only be used for short-term storage.
+% \end{variable}
 %
-% \section{Internal sequence functions}
+% \begin{variable}[added = 2012-04-26]{\g_tmpa_seq, \g_tmpb_seq}
+%   Scratch sequences for global assignment. These are never used by
+%   the kernel code, and so are safe for use with any \LaTeX3-defined
+%   function. However, they may be overwritten by other non-kernel
+%   code and so should only be used for short-term storage.
+% \end{variable}
+%
+% \section{Viewing sequences}
 %
-% \begin{function}{\seq_if_empty_err_break:N}
+% \begin{function}{\seq_show:N, \seq_show:c}
 %   \begin{syntax}
-%     \cs{seq_if_empty_err_break:N} \meta{sequence}
+%     \cs{seq_show:N} \meta{sequence}
 %   \end{syntax}
-%   Tests if the \meta{sequence} is empty, and if so issues an error
-%   message before skipping over any tokens up to \cs{prg_break_point:n}.
-%   This function is used to avoid more serious errors which would
-%   otherwise occur if some internal functions were applied to an
-%   empty \meta{sequence}.
+%   Displays the entries in the \meta{sequence} in the terminal.
 % \end{function}
 %
-% \begin{function}[EXP]{\seq_item:n}
+% \section{Internal sequence functions}
+%
+% \begin{function}[EXP]{\__seq_item:n}
 %   \begin{syntax}
-%     \cs{seq_item:n} \meta{item}
+%     \cs{__seq_item:n} \meta{item}
 %   \end{syntax}
 %   The internal token used to begin each sequence entry. If expanded
 %   outside of a mapping or manipulation function, an error will be
 %   raised. The definition should always be set globally.
 % \end{function}
 %
-% \begin{function}{\seq_push_item_def:n, \seq_push_item_def:x}
+% \begin{function}{\__seq_push_item_def:n, \__seq_push_item_def:x}
 %   \begin{syntax}
-%     \cs{seq_push_item_def:n} \Arg{code}
+%     \cs{__seq_push_item_def:n} \Arg{code}
 %   \end{syntax}
-%   Saves the definition of \cs{seq_item:n} and redefines it to
+%   Saves the definition of \cs{__seq_item:n} and redefines it to
 %   accept one parameter and expand to \meta{code}. This function
-%   should always be balanced by use of \cs{seq_pop_item_def:}.
-% \end{function}
-%
-% \begin{function}{\seq_pop_item_def:}
-%   \begin{syntax}
-%     \cs{seq_pop_item_def:}
-%   \end{syntax}
-%   Restores the definition of \cs{seq_item:n} most recently saved by
-%   \cs{seq_push_item_def:n}. This function should always be used in
-%   a balanced pair with \cs{seq_push_item_def:n}.
+%   should always be balanced by use of \cs{__seq_pop_item_def:}.
 % \end{function}
 %
-% \begin{function}[EXP]{\seq_break:}
+% \begin{function}{\__seq_pop_item_def:}
 %   \begin{syntax}
-%     \cs{seq_break:}
+%     \cs{__seq_pop_item_def:}
 %   \end{syntax}
-%   Used to terminate sequence functions by gobbling all tokens
-%   up to \cs{prg_break_point:n}. This function is a copy of
-%   \cs{seq_map_break:}, but is used in situations which are
-%   not mappings.
-% \end{function}
-%
-% \begin{function}[EXP]{\seq_break:n}
-%   \begin{syntax}
-%     \cs{seq_break:n} \Arg{tokens}
-%   \end{syntax}
-%   Used to terminate sequence functions by gobbling all tokens
-%   up to \cs{prg_break_point:n}, then inserting the \meta{tokens}
-%   before continuing reading the input stream. This function is a copy
-%   of \cs{seq_map_break:n}, but is used in situations which are
-%   not mappings.
+%   Restores the definition of \cs{__seq_item:n} most recently saved by
+%   \cs{__seq_push_item_def:n}. This function should always be used in
+%   a balanced pair with \cs{__seq_push_item_def:n}.
 % \end{function}
 %
 % \end{documentation}
@@ -757,41 +700,52 @@
 %    \end{macrocode}
 %
 %    \begin{macrocode}
+%<@@=seq>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
 % A sequence is a control sequence whose top-level expansion is of
-% the form \enquote{\cs{seq_item:n} \marg{item$_0$}
-% \ldots \cs{seq_item:n} \marg{item$_{n-1}$}}. An earlier implementation
-% used the structure \enquote{\cs{seq_elt:w} \meta{item$_1$}
-% \cs{seq_elt_end:} \ldots \cs{seq_elt:w} \meta{item$_n$}
+% the form \enquote{\cs{@@_item:n} \marg{item_1}
+% \ldots \cs{@@_item:n} \marg{item_n}}. An earlier implementation
+% used the structure \enquote{\cs{seq_elt:w} \meta{item_1}
+% \cs{seq_elt_end:} \ldots \cs{seq_elt:w} \meta{item_n}
 % \cs{seq_elt_end:}}. This allows rapid searching using a delimited
 % function, but is not suitable for items containing |{|, |}| and |#|
 % tokens, and also leads to the loss of surrounding braces
 % around items.
 %
-% \begin{macro}[int]{\seq_item:n}
+% \begin{macro}[int]{\@@_item:n}
 %   The delimiter is always defined, but when used incorrectly simply
 %   removes its argument and hits an undefined control sequence to
 %   raise an error.
 %    \begin{macrocode}
-\cs_new:Npn \seq_item:n
+\cs_new:Npn \@@_item:n
   {
-    \msg_expandable_kernel_error:nn { seq } { misused }
+    \__msg_kernel_expandable_error:nn { kernel } { misused-sequence }
     \use_none:n
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{variable}{\l_seq_internal_a_tl, \l_seq_internal_b_tl}
+% \begin{variable}{\l_@@_internal_a_tl, \l_@@_internal_b_tl}
 %   Scratch space for various internal uses.
 %    \begin{macrocode}
-\tl_new:N \l_seq_internal_a_tl
-\tl_new:N \l_seq_internal_b_tl
+\tl_new:N \l_@@_internal_a_tl
+\tl_new:N \l_@@_internal_b_tl
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\c_empty_seq}
+%   Simply copy the empty token list.
+%    \begin{macrocode}
+\cs_new_eq:NN \c_empty_seq \c_empty_tl
 %    \end{macrocode}
 % \end{variable}
 %
@@ -853,25 +807,29 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\seq_set_split:Nnn,\seq_gset_split:Nnn}
-% \begin{macro}[aux]{\seq_set_split_aux:NNnn}
+% \begin{macro}
+%   {
+%     \seq_set_split:Nnn , \seq_set_split:NnV ,
+%     \seq_gset_split:Nnn, \seq_gset_split:NnV
+%   }
+% \begin{macro}[aux]{\@@_set_split:NNnn}
 % \begin{macro}[aux]
 %   {
-%     \seq_set_split_aux_i:w, \seq_set_split_aux_ii:w,
-%     \seq_set_split_aux_end:
+%     \@@_set_split_i:w, \@@_set_split_ii:w,
+%     \@@_set_split_end:
 %   }
 %   The goal is to split a given token list at a marker,
 %   strip spaces from each item, and remove one set of
 %   outer braces if after removing leading and trailing
 %   spaces the item is enclosed within braces. After
-%   \cs{tl_replace_all:Nnn}, the token list \cs{l_seq_internal_a_tl}
+%   \cs{tl_replace_all:Nnn}, the token list \cs{l_@@_internal_a_tl}
 %   is a repetition of the pattern
-%   \cs{seq_set_split_aux_i:w} \cs{prg_do_nothing:}
-%   \meta{item with spaces} \cs{seq_set_split_aux_end:}.
-%   Then, \texttt{x}-expansion causes \cs{seq_set_split_aux_i:w}
+%   \cs{@@_set_split_i:w} \cs{prg_do_nothing:}
+%   \meta{item with spaces} \cs{@@_set_split_end:}.
+%   Then, \texttt{x}-expansion causes \cs{@@_set_split_i:w}
 %   to trim spaces, and leaves its result as
-%   \cs{seq_set_split_aux_ii:w} \meta{trimmed item}
-%   \cs{seq_set_split_aux_end:}. This is then converted
+%   \cs{@@_set_split_ii:w} \meta{trimmed item}
+%   \cs{@@_set_split_end:}. This is then converted
 %   to the \pkg{l3seq} internal structure by another
 %   \texttt{x}-expansion. In the first step, we insert
 %   \cs{prg_do_nothing:} to avoid losing braces too early:
@@ -880,37 +838,39 @@
 %   braces which are outermost after space trimming.
 %    \begin{macrocode}
 \cs_new_protected_nopar:Npn \seq_set_split:Nnn
-  { \seq_set_split_aux:NNnn \tl_set:Nx }
+  { \@@_set_split:NNnn \tl_set:Nx }
 \cs_new_protected_nopar:Npn \seq_gset_split:Nnn
-  { \seq_set_split_aux:NNnn \tl_gset:Nx }
-\cs_new_protected:Npn \seq_set_split_aux:NNnn #1 #2 #3 #4
+  { \@@_set_split:NNnn \tl_gset:Nx }
+\cs_new_protected:Npn \@@_set_split:NNnn #1 #2 #3 #4
   {
     \tl_if_empty:nTF {#3}
-      { #1 #2 { \tl_map_function:nN {#4} \seq_wrap_item:n } }
+      { #1 #2 { \tl_map_function:nN {#4} \@@_wrap_item:n } }
       {
-        \tl_set:Nn \l_seq_internal_a_tl
+        \tl_set:Nn \l_@@_internal_a_tl
           {
-            \seq_set_split_aux_i:w \prg_do_nothing:
+            \@@_set_split_i:w \prg_do_nothing:
             #4
-            \seq_set_split_aux_end:
+            \@@_set_split_end:
           }
-        \tl_replace_all:Nnn \l_seq_internal_a_tl { #3 }
+        \tl_replace_all:Nnn \l_@@_internal_a_tl { #3 }
           {
-            \seq_set_split_aux_end:
-            \seq_set_split_aux_i:w \prg_do_nothing:
+            \@@_set_split_end:
+            \@@_set_split_i:w \prg_do_nothing:
           }
-        \tl_set:Nx \l_seq_internal_a_tl { \l_seq_internal_a_tl }
-        #1 #2 { \l_seq_internal_a_tl }
+        \tl_set:Nx \l_@@_internal_a_tl { \l_@@_internal_a_tl }
+        #1 #2 { \l_@@_internal_a_tl }
       }
   }
-\cs_new:Npn \seq_set_split_aux_i:w #1 \seq_set_split_aux_end:
+\cs_new:Npn \@@_set_split_i:w #1 \@@_set_split_end:
   {
-    \exp_not:N \seq_set_split_aux_ii:w
+    \exp_not:N \@@_set_split_ii:w
     \exp_args:No \tl_trim_spaces:n {#1}
-    \exp_not:N \seq_set_split_aux_end:
+    \exp_not:N \@@_set_split_end:
   }
-\cs_new:Npn \seq_set_split_aux_ii:w #1 \seq_set_split_aux_end:
-  { \seq_wrap_item:n {#1} }
+\cs_new:Npn \@@_set_split_ii:w #1 \@@_set_split_end:
+  { \@@_wrap_item:n {#1} }
+\cs_generate_variant:Nn \seq_set_split:Nnn  { NnV }
+\cs_generate_variant:Nn \seq_gset_split:Nnn { NnV }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -965,9 +925,9 @@
 %   The code here is just a wrapper for adding to token lists.
 %    \begin{macrocode}
 \cs_new_protected:Npn \seq_put_left:Nn #1#2
-  { \tl_put_left:Nn #1 { \seq_item:n {#2} } }
+  { \tl_put_left:Nn #1 { \@@_item:n {#2} } }
 \cs_new_protected:Npn \seq_put_right:Nn #1#2
-  { \tl_put_right:Nn #1 { \seq_item:n {#2} } }
+  { \tl_put_right:Nn #1 { \@@_item:n {#2} } }
 \cs_generate_variant:Nn \seq_put_left:Nn  {     NV , Nv , No , Nx }
 \cs_generate_variant:Nn \seq_put_left:Nn  { c , cV , cv , co , cx }
 \cs_generate_variant:Nn \seq_put_right:Nn {     NV , Nv , No , Nx }
@@ -991,9 +951,9 @@
 %   The same for global addition.
 %    \begin{macrocode}
 \cs_new_protected:Npn \seq_gput_left:Nn #1#2
-  { \tl_gput_left:Nn #1 { \seq_item:n {#2} } }
+  { \tl_gput_left:Nn #1 { \@@_item:n {#2} } }
 \cs_new_protected:Npn \seq_gput_right:Nn #1#2
-  { \tl_gput_right:Nn #1 { \seq_item:n {#2} } }
+  { \tl_gput_right:Nn #1 { \@@_item:n {#2} } }
 \cs_generate_variant:Nn \seq_gput_left:Nn  {     NV , Nv , No , Nx }
 \cs_generate_variant:Nn \seq_gput_left:Nn  { c , cV , cv , co , cx }
 \cs_generate_variant:Nn \seq_gput_right:Nn {     NV , Nv , No , Nx }
@@ -1004,18 +964,18 @@
 %
 % \subsection{Modifying sequences}
 %
-% \begin{macro}[aux]{\seq_wrap_item:n}
+% \begin{macro}[aux]{\@@_wrap_item:n}
 %   This function converts its argument to a proper sequence item
 %   in an \texttt{x}-expansion context.
 %    \begin{macrocode}
-\cs_new:Npn \seq_wrap_item:n #1 { \exp_not:n { \seq_item:n {#1} } }
+\cs_new:Npn \@@_wrap_item:n #1 { \exp_not:n { \@@_item:n {#1} } }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{variable}{\l_seq_internal_remove_seq}
+% \begin{variable}{\l_@@_remove_seq}
 %   An internal sequence for the removal routines.
 %    \begin{macrocode}
-\seq_new:N \l_seq_internal_remove_seq
+\seq_new:N \l_@@_remove_seq
 %    \end{macrocode}
 % \end{variable}
 %
@@ -1023,22 +983,22 @@
 % \UnitTested
 % \begin{macro}{\seq_gremove_duplicates:N, \seq_gremove_duplicates:c}
 % \UnitTested
-% \begin{macro}[aux]{\seq_remove_duplicates_aux:NN}
+% \begin{macro}[aux]{\@@_remove_duplicates:NN}
 %   Removing duplicates means making a new list then copying it.
 %    \begin{macrocode}
 \cs_new_protected:Npn \seq_remove_duplicates:N
-  { \seq_remove_duplicates_aux:NN \seq_set_eq:NN }
+  { \@@_remove_duplicates:NN \seq_set_eq:NN }
 \cs_new_protected:Npn \seq_gremove_duplicates:N
-  { \seq_remove_duplicates_aux:NN \seq_gset_eq:NN }
-\cs_new_protected:Npn \seq_remove_duplicates_aux:NN #1#2
+  { \@@_remove_duplicates:NN \seq_gset_eq:NN }
+\cs_new_protected:Npn \@@_remove_duplicates:NN #1#2
   {
-    \seq_clear:N \l_seq_internal_remove_seq
+    \seq_clear:N \l_@@_remove_seq
     \seq_map_inline:Nn #2
       {
-        \seq_if_in:NnF \l_seq_internal_remove_seq {##1}
-          { \seq_put_right:Nn \l_seq_internal_remove_seq {##1} }
+        \seq_if_in:NnF \l_@@_remove_seq {##1}
+          { \seq_put_right:Nn \l_@@_remove_seq {##1} }
       }
-    #1 #2 \l_seq_internal_remove_seq
+    #1 #2 \l_@@_remove_seq
   }
 \cs_generate_variant:Nn \seq_remove_duplicates:N  { c }
 \cs_generate_variant:Nn \seq_gremove_duplicates:N { c }
@@ -1051,11 +1011,11 @@
 % \UnitTested
 % \begin{macro}{\seq_gremove_all:Nn, \seq_gremove_all:cn}
 % \UnitTested
-% \begin{macro}[aux]{\seq_remove_all_aux:NNn}
+% \begin{macro}[aux]{\@@_remove_all_aux:NNn}
 %   The idea of the code here is to avoid a relatively expensive addition of
 %   items one at a time to an intermediate sequence.
 %   The approach taken is therefore similar to
-%   that in \cs{seq_pop_right_aux_ii:NNN}, using a \enquote{flexible}
+%   that in \cs{@@_pop_right_aux_ii:NNN}, using a \enquote{flexible}
 %   \texttt{x}-type expansion to do most of the work. As \cs{tl_if_eq:nnT}
 %   is not expandable, a two-part strategy is needed. First, the
 %   \texttt{x}-type expansion uses \cs{str_if_eq:nnT} to find potential
@@ -1068,28 +1028,28 @@
 %   lost.
 %    \begin{macrocode}
 \cs_new_protected:Npn \seq_remove_all:Nn
-  { \seq_remove_all_aux:NNn \tl_set:Nx }
+  { \@@_remove_all_aux:NNn \tl_set:Nx }
 \cs_new_protected:Npn \seq_gremove_all:Nn
-  { \seq_remove_all_aux:NNn \tl_gset:Nx }
-\cs_new_protected:Npn \seq_remove_all_aux:NNn #1#2#3
+  { \@@_remove_all_aux:NNn \tl_gset:Nx }
+\cs_new_protected:Npn \@@_remove_all_aux:NNn #1#2#3
   {
-    \seq_push_item_def:n
+    \@@_push_item_def:n
       {
         \str_if_eq:nnT {##1} {#3}
           {
             \if_false: { \fi: }
-            \tl_set:Nn \l_seq_internal_b_tl {##1}
+            \tl_set:Nn \l_@@_internal_b_tl {##1}
             #1 #2
                { \if_false: } \fi:
                  \exp_not:o {#2}
-                 \tl_if_eq:NNT \l_seq_internal_a_tl \l_seq_internal_b_tl
+                 \tl_if_eq:NNT \l_@@_internal_a_tl \l_@@_internal_b_tl
                    { \use_none:nn }
           }
-        \seq_wrap_item:n {##1}
+        \@@_wrap_item:n {##1}
       }
-    \tl_set:Nn \l_seq_internal_a_tl {#3}
+    \tl_set:Nn \l_@@_internal_a_tl {#3}
     #1 #2 {#2}
-    \seq_pop_item_def:
+    \@@_pop_item_def:
   }
 \cs_generate_variant:Nn \seq_remove_all:Nn  { c }
 \cs_generate_variant:Nn \seq_gremove_all:Nn { c }
@@ -1117,33 +1077,35 @@
 %     \seq_if_in:cn, \seq_if_in:cV, \seq_if_in:cv, \seq_if_in:co, \seq_if_in:cx
 %   }
 % \UnitTested
-% \begin{macro}[aux]{\seq_if_in_aux:}
-%   The approach here is to define \cs{seq_item:n} to compare its
+% \begin{macro}[aux]{\@@_if_in:}
+%   The approach here is to define \cs{@@_item:n} to compare its
 %   argument with the test sequence. If the two items are equal, the
-%   mapping is terminated and \cs{prg_return_true:} is inserted. On the
+%   mapping is terminated and \cs{group_end:} \cs{prg_return_true:}
+%   is inserted after skipping over the rest of the recursion. On the
 %   other hand, if there is no match then the loop will break returning
-%   \cs{prg_return_false:}. In either case, \cs{prg_break_point:n}
-%   ensures that the group ends before the logical value is returned.
-%   Everything is inside a group so that \cs{seq_item:n} is preserved
+%   \cs{prg_return_false:}.
+%   Everything is inside a group so that \cs{@@_item:n} is preserved
 %   in nested situations.
 %    \begin{macrocode}
 \prg_new_protected_conditional:Npnn \seq_if_in:Nn #1#2
   { T , F , TF }
   {
     \group_begin:
-      \tl_set:Nn \l_seq_internal_a_tl {#2}
-      \cs_set_protected:Npn \seq_item:n ##1
+      \tl_set:Nn \l_@@_internal_a_tl {#2}
+      \cs_set_protected:Npn \@@_item:n ##1
         {
-          \tl_set:Nn \l_seq_internal_b_tl {##1}
-          \if_meaning:w \l_seq_internal_a_tl \l_seq_internal_b_tl
-            \exp_after:wN \seq_if_in_aux:
+          \tl_set:Nn \l_@@_internal_b_tl {##1}
+          \if_meaning:w \l_@@_internal_a_tl \l_@@_internal_b_tl
+            \exp_after:wN \@@_if_in:
           \fi:
         }
       #1
-      \seq_break:n { \prg_return_false: }
-    \prg_break_point:n { \group_end: }
+    \group_end:
+    \prg_return_false:
+    \__prg_break_point:
   }
-\cs_new_nopar:Npn \seq_if_in_aux: { \seq_break:n { \prg_return_true: } }
+\cs_new_nopar:Npn \@@_if_in:
+  { \__prg_break:n { \group_end: \prg_return_true: } }
 \cs_generate_variant:Nn \seq_if_in:NnT  {     NV , Nv , No , Nx }
 \cs_generate_variant:Nn \seq_if_in:NnT  { c , cV , cv , co , cx }
 \cs_generate_variant:Nn \seq_if_in:NnF  {     NV , Nv , No , Nx }
@@ -1156,21 +1118,50 @@
 %
 % \subsection{Recovering data from sequences}
 %
+% \begin{macro}[int]{\@@_pop:NNNN, \@@_pop_TF:NNNN}
+%   The two \texttt{pop} functions share their emptiness tests.  We also
+%   use a common emptiness test for all branching \texttt{get} and
+%   \texttt{pop} functions.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_pop:NNNN #1#2#3#4
+  {
+    \if_meaning:w #3 \c_empty_seq
+      \tl_set:Nn #4 { \q_no_value }
+    \else:
+      #1#2#3#4
+    \fi:
+  }
+\cs_new_protected:Npn \@@_pop_TF:NNNN #1#2#3#4
+  {
+    \if_meaning:w #3 \c_empty_seq
+      % \tl_set:Nn #4 { \q_no_value }
+      \prg_return_false:
+    \else:
+      #1#2#3#4
+      \prg_return_true:
+    \fi:
+  }
+%    \end{macrocode}
+% \end{macro}
+%
 % \begin{macro}{\seq_get_left:NN, \seq_get_left:cN}
 % \UnitTested
-% \begin{macro}[aux]{\seq_get_left_aux:NnwN}
+% \begin{macro}[aux]{\@@_get_left:NnwN}
 %   Getting an item from the left of a sequence is pretty easy: just
-%   trim off the first item after removing the \cs{seq_item:n} at
-%   the start.
+%   trim off the first item after removing the \cs{@@_item:n} at
+%   the start.  We first append a \cs{q_no_value} item to cover the case
+%   of an empty sequence
 %    \begin{macrocode}
 \cs_new_protected:Npn \seq_get_left:NN #1#2
   {
-    \seq_if_empty_err_break:N #1
-    \exp_after:wN \seq_get_left_aux:NnwN #1 \q_stop #2
-    \prg_break_point:n { }
+    \tl_set:Nx #2
+      {
+        \exp_after:wN \@@_get_left:Nnw
+        #1 \@@_item:n { \q_no_value } \q_stop
+      }
   }
-\cs_new_protected:Npn \seq_get_left_aux:NnwN \seq_item:n #1#2 \q_stop #3
-  { \tl_set:Nn #3 {#1} }
+\cs_new:Npn \@@_get_left:Nnw \@@_item:n #1#2 \q_stop
+  { \exp_not:n {#1} }
 \cs_generate_variant:Nn \seq_get_left:NN { c }
 %    \end{macrocode}
 % \end{macro}
@@ -1180,24 +1171,19 @@
 % \UnitTested
 % \begin{macro}{\seq_gpop_left:NN, \seq_gpop_left:cN}
 % \UnitTested
-% \begin{macro}[aux]{\seq_pop_left_aux:NNN}
-% \begin{macro}[aux]{\seq_pop_left_aux:NnwNNN}
+% \begin{macro}[aux]{\@@_pop_left:NNN, \@@_pop_left:NnwNNN}
 %   The approach to popping an item is pretty similar to that to get
 %   an item, with the only difference being that the sequence itself has
 %   to be redefined. This makes it more sensible to use an auxiliary
 %   function for the local and global cases.
 %    \begin{macrocode}
 \cs_new_protected_nopar:Npn \seq_pop_left:NN
-  { \seq_pop_left_aux:NNN \tl_set:Nn }
+  { \@@_pop:NNNN \@@_pop_left:NNN \tl_set:Nn }
 \cs_new_protected_nopar:Npn \seq_gpop_left:NN
-  { \seq_pop_left_aux:NNN \tl_gset:Nn }
-\cs_new_protected:Npn \seq_pop_left_aux:NNN #1#2#3
-  {
-    \seq_if_empty_err_break:N #2
-    \exp_after:wN \seq_pop_left_aux:NnwNNN #2 \q_stop #1#2#3
-    \prg_break_point:n { }
-  }
-\cs_new_protected:Npn \seq_pop_left_aux:NnwNNN \seq_item:n #1#2 \q_stop #3#4#5
+  { \@@_pop:NNNN \@@_pop_left:NNN \tl_gset:Nn }
+\cs_new_protected:Npn \@@_pop_left:NNN #1#2#3
+  { \exp_after:wN \@@_pop_left:NnwNNN #2 \q_stop #1#2#3 }
+\cs_new_protected:Npn \@@_pop_left:NnwNNN \@@_item:n #1#2 \q_stop #3#4#5
   {
     #3 #4 {#2}
     \tl_set:Nn #5 {#1}
@@ -1208,94 +1194,84 @@
 % \end{macro}
 % \end{macro}
 % \end{macro}
-% \end{macro}
 %
 % \begin{macro}{\seq_get_right:NN, \seq_get_right:cN}
 % \UnitTested
-% \begin{macro}[aux]{\seq_get_right_aux:NN}
-% \begin{macro}[aux]{\seq_get_right_loop:nn}
-%   The idea here is to remove the very first \cs{seq_item:n} from the
-%   sequence, leaving a token list starting with the first braced entry.
-%   Two arguments at a time are then grabbed: apart from the right-hand end of
-%   the sequence, this will be a brace group followed by \cs{seq_item:n}. The
-%   set up code means that these all disappear. At the end of the sequence,
-%   the assignment is placed in front of the very last entry in the sequence,
-%   before a tidying-up step takes place to remove the loop and reset the
-%   meaning of \cs{seq_item:n}.
+% \begin{macro}[aux]{\@@_get_right_loop:nn}
+%   First prepend \cs{q_no_value}, then take two arguments at a time.
+%   Apart from the right-hand end of the sequence, this be a brace group
+%   followed by \cs{@@_item:n}.  The \cs{use_none:nn} removes both of
+%   those.  At the end of the sequence, the two question marks are taken
+%   by \cs{use_none:nn}, and the assignment is placed before the
+%   right-most item.  The \tn{afterassignment} primitive places
+%   \cs{use_none:n} to get rid of a trailing \cs{@@_get_right_loop:nn}.
 %    \begin{macrocode}
 \cs_new_protected:Npn \seq_get_right:NN #1#2
   {
-    \seq_if_empty_err_break:N #1
-    \seq_get_right_aux:NN #1#2
-    \prg_break_point:n { }
+    \exp_after:wN \@@_get_right_loop:nn
+    \exp_after:wN \q_no_value
+    #1
+    {
+      ??
+      \tex_afterassignment:D \use_none:n
+      \tl_set:Nn #2
+    }
   }
-\cs_new_protected:Npn \seq_get_right_aux:NN #1#2
-  {
-    \seq_push_item_def:n { }
-    \exp_after:wN \exp_after:wN \exp_after:wN \seq_get_right_loop:nn
-      \exp_after:wN \use_none:n #1
-      { \tl_set:Nn #2 }
-      { }
-      {
-        \seq_pop_item_def:
-        \seq_break:
-      }
-}
-\cs_new:Npn \seq_get_right_loop:nn #1#2
+\cs_new_protected:Npn \@@_get_right_loop:nn #1#2
   {
-    #2 {#1}
-    \seq_get_right_loop:nn
+    \use_none:nn #2 {#1}
+    \@@_get_right_loop:nn
   }
 \cs_generate_variant:Nn \seq_get_right:NN { c }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
-% \end{macro}
 %
 % \begin{macro}{\seq_pop_right:NN, \seq_pop_right:cN}
 % \UnitTested
 % \begin{macro}{\seq_gpop_right:NN, \seq_gpop_right:cN}
 % \UnitTested
-% \begin{macro}[aux]{\seq_pop_right_aux:NNN, \seq_pop_right_aux_ii:NNN}
+% \begin{macro}[aux]{\@@_pop_right_aux:NNN, \@@_pop_right_loop:nn}
 %   The approach to popping from the right is a bit more involved, but does
 %   use some of the same ideas as getting from the right. What is needed is a
 %   \enquote{flexible length} way to set a token list variable. This is
-%   supplied by the |{ \if_false:} \fi:| \ldots
+%   supplied by the |{ \if_false: } \fi:| \ldots
 %   |\if_false: { \fi: }| construct. Using an \texttt{x}-type
-%   expansion and a \enquote{non-expanding} definition for \cs{seq_item:n},
+%   expansion and a \enquote{non-expanding} definition for \cs{@@_item:n},
 %   the left-most $n - 1$ entries in a sequence of $n$ items will be stored
 %   back in the sequence. That needs a loop of unknown length, hence using the
 %   strange \cs{if_false:} way of including brackets. When the last item
 %   of the sequence is reached, the closing bracket for the assignment is
-%   inserted, and |\tl_set:Nn #3| is inserted in front of the final entry.
-%   This therefore does the pop assignment, then a final loop clears up the
-%   code.
+%   inserted, and |\tl_set:Nn #3| is inserted in front of the final
+%   entry.  This therefore does the pop assignment.  The trailing
+%   looping macro is removed by placing a \cs{use_none:n} using the
+%   \tn{afterassignment} primitive.
 %    \begin{macrocode}
 \cs_new_protected_nopar:Npn \seq_pop_right:NN
-  { \seq_pop_right_aux:NNN \tl_set:Nx }
+  { \@@_pop:NNNN \@@_pop_right_aux:NNN \tl_set:Nx }
 \cs_new_protected_nopar:Npn \seq_gpop_right:NN
-  { \seq_pop_right_aux:NNN \tl_gset:Nx }
-\cs_new_protected:Npn \seq_pop_right_aux:NNN #1#2#3
-  {
-    \seq_if_empty_err_break:N #2
-    \seq_pop_right_aux_ii:NNN #1 #2 #3
-    \prg_break_point:n { }
-  }
-\cs_new_protected:Npn \seq_pop_right_aux_ii:NNN #1#2#3
+  { \@@_pop:NNNN \@@_pop_right_aux:NNN \tl_gset:Nx }
+\cs_new_protected:Npn \@@_pop_right_aux:NNN #1#2#3
   {
-    \seq_push_item_def:n { \seq_wrap_item:n {##1} }
-    #1 #2 { \if_false: } \fi:
-      \exp_after:wN \exp_after:wN \exp_after:wN \seq_get_right_loop:nn
-         \exp_after:wN \use_none:n #2
+    \cs_set_eq:NN \seq_tmp:w \@@_item:n
+    \cs_set_eq:NN \@@_item:n \scan_stop:
+    #1 #2
+      { \if_false: } \fi:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \@@_pop_right_loop:nn
+        \exp_after:wN \use_none:n
+        #2
         {
           \if_false: { \fi: }
-          \tl_set:Nn #3
-        }
-        { }
-        {
-          \seq_pop_item_def:
-          \seq_break:
+          \tex_afterassignment:D \use_none:n
+          \tl_set:Nx #3
         }
+    \cs_set_eq:NN \@@_item:n \seq_tmp:w
+  }
+\cs_new:Npn \@@_pop_right_loop:nn #1#2
+  {
+    #2 { \exp_not:n {#1} }
+    \@@_pop_right_loop:nn
   }
 \cs_generate_variant:Nn \seq_pop_right:NN  { c }
 \cs_generate_variant:Nn \seq_gpop_right:NN { c }
@@ -1304,99 +1280,130 @@
 % \end{macro}
 % \end{macro}
 %
+% \begin{macro}[TF]{\seq_get_left:NN, \seq_get_left:cN}
+% \begin{macro}[TF]{\seq_get_right:NN, \seq_get_right:cN}
+%   Getting from the left or right with a check on the results.  The
+%   first argument to \cs{@@_pop_TF:NNNN} is left unused.
+%    \begin{macrocode}
+\prg_new_protected_conditional:Npnn \seq_get_left:NN #1#2 { T , F , TF }
+  { \@@_pop_TF:NNNN \prg_do_nothing: \seq_get_left:NN #1#2 }
+\prg_new_protected_conditional:Npnn \seq_get_right:NN #1#2 { T , F , TF }
+  { \@@_pop_TF:NNNN \prg_do_nothing: \seq_get_right:NN #1#2 }
+\cs_generate_variant:Nn \seq_get_left:NNT   { c }
+\cs_generate_variant:Nn \seq_get_left:NNF   { c }
+\cs_generate_variant:Nn \seq_get_left:NNTF  { c }
+\cs_generate_variant:Nn \seq_get_right:NNT  { c }
+\cs_generate_variant:Nn \seq_get_right:NNF  { c }
+\cs_generate_variant:Nn \seq_get_right:NNTF { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[TF]{\seq_pop_left:NN, \seq_pop_left:cN}
+% \begin{macro}[TF]{\seq_gpop_left:NN, \seq_gpop_left:cN}
+% \begin{macro}[TF]{\seq_pop_right:NN, \seq_pop_right:cN}
+% \begin{macro}[TF]{\seq_gpop_right:NN, \seq_gpop_right:cN}
+%   More or less the same for popping.
+%    \begin{macrocode}
+\prg_new_protected_conditional:Npnn \seq_pop_left:NN #1#2 { T , F , TF }
+  { \@@_pop_TF:NNNN \@@_pop_left:NNN \tl_set:Nn #1 #2 }
+\prg_new_protected_conditional:Npnn \seq_gpop_left:NN #1#2 { T , F , TF }
+  { \@@_pop_TF:NNNN \@@_pop_left:NNN \tl_gset:Nn #1 #2 }
+\prg_new_protected_conditional:Npnn \seq_pop_right:NN #1#2 { T , F , TF }
+  { \@@_pop_TF:NNNN \@@_pop_right_aux:NNN \tl_set:Nx #1 #2 }
+\prg_new_protected_conditional:Npnn \seq_gpop_right:NN #1#2 { T , F , TF }
+  { \@@_pop_TF:NNNN \@@_pop_right_aux:NNN \tl_gset:Nx #1 #2 }
+\cs_generate_variant:Nn \seq_pop_left:NNT    { c }
+\cs_generate_variant:Nn \seq_pop_left:NNF    { c }
+\cs_generate_variant:Nn \seq_pop_left:NNTF   { c }
+\cs_generate_variant:Nn \seq_gpop_left:NNT   { c }
+\cs_generate_variant:Nn \seq_gpop_left:NNF   { c }
+\cs_generate_variant:Nn \seq_gpop_left:NNTF  { c }
+\cs_generate_variant:Nn \seq_pop_right:NNT   { c }
+\cs_generate_variant:Nn \seq_pop_right:NNF   { c }
+\cs_generate_variant:Nn \seq_pop_right:NNTF  { c }
+\cs_generate_variant:Nn \seq_gpop_right:NNT  { c }
+\cs_generate_variant:Nn \seq_gpop_right:NNF  { c }
+\cs_generate_variant:Nn \seq_gpop_right:NNTF { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
 % \subsection{Mapping to sequences}
 %
 % \begin{macro}{\seq_map_break:}
 % \UnitTested
 % \begin{macro}{\seq_map_break:n}
 % \UnitTested
-% \begin{macro}[int]{\seq_break:}
-% \begin{macro}[int]{\seq_break:n}
-%   To break a function, the special token \cs{prg_break_point:n} is
+%   To break a function, the special token \cs{__prg_break_point:Nn} is
 %   used to find the end of the code. Any ending code is then inserted
 %   before the return value of \cs{seq_map_break:n} is inserted.
-%   Semantically-logical copies of the break functions for use inside
-%   mappings.
 %    \begin{macrocode}
-\cs_new_eq:NN \seq_break:      \prg_map_break:
-\cs_new_eq:NN \seq_break:n     \prg_map_break:n
-\cs_new_eq:NN \seq_map_break:  \prg_map_break:
-\cs_new_eq:NN \seq_map_break:n \prg_map_break:n
+\cs_new_nopar:Npn \seq_map_break:
+  { \__prg_map_break:Nn \seq_map_break: { } }
+\cs_new_nopar:Npn \seq_map_break:n
+  { \__prg_map_break:Nn \seq_map_break: }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[int]{\seq_if_empty_err_break:N}
-%   A function to check that sequences really have some content. This
-%   is optimised for speed, hence the direct primitive use.
-%    \begin{macrocode}
-\cs_new_protected:Npn \seq_if_empty_err_break:N #1
-  {
-    \if_meaning:w #1 \c_empty_tl
-      \msg_kernel_error:nnx { seq } { empty-sequence } { \token_to_str:N #1 }
-      \exp_after:wN \seq_break:
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
 %
 % \begin{macro}{\seq_map_function:NN, \seq_map_function:cN}
 % \UnitTested
-% \begin{macro}[aux]{\seq_map_function_aux:NNn}
+% \begin{macro}[aux]{\@@_map_function:NNn}
 %   The idea here is to apply the code of |#2| to each item in the
-%   sequence without altering the definition of \cs{seq_item:n}. This
+%   sequence without altering the definition of \cs{@@_item:n}. This
 %   is done as by noting that every odd token in the sequence must be
-%   \cs{seq_item:n}, which can be gobbled by \cs{use_none:n}. At the end of
+%   \cs{@@_item:n}, which can be gobbled by \cs{use_none:n}. At the end of
 %   the loop, |#2| is instead |? \seq_map_break:|, which therefore breaks the
 %   loop without needing to do a (relatively-expensive) quark test.
 %    \begin{macrocode}
 \cs_new:Npn \seq_map_function:NN #1#2
   {
-    \exp_after:wN \seq_map_function_aux:NNn \exp_after:wN #2 #1
+    \exp_after:wN \@@_map_function:NNn \exp_after:wN #2 #1
       { ? \seq_map_break: } { }
-    \prg_break_point:n { }
+    \__prg_break_point:Nn \seq_map_break: { }
   }
-\cs_new:Npn \seq_map_function_aux:NNn #1#2#3
+\cs_new:Npn \@@_map_function:NNn #1#2#3
   {
     \use_none:n #2
     #1 {#3}
-    \seq_map_function_aux:NNn #1
+    \@@_map_function:NNn #1
   }
 \cs_generate_variant:Nn \seq_map_function:NN { c }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int]{\seq_push_item_def:n, \seq_push_item_def:x}
-% \begin{macro}[aux]{\seq_push_item_def_aux:}
-% \begin{macro}[int]{\seq_pop_item_def:}
-%   The definition of \cs{seq_item:n} needs to be saved and restored at
+% \begin{macro}[int]{\@@_push_item_def:n, \@@_push_item_def:x}
+% \begin{macro}[aux]{\@@_push_item_def:}
+% \begin{macro}[int]{\@@_pop_item_def:}
+%   The definition of \cs{@@_item:n} needs to be saved and restored at
 %   various points within the mapping and manipulation code. That is handled
 %   here: as always, this approach uses global assignments.
 %    \begin{macrocode}
-\cs_new_protected:Npn \seq_push_item_def:n
+\cs_new_protected:Npn \@@_push_item_def:n
   {
-    \seq_push_item_def_aux:
-    \cs_gset:Npn \seq_item:n ##1
+    \@@_push_item_def:
+    \cs_gset:Npn \@@_item:n ##1
   }
-\cs_new_protected:Npn \seq_push_item_def:x
+\cs_new_protected:Npn \@@_push_item_def:x
   {
-    \seq_push_item_def_aux:
-    \cs_gset:Npx \seq_item:n ##1
+    \@@_push_item_def:
+    \cs_gset:Npx \@@_item:n ##1
   }
-\cs_new_protected:Npn \seq_push_item_def_aux:
+\cs_new_protected:Npn \@@_push_item_def:
   {
-    \cs_gset_eq:cN { seq_item_ \int_use:N \g_prg_map_int :n }
-      \seq_item:n
-    \int_gincr:N \g_prg_map_int
+    \int_gincr:N \g__prg_map_int
+    \cs_gset_eq:cN { __prg_map_ \int_use:N \g__prg_map_int :w }
+      \@@_item:n
   }
-\cs_new_protected_nopar:Npn \seq_pop_item_def:
+\cs_new_protected_nopar:Npn \@@_pop_item_def:
   {
-    \int_gdecr:N \g_prg_map_int
-    \cs_gset_eq:Nc \seq_item:n
-      { seq_item_ \int_use:N \g_prg_map_int :n }
+    \cs_gset_eq:Nc \@@_item:n
+      { __prg_map_ \int_use:N \g__prg_map_int :w }
+    \int_gdecr:N \g__prg_map_int
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1405,15 +1412,15 @@
 %
 % \begin{macro}{\seq_map_inline:Nn, \seq_map_inline:cn}
 % \UnitTested
-%   The idea here is that \cs{seq_item:n} is already \enquote{applied} to
+%   The idea here is that \cs{@@_item:n} is already \enquote{applied} to
 %   each item in a sequence, and so an in-line mapping is just a case of
-%   redefining \cs{seq_item:n}.
+%   redefining \cs{@@_item:n}.
 %    \begin{macrocode}
 \cs_new_protected:Npn \seq_map_inline:Nn #1#2
   {
-    \seq_push_item_def:n {#2}
+    \@@_push_item_def:n {#2}
     #1
-    \prg_break_point:n { \seq_pop_item_def: }
+    \__prg_break_point:Nn \seq_map_break: { \@@_pop_item_def: }
   }
 \cs_generate_variant:Nn \seq_map_inline:Nn { c }
 %    \end{macrocode}
@@ -1431,18 +1438,38 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \seq_map_variable:NNn #1#2#3
   {
-    \seq_push_item_def:x
+    \@@_push_item_def:x
       {
         \tl_set:Nn \exp_not:N #2 {##1}
         \exp_not:n {#3}
       }
     #1
-    \prg_break_point:n { \seq_pop_item_def: }
+    \__prg_break_point:Nn \seq_map_break: { \@@_pop_item_def: }
   }
 \cs_generate_variant:Nn \seq_map_variable:NNn {     Nc }
 \cs_generate_variant:Nn \seq_map_variable:NNn { c , cc }
 %    \end{macrocode}
 % \end{macro}
+% 
+% \begin{macro}{\seq_count:N, \seq_count:c}
+% \begin{macro}[aux]{\@@_count:n}
+%   Counting the items in a sequence is done using the same approach as for
+%   other count functions: turn each entry into a \texttt{+1} then use
+%   integer evaluation to actually do the mathematics.
+%    \begin{macrocode}
+\cs_new:Npn \seq_count:N #1
+  {
+    \int_eval:n
+      {
+        0
+        \seq_map_function:NN #1 \@@_count:n
+      }
+  }
+\cs_new:Npn \@@_count:n #1 { + \c_one }
+\cs_generate_variant:Nn \seq_count:N { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
 %
 % \subsection{Sequence stacks}
 %
@@ -1504,379 +1531,50 @@
 % \end{macro}
 % \end{macro}
 %
+% \begin{macro}[TF]{\seq_get:NN, \seq_get:cN}
+% \begin{macro}[TF]{\seq_pop:NN, \seq_pop:cN}
+% \begin{macro}[TF]{\seq_gpop:NN, \seq_gpop:cN}
+%   More copies.
+%    \begin{macrocode}
+\prg_new_eq_conditional:NNn \seq_get:NN  \seq_get_left:NN  { T , F , TF }
+\prg_new_eq_conditional:NNn \seq_get:cN  \seq_get_left:cN  { T , F , TF }
+\prg_new_eq_conditional:NNn \seq_pop:NN  \seq_pop_left:NN  { T , F , TF }
+\prg_new_eq_conditional:NNn \seq_pop:cN  \seq_pop_left:cN  { T , F , TF }
+\prg_new_eq_conditional:NNn \seq_gpop:NN \seq_gpop_left:NN { T , F , TF }
+\prg_new_eq_conditional:NNn \seq_gpop:cN \seq_gpop_left:cN { T , F , TF }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
 % \subsection{Viewing sequences}
 %
 % \begin{macro}{\seq_show:N, \seq_show:c}
 % \UnitTested
-% Apply the general \cs{msg_aux_show:Nnx}.
+% Apply the general \cs{__msg_show_variable:Nnn}.
 %    \begin{macrocode}
 \cs_new_protected:Npn \seq_show:N #1
   {
-    \msg_aux_show:Nnx
+    \__msg_show_variable:Nnn
       #1
       { seq }
-      { \seq_map_function:NN #1 \msg_aux_show:n }
+      { \seq_map_function:NN #1 \__msg_show_item:n }
   }
 \cs_generate_variant:Nn \seq_show:N { c }
 %    \end{macrocode}
 % \end{macro}
 %
-% \subsection{Experimental functions}
+% \subsection{Scratch sequences}
 %
-% \begin{macro}[aux]{\seq_if_empty_break_return_false:N}
-% The name says it all: of the sequence is empty, returns logical
-% \texttt{false}.
+% \begin{variable}{\l_tmpa_seq, \l_tmpb_seq, \g_tmpa_seq, \g_tmpb_seq}
+%   Temporary comma list variables.
 %    \begin{macrocode}
-\cs_new:Npn \seq_if_empty_break_return_false:N #1
-  {
-    \if_meaning:w #1 \c_empty_tl
-      \prg_return_false:
-      \exp_after:wN \seq_break:
-    \fi:
-  }
+\seq_new:N \l_tmpa_seq
+\seq_new:N \l_tmpb_seq
+\seq_new:N \g_tmpa_seq
+\seq_new:N \g_tmpb_seq
 %    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[TF]{\seq_get_left:NN, \seq_get_left:cN}
-% \begin{macro}[TF]{\seq_get_right:NN, \seq_get_right:cN}
-% Getting from the left or right with a check on the results.
-%    \begin{macrocode}
-\prg_new_protected_conditional:Npnn \seq_get_left:NN #1 #2 { T , F , TF }
-  {
-    \seq_if_empty_break_return_false:N #1
-    \exp_after:wN \seq_get_left_aux:Nw #1 \q_stop #2
-    \prg_return_true:
-    \seq_break:
-    \prg_break_point:n { }
-  }
-\prg_new_protected_conditional:Npnn \seq_get_right:NN #1#2 { T , F , TF }
-  {
-    \seq_if_empty_break_return_false:N #1
-    \seq_get_right_aux:NN #1#2
-    \prg_return_true: \seq_break:
-    \prg_break_point:n { }
-  }
-\cs_generate_variant:Nn \seq_get_left:NNT   { c }
-\cs_generate_variant:Nn \seq_get_left:NNF   { c }
-\cs_generate_variant:Nn \seq_get_left:NNTF  { c }
-\cs_generate_variant:Nn \seq_get_right:NNT  { c }
-\cs_generate_variant:Nn \seq_get_right:NNF  { c }
-\cs_generate_variant:Nn \seq_get_right:NNTF { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[TF]{\seq_pop_left:NN, \seq_pop_left:cN}
-% \begin{macro}[TF]{\seq_gpop_left:NN, \seq_gpop_left:cN}
-% \begin{macro}[TF]{\seq_pop_right:NN, \seq_pop_right:cN}
-% \begin{macro}[TF]{\seq_gpop_right:NN, \seq_gpop_right:cN}
-% More or less the same for popping.
-%    \begin{macrocode}
-\prg_new_protected_conditional:Npnn \seq_pop_left:NN #1#2 { T , F , TF }
-  {
-    \seq_if_empty_break_return_false:N #1
-    \exp_after:wN \seq_pop_left_aux:NnwNNN #1 \q_stop \tl_set:Nn #1#2
-    \prg_return_true: \seq_break:
-    \prg_break_point:n { }
-  }
-\prg_new_protected_conditional:Npnn \seq_gpop_left:NN #1#2 { T , F , TF }
-  {
-    \seq_if_empty_break_return_false:N #1
-    \exp_after:wN \seq_pop_left_aux:NnwNNN #1 \q_stop \tl_gset:Nn #1#2
-    \prg_return_true: \seq_break:
-    \prg_break_point:n { }
-  }
-\prg_new_protected_conditional:Npnn \seq_pop_right:NN #1#2 { T , F , TF }
-  {
-    \seq_if_empty_break_return_false:N #1
-    \seq_pop_right_aux_ii:NNN \tl_set:Nx #1 #2
-    \prg_return_true: \seq_break:
-    \prg_break_point:n { }
-  }
-\prg_new_protected_conditional:Npnn \seq_gpop_right:NN #1#2 { T , F , TF }
-  {
-    \seq_if_empty_break_return_false:N #1
-    \seq_pop_right_aux_ii:NNN \tl_gset:Nx #1 #2
-    \prg_return_true: \seq_break:
-    \prg_break_point:n { }
-  }
-\cs_generate_variant:Nn \seq_pop_left:NNT    { c }
-\cs_generate_variant:Nn \seq_pop_left:NNF    { c }
-\cs_generate_variant:Nn \seq_pop_left:NNTF   { c }
-\cs_generate_variant:Nn \seq_gpop_left:NNT   { c }
-\cs_generate_variant:Nn \seq_gpop_left:NNF   { c }
-\cs_generate_variant:Nn \seq_gpop_left:NNTF  { c }
-\cs_generate_variant:Nn \seq_pop_right:NNT   { c }
-\cs_generate_variant:Nn \seq_pop_right:NNF   { c }
-\cs_generate_variant:Nn \seq_pop_right:NNTF  { c }
-\cs_generate_variant:Nn \seq_gpop_right:NNT  { c }
-\cs_generate_variant:Nn \seq_gpop_right:NNF  { c }
-\cs_generate_variant:Nn \seq_gpop_right:NNTF { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\seq_length:N, \seq_length:c}
-% \begin{macro}[aux]{\seq_length_aux:n}
-%   Counting the items in a sequence is done using the same approach as for
-%   other length functions: turn each entry into a \texttt{+1} then use
-%   integer evaluation to actually do the mathematics.
-%    \begin{macrocode}
-\cs_new:Npn \seq_length:N #1
-  {
-    \int_eval:n
-      {
-        0
-        \seq_map_function:NN #1 \seq_length_aux:n
-      }
-  }
-\cs_new:Npn \seq_length_aux:n #1 { +1 }
-\cs_generate_variant:Nn \seq_length:N { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\seq_item:Nn, \seq_item:cn}
-% \begin{macro}[aux]{\seq_item_aux:nnn}
-%   The idea here is to find the offset of the item from the left, then use
-%   a loop to grab the correct item. If the resulting offset is too large,
-%   then the stop code |{ ? \seq_break: } { }| will be used by the auxiliary,
-%   terminating the loop and returning nothing at all.
-%    \begin{macrocode}
-\cs_new:Npn \seq_item:Nn #1#2
-  {
-    \exp_last_unbraced:Nfo \seq_item_aux:nnn
-      {
-        \int_eval:n
-          {
-            \int_compare:nNnT {#2} < \c_zero
-              { \seq_length:N #1 + }
-            #2
-          }
-      }
-    #1
-    { ? \seq_break: }
-    { }
-    \prg_break_point:n { }
-  }
-\cs_new:Npn \seq_item_aux:nnn #1#2#3
-  {
-    \use_none:n #2
-    \int_compare:nNnTF {#1} = \c_zero
-      { \seq_break:n { \exp_not:n {#3} } }
-      { \exp_args:Nf \seq_item_aux:nnn { \int_eval:n { #1 - 1 } } }
-  }
-\cs_generate_variant:Nn \seq_item:Nn { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\seq_use:N, \seq_use:c}
-%   A simple short cut for a mapping.
-%    \begin{macrocode}
-\cs_new:Npn \seq_use:N #1 { \seq_map_function:NN #1 \use:n }
-\cs_generate_variant:Nn \seq_use:N { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}
-%   {
-%     \seq_mapthread_function:NNN, \seq_mapthread_function:NcN,
-%     \seq_mapthread_function:cNN, \seq_mapthread_function:ccN
-%   }
-% \begin{macro}[aux]{\seq_mapthread_function_aux:NN}
-% \begin{macro}[aux]{\seq_mapthread_function_aux:Nnnwnn}
-%   The idea here is to first expand both of the sequences, adding the usual
-%   |{ ? \seq_break: } { }| to the end of each on. This is most conveniently
-%   done in two steps using an auxiliary function. The mapping then throws
-%   away the first token of |#2| and |#5|, which for items in the sequences
-%   will both be \cs{seq_item:n}. The function to be mapped will then be
-%   applied to the two entries. When the code hits the end of one of the
-%   sequences, the break material will stop the entire loop and tidy up. This
-%   avoids needing to find the length of the two sequences, or worrying about
-%   which is longer.
-%    \begin{macrocode}
-\cs_new:Npn \seq_mapthread_function:NNN #1#2#3
-  {
-    \exp_after:wN \seq_mapthread_function_aux:NN
-      \exp_after:wN #3
-      \exp_after:wN #1
-      #2
-      { ? \seq_break: } { }
-    \prg_break_point:n { }
-  }
-\cs_new:Npn \seq_mapthread_function_aux:NN #1#2
-  {
-    \exp_after:wN \seq_mapthread_function_aux:Nnnwnn
-      \exp_after:wN #1
-      #2
-      { ? \seq_break: } { }
-      \q_stop
-  }
-\cs_new:Npn \seq_mapthread_function_aux:Nnnwnn #1#2#3#4 \q_stop #5#6
-  {
-    \use_none:n #2
-    \use_none:n #5
-    #1 {#3} {#6}
-    \seq_mapthread_function_aux:Nnnwnn #1 #4 \q_stop
-  }
-\cs_generate_variant:Nn \seq_mapthread_function:NNN {     Nc }
-\cs_generate_variant:Nn \seq_mapthread_function:NNN { c , cc }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}
-%   {
-%     \seq_set_from_clist:NN, \seq_set_from_clist:cN,
-%     \seq_set_from_clist:Nc, \seq_set_from_clist:cc,
-%     \seq_set_from_clist:Nn, \seq_set_from_clist:cn
-%   }
-% \begin{macro}
-%   {
-%     \seq_gset_from_clist:NN, \seq_gset_from_clist:cN,
-%     \seq_gset_from_clist:Nc, \seq_gset_from_clist:cc,
-%     \seq_gset_from_clist:Nn, \seq_gset_from_clist:cn
-%   }
-%   Setting a sequence from a comma-separated list is done using a simple
-%   mapping.
-%    \begin{macrocode}
-\cs_new_protected:Npn \seq_set_from_clist:NN #1#2
-  {
-    \tl_set:Nx #1
-      { \clist_map_function:NN #2 \seq_wrap_item:n }
-  }
-\cs_new_protected:Npn \seq_set_from_clist:Nn #1#2
-  {
-    \tl_set:Nx #1
-      { \clist_map_function:nN {#2} \seq_wrap_item:n }
-  }
-\cs_new_protected:Npn \seq_gset_from_clist:NN #1#2
-  {
-    \tl_gset:Nx #1
-      { \clist_map_function:NN #2 \seq_wrap_item:n }
-  }
-\cs_new_protected:Npn \seq_gset_from_clist:Nn #1#2
-  {
-    \tl_gset:Nx #1
-      { \clist_map_function:nN {#2} \seq_wrap_item:n }
-  }
-\cs_generate_variant:Nn \seq_set_from_clist:NN  {     Nc }
-\cs_generate_variant:Nn \seq_set_from_clist:NN  { c , cc }
-\cs_generate_variant:Nn \seq_set_from_clist:Nn  { c      }
-\cs_generate_variant:Nn \seq_gset_from_clist:NN {     Nc }
-\cs_generate_variant:Nn \seq_gset_from_clist:NN { c , cc }
-\cs_generate_variant:Nn \seq_gset_from_clist:Nn { c      }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}
-%   {\seq_reverse:N, \seq_reverse:c, \seq_greverse:N, \seq_greverse:c}
-% \begin{macro}[aux]{\seq_reverse_aux:NN}
-% \begin{macro}[aux]{\seq_reverse_aux_item:nwn}
-%   Previously, \cs{seq_reverse:N} was coded by collecting the items
-%   in reverse order after an \cs{exp_stop_f:} marker.
-%   \begin{verbatim}
-%     \cs_new_protected:Npn \seq_reverse:N #1
-%       {
-%         \cs_set_eq:NN \seq_item:n \seq_reverse_aux_item:nw
-%         \tl_set:Nf #2 { #2 \exp_stop_f: }
-%       }
-%     \cs_new:Npn \seq_reverse_aux_item:nw #1 #2 \exp_stop_f:
-%       {
-%         #2 \exp_stop_f:
-%         \seq_item:n {#1}
-%       }
-%   \end{verbatim}
-%   At first, this seems optimal, since we can forget about each item
-%   as soon as it is placed after \cs{exp_stop_f:}. Unfortunately,
-%   \TeX{}'s usual tail recursion does not take place in this case:
-%   since the following \cs{seq_reverse_aux_item:nw} only reads
-%   tokens until \cs{exp_stop_f:}, and never reads the
-%   |\seq_item:n {#1}| left by the previous call, \TeX{} cannot
-%   remove that previous call from the stack, and in particular
-%   must retain the various macro paramters in memory, until the
-%   end of the replacement text is reached. The stack is thus
-%   only flushed after all the \cs{seq_reverse_aux_item:nw} are
-%   expanded. Keeping track of the arguments of all those calls
-%   uses up a memory quadratic in the length of the sequence.
-%   \TeX{} can then not cope with more than a few thousand items.
-%
-%   Instead, we collect the items in the argument
-%   of \cs{exp_not:n}. The previous calls are cleanly removed
-%   from the stack, and the memory consumption becomes linear.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \seq_tmp:w { }
-\cs_new_protected_nopar:Npn \seq_reverse:N
-  { \seq_reverse_aux:NN \tl_set:Nx }
-\cs_new_protected_nopar:Npn \seq_greverse:N
-  { \seq_reverse_aux:NN \tl_gset:Nx }
-\cs_new_protected:Npn \seq_reverse_aux:NN #1 #2
-  {
-    \cs_set_eq:NN \seq_tmp:w \seq_item:n
-    \cs_set_eq:NN \seq_item:n \seq_reverse_aux_item:nwn
-    #1 #2 { #2 \exp_not:n { } }
-    \cs_set_eq:NN \seq_item:n \seq_tmp:w
-  }
-\cs_new:Npn \seq_reverse_aux_item:nwn #1 #2 \exp_not:n #3
-  {
-    #2
-    \exp_not:n { \seq_item:n {#1} #3 }
-  }
-\cs_generate_variant:Nn \seq_reverse:N  { c }
-\cs_generate_variant:Nn \seq_greverse:N { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\seq_set_filter:NNn, \seq_gset_filter:NNn}
-% \begin{macro}[aux]{\seq_set_filter_aux:NNNn}
-%   Similar to \cs{seq_map_inline:Nn}, without a
-%   \cs{prg_break_point:n} because the user's code
-%   is performed within the evaluation of a boolean expression,
-%   and skipping out of that would break horribly.
-%   The \cs{seq_wrap_item:n} function inserts the relevant
-%   \cs{seq_item:n} without expansion in the input stream,
-%   hence in the \texttt{x}-expanding assignment.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \seq_set_filter:NNn
-  { \seq_set_filter_aux:NNNn \tl_set:Nx }
-\cs_new_protected_nopar:Npn \seq_gset_filter:NNn
-  { \seq_set_filter_aux:NNNn \tl_gset:Nx }
-\cs_new_protected:Npn \seq_set_filter_aux:NNNn #1#2#3#4
-  {
-    \seq_push_item_def:n { \bool_if:nT {#4} { \seq_wrap_item:n {##1} } }
-    #1 #2 { #3 \prg_break_point:n { } }
-    \seq_pop_item_def:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\seq_set_map:NNn,\seq_gset_map:NNn}
-% \begin{macro}[aux]{\seq_set_map_aux:NNNn}
-%   Very similar to \cs{seq_set_filter:NNn}. We could actually
-%   merge the two within a single function, but it would have weird
-%   semantics.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \seq_set_map:NNn
-  { \seq_set_map_aux:NNNn \tl_set:Nx }
-\cs_new_protected_nopar:Npn \seq_gset_map:NNn
-  { \seq_set_map_aux:NNNn \tl_gset:Nx }
-\cs_new_protected:Npn \seq_set_map_aux:NNNn #1#2#3#4
-  {
-    \seq_push_item_def:n { \exp_not:N \seq_item:n {#4} }
-    #1 #2 { #3 }
-    \seq_pop_item_def:
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
+% \end{variable}
 %
 % \subsection{Deprecated interfaces}
 %
@@ -1904,6 +1602,25 @@
 %    \end{macrocode}
 % \end{macro}
 %
+% Deprecated 2012-05-13 for removal by 2012-11-30.
+%
+% \begin{macro}{\seq_length:N, \seq_length:c}
+%    \begin{macrocode}
+\cs_new_eq:NN \seq_length:N \seq_count:N
+\cs_new_eq:NN \seq_length:c \seq_count:c
+%    \end{macrocode}
+% \end{macro}
+% 
+% Deprecated 2012-05-23 for removal by 2012-08-30.
+%
+% \begin{macro}{\seq_use:N, \seq_use:c}
+%   A simple short cut for a mapping.
+%    \begin{macrocode}
+\cs_new:Npn \seq_use:N #1 { \seq_map_function:NN #1 \use:n }
+\cs_generate_variant:Nn \seq_use:N { c }
+%    \end{macrocode}
+% \end{macro}
+%
 %    \begin{macrocode}
 %</initex|package>
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3skip.dtx b/Master/texmf-dist/source/latex/l3kernel/l3skip.dtx
index 9bb1fa1eadc..b83319e74b3 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3skip.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3skip.dtx
@@ -36,8 +36,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3skip.dtx 3499 2012-03-05 16:08:55Z bruno $
-  {L3 Experimental dimensions and skips}
+\GetIdInfo$Id: l3skip.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Dimensions and skips}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -150,10 +150,10 @@
 %     \dim_gset_eq:NN, \dim_gset_eq:cN, \dim_gset_eq:Nc, \dim_gset_eq:cc
 %   }
 %   \begin{syntax}
-%     \cs{dim_set_eq:NN} \meta{dimension1} \meta{dimension2}
+%     \cs{dim_set_eq:NN} \meta{dimension_1} \meta{dimension_2}
 %   \end{syntax}
-%   Sets the content of \meta{dimension1} equal to that of
-%   \meta{dimension2}.
+%   Sets the content of \meta{dimension_1} equal to that of
+%   \meta{dimension_2}.
 % \end{function}
 %
 % \begin{function}[updated = 2012-02-06]
@@ -220,7 +220,7 @@
 %
 % \begin{function}[EXP,pTF]{\dim_compare:nNn}
 %   \begin{syntax}
-%     \cs{dim_compare_p:nNn} \Arg{dimexpr_1} \meta{relation} \Arg{dimexpr_2} \\
+%     \cs{@@_compare_p:nNn} \Arg{dimexpr_1} \meta{relation} \Arg{dimexpr_2} \\
 %     \cs{dim_compare:nNnTF}
 %     ~~\Arg{dimexpr_1} \meta{relation} \Arg{dimexpr_2}
 %     ~~\Arg{true code} \Arg{false code}
@@ -239,9 +239,9 @@
 %
 % \begin{function}[EXP,pTF]{\dim_compare:n}
 %   \begin{syntax}
-%     \cs{dim_compare_p:n} \{ \meta{dimexpr1} \meta{relation} \meta{dimexpr2} \} \\
+%     \cs{@@_compare_p:n} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \\
 %     \cs{dim_compare:nTF}
-%     ~~\{ \meta{dimexpr1} \meta{relation} \meta{dimexpr2} \}
+%     ~~\{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \}
 %     ~~\Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   This function first evaluates each of the \meta{dimension expressions}
@@ -259,6 +259,37 @@
 %   \end{center}
 % \end{function}
 %
+% \begin{function}[added = 2012-06-03, EXP]{\dim_case:nnn}
+%   \begin{syntax}
+%     \cs{dim_case:nnn} \Arg{test dimension expression} \\
+%     ~~|{| \\
+%     ~~~~\Arg{dimexpr case_1} \Arg{code case_1} \\
+%     ~~~~\Arg{dimexpr case_2} \Arg{code case_2} \\
+%     ~~~~\ldots \\
+%     ~~~~\Arg{dimexpr case_n} \Arg{code case_n} \\
+%     ~~|}| \\
+%     ~~\Arg{else code}
+%   \end{syntax}
+%   This function evaluates the \meta{test dimension expression} and
+%   compares this in turn to each of the
+%   \meta{dimension expression cases}. If the two are equal then the
+%   associated \meta{code} is left in the input stream. If none of
+%   the tests are \texttt{true} then the \texttt{else code} will be
+%   left in the input stream. For example
+%   \begin{verbatim}
+%     \dim_set:Nn \l_tmpa_dim { 5 pt }
+%     \dim_case:nnn
+%       { 2 \l_tmpa_dim }
+%       {
+%         { 5 pt }        { Small }
+%         { 4 pt + 6 pt } { Medium }
+%         { - 10 pt }     { Negative }
+%       }
+%       { No idea! }
+%    \end{verbatim}
+%    will leave \enquote{\texttt{Medium}} in the input stream.
+% \end{function}
+%
 % \section{Dimension expression loops}
 %
 % \begin{function}[rEXP]{\dim_do_while:nNnn}
@@ -311,7 +342,7 @@
 %
 % \begin{function}[rEXP]{\dim_do_while:nn}
 %   \begin{syntax}
-%      \cs{dim_do_while:nn} \{ \meta{dimexpr1} \meta{relation} \meta{dimexpr2} \} \Arg{code}
+%      \cs{dim_do_while:nn} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \Arg{code}
 %   \end{syntax}
 %   Evaluates the relationship between the two \meta{dimension expressions}
 %   as described for \cs{dim_compare:nTF}, and then places the
@@ -323,7 +354,7 @@
 %
 % \begin{function}[rEXP]{\dim_do_until:nn}
 %   \begin{syntax}
-%      \cs{dim_do_until:nn} \{ \meta{dimexpr1} \meta{relation} \meta{dimexpr2} \} \Arg{code}
+%      \cs{dim_do_until:nn} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \Arg{code}
 %   \end{syntax}
 %   Evaluates the relationship between the two \meta{dimension expressions}
 %   as described for \cs{dim_compare:nTF}, and then places the
@@ -335,7 +366,7 @@
 %
 % \begin{function}[rEXP]{\dim_until_do:nn}
 %   \begin{syntax}
-%      \cs{dim_until_do:nn} \{ \meta{dimexpr1} \meta{relation} \meta{dimexpr2} \} \Arg{code}
+%      \cs{dim_until_do:nn} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \Arg{code}
 %   \end{syntax}
 %   Places the \meta{code} in the input stream for \TeX{} to process, and
 %   then evaluates the relationship between the two
@@ -347,7 +378,7 @@
 %
 % \begin{function}[rEXP]{\dim_while_do:nn}
 %   \begin{syntax}
-%      \cs{dim_while_do:nn} \{ \meta{dimexpr1} \meta{relation} \meta{dimexpr2} \} \Arg{code}
+%      \cs{dim_while_do:nn} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \Arg{code}
 %   \end{syntax}
 %   Places the \meta{code} in the input stream for \TeX{} to process, and
 %   then evaluates the relationship between the two
@@ -398,7 +429,7 @@
 %   Displays the value of the \meta{dimension} on the terminal.
 % \end{function}
 %
-% \begin{function}[added = 2011-11-22]{\dim_show:n}
+% \begin{function}[added = 2011-11-22, updated = 2012-05-27]{\dim_show:n}
 %   \begin{syntax}
 %     \cs{dim_show:n} \meta{dimension expression}
 %    \end{syntax}
@@ -419,7 +450,7 @@
 %
 % \section{Scratch dimensions}
 %
-% \begin{variable}{\l_tmpa_dim, \l_tmpb_dim, \l_tmpc_dim}
+% \begin{variable}{\l_tmpa_dim, \l_tmpb_dim}
 %   Scratch dimension for local assignment. These are never used by
 %   the kernel code, and so are safe for use with any \LaTeX3-defined
 %   function. However, they may be overwritten by other non-kernel
@@ -507,9 +538,9 @@
 %     \skip_gset_eq:NN, \skip_gset_eq:cN, \skip_gset_eq:Nc, \skip_gset_eq:cc
 %   }
 %   \begin{syntax}
-%     \cs{skip_set_eq:NN} \meta{skip1} \meta{skip2}
+%     \cs{skip_set_eq:NN} \meta{skip_1} \meta{skip_2}
 %   \end{syntax}
-%   Sets the content of \meta{skip1} equal to that of \meta{skip2}.
+%   Sets the content of \meta{skip_1} equal to that of \meta{skip_2}.
 % \end{function}
 %
 % \begin{function}[updated = 2011-10-22]
@@ -527,7 +558,7 @@
 %   \begin{syntax}
 %     \cs{skip_if_eq_p:nn} \Arg{skipexpr_1} \Arg{skipexpr_2}
 %     \cs{dim_compare:nTF}
-%     ~~\Arg{skip expr1} \Arg{skip expr2}
+%     ~~\Arg{skipexpr_1} \Arg{skipexpr_2}
 %     ~~\Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   This function first evaluates each of the
@@ -537,16 +568,6 @@
 %   for the test to be true.
 % \end{function}
 %
-% \begin{function}[EXP, pTF, updated = 2012-03-05]{\skip_if_infinite_glue:n}
-%   \begin{syntax}
-%     \cs{skip_if_infinite_glue_p:n} \Arg{skipexpr}
-%     \cs{skip_if_infinite_glue:nTF} \Arg{skipexpr} \Arg{true code} \Arg{false code}
-%   \end{syntax}
-%   Evaluates the \meta{skip expression} as described for \cs{skip_eval:n},
-%   and then tests if this contains an infinite stretch or shrink
-%   component (or both).
-% \end{function}
-%
 % \begin{function}[EXP, pTF, added = 2012-03-05]{\skip_if_finite:n}
 %   \begin{syntax}
 %     \cs{skip_if_finite_p:n} \Arg{skipexpr}
@@ -596,7 +617,7 @@
 %   Displays the value of the \meta{skip} on the terminal.
 % \end{function}
 %
-% \begin{function}[added = 2011-11-22]{\skip_show:n}
+% \begin{function}[added = 2011-11-22, updated = 2012-05-27]{\skip_show:n}
 %   \begin{syntax}
 %     \cs{skip_show:n} \meta{skip expression}
 %    \end{syntax}
@@ -617,7 +638,7 @@
 %
 % \section{Scratch skips}
 %
-% \begin{variable}{\l_tmpa_skip, \l_tmpb_skip, \l_tmpc_skip}
+% \begin{variable}{\l_tmpa_skip, \l_tmpb_skip}
 %   Scratch skip for local assignment. These are never used by
 %   the kernel code, and so are safe for use with any \LaTeX3-defined
 %   function. However, they may be overwritten by other non-kernel
@@ -631,6 +652,32 @@
 %   code and so should only be used for short-term storage.
 % \end{variable}
 %
+% \section{Inserting skips into the output}
+%
+% \begin{function}[updated = 2011-10-22]
+%   {\skip_horizontal:N, \skip_horizontal:c, \skip_horizontal:n}
+%   \begin{syntax}
+%     \cs{skip_horizontal:N} \meta{skip}
+%     \cs{skip_horizontal:n} \Arg{skipexpr}
+%   \end{syntax}
+%   Inserts a horizontal \meta{skip} into the current list.
+%   \begin{texnote}
+%     \cs{skip_horizontal:N} is the \TeX{} primitive \tn{hskip} renamed.
+%   \end{texnote}
+% \end{function}
+%
+% \begin{function}[updated = 2011-10-22]
+%   {\skip_vertical:N, \skip_vertical:c, \skip_vertical:n}
+%   \begin{syntax}
+%     \cs{skip_vertical:N} \meta{skip}
+%     \cs{skip_vertical:n} \Arg{skipexpr}
+%   \end{syntax}
+%   Inserts a vertical \meta{skip} into the current list.
+%   \begin{texnote}
+%     \cs{skip_vertical:N} is the \TeX{} primitive \tn{vskip} renamed.
+%   \end{texnote}
+% \end{function}
+%
 % \section{Creating and initialising \texttt{muskip} variables}
 %
 % \begin{function}{\muskip_new:N, \muskip_new:c}
@@ -711,10 +758,10 @@
 %     \muskip_gset_eq:Nc, \muskip_gset_eq:cc
 %   }
 %   \begin{syntax}
-%     \cs{muskip_set_eq:NN} \meta{muskip1} \meta{muskip2}
+%     \cs{muskip_set_eq:NN} \meta{muskip_1} \meta{muskip_2}
 %   \end{syntax}
-%   Sets the content of \meta{muskip1} equal to that of
-%   \meta{muskip2}.
+%   Sets the content of \meta{muskip_1} equal to that of
+%   \meta{muskip_2}.
 % \end{function}
 %
 % \begin{function}[updated = 2011-10-22]
@@ -757,32 +804,6 @@
 %   \end{texnote}
 % \end{function}
 %
-% \section{Inserting skips into the output}
-%
-% \begin{function}[updated = 2011-10-22]
-%   {\skip_horizontal:N, \skip_horizontal:c, \skip_horizontal:n}
-%   \begin{syntax}
-%     \cs{skip_horizontal:N} \meta{skip}
-%     \cs{skip_horizontal:n} \Arg{skipexpr}
-%   \end{syntax}
-%   Inserts a horizontal \meta{skip} into the current list.
-%   \begin{texnote}
-%     \cs{skip_horizontal:N} is the \TeX{} primitive \tn{hskip} renamed.
-%   \end{texnote}
-% \end{function}
-%
-% \begin{function}[updated = 2011-10-22]
-%   {\skip_vertical:N, \skip_vertical:c, \skip_vertical:n}
-%   \begin{syntax}
-%     \cs{skip_vertical:N} \meta{skip}
-%     \cs{skip_vertical:n} \Arg{skipexpr}
-%   \end{syntax}
-%   Inserts a vertical \meta{skip} into the current list.
-%   \begin{texnote}
-%     \cs{skip_vertical:N} is the \TeX{} primitive \tn{vskip} renamed.
-%   \end{texnote}
-% \end{function}
-%
 % \section{Viewing \texttt{muskip} variables}
 %
 % \begin{function}{\muskip_show:N, \muskip_show:c}
@@ -792,7 +813,7 @@
 %   Displays the value of the \meta{muskip} on the terminal.
 % \end{function}
 %
-% \begin{function}[added = 2011-11-22]{\muskip_show:n}
+% \begin{function}[added = 2011-11-22, updated = 2012-05-27]{\muskip_show:n}
 %   \begin{syntax}
 %     \cs{muskip_show:n} \meta{muskip expression}
 %    \end{syntax}
@@ -800,11 +821,37 @@
 %   on the terminal.
 % \end{function}
 %
-% \section{Internal functions}
+% \section{Constant muskips}
+%
+% \begin{variable}{\c_max_muskip}
+%   The maximum value that can be stored as a muskip.
+% \end{variable}
+%
+% \begin{variable}{\c_zero_muskip}
+%   A zero length as a muskip.
+% \end{variable}
+%
+% \section{Scratch muskips}
+%
+% \begin{variable}{\l_tmpa_muskip, \l_tmpb_muskip}
+%   Scratch muskip for local assignment. These are never used by
+%   the kernel code, and so are safe for use with any \LaTeX3-defined
+%   function. However, they may be overwritten by other non-kernel
+%   code and so should only be used for short-term storage.
+% \end{variable}
+%
+% \begin{variable}{\g_tmpa_muskip, \g_tmpb_muskip}
+%   Scratch muskip for global assignment. These are never used by
+%   the kernel code, and so are safe for use with any \LaTeX3-defined
+%   function. However, they may be overwritten by other non-kernel
+%   code and so should only be used for short-term storage.
+% \end{variable}
+%
+% \section{Primitive conditional}
 %
 % \begin{function}{\if_dim:w}
 %   \begin{syntax}
-%     \cs{if_dim:w} \meta{dimen1} \meta{relation} \meta{dimen1}
+%     \cs{if_dim:w} \meta{dimen_1} \meta{relation} \meta{dimen_2}
 %     ~~\meta{true code}
 %     \cs{else:}
 %     ~~\meta{false}
@@ -817,44 +864,28 @@
 %   \end{texnote}
 % \end{function}
 %
-% \begin{function}[EXP]{\dim_eval:w, \dim_eval_end:}
+% \section{Internal functions}
+%
+% \begin{function}[EXP]{\__dim_eval:w, \__dim_eval_end:}
 %   \begin{syntax}
-%     \cs{dim_eval:w} \meta{dimexpr} \cs{dim_eval_end:}
+%     \cs{__dim_eval:w} \meta{dimexpr} \cs{__dim_eval_end:}
 %   \end{syntax}
 %   Evaluates \meta{dimension expression} as described for \cs{dim_eval:n}.
 %   The evaluation stops when an unexpandable token which is not a valid
-%   part of a dimension is read or when \cs{dim_eval_end:} is
+%   part of a dimension is read or when \cs{__dim_eval_end:} is
 %   reached. The latter is gobbled by the scanner mechanism:
-%   \cs{dim_eval_end:} itself is unexpandable but used correctly
+%   \cs{__dim_eval_end:} itself is unexpandable but used correctly
 %   the entire construct is expandable.
 %   \begin{texnote}
 %     This is the \eTeX{} primitive \tn{dimexpr}.
 %   \end{texnote}
 % \end{function}
 %
-% \section{Experimental skip functions}
-%
-% \begin{function}[updated = 2011-10-22]{\skip_split_finite_else_action:nnNN}
-%   \begin{syntax}
-%     \cs{skip_split_finite_else_action:nnNN} \Arg{skipexpr} \Arg{action}
-%     ~~\meta{dimen1} \meta{dimen2}
-%   \end{syntax}
-%   Checks if the \meta{skipexpr} contains finite glue. If it does then it
-%   assigns
-%   \meta{dimen1} the stretch component and \meta{dimen2} the shrink
-%   component. If
-%   it contains infinite glue set \meta{dimen1} and \meta{dimen2} to $0$\,pt
-%   and place |#2| into the input stream: this is usually an error or
-%   warning message of some sort.
-% \end{function}
-%
-% \section{Internal functions}
-%
 % \begin{function}[added = 2011-11-11, EXP]
-%   {\dim_strip_bp:n, \dim_strip_pt:n}
+%   {\__dim_strip_bp:n, \__dim_strip_pt:n}
 %   \begin{syntax}
-%     \cs{dim_strip_bp:n} \Arg{dimension expression}
-%     \cs{dim_strip_pt:n} \Arg{dimension expression}
+%     \cs{__dim_strip_bp:n} \Arg{dimension expression}
+%     \cs{__dim_strip_pt:n} \Arg{dimension expression}
 %   \end{syntax}
 %   Evaluates the \meta{dimension expression}, expanding any
 %   dimensions and token list variables within the \meta{expression}
@@ -867,7 +898,7 @@
 %   If the \Arg{dimension expression} contains additional units, these will
 %   be ignored, so for example
 %   \begin{verbatim}
-%     \dim_strip_pt:n { 1 bp pt }
+%     \__dim_strip_pt:n { 1 bp pt }
 %   \end{verbatim}
 %   will leave |1.00374| in the input stream (\emph{i.e.}~the magnitude of
 %   one \enquote{big point} when converted to points).
@@ -884,23 +915,27 @@
 %    \end{macrocode}
 %
 %    \begin{macrocode}
+%<@@=dim>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
 % \subsection{Length primitives renamed}
 %
 % \begin{macro}{\if_dim:w}
-% \begin{macro}{\dim_eval:w}
-% \begin{macro}{\dim_eval_end:}
+% \begin{macro}{\@@_eval:w}
+% \begin{macro}{\@@_eval_end:}
 %   Primitives renamed.
 %    \begin{macrocode}
 \cs_new_eq:NN \if_dim:w      \tex_ifdim:D
-\cs_new_eq:NN \dim_eval:w    \etex_dimexpr:D
-\cs_new_eq:NN \dim_eval_end: \tex_relax:D
+\cs_new_eq:NN \@@_eval:w      \etex_dimexpr:D
+\cs_new_eq:NN \@@_eval_end:   \tex_relax:D
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -914,7 +949,7 @@
 %<*package>
 \cs_new_protected:Npn \dim_new:N #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \newdimen #1
   }
 %</package>
@@ -981,7 +1016,7 @@
 %   Setting dimensions is easy enough.
 %    \begin{macrocode}
 \cs_new_protected:Npn \dim_set:Nn #1#2
-  { #1 ~ \dim_eval:w #2 \dim_eval_end: }
+  { #1 ~ \@@_eval:w #2 \@@_eval_end: }
 \cs_new_protected:Npn \dim_gset:Nn { \tex_global:D \dim_set:Nn }
 \cs_generate_variant:Nn \dim_set:Nn  { c }
 \cs_generate_variant:Nn \dim_gset:Nn { c }
@@ -1008,19 +1043,19 @@
 % \begin{macro}{\dim_set_min:Nn, \dim_set_min:cn}
 % \begin{macro}{\dim_gset_max:Nn, \dim_gset_max:cn}
 % \begin{macro}{\dim_gset_min:Nn, \dim_gset_min:cn}
-% \begin{macro}[aux]{\dim_set_max_aux:NNNn}
+% \begin{macro}[aux]{\@@_set_max:NNNn}
 %   Setting maximum and minimum values is simply a case of so build-in
 %   comparison. This only applies to dimensions as skips are not ordered.
 %    \begin{macrocode}
 \cs_new_protected_nopar:Npn \dim_set_max:Nn
-  { \dim_set_max_aux:NNNn < \dim_set:Nn }
+  { \@@_set_max:NNNn < \dim_set:Nn }
 \cs_new_protected_nopar:Npn \dim_gset_max:Nn
-  { \dim_set_max_aux:NNNn < \dim_gset:Nn }
+  { \@@_set_max:NNNn < \dim_gset:Nn }
 \cs_new_protected_nopar:Npn \dim_set_min:Nn
-  { \dim_set_max_aux:NNNn > \dim_set:Nn }
+  { \@@_set_max:NNNn > \dim_set:Nn }
 \cs_new_protected_nopar:Npn \dim_gset_min:Nn
-  { \dim_set_max_aux:NNNn > \dim_gset:Nn }
-\cs_new_protected:Npn \dim_set_max_aux:NNNn #1#2#3#4
+  { \@@_set_max:NNNn > \dim_gset:Nn }
+\cs_new_protected:Npn \@@_set_max:NNNn #1#2#3#4
   { \dim_compare:nNnT {#3} #1 {#4} { #2 #3 {#4} } }
 \cs_generate_variant:Nn \dim_set_max:Nn  { c }
 \cs_generate_variant:Nn \dim_gset_max:Nn { c }
@@ -1040,12 +1075,12 @@
 %   Using |by| here deals with the (incorrect) case |\dimen123|.
 %    \begin{macrocode}
 \cs_new_protected:Npn \dim_add:Nn #1#2
-  { \tex_advance:D #1 by \dim_eval:w #2 \dim_eval_end: }
+  { \tex_advance:D #1 by \@@_eval:w #2 \@@_eval_end: }
 \cs_new_protected:Npn \dim_gadd:Nn { \tex_global:D \dim_add:Nn }
 \cs_generate_variant:Nn \dim_add:Nn  { c }
 \cs_generate_variant:Nn \dim_gadd:Nn { c }
 \cs_new_protected:Npn \dim_sub:Nn #1#2
-  { \tex_advance:D #1 by - \dim_eval:w #2 \dim_eval_end: }
+  { \tex_advance:D #1 by - \@@_eval:w #2 \@@_eval_end: }
 \cs_new_protected:Npn \dim_gsub:Nn { \tex_global:D \dim_sub:Nn }
 \cs_generate_variant:Nn \dim_sub:Nn  { c }
 \cs_generate_variant:Nn \dim_gsub:Nn { c }
@@ -1065,57 +1100,55 @@
 \cs_new:Npn \dim_abs:n #1
   {
     \dim_use:N
-      \dim_eval:w
-        \if_dim:w \dim_eval:w #1 < \c_zero_dim
+      \@@_eval:w
+        \if_dim:w \@@_eval:w #1 < \c_zero_dim
           -
         \fi:
-      \dim_eval:w #1 \dim_eval_end:
-    \dim_eval_end:
+      \@@_eval:w #1 \@@_eval_end:
+    \@@_eval_end:
   }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}{\dim_ratio:nn}
-% \begin{macro}[aux]{\dim_ratio_aux:n}
+% \begin{macro}[aux]{\@@_ratio:n}
 %   With dimension expressions, something like |10 pt * ( 5 pt / 10 pt )| will
 %   not work. Instead, the ratio part needs to be converted to an integer
-%   expression. Using \cs{int_value:w} forces everything into |sp|, avoiding
+%   expression. Using \cs{__int_value:w} forces everything into |sp|, avoiding
 %   any decimal parts.
 %    \begin{macrocode}
 \cs_new:Npn \dim_ratio:nn #1#2
-  { \dim_ratio_aux:n {#1} / \dim_ratio_aux:n {#2} }
-\cs_new:Npn \dim_ratio_aux:n #1
-  { \int_value:w \dim_eval:w #1 \dim_eval_end: }
+  { \@@_ratio:n {#1} / \@@_ratio:n {#2} }
+\cs_new:Npn \@@_ratio:n #1
+  { \__int_value:w \@@_eval:w #1 \@@_eval_end: }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
 % \subsection{Dimension expression conditionals}
 %
-% \begin{macro}{\dim_compare_p:nNn}
-% \begin{macro}[TF]{\dim_compare:nNn}
+% \begin{macro}[pTF, EXP]{\dim_compare:nNn}
 %   Simple comparison.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \dim_compare:nNn #1#2#3 { p , T , F , TF }
   {
-    \if_dim:w \dim_eval:w #1 #2 \dim_eval:w #3 \dim_eval_end:
+    \if_dim:w \@@_eval:w #1 #2 \@@_eval:w #3 \@@_eval_end:
       \prg_return_true: \else: \prg_return_false: \fi:
   }
 %    \end{macrocode}
 % \end{macro}
-% \end{macro}
 %
 % \begin{macro}[pTF, EXP]{\dim_compare:n}
-% \begin{macro}[aux, EXP]{\dim_compare_aux:w, \dim_compare_aux:NNw}
+% \begin{macro}[aux, EXP]{\@@_compare_aux:w, \@@_compare_aux:NNw}
 % \begin{macro}[aux, EXP]
 %   {
-%     \dim_compare_=:NNw,
-%     \dim_compare_<:NNw,
-%     \dim_compare_>:NNw,
-%     \dim_compare_==:NNw,
-%     \dim_compare_!=:NNw,
-%     \dim_compare_<=:NNw,
-%     \dim_compare_>=:NNw
+%     \@@_compare_=:NNw,
+%     \@@_compare_<:NNw,
+%     \@@_compare_>:NNw,
+%     \@@_compare_==:NNw,
+%     \@@_compare_!=:NNw,
+%     \@@_compare_<=:NNw,
+%     \@@_compare_>=:NNw
 %   }
 %   This code is adapted from the \cs{int_compare:nTF} function.  First
 %   evaluate the left-hand side.  Then access the relation symbol by
@@ -1124,40 +1157,65 @@
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \dim_compare:n #1 { p , T , F , TF }
   {
-    \exp_after:wN \dim_compare_aux:w \dim_use:N \dim_eval:w #1
-        \kernel_compare_error: \dim_eval_end:
+    \exp_after:wN \@@_compare_aux:w \dim_use:N \@@_eval:w #1
+        \__prg_compare_error: \@@_eval_end:
       \prg_return_true:
     \else:
       \prg_return_false:
     \fi:
   }
 \exp_args:Nno \use:nn
-  { \cs_new:Npn \dim_compare_aux:w #1 }
+  { \cs_new:Npn \@@_compare_aux:w #1 }
   { \tl_to_str:n { pt } }
-  #2 \kernel_compare_error:
+  #2 \__prg_compare_error:
   {
-    \exp_after:wN \dim_compare_aux:NNw #2 ?? \q_mark
+    \exp_after:wN \@@_compare_aux:NNw #2 ?? \q_mark
     #1 pt #2
   }
-\cs_new:Npn \dim_compare_aux:NNw #1#2#3 \q_mark
+\cs_new:Npn \@@_compare_aux:NNw #1#2#3 \q_mark
   {
-    \use:c { dim_compare_  #1  \if_meaning:w = #2 =  \fi: :NNw }
-      \kernel_compare_error:Nw #1
+    \use:c { @@_compare_  #1  \if_meaning:w = #2 =  \fi: :NNw }
+      \__prg_compare_error:Nw #1
   }
-\cs_new:cpn { dim_compare_=:NNw } #1#2#3 =
-  { \if_dim:w #3 = \dim_eval:w }
-\cs_new:cpn { dim_compare_<:NNw } #1#2#3 <
-  { \if_dim:w #3 < \dim_eval:w }
-\cs_new:cpn { dim_compare_>:NNw } #1#2#3 >
-  { \if_dim:w #3 > \dim_eval:w }
-\cs_new:cpn { dim_compare_==:NNw } #1#2#3 ==
-  { \if_dim:w #3 = \dim_eval:w }
-\cs_new:cpn { dim_compare_!=:NNw } #1#2#3 !=
-  { \reverse_if:N \if_dim:w #3 = \dim_eval:w }
-\cs_new:cpn { dim_compare_<=:NNw } #1#2#3 <=
-  { \reverse_if:N \if_dim:w #3 > \dim_eval:w }
-\cs_new:cpn { dim_compare_>=:NNw } #1#2#3 >=
-  { \reverse_if:N \if_dim:w #3 < \dim_eval:w }
+\cs_new:cpn { @@_compare_=:NNw } #1#2#3 =
+  { \if_dim:w #3 = \@@_eval:w }
+\cs_new:cpn { @@_compare_<:NNw } #1#2#3 <
+  { \if_dim:w #3 < \@@_eval:w }
+\cs_new:cpn { @@_compare_>:NNw } #1#2#3 >
+  { \if_dim:w #3 > \@@_eval:w }
+\cs_new:cpn { @@_compare_==:NNw } #1#2#3 ==
+  { \if_dim:w #3 = \@@_eval:w }
+\cs_new:cpn { @@_compare_!=:NNw } #1#2#3 !=
+  { \reverse_if:N \if_dim:w #3 = \@@_eval:w }
+\cs_new:cpn { @@_compare_<=:NNw } #1#2#3 <=
+  { \reverse_if:N \if_dim:w #3 > \@@_eval:w }
+\cs_new:cpn { @@_compare_>=:NNw } #1#2#3 >=
+  { \reverse_if:N \if_dim:w #3 < \@@_eval:w }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\dim_case:nnn}
+% \begin{macro}[aux, EXP]{\@@_case_aux:nnn}
+% \begin{macro}[aux, EXP]{\@@_case_aux:nw,\@@_case_end:nw}
+%   The dimension function is the same as the \texttt{int} version, so there
+%   is not much to say here.
+%    \begin{macrocode}
+\cs_new:Npn \dim_case:nnn #1
+  {
+    \tex_romannumeral:D
+    \exp_args:Nf \@@_case_aux:nnn { \dim_eval:n {#1} }
+  }
+\cs_new:Npn \@@_case_aux:nnn #1#2#3
+  { \@@_case_aux:nw {#1} #2 {#1} {#3} \q_recursion_stop }
+\cs_new:Npn \@@_case_aux:nw #1#2#3
+  {
+    \dim_compare:nNnTF {#1} = {#2}
+      { \@@_case_end:nw {#3} }
+      { \@@_case_aux:nw {#1} }
+  }
+\cs_new_eq:NN \@@_case_end:nw \__prg_case_end:nw
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1253,33 +1311,33 @@
 %   Evaluating a dimension expression expandably.
 %    \begin{macrocode}
 \cs_new:Npn \dim_eval:n #1
-  { \dim_use:N \dim_eval:w #1 \dim_eval_end: }
+  { \dim_use:N \@@_eval:w #1 \@@_eval_end: }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[EXP]{\dim_strip_bp:n}
+% \begin{macro}[EXP, int]{\@@_strip_bp:n}
 %    \begin{macrocode}
-\cs_new:Npn \dim_strip_bp:n #1
-  { \dim_strip_pt:n { 0.996 26 \dim_eval:w #1 \dim_eval_end: } }
+\cs_new:Npn \@@_strip_bp:n #1
+  { \@@_strip_pt:n { 0.996 26 \@@_eval:w #1 \@@_eval_end: } }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[EXP]{\dim_strip_pt:n}
-% \begin{macro}[EXP, aux]{\dim_strip_pt:w}
+% \begin{macro}[EXP]{\@@_strip_pt:n}
+% \begin{macro}[EXP, aux]{\@@_strip_pt:w}
 %   A function which comes up often enough to deserve a place in the kernel.
 %   The idea here is that the input is assumed to be in \texttt{pt}, but can
 %   be given in other units, while the output is the value of the dimension
 %   in \texttt{pt} but with no units given. This is used a lot by low-level
 %   manipulations.
 %    \begin{macrocode}
-\cs_new:Npn \dim_strip_pt:n #1
+\cs_new:Npn \@@_strip_pt:n #1
   {
     \exp_after:wN
-      \dim_strip_pt:w \dim_use:N \dim_eval:w #1 \dim_eval_end: \q_stop
+      \@@_strip_pt:w \dim_use:N \@@_eval:w #1 \@@_eval_end: \q_stop
   }
 \use:x
   {
-    \cs_new:Npn \exp_not:N \dim_strip_pt:w
+    \cs_new:Npn \exp_not:N \@@_strip_pt:w
       ##1 . ##2 \tl_to_str:n { pt } ##3 \exp_not:N \q_stop
       {
         ##1
@@ -1304,16 +1362,18 @@
 % \begin{macro}{\dim_show:N, \dim_show:c}
 %   Diagnostics.
 %    \begin{macrocode}
-\cs_new_eq:NN  \dim_show:N \kernel_register_show:N
+\cs_new_eq:NN  \dim_show:N \__kernel_register_show:N
 \cs_generate_variant:Nn \dim_show:N { c }
 %    \end{macrocode}
 %  \end{macro}
 %
 % \begin{macro}{\dim_show:n}
-%   Diagnostics.
+%   Diagnostics.  We don't use the \TeX{} primitive \tn{showthe} to show
+%   dimension expressions: this gives a more unified output, since the
+%   closing brace is read by the dimension expression in all cases.
 %    \begin{macrocode}
 \cs_new_protected:Npn \dim_show:n #1
-  { \tex_showthe:D \dim_eval:w #1 \dim_eval_end: }
+  { \etex_showtokens:D \exp_after:wN { \dim_use:N \@@_eval:w #1 } }
 %    \end{macrocode}
 %  \end{macro}
 %
@@ -1338,14 +1398,13 @@
 %
 % \subsection{Scratch dimensions}
 %
-% \begin{variable}{\l_tmpa_dim, \l_tmpb_dim, \l_tmpc_dim}
+% \begin{variable}{\l_tmpa_dim, \l_tmpb_dim}
 % \begin{variable}{\g_tmpa_dim, \g_tmpb_dim}
-%    We provide three local and two global scratch registers, maybe we
+%    We provide two local and two global scratch registers, maybe we
 %    need more or less.
 %    \begin{macrocode}
 \dim_new:N \l_tmpa_dim
 \dim_new:N \l_tmpb_dim
-\dim_new:N \l_tmpc_dim
 \dim_new:N \g_tmpa_dim
 \dim_new:N \g_tmpb_dim
 %    \end{macrocode}
@@ -1360,7 +1419,7 @@
 %<*package>
 \cs_new_protected:Npn \skip_new:N #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \newskip #1
   }
 %</package>
@@ -1493,7 +1552,7 @@
 % \end{macro}
 %
 % \begin{macro}[EXP,pTF]{\skip_if_finite:n}
-% \begin{macro}[EXP,aux]{\skip_if_finite_aux:wwNw}
+% \begin{macro}[EXP,aux]{\__skip_if_finite:wwNw}
 %   With \eTeX{}, we have an easy access to the order of infinities of
 %   the stretch and shrink components of a skip.  However, to access
 %   both, we either need to evaluate the expression twice, or evaluate
@@ -1502,29 +1561,21 @@
 %   it is quicker to make it search for the string \texttt{fil} which
 %   characterizes infinite glue.
 %    \begin{macrocode}
-\cs_set_protected:Npn \cs_tmp:w #1
+\cs_set_protected:Npn \__cs_tmp:w #1
   {
     \prg_new_conditional:Npnn \skip_if_finite:n ##1 { p , T , F , TF }
       {
-        \exp_after:wN \skip_if_finite_aux:wwNw
+        \exp_after:wN \__skip_if_finite:wwNw
         \skip_use:N \etex_glueexpr:D ##1 ; \prg_return_false:
         #1 ; \prg_return_true: \q_stop
       }
-    \cs_new:Npn \skip_if_finite_aux:wwNw ##1 #1 ##2 ; ##3 ##4 \q_stop {##3}
+    \cs_new:Npn \__skip_if_finite:wwNw ##1 #1 ##2 ; ##3 ##4 \q_stop {##3}
   }
-\exp_args:No \cs_tmp:w { \tl_to_str:n { fil } }
+\exp_args:No \__cs_tmp:w { \tl_to_str:n { fil } }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[EXP, pTF]{\skip_if_infinite_glue:n}
-%   Reverse of \cs{skip_if_finite:nTF}.
-%    \begin{macrocode}
-\prg_new_conditional:Npnn \skip_if_infinite_glue:n #1 { p , T , F , TF }
-  { \skip_if_finite:nTF {#1} \prg_return_false: \prg_return_true: }
-%    \end{macrocode}
-% \end{macro}
-%
 % \subsection{Using \texttt{skip} expressions and variables}
 %
 % \begin{macro}{\skip_eval:n}
@@ -1566,16 +1617,18 @@
 % \begin{macro}{\skip_show:N, \skip_show:c}
 %   Diagnostics.
 %    \begin{macrocode}
-\cs_new_eq:NN  \skip_show:N \kernel_register_show:N
+\cs_new_eq:NN  \skip_show:N \__kernel_register_show:N
 \cs_generate_variant:Nn \skip_show:N { c }
 %    \end{macrocode}
 %  \end{macro}
 %
 % \begin{macro}{\skip_show:n}
-%   Diagnostics.
+%   Diagnostics.  We don't use the \TeX{} primitive \tn{showthe} to show
+%   skip expressions: this gives a more unified output, since the
+%   closing brace is read by the skip expression in all cases.
 %    \begin{macrocode}
 \cs_new_protected:Npn \skip_show:n #1
-  { \tex_showthe:D \etex_glueexpr:D #1 \scan_stop: }
+  { \etex_showtokens:D \exp_after:wN { \tex_the:D \etex_glueexpr:D #1 } }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1593,14 +1646,13 @@
 %
 % \subsection{Scratch skips}
 %
-% \begin{variable}{\l_tmpa_skip, \l_tmpb_skip, \l_tmpc_skip}
+% \begin{variable}{\l_tmpa_skip, \l_tmpb_skip}
 % \begin{variable}{\g_tmpa_skip, \g_tmpb_skip}
-%    We provide three local and two global scratch registers, maybe we
+%    We provide two local and two global scratch registers, maybe we
 %    need more or less.
 %    \begin{macrocode}
 \skip_new:N \l_tmpa_skip
 \skip_new:N \l_tmpb_skip
-\skip_new:N \l_tmpc_skip
 \skip_new:N \g_tmpa_skip
 \skip_new:N \g_tmpb_skip
 %    \end{macrocode}
@@ -1615,7 +1667,7 @@
 %<*package>
 \cs_new_protected:Npn \muskip_new:N #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \newmuskip #1
   }
 %</package>
@@ -1761,44 +1813,76 @@
 % \begin{macro}{\muskip_show:N, \muskip_show:c}
 %   Diagnostics.
 %    \begin{macrocode}
-\cs_new_eq:NN  \muskip_show:N \kernel_register_show:N
+\cs_new_eq:NN  \muskip_show:N \__kernel_register_show:N
 \cs_generate_variant:Nn \muskip_show:N { c }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}{\muskip_show:n}
-%   Diagnostics.
+%   Diagnostics.  We don't use the \TeX{} primitive \tn{showthe} to show
+%   muskip expressions: this gives a more unified output, since the
+%   closing brace is read by the muskip expression in all cases.
 %    \begin{macrocode}
 \cs_new_protected:Npn \muskip_show:n #1
-  { \tex_showthe:D \etex_muexpr:D #1 \scan_stop: }
+  { \etex_showtokens:D \exp_after:wN { \tex_the:D \etex_muexpr:D #1 } }
 %    \end{macrocode}
 % \end{macro}
 %
-% \subsection{Experimental skip functions}
+% \subsection{Constant muskips}
 %
-% \begin{macro}{\skip_split_finite_else_action:nnNN}
-%   This macro is useful when performing error checking in certain
-%   circumstances. If the \meta{skip} register holds finite glue it sets
-%   |#3| and |#4| to the stretch and shrink component, resp. If it holds
-%   infinite glue set |#3| and |#4| to zero and issue the special action
-%   |#2| which is probably an error message.
-%   Assignments are local.
+% \begin{macro}{\c_zero_muskip}
+% \begin{macro}{\c_max_muskip}
+%   Constant muskips given by their value.
 %    \begin{macrocode}
-\cs_new:Npn \skip_split_finite_else_action:nnNN #1#2#3#4
-  {
-    \skip_if_finite:nTF {#1}
-      {
-        #3 = \etex_gluestretch:D #1 \scan_stop:
-        #4 = \etex_glueshrink:D  #1 \scan_stop:
-      }
-      {
-        #3 = \c_zero_skip
-        #4 = \c_zero_skip
-        #2
-      }
-  }
+\muskip_const:Nn \c_zero_muskip { 0 mu }
+\muskip_const:Nn \c_max_muskip  { 16383.99999 mu }
 %    \end{macrocode}
-%  \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Scratch muskips}
+%
+% \begin{variable}{\l_tmpa_muskip, \l_tmpb_muskip}
+% \begin{variable}{\g_tmpa_muskip, \g_tmpb_muskip}
+%    We provide two local and two global scratch registers, maybe we
+%    need more or less.
+%    \begin{macrocode}
+\muskip_new:N \l_tmpa_muskip
+\muskip_new:N \l_tmpb_muskip
+\muskip_new:N \g_tmpa_muskip
+\muskip_new:N \g_tmpb_muskip
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+%
+% \subsection{Deprecated functions}
+%
+% Deprecated on 2012-05-10, for removal by 2012-08-31.
+%
+% \begin{macro}[EXP, pTF]{\skip_if_infinite_glue:n}
+%   Reverse of \cs{skip_if_finite:nTF}.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \skip_if_infinite_glue:n #1 { p , T , F , TF }
+  { \skip_if_finite:nTF {#1} \prg_return_false: \prg_return_true: }
+%    \end{macrocode}
+% \end{macro}
+%
+% Deprecated 2012-06-03 for removal after 2012-12-31.
+%
+% \begin{macro}[EXP]{\prg_case_dim:nnn}
+%   Moved here, was in \pkg{l3prg} but load order means we define it here
+%   now.
+%    \begin{macrocode}
+\cs_new_eq:NN \prg_case_dim:nnn \dim_case:nnn
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\dim_eval:w, \dim_eval_end:}
+%    \begin{macrocode}
+\cs_new_eq:NN \dim_eval:w    \__dim_eval:w
+\cs_new_eq:NN \dim_eval_end: \__dim_eval_end:
+%    \end{macrocode}
+% \end{macro}
 %
 %    \begin{macrocode}
 %</initex|package>
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3tl.dtx b/Master/texmf-dist/source/latex/l3kernel/l3tl.dtx
index 51fcddc242e..08d2630523d 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3tl.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3tl.dtx
@@ -35,8 +35,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3tl.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental token lists}
+\GetIdInfo$Id: l3tl.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Token lists}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -148,10 +148,23 @@
 %     \tl_gset_eq:NN, \tl_gset_eq:cN, \tl_gset_eq:Nc, \tl_gset_eq:cc
 %   }
 %   \begin{syntax}
-%     \cs{tl_set_eq:NN} \meta{tl~var1} \meta{tl~var2}
+%     \cs{tl_set_eq:NN} \meta{tl~var_1} \meta{tl~var_2}
 %   \end{syntax}
-%   Sets the content of \meta{tl~var1} equal to that of
-%   \meta{tl~var2}.
+%   Sets the content of \meta{tl~var_1} equal to that of
+%   \meta{tl~var_2}.
+% \end{function}
+%
+% \begin{function}[added = 2012-05-18]
+%   {
+%     \tl_concat:NNN,  \tl_concat:ccc,
+%     \tl_gconcat:NNN, \tl_gconcat:ccc
+%   }
+%   \begin{syntax}
+%     \cs{tl_concat:NNN} \meta{tl~var_1} \meta{tl~var_2} \meta{tl~var_3}
+%   \end{syntax}
+%   Concatenates the content of \meta{tl~var_2} and \meta{tl~var_3}
+%   together and saves the result in \meta{tl~var_1}. The \meta{tl~var_2}
+%   will be placed at the left side of the new token list.
 % \end{function}
 %
 % \begin{function}[EXP, pTF, added=2012-03-03]{\tl_if_exist:N, \tl_if_exist:c}
@@ -363,23 +376,21 @@
 %   (\emph{i.e.}~contains no tokens at all).
 % \end{function}
 %
-% \begin{function}[EXP,pTF]
-%   {\tl_if_empty:n, \tl_if_empty:V, \tl_if_empty:o, \tl_if_empty:x}
+% \begin{function}[added = 2012-05-24, updated = 2012-06-05, EXP,pTF]
+%   {\tl_if_empty:n, \tl_if_empty:V, \tl_if_empty:o}
 %   \begin{syntax}
 %     \cs{tl_if_empty_p:n} \Arg{token list}
 %     \cs{tl_if_empty:nTF} \Arg{token list} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   Tests if the \meta{token list} is entirely empty
 %   (\emph{i.e.}~contains no tokens at all).
-%   All versions of these functions are fully expandable
-%   (including those involving an \texttt{x}-type expansion).
 % \end{function}
 %
 % \begin{function}[EXP,pTF]
 %   {\tl_if_eq:NN, \tl_if_eq:Nc, \tl_if_eq:cN, \tl_if_eq:cc}
 %   \begin{syntax}
-%     \cs{tl_if_eq_p:NN} \Arg{tl var1} \Arg{tl var2}
-%     \cs{tl_if_eq:NNTF} \Arg{tl var1} \Arg{tl var2} \Arg{true code} \Arg{false code}
+%     \cs{tl_if_eq_p:NN} \Arg{tl var_1} \Arg{tl var_2}
+%     \cs{tl_if_eq:NNTF} \Arg{tl var_1} \Arg{tl var_2} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   Compares the content of two \meta{token list variables} and
 %   is logically \texttt{true} if the two contain the same list of
@@ -395,9 +406,9 @@
 %
 % \begin{function}[TF]{\tl_if_eq:nn}
 %   \begin{syntax}
-%     \cs{tl_if_eq:nnTF} \meta{token list1} \Arg{token list2} \Arg{true code} \Arg{false code}
+%     \cs{tl_if_eq:nnTF} \meta{token list_1} \Arg{token list_2} \Arg{true code} \Arg{false code}
 %   \end{syntax}
-%   Tests if \meta{token list1} and \meta{token list2} are equal, both in
+%   Tests if \meta{token list_1} and \meta{token list_2} are equal, both in
 %   respect of character codes and category codes.
 % \end{function}
 %
@@ -414,9 +425,9 @@
 % \begin{function}[TF]
 %   {\tl_if_in:nn, \tl_if_in:Vn, \tl_if_in:on, \tl_if_in:no}
 %   \begin{syntax}
-%     \cs{tl_if_in:nnTF} \Arg{token list1} \Arg{token list2} \Arg{true code} \Arg{false code}
+%     \cs{tl_if_in:nnTF} \Arg{token list_1} \Arg{token list_2} \Arg{true code} \Arg{false code}
 %   \end{syntax}
-%   Tests if <token list2> is found inside <token list1>.
+%   Tests if <token list_2> is found inside <token list_1>.
 %   The \meta{token list} cannot contain the tokens |{|, |}| or |#|
 %   (assuming the usual \TeX{} category codes apply).
 % \end{function}
@@ -430,8 +441,8 @@
 %   Tests if the content of the \meta{tl~var} consists of a single item,
 %   \emph{i.e.}~is either a single normal token (excluding spaces,
 %   and brace tokens) or a single brace group, surrounded by optional
-%   spaces on both sides. In other words, such a token list has length
-%   $1$ according to \cs{tl_length:N}.
+%   spaces on both sides. In other words, such a token list has token count
+%   $1$ according to \cs{tl_count:N}.
 % \end{function}
 %
 % \begin{function}[updated = 2011-08-13, EXP,pTF]{\tl_if_single:n}
@@ -442,22 +453,33 @@
 %   Tests if the token list has exactly one item, \emph{i.e.}~is either
 %   a single normal token or a single brace group, surrounded by
 %   optional spaces on both sides. In other words, such a token list
-%   has length $1$ according to \cs{tl_length:n}.
+%   has token count $1$ according to \cs{tl_count:n}.
 % \end{function}
 %
-% \begin{function}[added = 2011-08-11,EXP,pTF]{\tl_if_single_token:n}
+% \begin{function}[added = 2012-06-03, EXP]{\tl_case:Nnn, \tl_case:cnn}
 %   \begin{syntax}
-%   \cs{tl_if_single_token_p:n} \Arg{token list}
-%   \cs{tl_if_single_token:nTF} \Arg{token list} \Arg{true code} \Arg{false code}
+%     \cs{tl_case:Nnn} \meta{test token list variable} \\
+%     ~~"{" \\
+%     ~~~~\meta{token list variable case_1} \Arg{code case_1} \\
+%     ~~~~\meta{token list variable case_2} \Arg{code case_2} \\
+%     ~~~~\ldots \\
+%     ~~~~\meta{token list variable case_n} \Arg{code case_n} \\
+%     ~~"}" \\
+%     ~~\Arg{else code}
 %   \end{syntax}
-%   Tests if the token list consists of exactly one token, \emph{i.e.}~is
-%   either a single space character or a single \enquote{normal} token.
-%   Token groups (|{|\ldots|}|) are not single tokens.
+%   This function compares the \meta{test token list variable} in turn
+%   with each of the \meta{token list variable cases}. If the two
+%   are equal (as described for
+%   \cs{tl_if_eq:nnTF}
+%   then the associated \meta{code} is left in the input
+%   stream. If none of the tests are \texttt{true} then the
+%   \texttt{else code} will be left in the input stream.
 % \end{function}
 %
 % \section{Mapping to token lists}
 %
-% \begin{function}[rEXP]{\tl_map_function:NN, \tl_map_function:cN}
+% \begin{function}[updated = 2012-06-29, rEXP]
+%   {\tl_map_function:NN, \tl_map_function:cN}
 %   \begin{syntax}
 %     \cs{tl_map_function:NN} \meta{tl~var} \meta{function}
 %   \end{syntax}
@@ -468,7 +490,7 @@
 %   \texttt{n}-type arguments. See also \cs{tl_map_function:nN}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\tl_map_function:nN}
+% \begin{function}[updated = 2012-06-29, rEXP]{\tl_map_function:nN}
 %   \begin{syntax}
 %     \cs{tl_map_function:nN} \meta{token list} \meta{function}
 %   \end{syntax}
@@ -479,7 +501,8 @@
 %   \texttt{n}-type arguments. See also \cs{tl_map_function:NN}.
 % \end{function}
 %
-% \begin{function}{\tl_map_inline:Nn, \tl_map_inline:cn}
+% \begin{function}[updated = 2012-06-29]
+%   {\tl_map_inline:Nn, \tl_map_inline:cn}
 %   \begin{syntax}
 %     \cs{tl_map_inline:Nn} \meta{tl~var} \Arg{inline function}
 %   \end{syntax}
@@ -489,7 +512,7 @@
 %   inside another. See also \cs{tl_map_function:Nn}.
 % \end{function}
 %
-% \begin{function}{\tl_map_inline:nn}
+% \begin{function}[updated = 2012-06-29]{\tl_map_inline:nn}
 %   \begin{syntax}
 %     \cs{tl_map_inline:nn} \meta{token list} \Arg{inline function}
 %   \end{syntax}
@@ -499,7 +522,8 @@
 %   inside another. See also \cs{tl_map_function:nn}.
 % \end{function}
 %
-% \begin{function}{\tl_map_variable:NNn, \tl_map_variable:cNn}
+% \begin{function}[updated = 2012-06-29]
+%   {\tl_map_variable:NNn, \tl_map_variable:cNn}
 %   \begin{syntax}
 %     \cs{tl_map_variable:NNn} \meta{tl~var} \meta{variable} \Arg{function}
 %   \end{syntax}
@@ -510,7 +534,7 @@
 %   \cs{tl_map_inline:Nn}.
 % \end{function}
 %
-% \begin{function}{\tl_map_variable:nNn}
+% \begin{function}[updated = 2012-06-29]{\tl_map_variable:nNn}
 %   \begin{syntax}
 %     \cs{tl_map_variable:nNn} \meta{token list} \meta{variable} \Arg{function}
 %   \end{syntax}
@@ -521,7 +545,7 @@
 %   \cs{tl_map_inline:nn}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\tl_map_break:}
+% \begin{function}[updated = 2012-06-29, rEXP]{\tl_map_break:}
 %   \begin{syntax}
 %     \cs{tl_map_break:}
 %   \end{syntax}
@@ -540,6 +564,40 @@
 %   \end{verbatim}
 %   Use outside of a \cs{tl_map_\ldots} scenario will lead low
 %   level \TeX{} errors.
+%   \begin{texnote}
+%     When the mapping is broken, additional tokens may be inserted by the
+%     internal macro \cs{__prg_break_point:Nn} before the \meta{tokens} are
+%     inserted into the input stream.
+%     This will depend on the design of the mapping function.
+%   \end{texnote}
+% \end{function}
+%
+% \begin{function}[updated = 2012-06-29, rEXP]{\tl_map_break:n}
+%   \begin{syntax}
+%     \cs{tl_map_break:n} \Arg{tokens}
+%   \end{syntax}
+%   Used to terminate a \cs{tl_map_\ldots} function before all
+%   entries in the \meta{token list variable} have been processed, inserting
+%   the \meta{tokens} after the mapping has ended. This will
+%   normally take place within a conditional statement, for example
+%   \begin{verbatim}
+%     \tl_map_inline:Nn \l_my_tl
+%       {
+%         \str_if_eq:nnTF { #1 } { bingo }
+%           { \tl_map_break:n { <tokens> } }
+%           {
+%             % Do something useful
+%           }
+%       }
+%   \end{verbatim}
+%   Use outside of a \cs{tl_map_\ldots} scenario will lead to low
+%   level \TeX{} errors.
+%   \begin{texnote}
+%     When the mapping is broken, additional tokens may be inserted by the
+%     internal macro \cs{__prg_break_point:Nn} before the \meta{tokens} are
+%     inserted into the input stream.
+%     This will depend on the design of the mapping function.
+%   \end{texnote}
 % \end{function}
 %
 % \section{Using token lists}
@@ -564,7 +622,8 @@
 %   in the input stream. Note that this function requires only a single
 %   expansion.
 %   \begin{texnote}
-%     This is the \eTeX{} primitive \tn{detokenize}.
+%     This is the \eTeX{} primitive \tn{detokenize}.  Hence its argument
+%     \emph{must} be given within braces.
 %   \end{texnote}
 % \end{function}
 %
@@ -580,28 +639,28 @@
 %
 % \section{Working with the content of token lists}
 %
-% \begin{function}[updated = 2011-08-13, EXP]
-%   {\tl_length:n, \tl_length:V, \tl_length:o}
+% \begin{function}[added = 2012-05-13, EXP]
+%   {\tl_count:n, \tl_count:V, \tl_count:o}
 %   \begin{syntax}
-%     \cs{tl_length:n} \Arg{tokens}
+%     \cs{tl_count:n} \Arg{tokens}
 %   \end{syntax}
 %   Counts the number of \meta{items} in \meta{tokens} and leaves this
 %   information in the input stream. Unbraced tokens count as one
 %   element as do each token group (|{|\ldots|}|). This process will
 %   ignore any unprotected spaces within \meta{tokens}. See also
-%   \cs{tl_length:N}. This function requires three expansions,
+%   \cs{tl_count:N}. This function requires three expansions,
 %   giving an \meta{integer denotation}.
 % \end{function}
 %
-% \begin{function}[updated = 2011-08-13, EXP]{\tl_length:N, \tl_length:c}
+% \begin{function}[added = 2012-05-13, EXP]{\tl_count:N, \tl_count:c}
 %   \begin{syntax}
-%     \cs{tl_length:N} \Arg{tl~var}
+%     \cs{tl_count:N} \Arg{tl~var}
 %   \end{syntax}
 %   Counts the number of token groups in the \meta{tl~var}
 %   and leaves this information in the input stream. Unbraced tokens
 %   count as one element as do each token group (|{|\ldots|}|). This
 %   process will ignore any unprotected spaces within \meta{tokens}.
-%   See also \cs{tl_length:n}. This function requires three expansions,
+%   See also \cs{tl_count:n}. This function requires three expansions,
 %   giving an \meta{integer denotation}.
 % \end{function}
 %
@@ -611,8 +670,8 @@
 %     \cs{tl_reverse:n} \Arg{token list}
 %   \end{syntax}
 %   Reverses the order of the \meta{items} in the \meta{token list},
-%   so that \meta{item1}\meta{item2}\meta{item3} \ldots \meta{item$_n$}
-%   becomes \meta{item$_n$}\ldots \meta{item3}\meta{item2}\meta{item1}.
+%   so that \meta{item_1}\meta{item_2}\meta{item_3} \ldots \meta{item_n}
+%   becomes \meta{item_n}\ldots \meta{item_3}\meta{item_2}\meta{item_1}.
 %   This process will preserve unprotected space within the
 %   \meta{token list}. Tokens are not reversed within braced token
 %   groups, which keep their outer set of braces.
@@ -633,8 +692,8 @@
 %     \cs{tl_reverse:N} \Arg{tl~var}
 %   \end{syntax}
 %   Reverses the order of the \meta{items} stored in \meta{tl~var}, so
-%   that \meta{item1}\meta{item2}\meta{item3} \ldots \meta{item$_n$}
-%   becomes \meta{item$_n$}\ldots \meta{item3}\meta{item2}\meta{item1}.
+%   that \meta{item_1}\meta{item_2}\meta{item_3} \ldots \meta{item_n}
+%   becomes \meta{item_n}\ldots \meta{item_3}\meta{item_2}\meta{item_1}.
 %   This process will preserve unprotected spaces within the
 %   \meta{token list variable}. Braced token groups are copied without
 %   reversing the order of tokens, but keep the outer set of braces.
@@ -646,8 +705,8 @@
 %     \cs{tl_reverse_items:n} \Arg{token list}
 %   \end{syntax}
 %   Reverses the order of the \meta{items} stored in \meta{tl~var},
-%   so that \Arg{item_1}\Arg{item_2}\Arg{item_3} \ldots \Arg{item$_n$}
-%   becomes \Arg{item$_n$} \ldots{} \Arg{item_3}\Arg{item_2}\Arg{item_1}.
+%   so that \Arg{item_1}\Arg{item_2}\Arg{item_3} \ldots \Arg{item_n}
+%   becomes \Arg{item_n} \ldots{} \Arg{item_3}\Arg{item_2}\Arg{item_1}.
 %   This process will remove any unprotected space within the
 %   \meta{token list}. Braced token groups are copied without
 %   reversing the order of tokens, and keep the outer set of braces.
@@ -662,14 +721,14 @@
 %   \end{texnote}
 % \end{function}
 %
-% \begin{function}[added = 2011-07-09, updated = 2011-08-13, EXP]
+% \begin{function}[added = 2011-07-09, updated = 2012-06-25, EXP]
 %   {\tl_trim_spaces:n}
 %   \begin{syntax}
 %     \cs{tl_trim_spaces:n} \meta{token list}
 %   \end{syntax}
 %   Removes any leading and trailing explicit space characters
 %   from the \meta{token list} and leaves the result in the input
-%   stream. This process requires two expansions.
+%   stream.
 %   \begin{texnote}
 %     The result is returned within the \tn{unexpanded}
 %     primitive (\cs{exp_not:n}), which means that the token
@@ -793,78 +852,75 @@
 %   nothing is left in the input stream.
 % \end{function}
 %
-% \begin{function}[updated = 2011-08-10, EXP,pTF]{\tl_if_head_eq_catcode:nN}
+% \begin{function}[updated = 2012-07-09, EXP, pTF]{\tl_if_head_eq_catcode:nN}
 %   \begin{syntax}
 %     \cs{tl_if_head_eq_catcode_p:nN} \Arg{token list} \meta{test token}
 %     \cs{tl_if_head_eq_catcode:nNTF} \Arg{token list} \meta{test token}
 %     ~~\Arg{true code} \Arg{false code}
 %   \end{syntax}
-%   Tests if the first \meta{token} in the \meta{token list} has the same
-%   category code as the \meta{test token}. In the case where
-%   \meta{token list} is empty, its head is considered to be \cs{q_nil},
-%   and the test will be true if \meta{test token} is a control sequence.
+%   Tests if the first \meta{token} in the \meta{token list} has the
+%   same category code as the \meta{test token}.  In the case where the
+%   \meta{token list} is empty, the test will always be \texttt{false}.
 % \end{function}
 %
-% \begin{function}[updated = 2011-08-10, EXP,pTF]
+% \begin{function}[updated = 2012-07-09, EXP, pTF]
 %   {\tl_if_head_eq_charcode:nN, \tl_if_head_eq_charcode:fN}
 %   \begin{syntax}
 %     \cs{tl_if_head_eq_charcode_p:nN} \Arg{token list} \meta{test token}
 %     \cs{tl_if_head_eq_charcode:nNTF} \Arg{token list} \meta{test token}
 %     ~~\Arg{true code} \Arg{false code}
 %   \end{syntax}
-%   Tests if the first \meta{token} in the \meta{token list} has the same
-%   character code as the \meta{test token}. In the case where
-%   \meta{token list} is empty, its head is considered to be \cs{q_nil},
-%   and the test will be true if \meta{test token} is a control sequence.
+%   Tests if the first \meta{token} in the \meta{token list} has the
+%   same character code as the \meta{test token}.  In the case where the
+%   \meta{token list} is empty, the test will always be \texttt{false}.
 % \end{function}
 %
-% \begin{function}[updated = 2011-08-10, EXP,pTF]{\tl_if_head_eq_meaning:nN}
+% \begin{function}[updated = 2012-07-09, EXP, pTF]{\tl_if_head_eq_meaning:nN}
 %   \begin{syntax}
 %     \cs{tl_if_head_eq_meaning_p:nN} \Arg{token list} \meta{test token}
 %     \cs{tl_if_head_eq_meaning:nNTF} \Arg{token list} \meta{test token}
 %     ~~\Arg{true code} \Arg{false code}
 %   \end{syntax}
-%   Tests if the first \meta{token} in the \meta{token list} has the same
-%   meaning as the \meta{test token}. In the case where \meta{token list}
-%   is empty, its head is considered to be \cs{q_nil}, and the test will
-%   be true if \meta{test token} has the same meaning as \cs{q_nil}.
+%   Tests if the first \meta{token} in the \meta{token list} has the
+%   same meaning as the \meta{test token}.  In the case where
+%   \meta{token list} is empty, the test will always be \texttt{false}.
 % \end{function}
 %
-% \begin{function}[updated = 2011-08-11, EXP,pTF]{\tl_if_head_group:n}
+% \begin{function}[added = 2012-07-08, EXP, pTF]{\tl_if_head_is_group:n}
 %   \begin{syntax}
-%     \cs{tl_if_head_group_p:n} \Arg{token list}
-%     \cs{tl_if_head_group:nTF} \Arg{token list} \Arg{true code} \Arg{false code}
+%     \cs{tl_if_head_is_group_p:n} \Arg{token list}
+%     \cs{tl_if_head_is_group:nTF} \Arg{token list} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   Tests if the first \meta{token} in the \meta{token list}
 %   is an explicit begin-group character (with category code~1
 %   and any character code), in other words, if the \meta{token list}
-%   starts with a brace group. In particular, the test is false
+%   starts with a brace group. In particular, the test is \texttt{false}
 %   if the \meta{token list} starts with an implicit token such as
 %   \cs{c_group_begin_token}, or if it empty.
 %   This function is useful to implement actions on token lists on
 %   a token by token basis.
 % \end{function}
 %
-% \begin{function}[added = 2011-08-11,EXP,pTF]{\tl_if_head_N_type:n}
+% \begin{function}[added = 2012-07-08, EXP, pTF]{\tl_if_head_is_N_type:n}
 %   \begin{syntax}
-%     \cs{tl_if_head_N_type_p:n} \Arg{token list}
-%     \cs{tl_if_head_N_type:nTF} \Arg{token list} \Arg{true code} \Arg{false code}
+%     \cs{tl_if_head_is_N_type_p:n} \Arg{token list}
+%     \cs{tl_if_head_is_N_type:nTF} \Arg{token list} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   Tests if the first \meta{token} in the \meta{token list}
 %   is a normal \texttt{N}-type argument. In other words,
 %   it is neither an explicit space character (with category code~10
 %   and character code~32) nor an explicit begin-group character
 %   (with category code~1 and any character code). An empty
-%   argument yields false, as it does not have a \enquote{normal}
+%   argument yields \texttt{false}, as it does not have a \enquote{normal}
 %   first token.
 %   This function is useful to implement actions on token lists on
 %   a token by token basis.
 % \end{function}
 %
-% \begin{function}[updated = 2011-08-11,EXP,pTF]{\tl_if_head_space:n}
+% \begin{function}[updated = 2012-07-08, EXP, pTF]{\tl_if_head_is_space:n}
 %   \begin{syntax}
-%     \cs{tl_if_head_space_p:n} \Arg{token list}
-%     \cs{tl_if_head_space:nTF} \Arg{token list} \Arg{true code} \Arg{false code}
+%     \cs{tl_if_head_is_space_p:n} \Arg{token list}
+%     \cs{tl_if_head_is_space:nTF} \Arg{token list} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %^^A We need to add a discussion of
 %^^A explicit vs implicit tokens somewhere in the doc.
@@ -872,7 +928,7 @@
 %   is an explicit space character (with category code~$10$
 %   and character code~$32$). If \meta{token list} starts with
 %   an implicit token such as \cs{c_space_token}, the test
-%   will yield false, as well as if the argument is empty.
+%   will yield \texttt{false}, as well as if the argument is empty.
 %   This function is useful to implement actions on token lists on
 %   a token by token basis.
 %   \begin{texnote}
@@ -942,89 +998,22 @@
 %   code and so should only be used for short-term storage.
 % \end{variable}
 %
-% \section{Experimental token list functions}
-%
-% \begin{function}[added = 2012-01-08, EXP]{\tl_reverse_tokens:n}
-%   \begin{syntax}
-%     \cs{tl_reverse_tokens:n} \Arg{tokens}
-%   \end{syntax}
-%   This function, which works directly on \TeX{} tokens, reverses
-%   the order of the \meta{tokens}: the first will be the last and
-%   the last will become first. Spaces are preserved. The reversal
-%   also operates within brace groups, but the braces themselves
-%   are not exchanged, as this would lead to an unbalanced token
-%   list. For instance, \cs{tl_reverse_tokens:n} |{a~{b()}}|
-%   leaves |{)(b}~a| in the input stream. This function requires
-%   two steps of expansion.
-%   \begin{texnote}
-%     The result is returned within the \tn{unexpanded}
-%     primitive (\cs{exp_not:n}), which means that the token
-%     list will not expand further when appearing in an x-type
-%     argument expansion.
-%   \end{texnote}
-% \end{function}
-%
-% \begin{function}[added = 2011-08-11, EXP]{\tl_length_tokens:n}
-%   \begin{syntax}
-%     \cs{tl_length_tokens:n} \Arg{tokens}
-%   \end{syntax}
-%   Counts the number of \TeX{} tokens in the \meta{tokens} and leaves
-%   this information in the input stream. Every token, including spaces and
-%   braces, contributes one to the total; thus for instance, the length of
-%   |a~{bc}| is $6$.
-%   This function requires three expansions,
-%   giving an \meta{integer denotation}.
-% \end{function}
-%
-% \begin{function}[added = 2012-01-08, EXP]
-%   {\tl_expandable_uppercase:n,\tl_expandable_lowercase:n}
-%   \begin{syntax}
-%     \cs{tl_expandable_uppercase:n} \Arg{tokens}
-%     \cs{tl_expandable_lowercase:n} \Arg{tokens}
-%   \end{syntax}
-%   The \cs{tl_expandable_uppercase:n} function works through all of
-%   the \meta{tokens}, replacing characters in the range |a|--|z|
-%   (with arbitrary category code) by the corresponding letter
-%   in the range |A|--|Z|, with category code $11$ (letter). Similarly,
-%   \cs{tl_expandable_lowercase:n} replaces characters in the range
-%   |A|--|Z| by letters in the range |a|--|z|, and leaves other tokens
-%   unchanged. This function requires two steps of expansion.
-%   \begin{texnote}
-%     Begin-group and end-group characters are normalized and become
-%     |{| and |}|, respectively.
-%     The result is returned within the \tn{unexpanded}
-%     primitive (\cs{exp_not:n}), which means that the token
-%     list will not expand further when appearing in an x-type
-%     argument expansion.
-%   \end{texnote}
-% \end{function}
+% \section{Internal functions}
 %
-% \begin{function}[added = 2011-11-21, updated = 2012-01-08, EXP]
-%   {\tl_item:nn, \tl_item:Nn, \tl_item:cn}
+% \begin{function}{\__tl_trim_spaces:nn}
 %   \begin{syntax}
-%     \cs{tl_item:nn} \Arg{token list} \Arg{integer expression}
+%     \cs{__tl_trim_spaces:nn} |{ \q_mark| \meta{token list} |}| \Arg{continuation}
 %   \end{syntax}
-%   Indexing items in the \meta{token list} from $0$ on the left, this
-%   function will evaluate the \meta{integer expression} and leave the
-%   appropriate item from the \meta{token list} in the input stream.
-%   If the \meta{integer expression} is negative, indexing occurs from
-%   the right of the token list, starting at $-1$ for the right-most item.
-%   If the index is out of bounds, then thr function expands to nothing.
-%   \begin{texnote}
-%     The result is returned within the \tn{unexpanded}
-%     primitive (\cs{exp_not:n}), which means that the \meta{item}
-%     will not expand further when appearing in an x-type
-%     argument expansion.
-%   \end{texnote}
+%   This function removes all leading and trailing explicit space
+%   characters from the \meta{token list}, and expands to the
+%   \meta{continuation}, followed by a brace group containing
+%   \cs{use_none:n} \cs{q_mark} \meta{trimmed token list}.  For
+%   instance, \cs{tl_trim_spaces:n} is implemented by taking the
+%   \meta{continuation} to be \cs{exp_not:o}, and the \texttt{o}-type
+%   expansion removes the \cs{q_mark}.  This function is also used in
+%   \pkg{l3clist}.
 % \end{function}
 %
-% \section{Internal functions}
-%
-% \begin{variable}{\q_tl_act_mark,\q_tl_act_stop}
-%   Quarks which are only used for the particular purposes of
-%   \cs{tl_act_...} functions.
-% \end{variable}
-%
 % \end{documentation}
 %
 % \begin{implementation}
@@ -1036,10 +1025,14 @@
 %    \end{macrocode}
 %
 %    \begin{macrocode}
+%<@@=tl>
+%    \end{macrocode}
+%
+%    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
@@ -1055,7 +1048,7 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \tl_new:N #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \cs_gset_eq:NN #1 \c_empty_tl
   }
 \cs_generate_variant:Nn \tl_new:N { c }
@@ -1067,12 +1060,12 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \tl_const:Nn #1#2
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \cs_gset_nopar:Npx #1 { \exp_not:n {#2} }
   }
 \cs_new_protected:Npn \tl_const:Nx #1#2
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \cs_gset_nopar:Npx #1 {#2}
   }
 \cs_generate_variant:Nn \tl_const:Nn { c }
@@ -1134,6 +1127,20 @@
 % \end{macro}
 % \end{macro}
 %
+% \begin{macro}{\tl_concat:NNN, \tl_concat:ccc}
+% \begin{macro}{\tl_gconcat:NNN, \tl_gconcat:ccc}
+%   Concatenating token lists is easy.
+%    \begin{macrocode}
+\cs_new_protected:Npn \tl_concat:NNN #1#2#3
+  { \tl_set:Nx #1 { \exp_not:o {#2} \exp_not:o {#3} } }
+\cs_new_protected:Npn \tl_gconcat:NNN #1#2#3
+  { \tl_gset:Nx #1 { \exp_not:o {#2} \exp_not:o {#3} } }
+\cs_generate_variant:Nn \tl_concat:NNN  { ccc }
+\cs_generate_variant:Nn \tl_gconcat:NNN { ccc }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
 % \begin{macro}[pTF]{\tl_if_exist:N, \tl_if_exist:c}
 %   Copies of the \texttt{cs} functions defined in \pkg{l3basics}.
 %    \begin{macrocode}
@@ -1148,6 +1155,37 @@
 %    \end{macrocode}
 % \end{macro}
 %
+% \subsection{Constant token lists}
+%
+% \begin{variable}{\c_job_name_tl}
+%   Inherited from the \LaTeX3 name for the primitive: this needs to
+%   actually contain the text of the job name rather than the name of
+%   the primitive, of course. \LuaTeX{} does not quote file names containing
+%   spaces, whereas \pdfTeX{} and \XeTeX{} do. So there may be a correction to
+%   make in the \LuaTeX{} case.
+%    \begin{macrocode}
+%<*initex>
+\tex_everyjob:D \exp_after:wN
+  {
+    \tex_the:D \tex_everyjob:D
+    \luatex_if_engine:T
+      {
+        \lua_now:x
+          { dofile ( assert ( kpse.find_file ("lualatexquotejobname.lua" ) ) ) }
+      }
+  }
+%</initex>
+\tl_const:Nx \c_job_name_tl { \tex_jobname:D }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\c_space_tl}
+%   A space as a token list (as opposed to as a character).
+%    \begin{macrocode}
+\tl_const:Nn \c_space_tl { ~ }
+%    \end{macrocode}
+% \end{variable}
+%
 % \subsection{Adding to token list variables}
 %
 % \begin{macro}
@@ -1273,7 +1311,7 @@
 %
 % \subsection{Reassigning token list category codes}
 %
-% \begin{variable}{\c_tl_rescan_marker_tl}
+% \begin{variable}{\c_@@_rescan_marker_tl}
 %   The rescanning code needs a special token list containing the same
 %   character with two different category codes. This is set up here,
 %   while the detail is described below.
@@ -1286,7 +1324,7 @@
 \tex_lowercase:D
   {
     \group_end:
-    \tl_const:Nn \c_tl_rescan_marker_tl { A B }
+    \tl_const:Nn \c_@@_rescan_marker_tl { A B }
   }
 %    \end{macrocode}
 % \end{variable}
@@ -1302,8 +1340,8 @@
 %     \tl_gset_rescan:cnn, \tl_gset_rescan:cno, \tl_gset_rescan:cnx
 %   }
 % \begin{macro}{\tl_rescan:nn}
-% \begin{macro}[aux]{\tl_set_rescan_aux:NNnn}
-% \begin{macro}[aux]{\tl_rescan_aux:w}
+% \begin{macro}[aux]{\@@_set_rescan:NNnn}
+% \begin{macro}[aux]{\@@_rescan:w}
 %   The idea here is to deal cleanly with the problem that
 %   \tn{scantokens} treats the argument as a file, and without
 %   the correct settings a \TeX{} error occurs:
@@ -1322,15 +1360,15 @@
 %   \enquote{unprintable}.
 %    \begin{macrocode}
 \cs_new_protected_nopar:Npn \tl_set_rescan:Nnn
-  { \tl_set_rescan_aux:NNnn \tl_set:Nn }
+  { \@@_set_rescan:NNnn \tl_set:Nn }
 \cs_new_protected_nopar:Npn \tl_gset_rescan:Nnn
-  { \tl_set_rescan_aux:NNnn \tl_gset:Nn }
+  { \@@_set_rescan:NNnn \tl_gset:Nn }
 \cs_new_protected_nopar:Npn \tl_rescan:nn
-  { \tl_set_rescan_aux:NNnn \prg_do_nothing: \use:n }
-\cs_new_protected:Npn \tl_set_rescan_aux:NNnn #1#2#3#4
+  { \@@_set_rescan:NNnn \prg_do_nothing: \use:n }
+\cs_new_protected:Npn \@@_set_rescan:NNnn #1#2#3#4
   {
     \group_begin:
-      \exp_args:No \etex_everyeof:D { \c_tl_rescan_marker_tl \exp_not:N }
+      \exp_args:No \etex_everyeof:D { \c_@@_rescan_marker_tl \exp_not:N }
       \tex_endlinechar:D \c_minus_one
       \tex_newlinechar:D \c_minus_one
       #3
@@ -1339,7 +1377,7 @@
           \group_end:
           #1 \exp_not:N #2
             {
-              \exp_after:wN \tl_rescan_aux:w
+              \exp_after:wN \@@_rescan:w
               \exp_after:wN \prg_do_nothing:
               \etex_scantokens:D {#4}
             }
@@ -1347,8 +1385,8 @@
   }
 \use:x
   {
-    \cs_new:Npn \exp_not:N \tl_rescan_aux:w ##1
-      \c_tl_rescan_marker_tl
+    \cs_new:Npn \exp_not:N \@@_rescan:w ##1
+      \c_@@_rescan_marker_tl
       { \exp_not:N \exp_not:o { ##1 } }
   }
 \cs_generate_variant:Nn \tl_set_rescan:Nnn  {     Nno , Nnx }
@@ -1380,21 +1418,21 @@
 % \begin{macro}{\tl_greplace_all:Nnn, \tl_greplace_all:cnn}
 % \begin{macro}{\tl_replace_once:Nnn, \tl_replace_once:cnn}
 % \begin{macro}{\tl_greplace_once:Nnn, \tl_greplace_once:cnn}
-% \begin{macro}[aux]{\tl_replace_aux:NNNnn, \tl_replace_aux_ii:w}
-% \begin{macro}[aux]{\tl_replace_all_aux:, \tl_replace_once_aux:}
-% \begin{macro}[aux]{\tl_replace_once_aux_end:w}
-%   All of the replace functions are based on \cs{tl_replace_aux:NNNnn},
+% \begin{macro}[aux]{\@@_replace:NNNnn, \@@_replace:w}
+% \begin{macro}[aux]{\@@_replace_all:, \@@_replace_once:}
+% \begin{macro}[aux]{\@@_replace_once_end:w}
+%   All of the replace functions are based on \cs{@@_replace:NNNnn},
 %   whose arguments are: \meta{function}, \cs{tl_(g)set:Nx}, \meta{tl~var},
 %   \meta{search tokens}, \meta{replacement tokens}.
 %    \begin{macrocode}
 \cs_new_protected_nopar:Npn \tl_replace_once:Nnn
-  { \tl_replace_aux:NNNnn \tl_replace_once_aux: \tl_set:Nx }
+  { \@@_replace:NNNnn \@@_replace_once: \tl_set:Nx }
 \cs_new_protected_nopar:Npn \tl_greplace_once:Nnn
-  { \tl_replace_aux:NNNnn \tl_replace_once_aux: \tl_gset:Nx }
+  { \@@_replace:NNNnn \@@_replace_once: \tl_gset:Nx }
 \cs_new_protected_nopar:Npn \tl_replace_all:Nnn
-  { \tl_replace_aux:NNNnn \tl_replace_all_aux: \tl_set:Nx }
+  { \@@_replace:NNNnn \@@_replace_all: \tl_set:Nx }
 \cs_new_protected_nopar:Npn \tl_greplace_all:Nnn
-  { \tl_replace_aux:NNNnn \tl_replace_all_aux: \tl_gset:Nx }
+  { \@@_replace:NNNnn \@@_replace_all: \tl_gset:Nx }
 \cs_generate_variant:Nn \tl_replace_once:Nnn  { c }
 \cs_generate_variant:Nn \tl_greplace_once:Nnn { c }
 \cs_generate_variant:Nn \tl_replace_all:Nnn   { c }
@@ -1402,34 +1440,34 @@
 %    \end{macrocode}
 %   The idea is easier to understand by considering the case of
 %   \cs{tl_replace_all:Nnn}. The replacement happens within an
-%   \texttt{x}-type expansion. We use an auxiliary function \cs{tl_tmp:w},
+%   \texttt{x}-type expansion. We use an auxiliary function \cs{@@_tmp:w},
 %   which essentially replaces the next \meta{search tokens} by
 %   \meta{replacement tokens}. To avoid runaway arguments,
-%   we expand something like \cs{tl_tmp:w} \meta{token list} \cs{q_mark}
+%   we expand something like \cs{@@_tmp:w} \meta{token list} \cs{q_mark}
 %   \meta{search tokens} \cs{q_stop}, repeating until the end. How do we
 %   detect that we have reached the last occurrence of \meta{search tokens}?
 %   The last replacement is characterized by the fact that the argument of
-%   \cs{tl_tmp:w} contains \cs{q_mark}. In the code below,
-%   \cs{tl_replace_aux_ii:w} takes an argument delimited by \cs{q_mark},
+%   \cs{@@_tmp:w} contains \cs{q_mark}. In the code below,
+%   \cs{@@_replace:w} takes an argument delimited by \cs{q_mark},
 %   and removes the following token. Before we reach the end, this gobbles
 %   \cs{q_mark} \cs{use_none_delimit_by_q_stop:w} which appear in the
-%   definition of \cs{tl_tmp:w}, and leaves the \meta{replacement tokens},
+%   definition of \cs{@@_tmp:w}, and leaves the \meta{replacement tokens},
 %   passed to \cs{exp_not:n}, to be included in the \texttt{x}-expanding
 %   definition. At the end, the first \cs{q_mark} is within the argument
-%   of \cs{tl_tmp:w}, and \cs{tl_replace_aux_ii:w} gobbles the second
+%   of \cs{@@_tmp:w}, and \cs{@@_replace:w} gobbles the second
 %   \cs{q_mark} as well, leaving \cs{use_none_delimit_by_q_stop:w},
 %   which ends the recursion cleanly.
 %    \begin{macrocode}
-\cs_new_protected:Npn \tl_replace_aux:NNNnn #1#2#3#4#5
+\cs_new_protected:Npn \@@_replace:NNNnn #1#2#3#4#5
   {
     \tl_if_empty:nTF {#4}
       {
-         \msg_kernel_error:nnx { tl } { empty-search-pattern }
+         \__msg_kernel_error:nnx { kernel } { empty-search-pattern }
            { \tl_to_str:n {#5} }
       }
       {
         \group_align_safe_begin:
-        \cs_set:Npx \tl_tmp:w ##1##2 #4
+        \cs_set:Npx \@@_tmp:w ##1##2 #4
           {
             ##2
             \exp_not:N \q_mark
@@ -1445,12 +1483,12 @@
           }
       }
   }
-\cs_new:Npn \tl_replace_aux_ii:w #1 \q_mark #2 { \exp_not:o {#1} }
+\cs_new:Npn \@@_replace:w #1 \q_mark #2 { \exp_not:o {#1} }
 %    \end{macrocode}
-%   The first argument of \cs{tl_tmp:w} is responsible for repeating
+%   The first argument of \cs{@@_tmp:w} is responsible for repeating
 %   the replacement in the case of \texttt{replace_all}, and stopping
 %   it early for \texttt{replace_once}. Note also that we build
-%   \cs{tl_tmp:w} within an \texttt{x}-expansion so that the
+%   \cs{@@_tmp:w} within an \texttt{x}-expansion so that the
 %   \meta{replacement tokens} can contain |#|. The second
 %   \cs{exp_not:n} ensures that the \meta{replacement tokens}
 %   are not expanded by \cs{tl_(g)set:Nx}.
@@ -1460,17 +1498,17 @@
 %   ensure that we don't lose braces in case the tokens between two
 %   occurrences of the \meta{search tokens} form a brace group.
 %    \begin{macrocode}
-\cs_new:Npn \tl_replace_all_aux:
+\cs_new_nopar:Npn \@@_replace_all:
   {
-    \exp_after:wN \tl_replace_aux_ii:w
-    \tl_tmp:w \tl_replace_all_aux: \prg_do_nothing:
+    \exp_after:wN \@@_replace:w
+    \@@_tmp:w \@@_replace_all: \prg_do_nothing:
   }
-\cs_new_nopar:Npn \tl_replace_once_aux:
+\cs_new_nopar:Npn \@@_replace_once:
   {
-    \exp_after:wN \tl_replace_aux_ii:w
-    \tl_tmp:w { \tl_replace_once_aux_end:w \prg_do_nothing: } \prg_do_nothing:
+    \exp_after:wN \@@_replace:w
+    \@@_tmp:w { \@@_replace_once_end:w \prg_do_nothing: } \prg_do_nothing:
   }
-\cs_new:Npn \tl_replace_once_aux_end:w #1 \q_mark #2 \q_stop
+\cs_new:Npn \@@_replace_once_end:w #1 \q_mark #2 \q_stop
   { \exp_not:o {#1} }
 %    \end{macrocode}
 % \end{macro}
@@ -1511,7 +1549,7 @@
 % \subsection{Token list conditionals}
 %
 % \begin{macro}[pTF]{\tl_if_blank:n,\tl_if_blank:V,\tl_if_blank:o}
-% \begin{macro}[aux]{\tl_if_blank_p_aux:NNw}
+% \begin{macro}[aux]{\@@_if_blank_p:NNw}
 %   \TeX{} skips spaces when reading a non-delimited arguments. Thus,
 %   a \meta{token list} is blank if and only if \cs{use_none:n}
 %   \meta{token list} |?| is empty. For performance reasons, we hard-code
@@ -1525,7 +1563,7 @@
 %   while \tn{escapechar} is a space or is unprintable.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \tl_if_blank:n #1 { p , T , F , TF }
-  { \tl_if_empty_return:o { \use_none:n #1 ? } }
+  { \@@_if_empty_return:o { \use_none:n #1 ? } }
 \cs_generate_variant:Nn \tl_if_blank_p:n { V }
 \cs_generate_variant:Nn \tl_if_blank:nT  { V }
 \cs_generate_variant:Nn \tl_if_blank:nF  { V }
@@ -1561,14 +1599,15 @@
 % \begin{macro}[pTF]{\tl_if_empty:n,\tl_if_empty:V}
 %   It would be tempting to just use |\if_meaning:w \q_nil #1 \q_nil| as
 %   a test since this works really well. However, it fails on a token
-%   list starting with |\q_nil| of course but more troubling is the
-%   case where argument is a complete conditional such as |\if_true:|
-%   a |\else:| b |\fi:| because then |\if_true:| is used by
-%   |\if_meaning:w|, the test turns out false, the |\else:| executes
-%   the false branch, the |\fi:| ends it and the |\q_nil| at the end
+%   list starting with \cs{q_nil} of course but more troubling is the
+%   case where argument is a complete conditional such as \cs{if_true:}
+%   a \cs{else:} b \cs{fi:} because then \cs{if_true:} is used by
+%   \cs{if_meaning:w}, the test turns out \texttt{false}, the \cs{else:}
+%   executes the \texttt{false} branch, the \cs{fi:} ends it and the
+%   \cs{q_nil} at the end
 %   starts executing\dots{} A safer route is to convert the entire
 %   token list into harmless characters first and then compare
-%   that. This way the test will even accept |\q_nil| as the first
+%   that. This way the test will even accept \cs{q_nil} as the first
 %   token.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \tl_if_empty:n #1 { p , TF , T , F }
@@ -1587,8 +1626,8 @@
 % \end{macro}
 %
 % \begin{macro}[pTF]{\tl_if_empty:o}
-% \begin{macro}[EXP,aux]{\tl_if_empty_return:o}
-%   The auxiliary function \cs{tl_if_empty_return:o} is for use
+% \begin{macro}[EXP,aux]{\@@_if_empty_return:o}
+%   The auxiliary function \cs{@@_if_empty_return:o} is for use
 %   in conditionals on token lists, which mostly reduce to testing
 %   if a given token list is empty after applying a simple function
 %   to it.
@@ -1598,7 +1637,7 @@
 %   Note that this works because \cs{tl_to_str:n} expands tokens
 %   that follow until reading a catcode $1$ (begin-group) token.
 %    \begin{macrocode}
-\cs_new:Npn \tl_if_empty_return:o #1
+\cs_new:Npn \@@_if_empty_return:o #1
   {
     \exp_after:wN \if_meaning:w \exp_after:wN \q_nil
       \tl_to_str:n \exp_after:wN {#1} \q_nil
@@ -1608,7 +1647,7 @@
     \fi:
   }
 \prg_new_conditional:Npnn \tl_if_empty:o #1 { p , TF , T , F }
-  { \tl_if_empty_return:o {#1} }
+  { \@@_if_empty_return:o {#1} }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1670,10 +1709,10 @@
 %
 % \begin{macro}[TF]{\tl_if_in:nn, \tl_if_in:Vn, \tl_if_in:on, \tl_if_in:no}
 %   Once more, the test relies on \cs{tl_to_str:n} for robustness.
-%   The function \cs{tl_tmp:w} removes tokens until the first occurrence
+%   The function \cs{@@_tmp:w} removes tokens until the first occurrence
 %   of |#2|. If this does not appear in |#1|, then the final |#2| is removed,
 %   leaving an empty token list. Otherwise some tokens remain, and the
-%   test is false. See \cs{tl_if_empty:n(TF)} for details on
+%   test is \texttt{false}. See \cs{tl_if_empty:n(TF)} for details on
 %   the emptyness test.
 %
 %   Special care is needed to treat correctly cases like
@@ -1685,8 +1724,8 @@
 %    \begin{macrocode}
 \prg_new_protected_conditional:Npnn \tl_if_in:nn #1#2 { T  , F , TF }
   {
-    \cs_set:Npn \tl_tmp:w ##1 #2 { }
-    \tl_if_empty:oTF { \tl_tmp:w #1 {} {} #2 }
+    \cs_set:Npn \@@_tmp:w ##1 #2 { }
+    \tl_if_empty:oTF { \@@_tmp:w #1 {} {} #2 }
       { \prg_return_false: } { \prg_return_true: }
   }
 \cs_generate_variant:Nn \tl_if_in:nnT  { V , o , no }
@@ -1695,27 +1734,73 @@
 %    \end{macrocode}
 % \end{macro}
 %
+% \begin{macro}[EXP,pTF]{\tl_if_single:N}
+%   Expand the token list and feed it to \cs{tl_if_single:n}.
+%    \begin{macrocode}
+\cs_new:Npn \tl_if_single_p:N { \exp_args:No \tl_if_single_p:n }
+\cs_new:Npn \tl_if_single:NT  { \exp_args:No \tl_if_single:nT  }
+\cs_new:Npn \tl_if_single:NF  { \exp_args:No \tl_if_single:nF  }
+\cs_new:Npn \tl_if_single:NTF { \exp_args:No \tl_if_single:nTF }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP,pTF]{\tl_if_single:n}
+%   A token list has exactly one item if it is either a single
+%   token surrounded by optional explicit spaces, or a single brace
+%   group surrounded by optional explicit spaces. The naive
+%   version of this test would do \cs{use_none:n} |#1|, and
+%   test if the result is empty. However, this will fail when
+%   the token list is empty. Furthermore, it does not allow optional
+%   trailing spaces.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \tl_if_single:n #1 { p , T , F , TF }
+  { \__str_if_eq_x_return:nn { \exp_not:o { \use_none:nn #1 ?? } } {?} }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\tl_case:Nnn, \tl_case:cnn}
+% \begin{macro}[aux, EXP]{\@@_case:Nw}
+% \begin{macro}[aux, EXP]{\@@_case_end:nw}
+%    \begin{macrocode}
+\cs_new:Npn \tl_case:Nnn #1#2#3
+  {
+    \tex_romannumeral:D
+    \@@_case:Nw #1 #2 #1 {#3} \q_recursion_stop
+  }
+\cs_new:Npn \@@_case:Nw #1#2#3
+  {
+    \tl_if_eq:NNTF #1 #2
+      { \@@_case_end:nw {#3} }
+      { \@@_case:Nw #1 }
+  }
+\cs_generate_variant:Nn \tl_case:Nnn { c }
+\cs_new_eq:NN \@@_case_end:nw \__prg_case_end:nw
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
 % \subsection{Mapping to token lists}
 %
 % \begin{macro}{\tl_map_function:nN}
 % \begin{macro}{\tl_map_function:NN, \tl_map_function:cN}
-% \begin{macro}[aux]{\tl_map_function_aux:Nn}
+% \begin{macro}[aux]{\@@_map_function:Nn}
 %   Expandable loop macro for token lists. These have the advantage of not
 %   needing to test if the argument is empty, because if it is, the stop
 %   marker will be read immediately and the loop terminated.
 %    \begin{macrocode}
 \cs_new:Npn \tl_map_function:nN #1#2
   {
-    \tl_map_function_aux:Nn #2 #1
+    \@@_map_function:Nn #2 #1
       \q_recursion_tail
-    \prg_break_point:n { }
+    \__prg_break_point:Nn \tl_map_break: { }
   }
 \cs_new_nopar:Npn \tl_map_function:NN
   { \exp_args:No \tl_map_function:nN }
-\cs_new:Npn \tl_map_function_aux:Nn #1#2
+\cs_new:Npn \@@_map_function:Nn #1#2
   {
-    \quark_if_recursion_tail_break:n {#2}
-    #1 {#2} \tl_map_function_aux:Nn #1
+    \__quark_if_recursion_tail_break:nN {#2} \tl_map_break:
+    #1 {#2} \@@_map_function:Nn #1
   }
 \cs_generate_variant:Nn \tl_map_function:NN { c }
 %    \end{macrocode}
@@ -1726,19 +1811,18 @@
 % \begin{macro}{\tl_map_inline:nn}
 % \begin{macro}{\tl_map_inline:Nn, \tl_map_inline:cn}
 %   The inline functions are straight forward by now. We use a little
-%   trick with the counter \cs{g_prg_map_int} to make
-%   them nestable. We can also make use of \cs{tl_map_function_aux:Nn}
+%   trick with the counter \cs{g__prg_map_int} to make
+%   them nestable. We can also make use of \cs{@@_map_function:Nn}
 %   from before.
 %    \begin{macrocode}
 \cs_new_protected:Npn \tl_map_inline:nn #1#2
   {
-    \int_gincr:N \g_prg_map_int
-    \cs_gset:cpn { tl_map_inline_ \int_use:N \g_prg_map_int :n }
-      ##1 {#2}
-    \exp_args:Nc \tl_map_function_aux:Nn
-      { tl_map_inline_ \int_use:N \g_prg_map_int :n }
+    \int_gincr:N \g__prg_map_int
+    \cs_gset:cpn { __prg_map_ \int_use:N \g__prg_map_int :w } ##1 {#2}
+    \exp_args:Nc \@@_map_function:Nn
+      { __prg_map_ \int_use:N \g__prg_map_int :w }
       #1 \q_recursion_tail
-    \prg_break_point:n { \int_gdecr:N \g_prg_map_int }
+    \__prg_break_point:Nn \tl_map_break: { \int_gdecr:N \g__prg_map_int }
   }
 \cs_new_protected:Npn \tl_map_inline:Nn
   { \exp_args:No \tl_map_inline:nn }
@@ -1749,25 +1833,25 @@
 %
 % \begin{macro}{\tl_map_variable:nNn}
 % \begin{macro}{\tl_map_variable:NNn, \tl_map_variable:cNn}
-% \begin{macro}[aux]{\tl_map_variable_aux:Nnn}
+% \begin{macro}[aux]{\@@_map_variable:Nnn}
 %   \cs{tl_map_variable:nNn} \meta{token list} \meta{temp} \meta{action}
 %   assigns
 %   \meta{temp} to each element and executes \meta{action}.
 %    \begin{macrocode}
 \cs_new_protected:Npn \tl_map_variable:nNn #1#2#3
   {
-    \tl_map_variable_aux:Nnn #2 {#3} #1
+    \@@_map_variable:Nnn #2 {#3} #1
       \q_recursion_tail
-    \prg_break_point:n { }
+    \__prg_break_point:Nn \tl_map_break: { }
   }
 \cs_new_protected_nopar:Npn \tl_map_variable:NNn
   { \exp_args:No \tl_map_variable:nNn }
-\cs_new_protected:Npn \tl_map_variable_aux:Nnn #1#2#3
+\cs_new_protected:Npn \@@_map_variable:Nnn #1#2#3
   {
     \tl_set:Nn #1 {#3}
-    \quark_if_recursion_tail_break:N #1
+    \__quark_if_recursion_tail_break:NN #1 \tl_map_break:
     \use:n {#2}
-    \tl_map_variable_aux:Nnn #1 {#2}
+    \@@_map_variable:Nnn #1 {#2}
   }
 \cs_generate_variant:Nn \tl_map_variable:NNn { c }
 %    \end{macrocode}
@@ -1777,10 +1861,12 @@
 %
 % \begin{macro}{\tl_map_break:}
 % \begin{macro}{\tl_map_break:n}
-%   The break statements are simply copies.
+%   The break statements use the general \cs{__prg_map_break:Nn}.
 %    \begin{macrocode}
-\cs_new_eq:NN \tl_map_break:  \prg_map_break:
-\cs_new_eq:NN \tl_map_break:n \prg_map_break:n
+\cs_new_nopar:Npn \tl_map_break:
+  { \__prg_map_break:Nn \tl_map_break: { } }
+\cs_new_nopar:Npn \tl_map_break:n
+  { \__prg_map_break:Nn \tl_map_break: }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1811,7 +1897,7 @@
 \cs_new:Npn \tl_use:N #1
   {
     \tl_if_exist:NTF #1 {#1}
-      { \msg_expandable_kernel_error:nnn { kernel } { bad-var } {#1} }
+      { \__msg_kernel_expandable_error:nnn { kernel } { bad-variable } {#1} }
   }
 \cs_generate_variant:Nn \tl_use:N { c }
 %    \end{macrocode}
@@ -1819,54 +1905,54 @@
 %
 % \subsection{Working with the contents of token lists}
 %
-% \begin{macro}{\tl_length:n, \tl_length:V, \tl_length:o}
-% \begin{macro}{\tl_length:N, \tl_length:c}
-% \begin{macro}[aux]{\tl_length_aux:n}
+% \begin{macro}{\tl_count:n, \tl_count:V, \tl_count:o}
+% \begin{macro}{\tl_count:N, \tl_count:c}
+% \begin{macro}[aux]{\@@_count:n}
 %   Count number of elements within a token list or token list
 %   variable. Brace groups within the list are read as a single
 %   element. Spaces are ignored.
-%   \cs{tl_length_aux:n} grabs the element and replaces it by |+1|.
+%   \cs{@@_count:n} grabs the element and replaces it by |+1|.
 %   The |0| to ensure it works on an empty list.
 %    \begin{macrocode}
-\cs_new:Npn \tl_length:n #1
+\cs_new:Npn \tl_count:n #1
   {
     \int_eval:n
-      { 0 \tl_map_function:nN {#1} \tl_length_aux:n }
+      { 0 \tl_map_function:nN {#1} \@@_count:n }
   }
-\cs_new:Npn \tl_length:N #1
+\cs_new:Npn \tl_count:N #1
   {
     \int_eval:n
-      { 0 \tl_map_function:NN #1 \tl_length_aux:n }
+      { 0 \tl_map_function:NN #1 \@@_count:n }
   }
-\cs_new:Npn \tl_length_aux:n #1 { + \c_one }
-\cs_generate_variant:Nn \tl_length:n { V , o }
-\cs_generate_variant:Nn \tl_length:N { c }
+\cs_new:Npn \@@_count:n #1 { + \c_one }
+\cs_generate_variant:Nn \tl_count:n { V , o }
+\cs_generate_variant:Nn \tl_count:N { c }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 % \end{macro}
 %
 % \begin{macro}{\tl_reverse_items:n}
-% \begin{macro}[aux]{\tl_reverse_items_aux:nwNwn}
-% \begin{macro}[aux]{\tl_reverse_items_aux:wn}
+% \begin{macro}[aux]{\@@_reverse_items:nwNwn}
+% \begin{macro}[aux]{\@@_reverse_items:wn}
 %    Reversal of a token list is done by taking one item at a time
 %    and putting it after \cs{q_stop}.
 %    \begin{macrocode}
 \cs_new:Npn \tl_reverse_items:n #1
   {
-    \tl_reverse_items_aux:nwNwn #1 ?
-      \q_mark \tl_reverse_items_aux:nwNwn
-      \q_mark \tl_reverse_items_aux:wn
+    \@@_reverse_items:nwNwn #1 ?
+      \q_mark \@@_reverse_items:nwNwn
+      \q_mark \@@_reverse_items:wn
       \q_stop { }
   }
-\cs_new:Npn \tl_reverse_items_aux:nwNwn #1 #2 \q_mark #3 #4 \q_stop #5
+\cs_new:Npn \@@_reverse_items:nwNwn #1 #2 \q_mark #3 #4 \q_stop #5
   {
     #3 #2
-      \q_mark \tl_reverse_items_aux:nwNwn
-      \q_mark \tl_reverse_items_aux:wn
+      \q_mark \@@_reverse_items:nwNwn
+      \q_mark \@@_reverse_items:wn
       \q_stop { {#1} #5 }
   }
-\cs_new:Npn \tl_reverse_items_aux:wn #1 \q_stop #2
+\cs_new:Npn \@@_reverse_items:wn #1 \q_stop #2
   { \exp_not:o { \use_none:nn #2 } }
 %    \end{macrocode}
 % \end{macro}
@@ -1879,78 +1965,237 @@
 %     \tl_trim_spaces:N, \tl_trim_spaces:c,
 %     \tl_gtrim_spaces:N, \tl_gtrim_spaces:c
 %   }
+%   Trimming spaces from around the input is deferred to an internal
+%   function whose first argument is the token list to trim, augmented
+%   by an initial \cs{q_mark}, and whose second argument is a
+%   \meta{continuation}, which will receive as a braced argument
+%   \cs{use_none:n} \cs{q_mark} \meta{trimmed token list}.  In the case
+%   at hand, we take \cs{exp_not:o} as our continuation, so that space
+%   trimming will behave correctly within an \texttt{x}-type expansion.
+%    \begin{macrocode}
+\cs_new:Npn \tl_trim_spaces:n #1
+  { \@@_trim_spaces:nn { \q_mark #1 } \exp_not:o }
+\cs_new_protected:Npn \tl_trim_spaces:N #1
+  { \tl_set:Nx #1 { \exp_args:No \tl_trim_spaces:n {#1} } }
+\cs_new_protected:Npn \tl_gtrim_spaces:N #1
+  { \tl_gset:Nx #1 { \exp_args:No \tl_trim_spaces:n {#1} } }
+\cs_generate_variant:Nn \tl_trim_spaces:N  { c }
+\cs_generate_variant:Nn \tl_gtrim_spaces:N { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[int]{\@@_trim_spaces:nn}
 % \begin{macro}[aux]
 %   {
-%     \tl_trim_spaces_aux_i:w, \tl_trim_spaces_aux_ii:w
-%     \tl_trim_spaces_aux_iii:w, \tl_trim_spaces_aux_iv:w
+%     \@@_trim_spaces_i:w, \@@_trim_spaces_ii:w
+%     \@@_trim_spaces_iii:w, \@@_trim_spaces_iv:w
 %   }
 %   Trimming spaces from around the input is done using delimited
 %   arguments and quarks, and to get spaces at odd places in the
-%   definitions, we nest those in \cs{tl_tmp:w}, which then receives
+%   definitions, we nest those in \cs{@@_tmp:w}, which then receives
 %   a single space as its argument: |#1| is \verb*+ +.
-%   Removing leading spaces is done with \cs{tl_trim_spaces_aux_i:w},
+%   Removing leading spaces is done with \cs{@@_trim_spaces_i:w},
 %   which loops until \cs{q_mark}\verb*+ + matches the end of the token
 %   list: then |##1| is the token list and |##3| is
-%   \cs{tl_trim_spaces_aux_ii:w}. This hands the relevant tokens to the
-%   loop \cs{tl_trim_spaces_aux_iii:w}, responsible for trimming
+%   \cs{@@_trim_spaces_ii:w}. This hands the relevant tokens to the
+%   loop \cs{@@_trim_spaces_iii:w}, responsible for trimming
 %   trailing spaces. The end is reached when \verb*+ + \cs{q_nil}
 %   matches the one present in the definition of \cs{tl_trim_spacs:n}.
-%   Then \cs{tl_trim_spaces_aux_iv:w} puts the token list into a group,
-%   as the argument of the initial \tn{unexpanded}.
-%   The \tn{unexpanded} here is used so that space trimming will
-%   behave correctly within an \texttt{x}-type expansion.
-%
-%   Some of the auxiliaries used in this code are also used
-%   in the \pkg{l3clist} module. Change with care.
+%   Then \cs{@@_trim_spaces_iv:w} puts the token list into a group,
+%   with \cs{use_none:n} placed there to gobble a lingering \cs{q_mark},
+%   and feeds this to the \meta{continuation}.
 %    \begin{macrocode}
-\cs_set:Npn \tl_tmp:w #1
+\cs_set:Npn \@@_tmp:w #1
   {
-    \cs_new:Npn \tl_trim_spaces:n ##1
+    \cs_new:Npn \@@_trim_spaces:nn ##1
       {
-        \etex_unexpanded:D
-          \tl_trim_spaces_aux_i:w
-          \q_mark
+        \@@_trim_spaces_i:w
           ##1
           \q_nil
           \q_mark #1 { }
-          \q_mark \tl_trim_spaces_aux_ii:w
-          \tl_trim_spaces_aux_iii:w
+          \q_mark \@@_trim_spaces_ii:w
+          \@@_trim_spaces_iii:w
           #1 \q_nil
-          \tl_trim_spaces_aux_iv:w
-          \q_stop
+          \@@_trim_spaces_iv:w
+        \q_stop
       }
-    \cs_new:Npn \tl_trim_spaces_aux_i:w ##1 \q_mark #1 ##2 \q_mark ##3
+    \cs_new:Npn \@@_trim_spaces_i:w ##1 \q_mark #1 ##2 \q_mark ##3
       {
         ##3
-        \tl_trim_spaces_aux_i:w
+        \@@_trim_spaces_i:w
         \q_mark
         ##2
         \q_mark #1 {##1}
       }
-    \cs_new:Npn \tl_trim_spaces_aux_ii:w ##1 \q_mark \q_mark ##2
+    \cs_new:Npn \@@_trim_spaces_ii:w
+        \@@_trim_spaces_i:w \q_mark \q_mark ##1
       {
-        \tl_trim_spaces_aux_iii:w
-        ##2
+        \@@_trim_spaces_iii:w
+        ##1
       }
-    \cs_new:Npn \tl_trim_spaces_aux_iii:w ##1 #1 \q_nil ##2
+    \cs_new:Npn \@@_trim_spaces_iii:w ##1 #1 \q_nil ##2
       {
         ##2
         ##1 \q_nil
-        \tl_trim_spaces_aux_iii:w
+        \@@_trim_spaces_iii:w
       }
-    \cs_new:Npn \tl_trim_spaces_aux_iv:w ##1 \q_nil ##2 \q_stop
-      { \exp_after:wN { \use_none:n ##1 } }
+    \cs_new:Npn \@@_trim_spaces_iv:w ##1 \q_nil ##2 \q_stop ##3
+      { ##3 { \use_none:n ##1 } }
   }
-\tl_tmp:w { ~ }
-\cs_new_protected:Npn \tl_trim_spaces:N #1
-  { \tl_set:Nx #1 { \exp_after:wN \tl_trim_spaces:n \exp_after:wN {#1} } }
-\cs_new_protected:Npn \tl_gtrim_spaces:N #1
-  { \tl_gset:Nx #1 { \exp_after:wN \tl_trim_spaces:n \exp_after:wN {#1} } }
-\cs_generate_variant:Nn \tl_trim_spaces:N  { c }
-\cs_generate_variant:Nn \tl_gtrim_spaces:N { c }
+\@@_tmp:w { ~ }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
+%
+% \subsection{Token by token changes}
+%
+% \begin{variable}{\q__@@_act_mark,\q__@@_act_stop}
+%   The \cs{tl_act} functions may be applied to any token list.
+%   Hence, we use two private quarks, to allow any token, even quarks,
+%   in the token list.^^A in particular critical for future \::e.
+%   Only \cs{q__@@_act_mark} and \cs{q__@@_act_stop} may not appear
+%   in the token lists manipulated by \cs{@@_act:NNNnn} functions. The quarks
+%   are effectively defined in \pkg{l3quark}.
+% \end{variable}
+%
+% \begin{macro}[EXP,int]{\@@_act:NNNnn}
+% \begin{macro}[EXP,aux]{\@@_act_output:n, \@@_act_reverse_output:n}
+% \begin{macro}[EXP,aux]{\@@_act_loop:w}
+% \begin{macro}[EXP,aux]{\@@_act_normal:NwnNNN}
+% \begin{macro}[EXP,aux]{\@@_act_group:nwnNNN}
+% \begin{macro}[EXP,aux]{\@@_act_space:wwnNNN}
+% \begin{macro}[EXP,aux]{\@@_act_end:w}
+%   To help control the expansion, \cs{@@_act:NNNnn} should always
+%   be proceeded by \tn{romannumeral} and ends by producing \cs{c_zero}
+%   once the result has been obtained. Then loop over tokens,
+%   groups, and spaces in |#5|. The marker \cs{q__@@_act_mark}
+%   is used both to avoid losing outer braces and to detect the
+%   end of the token list more easily. The result is stored
+%   as an argument for the dummy function \cs{@@_act_result:n}.
+%    \begin{macrocode}
+\cs_new:Npn \@@_act:NNNnn #1#2#3#4#5
+  {
+    \group_align_safe_begin:
+    \@@_act_loop:w #5 \q__@@_act_mark \q__@@_act_stop
+    {#4} #1 #2 #3
+    \@@_act_result:n { }
+  }
+%    \end{macrocode}
+%   In the loop, we check how the token list begins and act
+%   accordingly. In the \enquote{normal} case, we may have
+%   reached \cs{q__@@_act_mark}, the end of the list. Then
+%   leave \cs{c_zero} and the result in the input stream,
+%   to terminate the expansion of \tn{romannumeral}.
+%   Otherwise, apply the relevant function to the
+%   \enquote{arguments}, |#3|
+%   and to the head of the token list. Then repeat the loop.
+%   The scheme is the same if the token list starts with a
+%   group or with a space. Some extra work is needed to
+%   make \cs{@@_act_space:wwnNNN} gobble the space.
+%    \begin{macrocode}
+\cs_new:Npn \@@_act_loop:w #1 \q__@@_act_stop
+  {
+    \tl_if_head_is_N_type:nTF {#1}
+      { \@@_act_normal:NwnNNN }
+      {
+        \tl_if_head_is_group:nTF {#1}
+          { \@@_act_group:nwnNNN }
+          { \@@_act_space:wwnNNN }
+      }
+    #1 \q__@@_act_stop
+  }
+\cs_new:Npn \@@_act_normal:NwnNNN #1 #2 \q__@@_act_stop #3#4
+  {
+    \if_meaning:w \q__@@_act_mark #1
+      \exp_after:wN \@@_act_end:wn
+    \fi:
+    #4 {#3} #1
+    \@@_act_loop:w #2 \q__@@_act_stop
+    {#3} #4
+  }
+\cs_new:Npn \@@_act_end:wn #1 \@@_act_result:n #2
+  { \group_align_safe_end: \c_zero #2 }
+\cs_new:Npn \@@_act_group:nwnNNN #1 #2 \q__@@_act_stop #3#4#5
+  {
+    #5 {#3} {#1}
+    \@@_act_loop:w #2 \q__@@_act_stop
+    {#3} #4 #5
+  }
+\exp_last_unbraced:NNo
+  \cs_new:Npn \@@_act_space:wwnNNN \c_space_tl #1 \q__@@_act_stop #2#3#4#5
+  {
+    #5 {#2}
+    \@@_act_loop:w #1 \q__@@_act_stop
+    {#2} #3 #4 #5
+  }
+%    \end{macrocode}
+%   Typically, the output is done to the right of what was already output,
+%   using \cs{@@_act_output:n}, but for the \cs{@@_act_reverse} functions,
+%   it should be done to the left.
+%    \begin{macrocode}
+\cs_new:Npn \@@_act_output:n #1 #2 \@@_act_result:n #3
+  { #2 \@@_act_result:n { #3 #1 } }
+\cs_new:Npn \@@_act_reverse_output:n #1 #2 \@@_act_result:n #3
+  { #2 \@@_act_result:n { #1 #3 } }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}[EXP]{\tl_reverse:n, \tl_reverse:o, \tl_reverse:V}
+% \begin{macro}[EXP,aux]{\@@_reverse_normal:nN}
+% \begin{macro}[EXP,aux]{\@@_reverse_group_preserve:nn}
+% \begin{macro}[EXP,aux]{\@@_reverse_space:n}
+%   The goal here is to reverse without losing spaces nor braces.
+%   This is done using the general internal function \cs{@@_act:NNNnn}.
+%   Spaces and \enquote{normal} tokens are output on the left of the current
+%   output. Grouped tokens are output to the left but without any reversal
+%   within the group. All of the internal functions here drop one argument:
+%   this is needed by \cs{@@_act:NNNnn} when changing case (to record
+%   which direction the change is in), but not when reversing the tokens.
+%    \begin{macrocode}
+\cs_new:Npn \tl_reverse:n #1
+  {
+    \etex_unexpanded:D \exp_after:wN
+      {
+        \tex_romannumeral:D
+        \@@_act:NNNnn
+          \@@_reverse_normal:nN
+          \@@_reverse_group_preserve:nn
+          \@@_reverse_space:n
+          { }
+          {#1}
+      }
+  }
+\cs_generate_variant:Nn \tl_reverse:n { o , V }
+\cs_new:Npn \@@_reverse_normal:nN #1#2
+  { \@@_act_reverse_output:n {#2} }
+\cs_new:Npn \@@_reverse_group_preserve:nn #1#2
+  { \@@_act_reverse_output:n { {#2} } }
+\cs_new:Npn \@@_reverse_space:n #1
+  { \@@_act_reverse_output:n { ~ } }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\tl_reverse:N, \tl_reverse:c, \tl_greverse:N, \tl_greverse:c}
+%   This reverses the list, leaving \cs{exp_stop_f:} in front,
+%   which stops the \texttt{f}-expansion.
+%    \begin{macrocode}
+\cs_new_protected:Npn \tl_reverse:N #1
+  { \tl_set:Nx #1 { \exp_args:No \tl_reverse:n { #1 } } }
+\cs_new_protected:Npn \tl_greverse:N #1
+  { \tl_gset:Nx #1 { \exp_args:No \tl_reverse:n { #1 } } }
+\cs_generate_variant:Nn \tl_reverse:N  { c }
+\cs_generate_variant:Nn \tl_greverse:N { c }
+%    \end{macrocode}
 % \end{macro}
 %
 % \subsection{The first token from a token list}
@@ -1959,6 +2204,7 @@
 % \begin{macro}{\tl_head:w}
 % \begin{macro}{\tl_tail:N, \tl_tail:n, \tl_tail:V, \tl_tail:v, \tl_tail:f}
 % \begin{macro}{\tl_tail:w}
+% \begin{macro}[aux]{\@@_tail:w}
 %  These functions pick up either the head or the tail of a list. The
 %  empty brace groups in \cs{tl_head:n} and \cs{tl_tail:n} ensure that
 %  a blank argument gives an empty result. The result is returned within
@@ -1969,8 +2215,8 @@
 \cs_new:Npn \tl_head:n #1
   { \etex_unexpanded:D \exp_after:wN { \tl_head:w #1 { } \q_stop } }
 \cs_new:Npn \tl_tail:n #1
-  { \etex_unexpanded:D \tl_tail_aux:w #1 \q_mark { } \q_mark \q_stop }
-\cs_new:Npn \tl_tail_aux:w #1 #2 \q_mark #3 \q_stop { {#2} }
+  { \etex_unexpanded:D \@@_tail:w #1 \q_mark { } \q_mark \q_stop }
+\cs_new:Npn \@@_tail:w #1 #2 \q_mark #3 \q_stop { {#2} }
 \cs_new_nopar:Npn \tl_head:N { \exp_args:No \tl_head:n }
 \cs_generate_variant:Nn \tl_head:n { V , v , f }
 \cs_new_nopar:Npn \tl_tail:N { \exp_args:No \tl_tail:n }
@@ -1980,46 +2226,47 @@
 % \end{macro}
 % \end{macro}
 % \end{macro}
+% \end{macro}
 %
 % \begin{macro}{\str_head:n, \str_tail:n}
-% \begin{macro}[aux]{\str_head_aux:w}
-% \begin{macro}[aux]{\str_tail_aux:w}
+% \begin{macro}[aux]{\__str_head:w}
+% \begin{macro}[aux]{\__str_tail:w}
 %   After \cs{tl_to_str:n}, we have a list of character tokens,
 %   all with category code 12, except the space, which has category
 %   code 10. Directly using \cs{tl_head:w} would thus lose leading spaces.
 %   Instead, we take an argument delimited by an explicit space, and
 %   then only use \cs{tl_head:w}. If the string started with a
-%   space, then the argument of \cs{str_head_aux:w} is empty, and
+%   space, then the argument of \cs{__str_head:w} is empty, and
 %   the function correctly returns a space character. Otherwise,
 %   it returns the first token of |#1|, which is the first token
 %   of the string. If the string is empty, we return an empty result.
 %
 %   To remove the first character of \cs{tl_to_str:n} |{#1}|,
 %   we test it using \cs{if_charcode:w} \cs{scan_stop:},
-%   always false for characters. If the argument was non-empty,
-%   then \cs{str_tail_aux:w} returns everything until the first
+%   always \texttt{false} for characters. If the argument was non-empty,
+%   then \cs{__str_tail:w} returns everything until the first
 %   \texttt{X} (with category code letter, no risk of confusing
 %   with the user input). If the argument was empty, the first
 %   \texttt{X} is taken by \cs{if_charcode:w}, and nothing
 %   is returned. We use \texttt{X} as a \meta{marker}, rather than
 %   a quark because the test \cs{if_charcode:w} \cs{scan_stop:}
-%   \meta{marker} has to be false.
+%   \meta{marker} has to be \texttt{false}.
 %    \begin{macrocode}
 \cs_new:Npn \str_head:n #1
   {
-    \exp_after:wN \str_head_aux:w
+    \exp_after:wN \__str_head:w
     \tl_to_str:n {#1}
     { { } } ~ \q_stop
   }
-\cs_new:Npn \str_head_aux:w #1 ~ %
+\cs_new:Npn \__str_head:w #1 ~ %
   { \tl_head:w #1 { ~ } }
 \cs_new:Npn \str_tail:n #1
   {
-    \exp_after:wN \str_tail_aux:w
+    \exp_after:wN \__str_tail:w
     \reverse_if:N \if_charcode:w
         \scan_stop: \tl_to_str:n {#1} X X \q_stop
   }
-\cs_new:Npn \str_tail_aux:w #1 X #2 \q_stop { \fi: #1 }
+\cs_new:Npn \__str_tail:w #1 X #2 \q_stop { \fi: #1 }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -2029,32 +2276,39 @@
 % \begin{macro}[pTF]{\tl_if_head_eq_charcode:nN}
 % \begin{macro}[pTF]{\tl_if_head_eq_charcode:fN}
 % \begin{macro}[pTF]{\tl_if_head_eq_catcode:nN}
-%   Accessing the first token of a token list is tricky in two cases:
-%   when it has category code $1$ (begin-group token), or when it is
-%   an explicit space, with category code $10$ and character code $32$.
-%
-%   Forgetting temporarily about this issue we would use the
-%   following test in \cs{tl_if_head_eq_charcode:nN}. Here,
-%   an empty |#1| argument yields \cs{q_nil}, otherwise the
-%   first token of the token list.
+%   Accessing the first token of a token list is tricky in three cases:
+%   when it has category code $1$ (begin-group token), when it is an
+%   explicit space, with category code $10$ and character code $32$, or
+%   when the token list is empty (obviously).
+%
+%   Forgetting temporarily about this issue we would use the following
+%   test in \cs{tl_if_head_eq_charcode:nN}.  Here, \cs{tl_head:w} yields
+%   the first token of the token list, then passed to \cs{exp_not:N}.
 % \begin{verbatim}
 % \if_charcode:w
 %     \exp_after:wN \exp_not:N \tl_head:w #1 \q_nil \q_stop
 %     \exp_not:N #2
 % \end{verbatim}
-%   The special cases are detected using \cs{tl_if_head_N_type:n}
-%   (the extra |?| takes care of empty arguments).
-%   In those cases, the first token is a character, and
-%   since we only care about its character code, we can
-%   use \cs{str_head:n} to access it (this works even if
-%   it is a space character).
+%   The two first special cases are detected by testing if the token
+%   list starts with an \texttt{N}-type token (the extra |?| sends empty
+%   token lists to the \texttt{true} branch of this test).  In those
+%   cases, the first token is a character, and since we only care about
+%   its character code, we can use \cs{str_head:n} to access it (this
+%   works even if it is a space character).  An empty argument will
+%   result in \cs{tl_head:w} leaving two tokens: |?| which is taken in
+%   the \cs{if_charcode:w} test, and \cs{use_none:nn}, which ensures
+%   that \cs{prg_return_false:} is returned regardless of whether the
+%   charcode test was \texttt{true} or \texttt{false}.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \tl_if_head_eq_charcode:nN #1#2 { p , T , F , TF }
   {
     \if_charcode:w
         \exp_not:N #2
-        \tl_if_head_N_type:nTF { #1 ? }
-          { \exp_after:wN \exp_not:N \tl_head:w #1 \q_nil \q_stop }
+        \tl_if_head_is_N_type:nTF { #1 ? }
+          {
+            \exp_after:wN \exp_not:N
+            \tl_head:w #1 { ? \use_none:nn } \q_stop
+          }
           { \str_head:n {#1} }
       \prg_return_true:
     \else:
@@ -2066,20 +2320,26 @@
 \cs_generate_variant:Nn \tl_if_head_eq_charcode:nNT  { f }
 \cs_generate_variant:Nn \tl_if_head_eq_charcode:nNF  { f }
 %    \end{macrocode}
-%   For \cs{tl_if_head_eq_catcode:nN}, again we detect special
-%   cases with a \cs{tl_if_head_N_type}. Then we need to test
-%   if the first token is a begin-group token or an explicit
-%   space token, and produce the relevant token, either
-%   \cs{c_group_begin_token} or \cs{c_space_token}.
+%   For \cs{tl_if_head_eq_catcode:nN}, again we detect special cases
+%   with a \cs{tl_if_head_is_N_type:n}.  Then we need to test if the
+%   first token is a begin-group token or an explicit space token, and
+%   produce the relevant token, either \cs{c_group_begin_token} or
+%   \cs{c_space_token}.  Again, for an empty argument, a hack is used,
+%   removing \cs{prg_return_true:} and \cs{else:} with \cs{use_none:nn}
+%   in case the catcode test with the (arbitrarily chosen) |?| is
+%   \texttt{true}.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \tl_if_head_eq_catcode:nN #1 #2 { p , T , F , TF }
   {
     \if_catcode:w
         \exp_not:N #2
-        \tl_if_head_N_type:nTF { #1 ? }
-          { \exp_after:wN \exp_not:N \tl_head:w #1 \q_nil \q_stop }
+        \tl_if_head_is_N_type:nTF { #1 ? }
           {
-            \tl_if_head_group:nTF {#1}
+            \exp_after:wN \exp_not:N
+            \tl_head:w #1 { ? \use_none:nn } \q_stop
+          }
+          {
+            \tl_if_head_is_group:nTF {#1}
               { \c_group_begin_token }
               { \c_space_token }
           }
@@ -2089,29 +2349,34 @@
     \fi:
   }
 %    \end{macrocode}
-%   For \cs{tl_if_head_eq_meaning:nN}, again, detect special cases.
-%   In the normal case, use \cs{tl_head:w}, with no \cs{exp_not:N}
-%   this time, since \cs{if_meaning:w} causes no expansion.
+%   For \cs{tl_if_head_eq_meaning:nN}, again, detect special cases.  In
+%   the normal case, use \cs{tl_head:w}, with no \cs{exp_not:N} this
+%   time, since \cs{if_meaning:w} causes no expansion.  With an empty
+%   argument, the test is \texttt{true}, and \cs{use_none:nnn} removes
+%   |#2| and the usual \cs{prg_return_true:} and \cs{else:}.
 %   In the special cases, we know that the first token is a character,
 %   hence \cs{if_charcode:w} and \cs{if_catcode:w} together are enough.
 %   We combine them in some order, hopefully faster than the reverse.
+%   Tests are not nested because the arguments may contain unmatched
+%   primitive conditionals.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \tl_if_head_eq_meaning:nN #1#2 { p , T , F , TF }
   {
-    \tl_if_head_N_type:nTF { #1 ? }
-      { \tl_if_head_eq_meaning_aux_normal:nN }
-      { \tl_if_head_eq_meaning_aux_special:nN }
+    \tl_if_head_is_N_type:nTF { #1 ? }
+      { \@@_if_head_eq_meaning_normal:nN }
+      { \@@_if_head_eq_meaning_special:nN }
     {#1} #2
   }
-\cs_new:Npn \tl_if_head_eq_meaning_aux_normal:nN #1 #2
+\cs_new:Npn \@@_if_head_eq_meaning_normal:nN #1 #2
   {
-    \exp_after:wN \if_meaning:w \tl_head:w #1 \q_nil \q_stop #2
+    \exp_after:wN \if_meaning:w
+        \tl_head:w #1 { ?? \use_none:nnn } \q_stop #2
       \prg_return_true:
     \else:
       \prg_return_false:
     \fi:
   }
-\cs_new:Npn \tl_if_head_eq_meaning_aux_special:nN #1 #2
+\cs_new:Npn \@@_if_head_eq_meaning_special:nN #1 #2
   {
     \if_charcode:w \str_head:n {#1} \exp_not:N #2
       \exp_after:wN \use:n
@@ -2121,7 +2386,7 @@
     \fi:
     {
       \if_catcode:w \exp_not:N #2
-                    \tl_if_head_group:nTF {#1}
+                    \tl_if_head_is_group:nTF {#1}
                       { \c_group_begin_token }
                       { \c_space_token }
         \prg_return_true:
@@ -2136,7 +2401,7 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[pTF]{\tl_if_head_N_type:n}
+% \begin{macro}[pTF]{\tl_if_head_is_N_type:n}
 %   The first token of a token list can be either an N-type argument,
 %   a begin-group token (catcode 1), or an explicit space token
 %   (catcode 10 and charcode 32). These two cases are characterized
@@ -2145,16 +2410,16 @@
 %   string representation). The extra brace group covers the case of
 %   an empty argument, whose head is not \enquote{normal}.
 %    \begin{macrocode}
-\prg_new_conditional:Npnn \tl_if_head_N_type:n #1 { p , T , F , TF }
+\prg_new_conditional:Npnn \tl_if_head_is_N_type:n #1 { p , T , F , TF }
   {
-    \str_if_eq_return:xx
+    \__str_if_eq_x_return:nn
       { \exp_not:o { \use:n #1 { } } }
       { \exp_not:n { #1 { } } }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[EXP,pTF]{\tl_if_head_group:n}
+% \begin{macro}[EXP,pTF]{\tl_if_head_is_group:n}
 %   Pass the first token of |#1| through \cs{token_to_str:N},
 %   then check for the brace balance. The extra \texttt{?}
 %   caters for an empty argument.\footnote{Bruno: this could
@@ -2163,7 +2428,7 @@
 %     to happen in one step of expansion, keeping the token
 %     list brace balanced at all times.}
 %    \begin{macrocode}
-\prg_new_conditional:Npnn \tl_if_head_group:n #1 { p , T , F , TF }
+\prg_new_conditional:Npnn \tl_if_head_is_group:n #1 { p , T , F , TF }
   {
     \if_catcode:w *
         \exp_after:wN \use_none:n
@@ -2181,22 +2446,22 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[EXP,pTF]{\tl_if_head_space:n}
-% \begin{macro}[EXP,aux]{\tl_if_head_space_aux:w}
+% \begin{macro}[EXP,pTF]{\tl_if_head_is_space:n}
+% \begin{macro}[EXP,aux]{\@@_if_head_is_space:w}
 %   If the first token of the token list is an explicit space, i.e.,
 %   a character token with character code $32$ and category code $10$,
-%   then this test will be \meta{true}. It is \meta{false} if the token
+%   then this test will be \texttt{true}. It is \texttt{false} if the token
 %   list is empty, if the first token is an implicit space token,
 %   such as \cs{c_space_token}, or any token other than an explicit space.
 %   The slightly convoluted approach with \tn{romannumeral} ensures that
 %   each expansion step gives a balanced token list.
 %    \begin{macrocode}
-\prg_new_conditional:Npnn \tl_if_head_space:n #1 { p , T , F , TF }
+\prg_new_conditional:Npnn \tl_if_head_is_space:n #1 { p , T , F , TF }
   {
     \tex_romannumeral:D \if_false: { \fi:
-      \tl_if_head_space_aux:w ? #1 ? ~ }
+      \@@_if_head_is_space:w ? #1 ? ~ }
   }
-\cs_new:Npn \tl_if_head_space_aux:w #1 ~
+\cs_new:Npn \@@_if_head_is_space:w #1 ~
   {
     \tl_if_empty:oTF { \use_none:n #1 }
       { \exp_after:wN \c_zero \exp_after:wN \prg_return_true: }
@@ -2225,37 +2490,6 @@
 %    \end{macrocode}
 %\end{macro}
 %
-% \subsection{Constant token lists}
-%
-% \begin{variable}{\c_job_name_tl}
-%   Inherited from the \LaTeX3 name for the primitive: this needs to
-%   actually contain the text of the job name rather than the name of
-%   the primitive, of course. \LuaTeX{} does not quote file names containing
-%   spaces, whereas \pdfTeX{} and \XeTeX{} do. So there may be a correction to
-%   make in the \LuaTeX{} case.
-%    \begin{macrocode}
-%<*initex>
-\tex_everyjob:D \exp_after:wN
-  {
-    \tex_the:D \tex_everyjob:D
-    \luatex_if_engine:T
-      {
-        \lua_now:x
-          { dofile ( assert ( kpse.find_file ("lualatexquotejobname.lua" ) ) ) }
-      }
-  }
-%</initex>
-\tl_const:Nx \c_job_name_tl { \tex_jobname:D }
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\c_space_tl}
-%   A space as a token list (as opposed to as a character).
-%    \begin{macrocode}
-\tl_const:Nn \c_space_tl { ~ }
-%    \end{macrocode}
-% \end{variable}
-%
 % \subsection{Scratch token lists}
 %
 % \begin{variable}{\g_tmpa_tl, \g_tmpb_tl}
@@ -2279,398 +2513,6 @@
 %    \end{macrocode}
 % \end{variable}
 %
-% \subsection{Experimental functions}
-%
-% \begin{macro}[EXP]{\str_if_eq_return:xx}
-%   It turns out that we often need to compare a token list
-%   with the result of applying some function to it, and
-%   return with \cs{prg_return_true/false:}. This test is
-%   similar to \cs{str_if_eq:nnTF}, but hard-coded for speed.
-%    \begin{macrocode}
-\cs_new:Npn \str_if_eq_return:xx #1 #2
-  {
-    \if_int_compare:w \pdftex_strcmp:D {#1} {#2} = \c_zero
-      \prg_return_true:
-    \else:
-      \prg_return_false:
-    \fi:
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[EXP,pTF]{\tl_if_single:N}
-%   Expand the token list and feed it to \cs{tl_if_single:n}.
-%    \begin{macrocode}
-\cs_new:Npn \tl_if_single_p:N { \exp_args:No \tl_if_single_p:n }
-\cs_new:Npn \tl_if_single:NT  { \exp_args:No \tl_if_single:nT  }
-\cs_new:Npn \tl_if_single:NF  { \exp_args:No \tl_if_single:nF  }
-\cs_new:Npn \tl_if_single:NTF { \exp_args:No \tl_if_single:nTF }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[EXP,pTF]{\tl_if_single:n}
-%   A token list has exactly one item if it is either a single
-%   token surrounded by optional explicit spaces, or a single brace
-%   group surrounded by optional explicit spaces. The naive
-%   version of this test would do \cs{use_none:n} |#1|, and
-%   test if the result is empty. However, this will fail when
-%   the token list is empty. Furthermore, it does not allow optional
-%   trailing spaces.
-%    \begin{macrocode}
-\prg_new_conditional:Npnn \tl_if_single:n #1 { p , T , F , TF }
-  { \str_if_eq_return:xx { \exp_not:o { \use_none:nn #1 ?? } } {?} }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[EXP,pTF]{\tl_if_single_token:n}
-%   There are four cases: empty token list, token list starting with
-%   a normal token, with a brace group, or with a space token.
-%   If the token list starts with a normal token, remove it
-%   and check for emptyness. Otherwise, compare with a single
-%   space, only case where we have a single token.
-%    \begin{macrocode}
-\prg_new_conditional:Npnn \tl_if_single_token:n #1 { p , T , F , TF }
-  {
-    \tl_if_head_N_type:nTF {#1}
-      { \str_if_eq_return:xx { \exp_not:o { \use_none:n #1 } } { } }
-      { \str_if_eq_return:xx { \exp_not:n {#1} } { ~ } }
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{variable}{\q_tl_act_mark,\q_tl_act_stop}
-%   The \cs{tl_act} functions may be applied to any token list.
-%   Hence, we use two private quarks, to allow any token, even quarks,
-%   in the token list.^^A in particular critical for future \::e.
-%   Only \cs{q_tl_act_mark} and \cs{q_tl_act_stop} may not appear
-%   in the token lists manipulated by \cs{tl_act} functions. The quarks
-%   are effectively defined in \pkg{l3quark}.
-% \end{variable}
-%
-% \begin{macro}[EXP]{\tl_act:NNNnn,\tl_act_aux:NNNnn}
-% \begin{macro}[EXP]{\tl_act_output:n,\tl_act_reverse_output:n,
-%     \tl_act_group_recurse:Nnn}
-% \begin{macro}[EXP,aux]{\tl_act_loop:w,\tl_act_normal:NwnNNN,
-%     \tl_act_group:nwnNNN,\tl_act_space:wwnNNN,\tl_act_end:w}
-%   To help control the expansion, \cs{tl_act:NNNnn} starts with
-%   \tn{romannumeral} and ends by producing \cs{c_zero}
-%   once the result has been obtained. Then loop over tokens,
-%   groups, and spaces in |#5|. The marker \cs{q_tl_act_mark}
-%   is used both to avoid losing outer braces and to detect the
-%   end of the token list more easily. The result is stored
-%   as an argument for the dummy function \cs{tl_act_result:n}.
-%    \begin{macrocode}
-\cs_new:Npn \tl_act:NNNnn { \tex_romannumeral:D \tl_act_aux:NNNnn }
-\cs_new:Npn \tl_act_aux:NNNnn #1 #2 #3 #4 #5
-  {
-    \group_align_safe_begin:
-    \tl_act_loop:w #5 \q_tl_act_mark \q_tl_act_stop
-    {#4} #1 #2 #3
-    \tl_act_result:n { }
-  }
-%    \end{macrocode}
-%   In the loop, we check how the token list begins and act
-%   accordingly. In the \enquote{normal} case, we may have
-%   reached \cs{q_tl_act_mark}, the end of the list. Then
-%   leave \cs{c_zero} and the result in the input stream,
-%   to terminate the expansion of \tn{romannumeral}.
-%   Otherwise, apply the relevant function to the
-%   \enquote{arguments}, |#3|
-%   and to the head of the token list. Then repeat the loop.
-%   The scheme is the same if the token list starts with a
-%   group or with a space. Some extra work is needed to
-%   make \cs{tl_act_space:wwnNNN} gobble the space.
-%    \begin{macrocode}
-\cs_new:Npn \tl_act_loop:w #1 \q_tl_act_stop
-  {
-    \tl_if_head_N_type:nTF {#1}
-      { \tl_act_normal:NwnNNN }
-      {
-        \tl_if_head_group:nTF {#1}
-          { \tl_act_group:nwnNNN }
-          { \tl_act_space:wwnNNN }
-      }
-    #1 \q_tl_act_stop
-  }
-\cs_new:Npn \tl_act_normal:NwnNNN #1 #2 \q_tl_act_stop #3#4
-  {
-    \if_meaning:w \q_tl_act_mark #1
-      \exp_after:wN \tl_act_end:wn
-    \fi:
-    #4 {#3} #1
-    \tl_act_loop:w #2 \q_tl_act_stop
-    {#3} #4
-  }
-\cs_new:Npn \tl_act_end:wn #1 \tl_act_result:n #2
-  { \group_align_safe_end: \c_zero #2 }
-\cs_new:Npn \tl_act_group:nwnNNN #1 #2 \q_tl_act_stop #3#4#5
-  {
-    #5 {#3} {#1}
-    \tl_act_loop:w #2 \q_tl_act_stop
-    {#3} #4 #5
-  }
-\exp_last_unbraced:NNo
-  \cs_new:Npn \tl_act_space:wwnNNN \c_space_tl #1 \q_tl_act_stop #2#3#4#5
-  {
-    #5 {#2}
-    \tl_act_loop:w #1 \q_tl_act_stop
-    {#2} #3 #4 #5
-  }
-%    \end{macrocode}
-%   Typically, the output is done to the right of what was already output,
-%   using \cs{tl_act_output:n}, but for the \cs{tl_act_reverse} functions,
-%   it should be done to the left.
-%    \begin{macrocode}
-\cs_new:Npn \tl_act_output:n #1 #2 \tl_act_result:n #3
-  { #2 \tl_act_result:n { #3 #1 } }
-\cs_new:Npn \tl_act_reverse_output:n #1 #2 \tl_act_result:n #3
-  { #2 \tl_act_result:n { #1 #3 } }
-%    \end{macrocode}
-%   In many applications of \cs{tl_act:NNNnn}, we need to recursively
-%   apply some transformation within brace groups, then output. In this
-%   code, |#1| is the output function, |#2| is the transformation,
-%   which should expand in two steps, and |#3| is the group.
-%    \begin{macrocode}
-\cs_new:Npn \tl_act_group_recurse:Nnn #1#2#3
-  {
-    \exp_args:Nf #1
-      { \exp_after:wN \exp_after:wN \exp_after:wN { #2 {#3} } }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[EXP]{\tl_reverse_tokens:n}
-% \begin{macro}[EXP,aux]{\tl_act_reverse_normal:nN,
-%     \tl_act_reverse_group:nn, \tl_act_reverse_space:n}
-%   The goal is to reverse a token list. This is done by feeding
-%   \cs{tl_act_aux:NNNnn} three functions, an empty fourth argument
-%   (we don't use it for \cs{tl_act_reverse_tokens:n}), and as
-%   a fifth argument the token list to be reversed.
-%   Spaces and normal tokens are output to the left of the current
-%   output. For groups, we must recursively apply
-%   \cs{tl_act_reverse_tokens:n} to the group, and output, still
-%   on the left. Note that in all three cases, we throw one argument
-%   away: this \meta{parameter} is where for instance the
-%   upper/lowercasing action stores the information of whether it
-%   is uppercasing or lowercasing.
-%    \begin{macrocode}
-\cs_new:Npn \tl_reverse_tokens:n #1
-  {
-    \etex_unexpanded:D \exp_after:wN
-      {
-        \tex_romannumeral:D
-        \tl_act_aux:NNNnn
-          \tl_act_reverse_normal:nN
-          \tl_act_reverse_group:nn
-          \tl_act_reverse_space:n
-          { }
-          {#1}
-      }
-  }
-\cs_new:Npn \tl_act_reverse_space:n #1
-  { \tl_act_reverse_output:n {~} }
-\cs_new:Npn \tl_act_reverse_normal:nN #1 #2
-  { \tl_act_reverse_output:n {#2} }
-\cs_new:Npn \tl_act_reverse_group:nn #1
-  {
-    \tl_act_group_recurse:Nnn
-      \tl_act_reverse_output:n
-      { \tl_reverse_tokens:n }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[EXP]{\tl_reverse:n,\tl_reverse:o,\tl_reverse:V}
-% \begin{macro}[EXP,aux]{\tl_reverse_group_preserve:nn}
-%     The goal here is to reverse without losing spaces nor braces.
-%     The only difference with \cs{tl_reverse_tokens:n} is that
-%     we now simply output groups without entering them.
-%    \begin{macrocode}
-\cs_new:Npn \tl_reverse:n #1
-  {
-    \etex_unexpanded:D \exp_after:wN
-      {
-        \tex_romannumeral:D
-        \tl_act_aux:NNNnn
-          \tl_act_reverse_normal:nN
-          \tl_act_reverse_group_preserve:nn
-          \tl_act_reverse_space:n
-          { }
-          {#1}
-      }
-  }
-\cs_new:Npn \tl_act_reverse_group_preserve:nn #1 #2
-  { \tl_act_reverse_output:n { {#2} } }
-\cs_generate_variant:Nn \tl_reverse:n { o , V }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\tl_reverse:N, \tl_reverse:c, \tl_greverse:N, \tl_greverse:c}
-%   This reverses the list, leaving \cs{exp_stop_f:} in front,
-%   which stops the \texttt{f}-expansion.
-%    \begin{macrocode}
-\cs_new_protected:Npn \tl_reverse:N #1
-  { \tl_set:Nx #1 { \exp_args:No \tl_reverse:n { #1 } } }
-\cs_new_protected:Npn \tl_greverse:N #1
-  { \tl_gset:Nx #1 { \exp_args:No \tl_reverse:n { #1 } } }
-\cs_generate_variant:Nn \tl_reverse:N  { c }
-\cs_generate_variant:Nn \tl_greverse:N { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}[EXP]{\tl_length_tokens:n}
-% \begin{macro}[EXP,aux]{\tl_act_length_normal:nN,
-%     \tl_act_length_group:nn,\tl_act_length_space:n}
-%   The length is computed through an \cs{int_eval:n} construction.
-%   Each \texttt{1+} is output to the \emph{left}, into the integer
-%   expression, and the sum is ended by the \cs{c_zero} inserted by
-%   \cs{tl_act_end:wn}. Somewhat a hack.
-%    \begin{macrocode}
-\cs_new:Npn \tl_length_tokens:n #1
-  {
-    \int_eval:n
-      {
-        \tl_act_aux:NNNnn
-          \tl_act_length_normal:nN
-          \tl_act_length_group:nn
-          \tl_act_length_space:n
-          { }
-          {#1}
-      }
-  }
-\cs_new:Npn \tl_act_length_normal:nN #1 #2 { 1 + }
-\cs_new:Npn \tl_act_length_space:n #1 { 1 + }
-\cs_new:Npn \tl_act_length_group:nn #1 #2
-  { 2 + \tl_length_tokens:n {#2} + }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{variable}{\c_tl_act_uppercase_tl, \c_tl_act_lowercase_tl}
-%   These constants contain the correspondance between lowercase
-%   and uppercase letters, in the form |aAbBcC...| and |AaBbCc...|
-%   respectively.
-%    \begin{macrocode}
-\tl_const:Nn \c_tl_act_uppercase_tl
-  {
-    aA bB cC dD eE fF gG hH iI jJ kK lL mM
-    nN oO pP qQ rR sS tT uU vV wW xX yY zZ
-  }
-\tl_const:Nn \c_tl_act_lowercase_tl
-  {
-    Aa Bb Cc Dd Ee Ff Gg Hh Ii Jj Kk Ll Mm
-    Nn Oo Pp Qq Rr Ss Tt Uu Vv Ww Xx Yy Zz
-  }
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{macro}[EXP]{\tl_expandable_uppercase:n,\tl_expandable_lowercase:n}
-% \begin{macro}[EXP,aux]{\tl_act_case_normal:nN,
-%     \tl_act_case_group:nn,\tl_act_case_space:n}
-%   The only difference between uppercasing and lowercasing is
-%   the table of correspondance that is used. As for other
-%   token list actions, we feed \cs{tl_act_aux:NNNnn} three
-%   functions, and this time, we use the \meta{parameters}
-%   argument to carry which case-changing we are applying.
-%   A space is simply output. A normal token is compared
-%   to each letter in the alphabet using \cs{str_if_eq:nn}
-%   tests, and converted if necessary to upper/lowercase,
-%   before being output. For a group, we must perform the
-%   conversion within the group (the \cs{exp_after:wN} trigger
-%   \tn{romannumeral}, which expands fully to give the
-%   converted group), then output.
-%    \begin{macrocode}
-\cs_new:Npn \tl_expandable_uppercase:n #1
-  {
-    \etex_unexpanded:D \exp_after:wN
-      {
-        \tex_romannumeral:D
-          \tl_act_case_aux:nn { \c_tl_act_uppercase_tl } {#1}
-      }
-  }
-\cs_new:Npn \tl_expandable_lowercase:n #1
-  {
-    \etex_unexpanded:D \exp_after:wN
-      {
-        \tex_romannumeral:D
-          \tl_act_case_aux:nn { \c_tl_act_lowercase_tl } {#1}
-      }
-  }
-\cs_new:Npn \tl_act_case_aux:nn
-  {
-    \tl_act_aux:NNNnn
-      \tl_act_case_normal:nN
-      \tl_act_case_group:nn
-      \tl_act_case_space:n
-  }
-\cs_new:Npn \tl_act_case_space:n #1 { \tl_act_output:n {~} }
-\cs_new:Npn \tl_act_case_normal:nN #1 #2
-  {
-    \exp_args:Nf \tl_act_output:n
-      {
-        \exp_args:NNo \prg_case_str:nnn #2 {#1}
-          { \exp_stop_f: #2 }
-      }
-  }
-\cs_new:Npn \tl_act_case_group:nn #1 #2
-  {
-    \exp_after:wN \tl_act_output:n \exp_after:wN
-      { \exp_after:wN { \tex_romannumeral:D \tl_act_case_aux:nn {#1} {#2} } }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\tl_item:nn, \tl_item:Nn, \tl_item:cn}
-% \begin{macro}[aux]{\tl_item_aux:nn}
-%   The idea here is to find the offset of the item from the left, then use
-%   a loop to grab the correct item. If the resulting offset is too large,
-%   then \cs{quark_if_recursion_tail_stop:n} terminates the loop, and returns
-%   nothing at all.
-%    \begin{macrocode}
-\cs_new:Npn \tl_item:nn #1#2
-  {
-    \exp_args:Nf \tl_item_aux:nn
-      {
-        \int_eval:n
-          {
-            \int_compare:nNnT {#2} < \c_zero
-              { \tl_length:n {#1} + }
-            #2
-          }
-      }
-    #1
-    \q_recursion_tail
-    \prg_break_point:n { }
-  }
-\cs_new:Npn \tl_item_aux:nn #1#2
-  {
-    \quark_if_recursion_tail_break:n {#2}
-    \int_compare:nNnTF {#1} = \c_zero
-      { \tl_map_break:n { \exp_not:n {#2} } }
-      { \exp_args:Nf \tl_item_aux:nn { \int_eval:n { #1 - 1 } } }
-  }
-\cs_new_nopar:Npn \tl_item:Nn { \exp_args:No \tl_item:nn }
-\cs_generate_variant:Nn \tl_item:Nn { c }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[pTF]{\tl_if_empty:x}
-%   We can test expandably the emptyness of an expanded token list
-%   thanks to the primitive \tn{pdfstrcmp} which expands its argument:
-%   a token list is empty if and only if its string representation is
-%   empty.
-%    \begin{macrocode}
-\prg_new_conditional:Npnn \tl_if_empty:x #1 { p , T , F , TF }
-  { \str_if_eq_return:xx { } {#1} }
-%    \end{macrocode}
-% \end{macro}
-%
 % \subsection{Deprecated functions}
 %
 % \begin{macro}{\tl_new:Nn, \tl_new:cn, \tl_new:Nx}
@@ -2751,11 +2593,11 @@
 % Another renaming job.
 %    \begin{macrocode}
 %<*deprecated>
-\cs_new_eq:NN \tl_elt_count:n \tl_length:n
-\cs_new_eq:NN \tl_elt_count:V \tl_length:V
-\cs_new_eq:NN \tl_elt_count:o \tl_length:o
-\cs_new_eq:NN \tl_elt_count:N \tl_length:N
-\cs_new_eq:NN \tl_elt_count:c \tl_length:c
+\cs_new_eq:NN \tl_elt_count:n \tl_count:n
+\cs_new_eq:NN \tl_elt_count:V \tl_count:V
+\cs_new_eq:NN \tl_elt_count:o \tl_count:o
+\cs_new_eq:NN \tl_elt_count:N \tl_count:N
+\cs_new_eq:NN \tl_elt_count:c \tl_count:c
 %</deprecated>
 %    \end{macrocode}
 % \end{macro}
@@ -2782,6 +2624,58 @@
 % \end{macro}
 % \end{macro}
 %
+% Deprecated on 2012-05-13 for removal by 2012-08-31.
+%
+% \begin{macro}{\tl_length_tokens:n}
+%    \begin{macrocode}
+\cs_new_eq:NN \tl_length_tokens:n \tl_count_tokens:n
+%    \end{macrocode}
+% \end{macro}
+%
+% Deprecated 2012-05-13 for removal by 2012-11-31.
+%
+% \begin{macro}
+%   {\tl_length:N, \tl_length:c, \tl_length:n, \tl_length:V, \tl_length:o}
+%   Renames.
+%    \begin{macrocode}
+\cs_new_eq:NN \tl_length:N \tl_count:N
+\cs_new_eq:NN \tl_length:c \tl_count:c
+\cs_new_eq:NN \tl_length:n \tl_count:n
+\cs_new_eq:NN \tl_length:V \tl_count:V
+\cs_new_eq:NN \tl_length:o \tl_count:o
+%    \end{macrocode}
+% \end{macro}
+%
+% Deprecated 2012-06-05 for removal after 2012-12-31.
+%
+% \begin{macro}[pTF]{\tl_if_empty:x}
+%   We can test expandably the emptiness of an expanded token list
+%   thanks to the primitive \tn{pdfstrcmp} which expands its argument:
+%   a token list is empty if and only if its string representation is
+%   empty.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \tl_if_empty:x #1 { p , T , F , TF }
+  { \__str_if_eq_x_return:nn { } {#1} }
+%    \end{macrocode}
+% \end{macro}
+% 
+% Deprecated 2012-07-08 for removal after 2012-10-31.
+%
+% \begin{macro}[EXP, pTF]{\tl_if_head_group:n}
+% \begin{macro}[EXP, pTF]{\tl_if_head_N_type:n}
+% \begin{macro}[EXP, pTF]{\tl_if_head_space:n}
+%    \begin{macrocode}
+\prg_new_eq_conditional:NNn \tl_if_head_group:n \tl_if_head_is_group:n
+  { p , T , F , TF }
+\prg_new_eq_conditional:NNn \tl_if_head_N_type:n \tl_if_head_is_N_type:n
+  { p , T , F , TF }
+\prg_new_eq_conditional:NNn \tl_if_head_space:n \tl_if_head_is_space:n
+  { p , T , F , TF }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
 %    \begin{macrocode}
 %</initex|package>
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3token.dtx b/Master/texmf-dist/source/latex/l3kernel/l3token.dtx
index b811e4a168a..6b1af27ca33 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3token.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3token.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3token.dtx 3491 2012-03-04 06:13:18Z bruno $
+\GetIdInfo$Id: l3token.dtx 3986 2012-07-15 19:23:51Z joseph $
   {L3 Experimental token manipulation}
 %</driver|package>
 %<*driver>
@@ -78,8 +78,8 @@
 % see if a certain character is present and maybe even remove it or
 % disregard other tokens while scanning. This module provides
 % functions for both and as such will have two primary function
-% categories: |\token| for anything that deals with tokens and
-% |\peek| for looking ahead in the token stream.
+% categories: |\token_| for anything that deals with tokens and
+% |\peek_| for looking ahead in the token stream.
 %
 % Most of the time we will be using the term \enquote{token} but most of the
 % time the function we're describing can equally well by used on a
@@ -206,8 +206,8 @@
 %     \cs{char_set_lcode:nn} \Arg{intexpr_1} \Arg{intexpr_2}
 %   \end{syntax}
 %   This function set up the behaviour of \meta{character} when
-%   found inside \cs{tl_to_lowercase:n}, such that \meta{character1}
-%   will be converted into \meta{character2}. The two \meta{characters}
+%   found inside \cs{tl_to_lowercase:n}, such that \meta{character_1}
+%   will be converted into \meta{character_2}. The two \meta{characters}
 %   may be specified using an \meta{integer expression} for the character code
 %   concerned. This may include the \TeX{} |`|\meta{character}
 %   method for converting a single character into its character
@@ -243,8 +243,8 @@
 %     \cs{char_set_uccode:nn} \Arg{intexpr_1} \Arg{intexpr_2}
 %   \end{syntax}
 %   This function set up the behaviour of \meta{character} when
-%   found inside \cs{tl_to_uppercase:n}, such that \meta{character1}
-%   will be converted into \meta{character2}. The two \meta{characters}
+%   found inside \cs{tl_to_uppercase:n}, such that \meta{character_1}
+%   will be converted into \meta{character_2}. The two \meta{characters}
 %   may be specified using an \meta{integer expression} for the character code
 %   concerned. This may include the \TeX{} |`|\meta{character}
 %   method for converting a single character into its character
@@ -354,10 +354,10 @@
 %
 % \begin{function}{\token_new:Nn}
 %   \begin{syntax}
-%     \cs{token_new:Nn} \meta{token1} \Arg{token_2}
+%     \cs{token_new:Nn} \meta{token_1} \Arg{token_2}
 %   \end{syntax}
-%   Defines \meta{token1} to globally be a snapshot of \meta{token2}.
-%   This will be an implicit representation of \meta{token2}.
+%   Defines \meta{token_1} to globally be a snapshot of \meta{token_2}.
+%   This will be an implicit representation of \meta{token_2}.
 % \end{function}
 %
 % ^^A Because it's late I can't figure out a better way to handle this:
@@ -540,24 +540,24 @@
 %
 % \begin{function}[EXP,pTF]{\token_if_eq_catcode:NN}
 %   \begin{syntax}
-%     \cs{token_if_eq_catcode_p:NN} \meta{token1} \meta{token2} \\
-%     \cs{token_if_eq_catcode:NNTF} \meta{token1} \meta{token2} \Arg{true code} \Arg{false code}
+%     \cs{token_if_eq_catcode_p:NN} \meta{token_1} \meta{token_2} \\
+%     \cs{token_if_eq_catcode:NNTF} \meta{token_1} \meta{token_2} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   Tests if the two \meta{tokens} have the same category code.
 % \end{function}
 %
 % \begin{function}[EXP,pTF]{\token_if_eq_charcode:NN}
 %   \begin{syntax}
-%     \cs{token_if_eq_charcode_p:NN} \meta{token1} \meta{token2} \\
-%     \cs{token_if_eq_charcode:NNTF} \meta{token1} \meta{token2} \Arg{true code} \Arg{false code}
+%     \cs{token_if_eq_charcode_p:NN} \meta{token_1} \meta{token_2} \\
+%     \cs{token_if_eq_charcode:NNTF} \meta{token_1} \meta{token_2} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   Tests if the two \meta{tokens} have the same character code.
 % \end{function}
 %
 % \begin{function}[EXP,pTF]{\token_if_eq_meaning:NN}
 %   \begin{syntax}
-%     \cs{token_if_eq_meaning_p:NN} \meta{token1} \meta{token2} \\
-%     \cs{token_if_eq_meaning:NNTF} \meta{token1} \meta{token2} \Arg{true code} \Arg{false code}
+%     \cs{token_if_eq_meaning_p:NN} \meta{token_1} \meta{token_2} \\
+%     \cs{token_if_eq_meaning:NNTF} \meta{token_1} \meta{token_2} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   Tests if the two \meta{tokens} have the same meaning when expanded.
 % \end{function}
@@ -941,79 +941,6 @@
 %   not a macro then \cs{scan_stop:} will be left in the input stream
 % \end{function}
 %
-% \section{Experimental token functions}
-%
-% \begin{function}[added = 2011-12-27]
-%   {\char_set_active:Npn,  \char_set_active:Npx}
-%   \begin{syntax}
-%      \cs{char_set_active:Npn} \meta{char} \meta{parameters} \Arg{code}
-%   \end{syntax}
-%   Makes \meta{char} an active character to expand to \meta{code} as
-%   replacement text.
-%   Within the \meta{code}, the \meta{parameters} (|#1|, |#2|,
-%   \emph{etc.}) will be replaced by those absorbed. The \meta{char} is
-%   made active within the current \TeX{} group level, and the definition
-%   is also local.
-% \end{function}
-%
-% \begin{function}[added = 2011-12-27]
-%   {\char_gset_active:Npn, \char_gset_active:Npx}
-%   \begin{syntax}
-%      \cs{char_gset_active:Npn} \meta{char} \meta{parameters} \Arg{code}
-%   \end{syntax}
-%   Makes \meta{char} an active character to expand to \meta{code} as
-%   replacement text.
-%   Within the \meta{code}, the \meta{parameters} (|#1|, |#2|,
-%   \emph{etc.}) will be replaced by those absorbed. The \meta{char} is
-%   made active within the current \TeX{} group level, but the definition
-%   is global. This function is therefore suited to cases where an active
-%   character definition should be applied only in some context (where the
-%   \meta{char} is again made active).
-% \end{function}
-%
-% \begin{function}[added = 2011-12-27]
-%   {\char_set_active_eq:NN}
-%   \begin{syntax}
-%      \cs{char_set_active_eq:NN} \meta{char} \meta{function}
-%   \end{syntax}
-%   Makes \meta{char} an active character equivalent in meaning to the
-%   \meta{function} (which may itself be an active character). The \meta{char}
-%   is made active within the current \TeX{} group level, and the definition
-%   is also local.
-% \end{function}
-%
-% \begin{function}[added = 2011-12-27]
-%   {\char_gset_active_eq:NN}
-%   \begin{syntax}
-%      \cs{char_gset_active_eq:NN} \meta{char} \meta{function}
-%   \end{syntax}
-%   Makes \meta{char} an active character equivalent in meaning to the
-%   \meta{function} (which may itself be an active character). The \meta{char}
-%   is made active within the current \TeX{} group level, but the definition
-%   is global. This function is therefore suited to cases where an active
-%   character definition should be applied only in some context (where the
-%   \meta{char} is again made active).
-% \end{function}
-%
-% \begin{function}[added = 2011-08-14,TF]{\peek_N_type:}
-%   \begin{syntax}
-%     \cs{peek_N_type:TF} \Arg{true code} \Arg{false code}
-%   \end{syntax}
-%   Tests if the next \meta{token} in the input stream can be safely
-%   grabbed as an \texttt{N}-type argument. The test will be \meta{false}
-%   if the next \meta{token} is either an explicit or implicit
-%   begin-group or end-group token (with any character code), or
-%   an explicit or implicit space character (with character code $32$
-%   and category code $10$), and \meta{true} in all other cases.
-%   Note that a \meta{true} result ensures that the next \meta{token} is
-%   a valid \texttt{N}-type argument. However, if the next \meta{token}
-%   is for instance \cs{c_space_token}, the test will take the
-%   \meta{false} branch, even though the next \meta{token} is in fact
-%   a valid \texttt{N}-type argument. The \meta{token} will be left
-%   in the input stream after the \meta{true code} or \meta{false code}
-%   (as appropriate to the result of the test).
-% \end{function}
-%
 % \end{documentation}
 %
 % \begin{implementation}
@@ -1023,12 +950,16 @@
 %    \begin{macrocode}
 %<*initex|package>
 %    \end{macrocode}
+%    
+%    \begin{macrocode}
+%<@@=token>
+%    \end{macrocode}
 %
 %    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
@@ -1040,11 +971,11 @@
 %   Category code changes.
 %    \begin{macrocode}
 \cs_new_protected:Npn \char_set_catcode:nn #1#2
-  { \tex_catcode:D #1 = \int_eval:w #2 \int_eval_end: }
+  { \tex_catcode:D #1 = \__int_eval:w #2 \__int_eval_end: }
 \cs_new:Npn \char_value_catcode:n #1
-  { \tex_the:D \tex_catcode:D \int_eval:w #1\int_eval_end: }
+  { \tex_the:D \tex_catcode:D \__int_eval:w #1\__int_eval_end: }
 \cs_new_protected:Npn \char_show_value_catcode:n #1
-  { \tex_showthe:D \tex_catcode:D \int_eval:w #1 \int_eval_end: }
+  { \tex_showthe:D \tex_catcode:D \__int_eval:w #1 \__int_eval_end: }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1175,29 +1106,29 @@
 %   Pretty repetitive, but necessary!
 %    \begin{macrocode}
 \cs_new_protected:Npn \char_set_mathcode:nn #1#2
-  { \tex_mathcode:D #1 = \int_eval:w #2 \int_eval_end: }
+  { \tex_mathcode:D #1 = \__int_eval:w #2 \__int_eval_end: }
 \cs_new:Npn \char_value_mathcode:n #1
-  { \tex_the:D \tex_mathcode:D \int_eval:w #1\int_eval_end: }
+  { \tex_the:D \tex_mathcode:D \__int_eval:w #1\__int_eval_end: }
 \cs_new_protected:Npn \char_show_value_mathcode:n #1
-  { \tex_showthe:D \tex_mathcode:D \int_eval:w #1 \int_eval_end: }
+  { \tex_showthe:D \tex_mathcode:D \__int_eval:w #1 \__int_eval_end: }
 \cs_new_protected:Npn \char_set_lccode:nn #1#2
-  { \tex_lccode:D #1 = \int_eval:w #2 \int_eval_end: }
+  { \tex_lccode:D #1 = \__int_eval:w #2 \__int_eval_end: }
 \cs_new:Npn \char_value_lccode:n #1
-  { \tex_the:D \tex_lccode:D \int_eval:w #1\int_eval_end: }
+  { \tex_the:D \tex_lccode:D \__int_eval:w #1\__int_eval_end: }
 \cs_new_protected:Npn \char_show_value_lccode:n #1
-  { \tex_showthe:D \tex_lccode:D \int_eval:w #1 \int_eval_end: }
+  { \tex_showthe:D \tex_lccode:D \__int_eval:w #1 \__int_eval_end: }
 \cs_new_protected:Npn \char_set_uccode:nn #1#2
-  { \tex_uccode:D #1 = \int_eval:w #2 \int_eval_end: }
+  { \tex_uccode:D #1 = \__int_eval:w #2 \__int_eval_end: }
 \cs_new:Npn \char_value_uccode:n #1
-  { \tex_the:D \tex_uccode:D \int_eval:w #1\int_eval_end: }
+  { \tex_the:D \tex_uccode:D \__int_eval:w #1\__int_eval_end: }
 \cs_new_protected:Npn \char_show_value_uccode:n #1
-  { \tex_showthe:D \tex_uccode:D \int_eval:w #1 \int_eval_end: }
+  { \tex_showthe:D \tex_uccode:D \__int_eval:w #1 \__int_eval_end: }
 \cs_new_protected:Npn \char_set_sfcode:nn #1#2
-  { \tex_sfcode:D #1 = \int_eval:w #2 \int_eval_end: }
+  { \tex_sfcode:D #1 = \__int_eval:w #2 \__int_eval_end: }
 \cs_new:Npn \char_value_sfcode:n #1
-  { \tex_the:D \tex_sfcode:D \int_eval:w #1\int_eval_end: }
+  { \tex_the:D \tex_sfcode:D \__int_eval:w #1\__int_eval_end: }
 \cs_new_protected:Npn \char_show_value_sfcode:n #1
-  { \tex_showthe:D \tex_sfcode:D \int_eval:w #1 \int_eval_end: }
+  { \tex_showthe:D \tex_sfcode:D \__int_eval:w #1 \__int_eval_end: }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -1288,13 +1219,13 @@
     \use:nn
       {
         \group_end:
-        \seq_set_from_clist:Nn \l_char_active_seq
+        \seq_set_split:Nnn \l_char_active_seq { }
       }
   }
-    { { " , $ , & , ^ , _ , ~ } } %$
+    { { " $ & ^ _ ~ } } %$
 \seq_new:N \l_char_special_seq
-\seq_set_from_clist:Nn \l_char_special_seq
-  { \  , \" , \# , \$ , \% , \& , \\ , \^ , \_ , \{ , \} , \~ }
+\seq_set_split:Nnn \l_char_special_seq { }
+  { \  \" \# \$ \% \& \\ \^ \_ \{ \} \~ }
 %    \end{macrocode}
 % \end{variable}
 %
@@ -1302,7 +1233,7 @@
 %
 % \begin{macro}[pTF]{\token_if_group_begin:N}
 %   Check if token is a begin group token. We use the constant
-%   |\c_group_begin_token| for this.
+%   \cs{c_group_begin_token} for this.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \token_if_group_begin:N #1 { p , T ,  F , TF }
   {
@@ -1314,7 +1245,7 @@
 %
 % \begin{macro}[pTF]{\token_if_group_end:N}
 %   Check if token is a end group token. We use the constant
-%   |\c_group_end_token| for this.
+%   \cs{c_group_end_token} for this.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \token_if_group_end:N #1 { p , T ,  F , TF }
   {
@@ -1326,7 +1257,7 @@
 %
 % \begin{macro}[pTF]{\token_if_math_toggle:N}
 %   Check if token is a math shift token. We use the constant
-%   |\c_math_toggle_token| for this.
+%   \cs{c_math_toggle_token} for this.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \token_if_math_toggle:N #1 { p , T ,  F , TF }
   {
@@ -1338,7 +1269,7 @@
 %
 % \begin{macro}[pTF]{\token_if_alignment:N}
 %   Check if token is an alignment tab token. We use the constant
-%   |\c_alignment_tab_token| for this.
+%   \cs{c_alignment_token} for this.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \token_if_alignment:N #1 { p , T ,  F , TF }
   {
@@ -1350,7 +1281,7 @@
 %
 % \begin{macro}[pTF]{\token_if_parameter:N}
 %   Check if token is a parameter token. We use the constant
-%   |\c_parameter_token| for this. We have to trick \TeX{} a bit to
+%   \cs{c_parameter_token} for this. We have to trick \TeX{} a bit to
 %   avoid an error message: within a group we prevent
 %   \cs{c_parameter_token} from behaving like a macro parameter character.
 %   The definitions of \cs{prg_new_conditional:Npnn} are global, so they
@@ -1369,7 +1300,7 @@
 %
 % \begin{macro}[pTF]{\token_if_math_superscript:N}
 %   Check if token is a math superscript token. We use the constant
-%   |\c_superscript_token| for this.
+%   \cs{c_math_superscript_token} for this.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \token_if_math_superscript:N #1 { p , T ,  F , TF }
   {
@@ -1381,7 +1312,7 @@
 %
 % \begin{macro}[pTF]{\token_if_math_subscript:N}
 %   Check if token is a math subscript token. We use the constant
-%   |\c_subscript_token| for this.
+%   \cs{c_math_subscript_token} for this.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \token_if_math_subscript:N #1 { p , T ,  F , TF }
   {
@@ -1393,7 +1324,7 @@
 %
 % \begin{macro}[pTF]{\token_if_space:N}
 %   Check if token is a space token. We use the constant
-%   |\c_space_token| for this.
+%   \cs{c_space_token} for this.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \token_if_space:N #1 { p , T ,  F , TF }
   {
@@ -1405,7 +1336,7 @@
 %
 % \begin{macro}[pTF]{\token_if_letter:N}
 %   Check if token is a letter token. We use the constant
-%   |\c_letter_token| for this.
+%   \cs{c_catcode_letter_token} for this.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \token_if_letter:N #1 { p , T ,  F , TF }
   {
@@ -1417,7 +1348,7 @@
 %
 % \begin{macro}[pTF]{\token_if_other:N}
 %   Check if token is an other char token. We use the constant
-%   |\c_other_char_token| for this.
+%   \cs{c_catcode_other_token} for this.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \token_if_other:N #1 { p , T ,  F , TF }
   {
@@ -1429,8 +1360,8 @@
 %
 % \begin{macro}[pTF]{\token_if_active:N}
 %   Check if token is an active char token. We use the constant
-%   |\c_active_char_tl| for this. A technical point is that
-%   \cs{c_active_char_tl} is in fact a macro expanding to
+%   \cs{c_catcode_active_tl} for this. A technical point is that
+%   \cs{c_catcode_active_tl} is in fact a macro expanding to
 %   |\exp_not:N *|, where |*| is active.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \token_if_active:N #1 { p , T ,  F , TF }
@@ -1475,8 +1406,8 @@
 % \end{macro}
 %
 % \begin{macro}[pTF]{\token_if_macro:N}
-% \begin{macro}[aux]{\token_if_macro_p_aux:w}
-%   When a token is a macro, |\token_to_meaning:N| will always output
+% \begin{macro}[aux]{\@@_if_macro_p:w}
+%   When a token is a macro, \cs{token_to_meaning:N} will always output
 %   something like |\long macro:#1->#1| so we could naively check to
 %   see if the meaning contains |->|. However, this can fail the five
 %   \tn{...mark} primitives, whose meaning has the form
@@ -1513,10 +1444,10 @@
     \group_end:
     \prg_new_conditional:Npnn \token_if_macro:N #1 { p , T ,  F , TF }
       {
-        \exp_after:wN \token_if_macro_p_aux:w
+        \exp_after:wN \@@_if_macro_p:w
         \token_to_meaning:N #1 MA; \q_stop
       }
-    \cs_new:Npn \token_if_macro_p_aux:w #1 MA #2 ; #3 \q_stop
+    \cs_new:Npn \@@_if_macro_p:w #1 MA #2 ; #3 \q_stop
       {
         \if_int_compare:w \pdftex_strcmp:D { #2 } { cro } = \c_zero
             \prg_return_true:
@@ -1532,7 +1463,7 @@
 % \begin{macro}[pTF]{\token_if_cs:N}
 %   Check if token has same catcode as a control sequence. This
 %   follows the same pattern as for \cs{token_if_letter:N} \emph{etc.}
-%   We use |\scan_stop:| for this.
+%   We use \cs{scan_stop:} for this.
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \token_if_cs:N #1 { p , T ,  F , TF }
   {
@@ -1544,17 +1475,23 @@
 %
 % \begin{macro}[pTF]{\token_if_expandable:N}
 %   Check if token is expandable. We use the fact that \TeX{} will
-%   temporarily convert |\exp_not:N| \meta{token} into |\scan_stop:| if
-%   \meta{token} is expandable.
+%   temporarily convert \cs{exp_not:N} \meta{token} into \cs{scan_stop:}
+%   if \meta{token} is expandable.  An \texttt{undefined} token is not
+%   considered as expandable.  No problem nesting the conditionals,
+%   since the third |#1| is only skipped if it is non-expandable (hence
+%   not part of \TeX{}'s conditional apparatus).
 %    \begin{macrocode}
 \prg_new_conditional:Npnn \token_if_expandable:N #1 { p , T ,  F , TF }
   {
-    \cs_if_exist:NTF #1
-      {
-        \exp_after:wN \if_meaning:w \exp_not:N #1 #1
-          \prg_return_false: \else: \prg_return_true: \fi:
-      }
-      { \prg_return_false: }
+    \exp_after:wN \if_meaning:w \exp_not:N #1 #1
+      \prg_return_false:
+    \else:
+      \if_cs_exist:N #1
+        \prg_return_true:
+      \else:
+        \prg_return_false:
+      \fi:
+    \fi:
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1570,18 +1507,18 @@
 %   }
 % \begin{macro}[aux]
 %   {
-%     \token_if_chardef_aux:w,
-%     \token_if_dim_register_aux:w,
-%     \token_if_int_register_aux:w,
-%     \token_if_muskip_register_aux:w,
-%     \token_if_skip_register_aux:w,
-%     \token_if_toks_register_aux:w,
-%     \token_if_protected_macro_aux:w,
-%     \token_if_long_macro_aux:w,
+%     \@@_if_chardef:w,
+%     \@@_if_dim_register:w,
+%     \@@_if_int_register:w,
+%     \@@_if_muskip_register:w,
+%     \@@_if_skip_register:w,
+%     \@@_if_toks_register:w,
+%     \@@_if_protected_macro:w,
+%     \@@_if_long_macro:w,
 %   }
 %   Most of these functions have to check the meaning of the token in
 %   question so we need to do some checkups on which characters are
-%   output by |\token_to_meaning:N|. As usual, these characters have
+%   output by \cs{token_to_meaning:N}. As usual, these characters have
 %   catcode 12 so we must do some serious substitutions in the code
 %   below\dots
 %    \begin{macrocode}
@@ -1613,23 +1550,23 @@
 %    \begin{macrocode}
     \prg_new_conditional:Npnn \token_if_chardef:N #1 { p , T ,  F , TF }
       {
-        \str_if_eq_return:xx
+        \__str_if_eq_x_return:nn
           {
-            \exp_after:wN \token_if_chardef_aux:w
+            \exp_after:wN \@@_if_chardef:w
               \token_to_meaning:N #1 CHAR" \q_stop
           }
           { \token_to_str:N \char }
       }
     \prg_new_conditional:Npnn \token_if_mathchardef:N #1 { p , T ,  F , TF }
       {
-        \str_if_eq_return:xx
+        \__str_if_eq_x_return:nn
           {
-            \exp_after:wN \token_if_chardef_aux:w
+            \exp_after:wN \@@_if_chardef:w
               \token_to_meaning:N #1 CHAR" \q_stop
           }
           { \token_to_str:N \mathchar }
       }
-    \cs_new:Npn \token_if_chardef_aux:w #1 CHAR" #2 \q_stop { #1 CHAR }
+    \cs_new:Npn \@@_if_chardef:w #1 CHAR" #2 \q_stop { #1 CHAR }
 %    \end{macrocode}
 %
 %   Dim registers are a little more difficult since their \tn{meaning}
@@ -1644,16 +1581,16 @@
           \if_meaning:w \tex_dimendef:D #1
             \prg_return_false:
           \else:
-            \str_if_eq_return:xx
+            \__str_if_eq_x_return:nn
               {
-                \exp_after:wN \token_if_dim_register_aux:w
+                \exp_after:wN \@@_if_dim_register:w
                   \token_to_meaning:N #1 ZIMEX \q_stop
               }
               { \token_to_str:N \  }
           \fi:
         \fi:
       }
-    \cs_new:Npn \token_if_dim_register_aux:w #1 ZIMEX #2 \q_stop { #1 ~ }
+    \cs_new:Npn \@@_if_dim_register:w #1 ZIMEX #2 \q_stop { #1 ~ }
 %    \end{macrocode}
 % Integer registers are one step harder since constants are implemented
 % differently from variables, and we also have to take care of the
@@ -1671,9 +1608,9 @@
           \if_meaning:w \tex_countdef:D #1
             \prg_return_false:
           \else:
-            \str_if_eq_return:xx
+            \__str_if_eq_x_return:nn
               {
-                \exp_after:wN \token_if_int_register_aux:w
+                \exp_after:wN \@@_if_int_register:w
                   \token_to_meaning:N #1 COUXY \q_stop
               }
               { \token_to_str:N \  }
@@ -1682,7 +1619,7 @@
         %       }
         %   }
       }
-    \cs_new:Npn \token_if_int_register_aux:w #1 COUXY #2 \q_stop { #1 ~ }
+    \cs_new:Npn \@@_if_int_register:w #1 COUXY #2 \q_stop { #1 ~ }
 %    \end{macrocode}
 %   Muskip registers are done the same way as the dimension registers.
 %    \begin{macrocode}
@@ -1694,16 +1631,16 @@
           \if_meaning:w \tex_muskipdef:D #1
             \prg_return_false:
           \else:
-            \str_if_eq_return:xx
+            \__str_if_eq_x_return:nn
               {
-                \exp_after:wN \token_if_muskip_register_aux:w
+                \exp_after:wN \@@_if_muskip_register:w
                   \token_to_meaning:N #1 MUSKIP \q_stop
               }
               { \token_to_str:N \  }
           \fi:
         \fi:
       }
-    \cs_new:Npn \token_if_muskip_register_aux:w #1 MUSKIP #2 \q_stop { #1 ~ }
+    \cs_new:Npn \@@_if_muskip_register:w #1 MUSKIP #2 \q_stop { #1 ~ }
 %    \end{macrocode}
 %   Skip registers.
 %    \begin{macrocode}
@@ -1715,16 +1652,16 @@
           \if_meaning:w \tex_skipdef:D #1
             \prg_return_false:
           \else:
-            \str_if_eq_return:xx
+            \__str_if_eq_x_return:nn
               {
-                \exp_after:wN \token_if_skip_register_aux:w
+                \exp_after:wN \@@_if_skip_register:w
                   \token_to_meaning:N #1 SKIP \q_stop
               }
               { \token_to_str:N \  }
           \fi:
         \fi:
       }
-    \cs_new:Npn \token_if_skip_register_aux:w #1 SKIP #2 \q_stop { #1 ~ }
+    \cs_new:Npn \@@_if_skip_register:w #1 SKIP #2 \q_stop { #1 ~ }
 %    \end{macrocode}
 %   Toks registers.
 %    \begin{macrocode}
@@ -1736,39 +1673,39 @@
           \if_meaning:w \tex_toksdef:D #1
             \prg_return_false:
           \else:
-            \str_if_eq_return:xx
+            \__str_if_eq_x_return:nn
               {
-                \exp_after:wN \token_if_toks_register_aux:w
+                \exp_after:wN \@@_if_toks_register:w
                   \token_to_meaning:N #1 YOKS \q_stop
               }
               { \token_to_str:N \  }
           \fi:
         \fi:
       }
-     \cs_new:Npn \token_if_toks_register_aux:w #1 YOKS #2 \q_stop { #1 ~ }
+     \cs_new:Npn \@@_if_toks_register:w #1 YOKS #2 \q_stop { #1 ~ }
 %    \end{macrocode}
 %   Protected macros.
 %    \begin{macrocode}
     \prg_new_conditional:Npnn \token_if_protected_macro:N #1
       { p , T ,  F , TF }
       {
-        \str_if_eq_return:xx
+        \__str_if_eq_x_return:nn
           {
-            \exp_after:wN \token_if_protected_macro_aux:w
+            \exp_after:wN \@@_if_protected_macro:w
               \token_to_meaning:N #1 PROYECYEZ~MACRO \q_stop
           }
           { \token_to_str:N \  }
       }
-    \cs_new:Npn \token_if_protected_macro_aux:w
+    \cs_new:Npn \@@_if_protected_macro:w
       #1 PROYECYEZ~MACRO #2 \q_stop { #1 ~ }
 %    \end{macrocode}
 %   Long macros and protected long macros share an auxiliary.
 %    \begin{macrocode}
     \prg_new_conditional:Npnn \token_if_long_macro:N #1 { p , T ,  F , TF }
       {
-        \str_if_eq_return:xx
+        \__str_if_eq_x_return:nn
           {
-            \exp_after:wN \token_if_long_macro_aux:w
+            \exp_after:wN \@@_if_long_macro:w
               \token_to_meaning:N #1 LOXG~MACRO \q_stop
           }
           { \token_to_str:N \  }
@@ -1776,16 +1713,16 @@
     \prg_new_conditional:Npnn \token_if_protected_long_macro:N #1
       { p , T ,  F , TF }
       {
-        \str_if_eq_return:xx
+        \__str_if_eq_x_return:nn
           {
-            \exp_after:wN \token_if_long_macro_aux:w
+            \exp_after:wN \@@_if_long_macro:w
               \token_to_meaning:N #1 LOXG~MACRO \q_stop
           }
           { \token_to_str:N \protected \token_to_str:N \  }
       }
-    \cs_new:Npn \token_if_long_macro_aux:w #1 LOXG~MACRO #2 \q_stop { #1 ~ }
+    \cs_new:Npn \@@_if_long_macro:w #1 LOXG~MACRO #2 \q_stop { #1 ~ }
 %    \end{macrocode}
-% Finally the |\tl_to_lowercase:n| ends!
+% Finally the \cs{tl_to_lowercase:n} ends!
 %    \begin{macrocode}
   }
 %    \end{macrocode}
@@ -1793,12 +1730,12 @@
 % \end{macro}
 %
 % \begin{macro}[pTF]{\token_if_primitive:N}
-% \begin{macro}[aux]{\token_if_primitive_aux:NNw,
-%     \token_if_primitive_aux_space:w,
-%     \token_if_primitive_aux_nullfont:N,
-%     \token_if_primitive_aux_loop:N,
-%     \token_if_primitive_auxii:Nw,
-%     \token_if_primitive_aux_undefined:N}
+% \begin{macro}[aux]{\@@_if_primitive:NNw,
+%     \@@_if_primitive_space:w,
+%     \@@_if_primitive_nullfont:N,
+%     \@@_if_primitive_loop:N,
+%     \@@_if_primitive:Nw,
+%     \@@_if_primitive_undefined:N}
 %^^A See http://groups.google.com/group/comp.text.tex/browse_thread/thread/0a72666873f8753d#
 %
 %   We filter out macros first, because they cause endless trouble later
@@ -1857,19 +1794,19 @@
       \token_if_macro:NTF #1
         \prg_return_false:
         {
-          \exp_after:wN \token_if_primitive_aux:NNw
+          \exp_after:wN \@@_if_primitive:NNw
           \token_to_meaning:N #1 ; ; ; \q_stop #1
         }
     }
-  \cs_new:Npn \token_if_primitive_aux:NNw #1#2 #3 ; #4 \q_stop
+  \cs_new:Npn \@@_if_primitive:NNw #1#2 #3 ; #4 \q_stop
     {
-      \tl_if_empty:oTF { \token_if_primitive_aux_space:w #3 ~ }
-        { \token_if_primitive_aux_loop:N #3 ; \q_stop }
-        { \token_if_primitive_aux_nullfont:N }
+      \tl_if_empty:oTF { \@@_if_primitive_space:w #3 ~ }
+        { \@@_if_primitive_loop:N #3 ; \q_stop }
+        { \@@_if_primitive_nullfont:N }
     }
 }
-\cs_new:Npn \token_if_primitive_aux_space:w #1 ~ { }
-\cs_new:Npn \token_if_primitive_aux_nullfont:N #1
+\cs_new:Npn \@@_if_primitive_space:w #1 ~ { }
+\cs_new:Npn \@@_if_primitive_nullfont:N #1
   {
     \if_meaning:w \tex_nullfont:D #1
       \prg_return_true:
@@ -1877,25 +1814,25 @@
       \prg_return_false:
     \fi:
   }
-\cs_new:Npn \token_if_primitive_aux_loop:N #1
+\cs_new:Npn \@@_if_primitive_loop:N #1
   {
-    \if_num:w `#1 < \c_token_A_int %
-      \exp_after:wN \token_if_primitive_auxii:Nw
+    \if_int_compare:w `#1 < \c_token_A_int %
+      \exp_after:wN \@@_if_primitive:Nw
       \exp_after:wN #1
     \else:
-      \exp_after:wN \token_if_primitive_aux_loop:N
+      \exp_after:wN \@@_if_primitive_loop:N
     \fi:
   }
-\cs_new:Npn \token_if_primitive_auxii:Nw #1 #2 \q_stop
+\cs_new:Npn \@@_if_primitive:Nw #1 #2 \q_stop
   {
     \if:w : #1
-      \exp_after:wN \token_if_primitive_aux_undefined:N
+      \exp_after:wN \@@_if_primitive_undefined:N
     \else:
       \prg_return_false:
       \exp_after:wN \use_none:n
     \fi:
   }
-\cs_new:Npn \token_if_primitive_aux_undefined:N #1
+\cs_new:Npn \@@_if_primitive_undefined:N #1
   {
     \if_cs_exist:N #1
       \prg_return_true:
@@ -1908,6 +1845,10 @@
 % \end{macro}
 %
 % \subsection{Peeking ahead at the next token}
+% 
+%    \begin{macrocode}
+%<@@=peek>
+%    \end{macrocode}
 %
 % Peeking ahead is implemented using a two part mechanism. The
 % outer level provides a defined interface to the lower level material.
@@ -1930,35 +1871,35 @@
 % \end{variable}
 % \end{variable}
 %
-% \begin{variable}{\l_peek_search_token}
+% \begin{variable}{\l_@@_search_token}
 %   The token to search for as an implicit token:
-%   \emph{cf.}~\cs{l_peek_search_tl}.
+%   \emph{cf.}~\cs{l_@@_search_tl}.
 %    \begin{macrocode}
-\cs_new_eq:NN \l_peek_search_token ?
+\cs_new_eq:NN \l_@@_search_token ?
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_peek_search_tl}
+% \begin{variable}{\l_@@_search_tl}
 %   The token to search for as an explicit token:
-%   \emph{cf.}~\cs{l_peek_search_token}.
+%   \emph{cf.}~\cs{l_@@_search_token}.
 %    \begin{macrocode}
-\tl_new:N \l_peek_search_tl
+\tl_new:N \l_@@_search_tl
 %    \end{macrocode}
 % \end{variable}
 %
 % \begin{macro}[aux]
-%   {\peek_true:w, \peek_true_aux:w, \peek_false:w, \peek_tmp:w}
+%   {\@@_true:w, \@@_true_aux:w, \@@_false:w, \@@_tmp:w}
 %   Functions used by the branching and space-stripping code.
 %    \begin{macrocode}
-\cs_new_nopar:Npn \peek_true:w  { }
-\cs_new_nopar:Npn \peek_true_aux:w  { }
-\cs_new_nopar:Npn \peek_false:w { }
-\cs_new:Npn \peek_tmp:w { }
+\cs_new_nopar:Npn \@@_true:w  { }
+\cs_new_nopar:Npn \@@_true_aux:w  { }
+\cs_new_nopar:Npn \@@_false:w { }
+\cs_new:Npn \@@_tmp:w { }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}{\peek_after:Nw}
-% \begin{macro}{\peek_after:Nw}
+% \begin{macro}{\peek_gafter:Nw}
 %   Simple wrappers for \tn{futurelet}: no arguments absorbed
 %   here.
 %    \begin{macrocode}
@@ -1970,34 +1911,34 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[aux]{\peek_true_remove:w}
+% \begin{macro}[aux]{\@@_true_remove:w}
 %   A function to remove the next token and then regain control.
 %    \begin{macrocode}
-\cs_new_protected:Npn \peek_true_remove:w
+\cs_new_protected:Npn \@@_true_remove:w
   {
     \group_align_safe_end:
-    \tex_afterassignment:D \peek_true_aux:w
-    \cs_set_eq:NN \peek_tmp:w
+    \tex_afterassignment:D \@@_true_aux:w
+    \cs_set_eq:NN \@@_tmp:w
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[TF]{\peek_token_generic:NN}
+% \begin{macro}[TF]{\@@_token_generic:NN}
 %   The generic function stores the test token in both implicit and
 %   explicit modes, and the \texttt{true} and \texttt{false} code as
 %   token lists, more or less. The two branches have to be absorbed here
 %   as the input stream needs to be cleared for the peek function itself.
 %    \begin{macrocode}
-\cs_new_protected:Npn \peek_token_generic:NNTF #1#2#3#4
+\cs_new_protected:Npn \@@_token_generic:NNTF #1#2#3#4
   {
-    \cs_set_eq:NN \l_peek_search_token #2
-    \tl_set:Nn \l_peek_search_tl {#2}
-    \cs_set_nopar:Npx \peek_true:w
+    \cs_set_eq:NN \l_@@_search_token #2
+    \tl_set:Nn \l_@@_search_tl {#2}
+    \cs_set_nopar:Npx \@@_true:w
       {
         \exp_not:N \group_align_safe_end:
         \exp_not:n {#3}
       }
-    \cs_set_nopar:Npx \peek_false:w
+    \cs_set_nopar:Npx \@@_false:w
       {
         \exp_not:N \group_align_safe_end:
         \exp_not:n {#4}
@@ -2005,24 +1946,24 @@
     \group_align_safe_begin:
       \peek_after:Nw #1
   }
-\cs_new_protected:Npn \peek_token_generic:NNT #1#2#3
-  { \peek_token_generic:NNTF #1 #2 {#3} { } }
-\cs_new_protected:Npn \peek_token_generic:NNF #1#2#3
-  { \peek_token_generic:NNTF #1 #2 { } {#3} }
+\cs_new_protected:Npn \@@_token_generic:NNT #1#2#3
+  { \@@_token_generic:NNTF #1 #2 {#3} { } }
+\cs_new_protected:Npn \@@_token_generic:NNF #1#2#3
+  { \@@_token_generic:NNTF #1 #2 { } {#3} }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[TF]{\peek_token_remove_generic:NN}
+% \begin{macro}[TF]{\@@_token_remove_generic:NN}
 %   For token removal there needs to be a call to the auxiliary
 %   function which does the work.
 %    \begin{macrocode}
-\cs_new_protected:Npn \peek_token_remove_generic:NNTF #1#2#3#4
+\cs_new_protected:Npn \@@_token_remove_generic:NNTF #1#2#3#4
   {
-    \cs_set_eq:NN \l_peek_search_token #2
-    \tl_set:Nn \l_peek_search_tl {#2}
-    \cs_set_eq:NN \peek_true:w \peek_true_remove:w
-    \cs_set_nopar:Npx \peek_true_aux:w { \exp_not:n {#3} }
-    \cs_set_nopar:Npx \peek_false:w
+    \cs_set_eq:NN \l_@@_search_token #2
+    \tl_set:Nn \l_@@_search_tl {#2}
+    \cs_set_eq:NN \@@_true:w \@@_true_remove:w
+    \cs_set_nopar:Npx \@@_true_aux:w { \exp_not:n {#3} }
+    \cs_set_nopar:Npx \@@_false:w
       {
         \exp_not:N \group_align_safe_end:
         \exp_not:n {#4}
@@ -2030,45 +1971,45 @@
     \group_align_safe_begin:
       \peek_after:Nw #1
   }
-\cs_new_protected:Npn \peek_token_remove_generic:NNT #1#2#3
-  { \peek_token_remove_generic:NNTF #1 #2 {#3} { } }
-\cs_new_protected:Npn \peek_token_remove_generic:NNF #1#2#3
-  { \peek_token_remove_generic:NNTF #1 #2 { } {#3} }
+\cs_new_protected:Npn \@@_token_remove_generic:NNT #1#2#3
+  { \@@_token_remove_generic:NNTF #1 #2 {#3} { } }
+\cs_new_protected:Npn \@@_token_remove_generic:NNF #1#2#3
+  { \@@_token_remove_generic:NNTF #1 #2 { } {#3} }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}
-%   {\peek_execute_branches_catcode:, \peek_execute_branches_meaning:}
+%   {\@@_execute_branches_catcode:, \@@_execute_branches_meaning:}
 %   The category code and meaning tests are straight forward.
 %    \begin{macrocode}
-\cs_new_nopar:Npn \peek_execute_branches_catcode:
+\cs_new_nopar:Npn \@@_execute_branches_catcode:
   {
     \if_catcode:w
-      \exp_not:N \l_peek_token \exp_not:N \l_peek_search_token
-      \exp_after:wN \peek_true:w
+      \exp_not:N \l_peek_token \exp_not:N \l_@@_search_token
+      \exp_after:wN \@@_true:w
     \else:
-      \exp_after:wN \peek_false:w
+      \exp_after:wN \@@_false:w
     \fi:
   }
-\cs_new_nopar:Npn \peek_execute_branches_meaning:
+\cs_new_nopar:Npn \@@_execute_branches_meaning:
   {
-    \if_meaning:w \l_peek_token \l_peek_search_token
-      \exp_after:wN \peek_true:w
+    \if_meaning:w \l_peek_token \l_@@_search_token
+      \exp_after:wN \@@_true:w
     \else:
-      \exp_after:wN \peek_false:w
+      \exp_after:wN \@@_false:w
     \fi:
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\peek_execute_branches_charcode:}
-% \begin{macro}[aux]{\peek_execute_branches_charcode:NN}
+% \begin{macro}{\@@_execute_branches_charcode:}
+% \begin{macro}[aux]{\@@_execute_branches_charcode:NN}
 %   First the character code test there is a need to worry about \TeX{}
 %   grabbing brace group or skipping spaces. These are all tested for
 %   using a category code check before grabbing what must be a real
 %   single token and doing the comparison.
 %    \begin{macrocode}
-\cs_new_nopar:Npn \peek_execute_branches_charcode:
+\cs_new_nopar:Npn \@@_execute_branches_charcode:
   {
     \bool_if:nTF
       {
@@ -2076,18 +2017,18 @@
         || \token_if_eq_catcode_p:NN \l_peek_token \c_group_end_token
         || \token_if_eq_meaning_p:NN \l_peek_token \c_space_token
       }
-      { \peek_false:w }
+      { \@@_false:w }
       {
-        \exp_after:wN \peek_execute_branches_charcode_aux:NN
-          \l_peek_search_tl
+        \exp_after:wN \@@_execute_branches_charcode_aux:NN
+          \l_@@_search_tl
       }
   }
-\cs_new:Npn \peek_execute_branches_charcode_aux:NN #1#2
+\cs_new:Npn \@@_execute_branches_charcode_aux:NN #1#2
   {
     \if:w \exp_not:N #1 \exp_not:N #2
-      \exp_after:wN \peek_true:w
+      \exp_after:wN \@@_true:w
     \else:
-      \exp_after:wN \peek_false:w
+      \exp_after:wN \@@_false:w
     \fi:
     #2
   }
@@ -2095,46 +2036,46 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\peek_ignore_spaces_execute_branches:}
-% \begin{macro}[aux]{\peek_ignore_spaces_execute_branches_aux:}
+% \begin{macro}{\@@_ignore_spaces_execute_branches:}
+% \begin{macro}[aux]{\@@_ignore_spaces_execute_branches_aux:}
 %   This function removes one token at a time with a mechanism that can
 %   be applied to things other than spaces.
 %    \begin{macrocode}
-\cs_new_protected_nopar:Npn \peek_ignore_spaces_execute_branches:
+\cs_new_protected_nopar:Npn \@@_ignore_spaces_execute_branches:
   {
     \token_if_eq_meaning:NNTF \l_peek_token \c_space_token
       {
-        \tex_afterassignment:D \peek_ignore_spaces_execute_branches_aux:
-        \cs_set_eq:NN \peek_tmp:w
+        \tex_afterassignment:D \@@_ignore_spaces_execute_branches_aux:
+        \cs_set_eq:NN \@@_tmp:w
       }
-      { \peek_execute_branches: }
+      { \@@_execute_branches: }
   }
-\cs_new_protected_nopar:Npn \peek_ignore_spaces_execute_branches_aux:
-  { \peek_after:Nw \peek_ignore_spaces_execute_branches: }
+\cs_new_protected_nopar:Npn \@@_ignore_spaces_execute_branches_aux:
+  { \peek_after:Nw \@@_ignore_spaces_execute_branches: }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[aux]{\peek_def:nnnn}
-% \begin{macro}[aux]{\peek_def_aux:nnnnn}
+% \begin{macro}[aux]{\@@_def:nnnn}
+% \begin{macro}[aux]{\@@_def:nnnnn}
 %   The public functions themselves cannot be defined using
 %   \cs{prg_new_conditional:Npnn} and so a couple of auxiliary functions
 %   are used. As a result, everything is done inside a group. As a result
 %   things are a bit complicated.
 %    \begin{macrocode}
 \group_begin:
-  \cs_set:Npn \peek_def:nnnn #1#2#3#4
+  \cs_set:Npn \@@_def:nnnn #1#2#3#4
     {
-      \peek_def_aux:nnnnn {#1} {#2} {#3} {#4} { TF }
-      \peek_def_aux:nnnnn {#1} {#2} {#3} {#4} { T }
-      \peek_def_aux:nnnnn {#1} {#2} {#3} {#4} { F }
+      \@@_def:nnnnn {#1} {#2} {#3} {#4} { TF }
+      \@@_def:nnnnn {#1} {#2} {#3} {#4} { T }
+      \@@_def:nnnnn {#1} {#2} {#3} {#4} { F }
     }
-  \cs_set:Npn \peek_def_aux:nnnnn #1#2#3#4#5
+  \cs_set:Npn \@@_def:nnnnn #1#2#3#4#5
     {
       \cs_new_nopar:cpx { #1 #5 }
         {
           \tl_if_empty:nF {#2}
-            { \exp_not:n { \cs_set_eq:NN \peek_execute_branches: #2 } }
+            { \exp_not:n { \cs_set_eq:NN \@@_execute_branches: #2 } }
           \exp_not:c { #3 #5 }
           \exp_not:n {#4}
         }
@@ -2150,22 +2091,22 @@
 %   With everything in place the definitions can take place. First for
 %   category codes.
 %    \begin{macrocode}
-  \peek_def:nnnn { peek_catcode:N }
+  \@@_def:nnnn { peek_catcode:N }
     { }
-    { peek_token_generic:NN }
-    { \peek_execute_branches_catcode: }
-  \peek_def:nnnn { peek_catcode_ignore_spaces:N }
-    { \peek_execute_branches_catcode: }
-    { peek_token_generic:NN }
-    { \peek_ignore_spaces_execute_branches: }
-  \peek_def:nnnn { peek_catcode_remove:N }
+    { @@_token_generic:NN }
+    { \@@_execute_branches_catcode: }
+  \@@_def:nnnn { peek_catcode_ignore_spaces:N }
+    { \@@_execute_branches_catcode: }
+    { @@_token_generic:NN }
+    { \@@_ignore_spaces_execute_branches: }
+  \@@_def:nnnn { peek_catcode_remove:N }
     { }
-    { peek_token_remove_generic:NN }
-    { \peek_execute_branches_catcode: }
-  \peek_def:nnnn { peek_catcode_remove_ignore_spaces:N }
-    { \peek_execute_branches_catcode: }
-    { peek_token_remove_generic:NN }
-    { \peek_ignore_spaces_execute_branches: }
+    { @@_token_remove_generic:NN }
+    { \@@_execute_branches_catcode: }
+  \@@_def:nnnn { peek_catcode_remove_ignore_spaces:N }
+    { \@@_execute_branches_catcode: }
+    { @@_token_remove_generic:NN }
+    { \@@_ignore_spaces_execute_branches: }
 %    \end{macrocode}
 % \end{macro}
 % \begin{macro}[TF]
@@ -2175,22 +2116,22 @@
 %   }
 %   Then for character codes.
 %    \begin{macrocode}
-  \peek_def:nnnn { peek_charcode:N }
+  \@@_def:nnnn { peek_charcode:N }
     { }
-    { peek_token_generic:NN }
-    { \peek_execute_branches_charcode: }
-  \peek_def:nnnn { peek_charcode_ignore_spaces:N }
-    { \peek_execute_branches_charcode: }
-    { peek_token_generic:NN }
-    { \peek_ignore_spaces_execute_branches: }
-  \peek_def:nnnn { peek_charcode_remove:N }
+    { @@_token_generic:NN }
+    { \@@_execute_branches_charcode: }
+  \@@_def:nnnn { peek_charcode_ignore_spaces:N }
+    { \@@_execute_branches_charcode: }
+    { @@_token_generic:NN }
+    { \@@_ignore_spaces_execute_branches: }
+  \@@_def:nnnn { peek_charcode_remove:N }
     { }
-    { peek_token_remove_generic:NN }
-    { \peek_execute_branches_charcode: }
-  \peek_def:nnnn { peek_charcode_remove_ignore_spaces:N }
-    { \peek_execute_branches_charcode: }
-    { peek_token_remove_generic:NN }
-    { \peek_ignore_spaces_execute_branches: }
+    { @@_token_remove_generic:NN }
+    { \@@_execute_branches_charcode: }
+  \@@_def:nnnn { peek_charcode_remove_ignore_spaces:N }
+    { \@@_execute_branches_charcode: }
+    { @@_token_remove_generic:NN }
+    { \@@_ignore_spaces_execute_branches: }
 %    \end{macrocode}
 % \end{macro}
 % \begin{macro}[TF]
@@ -2201,22 +2142,22 @@
 %   Finally for meaning, with the group closed to remove the temporary
 %   definition functions.
 %    \begin{macrocode}
-  \peek_def:nnnn { peek_meaning:N }
+  \@@_def:nnnn { peek_meaning:N }
     { }
-    { peek_token_generic:NN }
-    { \peek_execute_branches_meaning: }
-  \peek_def:nnnn { peek_meaning_ignore_spaces:N }
-    { \peek_execute_branches_meaning: }
-    { peek_token_generic:NN }
-    { \peek_ignore_spaces_execute_branches: }
-  \peek_def:nnnn { peek_meaning_remove:N }
+    { @@_token_generic:NN }
+    { \@@_execute_branches_meaning: }
+  \@@_def:nnnn { peek_meaning_ignore_spaces:N }
+    { \@@_execute_branches_meaning: }
+    { @@_token_generic:NN }
+    { \@@_ignore_spaces_execute_branches: }
+  \@@_def:nnnn { peek_meaning_remove:N }
     { }
-    { peek_token_remove_generic:NN }
-    { \peek_execute_branches_meaning: }
-  \peek_def:nnnn { peek_meaning_remove_ignore_spaces:N }
-    { \peek_execute_branches_meaning: }
-    { peek_token_remove_generic:NN }
-    { \peek_ignore_spaces_execute_branches: }
+    { @@_token_remove_generic:NN }
+    { \@@_execute_branches_meaning: }
+  \@@_def:nnnn { peek_meaning_remove_ignore_spaces:N }
+    { \@@_execute_branches_meaning: }
+    { @@_token_remove_generic:NN }
+    { \@@_ignore_spaces_execute_branches: }
 \group_end:
 %    \end{macrocode}
 % \end{macro}
@@ -2226,7 +2167,7 @@
 % \begin{macro}{\token_get_prefix_spec:N}
 % \begin{macro}{\token_get_arg_spec:N}
 % \begin{macro}{\token_get_replacement_spec:N}
-% \begin{macro}[aux]{\token_get_prefix_arg_replacement_aux:wN}
+% \begin{macro}[aux]{\@@_get_prefix_arg_replacement:wN}
 %   We sometimes want to test if a
 %   control sequence can be expanded to reveal a hidden
 %   value. However, we cannot just expand the macro blindly as it may
@@ -2234,18 +2175,18 @@
 %   these functions to pick either the prefix(es), the argument
 %   specification, or the replacement text from a macro. All of this
 %   information is returned as characters with catcode~$12$. If the
-%   token in question isn't a macro, the token |\scan_stop:| is
+%   token in question isn't a macro, the token \cs{scan_stop:} is
 %   returned instead.
 %    \begin{macrocode}
 \exp_args:Nno \use:nn
-  { \cs_new:Npn \token_get_prefix_arg_replacement_aux:wN #1 }
+  { \cs_new:Npn \@@_get_prefix_arg_replacement:wN #1 }
   { \tl_to_str:n { macro : } #2 -> #3 \q_stop #4 }
   { #4 {#1} {#2} {#3} }
 \cs_new:Npn \token_get_prefix_spec:N #1
   {
     \token_if_macro:NTF #1
       {
-        \exp_after:wN \token_get_prefix_arg_replacement_aux:wN
+        \exp_after:wN \@@_get_prefix_arg_replacement:wN
           \token_to_meaning:N #1 \q_stop \use_i:nnn
       }
       { \scan_stop: }
@@ -2254,7 +2195,7 @@
   {
     \token_if_macro:NTF #1
       {
-        \exp_after:wN \token_get_prefix_arg_replacement_aux:wN
+        \exp_after:wN \@@_get_prefix_arg_replacement:wN
           \token_to_meaning:N #1 \q_stop \use_ii:nnn
       }
       { \scan_stop: }
@@ -2263,7 +2204,7 @@
   {
     \token_if_macro:NTF #1
       {
-        \exp_after:wN \token_get_prefix_arg_replacement_aux:wN
+        \exp_after:wN \@@_get_prefix_arg_replacement:wN
           \token_to_meaning:N #1 \q_stop \use_iii:nnn
       }
       { \scan_stop: }
@@ -2274,66 +2215,6 @@
 % \end{macro}
 % \end{macro}
 %
-% \subsection{Experimental token functions}
-%
-% \begin{macro}{\char_set_active:Npn,\char_set_active:Npx}
-% \begin{macro}{\char_set_active:Npn,\char_set_active:Npx}
-% \begin{macro}{\char_set_active_eq:NN,\char_gset_active_eq:NN}
-%    \begin{macrocode}
-\group_begin:
-  \char_set_catcode_active:N \^^@
-  \cs_set:Npn \char_tmp:NN #1#2
-    {
-      \cs_new:Npn #1 ##1
-        {
-          \char_set_catcode_active:n { `##1 }
-          \group_begin:
-          \char_set_lccode:nn { `\^^@ } { `##1 }
-          \tl_to_lowercase:n { \group_end: #2 ^^@ }
-        }
-    }
-  \char_tmp:NN \char_set_active:Npn    \cs_set:Npn
-  \char_tmp:NN \char_set_active:Npx    \cs_set:Npx
-  \char_tmp:NN \char_gset_active:Npn   \cs_gset:Npn
-  \char_tmp:NN \char_gset_active:Npx   \cs_gset:Npx
-  \char_tmp:NN \char_set_active_eq:NN  \cs_set_eq:NN
-  \char_tmp:NN \char_gset_active_eq:NN \cs_gset_eq:NN
-\group_end:
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}[TF]{\peek_N_type:}
-% \begin{macro}{\peek_execute_branches_N_type:}
-%   The next token is normal if it is neither a begin-group token,
-%   nor an end-group token, nor a charcode-$32$ space token.
-%   Note that implicit begin-group tokens, end-group tokens, and
-%   spaces are also recognized as non-\texttt{N}-type.
-%   Here, there is no \meta{search token}, so we feed a dummy
-%   \cs{scan_stop:} to the \cs{peek_token_generic::NN} functions.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \peek_execute_branches_N_type:
-  {
-    \bool_if:nTF
-      {
-        \token_if_eq_catcode_p:NN \l_peek_token \c_group_begin_token ||
-        \token_if_eq_catcode_p:NN \l_peek_token \c_group_end_token   ||
-        \token_if_eq_meaning_p:NN \l_peek_token \c_space_token
-      }
-      { \peek_false:w }
-      { \peek_true:w }
-  }
-\cs_new_protected_nopar:Npn \peek_N_type:TF
-  { \peek_token_generic:NNTF \peek_execute_branches_N_type: \scan_stop: }
-\cs_new_protected_nopar:Npn \peek_N_type:T
-  { \peek_token_generic:NNT  \peek_execute_branches_N_type: \scan_stop: }
-\cs_new_protected_nopar:Npn \peek_N_type:F
-  { \peek_token_generic:NNF  \peek_execute_branches_N_type: \scan_stop: }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
 % \subsection{Deprecated functions}
 %
 % Deprecated on 2011-05-27, for removal by 2011-08-31.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/expl3.sty b/Master/texmf-dist/tex/latex/l3kernel/expl3.sty
index f264342f725..7b8c68154f9 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/expl3.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/expl3.sty
@@ -45,22 +45,23 @@
 %%   prior consultation with the LaTeX3 Project.
 %%
 %% -----------------------------------------------------------------------
-\RequirePackage{l3names}[2011/12/30]
-\@ifpackagelater{l3names}{2011/12/30}
+\RequirePackage{l3names}[2012/07/15]
+\@ifpackagelater{l3names}{2012/07/15}
   {}
-  {
+  {%
     \PackageError{expl3}{Mismatched LaTeX3 packages detected.}
-      {
+      {%
         Please install an up to date version of l3kernel
-        using your TeX package manager or from CTAN.\\ \\
-        Loading expl3 will abort!
-      }
+        using your TeX package manager or from CTAN.%
+        \MessageBreak \MessageBreak
+        Loading expl3 will abort!%
+      }%
     \endinput
   }
 \def\ExplFileName{expl3}
 \def\ExplFileDescription{L3 Experimental code bundle wrapper}
-\def\ExplFileDate{2012/04/23}
-\def\ExplFileVersion{3570}
+\def\ExplFileDate{2012/07/16}
+\def\ExplFileVersion{3990}
 \RequirePackage{etex}
 \reserveinserts{32}
 \ProvidesExplPackage
@@ -75,129 +76,128 @@
 \expl@create@bool@option { check-declarations } \l@expl@check@declarations@bool
 \expl@create@bool@option { log-functions }      \l@expl@log@functions@bool
 \expl@create@bool@option { native-drivers }     \l@expl@native@drivers@bool
-\ProcessOptions \relax
 \let \expl@create@bool@option \@undefined
-\ifodd \l@expl@native@drivers@bool \relax
-\else
-  \RequirePackage { color , graphics }
-\fi
-\RequirePackage{ l3basics, l3expan, l3tl }
+\ProcessOptions \relax
+\RequirePackage { l3basics, l3expan, l3tl }
 \ifodd \l@expl@check@declarations@bool \relax
-  \cs_new_protected:Npn \cs_check_exists:N #1
+  \cs_new_protected:Npn \__cs_check_exists:N #1
     {
       \cs_if_exist:NF #1
         {
-          \msg_kernel_error:nnx { check } { non-declared-variable }
+          \__msg_kernel_error:nnx { check } { non-declared-variable }
             { \token_to_str:N #1 }
         }
     }
   \cs_set_protected:Npn \tl_set:Nn #1#2
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_set_nopar:Npx #1 { \exp_not:n {#2} }
     }
   \cs_set_protected:Npn \tl_set:Nx #1#2
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_set_nopar:Npx #1 {#2}
     }
   \cs_set_protected:Npn \tl_gset:Nn #1#2
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_gset_nopar:Npx #1 { \exp_not:n {#2} }
     }
   \cs_set_protected:Npn \tl_gset:Nx #1#2
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_gset_nopar:Npx #1 {#2}
     }
   \cs_set_protected:Npn \tl_set_eq:NN #1#2
     {
-      \cs_check_exists:N #1
-      \cs_check_exists:N #2
+      \__cs_check_exists:N #1
+      \__cs_check_exists:N #2
       \cs_set_eq:NN #1 #2
     }
   \cs_set_protected:Npn \tl_gset_eq:NN #1#2
     {
-      \cs_check_exists:N #1
-      \cs_check_exists:N #2
+      \__cs_check_exists:N #1
+      \__cs_check_exists:N #2
       \cs_gset_eq:NN #1 #2
     }
 \fi
-\RequirePackage{
-  l3seq,
-  l3int,
-  l3quark,
-  l3prg}
+\RequirePackage { l3seq, l3int, l3quark, l3prg }
 \ifodd \l@expl@check@declarations@bool \relax
   \cs_set_protected:Npn \bool_set_true:N #1
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_set_eq:NN #1 \c_true_bool
     }
   \cs_set_protected:Npn \bool_set_false:N #1
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_set_eq:NN #1 \c_false_bool
     }
   \cs_set_protected:Npn \bool_gset_true:N #1
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_gset_eq:NN #1 \c_true_bool
     }
   \cs_set_protected:Npn \bool_gset_false:N #1
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_gset_eq:NN #1 \c_false_bool
     }
   \cs_set_protected:Npn \bool_set_eq:NN  #1
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_set_eq:NN #1
     }
   \cs_set_protected:Npn \bool_gset_eq:NN  #1
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \cs_gset_eq:NN #1
     }
   \cs_set_protected:Npn \bool_set:Nn #1#2
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \tex_chardef:D #1 = \bool_if_p:n {#2}
     }
   \cs_set_protected:Npn \bool_gset:Nn #1#2
     {
-      \cs_check_exists:N #1
+      \__cs_check_exists:N #1
       \tex_global:D \tex_chardef:D #1 = \bool_if_p:n {#2}
     }
 \fi
-\RequirePackage{
-  l3clist,
-  l3token,
-  l3prop,
-  l3msg,
-  l3file,
-  l3skip,
-  l3keys,
-  l3fp,
-  l3box,
-  l3coffins,
-  l3color,
-  l3luatex
-}
+\RequirePackage
+  {
+    l3clist,
+    l3token,
+    l3prop,
+    l3msg,
+    l3file,
+    l3skip,
+    l3keys,
+    l3fp,
+    l3box,
+    l3coffins,
+    l3color,
+    l3luatex,
+    l3candidates
+  }
 \bool_if:nT { \l@expl@check@declarations@bool }
   {
-    \msg_kernel_new:nnnn { check } { non-declared-variable }
+    \__msg_kernel_new:nnnn { check } { non-declared-variable }
       { The~variable~#1~has~not~been~declared~\msg_line_context:. }
       {
         Checking~is~active,~and~you~have~tried~do~so~something~like: \\
-        \ \ \tl_set:Nn ~ #1 ~ \iow_char:N \{ ~ ... ~ \iow_char:N \} \\
+        \ \ \tl_set:Nn ~ #1 ~ \{ ~ ... ~ \} \\
         without~first~having: \\
         \ \ \tl_new:N ~ #1  \\
         \\
         LaTeX~will~create~the~variable~and~continue.
       }
   }
+\AtBeginDocument
+  {
+    \cs_if_exist:NF \color
+      { \DeclareRobustCommand \color [2] [ ] { } }
+  }
 \bool_if:nTF { \l@expl@native@drivers@bool }
   {
     \xetex_if_engine:TF
@@ -210,13 +210,20 @@
           \file_input:n { l3dvips.def }
         \fi
       }
-    \AtBeginDocument
-      {
-        \cs_if_free:NT \color
-          { \DeclareRobustCommand \color [2] [ ] { } }
-      }
   }
   {
+    \tl_gput_left:Nn \@begindocumenthook { \RequirePackage { graphics } }
+    \__msg_kernel_new:nnnn { box } { clipping-not-available }
+      { Box~clipping~not~available. }
+      {
+        The~\box_clip:N~function~is~only~available~when~loading~expl3~
+        with~the~"native-drivers"~option.
+      }
+    \cs_set_protected:Npn \box_clip:N #1
+      {
+        \hbox_set:Nn #1 { \box_use:N #1 }
+        \__msg_kernel_error:nn { box } { clipping-not-available }
+      }
     \cs_set_protected:Npn \box_rotate:Nn #1#2
       { \hbox_set:Nn #1 { \rotatebox {#2} { \box_use:N #1 } } }
     \cs_set_protected:Npn \box_resize:Nnn #1#2#3
@@ -224,8 +231,8 @@
         \hbox_set:Nn #1
           {
             \resizebox *
-              { \etex_dimexpr:D #2 \scan_stop: }
-              { \etex_dimexpr:D #3 \scan_stop: }
+              { \__dim_eval:w #2 \__dim_eval_end: }
+              { \__dim_eval:w #3 \__dim_eval_end: }
               { \box_use:N #1 }
           }
       }
@@ -233,7 +240,7 @@
       {
         \hbox_set:Nn #1
           {
-            \resizebox * { ! } { \etex_dimexpr:D #2 \scan_stop: }
+            \resizebox * { ! } { \__dim_eval:w #2 \__dim_eval_end: }
               { \box_use:N #1 }
           }
       }
@@ -241,16 +248,23 @@
       {
         \hbox_set:Nn #1
           {
-            \resizebox * { \etex_dimexpr:D #2 \scan_stop: } { ! }
+            \resizebox * { \__dim_eval:w #2 \__dim_eval_end: } { ! }
               { \box_use:N #1 }
           }
       }
     \cs_set_protected:Npn \box_scale:Nnn #1#2#3
-      { \hbox_set:Nn #1 { \scalebox {#2} [#3] { \box_use:N #1 } } }
+      {
+        \hbox_set:Nn #1
+          {
+            \exp_last_unbraced:Nx \scalebox
+              { { \fp_eval:n {#2} } [ \fp_eval:n {#3} ] }
+              { \box_use:N #1 }
+          }
+      }
   }
 \cs_set_protected_nopar:Npn \ExplSyntaxOn
   {
-    \bool_if:NF \l_expl_status_bool
+    \bool_if:NF \l__kernel_expl_bool
       {
         \cs_set_protected_nopar:Npx \ExplSyntaxOff
           {
@@ -265,7 +279,7 @@
             \char_set_catcode:nn { 124 } { \char_value_catcode:n { 124 } }
             \char_set_catcode:nn { 126 } { \char_value_catcode:n { 126 } }
             \tex_endlinechar:D = \tex_the:D \tex_endlinechar:D \scan_stop:
-            \bool_set_false:N \l_expl_status_bool
+            \bool_set_false:N \l__kernel_expl_bool
             \cs_set_protected_nopar:Npn \ExplSyntaxOff { }
           }
       }
@@ -280,7 +294,7 @@
     \char_set_catcode_other:n            { 124 } % pipe
     \char_set_catcode_space:n            { 126 } % tilde
     \tex_endlinechar:D = 32 \scan_stop:
-    \bool_set_true:N \l_expl_status_bool
+    \bool_set_true:N \l__kernel_expl_bool
   }
 \cs_set_protected_nopar:Npx \ExplSyntaxOff
   {
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3basics.sty b/Master/texmf-dist/tex/latex/l3kernel/l3basics.sty
index 182505d931f..6b6c8e90276 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3basics.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3basics.sty
@@ -46,11 +46,11 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3basics.dtx 3491 2012-03-04 06:13:18Z bruno $
-  {L3 Experimental basic definitions}
+\GetIdInfo$Id: l3basics.dtx 3987 2012-07-15 21:57:39Z joseph $
+  {L3 Basic definitions}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 \tex_let:D \if_true:           \tex_iftrue:D
 \tex_let:D \if_false:          \tex_iffalse:D
 \tex_let:D \or:                \tex_or:D
@@ -80,11 +80,8 @@
 \tex_let:D \group_begin:       \tex_begingroup:D
 \tex_let:D \group_end:         \tex_endgroup:D
 \tex_let:D \if_int_compare:w   \tex_ifnum:D
-\tex_let:D \int_to_roman:w     \tex_romannumeral:D
+\tex_let:D \__int_to_roman:w     \tex_romannumeral:D
 \tex_let:D \group_insert_after:N \tex_aftergroup:D
-\tex_let:D \tex_global:D      \tex_global:D
-\tex_let:D \tex_long:D        \tex_long:D
-\tex_let:D \tex_protected:D   \etex_protected:D
 \tex_long:D \tex_def:D \exp_args:Nc #1#2 { \exp_after:wN #1 \cs:w #2 \cs_end: }
 \tex_def:D \token_to_str:c { \exp_args:Nc \token_to_str:N }
 \tex_long:D \tex_def:D \cs_meaning:c #1
@@ -97,14 +94,14 @@
     { \exp_args:Nc \cs_meaning:N {#1} }
     { \tl_to_str:n {undefined} }
   }
-\tex_protected:D \tex_def:D \cs_show:c
+\etex_protected:D \tex_def:D \cs_show:c
   { \group_begin: \exp_args:NNc \group_end: \cs_show:N }
 \tex_let:D \c_minus_one \m@ne
-\tex_chardef:D \c_sixteen = 16~
-\tex_chardef:D \c_zero    = 0~
-\tex_chardef:D \c_six     = 6~
-\tex_chardef:D \c_seven   = 7~
-\tex_chardef:D \c_twelve  = 12~
+\tex_chardef:D \c_sixteen = 16 ~
+\tex_chardef:D \c_zero    = 0 ~
+\tex_chardef:D \c_six     = 6 ~
+\tex_chardef:D \c_seven   = 7 ~
+\tex_chardef:D \c_twelve  = 12 ~
 \etex_ifdefined:D \luatex_luatexversion:D
   \tex_chardef:D \c_max_register_int = 65 535 ~
 \tex_else:D
@@ -112,18 +109,18 @@
 \tex_fi:D
 \tex_let:D \cs_set_nopar:Npn            \tex_def:D
 \tex_let:D \cs_set_nopar:Npx            \tex_edef:D
-\tex_protected:D \cs_set_nopar:Npn \cs_set:Npn
+\etex_protected:D \cs_set_nopar:Npn \cs_set:Npn
   { \tex_long:D \cs_set_nopar:Npn }
-\tex_protected:D \cs_set_nopar:Npn \cs_set:Npx
+\etex_protected:D \cs_set_nopar:Npn \cs_set:Npx
   { \tex_long:D \cs_set_nopar:Npx }
-\tex_protected:D \cs_set_nopar:Npn \cs_set_protected_nopar:Npn
-  { \tex_protected:D \cs_set_nopar:Npn }
-\tex_protected:D \cs_set_nopar:Npn \cs_set_protected_nopar:Npx
-  { \tex_protected:D \cs_set_nopar:Npx }
+\etex_protected:D \cs_set_nopar:Npn \cs_set_protected_nopar:Npn
+  { \etex_protected:D \cs_set_nopar:Npn }
+\etex_protected:D \cs_set_nopar:Npn \cs_set_protected_nopar:Npx
+  { \etex_protected:D \cs_set_nopar:Npx }
 \cs_set_protected_nopar:Npn \cs_set_protected:Npn
-  { \tex_protected:D \tex_long:D \cs_set_nopar:Npn }
+  { \etex_protected:D \tex_long:D \cs_set_nopar:Npn }
 \cs_set_protected_nopar:Npn \cs_set_protected:Npx
-  { \tex_protected:D \tex_long:D \cs_set_nopar:Npx }
+  { \etex_protected:D \tex_long:D \cs_set_nopar:Npx }
 \tex_let:D \cs_gset_nopar:Npn           \tex_gdef:D
 \tex_let:D \cs_gset_nopar:Npx           \tex_xdef:D
 \cs_set_protected_nopar:Npn \cs_gset:Npn
@@ -131,18 +128,18 @@
 \cs_set_protected_nopar:Npn \cs_gset:Npx
   { \tex_long:D \cs_gset_nopar:Npx }
 \cs_set_protected_nopar:Npn \cs_gset_protected_nopar:Npn
-  { \tex_protected:D \cs_gset_nopar:Npn }
+  { \etex_protected:D \cs_gset_nopar:Npn }
 \cs_set_protected_nopar:Npn \cs_gset_protected_nopar:Npx
-  { \tex_protected:D \cs_gset_nopar:Npx }
+  { \etex_protected:D \cs_gset_nopar:Npx }
 \cs_set_protected_nopar:Npn \cs_gset_protected:Npn
-  { \tex_protected:D \tex_long:D \cs_gset_nopar:Npn }
+  { \etex_protected:D \tex_long:D \cs_gset_nopar:Npn }
 \cs_set_protected_nopar:Npn \cs_gset_protected:Npx
-  { \tex_protected:D \tex_long:D \cs_gset_nopar:Npx }
+  { \etex_protected:D \tex_long:D \cs_gset_nopar:Npx }
 \cs_set:Npn \use:c #1 { \cs:w #1 \cs_end: }
 \cs_set_protected:Npn \use:x #1
   {
-    \cs_set_nopar:Npx \l_exp_internal_tl {#1}
-    \l_exp_internal_tl
+    \cs_set_nopar:Npx \l__exp_internal_tl {#1}
+    \l__exp_internal_tl
   }
 \cs_set:Npn \use:n    #1       {#1}
 \cs_set:Npn \use:nn   #1#2     {#1#2}
@@ -174,173 +171,198 @@
 \cs_set:Npn \use_none:nnnnnnnn  #1#2#3#4#5#6#7#8   { }
 \cs_set:Npn \use_none:nnnnnnnnn #1#2#3#4#5#6#7#8#9 { }
 \cs_set_nopar:Npn \prg_return_true:
-  { \exp_after:wN \use_i:nn  \int_to_roman:w }
+  { \exp_after:wN \use_i:nn  \__int_to_roman:w }
 \cs_set_nopar:Npn \prg_return_false:
-  { \exp_after:wN \use_ii:nn \int_to_roman:w}
+  { \exp_after:wN \use_ii:nn \__int_to_roman:w}
 \cs_set_protected_nopar:Npn \prg_set_conditional:Npnn
-  { \prg_generate_conditional_parm_aux:NNpnn \cs_set:Npn }
+  { \__prg_generate_conditional_parm:nnNpnn { set } { } }
 \cs_set_protected_nopar:Npn \prg_new_conditional:Npnn
-  { \prg_generate_conditional_parm_aux:NNpnn \cs_new:Npn }
+  { \__prg_generate_conditional_parm:nnNpnn { new } { } }
 \cs_set_protected_nopar:Npn \prg_set_protected_conditional:Npnn
-  { \prg_generate_conditional_parm_aux:NNpnn \cs_set_protected:Npn }
+  { \__prg_generate_conditional_parm:nnNpnn { set } { _protected } }
 \cs_set_protected_nopar:Npn \prg_new_protected_conditional:Npnn
-  { \prg_generate_conditional_parm_aux:NNpnn \cs_new_protected:Npn }
-\cs_set_protected:Npn \prg_generate_conditional_parm_aux:NNpnn #1#2#3#
+  { \__prg_generate_conditional_parm:nnNpnn { new } { _protected } }
+\cs_set_protected:Npn \__prg_generate_conditional_parm:nnNpnn #1#2#3#4#
   {
-    \cs_split_function:NN #2 \prg_generate_conditional_aux:nnNNnnnn
-    #1 { parm } {#3}
+    \__cs_split_function:NN #3 \__prg_generate_conditional:nnNnnnnn
+    {#1} {#2} {#4}
   }
 \cs_set_protected_nopar:Npn \prg_set_conditional:Nnn
-  { \prg_generate_conditional_count_aux:NNnn \cs_set:Npn }
+  { \__prg_generate_conditional_count:nnNnn { set } { } }
 \cs_set_protected_nopar:Npn \prg_new_conditional:Nnn
-  { \prg_generate_conditional_count_aux:NNnn \cs_new:Npn }
+  { \__prg_generate_conditional_count:nnNnn { new } { } }
 \cs_set_protected_nopar:Npn \prg_set_protected_conditional:Nnn
-  { \prg_generate_conditional_count_aux:NNnn \cs_set_protected:Npn }
+  { \__prg_generate_conditional_count:nnNnn { set } { _protected } }
 \cs_set_protected_nopar:Npn \prg_new_protected_conditional:Nnn
-  { \prg_generate_conditional_count_aux:NNnn \cs_new_protected:Npn }
-\cs_set_protected:Npn \prg_generate_conditional_count_aux:NNnn #1#2
+  { \__prg_generate_conditional_count:nnNnn { new } { _protected } }
+\cs_set_protected:Npn \__prg_generate_conditional_count:nnNnn #1#2#3
   {
-    \exp_args:Nnf \use:n
-      {
-        \cs_split_function:NN #2 \prg_generate_conditional_aux:nnNNnnnn
-        #1 { count }
-      }
-      { \cs_get_arg_count_from_signature:N #2 }
+    \__cs_split_function:NN #3 \__prg_generate_conditional_count:nnNnnnn
+    {#1} {#2}
   }
-\cs_set_protected:Npn \prg_set_eq_conditional:NNn #1#2#3
-  { \prg_set_eq_conditional_aux:NNNn \cs_set_eq:cc #1#2 {#3} }
-\cs_set_protected:Npn \prg_new_eq_conditional:NNn #1#2#3
-  { \prg_set_eq_conditional_aux:NNNn \cs_new_eq:cc #1#2 {#3} }
-\cs_set_protected:Npn \prg_generate_conditional_aux:nnNNnnnn #1#2#3#4#5#6#7#8
+\cs_set_protected:Npn \__prg_generate_conditional_count:nnNnnnn #1#2#3#4#5
   {
-    \prg_generate_conditional_aux:nnw {#5}
+    \__cs_parm_from_arg_count:nnF
+      { \__prg_generate_conditional:nnNnnnnn {#1} {#2} #3 {#4} {#5} }
+      { \tl_count:n {#2} }
       {
-        #4 {#1} {#2} {#6} {#8}
+        \__msg_kernel_error:nnxx { kernel } { bad-number-of-arguments }
+          { \token_to_str:c { #1 : #2 } }
+          { \tl_count:n {#2} }
+        \use_none:nn
       }
-      #7 , ? , \q_recursion_stop
   }
-\cs_set_protected:Npn \prg_generate_conditional_aux:nnw #1#2#3 ,
+\cs_set_protected:Npn \__prg_generate_conditional:nnNnnnnn #1#2#3#4#5#6#7#8
   {
-    \if:w ?#3
-      \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
+    \if_meaning:w \c_true_bool #3
+      \exp_after:wN \use_i:nn
+    \else:
+      \exp_after:wN \use_ii:nn
     \fi:
-    \use:c { prg_generate_#3_form_#1:Nnnnn } #2
-    \prg_generate_conditional_aux:nnw {#1} {#2}
+    {
+      \__prg_generate_conditional:nnnnnnw
+        {#4} {#5} {#1} {#2} {#6} {#8}
+        #7 , , \q_recursion_stop
+    }
+    {
+      \__msg_kernel_error:nnx { kernel } { missing-colon }
+        { \token_to_str:c {#1} }
+    }
   }
-\cs_set_protected:Npn \prg_generate_p_form_parm:Nnnnn #1#2#3#4#5
+\cs_set_protected:Npn \__prg_generate_conditional:nnnnnnw #1#2#3#4#5#6#7 ,
   {
-    \exp_args:Nc #1 { #2 _p: #3 } #4
+    \if_catcode:w \scan_stop: \etex_detokenize:D {#7} \scan_stop:
+      \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
+    \fi:
+    \use:c { __prg_generate_ \etex_detokenize:D {#7} _form:wnnnnnn }
+        \__msg_kernel_error:nnxx
+          { kernel } { conditional-form-unknown }
+          { \tl_to_str:n {#7} } { \token_to_str:c { #3 : #4 } }
+        \use_none:nnnnnnn
+      \q_stop
+      {#1} {#2} {#3} {#4} {#5} {#6}
+    \__prg_generate_conditional:nnnnnnw {#1} {#2} {#3} {#4} {#5} {#6}
+  }
+\cs_set_protected:Npn \__prg_generate_p_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
+  {
+    \if_meaning:w \scan_stop: #3 \scan_stop:
+      \exp_after:wN \use_i:nn
+    \else:
+      \exp_after:wN \use_ii:nn
+    \fi:
       {
-        #5 \c_zero
-        \c_true_bool \c_false_bool
+        \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 _p: #5 } #6
+          { #7 \c_zero \c_true_bool \c_false_bool }
       }
-  }
-\cs_set_protected:Npn \prg_generate_T_form_parm:Nnnnn #1#2#3#4#5
-  {
-    \exp_args:Nc #1 { #2 : #3 T } #4
       {
-        #5 \c_zero
-        \use:n \use_none:n
+        \__msg_kernel_error:nnx { kernel } { protected-predicate }
+          { \token_to_str:c { #4 _p: #5 } }
       }
   }
-\cs_set_protected:Npn \prg_generate_F_form_parm:Nnnnn #1#2#3#4#5
+\cs_set_protected:Npn \__prg_generate_T_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc #1 { #2 : #3 F } #4
-      {
-        #5 \c_zero
-        { }
-      }
+    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 T } #6
+      { #7 \c_zero \use:n \use_none:n }
   }
-\cs_set_protected:Npn \prg_generate_TF_form_parm:Nnnnn #1#2#3#4#5
+\cs_set_protected:Npn \__prg_generate_F_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc #1 { #2 : #3 TF } #4
-      { #5 \c_zero }
+    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 F } #6
+      { #7 \c_zero { } }
   }
-\cs_set_protected:Npn \prg_generate_p_form_count:Nnnnn #1#2#3#4#5
+\cs_set_protected:Npn \__prg_generate_TF_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \cs_generate_from_arg_count:cNnn { #2 _p: #3 } #1 {#4}
-      {
-        #5 \c_zero
-        \c_true_bool \c_false_bool
-      }
+    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 TF } #6
+      { #7 \c_zero }
   }
-\cs_set_protected:Npn \prg_generate_T_form_count:Nnnnn #1#2#3#4#5
+\cs_set_protected:Npn \prg_set_eq_conditional:NNn #1#2
   {
-    \cs_generate_from_arg_count:cNnn { #2 : #3 T } #1 {#4}
-      {
-        #5 \c_zero
-        \use:n \use_none:n
-      }
+    \__cs_split_function:NN #2 \__prg_set_eq_conditional:nnNNNn
+    \cs_set_eq:cc #1
   }
-\cs_set_protected:Npn \prg_generate_F_form_count:Nnnnn #1#2#3#4#5
+\cs_set_protected:Npn \prg_new_eq_conditional:NNn #1#2
   {
-    \cs_generate_from_arg_count:cNnn { #2 : #3 F } #1 {#4}
-      {
-        #5 \c_zero
-        { }
-      }
+    \__cs_split_function:NN #2 \__prg_set_eq_conditional:nnNNNn
+    \cs_new_eq:cc #1
   }
-\cs_set_protected:Npn \prg_generate_TF_form_count:Nnnnn #1#2#3#4#5
+\cs_set_protected:Npn \__prg_set_eq_conditional:nnNNNn #1#2#3#4#5#6
   {
-    \cs_generate_from_arg_count:cNnn { #2 : #3 TF } #1 {#4}
-      { #5 \c_zero }
+    \__cs_split_function:NN #5 \__prg_set_eq_conditional:nnNnnNNw
+    {#1} {#2} #3 #4
+    #6 , \scan_stop: , \q_recursion_stop
+  }
+\cs_set_protected:Npn \__prg_set_eq_conditional:nnNnnNNw #1#2#3#4#5#6
+  {
+    \if_meaning:w \c_false_bool #3
+      \__msg_kernel_error:nnx { kernel } { missing-colon }
+        { \token_to_str:c {#1} }
+      \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
+    \fi:
+    \if_meaning:w \c_false_bool #6
+      \__msg_kernel_error:nnx { kernel } { missing-colon }
+        { \token_to_str:c {#4} }
+      \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
+    \fi:
+    \__prg_set_eq_conditional_loop:nnnnNw {#1} {#2} {#4} {#5}
   }
-\cs_set_protected:Npn \prg_set_eq_conditional_aux:NNNn #1#2#3#4
-  { \prg_set_eq_conditional_aux:NNNw #1#2#3#4 , ? , \q_recursion_stop }
-\cs_set_protected:Npn \prg_set_eq_conditional_aux:NNNw #1#2#3#4 ,
+\cs_set_protected:Npn \__prg_set_eq_conditional_loop:nnnnNw #1#2#3#4#5#6 ,
   {
-    \if:w ? #4 \scan_stop:
+    \if_meaning:w \scan_stop: #6 \scan_stop:
       \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
     \fi:
-    #1
-    { \exp_args:NNc \cs_split_function:NN #2 { prg_conditional_form_#4:nnn } }
-    { \exp_args:NNc \cs_split_function:NN #3 { prg_conditional_form_#4:nnn } }
-    \prg_set_eq_conditional_aux:NNNw #1 {#2} {#3}
-  }
-\cs_set:Npn \prg_conditional_form_p:nnn  #1#2#3 { #1 _p : #2 }
-\cs_set:Npn \prg_conditional_form_TF:nnn #1#2#3 { #1    : #2 TF }
-\cs_set:Npn \prg_conditional_form_T:nnn  #1#2#3 { #1    : #2 T }
-\cs_set:Npn \prg_conditional_form_F:nnn  #1#2#3 { #1    : #2 F }
-\tex_chardef:D \c_true_bool  = 1~
-\tex_chardef:D \c_false_bool = 0~
+    \cs_if_exist:cTF
+      { \use:c { __prg_conditional_ #6 _form:nn } {#3} {#4} }
+      {
+        #5
+          { \use:c { __prg_conditional_ #6 _form:nn } {#1} {#2} }
+          { \use:c { __prg_conditional_ #6 _form:nn } {#3} {#4} }
+      }
+      {
+        \__msg_kernel_error:nnx { kernel } { command-not-defined }
+          {
+            \token_to_str:c
+              { \use:c { __prg_conditional_ #6 _form:nn } {#3} {#4} }
+          }
+      }
+    \__prg_set_eq_conditional_loop:nnnnNw {#1} {#2} {#3} {#4} #5
+  }
+\cs_set:Npn \__prg_conditional_p_form:nn  #1#2 { #1 _p : #2 }
+\cs_set:Npn \__prg_conditional_TF_form:nn #1#2 { #1    : #2 TF }
+\cs_set:Npn \__prg_conditional_T_form:nn  #1#2 { #1    : #2 T }
+\cs_set:Npn \__prg_conditional_F_form:nn  #1#2 { #1    : #2 F }
+\tex_chardef:D \c_true_bool  = 1 ~
+\tex_chardef:D \c_false_bool = 0 ~
 \cs_set_nopar:Npn \cs_to_str:N
   {
-    \int_to_roman:w
-      \if:w \token_to_str:N \ \cs_to_str_aux:w \fi:
-      \exp_after:wN \cs_to_str_aux:N \token_to_str:N
+    \__int_to_roman:w
+      \if:w \token_to_str:N \ \__cs_to_str:w \fi:
+      \exp_after:wN \__cs_to_str:N \token_to_str:N
   }
-\cs_set:Npn \cs_to_str_aux:N #1 { \c_zero }
-\cs_set:Npn \cs_to_str_aux:w #1 \cs_to_str_aux:N
-  { - \int_value:w \fi: \exp_after:wN \c_zero }
+\cs_set:Npn \__cs_to_str:N #1 { \c_zero }
+\cs_set:Npn \__cs_to_str:w #1 \__cs_to_str:N
+  { - \__int_value:w \fi: \exp_after:wN \c_zero }
 \group_begin:
-  \tex_lccode:D  `\@ = `\: \scan_stop:
-  \tex_catcode:D `\@ = 12~
+\tex_lccode:D  `\@ = `\: \scan_stop:
+\tex_catcode:D `\@ = 12 ~
 \tex_lowercase:D
   {
     \group_end:
-    \cs_set:Npn \cs_split_function:NN #1#2
+    \cs_set:Npn \__cs_split_function:NN #1
       {
         \exp_after:wN \exp_after:wN
-        \exp_after:wN \cs_split_function_aux:w
-          \cs_to_str:N #1 @ a \q_stop #2
+        \exp_after:wN \__cs_split_function_i:w
+          \cs_to_str:N #1 \q_mark \c_true_bool
+          @ \q_mark \c_false_bool
+          \q_stop
       }
-    \cs_set:Npn \cs_split_function_aux:w #1 @ #2#3 \q_stop #4
-      {
-        \if_meaning:w a #2
-          \exp_after:wN \use_i:nn
-        \else:
-          \exp_after:wN\use_ii:nn
-        \fi:
-        { #4 {#1} { } \c_false_bool }
-        { \cs_split_function_auxii:w #2#3 \q_stop #4 {#1} }
-      }
-    \cs_set:Npn \cs_split_function_auxii:w #1 @a \q_stop #2#3
-      { #2{#3}{#1}\c_true_bool }
-  }
-\cs_set:Npn \cs_get_function_name:N #1
-  { \cs_split_function:NN #1 \use_i:nnn }
-\cs_set:Npn \cs_get_function_signature:N #1
-  { \cs_split_function:NN #1 \use_ii:nnn }
+    \cs_set:Npn \__cs_split_function_i:w #1 @ #2 \q_mark #3#4 \q_stop #5
+      { \__cs_split_function_ii:w #5 #1 \q_mark \q_stop {#2} #3 }
+    \cs_set:Npn \__cs_split_function_ii:w #1#2 \q_mark #3 \q_stop
+      { #1 {#2} }
+  }
+\cs_set:Npn \__cs_get_function_name:N #1
+  { \__cs_split_function:NN #1 \use_i:nnn }
+\cs_set:Npn \__cs_get_function_signature:N #1
+  { \__cs_split_function:NN #1 \use_ii:nnn }
 \prg_set_conditional:Npnn \cs_if_exist:N #1 { p , T , F , TF }
   {
     \if_meaning:w #1 \scan_stop:
@@ -417,7 +439,7 @@
   { \tex_immediate:D \tex_write:D \c_minus_one }
 \cs_set_protected_nopar:Npn \iow_term:x
   { \tex_immediate:D \tex_write:D \c_sixteen }
-\cs_set_protected:Npn \msg_kernel_error:nnxx #1#2#3#4
+\cs_set_protected:Npn \__msg_kernel_error:nnxx #1#2#3#4
   {
     \tex_errmessage:D
       {
@@ -429,85 +451,85 @@
       }
     \tex_end:D
   }
-\cs_set_protected:Npn \msg_kernel_error:nnx #1#2#3
-  { \msg_kernel_error:nnxx {#1} {#2} {#3} { } }
-\cs_set_protected:Npn \msg_kernel_error:nn #1#2
-  { \msg_kernel_error:nnxx {#1} {#2} { } { } }
+\cs_set_protected:Npn \__msg_kernel_error:nnx #1#2#3
+  { \__msg_kernel_error:nnxx {#1} {#2} {#3} { } }
+\cs_set_protected:Npn \__msg_kernel_error:nn #1#2
+  { \__msg_kernel_error:nnxx {#1} {#2} { } { } }
 \cs_set_nopar:Npn \msg_line_context:
-  { on~line~\tex_the:D \tex_inputlineno:D }
-\cs_set_protected:Npn \chk_if_free_cs:N #1
+  { on~line~ \tex_the:D \tex_inputlineno:D }
+\cs_set_protected:Npn \__chk_if_free_cs:N #1
   {
     \cs_if_free:NF #1
       {
-        \msg_kernel_error:nnxx { kernel } { command-already-defined }
+        \__msg_kernel_error:nnxx { kernel } { command-already-defined }
           { \token_to_str:N #1 } { \token_to_meaning:N #1 }
       }
 }
 \tex_ifodd:D \l@expl@log@functions@bool
-  \cs_set_protected:Npn \chk_if_free_cs:N #1
+  \cs_set_protected:Npn \__chk_if_free_cs:N #1
     {
       \cs_if_free:NF #1
         {
-          \msg_kernel_error:nnxx { kernel } { command-already-defined }
+          \__msg_kernel_error:nnxx { kernel } { command-already-defined }
             { \token_to_str:N #1 } { \token_to_meaning:N #1 }
         }
       \iow_log:x { Defining~\token_to_str:N #1~ \msg_line_context: }
     }
 \fi:
-\cs_set_protected_nopar:Npn \chk_if_free_cs:c
-  { \exp_args:Nc \chk_if_free_cs:N }
-\cs_set_protected:Npn \chk_if_exist_cs:N #1
+\cs_set_protected_nopar:Npn \__chk_if_free_cs:c
+  { \exp_args:Nc \__chk_if_free_cs:N }
+\cs_set_protected:Npn \__chk_if_exist_cs:N #1
   {
     \cs_if_exist:NF #1
       {
-        \msg_kernel_error:nnxx { kernel } { command-not-defined }
-          { \token_to_str:N #1 } { \token_to_meaning:N #1 }
+        \__msg_kernel_error:nnx { kernel } { command-not-defined }
+          { \token_to_str:N #1 }
       }
   }
-\cs_set_protected_nopar:Npn \chk_if_exist_cs:c
-  { \exp_args:Nc \chk_if_exist_cs:N }
-\cs_set:Npn \cs_tmp:w #1#2
+\cs_set_protected_nopar:Npn \__chk_if_exist_cs:c
+  { \exp_args:Nc \__chk_if_exist_cs:N }
+\cs_set:Npn \__cs_tmp:w #1#2
   {
     \cs_set_protected:Npn #1 ##1
        {
-         \chk_if_free_cs:N ##1
+         \__chk_if_free_cs:N ##1
          #2 ##1
       }
   }
-\cs_tmp:w \cs_new_nopar:Npn           \cs_gset_nopar:Npn
-\cs_tmp:w \cs_new_nopar:Npx           \cs_gset_nopar:Npx
-\cs_tmp:w \cs_new:Npn                 \cs_gset:Npn
-\cs_tmp:w \cs_new:Npx                 \cs_gset:Npx
-\cs_tmp:w \cs_new_protected_nopar:Npn \cs_gset_protected_nopar:Npn
-\cs_tmp:w \cs_new_protected_nopar:Npx \cs_gset_protected_nopar:Npx
-\cs_tmp:w \cs_new_protected:Npn       \cs_gset_protected:Npn
-\cs_tmp:w \cs_new_protected:Npx       \cs_gset_protected:Npx
-\cs_set:Npn \cs_tmp:w #1#2
+\__cs_tmp:w \cs_new_nopar:Npn           \cs_gset_nopar:Npn
+\__cs_tmp:w \cs_new_nopar:Npx           \cs_gset_nopar:Npx
+\__cs_tmp:w \cs_new:Npn                 \cs_gset:Npn
+\__cs_tmp:w \cs_new:Npx                 \cs_gset:Npx
+\__cs_tmp:w \cs_new_protected_nopar:Npn \cs_gset_protected_nopar:Npn
+\__cs_tmp:w \cs_new_protected_nopar:Npx \cs_gset_protected_nopar:Npx
+\__cs_tmp:w \cs_new_protected:Npn       \cs_gset_protected:Npn
+\__cs_tmp:w \cs_new_protected:Npx       \cs_gset_protected:Npx
+\cs_set:Npn \__cs_tmp:w #1#2
   { \cs_new_protected_nopar:Npn #1 { \exp_args:Nc #2 } }
-\cs_tmp:w \cs_set_nopar:cpn  \cs_set_nopar:Npn
-\cs_tmp:w \cs_set_nopar:cpx  \cs_set_nopar:Npx
-\cs_tmp:w \cs_gset_nopar:cpn \cs_gset_nopar:Npn
-\cs_tmp:w \cs_gset_nopar:cpx \cs_gset_nopar:Npx
-\cs_tmp:w \cs_new_nopar:cpn  \cs_new_nopar:Npn
-\cs_tmp:w \cs_new_nopar:cpx  \cs_new_nopar:Npx
-\cs_tmp:w \cs_set:cpn  \cs_set:Npn
-\cs_tmp:w \cs_set:cpx  \cs_set:Npx
-\cs_tmp:w \cs_gset:cpn \cs_gset:Npn
-\cs_tmp:w \cs_gset:cpx \cs_gset:Npx
-\cs_tmp:w \cs_new:cpn  \cs_new:Npn
-\cs_tmp:w \cs_new:cpx  \cs_new:Npx
-\cs_tmp:w \cs_set_protected_nopar:cpn  \cs_set_protected_nopar:Npn
-\cs_tmp:w \cs_set_protected_nopar:cpx  \cs_set_protected_nopar:Npx
-\cs_tmp:w \cs_gset_protected_nopar:cpn \cs_gset_protected_nopar:Npn
-\cs_tmp:w \cs_gset_protected_nopar:cpx \cs_gset_protected_nopar:Npx
-\cs_tmp:w \cs_new_protected_nopar:cpn  \cs_new_protected_nopar:Npn
-\cs_tmp:w \cs_new_protected_nopar:cpx  \cs_new_protected_nopar:Npx
-\cs_tmp:w \cs_set_protected:cpn  \cs_set_protected:Npn
-\cs_tmp:w \cs_set_protected:cpx  \cs_set_protected:Npx
-\cs_tmp:w \cs_gset_protected:cpn \cs_gset_protected:Npn
-\cs_tmp:w \cs_gset_protected:cpx \cs_gset_protected:Npx
-\cs_tmp:w \cs_new_protected:cpn  \cs_new_protected:Npn
-\cs_tmp:w \cs_new_protected:cpx  \cs_new_protected:Npx
+\__cs_tmp:w \cs_set_nopar:cpn  \cs_set_nopar:Npn
+\__cs_tmp:w \cs_set_nopar:cpx  \cs_set_nopar:Npx
+\__cs_tmp:w \cs_gset_nopar:cpn \cs_gset_nopar:Npn
+\__cs_tmp:w \cs_gset_nopar:cpx \cs_gset_nopar:Npx
+\__cs_tmp:w \cs_new_nopar:cpn  \cs_new_nopar:Npn
+\__cs_tmp:w \cs_new_nopar:cpx  \cs_new_nopar:Npx
+\__cs_tmp:w \cs_set:cpn  \cs_set:Npn
+\__cs_tmp:w \cs_set:cpx  \cs_set:Npx
+\__cs_tmp:w \cs_gset:cpn \cs_gset:Npn
+\__cs_tmp:w \cs_gset:cpx \cs_gset:Npx
+\__cs_tmp:w \cs_new:cpn  \cs_new:Npn
+\__cs_tmp:w \cs_new:cpx  \cs_new:Npx
+\__cs_tmp:w \cs_set_protected_nopar:cpn  \cs_set_protected_nopar:Npn
+\__cs_tmp:w \cs_set_protected_nopar:cpx  \cs_set_protected_nopar:Npx
+\__cs_tmp:w \cs_gset_protected_nopar:cpn \cs_gset_protected_nopar:Npn
+\__cs_tmp:w \cs_gset_protected_nopar:cpx \cs_gset_protected_nopar:Npx
+\__cs_tmp:w \cs_new_protected_nopar:cpn  \cs_new_protected_nopar:Npn
+\__cs_tmp:w \cs_new_protected_nopar:cpx  \cs_new_protected_nopar:Npx
+\__cs_tmp:w \cs_set_protected:cpn  \cs_set_protected:Npn
+\__cs_tmp:w \cs_set_protected:cpx  \cs_set_protected:Npx
+\__cs_tmp:w \cs_gset_protected:cpn \cs_gset_protected:Npn
+\__cs_tmp:w \cs_gset_protected:cpx \cs_gset_protected:Npx
+\__cs_tmp:w \cs_new_protected:cpn  \cs_new_protected:Npn
+\__cs_tmp:w \cs_new_protected:cpx  \cs_new_protected:Npx
 \cs_new_protected:Npn \cs_set_eq:NN #1 { \tex_let:D #1 =~ }
 \cs_new_protected_nopar:Npn \cs_set_eq:cN { \exp_args:Nc  \cs_set_eq:NN }
 \cs_new_protected_nopar:Npn \cs_set_eq:Nc { \exp_args:NNc \cs_set_eq:NN }
@@ -518,7 +540,7 @@
 \cs_new_protected_nopar:Npn \cs_gset_eq:cc { \exp_args:Ncc  \cs_gset_eq:NN }
 \cs_new_protected:Npn \cs_new_eq:NN #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \tex_global:D \cs_set_eq:NN #1
   }
 \cs_new_protected_nopar:Npn \cs_new_eq:cN { \exp_args:Nc  \cs_new_eq:NN }
@@ -535,122 +557,142 @@
     \fi:
     { \cs_gset_eq:cN {#1} \c_undefined:D }
   }
-\cs_new:Npn \cs_get_arg_count_from_signature:N #1
-  { \cs_split_function:NN #1 \cs_get_arg_count_from_signature_aux:nnN }
-\cs_new:Npn \cs_get_arg_count_from_signature_aux:nnN #1#2#3
+\cs_set_protected:Npn \__cs_parm_from_arg_count:nnF #1#2
   {
-    \if_meaning:w \c_true_bool #3
-      \exp_after:wN \use_i:nn
+    \exp_args:Nx \__cs_parm_from_arg_count_test:nnF
+      {
+        \exp_after:wN \exp_not:n
+        \if_case:w \__int_eval:w #2 \__int_eval_end:
+             { }
+        \or: { ##1 }
+        \or: { ##1##2 }
+        \or: { ##1##2##3 }
+        \or: { ##1##2##3##4 }
+        \or: { ##1##2##3##4##5 }
+        \or: { ##1##2##3##4##5##6 }
+        \or: { ##1##2##3##4##5##6##7 }
+        \or: { ##1##2##3##4##5##6##7##8 }
+        \or: { ##1##2##3##4##5##6##7##8##9 }
+        \else: { \c_false_bool }
+        \fi:
+      }
+      {#1}
+  }
+\cs_set_protected:Npn \__cs_parm_from_arg_count_test:nnF #1#2
+  {
+    \if_meaning:w \c_false_bool #1
+      \exp_after:wN \use_ii:nn
     \else:
-      \exp_after:wN\use_ii:nn
+      \exp_after:wN \use_i:nn
     \fi:
-    {
-      \exp_after:wN \cs_get_arg_count_from_signature_auxii:w
-        \use_none:nnnnnnnnn  #2 9876543210 \q_stop
-    }
-    { -1 }
-}
-\cs_new:Npn \cs_get_arg_count_from_signature_auxii:w #1#2 \q_stop {#1}
-\cs_new_nopar:Npn \cs_get_arg_count_from_signature:c
-  { \exp_args:Nc \cs_get_arg_count_from_signature:N }
-\cs_new_protected:Npn \cs_generate_from_arg_count:NNnn #1#2#3#4
+    { #2 {#1} }
+  }
+\cs_new:Npn \__cs_count_signature:N #1
+  { \int_eval:n { \__cs_split_function:NN #1 \__cs_count_signature:nnN } }
+\cs_new:Npn \__cs_count_signature:nnN #1#2#3
   {
-    \if_case:w \int_eval:w #3 \int_eval_end:
-         \cs_generate_from_arg_count_aux:nwn {}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3##4}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3##4##5}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3##4##5##6}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3##4##5##6##7}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3##4##5##6##7##8}
-    \or: \cs_generate_from_arg_count_aux:nwn {##1##2##3##4##5##6##7##8##9}
+    \if_meaning:w \c_true_bool #3
+      \tl_count:n {#2}
     \else:
-      \cs_generate_from_arg_count_error_msg:Nn #1 {#3}
-      \use_i:nnn
+      \c_minus_one
     \fi:
-    {#2#1}
-    {#4}
   }
-\cs_new_protected:Npn
-  \cs_generate_from_arg_count_aux:nwn #1 #2 \fi: #3
-  { \fi: #3 #1 }
+\cs_new_nopar:Npn \__cs_count_signature:c
+  { \exp_args:Nc \__cs_count_signature:N }
+\cs_new_protected:Npn \cs_generate_from_arg_count:NNnn #1#2#3#4
+  {
+    \__cs_parm_from_arg_count:nnF { \use:nnn #2 #1 } {#3}
+      {
+        \__msg_kernel_error:nnxx { kernel } { bad-number-of-arguments }
+          { \token_to_str:N #1 } { \int_eval:n {#3} }
+      }
+      {#4}
+  }
 \cs_new_protected_nopar:Npn \cs_generate_from_arg_count:cNnn
   { \exp_args:Nc \cs_generate_from_arg_count:NNnn }
 \cs_new_protected_nopar:Npn \cs_generate_from_arg_count:Ncnn
   { \exp_args:NNc \cs_generate_from_arg_count:NNnn }
-\cs_new_protected:Npn \cs_generate_from_arg_count_error_msg:Nn #1#2
+\cs_set:Npn \__cs_tmp:w #1#2#3
+  {
+    \cs_new_protected_nopar:cpx { cs_ #1 : #2 }
+      {
+        \exp_not:N \__cs_generate_from_signature:NNn
+        \exp_after:wN \exp_not:N \cs:w cs_ #1 : #3 \cs_end:
+      }
+  }
+\cs_new_protected:Npn \__cs_generate_from_signature:NNn #1#2
   {
-    \msg_kernel_error:nnxx { kernel } { bad-number-of-arguments }
-      { \token_to_str:N #1 } { \int_eval:n {#2} }
+    \__cs_split_function:NN #2 \__cs_generate_from_signature:nnNNNn
+    #1 #2
   }
-\cs_set:Npn \cs_tmp:w #1#2#3
+\cs_new_protected:Npn \__cs_generate_from_signature:nnNNNn #1#2#3#4#5#6
   {
-    \cs_new_protected:cpx { cs_ #1 : #2 } ##1##2
+    \bool_if:NTF #3
+      {
+        \cs_generate_from_arg_count:NNnn
+          #5 #4 { \tl_count:n {#2} } {#6}
+      }
       {
-        \exp_not:N \cs_generate_from_arg_count:NNnn ##1
-        \exp_after:wN \exp_not:N \cs:w cs_#1 : #3 \cs_end:
-          { \exp_not:N \cs_get_arg_count_from_signature:N ##1 }{##2}
+        \__msg_kernel_error:nnx { kernel } { missing-colon }
+          { \token_to_str:N #5 }
       }
   }
-\cs_tmp:w { set }                  { Nn } { Npn }
-\cs_tmp:w { set }                  { Nx } { Npx }
-\cs_tmp:w { set_nopar }            { Nn } { Npn }
-\cs_tmp:w { set_nopar }            { Nx } { Npx }
-\cs_tmp:w { set_protected }        { Nn } { Npn }
-\cs_tmp:w { set_protected }        { Nx } { Npx }
-\cs_tmp:w { set_protected_nopar }  { Nn } { Npn }
-\cs_tmp:w { set_protected_nopar }  { Nx } { Npx }
-\cs_tmp:w { gset }                 { Nn } { Npn }
-\cs_tmp:w { gset }                 { Nx } { Npx }
-\cs_tmp:w { gset_nopar }           { Nn } { Npn }
-\cs_tmp:w { gset_nopar }           { Nx } { Npx }
-\cs_tmp:w { gset_protected }       { Nn } { Npn }
-\cs_tmp:w { gset_protected }       { Nx } { Npx }
-\cs_tmp:w { gset_protected_nopar } { Nn } { Npn }
-\cs_tmp:w { gset_protected_nopar } { Nx } { Npx }
-\cs_tmp:w { new }                  { Nn } { Npn }
-\cs_tmp:w { new }                  { Nx } { Npx }
-\cs_tmp:w { new_nopar }            { Nn } { Npn }
-\cs_tmp:w { new_nopar }            { Nx } { Npx }
-\cs_tmp:w { new_protected }        { Nn } { Npn }
-\cs_tmp:w { new_protected }        { Nx } { Npx }
-\cs_tmp:w { new_protected_nopar }  { Nn } { Npn }
-\cs_tmp:w { new_protected_nopar }  { Nx } { Npx }
-\cs_set:Npn \cs_tmp:w #1#2#3
-  {
-    \cs_new_protected:cpx {cs_#1:#2} ##1##2
+\__cs_tmp:w { set }                  { Nn } { Npn }
+\__cs_tmp:w { set }                  { Nx } { Npx }
+\__cs_tmp:w { set_nopar }            { Nn } { Npn }
+\__cs_tmp:w { set_nopar }            { Nx } { Npx }
+\__cs_tmp:w { set_protected }        { Nn } { Npn }
+\__cs_tmp:w { set_protected }        { Nx } { Npx }
+\__cs_tmp:w { set_protected_nopar }  { Nn } { Npn }
+\__cs_tmp:w { set_protected_nopar }  { Nx } { Npx }
+\__cs_tmp:w { gset }                 { Nn } { Npn }
+\__cs_tmp:w { gset }                 { Nx } { Npx }
+\__cs_tmp:w { gset_nopar }           { Nn } { Npn }
+\__cs_tmp:w { gset_nopar }           { Nx } { Npx }
+\__cs_tmp:w { gset_protected }       { Nn } { Npn }
+\__cs_tmp:w { gset_protected }       { Nx } { Npx }
+\__cs_tmp:w { gset_protected_nopar } { Nn } { Npn }
+\__cs_tmp:w { gset_protected_nopar } { Nx } { Npx }
+\__cs_tmp:w { new }                  { Nn } { Npn }
+\__cs_tmp:w { new }                  { Nx } { Npx }
+\__cs_tmp:w { new_nopar }            { Nn } { Npn }
+\__cs_tmp:w { new_nopar }            { Nx } { Npx }
+\__cs_tmp:w { new_protected }        { Nn } { Npn }
+\__cs_tmp:w { new_protected }        { Nx } { Npx }
+\__cs_tmp:w { new_protected_nopar }  { Nn } { Npn }
+\__cs_tmp:w { new_protected_nopar }  { Nx } { Npx }
+\cs_set:Npn \__cs_tmp:w #1#2
+  {
+    \cs_new_protected_nopar:cpx { cs_ #1 : c #2 }
       {
-        \exp_not:N \cs_generate_from_arg_count:cNnn {##1}
-        \exp_after:wN \exp_not:N \cs:w cs_#1:#3 \cs_end:
-          { \exp_not:N \cs_get_arg_count_from_signature:c {##1} } {##2}
+        \exp_not:N \exp_args:Nc
+        \exp_after:wN \exp_not:N \cs:w cs_ #1 : N #2 \cs_end:
       }
   }
-\cs_tmp:w { set }                  { cn } { Npn }
-\cs_tmp:w { set }                  { cx } { Npx }
-\cs_tmp:w { set_nopar }            { cn } { Npn }
-\cs_tmp:w { set_nopar }            { cx } { Npx }
-\cs_tmp:w { set_protected }        { cn } { Npn }
-\cs_tmp:w { set_protected }        { cx } { Npx }
-\cs_tmp:w { set_protected_nopar }  { cn } { Npn }
-\cs_tmp:w { set_protected_nopar }  { cx } { Npx }
-\cs_tmp:w { gset }                 { cn } { Npn }
-\cs_tmp:w { gset }                 { cx } { Npx }
-\cs_tmp:w { gset_nopar }           { cn } { Npn }
-\cs_tmp:w { gset_nopar }           { cx } { Npx }
-\cs_tmp:w { gset_protected }       { cn } { Npn }
-\cs_tmp:w { gset_protected }       { cx } { Npx }
-\cs_tmp:w { gset_protected_nopar } { cn } { Npn }
-\cs_tmp:w { gset_protected_nopar } { cx } { Npx }
-\cs_tmp:w { new }                  { cn } { Npn }
-\cs_tmp:w { new }                  { cx } { Npx }
-\cs_tmp:w { new_nopar }            { cn } { Npn }
-\cs_tmp:w { new_nopar }            { cx } { Npx }
-\cs_tmp:w { new_protected }        { cn } { Npn }
-\cs_tmp:w { new_protected }        { cx } { Npx }
-\cs_tmp:w { new_protected_nopar }  { cn } { Npn }
-\cs_tmp:w { new_protected_nopar }  { cx } { Npx }
+\__cs_tmp:w { set }                  { n }
+\__cs_tmp:w { set }                  { x }
+\__cs_tmp:w { set_nopar }            { n }
+\__cs_tmp:w { set_nopar }            { x }
+\__cs_tmp:w { set_protected }        { n }
+\__cs_tmp:w { set_protected }        { x }
+\__cs_tmp:w { set_protected_nopar }  { n }
+\__cs_tmp:w { set_protected_nopar }  { x }
+\__cs_tmp:w { gset }                 { n }
+\__cs_tmp:w { gset }                 { x }
+\__cs_tmp:w { gset_nopar }           { n }
+\__cs_tmp:w { gset_nopar }           { x }
+\__cs_tmp:w { gset_protected }       { n }
+\__cs_tmp:w { gset_protected }       { x }
+\__cs_tmp:w { gset_protected_nopar } { n }
+\__cs_tmp:w { gset_protected_nopar } { x }
+\__cs_tmp:w { new }                  { n }
+\__cs_tmp:w { new }                  { x }
+\__cs_tmp:w { new_nopar }            { n }
+\__cs_tmp:w { new_nopar }            { x }
+\__cs_tmp:w { new_protected }        { n }
+\__cs_tmp:w { new_protected }        { x }
+\__cs_tmp:w { new_protected_nopar }  { n }
+\__cs_tmp:w { new_protected_nopar }  { x }
 \prg_new_conditional:Npnn \cs_if_eq:NN #1#2 { p , T , F , TF }
   {
     \if_meaning:w #1#2
@@ -668,17 +710,17 @@
 \cs_new_nopar:Npn \cs_if_eq:ccTF { \exp_args:Ncc \cs_if_eq:NNTF }
 \cs_new_nopar:Npn \cs_if_eq:ccT  { \exp_args:Ncc \cs_if_eq:NNT }
 \cs_new_nopar:Npn \cs_if_eq:ccF  { \exp_args:Ncc \cs_if_eq:NNF }
-\cs_new:Npn \kernel_register_show:N #1
+\cs_new_protected:Npn \__kernel_register_show:N #1
   {
     \cs_if_exist:NTF #1
       { \tex_showthe:D \use:n {#1} }
       {
-        \msg_kernel_error:nnx { kernel } { variable-not-defined }
+        \__msg_kernel_error:nnx { kernel } { variable-not-defined }
           { \token_to_str:N #1 }
       }
   }
-\cs_new_nopar:Npn \kernel_register_show:c
-  { \exp_args:Nc \kernel_register_show:N }
+\cs_new_protected_nopar:Npn \__kernel_register_show:c
+  { \exp_args:Nc \__kernel_register_show:N }
 \cs_new_eq:NN \luatex_if_engine:T  \use_none:n
 \cs_new_eq:NN \luatex_if_engine:F  \use:n
 \cs_new_eq:NN \luatex_if_engine:TF \use_ii:nn
@@ -720,14 +762,57 @@
       = \c_zero
       \prg_return_true: \else: \prg_return_false: \fi:
   }
-\prg_new_conditional:Npnn \str_if_eq:xx #1#2 { p , T , F , TF }
+\prg_new_conditional:Npnn \str_if_eq_x:nn #1#2 { p , T , F , TF }
   {
     \if_int_compare:w \pdftex_strcmp:D {#1} {#2} = \c_zero
       \prg_return_true: \else: \prg_return_false: \fi:
   }
-\cs_new_eq:NN \prg_break_point:n \use:n
-\cs_new:Npn \prg_map_break: #1 \prg_break_point:n #2 { #2 }
-\cs_new:Npn \prg_map_break:n #1 #2 \prg_break_point:n #3 { #3 #1 }
+\cs_new:Npn \__str_if_eq_x_return:nn #1 #2
+  {
+    \if_int_compare:w \pdftex_strcmp:D {#1} {#2} = \c_zero
+      \prg_return_true:
+    \else:
+      \prg_return_false:
+    \fi:
+  }
+\cs_new:Npn \str_case:nnn #1#2#3
+  {
+    \tex_romannumeral:D
+    \__str_case:nw {#1} #2 {#1} {#3} \q_recursion_stop
+  }
+\cs_new:Npn \__str_case:nw #1#2#3
+  {
+    \str_if_eq:nnTF {#1} {#2}
+      { \__str_case_end:nw {#3} }
+      { \__str_case:nw {#1} }
+  }
+\cs_new:Npn \str_case_x:nnn #1#2#3
+  {
+    \tex_romannumeral:D
+    \__str_case_x:nw {#1} #2 {#1} {#3} \q_recursion_stop
+  }
+\cs_new:Npn \__str_case_x:nw #1#2#3
+  {
+    \str_if_eq_x:nnTF {#1} {#2}
+      { \__str_case_end:nw {#3} }
+      { \__str_case_x:nw {#1} }
+  }
+\cs_new:Npn \__prg_case_end:nw #1#2 \q_recursion_stop { \c_zero #1 }
+\cs_new_eq:NN \__str_case_end:nw \__prg_case_end:nw
+\cs_new_eq:NN \__prg_break_point:Nn \use_ii:nn
+\cs_new:Npn \__prg_map_break:Nn #1#2#3 \__prg_break_point:Nn #4#5
+  {
+    #5
+    \if_meaning:w #1 #4
+      \exp_after:wN \use_iii:nnn
+    \fi:
+    \__prg_map_break:Nn #1 {#2}
+  }
+\cs_new_eq:NN \str_if_eq_p:xx \str_if_eq_x_p:nn
+\cs_new_eq:NN \str_if_eq:xxT  \str_if_eq_x:nnT
+\cs_new_eq:NN \str_if_eq:xxF  \str_if_eq_x:nnF
+\cs_new_eq:NN \str_if_eq:xxTF \str_if_eq_x:nnTF
+\cs_new_eq:NN \chk_if_free_cs:N \__chk_if_free_cs:N
 %% 
 %%
 %% End of file `l3basics.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3bootstrap.sty b/Master/texmf-dist/tex/latex/l3kernel/l3bootstrap.sty
index f5320078a78..8a260b26410 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3bootstrap.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3bootstrap.sty
@@ -13,7 +13,7 @@
 %% 
 %% Do not distribute a modified version of this file.
 %% 
-%% File: l3bootstrap.dtx Copyright (C) 2011 The LaTeX3 project
+%% File: l3bootstrap.dtx Copyright (C) 2011-2012 The LaTeX3 project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -46,20 +46,20 @@
 %%
 %% -----------------------------------------------------------------------
 \protected\def\GetIdInfo
-  {
+  {%
     \begingroup
-    \catcode 32 = 10 \relax
-    \GetIdInfoAuxI
+      \catcode 32 = 10 %
+      \GetIdInfoAuxI
   }
 \protected\def\GetIdInfoAuxI$#1$#2%
-  {
+  {%
     \def\tempa{#1}%
     \def\tempb{Id}%
     \ifx\tempa\tempb
       \def\tempa
         {%
           \endgroup
-          \def\ExplFileDate{9999/99/99}%
+          \def\ExplFileDate{9999/12/31}%
           \def\ExplFileDescription{#2}%
           \def\ExplFileName{[unknown name]}%
           \def\ExplFileExtension{[unknown extension]}%
@@ -69,33 +69,41 @@
       \def\tempa
         {%
           \endgroup
-          \GetIdInfoAuxII$#1${#2}%
+          \def\ExplFileDescription{#2}%
+          \GetIdInfoAuxII$#1 $%
         }%
     \fi
     \tempa
   }
-\protected\def\GetIdInfoAuxII$#1 #2.#3 #4 #5 #6 #7 #8$#9%
+\protected\def\GetIdInfoAuxII$#1 #2.#3 #4 #5 #6$%
   {%
     \def\ExplFileName{#2}%
     \def\ExplFileExtension{#3}%
     \def\ExplFileVersion{#4}%
-    \def\ExplFileDescription{#9}%
-    \GetIdInfoAuxIII#5\relax#3\relax#5\relax#6\relax
+    \begingroup
+      \def\tempa{#4}%
+      \def\tempb{-1}%
+      \ifx\tempa\tempb
+        \def\tempa
+          {%
+            \endgroup
+            \def\ExplFileDate{0000/00/00}%
+          }%
+      \else
+        \def\tempa
+          {%
+            \endgroup
+            \GetIdInfoAuxIII$#5$%
+          }%
+      \fi
+      \tempa
   }
-\protected\def\GetIdInfoAuxIII#1#2#3#4#5#6\relax
+\protected\def\GetIdInfoAuxIII$#1-#2-#3$%
   {%
-    \ifx#5/%
-      \expandafter\GetIdInfoAuxCVS
-    \else
-      \expandafter\GetIdInfoAuxSVN
-    \fi
+    \def\ExplFileDate{#1/#2/#3}%
   }
-\protected\def\GetIdInfoAuxCVS#1,v\relax#2\relax#3\relax
-  {\def\ExplFileDate{#2}}
-\protected\def\GetIdInfoAuxSVN#1\relax#2-#3-#4\relax#5Z\relax
-  {\def\ExplFileDate{#2/#3/#4}}
-\GetIdInfo$Id: l3bootstrap.dtx 3110 2011-12-29 14:23:48Z joseph $
-  {L3 experimental bootstrap code}
+\GetIdInfo$Id: l3bootstrap.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Bootstrap code}
 \ProvidesPackage{l3bootstrap}
   [%
     \ExplFileDate\space v\ExplFileVersion\space
@@ -113,6 +121,26 @@
 \else
   \expandafter\@tempa
 \fi
+\begingroup\expandafter\expandafter\expandafter\endgroup
+  \expandafter\ifx\csname pdfstrcmp\endcsname\relax
+  \let\pdfstrcmp\strcmp
+\fi
+\begingroup\expandafter\expandafter\expandafter\endgroup
+\expandafter\ifx\csname pdfstrcmp\endcsname\relax
+  \PackageError{expl3}{Required primitives not found}
+    {%
+      LaTeX3 requires the e-TeX primitives and \string\pdfstrcmp.\MessageBreak
+      \MessageBreak
+      These are available in engine versions:\MessageBreak
+      - pdfTeX 1.30\MessageBreak
+      - XeTeX 0.9994\MessageBreak
+      - LuaTeX 0.40\MessageBreak
+      or later.\MessageBreak
+      \MessageBreak
+      Loading of expl3 will abort!%
+    }
+  \expandafter\endinput
+\fi
 \protected\edef\ExplSyntaxOff
   {%
     \catcode   9 = \the\catcode   9\relax
@@ -125,7 +153,7 @@
     \catcode 124 = \the\catcode 124\relax
     \catcode 126 = \the\catcode 126\relax
     \endlinechar = \the\endlinechar\relax
-    \chardef\csname\detokenize{l_expl_status_bool}\endcsname = 0 \relax
+    \chardef\csname\detokenize{l__kernel_expl_bool}\endcsname = 0 \relax
   }
 \protected\edef\ExplSyntaxOn
   {
@@ -138,56 +166,9 @@
     \catcode 124 = 12 \relax
     \catcode 126 = 10 \relax
     \endlinechar = 32 \relax
-    \chardef\csname\detokenize{l_expl_status_bool}\endcsname = 1 \relax
+    \chardef\csname\detokenize{l__kernel_expl_bool}\endcsname = 1 \relax
   }
-\expandafter\chardef\csname\detokenize{l_expl_status_bool}\endcsname = 0 \relax
-\protected\def\GetIdInfo
-  {
-    \begingroup
-    \catcode 32 = 10 \relax
-    \GetIdInfoAuxI
-  }
-\protected\def\GetIdInfoAuxI$#1$#2%
-  {
-    \def\tempa{#1}%
-    \def\tempb{Id}%
-    \ifx\tempa\tempb
-      \def\tempa
-        {%
-          \endgroup
-          \def\ExplFileDate{9999/99/99}%
-          \def\ExplFileDescription{#2}%
-          \def\ExplFileName{[unknown name]}%
-          \def\ExplFileVersion{999}%
-        }%
-    \else
-      \def\tempa
-        {%
-          \endgroup
-          \GetIdInfoAuxII$#1${#2}%
-        }%
-    \fi
-    \tempa
-  }
-\protected\def\GetIdInfoAuxII$#1 #2.#3 #4 #5 #6 #7 #8$#9%
-  {%
-    \def\ExplFileName{#2}%
-    \def\ExplFileVersion{#4}%
-    \def\ExplFileDescription{#9}%
-    \GetIdInfoAuxIII#5\relax#3\relax#5\relax#6\relax
-  }
-\protected\def\GetIdInfoAuxIII#1#2#3#4#5#6\relax
-  {%
-    \ifx#5/%
-      \expandafter\GetIdInfoAuxCVS
-    \else
-      \expandafter\GetIdInfoAuxSVN
-    \fi
-  }
-\protected\def\GetIdInfoAuxCVS#1,v\relax#2\relax#3\relax
-  {\def\ExplFileDate{#2}}
-\protected\def\GetIdInfoAuxSVN#1\relax#2-#3-#4\relax#5Z\relax
-  {\def\ExplFileDate{#2/#3/#4}}
+\expandafter\chardef\csname\detokenize{l__kernel_expl_bool}\endcsname = 0 \relax
 \protected\def\ProvidesExplPackage#1#2#3#4%
   {%
     \ProvidesPackage{#1}[#2 v#3 #4]%
@@ -206,16 +187,16 @@
 \edef\@pushfilename
   {%
     \edef\expandafter\noexpand
-      \csname\detokenize{l_expl_status_stack_tl}\endcsname
+      \csname\detokenize{l__expl_status_stack_tl}\endcsname
       {%
         \noexpand\ifodd\expandafter\noexpand
-          \csname\detokenize{l_expl_status_bool}\endcsname
+          \csname\detokenize{l__kernel_expl_bool}\endcsname
           1%
         \noexpand\else
           0%
         \noexpand\fi
         \expandafter\noexpand
-          \csname\detokenize{l_expl_status_stack_tl}\endcsname
+          \csname\detokenize{l__expl_status_stack_tl}\endcsname
       }%
     \ExplSyntaxOff
     \unexpanded\expandafter{\@pushfilename}%
@@ -224,22 +205,22 @@
   {%
     \unexpanded\expandafter{\@popfilename}%
     \noexpand\if a\expandafter\noexpand\csname
-      \detokenize{l_expl_status_stack_tl}\endcsname a%
+      \detokenize{l__expl_status_stack_tl}\endcsname a%
       \ExplSyntaxOff
     \noexpand\else
       \noexpand\expandafter
         \expandafter\noexpand\csname
-          \detokenize{expl_status_pop:w}\endcsname
+          \detokenize{__expl_status_pop:w}\endcsname
           \expandafter\noexpand\csname
-            \detokenize{l_expl_status_stack_tl}\endcsname
+            \detokenize{l__expl_status_stack_tl}\endcsname
           \noexpand\@nil
    \noexpand\fi
   }
-\@namedef{\detokenize{l_expl_status_stack_tl}}{0}
-\expandafter\edef\csname\detokenize{expl_status_pop:w}\endcsname#1#2\@nil
+\@namedef{\detokenize{l__expl_status_stack_tl}}{0}
+\expandafter\edef\csname\detokenize{__expl_status_pop:w}\endcsname#1#2\@nil
   {%
     \def\expandafter\noexpand
-      \csname\detokenize{l_expl_status_stack_tl}\endcsname{#2}%
+      \csname\detokenize{l__expl_status_stack_tl}\endcsname{#2}%
     \noexpand\ifodd#1\space
       \noexpand\expandafter\noexpand\ExplSyntaxOn
     \noexpand\else
@@ -247,7 +228,7 @@
     \noexpand\fi
   }
 \expandafter\protected\expandafter\def
-  \csname\detokenize{package_check_loaded_expl:}\endcsname
+  \csname\detokenize{__expl_package_check:}\endcsname
   {%
     \@ifpackageloaded{expl3}
       {}
@@ -256,30 +237,10 @@
           {Cannot load the expl3 modules separately}
           {%
             The expl3 modules cannot be loaded separately;\MessageBreak
-            please \string\usepackage\string{expl3\string} instead.
+            please \string\usepackage\string{expl3\string} instead.%
           }%
       }%
   }
-\begingroup\expandafter\expandafter\expandafter\endgroup
-  \expandafter\ifx\csname pdfstrcmp\endcsname\relax
-  \let\pdfstrcmp\strcmp
-\fi
-\begingroup\expandafter\expandafter\expandafter\endgroup
-\expandafter\ifx\csname pdfstrcmp\endcsname\relax
-  \PackageError{l3names}{Required primitive not found: \protect\pdfstrcmp}
-    {%
-      LaTeX3 requires the e-TeX primitives and
-        \string\pdfstrcmp.\MessageBreak
-      These are available in engine versions: \MessageBreak
-      - pdfTeX 1.30 \MessageBreak
-      - XeTeX 0.9994 \MessageBreak
-      - LuaTeX 0.60 \MessageBreak
-      or later. \MessageBreak
-      \MessageBreak
-      Loading of expl3 will abort!
-    }
-  \expandafter\endinput
-\fi
 \protected\edef\ExplSyntaxNamesOn
   {%
     \expandafter\noexpand
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3box.sty b/Master/texmf-dist/tex/latex/l3kernel/l3box.sty
index c78a4f2122e..7e275624379 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3box.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3box.sty
@@ -46,14 +46,14 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3box.dtx 3490 2012-03-04 01:00:53Z bruno $
+\GetIdInfo$Id: l3box.dtx 3986 2012-07-15 19:23:51Z joseph $
   {L3 Experimental boxes}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 \cs_new_protected:Npn \box_new:N #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \newbox #1
   }
 \cs_generate_variant:Nn \box_new:N { c }
@@ -73,14 +73,14 @@
   { \tex_setbox:D #1 \tex_copy:D #2 }
 \cs_new_protected:Npn \box_gset_eq:NN
   { \tex_global:D \box_set_eq:NN }
-\cs_generate_variant:Nn \box_set_eq:NN  { cN , Nc , cc }
-\cs_generate_variant:Nn \box_gset_eq:NN { cN , Nc , cc }
+\cs_generate_variant:Nn \box_set_eq:NN  { c , Nc , cc }
+\cs_generate_variant:Nn \box_gset_eq:NN { c , Nc , cc }
 \cs_new_protected:Npn \box_set_eq_clear:NN #1#2
   { \tex_setbox:D #1 \tex_box:D #2 }
 \cs_new_protected:Npn \box_gset_eq_clear:NN
   { \tex_global:D  \box_set_eq_clear:NN }
-\cs_generate_variant:Nn \box_set_eq_clear:NN  { cN , Nc , cc }
-\cs_generate_variant:Nn \box_gset_eq_clear:NN { cN , Nc , cc }
+\cs_generate_variant:Nn \box_set_eq_clear:NN  { c , Nc , cc }
+\cs_generate_variant:Nn \box_gset_eq_clear:NN { c , Nc , cc }
 \cs_new_eq:NN \box_if_exist:NTF \cs_if_exist:NTF
 \cs_new_eq:NN \box_if_exist:NT  \cs_if_exist:NT
 \cs_new_eq:NN \box_if_exist:NF  \cs_if_exist:NF
@@ -96,11 +96,11 @@
 \cs_generate_variant:Nn \box_dp:N { c }
 \cs_generate_variant:Nn \box_wd:N { c }
 \cs_new_protected:Npn \box_set_dp:Nn #1#2
-  { \box_dp:N #1 \dim_eval:w #2 \dim_eval_end: }
+  { \box_dp:N #1 \__dim_eval:w #2 \__dim_eval_end: }
 \cs_new_protected:Npn \box_set_ht:Nn #1#2
-  { \box_ht:N #1 \dim_eval:w #2 \dim_eval_end: }
+  { \box_ht:N #1 \__dim_eval:w #2 \__dim_eval_end: }
 \cs_new_protected:Npn \box_set_wd:Nn #1#2
-  { \box_wd:N #1 \dim_eval:w #2 \dim_eval_end: }
+  { \box_wd:N #1 \__dim_eval:w #2 \__dim_eval_end: }
 \cs_generate_variant:Nn \box_set_ht:Nn { c }
 \cs_generate_variant:Nn \box_set_dp:Nn { c }
 \cs_generate_variant:Nn \box_set_wd:Nn { c }
@@ -109,13 +109,13 @@
 \cs_generate_variant:Nn \box_use_clear:N { c }
 \cs_generate_variant:Nn \box_use:N { c }
 \cs_new_protected:Npn \box_move_left:nn #1#2
-  { \tex_moveleft:D \dim_eval:w #1 \dim_eval_end: #2 }
+  { \tex_moveleft:D \__dim_eval:w #1 \__dim_eval_end: #2 }
 \cs_new_protected:Npn \box_move_right:nn #1#2
-  { \tex_moveright:D \dim_eval:w #1 \dim_eval_end: #2 }
+  { \tex_moveright:D \__dim_eval:w #1 \__dim_eval_end: #2 }
 \cs_new_protected:Npn \box_move_up:nn #1#2
-  { \tex_raise:D \dim_eval:w #1 \dim_eval_end: #2 }
+  { \tex_raise:D \__dim_eval:w #1 \__dim_eval_end: #2 }
 \cs_new_protected:Npn \box_move_down:nn #1#2
-  { \tex_lower:D \dim_eval:w #1 \dim_eval_end: #2 }
+  { \tex_lower:D \__dim_eval:w #1 \__dim_eval_end: #2 }
 \cs_new_eq:NN \if_hbox:N      \tex_ifhbox:D
 \cs_new_eq:NN \if_vbox:N      \tex_ifvbox:D
 \cs_new_eq:NN \if_box_empty:N \tex_ifvoid:D
@@ -146,36 +146,50 @@
 \cs_new_eq:NN \c_empty_box \voidb@x
 \cs_new_eq:NN \l_tmpa_box \@tempboxa
 \box_new:N \l_tmpb_box
+\box_new:N \g_tmpa_box
+\box_new:N \g_tmpb_box
 \cs_new_protected:Npn \box_show:N #1
+  { \box_show:Nnn #1 \c_max_int \c_max_int }
+\cs_generate_variant:Nn \box_show:N { c }
+\cs_new_protected_nopar:Npn \box_show:Nnn
+  { \__box_show:NNnn \c_one }
+\cs_generate_variant:Nn \box_show:Nnn { c }
+\cs_new_protected:Npn \box_log:N #1
+  { \box_log:Nnn #1 \c_max_int \c_max_int }
+\cs_generate_variant:Nn \box_log:N { c }
+\cs_new_protected:Npn \box_log:Nnn #1#2#3
   {
-    \box_if_exist:NTF #1
-      { \tex_showbox:D \use:n {#1} }
+    \use:x
       {
-        \msg_kernel_error:nnx { kernel } { variable-not-defined }
-          { \token_to_str:N #1 }
+        \etex_interactionmode:D \c_zero
+        \__box_show:NNnn \c_zero \exp_not:N #1
+          { \int_eval:n {#2} } { \int_eval:n {#3} }
+        \etex_interactionmode:D
+            = \tex_the:D \etex_interactionmode:D \scan_stop:
       }
   }
-\cs_generate_variant:Nn \box_show:N { c }
-\cs_new_protected:Npn \box_show:Nnn #1#2#3
+\cs_generate_variant:Nn \box_log:Nnn { c }
+\cs_new_protected:Npn \__box_show:NNnn #1#2#3#4
   {
     \group_begin:
-      \int_set:Nn \tex_showboxbreadth:D {#2}
-      \int_set:Nn \tex_showboxdepth:D {#3}
-      \int_set_eq:NN \tex_tracingonline:D \c_one
-      \box_show:N #1
+      \int_set:Nn \tex_showboxbreadth:D {#3}
+      \int_set:Nn \tex_showboxdepth:D   {#4}
+      \int_set_eq:NN \tex_tracingonline:D #1
+      \box_if_exist:NTF #2
+        { \tex_showbox:D \use:n {#2} }
+        {
+          \__msg_kernel_error:nnx { kernel } { variable-not-defined }
+            { \token_to_str:N #2 }
+        }
     \group_end:
   }
-\cs_generate_variant:Nn \box_show:Nnn { c }
-\cs_new_protected:Npn \box_show_full:N #1
-  { \box_show:Nnn #1 { \c_max_int } { \c_max_int } }
-\cs_generate_variant:Nn \box_show_full:N { c }
 \cs_new_protected:Npn \hbox:n { \tex_hbox:D \scan_stop: }
 \cs_new_protected:Npn \hbox_set:Nn #1#2 { \tex_setbox:D #1 \tex_hbox:D {#2} }
 \cs_new_protected:Npn \hbox_gset:Nn { \tex_global:D \hbox_set:Nn }
 \cs_generate_variant:Nn \hbox_set:Nn { c }
 \cs_generate_variant:Nn \hbox_gset:Nn { c }
 \cs_new_protected:Npn \hbox_set_to_wd:Nnn #1#2#3
-  { \tex_setbox:D #1 \tex_hbox:D to \dim_eval:w #2 \dim_eval_end: {#3} }
+  { \tex_setbox:D #1 \tex_hbox:D to \__dim_eval:w #2 \__dim_eval_end: {#3} }
 \cs_new_protected:Npn \hbox_gset_to_wd:Nnn
   { \tex_global:D \hbox_set_to_wd:Nnn }
 \cs_generate_variant:Nn \hbox_set_to_wd:Nnn { c }
@@ -195,7 +209,7 @@
 \cs_new_eq:NN \hbox_gset_inline_begin:c \hbox_gset:cw
 \cs_new_eq:NN \hbox_gset_inline_end:    \hbox_gset_end:
 \cs_new_protected:Npn \hbox_to_wd:nn #1#2
-   { \tex_hbox:D to \dim_eval:w #1 \dim_eval_end: {#2} }
+   { \tex_hbox:D to \__dim_eval:w #1 \__dim_eval_end: {#2} }
 \cs_new_protected:Npn \hbox_to_zero:n #1 { \tex_hbox:D to \c_zero_skip {#1} }
 \cs_new_protected:Npn \hbox_overlap_left:n  #1
   { \hbox_to_zero:n { \tex_hss:D #1 } }
@@ -208,7 +222,7 @@
 \cs_new_protected:Npn \vbox:n #1     { \tex_vbox:D { #1 \par } }
 \cs_new_protected:Npn \vbox_top:n #1 { \tex_vtop:D { #1 \par } }
 \cs_new_protected:Npn \vbox_to_ht:nn #1#2
-  { \tex_vbox:D to \dim_eval:w #1 \dim_eval_end: { #2 \par } }
+  { \tex_vbox:D to \__dim_eval:w #1 \__dim_eval_end: { #2 \par } }
 \cs_new_protected:Npn \vbox_to_zero:n #1
   { \tex_vbox:D to \c_zero_dim { #1 \par } }
 \cs_new_protected:Npn \vbox_set:Nn #1#2
@@ -223,7 +237,7 @@
 \cs_generate_variant:Nn \vbox_set_top:Nn { c }
 \cs_generate_variant:Nn \vbox_gset_top:Nn { c }
 \cs_new_protected:Npn \vbox_set_to_ht:Nnn #1#2#3
-  { \tex_setbox:D #1 \tex_vbox:D to \dim_eval:w #2 \dim_eval_end: { #3 \par } }
+  { \tex_setbox:D #1 \tex_vbox:D to \__dim_eval:w #2 \__dim_eval_end: { #3 \par } }
 \cs_new_protected:Npn \vbox_gset_to_ht:Nnn
   { \tex_global:D \vbox_set_to_ht:Nnn }
 \cs_generate_variant:Nn \vbox_set_to_ht:Nnn  { c }
@@ -251,358 +265,7 @@
 \cs_generate_variant:Nn \vbox_unpack:N { c }
 \cs_generate_variant:Nn \vbox_unpack_clear:N { c }
 \cs_new_protected:Npn \vbox_set_split_to_ht:NNn #1#2#3
-  { \tex_setbox:D #1 \tex_vsplit:D #2 to \dim_eval:w #3 \dim_eval_end: }
-\fp_new:N \l_box_angle_fp
-\fp_new:N \l_box_cos_fp
-\fp_new:N \l_box_sin_fp
-\dim_new:N \l_box_top_dim
-\dim_new:N \l_box_bottom_dim
-\dim_new:N \l_box_left_dim
-\dim_new:N \l_box_right_dim
-\dim_new:N \l_box_top_new_dim
-\dim_new:N \l_box_bottom_new_dim
-\dim_new:N \l_box_left_new_dim
-\dim_new:N \l_box_right_new_dim
-\box_new:N \l_box_internal_box
-\fp_new:N \l_box_internal_fp
-\fp_new:N \l_box_x_fp
-\fp_new:N \l_box_y_fp
-\fp_new:N \l_box_x_new_fp
-\fp_new:N \l_box_y_new_fp
-\cs_new_protected:Npn \box_rotate:Nn #1#2
-  {
-    \hbox_set:Nn #1
-      {
-        \group_begin:
-          \fp_set:Nn \l_box_angle_fp {#2}
-          \box_rotate_set_sin_cos:
-          \fp_compare:NNNTF \l_box_sin_fp = \c_zero_fp
-            {
-               \fp_compare:NNNTF \l_box_cos_fp = \c_one_fp
-                 { \box_use:N #1 }
-                 { \box_rotate_aux:N #1 }
-            }
-            { \box_rotate_aux:N #1 }
-        \group_end:
-    }
-  }
-\cs_new_protected:Npn \box_rotate_aux:N #1
-  {
-    \dim_set:Nn \l_box_top_dim    {  \box_ht:N #1 }
-    \dim_set:Nn \l_box_bottom_dim { -\box_dp:N #1 }
-    \dim_set:Nn \l_box_right_dim  {  \box_wd:N #1 }
-    \dim_zero:N \l_box_left_dim
-    \fp_compare:NNNTF \l_box_sin_fp > \c_zero_fp
-      {
-        \fp_compare:NNNTF \l_box_cos_fp > \c_zero_fp
-          { \box_rotate_quadrant_one: }
-          { \box_rotate_quadrant_two: }
-      }
-      {
-        \fp_compare:NNNTF \l_box_cos_fp < \c_zero_fp
-          { \box_rotate_quadrant_three: }
-          { \box_rotate_quadrant_four: }
-      }
-    \hbox_set:Nn \l_box_internal_box { \box_use:N #1 }
-    \hbox_set:Nn \l_box_internal_box
-      {
-        \tex_kern:D -\l_box_left_new_dim
-        \hbox:n
-          {
-            \driver_box_rotate_begin:
-            \box_use:N \l_box_internal_box
-            \driver_box_rotate_end:
-          }
-      }
-    \box_set_ht:Nn \l_box_internal_box {  \l_box_top_new_dim }
-    \box_set_dp:Nn \l_box_internal_box { -\l_box_bottom_new_dim }
-    \box_set_wd:Nn \l_box_internal_box
-      { \l_box_right_new_dim - \l_box_left_new_dim }
-    \box_use:N \l_box_internal_box
-  }
-\cs_new_protected:Npn \box_rotate_set_sin_cos:
-  {
-    \fp_set_eq:NN \l_box_internal_fp \l_box_angle_fp
-    \fp_div:Nn \l_box_internal_fp { 180 }
-    \fp_mul:Nn \l_box_internal_fp { \c_pi_fp }
-    \fp_sin:Nn \l_box_sin_fp { \l_box_internal_fp }
-    \fp_cos:Nn \l_box_cos_fp { \l_box_internal_fp }
-  }
-\cs_new_protected:Npn \box_rotate_x:nnN #1#2#3
-  {
-    \fp_set_from_dim:Nn \l_box_x_fp {#1}
-    \fp_set_from_dim:Nn \l_box_y_fp {#2}
-    \fp_set_eq:NN \l_box_x_new_fp \l_box_x_fp
-    \fp_set_eq:NN \l_box_internal_fp   \l_box_y_fp
-    \fp_mul:Nn \l_box_x_new_fp { \l_box_cos_fp }
-    \fp_mul:Nn \l_box_internal_fp   { \l_box_sin_fp }
-    \fp_sub:Nn \l_box_x_new_fp { \l_box_internal_fp }
-    \dim_set:Nn #3 { \fp_to_dim:N \l_box_x_new_fp }
-  }
-\cs_new_protected:Npn \box_rotate_y:nnN #1#2#3
-  {
-    \fp_set_from_dim:Nn \l_box_x_fp {#1}
-    \fp_set_from_dim:Nn \l_box_y_fp {#2}
-    \fp_set_eq:NN \l_box_y_new_fp \l_box_y_fp
-    \fp_set_eq:NN \l_box_internal_fp   \l_box_x_fp
-    \fp_mul:Nn \l_box_y_new_fp { \l_box_cos_fp }
-    \fp_mul:Nn \l_box_internal_fp   { \l_box_sin_fp }
-    \fp_add:Nn \l_box_y_new_fp { \l_box_internal_fp }
-    \dim_set:Nn #3 { \fp_to_dim:N \l_box_y_new_fp }
-}
-\cs_new_protected:Npn \box_rotate_quadrant_one:
-  {
-    \box_rotate_y:nnN \l_box_right_dim \l_box_top_dim
-      \l_box_top_new_dim
-    \box_rotate_y:nnN \l_box_left_dim  \l_box_bottom_dim
-      \l_box_bottom_new_dim
-    \box_rotate_x:nnN \l_box_left_dim  \l_box_top_dim
-      \l_box_left_new_dim
-    \box_rotate_x:nnN \l_box_right_dim \l_box_bottom_dim
-      \l_box_right_new_dim
-  }
-\cs_new_protected:Npn \box_rotate_quadrant_two:
-  {
-    \box_rotate_y:nnN \l_box_right_dim \l_box_bottom_dim
-      \l_box_top_new_dim
-    \box_rotate_y:nnN \l_box_left_dim  \l_box_top_dim
-      \l_box_bottom_new_dim
-    \box_rotate_x:nnN \l_box_right_dim  \l_box_top_dim
-      \l_box_left_new_dim
-    \box_rotate_x:nnN \l_box_left_dim   \l_box_bottom_dim
-      \l_box_right_new_dim
-  }
-\cs_new_protected:Npn \box_rotate_quadrant_three:
-  {
-    \box_rotate_y:nnN \l_box_left_dim  \l_box_bottom_dim
-      \l_box_top_new_dim
-    \box_rotate_y:nnN \l_box_right_dim \l_box_top_dim
-      \l_box_bottom_new_dim
-    \box_rotate_x:nnN \l_box_right_dim \l_box_bottom_dim
-      \l_box_left_new_dim
-    \box_rotate_x:nnN \l_box_left_dim   \l_box_top_dim
-      \l_box_right_new_dim
-  }
-\cs_new_protected:Npn \box_rotate_quadrant_four:
-  {
-    \box_rotate_y:nnN \l_box_left_dim  \l_box_top_dim
-      \l_box_top_new_dim
-    \box_rotate_y:nnN \l_box_right_dim \l_box_bottom_dim
-      \l_box_bottom_new_dim
-    \box_rotate_x:nnN \l_box_left_dim  \l_box_bottom_dim
-      \l_box_left_new_dim
-    \box_rotate_x:nnN \l_box_right_dim \l_box_top_dim
-      \l_box_right_new_dim
-  }
-\fp_new:N \l_box_scale_x_fp
-\fp_new:N \l_box_scale_y_fp
-\cs_new_protected:Npn \box_resize:Nnn #1#2#3
-  {
-    \hbox_set:Nn #1
-      {
-        \group_begin:
-          \dim_set:Nn \l_box_top_dim    {  \box_ht:N #1 }
-          \dim_set:Nn \l_box_bottom_dim { -\box_dp:N #1 }
-          \dim_set:Nn \l_box_right_dim  {  \box_wd:N #1 }
-          \dim_zero:N \l_box_left_dim
-          \fp_set_from_dim:Nn \l_box_scale_x_fp {#2}
-          \fp_set_from_dim:Nn \l_box_internal_fp { \l_box_right_dim }
-          \fp_div:Nn \l_box_scale_x_fp { \l_box_internal_fp }
-          \fp_set_from_dim:Nn \l_box_scale_y_fp {#3}
-          \fp_set_from_dim:Nn \l_box_internal_fp
-            { \l_box_top_dim - \l_box_bottom_dim }
-          \fp_div:Nn \l_box_scale_y_fp { \l_box_internal_fp }
-          \fp_compare:NNNTF \l_box_scale_x_fp = \c_one_fp
-            {
-              \fp_compare:NNNTF \l_box_scale_y_fp = \c_one_fp
-                { \box_use:N #1 }
-                { \box_resize_aux:Nnn #1 {#2} {#3} }
-            }
-            { \box_resize_aux:Nnn #1 {#2} {#3} }
-        \group_end:
-      }
-  }
-\cs_generate_variant:Nn \box_resize:Nnn { c }
-\cs_new_protected:Npn \box_resize_aux:Nnn #1#2#3
-  {
-    \dim_compare:nNnTF {#2} > \c_zero_dim
-      { \dim_set:Nn \l_box_right_new_dim {#2} }
-      { \dim_set:Nn \l_box_right_new_dim { \c_zero_dim - ( #2 ) } }
-    \dim_compare:nNnTF {#3} > \c_zero_dim
-      {
-        \dim_set:Nn \l_box_top_new_dim
-          { \fp_use:N \l_box_scale_y_fp \l_box_top_dim }
-        \dim_set:Nn \l_box_bottom_new_dim
-          { \fp_use:N \l_box_scale_y_fp \l_box_bottom_dim }
-      }
-      {
-        \dim_set:Nn \l_box_top_new_dim
-          { - \fp_use:N \l_box_scale_y_fp \l_box_top_dim }
-        \dim_set:Nn \l_box_bottom_new_dim
-          { - \fp_use:N \l_box_scale_y_fp \l_box_bottom_dim }
-      }
-    \box_resize_common:N #1
-  }
-\cs_new_protected:Npn \box_resize_to_ht_plus_dp:Nn #1#2
-  {
-    \hbox_set:Nn #1
-      {
-        \group_begin:
-          \dim_set:Nn \l_box_top_dim    {  \box_ht:N #1 }
-          \dim_set:Nn \l_box_bottom_dim { -\box_dp:N #1 }
-          \dim_set:Nn \l_box_right_dim  {  \box_wd:N #1 }
-          \dim_zero:N \l_box_left_dim
-          \fp_set_from_dim:Nn \l_box_scale_y_fp {#2}
-          \fp_set_from_dim:Nn \l_box_internal_fp
-            { \l_box_top_dim - \l_box_bottom_dim }
-          \fp_div:Nn \l_box_scale_y_fp { \l_box_internal_fp }
-          \fp_set_eq:NN \l_box_scale_x_fp \l_box_scale_y_fp
-          \fp_compare:NNNTF \l_box_scale_y_fp = \c_one_fp
-            { \box_use:N #1 }
-            { \box_resize_aux:Nnn #1 {#2} {#2} }
-        \group_end:
-      }
-  }
-\cs_generate_variant:Nn \box_resize_to_ht_plus_dp:Nn { c }
-\cs_new_protected:Npn \box_resize_to_wd:Nn #1#2
-  {
-    \hbox_set:Nn #1
-      {
-        \group_begin:
-          \dim_set:Nn \l_box_top_dim    {  \box_ht:N #1 }
-          \dim_set:Nn \l_box_bottom_dim { -\box_dp:N #1 }
-          \dim_set:Nn \l_box_right_dim  {  \box_wd:N #1 }
-          \dim_zero:N \l_box_left_dim
-          \fp_set_from_dim:Nn \l_box_scale_x_fp {#2}
-          \fp_set_from_dim:Nn \l_box_internal_fp { \l_box_right_dim }
-          \fp_div:Nn \l_box_scale_x_fp { \l_box_internal_fp }
-          \fp_set_eq:NN \l_box_scale_y_fp \l_box_scale_x_fp
-          \fp_compare:NNNTF \l_box_scale_x_fp = \c_one_fp
-            { \box_use:N #1 }
-            { \box_resize_aux:Nnn #1 {#2} {#2} }
-        \group_end:
-      }
-  }
-\cs_generate_variant:Nn \box_resize_to_wd:Nn { c }
-\cs_new_protected:Npn \box_scale:Nnn #1#2#3
-  {
-    \hbox_set:Nn #1
-      {
-        \group_begin:
-          \fp_set:Nn \l_box_scale_x_fp {#2}
-          \fp_set:Nn \l_box_scale_y_fp {#3}
-          \dim_set:Nn \l_box_top_dim    {  \box_ht:N #1 }
-          \dim_set:Nn \l_box_bottom_dim { -\box_dp:N #1 }
-          \dim_set:Nn \l_box_right_dim  {  \box_wd:N #1 }
-          \dim_zero:N \l_box_left_dim
-          \fp_compare:NNNTF \l_box_scale_x_fp = \c_one_fp
-            {
-              \fp_compare:NNNTF \l_box_scale_y_fp = \c_one_fp
-                { \box_use:N #1 }
-                { \box_scale_aux:Nnn #1 {#2} {#3} }
-            }
-            { \box_scale_aux:Nnn #1 {#2} {#3} }
-        \group_end:
-      }
-  }
-\cs_generate_variant:Nn \box_scale:Nnn { c }
-\cs_new_protected:Npn \box_scale_aux:Nnn #1#2#3
-  {
-    \fp_compare:NNNTF \l_box_scale_y_fp > \c_zero_fp
-      {
-        \dim_set:Nn \l_box_top_new_dim    { #3 \l_box_top_dim }
-        \dim_set:Nn \l_box_bottom_new_dim { #3 \l_box_bottom_dim }
-      }
-      {
-        \dim_set:Nn  \l_box_top_new_dim    { -#3 \l_box_bottom_dim }
-        \dim_set:Nn  \l_box_bottom_new_dim { -#3 \l_box_top_dim }
-      }
-    \fp_compare:NNNTF \l_box_scale_x_fp > \c_zero_fp
-      { \l_box_right_new_dim #2 \l_box_right_dim }
-      { \l_box_right_new_dim -#2 \l_box_right_dim }
-    \box_resize_common:N #1
-  }
-\cs_new_protected:Npn \box_resize_common:N #1
-  {
-    \hbox_set:Nn \l_box_internal_box
-      {
-        \driver_box_scale_begin:
-        \hbox_overlap_right:n { \box_use:N #1 }
-        \driver_box_scale_end:
-      }
-    \box_set_ht:Nn \l_box_internal_box { \l_box_top_new_dim }
-    \box_set_dp:Nn \l_box_internal_box { \l_box_bottom_new_dim }
-    \fp_compare:NNNTF \l_box_scale_x_fp < \c_zero_fp
-      {
-        \hbox_to_wd:nn { \l_box_right_new_dim }
-          {
-            \tex_kern:D \l_box_right_new_dim
-            \box_use:N \l_box_internal_box
-            \tex_hss:D
-          }
-      }
-      {
-        \box_set_wd:Nn \l_box_internal_box { \l_box_right_new_dim }
-        \box_use:N \l_box_internal_box
-      }
-  }
-\cs_new_protected:Npn \box_clip:N #1
-  { \hbox_set:Nn #1 { \driver_box_use_clip:N #1 } }
-\cs_generate_variant:Nn \box_clip:N { c }
-\cs_new_protected:Npn \box_trim:Nnnnn #1#2#3#4#5
-  {
-    \box_set_wd:Nn #1 { \box_wd:N #1 - \dim_eval:n {#4} - \dim_eval:n {#2} }
-    \hbox_set:Nn #1
-      {
-        \skip_horizontal:n { - \dim_eval:n {#2} }
-        \box_use:N #1
-      }
-    \dim_compare:nNnTF { \box_dp:N #1 } > {#3}
-      { \box_set_dp:Nn #1 { \box_dp:N #1 - \dim_eval:n {#3} } }
-      {
-        \hbox_set:Nn #1
-          {
-            \box_move_down:nn { \dim_eval:n {#3} - \box_dp:N #1 }
-              { \box_use:N #1 }
-          }
-        \box_set_dp:Nn #1 \c_zero_dim
-      }
-    \dim_compare:nNnTF { \box_ht:N #1 } > {#5}
-      { \box_set_ht:Nn #1 { \box_ht:N #1 - \dim_eval:n {#5} } }
-      {
-        \hbox_set:Nn #1
-          {
-            \box_move_up:nn { \dim_eval:n {#5} - \box_ht:N #1 }
-              { \box_use:N #1 }
-          }
-        \box_set_ht:Nn #1 \c_zero_dim
-      }
-  }
-\cs_generate_variant:Nn \box_trim:Nnnnn { c }
-\cs_new_protected:Npn \box_viewport:Nnnnn #1#2#3#4#5
-  {
-    \box_set_wd:Nn #1 { \dim_eval:n {#4} - \dim_eval:n {#2} }
-    \hbox_set:Nn #1
-      {
-        \skip_horizontal:n { - \dim_eval:n {#2} }
-        \box_use:N #1
-      }
-    \dim_compare:nNnTF {#3} > \c_zero_dim
-      {
-        \hbox_set:Nn #1 { \box_move_down:nn {#3} { \box_use:N #1 } }
-        \box_set_dp:Nn #1 \c_zero_dim
-      }
-      { \box_set_dp:Nn #1 { - \dim_eval:n {#3} } }
-    \dim_compare:nNnTF {#5} > \c_zero_dim
-      { \box_set_ht:Nn #1 {#5} }
-      {
-        \hbox_set:Nn #1
-          { \box_move_up:nn { -\dim_eval:n {#5} } { \box_use:N #1 } }
-        \box_set_ht:Nn #1 \c_zero_dim
-      }
-  }
-\cs_generate_variant:Nn \box_viewport:Nnnnn { c }
-\cs_new_eq:NN \l_last_box \tex_lastbox:D
+  { \tex_setbox:D #1 \tex_vsplit:D #2 to \__dim_eval:w #3 \__dim_eval_end: }
 %% 
 %%
 %% End of file `l3box.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3candidates.sty b/Master/texmf-dist/tex/latex/l3kernel/l3candidates.sty
new file mode 100644
index 00000000000..1a867d3501c
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3candidates.sty
@@ -0,0 +1,1093 @@
+%%
+%% This is file `l3candidates.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% l3candidates.dtx  (with options: `package')
+%% 
+%% EXPERIMENTAL CODE
+%% 
+%% Do not distribute this file without also distributing the
+%% source files specified above.
+%% 
+%% Do not distribute a modified version of this file.
+%% 
+%% File: l3candidates.dtx Copyright(C) 2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3candidates.dtx 3633 2012-05-12 20:11:32Z joseph $
+  {L3 Experimental additions to l3kernel}
+\ProvidesExplPackage
+  {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
+\__expl_package_check:
+\fp_new:N \l__box_angle_fp
+\fp_new:N \l__box_cos_fp
+\fp_new:N \l__box_sin_fp
+\dim_new:N \l__box_top_dim
+\dim_new:N \l__box_bottom_dim
+\dim_new:N \l__box_left_dim
+\dim_new:N \l__box_right_dim
+\dim_new:N \l__box_top_new_dim
+\dim_new:N \l__box_bottom_new_dim
+\dim_new:N \l__box_left_new_dim
+\dim_new:N \l__box_right_new_dim
+\box_new:N \l__box_internal_box
+\cs_new_protected:Npn \box_rotate:Nn #1#2
+  {
+    \hbox_set:Nn #1
+      {
+        \group_begin:
+          \fp_set:Nn \l__box_angle_fp {#2}
+          \fp_set:Nn \l__box_sin_fp { sin ( \l__box_angle_fp * deg ) }
+          \fp_set:Nn \l__box_cos_fp { cos ( \l__box_angle_fp * deg ) }
+          \__box_rotate:N #1
+        \group_end:
+    }
+  }
+\cs_new_protected:Npn \__box_rotate:N #1
+  {
+    \dim_set:Nn \l__box_top_dim    {  \box_ht:N #1 }
+    \dim_set:Nn \l__box_bottom_dim { -\box_dp:N #1 }
+    \dim_set:Nn \l__box_right_dim  {  \box_wd:N #1 }
+    \dim_zero:N \l__box_left_dim
+    \fp_compare:nNnTF \l__box_sin_fp > \c_zero_fp
+      {
+        \fp_compare:nNnTF \l__box_cos_fp > \c_zero_fp
+          { \__box_rotate_quadrant_one: }
+          { \__box_rotate_quadrant_two: }
+      }
+      {
+        \fp_compare:nNnTF \l__box_cos_fp < \c_zero_fp
+          { \__box_rotate_quadrant_three: }
+          { \__box_rotate_quadrant_four: }
+      }
+    \hbox_set:Nn \l__box_internal_box { \box_use:N #1 }
+    \hbox_set:Nn \l__box_internal_box
+      {
+        \tex_kern:D -\l__box_left_new_dim
+        \hbox:n
+          {
+            \__driver_box_rotate_begin:
+            \box_use:N \l__box_internal_box
+            \__driver_box_rotate_end:
+          }
+      }
+    \box_set_ht:Nn \l__box_internal_box {  \l__box_top_new_dim }
+    \box_set_dp:Nn \l__box_internal_box { -\l__box_bottom_new_dim }
+    \box_set_wd:Nn \l__box_internal_box
+      { \l__box_right_new_dim - \l__box_left_new_dim }
+    \box_use:N \l__box_internal_box
+  }
+\cs_new_protected:Npn \__box_rotate_x:nnN #1#2#3
+  {
+    \dim_set:Nn #3
+      {
+        \fp_to_dim:n
+          {
+                \l__box_cos_fp * \dim_to_fp:n {#1}
+            - ( \l__box_sin_fp * \dim_to_fp:n {#2} )
+          }
+      }
+  }
+\cs_new_protected:Npn \__box_rotate_y:nnN #1#2#3
+  {
+    \dim_set:Nn #3
+      {
+        \fp_to_dim:n
+          {
+              \l__box_sin_fp * \dim_to_fp:n {#1}
+            + \l__box_cos_fp * \dim_to_fp:n {#2}
+          }
+      }
+  }
+\cs_new_protected:Npn \__box_rotate_quadrant_one:
+  {
+    \__box_rotate_y:nnN \l__box_right_dim \l__box_top_dim
+      \l__box_top_new_dim
+    \__box_rotate_y:nnN \l__box_left_dim  \l__box_bottom_dim
+      \l__box_bottom_new_dim
+    \__box_rotate_x:nnN \l__box_left_dim  \l__box_top_dim
+      \l__box_left_new_dim
+    \__box_rotate_x:nnN \l__box_right_dim \l__box_bottom_dim
+      \l__box_right_new_dim
+  }
+\cs_new_protected:Npn \__box_rotate_quadrant_two:
+  {
+    \__box_rotate_y:nnN \l__box_right_dim \l__box_bottom_dim
+      \l__box_top_new_dim
+    \__box_rotate_y:nnN \l__box_left_dim  \l__box_top_dim
+      \l__box_bottom_new_dim
+    \__box_rotate_x:nnN \l__box_right_dim  \l__box_top_dim
+      \l__box_left_new_dim
+    \__box_rotate_x:nnN \l__box_left_dim   \l__box_bottom_dim
+      \l__box_right_new_dim
+  }
+\cs_new_protected:Npn \__box_rotate_quadrant_three:
+  {
+    \__box_rotate_y:nnN \l__box_left_dim  \l__box_bottom_dim
+      \l__box_top_new_dim
+    \__box_rotate_y:nnN \l__box_right_dim \l__box_top_dim
+      \l__box_bottom_new_dim
+    \__box_rotate_x:nnN \l__box_right_dim \l__box_bottom_dim
+      \l__box_left_new_dim
+    \__box_rotate_x:nnN \l__box_left_dim   \l__box_top_dim
+      \l__box_right_new_dim
+  }
+\cs_new_protected:Npn \__box_rotate_quadrant_four:
+  {
+    \__box_rotate_y:nnN \l__box_left_dim  \l__box_top_dim
+      \l__box_top_new_dim
+    \__box_rotate_y:nnN \l__box_right_dim \l__box_bottom_dim
+      \l__box_bottom_new_dim
+    \__box_rotate_x:nnN \l__box_left_dim  \l__box_bottom_dim
+      \l__box_left_new_dim
+    \__box_rotate_x:nnN \l__box_right_dim \l__box_top_dim
+      \l__box_right_new_dim
+  }
+\fp_new:N \l__box_scale_x_fp
+\fp_new:N \l__box_scale_y_fp
+\cs_new_protected:Npn \box_resize:Nnn #1#2#3
+  {
+    \hbox_set:Nn #1
+      {
+        \group_begin:
+          \dim_set:Nn \l__box_top_dim    {  \box_ht:N #1 }
+          \dim_set:Nn \l__box_bottom_dim { -\box_dp:N #1 }
+          \dim_set:Nn \l__box_right_dim  {  \box_wd:N #1 }
+          \dim_zero:N \l__box_left_dim
+          \fp_set:Nn \l__box_scale_x_fp
+            { \dim_to_fp:n {#2} / ( \dim_to_fp:n \l__box_right_dim ) }
+          \fp_set:Nn \l__box_scale_y_fp
+            {
+              \dim_to_fp:n {#3} /
+                ( \dim_to_fp:n { \l__box_top_dim - \l__box_bottom_dim } )
+            }
+          \__box_resize:Nnn #1 {#2} {#3}
+        \group_end:
+      }
+  }
+\cs_generate_variant:Nn \box_resize:Nnn { c }
+\cs_new_protected:Npn \__box_resize:Nnn #1#2#3
+  {
+    \dim_compare:nNnTF {#2} > \c_zero_dim
+      { \dim_set:Nn \l__box_right_new_dim {#2} }
+      { \dim_set:Nn \l__box_right_new_dim { \c_zero_dim - ( #2 ) } }
+    \dim_compare:nNnTF {#3} > \c_zero_dim
+      {
+        \dim_set:Nn \l__box_top_new_dim
+          { \fp_use:N \l__box_scale_y_fp \l__box_top_dim }
+        \dim_set:Nn \l__box_bottom_new_dim
+          { \fp_use:N \l__box_scale_y_fp \l__box_bottom_dim }
+      }
+      {
+        \dim_set:Nn \l__box_top_new_dim
+          { - \fp_use:N \l__box_scale_y_fp \l__box_top_dim }
+        \dim_set:Nn \l__box_bottom_new_dim
+          { - \fp_use:N \l__box_scale_y_fp \l__box_bottom_dim }
+      }
+    \__box_resize_common:N #1
+  }
+\cs_new_protected:Npn \box_resize_to_ht_plus_dp:Nn #1#2
+  {
+    \hbox_set:Nn #1
+      {
+        \group_begin:
+          \dim_set:Nn \l__box_top_dim    {  \box_ht:N #1 }
+          \dim_set:Nn \l__box_bottom_dim { -\box_dp:N #1 }
+          \dim_set:Nn \l__box_right_dim  {  \box_wd:N #1 }
+          \dim_zero:N \l__box_left_dim
+          \fp_set:Nn \l__box_scale_y_fp
+            {
+              \dim_to_fp:n {#2} /
+                ( \dim_to_fp:n { \l__box_top_dim - \l__box_bottom_dim } )
+            }
+          \fp_set_eq:NN \l__box_scale_x_fp \l__box_scale_y_fp
+          \__box_resize:Nnn #1 {#2} {#2}
+        \group_end:
+      }
+  }
+\cs_generate_variant:Nn \box_resize_to_ht_plus_dp:Nn { c }
+\cs_new_protected:Npn \box_resize_to_wd:Nn #1#2
+  {
+    \hbox_set:Nn #1
+      {
+        \group_begin:
+          \dim_set:Nn \l__box_top_dim    {  \box_ht:N #1 }
+          \dim_set:Nn \l__box_bottom_dim { -\box_dp:N #1 }
+          \dim_set:Nn \l__box_right_dim  {  \box_wd:N #1 }
+          \dim_zero:N \l__box_left_dim
+          \fp_set:Nn \l__box_scale_x_fp
+            { \dim_to_fp:n {#2} / ( \dim_to_fp:n \l__box_right_dim ) }
+          \fp_set_eq:NN \l__box_scale_y_fp \l__box_scale_x_fp
+          \__box_resize:Nnn #1 {#2} {#2}
+        \group_end:
+      }
+  }
+\cs_generate_variant:Nn \box_resize_to_wd:Nn { c }
+\cs_new_protected:Npn \box_scale:Nnn #1#2#3
+  {
+    \hbox_set:Nn #1
+      {
+        \group_begin:
+          \fp_set:Nn \l__box_scale_x_fp {#2}
+          \fp_set:Nn \l__box_scale_y_fp {#3}
+          \dim_set:Nn \l__box_top_dim    {  \box_ht:N #1 }
+          \dim_set:Nn \l__box_bottom_dim { -\box_dp:N #1 }
+          \dim_set:Nn \l__box_right_dim  {  \box_wd:N #1 }
+          \dim_zero:N \l__box_left_dim
+          \__box_scale:Nnn #1 {#2} {#3}
+        \group_end:
+      }
+  }
+\cs_generate_variant:Nn \box_scale:Nnn { c }
+\cs_new_protected:Npn \__box_scale:Nnn #1#2#3
+  {
+    \fp_compare:nNnTF \l__box_scale_y_fp > \c_zero_fp
+      {
+        \dim_set:Nn \l__box_top_new_dim    { #3 \l__box_top_dim }
+        \dim_set:Nn \l__box_bottom_new_dim { #3 \l__box_bottom_dim }
+      }
+      {
+        \dim_set:Nn  \l__box_top_new_dim    { -#3 \l__box_bottom_dim }
+        \dim_set:Nn  \l__box_bottom_new_dim { -#3 \l__box_top_dim }
+      }
+    \fp_compare:nNnTF \l__box_scale_x_fp > \c_zero_fp
+      { \l__box_right_new_dim #2 \l__box_right_dim }
+      { \l__box_right_new_dim -#2 \l__box_right_dim }
+    \__box_resize_common:N #1
+  }
+\cs_new_protected:Npn \__box_resize_common:N #1
+  {
+    \hbox_set:Nn \l__box_internal_box
+      {
+        \__driver_box_scale_begin:
+        \hbox_overlap_right:n { \box_use:N #1 }
+        \__driver_box_scale_end:
+      }
+    \box_set_ht:Nn \l__box_internal_box { \l__box_top_new_dim }
+    \box_set_dp:Nn \l__box_internal_box { \l__box_bottom_new_dim }
+    \fp_compare:nNnTF \l__box_scale_x_fp < \c_zero_fp
+      {
+        \hbox_to_wd:nn { \l__box_right_new_dim }
+          {
+            \tex_kern:D \l__box_right_new_dim
+            \box_use:N \l__box_internal_box
+            \tex_hss:D
+          }
+      }
+      {
+        \box_set_wd:Nn \l__box_internal_box { \l__box_right_new_dim }
+        \box_use:N \l__box_internal_box
+      }
+  }
+\cs_new_protected:Npn \box_clip:N #1
+  { \hbox_set:Nn #1 { \__driver_box_use_clip:N #1 } }
+\cs_generate_variant:Nn \box_clip:N { c }
+\cs_new_protected:Npn \box_trim:Nnnnn #1#2#3#4#5
+  {
+    \box_set_wd:Nn #1 { \box_wd:N #1 - (#4) - (#2) }
+    \hbox_set:Nn #1
+      {
+        \skip_horizontal:n { - \dim_eval:n {#2} }
+        \box_use:N #1
+      }
+    \dim_compare:nNnTF { \box_dp:N #1 } > {#3}
+      { \box_set_dp:Nn #1 { \box_dp:N #1 - (#3) } }
+      {
+        \hbox_set:Nn #1
+          { \box_move_down:nn { #3 - \box_dp:N #1 } { \box_use:N #1 } }
+        \box_set_dp:Nn #1 \c_zero_dim
+      }
+    \dim_compare:nNnTF { \box_ht:N #1 } > {#5}
+      { \box_set_ht:Nn #1 { \box_ht:N #1 - (#5) } }
+      {
+        \hbox_set:Nn #1
+          { \box_move_up:nn { #5 - \box_ht:N #1 } { \box_use:N #1 } }
+        \box_set_ht:Nn #1 \c_zero_dim
+      }
+  }
+\cs_generate_variant:Nn \box_trim:Nnnnn { c }
+\cs_new_protected:Npn \box_viewport:Nnnnn #1#2#3#4#5
+  {
+    \box_set_wd:Nn #1 { (#4) - (#2) }
+    \hbox_set:Nn #1
+      {
+        \skip_horizontal:n { - \dim_eval:n {#2} }
+        \box_use:N #1
+      }
+    \dim_compare:nNnTF {#3} > \c_zero_dim
+      {
+        \hbox_set:Nn #1 { \box_move_down:nn {#3} { \box_use:N #1 } }
+        \box_set_dp:Nn #1 \c_zero_dim
+      }
+      { \box_set_dp:Nn #1 { - \dim_eval:n {#3} } }
+    \dim_compare:nNnTF {#5} > \c_zero_dim
+      { \box_set_ht:Nn #1 {#5} }
+      {
+        \hbox_set:Nn #1
+          { \box_move_up:nn { -\dim_eval:n {#5} } { \box_use:N #1 } }
+        \box_set_ht:Nn #1 \c_zero_dim
+      }
+  }
+\cs_generate_variant:Nn \box_viewport:Nnnnn { c }
+\cs_new:Npn \clist_item:Nn #1#2
+  {
+    \exp_args:Nfo \__clist_item:nnNn
+      { \clist_count:N #1 }
+      #1
+      \__clist_item_N_loop:nw
+      {#2}
+  }
+\cs_new:Npn \__clist_item:nnNn #1#2#3#4
+  {
+    \int_compare:nNnTF {#4} < \c_zero
+      {
+        \int_compare:nNnTF {#4} < { - #1 }
+          { \use_none_delimit_by_q_stop:w }
+          { \exp_args:Nf #3 { \int_eval:n { #4 + \c_one + #1 } } }
+      }
+      {
+        \int_compare:nNnTF {#4} > {#1}
+          { \use_none_delimit_by_q_stop:w }
+          { #3 {#4} }
+      }
+    { } , #2 , \q_stop
+  }
+\cs_new:Npn \__clist_item_N_loop:nw #1 #2,
+  {
+    \int_compare:nNnTF {#1} = \c_zero
+      { \use_i_delimit_by_q_stop:nw { \exp_not:n {#2} } }
+      { \exp_args:Nf \__clist_item_N_loop:nw { \int_eval:n { #1 - 1 } } }
+  }
+\cs_generate_variant:Nn \clist_item:Nn { c }
+\cs_new:Npn \clist_item:nn #1#2
+  {
+    \exp_args:Nf \__clist_item:nnNn
+      { \clist_count:n {#1} }
+      {#1}
+      \__clist_item_n:nw
+      {#2}
+  }
+\cs_new:Npn \__clist_item_n:nw #1
+  { \__clist_item_n_loop:nw {#1} \prg_do_nothing: }
+\cs_new:Npn \__clist_item_n_loop:nw #1 #2,
+  {
+    \exp_args:No \tl_if_blank:nTF {#2}
+      { \__clist_item_n_loop:nw {#1} \prg_do_nothing: }
+      {
+        \int_compare:nNnTF {#1} = \c_zero
+          { \exp_args:No \__clist_item_n_end:n {#2} }
+          {
+            \exp_args:Nf \__clist_item_n_loop:nw
+              { \int_eval:n { #1 - 1 } }
+              \prg_do_nothing:
+          }
+      }
+  }
+\cs_new:Npn \__clist_item_n_end:n #1 #2 \q_stop
+  {
+    \__tl_trim_spaces:nn { \q_mark #1 }
+      { \exp_last_unbraced:No \__clist_item_n_strip:w } ,
+  }
+\cs_new:Npn \__clist_item_n_strip:w #1 , { \exp_not:n {#1} }
+\cs_new_protected:Npn \clist_set_from_seq:NN
+  { \__clist_set_from_seq:NNNN \clist_clear:N  \tl_set:Nx  }
+\cs_new_protected:Npn \clist_gset_from_seq:NN
+  { \__clist_set_from_seq:NNNN \clist_gclear:N \tl_gset:Nx }
+\cs_new_protected:Npn \__clist_set_from_seq:NNNN #1#2#3#4
+  {
+    \seq_if_empty:NTF #4
+      { #1 #3 }
+      {
+        #2 #3
+          {
+            \exp_last_unbraced:Nf \use_none:n
+              { \seq_map_function:NN #4 \__clist_wrap_item:n }
+          }
+      }
+  }
+\cs_new:Npn \__clist_wrap_item:n #1
+  {
+    ,
+    \tl_if_empty:oTF { \__clist_set_from_seq:w #1 ~ , #1 ~ }
+      { \exp_not:n   {#1}   }
+      { \exp_not:n { {#1} } }
+  }
+\cs_new:Npn \__clist_set_from_seq:w #1 , #2 ~ { }
+\cs_generate_variant:Nn \clist_set_from_seq:NN  {     Nc }
+\cs_generate_variant:Nn \clist_set_from_seq:NN  { c , cc }
+\cs_generate_variant:Nn \clist_gset_from_seq:NN {     Nc }
+\cs_generate_variant:Nn \clist_gset_from_seq:NN { c , cc }
+\cs_new_protected:Npn \clist_const:Nn #1#2
+  { \tl_const:Nx #1 { \__clist_trim_spaces:n {#2} } }
+\cs_generate_variant:Nn \clist_const:Nn { c , Nx , cx }
+\prg_new_conditional:Npnn \clist_if_empty:n #1 { p , T , F , TF }
+  {
+    \__clist_if_empty_n:w ? #1
+    , \q_mark \prg_return_false:
+    , \q_mark \prg_return_true:
+    \q_stop
+  }
+\cs_new:Npn \__clist_if_empty_n:w #1 ,
+  {
+    \tl_if_empty:oTF { \use_none:nn #1 ? }
+      { \__clist_if_empty_n:w ? }
+      { \__clist_if_empty_n:wNw }
+  }
+\cs_new:Npn \__clist_if_empty_n:wNw #1 \q_mark #2#3 \q_stop {#2}
+\cs_new:Npn \clist_use:Nnnn #1#2#3#4
+  {
+    \clist_if_exist:NTF #1
+      {
+        \int_case:nnn { \clist_count:N #1 }
+          {
+            { 0 } { }
+            { 1 } { \exp_after:wN \__clist_use:wwn #1 , , { } }
+            { 2 } { \exp_after:wN \__clist_use:wwn #1 , {#2} }
+          }
+          {
+            \exp_after:wN \__clist_use_ii:nwwwwnwn
+            \exp_after:wN { \exp_after:wN } #1 ,
+            \q_mark , { \__clist_use_ii:nwwwwnwn {#3} }
+            \q_mark , { \__clist_use_iii:nwwn {#4} }
+            \q_stop { }
+          }
+      }
+      { \__msg_kernel_expandable_error:nnn { kernel } { bad-variable } {#1} }
+  }
+\cs_new:Npn \__clist_use:wwn #1 , #2 , #3 { \exp_not:n { #1 #3 #2 } }
+\cs_new:Npn \__clist_use_ii:nwwwwnwn
+    #1#2 , #3 , #4 , #5 \q_mark , #6#7 \q_stop #8
+  { #6 {#3} , {#4} , #5 \q_mark , {#6} #7 \q_stop { #8 #1 #2 } }
+\cs_new:Npn \__clist_use_iii:nwwn #1#2 , #3 \q_stop #4
+  { \exp_not:n { #4 #1 #2 } }
+\fp_new:N \l__coffin_sin_fp
+\fp_new:N \l__coffin_cos_fp
+\prop_new:N \l__coffin_bounding_prop
+\dim_new:N \l__coffin_bounding_shift_dim
+\dim_new:N \l__coffin_left_corner_dim
+\dim_new:N \l__coffin_right_corner_dim
+\dim_new:N \l__coffin_bottom_corner_dim
+\dim_new:N \l__coffin_top_corner_dim
+\cs_new_protected:Npn \coffin_rotate:Nn #1#2
+  {
+    \fp_set:Nn \l__coffin_sin_fp { sin ( ( #2 ) * deg ) }
+    \fp_set:Nn \l__coffin_cos_fp { cos ( ( #2 ) * deg ) }
+    \prop_map_inline:cn { l__coffin_corners_ \__int_value:w #1 _prop }
+      { \__coffin_rotate_corner:Nnnn #1 {##1} ##2 }
+    \prop_map_inline:cn { l__coffin_poles_ \__int_value:w #1 _prop }
+      { \__coffin_rotate_pole:Nnnnnn #1 {##1} ##2 }
+    \__coffin_set_bounding:N #1
+    \prop_map_inline:Nn \l__coffin_bounding_prop
+      { \__coffin_rotate_bounding:nnn {##1} ##2 }
+    \__coffin_find_corner_maxima:N #1
+    \__coffin_find_bounding_shift:
+    \box_rotate:Nn #1 {#2}
+    \hbox_set:Nn #1
+      {
+        \tex_kern:D \l__coffin_bounding_shift_dim
+        \tex_kern:D -\l__coffin_left_corner_dim
+        \box_move_down:nn { \l__coffin_bottom_corner_dim }
+          { \box_use:N #1 }
+      }
+    \box_set_ht:Nn #1
+      { \l__coffin_top_corner_dim - \l__coffin_bottom_corner_dim }
+    \box_set_dp:Nn #1 { 0 pt }
+    \box_set_wd:Nn #1
+      { \l__coffin_right_corner_dim - \l__coffin_left_corner_dim }
+    \prop_map_inline:cn { l__coffin_corners_ \__int_value:w #1 _prop }
+      { \__coffin_shift_corner:Nnnn #1 {##1} ##2 }
+    \prop_map_inline:cn { l__coffin_poles_ \__int_value:w #1 _prop }
+      { \__coffin_shift_pole:Nnnnnn #1 {##1} ##2 }
+  }
+\cs_generate_variant:Nn \coffin_rotate:Nn { c }
+\cs_new_protected:Npn \__coffin_set_bounding:N #1
+  {
+    \prop_put:Nnx \l__coffin_bounding_prop { tl }
+      { { 0 pt } { \dim_use:N \box_ht:N #1 } }
+    \prop_put:Nnx \l__coffin_bounding_prop { tr }
+      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \box_ht:N #1 } }
+    \dim_set:Nn \l__coffin_internal_dim { - \box_dp:N #1 }
+    \prop_put:Nnx \l__coffin_bounding_prop { bl }
+      { { 0 pt } { \dim_use:N \l__coffin_internal_dim } }
+    \prop_put:Nnx \l__coffin_bounding_prop { br }
+      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \l__coffin_internal_dim } }
+  }
+\cs_new_protected:Npn \__coffin_rotate_bounding:nnn #1#2#3
+  {
+    \__coffin_rotate_vector:nnNN {#2} {#3} \l__coffin_x_dim \l__coffin_y_dim
+    \prop_put:Nnx \l__coffin_bounding_prop {#1}
+      { { \dim_use:N \l__coffin_x_dim } { \dim_use:N \l__coffin_y_dim } }
+  }
+\cs_new_protected:Npn \__coffin_rotate_corner:Nnnn #1#2#3#4
+  {
+    \__coffin_rotate_vector:nnNN {#3} {#4} \l__coffin_x_dim \l__coffin_y_dim
+    \prop_put:cnx { l__coffin_corners_ \__int_value:w #1 _prop } {#2}
+      { { \dim_use:N \l__coffin_x_dim } { \dim_use:N \l__coffin_y_dim } }
+  }
+\cs_new_protected:Npn \__coffin_rotate_pole:Nnnnnn #1#2#3#4#5#6
+  {
+    \__coffin_rotate_vector:nnNN {#3} {#4} \l__coffin_x_dim \l__coffin_y_dim
+    \__coffin_rotate_vector:nnNN {#5} {#6}
+      \l__coffin_x_prime_dim \l__coffin_y_prime_dim
+    \__coffin_set_pole:Nnx #1 {#2}
+      {
+        { \dim_use:N \l__coffin_x_dim } { \dim_use:N \l__coffin_y_dim }
+        { \dim_use:N \l__coffin_x_prime_dim }
+        { \dim_use:N \l__coffin_y_prime_dim }
+      }
+  }
+\cs_new_protected:Npn \__coffin_rotate_vector:nnNN #1#2#3#4
+  {
+    \dim_set:Nn #3
+      {
+        \fp_to_dim:n
+          {
+                \dim_to_fp:n {#1} * \l__coffin_cos_fp
+            - ( \dim_to_fp:n {#2} * \l__coffin_sin_fp )
+          }
+      }
+    \dim_set:Nn #4
+      {
+        \fp_to_dim:n
+          {
+                \dim_to_fp:n {#1} * \l__coffin_sin_fp
+            + ( \dim_to_fp:n {#2} * \l__coffin_cos_fp )
+          }
+      }
+  }
+\cs_new_protected:Npn \__coffin_find_corner_maxima:N #1
+  {
+    \dim_set:Nn \l__coffin_top_corner_dim   { -\c_max_dim }
+    \dim_set:Nn \l__coffin_right_corner_dim { -\c_max_dim }
+    \dim_set:Nn \l__coffin_bottom_corner_dim { \c_max_dim }
+    \dim_set:Nn \l__coffin_left_corner_dim   { \c_max_dim }
+    \prop_map_inline:cn { l__coffin_corners_ \__int_value:w #1 _prop }
+      { \__coffin_find_corner_maxima_aux:nn ##2 }
+  }
+\cs_new_protected:Npn \__coffin_find_corner_maxima_aux:nn #1#2
+  {
+    \dim_set_min:Nn \l__coffin_left_corner_dim   {#1}
+    \dim_set_max:Nn \l__coffin_right_corner_dim  {#1}
+    \dim_set_min:Nn \l__coffin_bottom_corner_dim {#2}
+    \dim_set_max:Nn \l__coffin_top_corner_dim    {#2}
+  }
+\cs_new_protected_nopar:Npn \__coffin_find_bounding_shift:
+  {
+    \dim_set:Nn \l__coffin_bounding_shift_dim { \c_max_dim }
+    \prop_map_inline:Nn \l__coffin_bounding_prop
+      { \__coffin_find_bounding_shift_aux:nn ##2 }
+  }
+\cs_new_protected:Npn \__coffin_find_bounding_shift_aux:nn #1#2
+  { \dim_set_min:Nn \l__coffin_bounding_shift_dim {#1} }
+\cs_new_protected:Npn \__coffin_shift_corner:Nnnn #1#2#3#4
+  {
+    \prop_put:cnx { l__coffin_corners_ \__int_value:w #1 _ prop } {#2}
+      {
+        { \dim_eval:n { #3 - \l__coffin_left_corner_dim } }
+        { \dim_eval:n { #4 - \l__coffin_bottom_corner_dim } }
+      }
+  }
+\cs_new_protected:Npn \__coffin_shift_pole:Nnnnnn #1#2#3#4#5#6
+  {
+    \prop_put:cnx { l__coffin_poles_ \__int_value:w #1 _ prop } {#2}
+      {
+        { \dim_eval:n { #3 - \l__coffin_left_corner_dim } }
+        { \dim_eval:n { #4 - \l__coffin_bottom_corner_dim } }
+        {#5} {#6}
+      }
+  }
+\fp_new:N \l__coffin_scale_x_fp
+\fp_new:N \l__coffin_scale_y_fp
+\dim_new:N \l__coffin_scaled_total_height_dim
+\dim_new:N \l__coffin_scaled_width_dim
+\cs_new_protected:Npn \coffin_resize:Nnn #1#2#3
+  {
+    \__coffin_set_user_dimensions:N #1
+    \box_resize:Nnn #1 {#2} {#3}
+    \fp_set:Nn \l__coffin_scale_x_fp
+      { \dim_to_fp:n {#2} / \dim_to_fp:n \Width }
+    \fp_set:Nn \l__coffin_scale_y_fp
+      { \dim_to_fp:n {#3} / \dim_to_fp:n \TotalHeight }
+    \__coffin_resize_common:Nnn #1 {#2} {#3}
+  }
+\cs_generate_variant:Nn \coffin_resize:Nnn { c }
+\cs_new_protected:Npn \__coffin_resize_common:Nnn #1#2#3
+  {
+    \prop_map_inline:cn { l__coffin_corners_ \__int_value:w #1 _prop }
+      { \__coffin_scale_corner:Nnnn #1 {##1} ##2 }
+    \prop_map_inline:cn { l__coffin_poles_ \__int_value:w #1 _prop }
+      { \__coffin_scale_pole:Nnnnnn #1 {##1} ##2 }
+    \fp_compare:nNnT \l__coffin_scale_x_fp < \c_zero_fp
+      {
+        \prop_map_inline:cn { l__coffin_corners_ \__int_value:w #1 _prop }
+          { \__coffin_x_shift_corner:Nnnn #1 {##1} ##2 }
+        \prop_map_inline:cn { l__coffin_poles_ \__int_value:w #1 _prop }
+          { \__coffin_x_shift_pole:Nnnnnn #1 {##1} ##2 }
+      }
+    \__coffin_end_user_dimensions:
+  }
+\cs_new_protected:Npn \coffin_scale:Nnn #1#2#3
+  {
+    \box_scale:Nnn #1 {#2} {#3}
+    \__coffin_set_user_dimensions:N #1
+    \fp_set:Nn \l__coffin_scale_x_fp {#2}
+    \fp_set:Nn \l__coffin_scale_y_fp {#3}
+    \fp_compare:nNnTF \l__coffin_scale_y_fp > \c_zero_fp
+      { \l__coffin_scaled_total_height_dim #3 \TotalHeight }
+      { \l__coffin_scaled_total_height_dim -#3 \TotalHeight }
+    \fp_compare:nNnTF \l__coffin_scale_x_fp > \c_zero_fp
+      { \l__coffin_scaled_width_dim -#2 \Width }
+      { \l__coffin_scaled_width_dim #2 \Width }
+    \__coffin_resize_common:Nnn #1
+      { \l__coffin_scaled_width_dim } { \l__coffin_scaled_total_height_dim }
+  }
+\cs_generate_variant:Nn \coffin_scale:Nnn { c }
+\cs_new_protected:Npn \__coffin_scale_vector:nnNN #1#2#3#4
+  {
+    \dim_set:Nn #3
+      { \fp_to_dim:n { \dim_to_fp:n {#1} * \l__coffin_scale_x_fp } }
+    \dim_set:Nn #4
+      { \fp_to_dim:n { \dim_to_fp:n {#2} * \l__coffin_scale_y_fp } }
+  }
+\cs_new_protected:Npn \__coffin_scale_corner:Nnnn #1#2#3#4
+  {
+    \__coffin_scale_vector:nnNN {#3} {#4} \l__coffin_x_dim \l__coffin_y_dim
+    \prop_put:cnx { l__coffin_corners_ \__int_value:w #1 _prop } {#2}
+      { { \dim_use:N \l__coffin_x_dim } { \dim_use:N \l__coffin_y_dim } }
+  }
+\cs_new_protected:Npn \__coffin_scale_pole:Nnnnnn #1#2#3#4#5#6
+  {
+    \__coffin_scale_vector:nnNN {#3} {#4} \l__coffin_x_dim \l__coffin_y_dim
+    \__coffin_set_pole:Nnx #1 {#2}
+      {
+        { \dim_use:N \l__coffin_x_dim } { \dim_use:N \l__coffin_y_dim }
+        {#5} {#6}
+      }
+  }
+\cs_new_protected:Npn \__coffin_x_shift_corner:Nnnn #1#2#3#4
+  {
+    \prop_put:cnx { l__coffin_corners_ \__int_value:w #1 _prop } {#2}
+      {
+        { \dim_eval:n { #3 + \box_wd:N #1 } } {#4}
+      }
+  }
+\cs_new_protected:Npn \__coffin_x_shift_pole:Nnnnnn #1#2#3#4#5#6
+  {
+    \prop_put:cnx { l__coffin_poles_ \__int_value:w #1 _prop } {#2}
+      {
+        { \dim_eval:n #3 + \box_wd:N #1 } {#4}
+        {#5} {#6}
+      }
+  }
+\cs_new_nopar:Npn \ior_map_break:
+  { \__prg_map_break:Nn \ior_map_break: { } }
+\cs_new_nopar:Npn \ior_map_break:n
+  { \__prg_map_break:Nn \ior_map_break: }
+\cs_new_protected_nopar:Npn \ior_map_inline:Nn
+  { \__ior_map_inline:NNn \ior_get:NN }
+\cs_new_protected_nopar:Npn \ior_str_map_inline:Nn
+  { \__ior_map_inline:NNn \ior_get_str:NN }
+\cs_new_protected_nopar:Npn \__ior_map_inline:NNn
+  {
+    \int_gincr:N \g__prg_map_int
+    \exp_args:Nc \__ior_map_inline:NNNn
+      { __prg_map_ \int_use:N \g__prg_map_int :n }
+  }
+\cs_new_protected:Npn \__ior_map_inline:NNNn #1#2#3#4
+  {
+    \cs_set:Npn #1 ##1 {#4}
+    \ior_if_eof:NF #3 { \__ior_map_inline_loop:NNN #1#2#3 }
+    \__prg_break_point:Nn \ior_map_break:
+      { \int_gdecr:N \g__prg_map_int }
+  }
+\cs_new_protected:Npn \__ior_map_inline_loop:NNN #1#2#3
+  {
+    #2 #3 \l__ior_internal_tl
+    \ior_if_eof:NF #3
+      {
+        \exp_args:No #1 \l__ior_internal_tl
+        \__ior_map_inline_loop:NNN #1#2#3
+      }
+  }
+\tl_new:N  \l__ior_internal_tl
+\cs_new_protected:Npn \fp_set_from_dim:Nn #1#2
+  { \tl_set:Nx #1 { \dim_to_fp:n {#2} } }
+\cs_new_protected:Npn \fp_gset_from_dim:Nn #1#2
+  { \tl_gset:Nx #1 { \dim_to_fp:n {#2} } }
+\cs_generate_variant:Nn \fp_set_from_dim:Nn  { c }
+\cs_generate_variant:Nn \fp_gset_from_dim:Nn { c }
+\cs_new:Npn \prop_map_tokens:Nn #1#2
+  {
+    \exp_last_unbraced:Nno \__prop_map_tokens:nwn {#2} #1
+    \q_recursion_tail \q__prop { }
+    \__prg_break_point:Nn \prop_map_break: { }
+  }
+\cs_new:Npn \__prop_map_tokens:nwn #1 \q__prop #2 \q__prop #3
+  {
+    \__quark_if_recursion_tail_break:NN #2 \prop_map_break:
+    \use:n {#1} {#2} {#3}
+    \__prop_map_tokens:nwn {#1}
+  }
+\cs_generate_variant:Nn \prop_map_tokens:Nn { c }
+\cs_new:Npn \prop_get:Nn #1#2
+  {
+    \exp_last_unbraced:Noo \__prop_get_Nn:nwn
+      { \tl_to_str:n {#2} } #1
+      \tl_to_str:n {#2} \q__prop { }
+    \__prg_break_point:
+  }
+\cs_new:Npn \__prop_get_Nn:nwn #1 \q__prop #2 \q__prop #3
+  {
+    \str_if_eq_x:nnTF {#1} {#2}
+      { \__prg_break:n { \exp_not:n {#3} } }
+      { \__prop_get_Nn:nwn {#1} }
+  }
+\cs_generate_variant:Nn \prop_get:Nn { c }
+\cs_new:Npn \seq_item:Nn #1#2
+  {
+    \exp_last_unbraced:Nfo \__seq_item:nnn
+      {
+        \int_eval:n
+          {
+            \int_compare:nNnT {#2} < \c_zero
+              { \seq_count:N #1 + \c_one + }
+            #2
+          }
+      }
+    #1
+    { ? \__prg_break: }
+    { }
+    \__prg_break_point:
+  }
+\cs_new:Npn \__seq_item:nnn #1#2#3
+  {
+    \use_none:n #2
+    \int_compare:nNnTF {#1} = \c_one
+      { \__prg_break:n { \exp_not:n {#3} } }
+      { \exp_args:Nf \__seq_item:nnn { \int_eval:n { #1 - 1 } } }
+  }
+\cs_generate_variant:Nn \seq_item:Nn { c }
+\cs_new:Npn \seq_mapthread_function:NNN #1#2#3
+  {
+    \exp_after:wN \__seq_mapthread_function:NN
+      \exp_after:wN #3
+      \exp_after:wN #1
+      #2
+      { ? \__prg_break: } { }
+    \__prg_break_point:
+  }
+\cs_new:Npn \__seq_mapthread_function:NN #1#2
+  {
+    \exp_after:wN \__seq_mapthread_function:Nnnwnn
+      \exp_after:wN #1
+      #2
+      { ? \__prg_break: } { }
+      \q_stop
+  }
+\cs_new:Npn \__seq_mapthread_function:Nnnwnn #1#2#3#4 \q_stop #5#6
+  {
+    \use_none:n #2
+    \use_none:n #5
+    #1 {#3} {#6}
+    \__seq_mapthread_function:Nnnwnn #1 #4 \q_stop
+  }
+\cs_generate_variant:Nn \seq_mapthread_function:NNN {     Nc }
+\cs_generate_variant:Nn \seq_mapthread_function:NNN { c , cc }
+\cs_new_protected:Npn \seq_set_from_clist:NN #1#2
+  {
+    \tl_set:Nx #1
+      { \clist_map_function:NN #2 \__seq_wrap_item:n }
+  }
+\cs_new_protected:Npn \seq_set_from_clist:Nn #1#2
+  {
+    \tl_set:Nx #1
+      { \clist_map_function:nN {#2} \__seq_wrap_item:n }
+  }
+\cs_new_protected:Npn \seq_gset_from_clist:NN #1#2
+  {
+    \tl_gset:Nx #1
+      { \clist_map_function:NN #2 \__seq_wrap_item:n }
+  }
+\cs_new_protected:Npn \seq_gset_from_clist:Nn #1#2
+  {
+    \tl_gset:Nx #1
+      { \clist_map_function:nN {#2} \__seq_wrap_item:n }
+  }
+\cs_generate_variant:Nn \seq_set_from_clist:NN  {     Nc }
+\cs_generate_variant:Nn \seq_set_from_clist:NN  { c , cc }
+\cs_generate_variant:Nn \seq_set_from_clist:Nn  { c      }
+\cs_generate_variant:Nn \seq_gset_from_clist:NN {     Nc }
+\cs_generate_variant:Nn \seq_gset_from_clist:NN { c , cc }
+\cs_generate_variant:Nn \seq_gset_from_clist:Nn { c      }
+\cs_new_protected_nopar:Npn \__seq_tmp:w { }
+\cs_new_protected_nopar:Npn \seq_reverse:N
+  { \__seq_reverse:NN \tl_set:Nx }
+\cs_new_protected_nopar:Npn \seq_greverse:N
+  { \__seq_reverse:NN \tl_gset:Nx }
+\cs_new_protected:Npn \__seq_reverse:NN #1 #2
+  {
+    \cs_set_eq:NN \__seq_tmp:w \__seq_item:n
+    \cs_set_eq:NN \__seq_item:n \__seq_reverse_item:nwn
+    #1 #2 { #2 \exp_not:n { } }
+    \cs_set_eq:NN \__seq_item:n \__seq_tmp:w
+  }
+\cs_new:Npn \__seq_reverse_item:nwn #1 #2 \exp_not:n #3
+  {
+    #2
+    \exp_not:n { \__seq_item:n {#1} #3 }
+  }
+\cs_generate_variant:Nn \seq_reverse:N  { c }
+\cs_generate_variant:Nn \seq_greverse:N { c }
+\cs_new_protected_nopar:Npn \seq_set_filter:NNn
+  { \__seq_set_filter:NNNn \tl_set:Nx }
+\cs_new_protected_nopar:Npn \seq_gset_filter:NNn
+  { \__seq_set_filter:NNNn \tl_gset:Nx }
+\cs_new_protected:Npn \__seq_set_filter:NNNn #1#2#3#4
+  {
+    \__seq_push_item_def:n { \bool_if:nT {#4} { \__seq_wrap_item:n {##1} } }
+    #1 #2 { #3 }
+    \__seq_pop_item_def:
+  }
+\cs_new_protected_nopar:Npn \seq_set_map:NNn
+  { \__seq_set_map:NNNn \tl_set:Nx }
+\cs_new_protected_nopar:Npn \seq_gset_map:NNn
+  { \__seq_set_map:NNNn \tl_gset:Nx }
+\cs_new_protected:Npn \__seq_set_map:NNNn #1#2#3#4
+  {
+    \__seq_push_item_def:n { \exp_not:N \__seq_item:n {#4} }
+    #1 #2 { #3 }
+    \__seq_pop_item_def:
+  }
+\cs_new:Npn \seq_use:Nnnn #1#2#3#4
+  {
+    \seq_if_exist:NTF #1
+      {
+        \int_case:nnn { \seq_count:N #1 }
+          {
+            { 0 } { }
+            { 1 } { \exp_after:wN \__seq_use:NnNnn #1 \__seq_item:n { } { } }
+            { 2 } { \exp_after:wN \__seq_use:NnNnn #1 {#2} }
+          }
+          {
+            \exp_after:wN \__seq_use_ii:nwwwwnwn
+            \exp_after:wN { \exp_after:wN } #1 \__seq_item:n
+            \q_mark { \__seq_use_ii:nwwwwnwn {#3} }
+            \q_mark { \__seq_use_iii:nwwn {#4} }
+            \q_stop { }
+          }
+      }
+      { \__msg_kernel_expandable_error:nnn { kernel } { bad-variable } {#1} }
+  }
+\cs_new:Npn \__seq_use:NnNnn \__seq_item:n #1 \__seq_item:n #2#3
+  { \exp_not:n { #1 #3 #2 } }
+\cs_new:Npn \__seq_use_ii:nwwwwnwn
+    #1 \__seq_item:n #2 \__seq_item:n #3 \__seq_item:n #4#5
+    \q_mark #6#7 \q_stop #8
+  {
+    #6 \__seq_item:n {#3} \__seq_item:n {#4} #5
+    \q_mark {#6} #7 \q_stop { #8 #1 #2 }
+  }
+\cs_new:Npn \__seq_use_iii:nwwn #1 \__seq_item:n #2 #3 \q_stop #4
+  { \exp_not:n { #4 #1 #2 } }
+\cs_new:Npn \skip_split_finite_else_action:nnNN #1#2#3#4
+  {
+    \skip_if_finite:nTF {#1}
+      {
+        #3 = \etex_gluestretch:D #1 \scan_stop:
+        #4 = \etex_glueshrink:D  #1 \scan_stop:
+      }
+      {
+        #3 = \c_zero_skip
+        #4 = \c_zero_skip
+        #2
+      }
+  }
+\prg_new_conditional:Npnn \tl_if_single_token:n #1 { p , T , F , TF }
+  {
+    \tl_if_head_is_N_type:nTF {#1}
+      { \__str_if_eq_x_return:nn { \exp_not:o { \use_none:n #1 } } { } }
+      { \__str_if_eq_x_return:nn { \exp_not:n {#1} } { ~ } }
+  }
+\cs_new:Npn \tl_reverse_tokens:n #1
+  {
+    \etex_unexpanded:D \exp_after:wN
+      {
+        \tex_romannumeral:D
+        \__tl_act:NNNnn
+          \__tl_reverse_normal:nN
+          \__tl_reverse_group:nn
+          \__tl_reverse_space:n
+          { }
+          {#1}
+      }
+  }
+\cs_new:Npn \__tl_reverse_group:nn #1
+  {
+    \__tl_act_group_recurse:Nnn
+      \__tl_act_reverse_output:n
+      { \tl_reverse_tokens:n }
+  }
+\cs_new:Npn \__tl_act_group_recurse:Nnn #1#2#3
+  {
+    \exp_args:Nf #1
+      { \exp_after:wN \exp_after:wN \exp_after:wN { #2 {#3} } }
+  }
+\cs_new:Npn \tl_count_tokens:n #1
+  {
+    \int_eval:n
+      {
+        \__tl_act:NNNnn
+          \__tl_act_count_normal:nN
+          \__tl_act_count_group:nn
+          \__tl_act_count_space:n
+          { }
+          {#1}
+      }
+  }
+\cs_new:Npn \__tl_act_count_normal:nN #1 #2 { 1 + }
+\cs_new:Npn \__tl_act_count_space:n #1 { 1 + }
+\cs_new:Npn \__tl_act_count_group:nn #1 #2
+  { 2 + \tl_count_tokens:n {#2} + }
+\tl_const:Nn \c__tl_act_uppercase_tl
+  {
+    aA bB cC dD eE fF gG hH iI jJ kK lL mM
+    nN oO pP qQ rR sS tT uU vV wW xX yY zZ
+  }
+\tl_const:Nn \c__tl_act_lowercase_tl
+  {
+    Aa Bb Cc Dd Ee Ff Gg Hh Ii Jj Kk Ll Mm
+    Nn Oo Pp Qq Rr Ss Tt Uu Vv Ww Xx Yy Zz
+  }
+\cs_new:Npn \tl_expandable_uppercase:n #1
+  {
+    \etex_unexpanded:D \exp_after:wN
+      {
+        \tex_romannumeral:D
+          \__tl_act_case_aux:nn { \c__tl_act_uppercase_tl } {#1}
+      }
+  }
+\cs_new:Npn \tl_expandable_lowercase:n #1
+  {
+    \etex_unexpanded:D \exp_after:wN
+      {
+        \tex_romannumeral:D
+          \__tl_act_case_aux:nn { \c__tl_act_lowercase_tl } {#1}
+      }
+  }
+\cs_new:Npn \__tl_act_case_aux:nn
+  {
+    \__tl_act:NNNnn
+      \__tl_act_case_normal:nN
+      \__tl_act_case_group:nn
+      \__tl_act_case_space:n
+  }
+\cs_new:Npn \__tl_act_case_space:n #1 { \__tl_act_output:n {~} }
+\cs_new:Npn \__tl_act_case_normal:nN #1 #2
+  {
+    \exp_args:Nf \__tl_act_output:n
+      {
+        \exp_args:NNo \str_case:nnn #2 {#1}
+          { \exp_stop_f: #2 }
+      }
+  }
+\cs_new:Npn \__tl_act_case_group:nn #1 #2
+  {
+    \exp_after:wN \__tl_act_output:n \exp_after:wN
+      { \exp_after:wN { \tex_romannumeral:D \__tl_act_case_aux:nn {#1} {#2} } }
+  }
+\cs_new:Npn \tl_item:nn #1#2
+  {
+    \exp_args:Nf \__tl_item:nn
+      {
+        \int_eval:n
+          {
+            \int_compare:nNnT {#2} < \c_zero
+              { \tl_count:n {#1} + \c_one + }
+            #2
+          }
+      }
+    #1
+    \q_recursion_tail
+    \__prg_break_point:
+  }
+\cs_new:Npn \__tl_item:nn #1#2
+  {
+    \__quark_if_recursion_tail_break:nN {#2} \__prg_break:
+    \int_compare:nNnTF {#1} = \c_one
+      { \__prg_break:n { \exp_not:n {#2} } }
+      { \exp_args:Nf \__tl_item:nn { \int_eval:n { #1 - 1 } } }
+  }
+\cs_new_nopar:Npn \tl_item:Nn { \exp_args:No \tl_item:nn }
+\cs_generate_variant:Nn \tl_item:Nn { c }
+\group_begin:
+  \char_set_catcode_active:N \^^@
+  \cs_set:Npn \char_tmp:NN #1#2
+    {
+      \cs_new:Npn #1 ##1
+        {
+          \char_set_catcode_active:n { `##1 }
+          \group_begin:
+          \char_set_lccode:nn { `\^^@ } { `##1 }
+          \tl_to_lowercase:n { \group_end: #2 ^^@ }
+        }
+    }
+  \char_tmp:NN \char_set_active:Npn    \cs_set:Npn
+  \char_tmp:NN \char_set_active:Npx    \cs_set:Npx
+  \char_tmp:NN \char_gset_active:Npn   \cs_gset:Npn
+  \char_tmp:NN \char_gset_active:Npx   \cs_gset:Npx
+  \char_tmp:NN \char_set_active_eq:NN  \cs_set_eq:NN
+  \char_tmp:NN \char_gset_active_eq:NN \cs_gset_eq:NN
+\group_end:
+\cs_new_protected_nopar:Npn \__peek_execute_branches_N_type:
+  {
+    \bool_if:nTF
+      {
+        \token_if_eq_catcode_p:NN \l_peek_token \c_group_begin_token ||
+        \token_if_eq_catcode_p:NN \l_peek_token \c_group_end_token   ||
+        \token_if_eq_meaning_p:NN \l_peek_token \c_space_token
+      }
+      { \__peek_false:w }
+      { \__peek_true:w }
+  }
+\cs_new_protected_nopar:Npn \peek_N_type:TF
+  { \__peek_token_generic:NNTF \__peek_execute_branches_N_type: \scan_stop: }
+\cs_new_protected_nopar:Npn \peek_N_type:T
+  { \__peek_token_generic:NNT  \__peek_execute_branches_N_type: \scan_stop: }
+\cs_new_protected_nopar:Npn \peek_N_type:F
+  { \__peek_token_generic:NNF  \__peek_execute_branches_N_type: \scan_stop: }
+%% 
+%%
+%% End of file `l3candidates.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3clist.sty b/Master/texmf-dist/tex/latex/l3kernel/l3clist.sty
index 75ef38900cc..1f78b1b4851 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3clist.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3clist.sty
@@ -48,13 +48,14 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3clist.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental comma separated lists}
+\GetIdInfo$Id: l3clist.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Comma separated lists}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
-\tl_new:N \l_clist_internal_clist
-\cs_new_protected:Npn \clist_tmp:w { }
+\__expl_package_check:
+\cs_new_eq:NN \c_empty_clist \c_empty_tl
+\tl_new:N \l__clist_internal_clist
+\cs_new_protected:Npn \__clist_tmp:w { }
 \cs_new_eq:NN \clist_new:N \tl_new:N
 \cs_new_eq:NN \clist_new:c \tl_new:c
 \cs_new_eq:NN \clist_clear:N  \tl_clear:N
@@ -74,10 +75,10 @@
 \cs_new_eq:NN \clist_gset_eq:cN \tl_gset_eq:cN
 \cs_new_eq:NN \clist_gset_eq:cc \tl_gset_eq:cc
 \cs_new_protected_nopar:Npn \clist_concat:NNN
-  { \clist_concat_aux:NNNN \tl_set:Nx }
+  { \__clist_concat:NNNN \tl_set:Nx }
 \cs_new_protected_nopar:Npn \clist_gconcat:NNN
-  { \clist_concat_aux:NNNN \tl_gset:Nx }
-\cs_new_protected:Npn \clist_concat_aux:NNNN #1#2#3#4
+  { \__clist_concat:NNNN \tl_gset:Nx }
+\cs_new_protected:Npn \__clist_concat:NNNN #1#2#3#4
   {
     #1 #2
       {
@@ -96,102 +97,133 @@
 \cs_new_eq:NN \clist_if_exist:cT  \cs_if_exist:cT
 \cs_new_eq:NN \clist_if_exist:cF  \cs_if_exist:cF
 \cs_new_eq:NN \clist_if_exist_p:c \cs_if_exist_p:c
-\cs_set:Npn \clist_tmp:w #1
+\cs_new:Npn \__clist_trim_spaces_generic:nw #1#2 ,
   {
-    \cs_new:Npn \clist_trim_spaces_generic:nw ##1 ##2 ,
-      {
-        \tl_trim_spaces_aux_i:w
-        ##2
-        \q_nil
-        \q_mark #1 { }
-        \q_mark \tl_trim_spaces_aux_ii:w
-        \tl_trim_spaces_aux_iii:w
-        #1 \q_nil
-        \clist_trim_spaces_generic_aux:w
-        \q_stop
-        {##1}
-      }
+    \__tl_trim_spaces:nn {#2}
+      { \exp_args:No \__clist_trim_spaces_generic:nn } {#1}
   }
-\clist_tmp:w {~}
-\cs_new:Npn \clist_trim_spaces_generic_aux:w #1 \q_nil #2 \q_stop
-  { \exp_args:No \clist_trim_spaces_generic_aux_ii:nn { \use_none:n #1 } }
-\cs_new:Npn \clist_trim_spaces_generic_aux_ii:nn #1 #2 { #2 {#1} }
-\cs_new:Npn \clist_trim_spaces:n #1
+\cs_new:Npn \__clist_trim_spaces_generic:nn #1#2 { #2 {#1} }
+\cs_new:Npn \__clist_trim_spaces:n #1
   {
-    \clist_trim_spaces_generic:nw
-      { \clist_trim_spaces_aux:nn { } }
+    \__clist_trim_spaces_generic:nw
+      { \__clist_trim_spaces_ii:nn { } }
       \q_mark #1 ,
     \q_recursion_tail, \q_recursion_stop
   }
-\cs_new:Npn \clist_trim_spaces_aux:nn #1 #2
+\cs_new:Npn \__clist_trim_spaces_ii:nn #1 #2
   {
     \quark_if_recursion_tail_stop:n {#2}
     \tl_if_empty:nTF {#2}
       {
-        \clist_trim_spaces_generic:nw
-          { \clist_trim_spaces_aux:nn {#1} } \q_mark
+        \__clist_trim_spaces_generic:nw
+          { \__clist_trim_spaces_ii:nn {#1} } \q_mark
       }
       {
         #1 \exp_not:n {#2}
-        \clist_trim_spaces_generic:nw
-          { \clist_trim_spaces_aux:nn { , } } \q_mark
+        \__clist_trim_spaces_generic:nw
+          { \__clist_trim_spaces_ii:nn { , } } \q_mark
       }
   }
 \cs_new_protected:Npn \clist_set:Nn #1#2
-  { \tl_set:Nx #1 { \clist_trim_spaces:n {#2} } }
+  { \tl_set:Nx #1 { \__clist_trim_spaces:n {#2} } }
 \cs_new_protected:Npn \clist_gset:Nn #1#2
-  { \tl_gset:Nx #1 { \clist_trim_spaces:n {#2} } }
+  { \tl_gset:Nx #1 { \__clist_trim_spaces:n {#2} } }
 \cs_generate_variant:Nn \clist_set:Nn  { NV , No , Nx , c , cV , co , cx }
 \cs_generate_variant:Nn \clist_gset:Nn { NV , No , Nx , c , cV , co , cx }
 \cs_new_protected_nopar:Npn \clist_put_left:Nn
-  { \clist_put_left_aux:NNNn \clist_concat:NNN \clist_set:Nn }
+  { \__clist_put_left:NNNn \clist_concat:NNN \clist_set:Nn }
 \cs_new_protected_nopar:Npn \clist_gput_left:Nn
-  { \clist_put_left_aux:NNNn \clist_gconcat:NNN \clist_set:Nn }
-\cs_new_protected:Npn \clist_put_left_aux:NNNn #1#2#3#4
+  { \__clist_put_left:NNNn \clist_gconcat:NNN \clist_set:Nn }
+\cs_new_protected:Npn \__clist_put_left:NNNn #1#2#3#4
   {
-    #2 \l_clist_internal_clist {#4}
-    #1 #3 \l_clist_internal_clist #3
+    #2 \l__clist_internal_clist {#4}
+    #1 #3 \l__clist_internal_clist #3
   }
 \cs_generate_variant:Nn \clist_put_left:Nn  {     NV , No , Nx }
 \cs_generate_variant:Nn \clist_put_left:Nn  { c , cV , co , cx }
 \cs_generate_variant:Nn \clist_gput_left:Nn {     NV , No , Nx }
 \cs_generate_variant:Nn \clist_gput_left:Nn { c , cV , co , cx }
 \cs_new_protected_nopar:Npn \clist_put_right:Nn
-  { \clist_put_right_aux:NNNn \clist_concat:NNN \clist_set:Nn }
+  { \__clist_put_right:NNNn \clist_concat:NNN \clist_set:Nn }
 \cs_new_protected_nopar:Npn \clist_gput_right:Nn
-  { \clist_put_right_aux:NNNn \clist_gconcat:NNN \clist_gset:Nn }
-\cs_new_protected:Npn \clist_put_right_aux:NNNn #1#2#3#4
+  { \__clist_put_right:NNNn \clist_gconcat:NNN \clist_gset:Nn }
+\cs_new_protected:Npn \__clist_put_right:NNNn #1#2#3#4
   {
-    #2 \l_clist_internal_clist {#4}
-    #1 #3 #3 \l_clist_internal_clist
+    #2 \l__clist_internal_clist {#4}
+    #1 #3 #3 \l__clist_internal_clist
   }
 \cs_generate_variant:Nn \clist_put_right:Nn  {     NV , No , Nx }
 \cs_generate_variant:Nn \clist_put_right:Nn  { c , cV , co , cx }
 \cs_generate_variant:Nn \clist_gput_right:Nn {     NV , No , Nx }
 \cs_generate_variant:Nn \clist_gput_right:Nn { c , cV , co , cx }
 \cs_new_protected:Npn \clist_get:NN #1#2
-  { \exp_after:wN \clist_get_aux:wN #1 , \q_stop #2 }
-\cs_new_protected:Npn \clist_get_aux:wN #1 , #2 \q_stop #3
+  {
+    \if_meaning:w #1 \c_empty_clist
+      \tl_set:Nn #2 { \q_no_value }
+    \else:
+      \exp_after:wN \__clist_get:wN #1 , \q_stop #2
+    \fi:
+  }
+\cs_new_protected:Npn \__clist_get:wN #1 , #2 \q_stop #3
   { \tl_set:Nn #3 {#1} }
 \cs_generate_variant:Nn \clist_get:NN { c }
 \cs_new_protected_nopar:Npn \clist_pop:NN
-  { \clist_pop_aux:NNN \tl_set:Nf }
+  { \__clist_pop:NNN \tl_set:Nx }
 \cs_new_protected_nopar:Npn \clist_gpop:NN
-  { \clist_pop_aux:NNN \tl_gset:Nf }
-\cs_new_protected:Npn \clist_pop_aux:NNN #1#2#3
+  { \__clist_pop:NNN \tl_gset:Nx }
+\cs_new_protected:Npn \__clist_pop:NNN #1#2#3
   {
-    \exp_after:wN \clist_pop_aux:wNNN #2 , \q_nil \q_stop #1#2#3
+    \if_meaning:w #2 \c_empty_clist
+      \tl_set:Nn #3 { \q_no_value }
+    \else:
+      \exp_after:wN \__clist_pop:wwNNN #2 , \q_mark \q_stop #1#2#3
+    \fi:
   }
-\cs_new_protected:Npn \clist_pop_aux:wNNN #1 , #2 \q_stop #3#4#5
+\cs_new_protected:Npn \__clist_pop:wwNNN #1 , #2 \q_stop #3#4#5
   {
     \tl_set:Nn #5 {#1}
-    \quark_if_nil:nTF {#2}
-      { #3 #4 { } }
-      { #3 #4 { \clist_pop_aux:w \exp_stop_f: #2 } }
+    #3 #4
+      {
+        \__clist_pop:wN \prg_do_nothing:
+          #2 \exp_not:o
+          , \q_mark \use_none:n
+        \q_stop
+      }
   }
-\cs_new_protected:Npn \clist_pop_aux:w #1 , \q_nil {#1}
+\cs_new:Npn \__clist_pop:wN #1 , \q_mark #2 #3 \q_stop { #2 {#1} }
 \cs_generate_variant:Nn \clist_pop:NN  { c }
 \cs_generate_variant:Nn \clist_gpop:NN { c }
+\prg_new_protected_conditional:Npnn \clist_get:NN #1#2 { T , F , TF }
+  {
+    \if_meaning:w #1 \c_empty_clist
+      \prg_return_false:
+    \else:
+      \exp_after:wN \__clist_get:wN #1 , \q_stop #2
+      \prg_return_true:
+    \fi:
+  }
+\cs_generate_variant:Nn \clist_get:NNT  { c }
+\cs_generate_variant:Nn \clist_get:NNF  { c }
+\cs_generate_variant:Nn \clist_get:NNTF { c }
+\prg_new_protected_conditional:Npnn \clist_pop:NN #1#2 { T , F , TF }
+  { \__clist_pop_TF:NNN \tl_set:Nx #1 #2 }
+\prg_new_protected_conditional:Npnn \clist_gpop:NN #1#2 { T , F , TF }
+  { \__clist_pop_TF:NNN \tl_gset:Nx #1 #2 }
+\cs_new_protected:Npn \__clist_pop_TF:NNN #1#2#3
+  {
+    \if_meaning:w #2 \c_empty_clist
+      \prg_return_false:
+    \else:
+      \exp_after:wN \__clist_pop:wwNNN #2 , \q_mark \q_stop #1#2#3
+      \prg_return_true:
+    \fi:
+  }
+\cs_generate_variant:Nn \clist_pop:NNT   { c }
+\cs_generate_variant:Nn \clist_pop:NNF   { c }
+\cs_generate_variant:Nn \clist_pop:NNTF  { c }
+\cs_generate_variant:Nn \clist_gpop:NNT  { c }
+\cs_generate_variant:Nn \clist_gpop:NNF  { c }
+\cs_generate_variant:Nn \clist_gpop:NNTF { c }
 \cs_new_eq:NN \clist_push:Nn  \clist_put_left:Nn
 \cs_new_eq:NN \clist_push:NV  \clist_put_left:NV
 \cs_new_eq:NN \clist_push:No  \clist_put_left:No
@@ -208,40 +240,38 @@
 \cs_new_eq:NN \clist_gpush:cV \clist_gput_left:cV
 \cs_new_eq:NN \clist_gpush:co \clist_gput_left:co
 \cs_new_eq:NN \clist_gpush:cx \clist_gput_left:cx
-\cs_new_eq:NN \clist_use:N \tl_use:N
-\cs_new_eq:NN \clist_use:c \tl_use:c
-\clist_new:N \l_clist_internal_remove_clist
+\clist_new:N \l__clist_internal_remove_clist
 \cs_new_protected:Npn \clist_remove_duplicates:N
-  { \clist_remove_duplicates_aux:NN \clist_set_eq:NN }
+  { \__clist_remove_duplicates:NN \clist_set_eq:NN }
 \cs_new_protected:Npn \clist_gremove_duplicates:N
-  { \clist_remove_duplicates_aux:NN \clist_gset_eq:NN }
-\cs_new_protected:Npn \clist_remove_duplicates_aux:NN #1#2
+  { \__clist_remove_duplicates:NN \clist_gset_eq:NN }
+\cs_new_protected:Npn \__clist_remove_duplicates:NN #1#2
   {
-    \clist_clear:N \l_clist_internal_remove_clist
+    \clist_clear:N \l__clist_internal_remove_clist
     \clist_map_inline:Nn #2
       {
-        \clist_if_in:NnF \l_clist_internal_remove_clist {##1}
-          { \clist_put_right:Nn \l_clist_internal_remove_clist {##1} }
+        \clist_if_in:NnF \l__clist_internal_remove_clist {##1}
+          { \clist_put_right:Nn \l__clist_internal_remove_clist {##1} }
       }
-    #1 #2 \l_clist_internal_remove_clist
+    #1 #2 \l__clist_internal_remove_clist
   }
 \cs_generate_variant:Nn \clist_remove_duplicates:N  { c }
 \cs_generate_variant:Nn \clist_gremove_duplicates:N { c }
 \cs_new_protected:Npn \clist_remove_all:Nn
-  { \clist_remove_all_aux:NNn \tl_set:Nx }
+  { \__clist_remove_all:NNn \tl_set:Nx }
 \cs_new_protected:Npn \clist_gremove_all:Nn
-  { \clist_remove_all_aux:NNn \tl_gset:Nx }
-\cs_new_protected:Npn \clist_remove_all_aux:NNn #1#2#3
+  { \__clist_remove_all:NNn \tl_gset:Nx }
+\cs_new_protected:Npn \__clist_remove_all:NNn #1#2#3
   {
-    \cs_set:Npn \clist_tmp:w ##1 , #3 ,
+    \cs_set:Npn \__clist_tmp:w ##1 , #3 ,
       {
         ##1
         , \q_mark , \use_none_delimit_by_q_stop:w ,
-        \clist_remove_all_aux:
+        \__clist_remove_all:
       }
     #1 #2
       {
-        \exp_after:wN \clist_remove_all_aux:
+        \exp_after:wN \__clist_remove_all:
         #2 , \q_mark , #3 , \q_stop
       }
     \clist_if_empty:NF #2
@@ -253,31 +283,27 @@
           }
       }
   }
-\cs_new:Npn \clist_remove_all_aux:
-  { \exp_after:wN \clist_remove_all_aux:w \clist_tmp:w , }
-\cs_new:Npn \clist_remove_all_aux:w #1 , \q_mark , #2 , { \exp_not:n {#1} }
+\cs_new:Npn \__clist_remove_all:
+  { \exp_after:wN \__clist_remove_all:w \__clist_tmp:w , }
+\cs_new:Npn \__clist_remove_all:w #1 , \q_mark , #2 , { \exp_not:n {#1} }
 \cs_generate_variant:Nn \clist_remove_all:Nn  { c }
 \cs_generate_variant:Nn \clist_gremove_all:Nn { c }
 \prg_new_eq_conditional:NNn \clist_if_empty:N \tl_if_empty:N { p , T , F , TF }
 \prg_new_eq_conditional:NNn \clist_if_empty:c \tl_if_empty:c { p , T , F , TF }
-\prg_new_eq_conditional:NNn \clist_if_eq:NN \tl_if_eq:NN { p , T , F , TF }
-\prg_new_eq_conditional:NNn \clist_if_eq:Nc \tl_if_eq:Nc { p , T , F , TF }
-\prg_new_eq_conditional:NNn \clist_if_eq:cN \tl_if_eq:cN { p , T , F , TF }
-\prg_new_eq_conditional:NNn \clist_if_eq:cc \tl_if_eq:cc { p , T , F , TF }
 \prg_new_protected_conditional:Npnn \clist_if_in:Nn #1#2 { T  , F , TF }
   {
-    \exp_args:No \clist_if_in_return:nn #1 {#2}
+    \exp_args:No \__clist_if_in_return:nn #1 {#2}
   }
 \prg_new_protected_conditional:Npnn \clist_if_in:nn #1#2 { T  , F , TF }
   {
-    \clist_set:Nn \l_clist_internal_clist {#1}
-    \exp_args:No \clist_if_in_return:nn \l_clist_internal_clist {#2}
+    \clist_set:Nn \l__clist_internal_clist {#1}
+    \exp_args:No \__clist_if_in_return:nn \l__clist_internal_clist {#2}
   }
-\cs_new_protected:Npn \clist_if_in_return:nn #1#2
+\cs_new_protected:Npn \__clist_if_in_return:nn #1#2
   {
-    \cs_set:Npn \clist_tmp:w ##1 ,#2, { }
+    \cs_set:Npn \__clist_tmp:w ##1 ,#2, { }
     \tl_if_empty:oTF
-      { \clist_tmp:w ,#1, {} {} ,#2, }
+      { \__clist_tmp:w ,#1, {} {} ,#2, }
       { \prg_return_false: } { \prg_return_true: }
   }
 \cs_generate_variant:Nn \clist_if_in:NnT  {     NV , No }
@@ -293,48 +319,49 @@
   {
     \clist_if_empty:NF #1
       {
-        \exp_last_unbraced:NNo \clist_map_function_aux:Nw #2 #1
+        \exp_last_unbraced:NNo \__clist_map_function:Nw #2 #1
           , \q_recursion_tail ,
-        \prg_break_point:n { }
+        \__prg_break_point:Nn \clist_map_break: { }
       }
   }
-\cs_new:Npn \clist_map_function_aux:Nw #1#2 ,
+\cs_new:Npn \__clist_map_function:Nw #1#2 ,
   {
-    \quark_if_recursion_tail_break:n {#2}
+    \__quark_if_recursion_tail_break:nN {#2} \clist_map_break:
     #1 {#2}
-    \clist_map_function_aux:Nw #1
+    \__clist_map_function:Nw #1
   }
 \cs_generate_variant:Nn \clist_map_function:NN { c }
 \cs_new:Npn \clist_map_function:nN #1#2
   {
-    \clist_trim_spaces_generic:nw { \clist_map_function_n_aux:Nn #2 }
+    \__clist_trim_spaces_generic:nw { \__clist_map_function_n:Nn #2 }
     \q_mark #1, \q_recursion_tail,
-    \prg_break_point:n { }
+    \__prg_break_point:Nn \clist_map_break: { }
   }
-\cs_new:Npn \clist_map_function_n_aux:Nn #1 #2
+\cs_new:Npn \__clist_map_function_n:Nn #1 #2
   {
-    \quark_if_recursion_tail_break:n {#2}
-    \tl_if_empty:nF {#2} { \clist_map_aux_unbrace:Nw #1 #2, }
-    \clist_trim_spaces_generic:nw { \clist_map_function_n_aux:Nn #1 }
+    \__quark_if_recursion_tail_break:nN {#2} \clist_map_break:
+    \tl_if_empty:nF {#2} { \__clist_map_unbrace:Nw #1 #2, }
+    \__clist_trim_spaces_generic:nw { \__clist_map_function_n:Nn #1 }
     \q_mark
   }
-\cs_new:Npn \clist_map_aux_unbrace:Nw #1 #2, { #1 {#2} }
+\cs_new:Npn \__clist_map_unbrace:Nw #1 #2, { #1 {#2} }
 \cs_new_protected:Npn \clist_map_inline:Nn #1#2
   {
     \clist_if_empty:NF #1
       {
-        \int_gincr:N \g_prg_map_int
-        \cs_gset:cpn { clist_map_ \int_use:N \g_prg_map_int :n } ##1 {#2}
-        \exp_last_unbraced:Nco \clist_map_function_aux:Nw
-          { clist_map_ \int_use:N \g_prg_map_int :n }
+        \int_gincr:N \g__prg_map_int
+        \cs_gset:cpn { __prg_map_ \int_use:N \g__prg_map_int :w } ##1 {#2}
+        \exp_last_unbraced:Nco \__clist_map_function:Nw
+          { __prg_map_ \int_use:N \g__prg_map_int :w }
           #1 , \q_recursion_tail ,
-        \prg_break_point:n { \int_gdecr:N \g_prg_map_int }
+        \__prg_break_point:Nn \clist_map_break:
+          { \int_gdecr:N \g__prg_map_int }
       }
   }
 \cs_new_protected:Npn \clist_map_inline:nn #1
   {
-    \clist_set:Nn \l_clist_internal_clist {#1}
-    \clist_map_inline:Nn \l_clist_internal_clist
+    \clist_set:Nn \l__clist_internal_clist {#1}
+    \clist_map_inline:Nn \l__clist_internal_clist
   }
 \cs_generate_variant:Nn \clist_map_inline:Nn { c }
 \cs_new_protected:Npn \clist_map_variable:NNn #1#2#3
@@ -342,177 +369,83 @@
     \clist_if_empty:NF #1
       {
         \exp_args:Nno \use:nn
-          { \clist_map_variable_aux:Nnw #2 {#3} }
+          { \__clist_map_variable:Nnw #2 {#3} }
           #1
           , \q_recursion_tail , \q_recursion_stop
-        \prg_break_point:n { }
+        \__prg_break_point:Nn \clist_map_break: { }
       }
   }
 \cs_new_protected:Npn \clist_map_variable:nNn #1
   {
-    \clist_set:Nn \l_clist_internal_clist {#1}
-    \clist_map_variable:NNn \l_clist_internal_clist
+    \clist_set:Nn \l__clist_internal_clist {#1}
+    \clist_map_variable:NNn \l__clist_internal_clist
   }
-\cs_new_protected:Npn \clist_map_variable_aux:Nnw #1#2#3,
+\cs_new_protected:Npn \__clist_map_variable:Nnw #1#2#3,
   {
     \tl_set:Nn #1 {#3}
     \quark_if_recursion_tail_stop:N #1
     \use:n {#2}
-    \clist_map_variable_aux:Nnw #1 {#2}
+    \__clist_map_variable:Nnw #1 {#2}
   }
 \cs_generate_variant:Nn \clist_map_variable:NNn { c }
-\cs_new_eq:NN \clist_map_break:  \prg_map_break:
-\cs_new_eq:NN \clist_map_break:n \prg_map_break:n
-\cs_new_protected:Npn \clist_show:N #1
-  {
-    \msg_aux_show:Nnx
-      #1
-      { clist }
-      { \clist_map_function:NN #1 \msg_aux_show:n }
-  }
-\cs_new_protected:Npn \clist_show:n #1
-  {
-    \clist_set:Nn \l_clist_internal_clist {#1}
-    \msg_aux_show:Nnx
-      \l_clist_internal_clist
-      { clist }
-      { \clist_map_function:NN \l_clist_internal_clist \msg_aux_show:n }
-  }
-\cs_generate_variant:Nn \clist_show:N { c }
-\clist_new:N \l_tmpa_clist
-\clist_new:N \l_tmpb_clist
-\clist_new:N \g_tmpa_clist
-\clist_new:N \g_tmpb_clist
-\cs_new:Npn \clist_length:N #1
+\cs_new_nopar:Npn \clist_map_break:
+  { \__prg_map_break:Nn \clist_map_break: { } }
+\cs_new_nopar:Npn \clist_map_break:n
+  { \__prg_map_break:Nn \clist_map_break: }
+\cs_new:Npn \clist_count:N #1
   {
     \int_eval:n
       {
         0
-        \clist_map_function:NN #1 \clist_length_aux:n
+        \clist_map_function:NN #1 \__clist_count:n
       }
   }
-\cs_new:Npn \clist_length_aux:n #1 { +1 }
-\cs_new:Npx \clist_length:n #1
+\cs_generate_variant:Nn \clist_count:N { c }
+\cs_new:Npx \clist_count:n #1
   {
     \exp_not:N \int_eval:n
       {
         0
-        \exp_not:N \clist_length_n_aux:w \c_space_tl
+        \exp_not:N \__clist_count:w \c_space_tl
         #1 \exp_not:n { , \q_recursion_tail , \q_recursion_stop }
       }
   }
-\cs_new:Npx \clist_length_n_aux:w #1 ,
+\cs_new:Npn \__clist_count:n #1 { + \c_one }
+\cs_new:Npx \__clist_count:w #1 ,
   {
     \exp_not:n { \exp_args:Nf \quark_if_recursion_tail_stop:n } {#1}
     \exp_not:N \tl_if_blank:nF {#1} { + \c_one }
-    \exp_not:N \clist_length_n_aux:w \c_space_tl
+    \exp_not:N \__clist_count:w \c_space_tl
   }
-\cs_generate_variant:Nn \clist_length:N { c }
-\cs_new:Npn \clist_item:Nn #1#2
+\cs_new_protected:Npn \clist_show:N #1
   {
-    \exp_args:Nfo \clist_item_aux:nnNn
-      { \clist_length:N #1 }
+    \__msg_show_variable:Nnn
       #1
-      \clist_item_N_loop:nw
-      {#2}
-  }
-\cs_new:Npn \clist_item_aux:nnNn #1#2#3#4
-  {
-    \int_compare:nNnTF {#4} < \c_zero
-      {
-        \int_compare:nNnTF {#4} < { - #1 }
-          { \use_none_delimit_by_q_stop:w }
-          { \exp_args:Nf #3 { \int_eval:n { #4 + #1 } } }
-      }
-      {
-        \int_compare:nNnTF {#4} < {#1}
-          { #3 {#4} }
-          { \use_none_delimit_by_q_stop:w }
-      }
-    #2, \q_stop
-  }
-\cs_new:Npn \clist_item_N_loop:nw #1 #2,
-  {
-    \int_compare:nNnTF {#1} = \c_zero
-      { \use_i_delimit_by_q_stop:nw { \exp_not:n {#2} } }
-      { \exp_args:Nf \clist_item_N_loop:nw { \int_eval:n { #1 - 1 } } }
-  }
-\cs_generate_variant:Nn \clist_item:Nn { c }
-\cs_new:Npn \clist_item:nn #1#2
-  {
-    \exp_args:Nf \clist_item_aux:nnNn
-      { \clist_length:n {#1} }
-      {#1}
-      \clist_item_n_aux:nw
-      {#2}
-  }
-\cs_new:Npn \clist_item_n_aux:nw #1
-  { \clist_item_n_loop:nw {#1} \prg_do_nothing: }
-\cs_new:Npn \clist_item_n_loop:nw #1 #2,
-  {
-    \exp_args:No \tl_if_blank:nTF {#2}
-      { \clist_item_n_loop:nw {#1} \prg_do_nothing: }
-      {
-        \int_compare:nNnTF {#1} = \c_zero
-          { \exp_args:No \clist_item_n_end:n {#2} }
-          {
-            \exp_args:Nf \clist_item_n_loop:nw
-              { \int_eval:n { #1 - 1 } }
-              \prg_do_nothing:
-          }
-      }
-  }
-\cs_new:Npn \clist_item_n_end:n #1 #2 \q_stop
-  {
-    \exp_after:wN \exp_after:wN \exp_after:wN \clist_item_n_strip:w
-    \tl_trim_spaces:n {#1} ,
-  }
-\cs_new:Npn \clist_item_n_strip:w #1 , { \exp_not:n {#1} }
-\cs_new_protected:Npn \clist_set_from_seq:NN
-  { \clist_set_from_seq_aux:NNNN \clist_clear:N  \tl_set:Nx  }
-\cs_new_protected:Npn \clist_gset_from_seq:NN
-  { \clist_set_from_seq_aux:NNNN \clist_gclear:N \tl_gset:Nx }
-\cs_new_protected:Npn \clist_set_from_seq_aux:NNNN #1#2#3#4
-  {
-    \seq_if_empty:NTF #4
-      { #1 #3 }
-      {
-        #2 #3
-          {
-            \exp_last_unbraced:Nf \use_none:n
-              { \seq_map_function:NN #4 \clist_wrap_item:n }
-          }
-      }
-  }
-\cs_new:Npn \clist_wrap_item:n #1
-  {
-    ,
-    \tl_if_empty:oTF { \clist_set_from_seq_aux:w #1 ~ , #1 ~ }
-      { \exp_not:n   {#1}   }
-      { \exp_not:n { {#1} } }
-  }
-\cs_new:Npn \clist_set_from_seq_aux:w #1 , #2 ~ { }
-\cs_generate_variant:Nn \clist_set_from_seq:NN  {     Nc }
-\cs_generate_variant:Nn \clist_set_from_seq:NN  { c , cc }
-\cs_generate_variant:Nn \clist_gset_from_seq:NN {     Nc }
-\cs_generate_variant:Nn \clist_gset_from_seq:NN { c , cc }
-\cs_new_protected:Npn \clist_const:Nn #1#2
-  { \tl_const:Nx #1 { \clist_trim_spaces:n {#2} } }
-\cs_generate_variant:Nn \clist_const:Nn { c , Nx , cx }
-\prg_new_conditional:Npnn \clist_if_empty:n #1 { p , T , F , TF }
-  {
-    \clist_if_empty_n_aux:w ? #1
-    , \q_mark \prg_return_false:
-    , \q_mark \prg_return_true:
-    \q_stop
+      { clist }
+      { \clist_map_function:NN #1 \__msg_show_item:n }
   }
-\cs_new:Npn \clist_if_empty_n_aux:w #1 ,
+\cs_new_protected:Npn \clist_show:n #1
   {
-    \tl_if_empty:oTF { \use_none:nn #1 ? }
-      { \clist_if_empty_n_aux:w ? }
-      { \clist_if_empty_n_aux:wNw }
+    \clist_set:Nn \l__clist_internal_clist {#1}
+    \__msg_show_variable:Nnn
+      \l__clist_internal_clist
+      { clist }
+      { \clist_map_function:NN \l__clist_internal_clist \__msg_show_item:n }
   }
-\cs_new:Npn \clist_if_empty_n_aux:wNw #1 \q_mark #2#3 \q_stop {#2}
+\cs_generate_variant:Nn \clist_show:N { c }
+\clist_new:N \l_tmpa_clist
+\clist_new:N \l_tmpb_clist
+\clist_new:N \g_tmpa_clist
+\clist_new:N \g_tmpb_clist
+\prg_new_eq_conditional:NNn \clist__if_eq:NN \tl_if_eq:NN { p , T , F , TF }
+\prg_new_eq_conditional:NNn \clist_if_eq:Nc \tl_if_eq:Nc { p , T , F , TF }
+\prg_new_eq_conditional:NNn \clist_if_eq:cN \tl_if_eq:cN { p , T , F , TF }
+\prg_new_eq_conditional:NNn \clist_if_eq:cc \tl_if_eq:cc { p , T , F , TF }
+\cs_new_eq:NN \clist_length:N \clist_count:N
+\cs_new_eq:NN \clist_length:n \clist_count:c
+\cs_new_eq:NN \clist_length:c \clist_count:n
+\cs_new_eq:NN \clist_use:N \tl_use:N
+\cs_new_eq:NN \clist_use:c \tl_use:c
 %% 
 %%
 %% End of file `l3clist.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty b/Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty
index cd84ef63e8e..75927ce708b 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty
@@ -47,99 +47,96 @@
 %% -----------------------------------------------------------------------
 %%
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3coffins.dtx 3482 2012-03-03 18:48:06Z bruno $
-  {L3 Experimental coffin code layer}
+\GetIdInfo$Id: l3coffins.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Coffin code layer}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
-\box_new:N \l_coffin_internal_box
-\dim_new:N \l_coffin_internal_dim
-\fp_new:N  \l_coffin_internal_fp
-\tl_new:N  \l_coffin_internal_tl
-\prop_new:N \c_coffin_corners_prop
-\prop_put:Nnn \c_coffin_corners_prop { tl } { { 0 pt } { 0 pt } }
-\prop_put:Nnn \c_coffin_corners_prop { tr } { { 0 pt } { 0 pt } }
-\prop_put:Nnn \c_coffin_corners_prop { bl } { { 0 pt } { 0 pt } }
-\prop_put:Nnn \c_coffin_corners_prop { br } { { 0 pt } { 0 pt } }
-\prop_new:N \c_coffin_poles_prop
-\tl_set:Nn \l_coffin_internal_tl { { 0 pt } { 0 pt } { 0 pt } { 1000 pt } }
-\prop_put:Nno \c_coffin_poles_prop { l }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { hc } { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { r }  { \l_coffin_internal_tl }
-\tl_set:Nn \l_coffin_internal_tl { { 0 pt } { 0 pt } { 1000 pt } { 0 pt } }
-\prop_put:Nno \c_coffin_poles_prop { b }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { vc } { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { t }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { B }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { H }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { T }  { \l_coffin_internal_tl }
-\fp_new:N \l_coffin_calc_a_fp
-\fp_new:N \l_coffin_calc_b_fp
-\fp_new:N \l_coffin_calc_c_fp
-\fp_new:N \l_coffin_calc_d_fp
-\fp_new:N \l_coffin_calc_result_fp
-\bool_new:N \l_coffin_error_bool
-\dim_new:N \l_coffin_offset_x_dim
-\dim_new:N \l_coffin_offset_y_dim
-\tl_new:N \l_coffin_pole_a_tl
-\tl_new:N \l_coffin_pole_b_tl
-\fp_new:N \l_coffin_sin_fp
-\fp_new:N \l_coffin_cos_fp
-\dim_new:N \l_coffin_x_dim
-\dim_new:N \l_coffin_y_dim
-\dim_new:N \l_coffin_x_prime_dim
-\dim_new:N \l_coffin_y_prime_dim
-\fp_new:N \l_coffin_x_fp
-\fp_new:N \l_coffin_y_fp
-\fp_new:N \l_coffin_x_prime_fp
-\fp_new:N \l_coffin_y_prime_fp
-\dim_new:N \l_coffin_Depth_dim
-\dim_new:N \l_coffin_Height_dim
-\dim_new:N \l_coffin_TotalHeight_dim
-\dim_new:N \l_coffin_Width_dim
-\cs_new_nopar:Npn \coffin_saved_Depth:       { }
-\cs_new_nopar:Npn \coffin_saved_Height:      { }
-\cs_new_nopar:Npn \coffin_saved_TotalHeight: { }
-\cs_new_nopar:Npn \coffin_saved_Width:       { }
-\cs_new_protected:Npn \coffin_if_exist:NT #1#2
+\__expl_package_check:
+\box_new:N \l__coffin_internal_box
+\dim_new:N \l__coffin_internal_dim
+\tl_new:N  \l__coffin_internal_tl
+\prop_new:N \c__coffin_corners_prop
+\prop_put:Nnn \c__coffin_corners_prop { tl } { { 0 pt } { 0 pt } }
+\prop_put:Nnn \c__coffin_corners_prop { tr } { { 0 pt } { 0 pt } }
+\prop_put:Nnn \c__coffin_corners_prop { bl } { { 0 pt } { 0 pt } }
+\prop_put:Nnn \c__coffin_corners_prop { br } { { 0 pt } { 0 pt } }
+\prop_new:N \c__coffin_poles_prop
+\tl_set:Nn \l__coffin_internal_tl { { 0 pt } { 0 pt } { 0 pt } { 1000 pt } }
+\prop_put:Nno \c__coffin_poles_prop { l }  { \l__coffin_internal_tl }
+\prop_put:Nno \c__coffin_poles_prop { hc } { \l__coffin_internal_tl }
+\prop_put:Nno \c__coffin_poles_prop { r }  { \l__coffin_internal_tl }
+\tl_set:Nn \l__coffin_internal_tl { { 0 pt } { 0 pt } { 1000 pt } { 0 pt } }
+\prop_put:Nno \c__coffin_poles_prop { b }  { \l__coffin_internal_tl }
+\prop_put:Nno \c__coffin_poles_prop { vc } { \l__coffin_internal_tl }
+\prop_put:Nno \c__coffin_poles_prop { t }  { \l__coffin_internal_tl }
+\prop_put:Nno \c__coffin_poles_prop { B }  { \l__coffin_internal_tl }
+\prop_put:Nno \c__coffin_poles_prop { H }  { \l__coffin_internal_tl }
+\prop_put:Nno \c__coffin_poles_prop { T }  { \l__coffin_internal_tl }
+\fp_new:N \l__coffin_slope_x_fp
+\fp_new:N \l__coffin_slope_y_fp
+\bool_new:N \l__coffin_error_bool
+\dim_new:N \l__coffin_offset_x_dim
+\dim_new:N \l__coffin_offset_y_dim
+\tl_new:N \l__coffin_pole_a_tl
+\tl_new:N \l__coffin_pole_b_tl
+\dim_new:N \l__coffin_x_dim
+\dim_new:N \l__coffin_y_dim
+\dim_new:N \l__coffin_x_prime_dim
+\dim_new:N \l__coffin_y_prime_dim
+\dim_new:N \l__coffin_Depth_dim
+\dim_new:N \l__coffin_Height_dim
+\dim_new:N \l__coffin_TotalHeight_dim
+\dim_new:N \l__coffin_Width_dim
+\cs_new_nopar:Npn \__coffin_saved_Depth:       { }
+\cs_new_nopar:Npn \__coffin_saved_Height:      { }
+\cs_new_nopar:Npn \__coffin_saved_TotalHeight: { }
+\cs_new_nopar:Npn \__coffin_saved_Width:       { }
+\prg_new_conditional:Npnn \coffin_if_exist:N #1 { p , T , F , TF }
   {
     \cs_if_exist:NTF #1
       {
-        \cs_if_exist:cTF { l_coffin_poles_ \int_value:w #1 _prop }
-          { #2 }
-          {
-            \msg_kernel_error:nnx { coffins } { unknown-coffin }
-              { \token_to_str:N #1 }
-          }
+        \cs_if_exist:cTF { l__coffin_poles_ \__int_value:w #1 _prop }
+          { \prg_return_true: }
+          { \prg_return_false: }
       }
+      { \prg_return_false: }
+  }
+\cs_generate_variant:Nn \coffin_if_exist_p:N { c }
+\cs_generate_variant:Nn \coffin_if_exist:NT  { c }
+\cs_generate_variant:Nn \coffin_if_exist:NF  { c }
+\cs_generate_variant:Nn \coffin_if_exist:NTF { c }
+\cs_new_protected:Npn \__coffin_if_exist:NT #1#2
+  {
+    \coffin_if_exist:NTF #1
+      { #2 }
       {
-        \msg_kernel_error:nnx { coffins } { unknown-coffin }
+        \__msg_kernel_error:nnx { kernel } { unknown-coffin }
           { \token_to_str:N #1 }
       }
   }
 \cs_new_protected:Npn \coffin_clear:N #1
   {
-    \coffin_if_exist:NT #1
+    \__coffin_if_exist:NT #1
       {
         \box_clear:N #1
-        \coffin_reset_structure:N #1
+        \__coffin_reset_structure:N #1
       }
   }
 \cs_generate_variant:Nn \coffin_clear:N { c }
 \cs_new_protected:Npn \coffin_new:N #1
   {
     \box_new:N #1
-    \prop_clear_new:c { l_coffin_corners_ \int_value:w #1 _prop }
-    \prop_clear_new:c { l_coffin_poles_   \int_value:w #1 _prop }
-    \prop_gset_eq:cN { l_coffin_corners_ \int_value:w #1 _prop }
-      \c_coffin_corners_prop
-    \prop_gset_eq:cN { l_coffin_poles_ \int_value:w #1 _prop }
-      \c_coffin_poles_prop
+    \prop_clear_new:c { l__coffin_corners_ \__int_value:w #1 _prop }
+    \prop_clear_new:c { l__coffin_poles_   \__int_value:w #1 _prop }
+    \prop_gset_eq:cN { l__coffin_corners_ \__int_value:w #1 _prop }
+      \c__coffin_corners_prop
+    \prop_gset_eq:cN { l__coffin_poles_ \__int_value:w #1 _prop }
+      \c__coffin_poles_prop
   }
 \cs_generate_variant:Nn \coffin_new:N { c }
 \cs_new_protected:Npn \hcoffin_set:Nn #1#2
   {
-    \coffin_if_exist:NT #1
+    \__coffin_if_exist:NT #1
       {
         \hbox_set:Nn #1
           {
@@ -148,51 +145,52 @@
               #2
             \color_group_end:
           }
-        \coffin_reset_structure:N #1
-        \coffin_update_poles:N #1
-        \coffin_update_corners:N #1
+        \__coffin_reset_structure:N #1
+        \__coffin_update_poles:N #1
+        \__coffin_update_corners:N #1
       }
   }
 \cs_generate_variant:Nn \hcoffin_set:Nn { c }
 \cs_new_protected:Npn \vcoffin_set:Nnn #1#2#3
   {
-    \coffin_if_exist:NT #1
+    \__coffin_if_exist:NT #1
       {
         \vbox_set:Nn #1
           {
             \dim_set:Nn \tex_hsize:D {#2}
+            \dim_set_eq:NN \linewidth   \tex_hsize:D
+            \dim_set_eq:NN \columnwidth \tex_hsize:D
             \color_group_begin:
-              \color_ensure_current:
               #3
             \color_group_end:
           }
-        \coffin_reset_structure:N #1
-        \coffin_update_poles:N #1
-        \coffin_update_corners:N #1
-        \vbox_set_top:Nn \l_coffin_internal_box { \vbox_unpack:N #1 }
-        \coffin_set_pole:Nnx #1 { T }
+        \__coffin_reset_structure:N #1
+        \__coffin_update_poles:N #1
+        \__coffin_update_corners:N #1
+        \vbox_set_top:Nn \l__coffin_internal_box { \vbox_unpack:N #1 }
+        \__coffin_set_pole:Nnx #1 { T }
           {
             { 0 pt }
-            { \dim_eval:n { \box_ht:N #1 - \box_ht:N \l_coffin_internal_box } }
+            { \dim_eval:n { \box_ht:N #1 - \box_ht:N \l__coffin_internal_box } }
             { 1000 pt }
             { 0 pt }
           }
-        \box_clear:N \l_coffin_internal_box
+        \box_clear:N \l__coffin_internal_box
       }
   }
 \cs_generate_variant:Nn \vcoffin_set:Nnn { c }
 \cs_new_protected:Npn \hcoffin_set:Nw #1
   {
-    \coffin_if_exist:NT #1
+    \__coffin_if_exist:NT #1
       {
         \hbox_set:Nw #1 \color_group_begin: \color_ensure_current:
           \cs_set_protected_nopar:Npn \hcoffin_set_end:
             {
                 \color_group_end:
               \hbox_set_end:
-              \coffin_reset_structure:N #1
-              \coffin_update_poles:N #1
-              \coffin_update_corners:N #1
+              \__coffin_reset_structure:N #1
+              \__coffin_update_poles:N #1
+              \__coffin_update_corners:N #1
             }
       }
   }
@@ -200,29 +198,31 @@
 \cs_generate_variant:Nn \hcoffin_set:Nw { c }
 \cs_new_protected:Npn \vcoffin_set:Nnw #1#2
   {
-    \coffin_if_exist:NT #1
+    \__coffin_if_exist:NT #1
       {
         \vbox_set:Nw #1
           \dim_set:Nn \tex_hsize:D {#2}
+            \dim_set_eq:NN \linewidth   \tex_hsize:D
+            \dim_set_eq:NN \columnwidth \tex_hsize:D
           \color_group_begin: \color_ensure_current:
           \cs_set_protected:Npn \vcoffin_set_end:
             {
                 \color_group_end:
               \vbox_set_end:
-              \coffin_reset_structure:N #1
-              \coffin_update_poles:N #1
-              \coffin_update_corners:N #1
-              \vbox_set_top:Nn \l_coffin_internal_box { \vbox_unpack:N #1 }
-              \coffin_set_pole:Nnx #1 { T }
+              \__coffin_reset_structure:N #1
+              \__coffin_update_poles:N #1
+              \__coffin_update_corners:N #1
+              \vbox_set_top:Nn \l__coffin_internal_box { \vbox_unpack:N #1 }
+              \__coffin_set_pole:Nnx #1 { T }
                 {
                   { 0 pt }
                   {
-                    \dim_eval:n { \box_ht:N #1 - \box_ht:N \l_coffin_internal_box }
+                    \dim_eval:n { \box_ht:N #1 - \box_ht:N \l__coffin_internal_box }
                   }
                   { 1000 pt }
                   { 0 pt }
                 }
-              \box_clear:N \l_coffin_internal_box
+              \box_clear:N \l__coffin_internal_box
             }
       }
   }
@@ -230,145 +230,147 @@
 \cs_generate_variant:Nn \vcoffin_set:Nnw { c }
 \cs_new_protected:Npn \coffin_set_eq:NN #1#2
   {
-    \coffin_if_exist:NT #1
+    \__coffin_if_exist:NT #1
       {
         \box_set_eq:NN #1 #2
-        \coffin_set_eq_structure:NN #1 #2
+        \__coffin_set_eq_structure:NN #1 #2
       }
   }
 \cs_generate_variant:Nn \coffin_set_eq:NN { c , Nc , cc }
 \coffin_new:N \c_empty_coffin
 \hbox_set:Nn  \c_empty_coffin { }
-\coffin_new:N \l_coffin_aligned_coffin
-\coffin_new:N \l_coffin_aligned_internal_coffin
+\coffin_new:N \l__coffin_aligned_coffin
+\coffin_new:N \l__coffin_aligned_internal_coffin
+\coffin_new:N \l_tmpa_coffin
+\coffin_new:N \l_tmpb_coffin
 \cs_new_eq:NN \coffin_dp:N \box_dp:N
 \cs_new_eq:NN \coffin_dp:c \box_dp:c
 \cs_new_eq:NN \coffin_ht:N \box_ht:N
 \cs_new_eq:NN \coffin_ht:c \box_ht:c
 \cs_new_eq:NN \coffin_wd:N \box_wd:N
 \cs_new_eq:NN \coffin_wd:c \box_wd:c
-\cs_new_protected:Npn \coffin_get_pole:NnN #1#2#3
+\cs_new_protected:Npn \__coffin_get_pole:NnN #1#2#3
   {
     \prop_get:cnNF
-      { l_coffin_poles_ \int_value:w #1 _prop } {#2} #3
+      { l__coffin_poles_ \__int_value:w #1 _prop } {#2} #3
       {
-        \msg_kernel_error:nnxx { coffins } { unknown-coffin-pole }
+        \__msg_kernel_error:nnxx { kernel } { unknown-coffin-pole }
           {#2} { \token_to_str:N #1 }
         \tl_set:Nn #3 { { 0 pt } { 0 pt } { 0 pt } { 0 pt } }
       }
   }
-\cs_new_protected:Npn \coffin_reset_structure:N #1
+\cs_new_protected:Npn \__coffin_reset_structure:N #1
   {
-    \prop_set_eq:cN { l_coffin_corners_ \int_value:w #1 _prop }
-      \c_coffin_corners_prop
-    \prop_set_eq:cN { l_coffin_poles_ \int_value:w #1 _prop }
-      \c_coffin_poles_prop
+    \prop_set_eq:cN { l__coffin_corners_ \__int_value:w #1 _prop }
+      \c__coffin_corners_prop
+    \prop_set_eq:cN { l__coffin_poles_ \__int_value:w #1 _prop }
+      \c__coffin_poles_prop
   }
-\cs_new_protected:Npn \coffin_set_eq_structure:NN #1#2
+\cs_new_protected:Npn \__coffin_set_eq_structure:NN #1#2
   {
-    \prop_set_eq:cc { l_coffin_corners_ \int_value:w #1 _prop }
-      { l_coffin_corners_ \int_value:w #2 _prop }
-    \prop_set_eq:cc { l_coffin_poles_ \int_value:w #1 _prop }
-      { l_coffin_poles_ \int_value:w #2 _prop }
+    \prop_set_eq:cc { l__coffin_corners_ \__int_value:w #1 _prop }
+      { l__coffin_corners_ \__int_value:w #2 _prop }
+    \prop_set_eq:cc { l__coffin_poles_ \__int_value:w #1 _prop }
+      { l__coffin_poles_ \__int_value:w #2 _prop }
   }
-\cs_new_protected:Npn \coffin_gset_eq_structure:NN #1#2
+\cs_new_protected:Npn \__coffin_gset_eq_structure:NN #1#2
   {
-    \prop_gset_eq:cc { l_coffin_corners_ \int_value:w #1 _prop }
-      { l_coffin_corners_ \int_value:w #2 _prop }
-    \prop_gset_eq:cc { l_coffin_poles_ \int_value:w #1 _prop }
-      { l_coffin_poles_ \int_value:w #2 _prop }
+    \prop_gset_eq:cc { l__coffin_corners_ \__int_value:w #1 _prop }
+      { l__coffin_corners_ \__int_value:w #2 _prop }
+    \prop_gset_eq:cc { l__coffin_poles_ \__int_value:w #1 _prop }
+      { l__coffin_poles_ \__int_value:w #2 _prop }
   }
-\cs_new_protected:Npn \coffin_set_user_dimensions:N #1
+\cs_new_protected:Npn \__coffin_set_user_dimensions:N #1
   {
-    \cs_set_eq:NN \coffin_saved_Height:      \Height
-    \cs_set_eq:NN \coffin_saved_Depth:       \Depth
-    \cs_set_eq:NN \coffin_saved_TotalHeight: \TotalHeight
-    \cs_set_eq:NN \coffin_saved_Width:       \Width
-    \cs_set_eq:NN \Height      \l_coffin_Height_dim
-    \cs_set_eq:NN \Depth       \l_coffin_Depth_dim
-    \cs_set_eq:NN \TotalHeight \l_coffin_TotalHeight_dim
-    \cs_set_eq:NN \Width       \l_coffin_Width_dim
+    \cs_set_eq:NN \__coffin_saved_Height:      \Height
+    \cs_set_eq:NN \__coffin_saved_Depth:       \Depth
+    \cs_set_eq:NN \__coffin_saved_TotalHeight: \TotalHeight
+    \cs_set_eq:NN \__coffin_saved_Width:       \Width
+    \cs_set_eq:NN \Height      \l__coffin_Height_dim
+    \cs_set_eq:NN \Depth       \l__coffin_Depth_dim
+    \cs_set_eq:NN \TotalHeight \l__coffin_TotalHeight_dim
+    \cs_set_eq:NN \Width       \l__coffin_Width_dim
     \dim_set:Nn \Height      { \box_ht:N #1 }
     \dim_set:Nn \Depth       { \box_dp:N #1 }
     \dim_set:Nn \TotalHeight { \box_ht:N #1 + \box_dp:N #1 }
     \dim_set:Nn \Width       { \box_wd:N #1 }
   }
-\cs_new_protected_nopar:Npn \coffin_end_user_dimensions:
+\cs_new_protected_nopar:Npn \__coffin_end_user_dimensions:
   {
-    \cs_set_eq:NN \Height      \coffin_saved_Height:
-    \cs_set_eq:NN \Depth       \coffin_saved_Depth:
-    \cs_set_eq:NN \TotalHeight \coffin_saved_TotalHeight:
-    \cs_set_eq:NN \Width       \coffin_saved_Width:
+    \cs_set_eq:NN \Height      \__coffin_saved_Height:
+    \cs_set_eq:NN \Depth       \__coffin_saved_Depth:
+    \cs_set_eq:NN \TotalHeight \__coffin_saved_TotalHeight:
+    \cs_set_eq:NN \Width       \__coffin_saved_Width:
   }
 \cs_new_protected:Npn \coffin_set_horizontal_pole:Nnn #1#2#3
   {
-    \coffin_if_exist:NT #1
+    \__coffin_if_exist:NT #1
       {
-        \coffin_set_user_dimensions:N #1
-        \coffin_set_pole:Nnx #1 {#2}
+        \__coffin_set_user_dimensions:N #1
+        \__coffin_set_pole:Nnx #1 {#2}
           {
             { 0 pt } { \dim_eval:n {#3} }
             { 1000 pt } { 0 pt }
           }
-        \coffin_end_user_dimensions:
+        \__coffin_end_user_dimensions:
       }
   }
 \cs_new_protected:Npn \coffin_set_vertical_pole:Nnn #1#2#3
   {
-    \coffin_if_exist:NT #1
+    \__coffin_if_exist:NT #1
       {
-        \coffin_set_user_dimensions:N #1
-        \coffin_set_pole:Nnx #1 {#2}
+        \__coffin_set_user_dimensions:N #1
+        \__coffin_set_pole:Nnx #1 {#2}
           {
             { \dim_eval:n {#3} } { 0 pt }
             { 0 pt } { 1000 pt }
           }
-        \coffin_end_user_dimensions:
+        \__coffin_end_user_dimensions:
       }
   }
-\cs_new_protected:Npn \coffin_set_pole:Nnn #1#2#3
-  { \prop_put:cnn { l_coffin_poles_ \int_value:w #1 _prop } {#2} {#3} }
+\cs_new_protected:Npn \__coffin_set_pole:Nnn #1#2#3
+  { \prop_put:cnn { l__coffin_poles_ \__int_value:w #1 _prop } {#2} {#3} }
 \cs_generate_variant:Nn \coffin_set_horizontal_pole:Nnn { c }
 \cs_generate_variant:Nn \coffin_set_vertical_pole:Nnn { c }
-\cs_generate_variant:Nn \coffin_set_pole:Nnn { Nnx }
-\cs_new_protected:Npn \coffin_update_corners:N #1
+\cs_generate_variant:Nn \__coffin_set_pole:Nnn { Nnx }
+\cs_new_protected:Npn \__coffin_update_corners:N #1
   {
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { tl }
+    \prop_put:cnx { l__coffin_corners_ \__int_value:w #1 _prop } { tl }
       { { 0 pt } { \dim_use:N \box_ht:N #1 } }
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { tr }
+    \prop_put:cnx { l__coffin_corners_ \__int_value:w #1 _prop } { tr }
       { { \dim_use:N \box_wd:N #1 } { \dim_use:N \box_ht:N #1 } }
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { bl }
+    \prop_put:cnx { l__coffin_corners_ \__int_value:w #1 _prop } { bl }
       { { 0 pt } { \dim_eval:n { - \box_dp:N #1 } } }
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { br }
+    \prop_put:cnx { l__coffin_corners_ \__int_value:w #1 _prop } { br }
       { { \dim_use:N \box_wd:N #1 } { \dim_eval:n { - \box_dp:N #1 } } }
   }
-\cs_new_protected:Npn \coffin_update_poles:N #1
+\cs_new_protected:Npn \__coffin_update_poles:N #1
   {
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { hc }
+    \prop_put:cnx { l__coffin_poles_ \__int_value:w #1 _prop } { hc }
       {
         { \dim_eval:n { 0.5 \box_wd:N #1 } }
         { 0 pt } { 0 pt } { 1000 pt }
       }
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { r }
+    \prop_put:cnx { l__coffin_poles_ \__int_value:w #1 _prop } { r }
       {
         { \dim_use:N \box_wd:N #1 }
         { 0 pt } { 0 pt } { 1000 pt }
       }
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { vc }
+    \prop_put:cnx { l__coffin_poles_ \__int_value:w #1 _prop } { vc }
       {
         { 0 pt }
         { \dim_eval:n { ( \box_ht:N #1 - \box_dp:N #1 ) / 2 } }
         { 1000 pt }
         { 0 pt }
       }
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { t }
+    \prop_put:cnx { l__coffin_poles_ \__int_value:w #1 _prop } { t }
       {
         { 0 pt }
         { \dim_use:N \box_ht:N #1 }
         { 1000 pt }
         { 0 pt }
       }
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { b }
+    \prop_put:cnx { l__coffin_poles_ \__int_value:w #1 _prop } { b }
       {
         { 0 pt }
         { \dim_eval:n { - \box_dp:N #1 } }
@@ -376,710 +378,479 @@
         { 0 pt }
       }
   }
-\cs_new_protected:Npn \coffin_calculate_intersection:Nnn #1#2#3
+\cs_new_protected:Npn \__coffin_calculate_intersection:Nnn #1#2#3
   {
-    \coffin_get_pole:NnN #1 {#2} \l_coffin_pole_a_tl
-    \coffin_get_pole:NnN #1 {#3} \l_coffin_pole_b_tl
-    \bool_set_false:N \l_coffin_error_bool
+    \__coffin_get_pole:NnN #1 {#2} \l__coffin_pole_a_tl
+    \__coffin_get_pole:NnN #1 {#3} \l__coffin_pole_b_tl
+    \bool_set_false:N \l__coffin_error_bool
     \exp_last_two_unbraced:Noo
-      \coffin_calculate_intersection:nnnnnnnn
-        \l_coffin_pole_a_tl \l_coffin_pole_b_tl
-    \bool_if:NT \l_coffin_error_bool
+      \__coffin_calculate_intersection:nnnnnnnn
+        \l__coffin_pole_a_tl \l__coffin_pole_b_tl
+    \bool_if:NT \l__coffin_error_bool
       {
-        \msg_kernel_error:nn { coffins } { no-pole-intersection }
-        \dim_zero:N \l_coffin_x_dim
-        \dim_zero:N \l_coffin_y_dim
+        \__msg_kernel_error:nn { kernel } { no-pole-intersection }
+        \dim_zero:N \l__coffin_x_dim
+        \dim_zero:N \l__coffin_y_dim
       }
   }
-\cs_new_protected:Npn \coffin_calculate_intersection:nnnnnnnn
+\cs_new_protected:Npn \__coffin_calculate_intersection:nnnnnnnn
   #1#2#3#4#5#6#7#8
   {
     \dim_compare:nNnTF {#3} = { \c_zero_dim }
       {
-        \dim_set:Nn \l_coffin_x_dim {#1}
+        \dim_set:Nn \l__coffin_x_dim {#1}
         \dim_compare:nNnTF {#7} = \c_zero_dim
-          { \bool_set_true:N \l_coffin_error_bool }
+          { \bool_set_true:N \l__coffin_error_bool }
           {
             \dim_compare:nNnTF {#8} = \c_zero_dim
-              { \dim_set:Nn \l_coffin_y_dim {#6} }
+              { \dim_set:Nn \l__coffin_y_dim {#6} }
               {
-                \coffin_calculate_intersection_aux:nnnnnN
-                  {#1} {#5} {#6} {#7} {#8} \l_coffin_y_dim
+                \__coffin_calculate_intersection_aux:nnnnnN
+                  {#1} {#5} {#6} {#7} {#8} \l__coffin_y_dim
               }
           }
       }
       {
         \dim_compare:nNnTF {#4} = \c_zero_dim
           {
-            \dim_set:Nn \l_coffin_y_dim {#2}
+            \dim_set:Nn \l__coffin_y_dim {#2}
             \dim_compare:nNnTF {#8} = { \c_zero_dim }
-              { \bool_set_true:N \l_coffin_error_bool }
+              { \bool_set_true:N \l__coffin_error_bool }
               {
                 \dim_compare:nNnTF {#7} = \c_zero_dim
-                  { \dim_set:Nn \l_coffin_x_dim {#5} }
+                  { \dim_set:Nn \l__coffin_x_dim {#5} }
                   {
-                    \coffin_calculate_intersection_aux:nnnnnN
-                      {#2} {#6} {#5} {#8} {#7} \l_coffin_x_dim
+                    \__coffin_calculate_intersection_aux:nnnnnN
+                      {#2} {#6} {#5} {#8} {#7} \l__coffin_x_dim
                   }
               }
           }
           {
             \dim_compare:nNnTF {#7} = \c_zero_dim
               {
-                \dim_set:Nn \l_coffin_x_dim {#5}
-                \coffin_calculate_intersection_aux:nnnnnN
-                  {#5} {#1} {#2} {#3} {#4} \l_coffin_y_dim
+                \dim_set:Nn \l__coffin_x_dim {#5}
+                \__coffin_calculate_intersection_aux:nnnnnN
+                  {#5} {#1} {#2} {#3} {#4} \l__coffin_y_dim
               }
               {
                 \dim_compare:nNnTF {#8} = \c_zero_dim
                   {
-                    \dim_set:Nn \l_coffin_x_dim {#6}
-                    \coffin_calculate_intersection_aux:nnnnnN
-                      {#6} {#2} {#1} {#4} {#3} \l_coffin_x_dim
+                    \dim_set:Nn \l__coffin_x_dim {#6}
+                    \__coffin_calculate_intersection_aux:nnnnnN
+                      {#6} {#2} {#1} {#4} {#3} \l__coffin_x_dim
                   }
-                {
-                    \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#3}
-                    \fp_set_from_dim:Nn \l_coffin_calc_b_fp {#4}
-                    \fp_set_from_dim:Nn \l_coffin_calc_c_fp {#7}
-                    \fp_set_from_dim:Nn \l_coffin_calc_d_fp {#8}
-                    \fp_div:Nn \l_coffin_calc_b_fp \l_coffin_calc_a_fp
-                    \fp_div:Nn \l_coffin_calc_d_fp \l_coffin_calc_c_fp
+                  {
+                    \fp_set:Nn \l__coffin_slope_x_fp
+                      { \dim_to_fp:n {#4} / \dim_to_fp:n {#3} }
+                    \fp_set:Nn \l__coffin_slope_y_fp
+                      { \dim_to_fp:n {#8} / \dim_to_fp:n {#7} }
                     \fp_compare:nNnTF
-                      \l_coffin_calc_b_fp = \l_coffin_calc_d_fp
-                      { \bool_set_true:N \l_coffin_error_bool }
+                      \l__coffin_slope_x_fp = \l__coffin_slope_y_fp
+                      { \bool_set_true:N \l__coffin_error_bool }
                       {
-                        \fp_set_from_dim:Nn \l_coffin_calc_result_fp {#6}
-                        \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#2}
-                        \fp_sub:Nn \l_coffin_calc_result_fp
-                          { \l_coffin_calc_a_fp }
-                        \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#1}
-                        \fp_mul:Nn \l_coffin_calc_a_fp
-                          { \l_coffin_calc_b_fp }
-                        \fp_add:Nn \l_coffin_calc_result_fp
-                          { \l_coffin_calc_a_fp }
-                        \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#5}
-                        \fp_mul:Nn \l_coffin_calc_a_fp
-                          { \l_coffin_calc_d_fp }
-                        \fp_sub:Nn \l_coffin_calc_result_fp
-                          { \l_coffin_calc_a_fp }
-                        \fp_sub:Nn \l_coffin_calc_b_fp
-                          { \l_coffin_calc_d_fp }
-                        \fp_div:Nn \l_coffin_calc_result_fp
-                          { \l_coffin_calc_b_fp }
-                        \dim_set:Nn \l_coffin_x_dim
-                          { \fp_to_dim:N \l_coffin_calc_result_fp }
-                        \coffin_calculate_intersection_aux:nnnnnN
-                          { \l_coffin_x_dim }
-                          {#5} {#6} {#8} {#7} \l_coffin_y_dim
+                        \dim_set:Nn \l__coffin_x_dim
+                          {
+                            \fp_to_dim:n
+                              {
+                                (
+                                      \dim_to_fp:n {#1} * \l__coffin_slope_x_fp
+                                  - ( \dim_to_fp:n {#5} * \l__coffin_slope_y_fp )
+                                  -   \dim_to_fp:n {#2}
+                                  +   \dim_to_fp:n {#6}
+                                )
+                                /
+                                ( \l__coffin_slope_x_fp - \l__coffin_slope_y_fp )
+                            }
+                          }
+                        \__coffin_calculate_intersection_aux:nnnnnN
+                          { \l__coffin_x_dim }
+                          {#5} {#6} {#8} {#7} \l__coffin_y_dim
                       }
                   }
               }
           }
       }
   }
-\cs_new_protected:Npn \coffin_calculate_intersection_aux:nnnnnN
-  #1#2#3#4#5#6
+\cs_new_protected:Npn \__coffin_calculate_intersection_aux:nnnnnN #1#2#3#4#5#6
   {
-    \fp_set_from_dim:Nn \l_coffin_calc_result_fp {#1}
-    \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#2}
-    \fp_set_from_dim:Nn \l_coffin_calc_b_fp {#3}
-    \fp_set_from_dim:Nn \l_coffin_calc_c_fp {#4}
-    \fp_set_from_dim:Nn \l_coffin_calc_d_fp {#5}
-    \fp_sub:Nn \l_coffin_calc_result_fp { \l_coffin_calc_a_fp }
-    \fp_div:Nn \l_coffin_calc_result_fp { \l_coffin_calc_d_fp }
-    \fp_mul:Nn \l_coffin_calc_result_fp { \l_coffin_calc_c_fp }
-    \fp_add:Nn \l_coffin_calc_result_fp { \l_coffin_calc_b_fp }
-    \dim_set:Nn #6 { \fp_to_dim:N \l_coffin_calc_result_fp }
+    \dim_set:Nn #6
+      {
+        \fp_to_dim:n
+          {
+            \dim_to_fp:n {#4} *
+            ( \dim_to_fp:n {#1} - \dim_to_fp:n {#2} ) /
+            \dim_to_fp:n {#5}
+            + \dim_to_fp:n {#3}
+          }
+      }
   }
 \cs_new_protected:Npn \coffin_join:NnnNnnnn #1#2#3#4#5#6#7#8
   {
-    \coffin_align:NnnNnnnnN
-      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_coffin_aligned_coffin
-    \hbox_set:Nn \l_coffin_aligned_coffin
+    \__coffin_align:NnnNnnnnN
+      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l__coffin_aligned_coffin
+    \hbox_set:Nn \l__coffin_aligned_coffin
       {
-        \dim_compare:nNnT { \l_coffin_offset_x_dim } < \c_zero_dim
-          { \tex_kern:D -\l_coffin_offset_x_dim }
-        \hbox_unpack:N \l_coffin_aligned_coffin
-        \dim_set:Nn \l_coffin_internal_dim
-          { \l_coffin_offset_x_dim - \box_wd:N #1 + \box_wd:N #4 }
-        \dim_compare:nNnT \l_coffin_internal_dim < \c_zero_dim
-          { \tex_kern:D -\l_coffin_internal_dim }
+        \dim_compare:nNnT { \l__coffin_offset_x_dim } < \c_zero_dim
+          { \tex_kern:D -\l__coffin_offset_x_dim }
+        \hbox_unpack:N \l__coffin_aligned_coffin
+        \dim_set:Nn \l__coffin_internal_dim
+          { \l__coffin_offset_x_dim - \box_wd:N #1 + \box_wd:N #4 }
+        \dim_compare:nNnT \l__coffin_internal_dim < \c_zero_dim
+          { \tex_kern:D -\l__coffin_internal_dim }
       }
-   \coffin_reset_structure:N \l_coffin_aligned_coffin
+   \__coffin_reset_structure:N \l__coffin_aligned_coffin
     \prop_clear:c
-      {  l_coffin_corners_ \int_value:w \l_coffin_aligned_coffin _ prop }
-    \coffin_update_poles:N \l_coffin_aligned_coffin
-    \dim_compare:nNnTF \l_coffin_offset_x_dim < \c_zero_dim
+      {  l__coffin_corners_ \__int_value:w \l__coffin_aligned_coffin _ prop }
+    \__coffin_update_poles:N \l__coffin_aligned_coffin
+    \dim_compare:nNnTF \l__coffin_offset_x_dim < \c_zero_dim
       {
-        \coffin_offset_poles:Nnn #1 { -\l_coffin_offset_x_dim } { 0 pt }
-        \coffin_offset_poles:Nnn #4 { 0 pt } { \l_coffin_offset_y_dim }
-        \coffin_offset_corners:Nnn #1 { -\l_coffin_offset_x_dim } { 0 pt }
-        \coffin_offset_corners:Nnn #4 { 0 pt } { \l_coffin_offset_y_dim }
+        \__coffin_offset_poles:Nnn #1 { -\l__coffin_offset_x_dim } { 0 pt }
+        \__coffin_offset_poles:Nnn #4 { 0 pt } { \l__coffin_offset_y_dim }
+        \__coffin_offset_corners:Nnn #1 { -\l__coffin_offset_x_dim } { 0 pt }
+        \__coffin_offset_corners:Nnn #4 { 0 pt } { \l__coffin_offset_y_dim }
       }
       {
-        \coffin_offset_poles:Nnn #1 { 0 pt } { 0 pt }
-        \coffin_offset_poles:Nnn #4
-          { \l_coffin_offset_x_dim } { \l_coffin_offset_y_dim }
-        \coffin_offset_corners:Nnn #1 { 0 pt } { 0 pt }
-        \coffin_offset_corners:Nnn #4
-          { \l_coffin_offset_x_dim } { \l_coffin_offset_y_dim }
+        \__coffin_offset_poles:Nnn #1 { 0 pt } { 0 pt }
+        \__coffin_offset_poles:Nnn #4
+          { \l__coffin_offset_x_dim } { \l__coffin_offset_y_dim }
+        \__coffin_offset_corners:Nnn #1 { 0 pt } { 0 pt }
+        \__coffin_offset_corners:Nnn #4
+          { \l__coffin_offset_x_dim } { \l__coffin_offset_y_dim }
       }
-    \coffin_update_vertical_poles:NNN #1 #4 \l_coffin_aligned_coffin
-    \coffin_set_eq:NN #1 \l_coffin_aligned_coffin
+    \__coffin_update_vertical_poles:NNN #1 #4 \l__coffin_aligned_coffin
+    \coffin_set_eq:NN #1 \l__coffin_aligned_coffin
   }
 \cs_generate_variant:Nn \coffin_join:NnnNnnnn { c , Nnnc , cnnc }
 \cs_new_protected:Npn \coffin_attach:NnnNnnnn #1#2#3#4#5#6#7#8
   {
-    \coffin_align:NnnNnnnnN
-      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_coffin_aligned_coffin
-    \box_set_ht:Nn \l_coffin_aligned_coffin { \box_ht:N #1 }
-    \box_set_dp:Nn \l_coffin_aligned_coffin { \box_dp:N #1 }
-    \box_set_wd:Nn \l_coffin_aligned_coffin { \box_wd:N #1 }
-    \coffin_reset_structure:N \l_coffin_aligned_coffin
+    \__coffin_align:NnnNnnnnN
+      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l__coffin_aligned_coffin
+    \box_set_ht:Nn \l__coffin_aligned_coffin { \box_ht:N #1 }
+    \box_set_dp:Nn \l__coffin_aligned_coffin { \box_dp:N #1 }
+    \box_set_wd:Nn \l__coffin_aligned_coffin { \box_wd:N #1 }
+    \__coffin_reset_structure:N \l__coffin_aligned_coffin
     \prop_set_eq:cc
-      { l_coffin_corners_ \int_value:w \l_coffin_aligned_coffin _prop }
-      { l_coffin_corners_ \int_value:w #1 _prop }
-    \coffin_update_poles:N  \l_coffin_aligned_coffin
-    \coffin_offset_poles:Nnn #1 { 0 pt } { 0 pt }
-    \coffin_offset_poles:Nnn #4
-      { \l_coffin_offset_x_dim } { \l_coffin_offset_y_dim }
-    \coffin_update_vertical_poles:NNN #1 #4 \l_coffin_aligned_coffin
-    \coffin_set_eq:NN #1 \l_coffin_aligned_coffin
+      { l__coffin_corners_ \__int_value:w \l__coffin_aligned_coffin _prop }
+      { l__coffin_corners_ \__int_value:w #1 _prop }
+    \__coffin_update_poles:N  \l__coffin_aligned_coffin
+    \__coffin_offset_poles:Nnn #1 { 0 pt } { 0 pt }
+    \__coffin_offset_poles:Nnn #4
+      { \l__coffin_offset_x_dim } { \l__coffin_offset_y_dim }
+    \__coffin_update_vertical_poles:NNN #1 #4 \l__coffin_aligned_coffin
+    \coffin_set_eq:NN #1 \l__coffin_aligned_coffin
   }
 \cs_new_protected:Npn \coffin_attach_mark:NnnNnnnn #1#2#3#4#5#6#7#8
   {
-    \coffin_align:NnnNnnnnN
-      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_coffin_aligned_coffin
-    \box_set_ht:Nn \l_coffin_aligned_coffin { \box_ht:N #1 }
-    \box_set_dp:Nn \l_coffin_aligned_coffin { \box_dp:N #1 }
-    \box_set_wd:Nn \l_coffin_aligned_coffin { \box_wd:N #1 }
-    \box_set_eq:NN #1 \l_coffin_aligned_coffin
+    \__coffin_align:NnnNnnnnN
+      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l__coffin_aligned_coffin
+    \box_set_ht:Nn \l__coffin_aligned_coffin { \box_ht:N #1 }
+    \box_set_dp:Nn \l__coffin_aligned_coffin { \box_dp:N #1 }
+    \box_set_wd:Nn \l__coffin_aligned_coffin { \box_wd:N #1 }
+    \box_set_eq:NN #1 \l__coffin_aligned_coffin
   }
 \cs_generate_variant:Nn \coffin_attach:NnnNnnnn { c , Nnnc , cnnc }
-\cs_new_protected:Npn \coffin_align:NnnNnnnnN #1#2#3#4#5#6#7#8#9
-  {
-    \coffin_calculate_intersection:Nnn #4 {#5} {#6}
-    \dim_set:Nn \l_coffin_x_prime_dim { \l_coffin_x_dim }
-    \dim_set:Nn \l_coffin_y_prime_dim { \l_coffin_y_dim }
-    \coffin_calculate_intersection:Nnn #1 {#2} {#3}
-    \dim_set:Nn \l_coffin_offset_x_dim
-      { \l_coffin_x_dim - \l_coffin_x_prime_dim + #7 }
-    \dim_set:Nn \l_coffin_offset_y_dim
-      { \l_coffin_y_dim - \l_coffin_y_prime_dim + #8 }
-    \hbox_set:Nn \l_coffin_aligned_internal_coffin
+\cs_new_protected:Npn \__coffin_align:NnnNnnnnN #1#2#3#4#5#6#7#8#9
+  {
+    \__coffin_calculate_intersection:Nnn #4 {#5} {#6}
+    \dim_set:Nn \l__coffin_x_prime_dim { \l__coffin_x_dim }
+    \dim_set:Nn \l__coffin_y_prime_dim { \l__coffin_y_dim }
+    \__coffin_calculate_intersection:Nnn #1 {#2} {#3}
+    \dim_set:Nn \l__coffin_offset_x_dim
+      { \l__coffin_x_dim - \l__coffin_x_prime_dim + #7 }
+    \dim_set:Nn \l__coffin_offset_y_dim
+      { \l__coffin_y_dim - \l__coffin_y_prime_dim + #8 }
+    \hbox_set:Nn \l__coffin_aligned_internal_coffin
       {
         \box_use:N #1
         \tex_kern:D -\box_wd:N #1
-        \tex_kern:D \l_coffin_offset_x_dim
-        \box_move_up:nn { \l_coffin_offset_y_dim } { \box_use:N #4 }
+        \tex_kern:D \l__coffin_offset_x_dim
+        \box_move_up:nn { \l__coffin_offset_y_dim } { \box_use:N #4 }
       }
-    \coffin_set_eq:NN #9 \l_coffin_aligned_internal_coffin
+    \coffin_set_eq:NN #9 \l__coffin_aligned_internal_coffin
   }
-\cs_new_protected:Npn \coffin_offset_poles:Nnn #1#2#3
+\cs_new_protected:Npn \__coffin_offset_poles:Nnn #1#2#3
   {
-    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-      { \coffin_offset_pole:Nnnnnnn #1 {##1} ##2 {#2} {#3} }
+    \prop_map_inline:cn { l__coffin_poles_ \__int_value:w #1 _prop }
+      { \__coffin_offset_pole:Nnnnnnn #1 {##1} ##2 {#2} {#3} }
   }
-\cs_new_protected:Npn \coffin_offset_pole:Nnnnnnn #1#2#3#4#5#6#7#8
+\cs_new_protected:Npn \__coffin_offset_pole:Nnnnnnn #1#2#3#4#5#6#7#8
   {
-    \dim_set:Nn \l_coffin_x_dim { #3 + #7 }
-    \dim_set:Nn \l_coffin_y_dim { #4 + #8 }
+    \dim_set:Nn \l__coffin_x_dim { #3 + #7 }
+    \dim_set:Nn \l__coffin_y_dim { #4 + #8 }
     \tl_if_in:nnTF {#2} { - }
-      { \tl_set:Nn \l_coffin_internal_tl { {#2} } }
-      { \tl_set:Nn \l_coffin_internal_tl { { #1 - #2 } } }
-    \exp_last_unbraced:NNo \coffin_set_pole:Nnx \l_coffin_aligned_coffin
-      { \l_coffin_internal_tl }
+      { \tl_set:Nn \l__coffin_internal_tl { {#2} } }
+      { \tl_set:Nn \l__coffin_internal_tl { { #1 - #2 } } }
+    \exp_last_unbraced:NNo \__coffin_set_pole:Nnx \l__coffin_aligned_coffin
+      { \l__coffin_internal_tl }
       {
-        { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim }
+        { \dim_use:N \l__coffin_x_dim } { \dim_use:N \l__coffin_y_dim }
         {#5} {#6}
       }
   }
-\cs_new_protected:Npn \coffin_offset_corners:Nnn #1#2#3
+\cs_new_protected:Npn \__coffin_offset_corners:Nnn #1#2#3
   {
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_offset_corner:Nnnnn #1 {##1} ##2 {#2} {#3} }
+    \prop_map_inline:cn { l__coffin_corners_ \__int_value:w #1 _prop }
+      { \__coffin_offset_corner:Nnnnn #1 {##1} ##2 {#2} {#3} }
   }
-\cs_new_protected:Npn \coffin_offset_corner:Nnnnn #1#2#3#4#5#6
+\cs_new_protected:Npn \__coffin_offset_corner:Nnnnn #1#2#3#4#5#6
   {
     \prop_put:cnx
-      { l_coffin_corners_ \int_value:w \l_coffin_aligned_coffin _prop }
+      { l__coffin_corners_ \__int_value:w \l__coffin_aligned_coffin _prop }
       { #1 - #2 }
       {
         { \dim_eval:n { #3 + #5 } }
         { \dim_eval:n { #4 + #6 } }
       }
   }
-\cs_new_protected:Npn \coffin_update_vertical_poles:NNN #1#2#3
+\cs_new_protected:Npn \__coffin_update_vertical_poles:NNN #1#2#3
   {
-    \coffin_get_pole:NnN #3 { #1 -T } \l_coffin_pole_a_tl
-    \coffin_get_pole:NnN #3 { #2 -T } \l_coffin_pole_b_tl
-    \exp_last_two_unbraced:Noo \coffin_update_T:nnnnnnnnN
-      \l_coffin_pole_a_tl \l_coffin_pole_b_tl #3
-    \coffin_get_pole:NnN #3 { #1 -B } \l_coffin_pole_a_tl
-    \coffin_get_pole:NnN #3 { #2 -B } \l_coffin_pole_b_tl
-    \exp_last_two_unbraced:Noo \coffin_update_B:nnnnnnnnN
-      \l_coffin_pole_a_tl \l_coffin_pole_b_tl #3
+    \__coffin_get_pole:NnN #3 { #1 -T } \l__coffin_pole_a_tl
+    \__coffin_get_pole:NnN #3 { #2 -T } \l__coffin_pole_b_tl
+    \exp_last_two_unbraced:Noo \__coffin_update_T:nnnnnnnnN
+      \l__coffin_pole_a_tl \l__coffin_pole_b_tl #3
+    \__coffin_get_pole:NnN #3 { #1 -B } \l__coffin_pole_a_tl
+    \__coffin_get_pole:NnN #3 { #2 -B } \l__coffin_pole_b_tl
+    \exp_last_two_unbraced:Noo \__coffin_update_B:nnnnnnnnN
+      \l__coffin_pole_a_tl \l__coffin_pole_b_tl #3
   }
-\cs_new_protected:Npn \coffin_update_T:nnnnnnnnN #1#2#3#4#5#6#7#8#9
+\cs_new_protected:Npn \__coffin_update_T:nnnnnnnnN #1#2#3#4#5#6#7#8#9
   {
     \dim_compare:nNnTF {#2} < {#6}
       {
-        \coffin_set_pole:Nnx #9 { T }
+        \__coffin_set_pole:Nnx #9 { T }
           { { 0 pt } {#6} { 1000 pt } { 0 pt } }
       }
       {
-        \coffin_set_pole:Nnx #9 { T }
+        \__coffin_set_pole:Nnx #9 { T }
           { { 0 pt } {#2} { 1000 pt } { 0 pt } }
       }
   }
-\cs_new_protected:Npn \coffin_update_B:nnnnnnnnN #1#2#3#4#5#6#7#8#9
+\cs_new_protected:Npn \__coffin_update_B:nnnnnnnnN #1#2#3#4#5#6#7#8#9
   {
     \dim_compare:nNnTF {#2} < {#6}
       {
-        \coffin_set_pole:Nnx #9 { B }
+        \__coffin_set_pole:Nnx #9 { B }
           { { 0 pt } {#2}  { 1000 pt } { 0 pt } }
       }
       {
-        \coffin_set_pole:Nnx #9 { B }
+        \__coffin_set_pole:Nnx #9 { B }
           { { 0 pt } {#6} { 1000 pt } { 0 pt } }
       }
   }
 \cs_new_protected:Npn \coffin_typeset:Nnnnn #1#2#3#4#5
   {
-    \coffin_align:NnnNnnnnN \c_empty_coffin { H } { l }
-      #1 {#2} {#3} {#4} {#5} \l_coffin_aligned_coffin
+    \__coffin_align:NnnNnnnnN \c_empty_coffin { H } { l }
+      #1 {#2} {#3} {#4} {#5} \l__coffin_aligned_coffin
     \hbox_unpack:N \c_empty_box
-    \box_use:N \l_coffin_aligned_coffin
+    \box_use:N \l__coffin_aligned_coffin
   }
 \cs_generate_variant:Nn \coffin_typeset:Nnnnn { c }
-\prop_new:N \l_coffin_bounding_prop
-\dim_new:N \l_coffin_bounding_shift_dim
-\dim_new:N \l_coffin_left_corner_dim
-\dim_new:N \l_coffin_right_corner_dim
-\dim_new:N \l_coffin_bottom_corner_dim
-\dim_new:N \l_coffin_top_corner_dim
-\cs_new_protected:Npn \coffin_rotate:Nn #1#2
-  {
-    \fp_set:Nn \l_coffin_internal_fp {#2}
-    \fp_div:Nn \l_coffin_internal_fp { 180 }
-    \fp_mul:Nn \l_coffin_internal_fp { \c_pi_fp }
-    \fp_sin:Nn \l_coffin_sin_fp { \l_coffin_internal_fp }
-    \fp_cos:Nn \l_coffin_cos_fp { \l_coffin_internal_fp }
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_rotate_corner:Nnnn #1 {##1} ##2 }
-    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-      { \coffin_rotate_pole:Nnnnnn #1 {##1} ##2 }
-    \coffin_set_bounding:N #1
-    \prop_map_inline:Nn \l_coffin_bounding_prop
-      { \coffin_rotate_bounding:nnn {##1} ##2 }
-    \coffin_find_corner_maxima:N #1
-    \coffin_find_bounding_shift:
-    \box_rotate:Nn #1 {#2}
-    \hbox_set:Nn #1
-      {
-        \tex_kern:D \l_coffin_bounding_shift_dim
-        \tex_kern:D -\l_coffin_left_corner_dim
-        \box_move_down:nn { \l_coffin_bottom_corner_dim }
-          { \box_use:N #1 }
-      }
-    \box_set_ht:Nn #1
-      { \l_coffin_top_corner_dim - \l_coffin_bottom_corner_dim }
-    \box_set_dp:Nn #1 { 0 pt }
-    \box_set_wd:Nn #1
-      { \l_coffin_right_corner_dim - \l_coffin_left_corner_dim }
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_shift_corner:Nnnn #1 {##1} ##2 }
-    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-      { \coffin_shift_pole:Nnnnnn #1 {##1} ##2 }
-  }
-\cs_generate_variant:Nn \coffin_rotate:Nn { c }
-\cs_new_protected:Npn \coffin_set_bounding:N #1
-  {
-   \prop_put:Nnx \l_coffin_bounding_prop { tl }
-      { { 0 pt } { \dim_use:N \box_ht:N #1 } }
-    \prop_put:Nnx \l_coffin_bounding_prop { tr }
-      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \box_ht:N #1 } }
-    \dim_set:Nn \l_coffin_internal_dim { - \box_dp:N #1 }
-    \prop_put:Nnx \l_coffin_bounding_prop { bl }
-      { { 0 pt } { \dim_use:N \l_coffin_internal_dim } }
-    \prop_put:Nnx \l_coffin_bounding_prop { br }
-      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \l_coffin_internal_dim } }
-  }
-\cs_new_protected:Npn \coffin_rotate_bounding:nnn #1#2#3
-  {
-    \coffin_rotate_vector:nnNN {#2} {#3} \l_coffin_x_dim \l_coffin_y_dim
-    \prop_put:Nnx \l_coffin_bounding_prop {#1}
-      { { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim } }
-  }
-\cs_new_protected:Npn \coffin_rotate_corner:Nnnn #1#2#3#4
-  {
-    \coffin_rotate_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } {#2}
-      { { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim } }
-  }
-\cs_new_protected:Npn \coffin_rotate_pole:Nnnnnn #1#2#3#4#5#6
-  {
-    \coffin_rotate_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
-    \coffin_rotate_vector:nnNN {#5} {#6}
-      \l_coffin_x_prime_dim \l_coffin_y_prime_dim
-    \coffin_set_pole:Nnx #1 {#2}
-      {
-        { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim }
-        { \dim_use:N \l_coffin_x_prime_dim }
-        { \dim_use:N \l_coffin_y_prime_dim }
-      }
-  }
-\cs_new_protected:Npn \coffin_rotate_vector:nnNN #1#2#3#4
-  {
-    \fp_set_from_dim:Nn \l_coffin_x_fp {#1}
-    \fp_set_from_dim:Nn \l_coffin_y_fp {#2}
-    \fp_set_eq:NN \l_coffin_x_prime_fp \l_coffin_x_fp
-    \fp_set_eq:NN \l_coffin_internal_fp     \l_coffin_y_fp
-    \fp_mul:Nn \l_coffin_x_prime_fp { \l_coffin_cos_fp }
-    \fp_mul:Nn \l_coffin_internal_fp     { \l_coffin_sin_fp }
-    \fp_sub:Nn \l_coffin_x_prime_fp { \l_coffin_internal_fp }
-    \fp_set_eq:NN \l_coffin_y_prime_fp \l_coffin_y_fp
-    \fp_set_eq:NN \l_coffin_internal_fp     \l_coffin_x_fp
-    \fp_mul:Nn \l_coffin_y_prime_fp { \l_coffin_cos_fp }
-    \fp_mul:Nn \l_coffin_internal_fp     { \l_coffin_sin_fp }
-    \fp_add:Nn \l_coffin_y_prime_fp { \l_coffin_internal_fp }
-    \dim_set:Nn #3 { \fp_to_dim:N \l_coffin_x_prime_fp }
-    \dim_set:Nn #4 { \fp_to_dim:N \l_coffin_y_prime_fp }
-  }
-\cs_new_protected:Npn \coffin_find_corner_maxima:N #1
-  {
-    \dim_set:Nn \l_coffin_top_corner_dim   { -\c_max_dim }
-    \dim_set:Nn \l_coffin_right_corner_dim { -\c_max_dim }
-    \dim_set:Nn \l_coffin_bottom_corner_dim { \c_max_dim }
-    \dim_set:Nn \l_coffin_left_corner_dim   { \c_max_dim }
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_find_corner_maxima_aux:nn ##2 }
-  }
-\cs_new_protected:Npn \coffin_find_corner_maxima_aux:nn #1#2
-  {
-    \dim_set_min:Nn \l_coffin_left_corner_dim   {#1}
-    \dim_set_max:Nn \l_coffin_right_corner_dim  {#1}
-    \dim_set_min:Nn \l_coffin_bottom_corner_dim {#2}
-    \dim_set_max:Nn \l_coffin_top_corner_dim    {#2}
-  }
-\cs_new_protected_nopar:Npn \coffin_find_bounding_shift:
-  {
-    \dim_set:Nn \l_coffin_bounding_shift_dim { \c_max_dim }
-    \prop_map_inline:Nn \l_coffin_bounding_prop
-      { \coffin_find_bounding_shift_aux:nn ##2 }
-  }
-\cs_new_protected:Npn \coffin_find_bounding_shift_aux:nn #1#2
-  { \dim_set_min:Nn \l_coffin_bounding_shift_dim {#1} }
-\cs_new_protected:Npn \coffin_shift_corner:Nnnn #1#2#3#4
-  {
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _ prop } {#2}
-      {
-        { \dim_eval:n { #3 - \l_coffin_left_corner_dim } }
-        { \dim_eval:n { #4 - \l_coffin_bottom_corner_dim } }
-      }
-  }
-\cs_new_protected:Npn \coffin_shift_pole:Nnnnnn #1#2#3#4#5#6
-  {
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _ prop } {#2}
-      {
-        { \dim_eval:n { #3 - \l_coffin_left_corner_dim } }
-        { \dim_eval:n { #4 - \l_coffin_bottom_corner_dim } }
-        {#5} {#6}
-      }
-  }
-\fp_new:N \l_coffin_scale_x_fp
-\fp_new:N \l_coffin_scale_y_fp
-\dim_new:N \l_coffin_scaled_total_height_dim
-\dim_new:N \l_coffin_scaled_width_dim
-\cs_new_protected:Npn \coffin_resize:Nnn #1#2#3
-  {
-    \coffin_set_user_dimensions:N #1
-    \box_resize:Nnn #1 {#2} {#3}
-    \fp_set_from_dim:Nn \l_coffin_scale_x_fp {#2}
-    \fp_set_from_dim:Nn \l_coffin_internal_fp { \Width }
-    \fp_div:Nn \l_coffin_scale_x_fp { \l_coffin_internal_fp }
-    \fp_set_from_dim:Nn \l_coffin_scale_y_fp {#3}
-    \fp_set_from_dim:Nn \l_coffin_internal_fp { \TotalHeight }
-    \fp_div:Nn \l_coffin_scale_y_fp { \l_coffin_internal_fp }
-    \coffin_resize_common:Nnn #1 {#2} {#3}
-  }
-\cs_generate_variant:Nn \coffin_resize:Nnn { c }
-\cs_new_protected:Npn \coffin_resize_common:Nnn #1#2#3
-  {
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_scale_corner:Nnnn #1 {##1} ##2 }
-    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-      { \coffin_scale_pole:Nnnnnn #1 {##1} ##2 }
-    \fp_compare:NNNT \l_coffin_scale_x_fp < \c_zero_fp
-      {
-        \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-          { \coffin_x_shift_corner:Nnnn #1 {##1} ##2 }
-        \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-          { \coffin_x_shift_pole:Nnnnnn #1 {##1} ##2 }
-      }
-    \coffin_end_user_dimensions:
-  }
-\cs_new_protected:Npn \coffin_scale:Nnn #1#2#3
-  {
-    \box_scale:Nnn #1 {#2} {#3}
-    \coffin_set_user_dimensions:N #1
-    \fp_set:Nn \l_coffin_scale_x_fp {#2}
-    \fp_set:Nn \l_coffin_scale_y_fp {#3}
-    \fp_compare:NNNTF \l_coffin_scale_y_fp > \c_zero_fp
-      { \l_coffin_scaled_total_height_dim #3 \TotalHeight }
-      { \l_coffin_scaled_total_height_dim -#3 \TotalHeight }
-    \fp_compare:NNNTF \l_coffin_scale_x_fp > \c_zero_fp
-      { \l_coffin_scaled_width_dim -#2 \Width }
-      { \l_coffin_scaled_width_dim #2 \Width }
-    \coffin_resize_common:Nnn #1
-      { \l_coffin_scaled_width_dim } { \l_coffin_scaled_total_height_dim }
-  }
-\cs_generate_variant:Nn \coffin_scale:Nnn { c }
-\cs_new_protected:Npn \coffin_scale_vector:nnNN #1#2#3#4
-  {
-    \fp_set_from_dim:Nn \l_coffin_internal_fp {#1}
-    \fp_mul:Nn \l_coffin_internal_fp { \l_coffin_scale_x_fp }
-    \dim_set:Nn #3 { \fp_to_dim:N \l_coffin_internal_fp }
-    \fp_set_from_dim:Nn \l_coffin_internal_fp {#2}
-    \fp_mul:Nn \l_coffin_internal_fp { \l_coffin_scale_y_fp }
-    \dim_set:Nn #4 { \fp_to_dim:N \l_coffin_internal_fp }
-  }
-\cs_new_protected:Npn \coffin_scale_corner:Nnnn #1#2#3#4
-  {
-    \coffin_scale_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } {#2}
-      { { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim } }
-  }
-\cs_new_protected:Npn \coffin_scale_pole:Nnnnnn #1#2#3#4#5#6
-  {
-    \coffin_scale_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
-    \coffin_set_pole:Nnx #1 {#2}
-      {
-        { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim }
-        {#5} {#6}
-      }
-  }
-\cs_new_protected:Npn \coffin_x_shift_corner:Nnnn #1#2#3#4
-  {
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } {#2}
-      {
-        { \dim_eval:n { #3 + \box_wd:N #1 } } {#4}
-    }
-  }
-\cs_new_protected:Npn \coffin_x_shift_pole:Nnnnnn #1#2#3#4#5#6
-  {
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } {#2}
-      {
-        { \dim_eval:n #3 + \box_wd:N #1 } {#4}
-        {#5} {#6}
-      }
-  }
-\coffin_new:N \l_coffin_display_coffin
-\coffin_new:N \l_coffin_display_coord_coffin
-\coffin_new:N \l_coffin_display_pole_coffin
-\prop_new:N \l_coffin_display_handles_prop
-\prop_put:Nnn \l_coffin_display_handles_prop { tl }
+\coffin_new:N \l__coffin_display_coffin
+\coffin_new:N \l__coffin_display_coord_coffin
+\coffin_new:N \l__coffin_display_pole_coffin
+\prop_new:N \l__coffin_display_handles_prop
+\prop_put:Nnn \l__coffin_display_handles_prop { tl }
   { { b } { r } { -1 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { thc }
+\prop_put:Nnn \l__coffin_display_handles_prop { thc }
   { { b } { hc } { 0 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { tr }
+\prop_put:Nnn \l__coffin_display_handles_prop { tr }
   { { b } { l } { 1 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { vcl }
+\prop_put:Nnn \l__coffin_display_handles_prop { vcl }
   { { vc } { r } { -1 } { 0 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { vchc }
+\prop_put:Nnn \l__coffin_display_handles_prop { vchc }
   { { vc } { hc } { 0 } { 0 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { vcr }
+\prop_put:Nnn \l__coffin_display_handles_prop { vcr }
   { { vc } { l } { 1 } { 0 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { bl }
+\prop_put:Nnn \l__coffin_display_handles_prop { bl }
   { { t } { r } { -1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { bhc }
+\prop_put:Nnn \l__coffin_display_handles_prop { bhc }
   { { t } { hc } { 0 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { br }
+\prop_put:Nnn \l__coffin_display_handles_prop { br }
   { { t } { l } { 1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Tl }
+\prop_put:Nnn \l__coffin_display_handles_prop { Tl }
   { { t } { r } { -1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Thc }
+\prop_put:Nnn \l__coffin_display_handles_prop { Thc }
   { { t } { hc } { 0 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Tr }
+\prop_put:Nnn \l__coffin_display_handles_prop { Tr }
   { { t } { l } { 1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Hl }
+\prop_put:Nnn \l__coffin_display_handles_prop { Hl }
   { { vc } { r } { -1 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Hhc }
+\prop_put:Nnn \l__coffin_display_handles_prop { Hhc }
   { { vc } { hc } { 0 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Hr }
+\prop_put:Nnn \l__coffin_display_handles_prop { Hr }
   { { vc } { l } { 1 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Bl }
+\prop_put:Nnn \l__coffin_display_handles_prop { Bl }
   { { b } { r } { -1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Bhc }
+\prop_put:Nnn \l__coffin_display_handles_prop { Bhc }
   { { b } { hc } { 0 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Br }
+\prop_put:Nnn \l__coffin_display_handles_prop { Br }
   { { b } { l } { 1 } { -1 } }
-\dim_new:N  \l_coffin_display_offset_dim
-\dim_set:Nn \l_coffin_display_offset_dim { 2 pt }
-\dim_new:N \l_coffin_display_x_dim
-\dim_new:N \l_coffin_display_y_dim
-\prop_new:N \l_coffin_display_poles_prop
-\tl_new:N  \l_coffin_display_font_tl
-\tl_set:Nn \l_coffin_display_font_tl { \sffamily \tiny }
+\dim_new:N  \l__coffin_display_offset_dim
+\dim_set:Nn \l__coffin_display_offset_dim { 2 pt }
+\dim_new:N \l__coffin_display_x_dim
+\dim_new:N \l__coffin_display_y_dim
+\prop_new:N \l__coffin_display_poles_prop
+\tl_new:N  \l__coffin_display_font_tl
+\tl_set:Nn \l__coffin_display_font_tl { \sffamily \tiny }
 \cs_new_protected:Npn \coffin_mark_handle:Nnnn #1#2#3#4
   {
-    \hcoffin_set:Nn \l_coffin_display_pole_coffin
+    \hcoffin_set:Nn \l__coffin_display_pole_coffin
       {
         \color {#4}
         \rule { 1 pt } { 1 pt }
       }
     \coffin_attach_mark:NnnNnnnn #1 {#2} {#3}
-      \l_coffin_display_pole_coffin { hc } { vc } { 0 pt } { 0 pt }
-    \hcoffin_set:Nn \l_coffin_display_coord_coffin
+      \l__coffin_display_pole_coffin { hc } { vc } { 0 pt } { 0 pt }
+    \hcoffin_set:Nn \l__coffin_display_coord_coffin
       {
         \color {#4}
-        \l_coffin_display_font_tl
+        \l__coffin_display_font_tl
         ( \tl_to_str:n { #2 , #3 } )
       }
-    \prop_get:NnN \l_coffin_display_handles_prop
-      { #2 #3 } \l_coffin_internal_tl
-    \quark_if_no_value:NTF \l_coffin_internal_tl
+    \prop_get:NnN \l__coffin_display_handles_prop
+      { #2 #3 } \l__coffin_internal_tl
+    \quark_if_no_value:NTF \l__coffin_internal_tl
       {
-        \prop_get:NnN \l_coffin_display_handles_prop
-          { #3 #2 } \l_coffin_internal_tl
-        \quark_if_no_value:NTF \l_coffin_internal_tl
+        \prop_get:NnN \l__coffin_display_handles_prop
+          { #3 #2 } \l__coffin_internal_tl
+        \quark_if_no_value:NTF \l__coffin_internal_tl
           {
             \coffin_attach_mark:NnnNnnnn #1 {#2} {#3}
-              \l_coffin_display_coord_coffin { l } { vc }
+              \l__coffin_display_coord_coffin { l } { vc }
                 { 1 pt } { 0 pt }
           }
           {
-            \exp_last_unbraced:No \coffin_mark_handle_aux:nnnnNnn
-              \l_coffin_internal_tl #1 {#2} {#3}
+            \exp_last_unbraced:No \__coffin_mark_handle_aux:nnnnNnn
+              \l__coffin_internal_tl #1 {#2} {#3}
           }
       }
       {
-        \exp_last_unbraced:No \coffin_mark_handle_aux:nnnnNnn
-          \l_coffin_internal_tl #1 {#2} {#3}
+        \exp_last_unbraced:No \__coffin_mark_handle_aux:nnnnNnn
+          \l__coffin_internal_tl #1 {#2} {#3}
       }
   }
-\cs_new_protected:Npn \coffin_mark_handle_aux:nnnnNnn #1#2#3#4#5#6#7
+\cs_new_protected:Npn \__coffin_mark_handle_aux:nnnnNnn #1#2#3#4#5#6#7
   {
     \coffin_attach_mark:NnnNnnnn #5 {#6} {#7}
-      \l_coffin_display_coord_coffin {#1} {#2}
-      { #3 \l_coffin_display_offset_dim }
-      { #4 \l_coffin_display_offset_dim }
+      \l__coffin_display_coord_coffin {#1} {#2}
+      { #3 \l__coffin_display_offset_dim }
+      { #4 \l__coffin_display_offset_dim }
   }
 \cs_generate_variant:Nn \coffin_mark_handle:Nnnn { c }
 \cs_new_protected:Npn \coffin_display_handles:Nn #1#2
   {
-    \hcoffin_set:Nn \l_coffin_display_pole_coffin
+    \hcoffin_set:Nn \l__coffin_display_pole_coffin
       {
         \color {#2}
         \rule { 1 pt } { 1 pt }
       }
-    \prop_set_eq:Nc \l_coffin_display_poles_prop
-      { l_coffin_poles_ \int_value:w #1 _prop }
-    \coffin_get_pole:NnN #1 { H } \l_coffin_pole_a_tl
-    \coffin_get_pole:NnN #1 { T } \l_coffin_pole_b_tl
-    \tl_if_eq:NNT \l_coffin_pole_a_tl \l_coffin_pole_b_tl
-      { \prop_del:Nn \l_coffin_display_poles_prop { T } }
-    \coffin_get_pole:NnN #1 { B } \l_coffin_pole_b_tl
-    \tl_if_eq:NNT \l_coffin_pole_a_tl \l_coffin_pole_b_tl
-      { \prop_del:Nn \l_coffin_display_poles_prop { B } }
-    \coffin_set_eq:NN \l_coffin_display_coffin #1
-    \prop_map_inline:Nn \l_coffin_display_poles_prop
+    \prop_set_eq:Nc \l__coffin_display_poles_prop
+      { l__coffin_poles_ \__int_value:w #1 _prop }
+    \__coffin_get_pole:NnN #1 { H } \l__coffin_pole_a_tl
+    \__coffin_get_pole:NnN #1 { T } \l__coffin_pole_b_tl
+    \tl_if_eq:NNT \l__coffin_pole_a_tl \l__coffin_pole_b_tl
+      { \prop_remove:Nn \l__coffin_display_poles_prop { T } }
+    \__coffin_get_pole:NnN #1 { B } \l__coffin_pole_b_tl
+    \tl_if_eq:NNT \l__coffin_pole_a_tl \l__coffin_pole_b_tl
+      { \prop_remove:Nn \l__coffin_display_poles_prop { B } }
+    \coffin_set_eq:NN \l__coffin_display_coffin #1
+    \prop_map_inline:Nn \l__coffin_display_poles_prop
       {
-        \prop_del:Nn \l_coffin_display_poles_prop {##1}
-        \coffin_display_handles_aux:nnnnnn {##1} ##2 {#2}
+        \prop_remove:Nn \l__coffin_display_poles_prop {##1}
+        \__coffin_display_handles_aux:nnnnnn {##1} ##2 {#2}
       }
-    \box_use:N \l_coffin_display_coffin
+    \box_use:N \l__coffin_display_coffin
   }
-\cs_new_protected:Npn \coffin_display_handles_aux:nnnnnn #1#2#3#4#5#6
+\cs_new_protected:Npn \__coffin_display_handles_aux:nnnnnn #1#2#3#4#5#6
   {
-    \prop_map_inline:Nn \l_coffin_display_poles_prop
+    \prop_map_inline:Nn \l__coffin_display_poles_prop
       {
-        \bool_set_false:N \l_coffin_error_bool
-        \coffin_calculate_intersection:nnnnnnnn {#2} {#3} {#4} {#5} ##2
-        \bool_if:NF \l_coffin_error_bool
+        \bool_set_false:N \l__coffin_error_bool
+        \__coffin_calculate_intersection:nnnnnnnn {#2} {#3} {#4} {#5} ##2
+        \bool_if:NF \l__coffin_error_bool
           {
-            \dim_set:Nn \l_coffin_display_x_dim { \l_coffin_x_dim }
-            \dim_set:Nn \l_coffin_display_y_dim { \l_coffin_y_dim }
-            \coffin_display_attach:Nnnnn
-              \l_coffin_display_pole_coffin { hc } { vc }
+            \dim_set:Nn \l__coffin_display_x_dim { \l__coffin_x_dim }
+            \dim_set:Nn \l__coffin_display_y_dim { \l__coffin_y_dim }
+            \__coffin_display_attach:Nnnnn
+              \l__coffin_display_pole_coffin { hc } { vc }
               { 0 pt } { 0 pt }
-            \hcoffin_set:Nn \l_coffin_display_coord_coffin
+            \hcoffin_set:Nn \l__coffin_display_coord_coffin
               {
                 \color {#6}
-                \l_coffin_display_font_tl
+                \l__coffin_display_font_tl
                 ( \tl_to_str:n { #1 , ##1 } )
               }
-            \prop_get:NnN \l_coffin_display_handles_prop
-              { #1 ##1 } \l_coffin_internal_tl
-            \quark_if_no_value:NTF \l_coffin_internal_tl
+            \prop_get:NnN \l__coffin_display_handles_prop
+              { #1 ##1 } \l__coffin_internal_tl
+            \quark_if_no_value:NTF \l__coffin_internal_tl
               {
-                \prop_get:NnN \l_coffin_display_handles_prop
-                  { ##1 #1 } \l_coffin_internal_tl
-                \quark_if_no_value:NTF \l_coffin_internal_tl
+                \prop_get:NnN \l__coffin_display_handles_prop
+                  { ##1 #1 } \l__coffin_internal_tl
+                \quark_if_no_value:NTF \l__coffin_internal_tl
                   {
-                    \coffin_display_attach:Nnnnn
-                      \l_coffin_display_coord_coffin { l } { vc }
+                    \__coffin_display_attach:Nnnnn
+                      \l__coffin_display_coord_coffin { l } { vc }
                       { 1 pt } { 0 pt }
                   }
                   {
                     \exp_last_unbraced:No
-                      \coffin_display_handles_aux:nnnn
-                      \l_coffin_internal_tl
+                      \__coffin_display_handles_aux:nnnn
+                      \l__coffin_internal_tl
                   }
               }
               {
-                \exp_last_unbraced:No \coffin_display_handles_aux:nnnn
-                  \l_coffin_internal_tl
+                \exp_last_unbraced:No \__coffin_display_handles_aux:nnnn
+                  \l__coffin_internal_tl
               }
           }
       }
   }
-\cs_new_protected:Npn \coffin_display_handles_aux:nnnn #1#2#3#4
+\cs_new_protected:Npn \__coffin_display_handles_aux:nnnn #1#2#3#4
   {
-    \coffin_display_attach:Nnnnn
-      \l_coffin_display_coord_coffin {#1} {#2}
-      { #3 \l_coffin_display_offset_dim }
-      { #4 \l_coffin_display_offset_dim }
+    \__coffin_display_attach:Nnnnn
+      \l__coffin_display_coord_coffin {#1} {#2}
+      { #3 \l__coffin_display_offset_dim }
+      { #4 \l__coffin_display_offset_dim }
   }
 \cs_generate_variant:Nn \coffin_display_handles:Nn { c }
-\cs_new_protected:Npn \coffin_display_attach:Nnnnn #1#2#3#4#5
-  {
-    \coffin_calculate_intersection:Nnn #1 {#2} {#3}
-    \dim_set:Nn \l_coffin_x_prime_dim { \l_coffin_x_dim }
-    \dim_set:Nn \l_coffin_y_prime_dim { \l_coffin_y_dim }
-    \dim_set:Nn \l_coffin_offset_x_dim
-      { \l_coffin_display_x_dim - \l_coffin_x_prime_dim + #4 }
-    \dim_set:Nn \l_coffin_offset_y_dim
-      { \l_coffin_display_y_dim - \l_coffin_y_prime_dim + #5 }
-    \hbox_set:Nn \l_coffin_aligned_coffin
-      {
-        \box_use:N \l_coffin_display_coffin
-        \tex_kern:D -\box_wd:N \l_coffin_display_coffin
-        \tex_kern:D \l_coffin_offset_x_dim
-        \box_move_up:nn { \l_coffin_offset_y_dim } { \box_use:N #1 }
-      }
-    \box_set_ht:Nn \l_coffin_aligned_coffin
-      { \box_ht:N \l_coffin_display_coffin }
-    \box_set_dp:Nn \l_coffin_aligned_coffin
-      { \box_dp:N \l_coffin_display_coffin }
-    \box_set_wd:Nn \l_coffin_aligned_coffin
-      { \box_wd:N \l_coffin_display_coffin }
-    \box_set_eq:NN \l_coffin_display_coffin \l_coffin_aligned_coffin
+\cs_new_protected:Npn \__coffin_display_attach:Nnnnn #1#2#3#4#5
+  {
+    \__coffin_calculate_intersection:Nnn #1 {#2} {#3}
+    \dim_set:Nn \l__coffin_x_prime_dim { \l__coffin_x_dim }
+    \dim_set:Nn \l__coffin_y_prime_dim { \l__coffin_y_dim }
+    \dim_set:Nn \l__coffin_offset_x_dim
+      { \l__coffin_display_x_dim - \l__coffin_x_prime_dim + #4 }
+    \dim_set:Nn \l__coffin_offset_y_dim
+      { \l__coffin_display_y_dim - \l__coffin_y_prime_dim + #5 }
+    \hbox_set:Nn \l__coffin_aligned_coffin
+      {
+        \box_use:N \l__coffin_display_coffin
+        \tex_kern:D -\box_wd:N \l__coffin_display_coffin
+        \tex_kern:D \l__coffin_offset_x_dim
+        \box_move_up:nn { \l__coffin_offset_y_dim } { \box_use:N #1 }
+      }
+    \box_set_ht:Nn \l__coffin_aligned_coffin
+      { \box_ht:N \l__coffin_display_coffin }
+    \box_set_dp:Nn \l__coffin_aligned_coffin
+      { \box_dp:N \l__coffin_display_coffin }
+    \box_set_wd:Nn \l__coffin_aligned_coffin
+      { \box_wd:N \l__coffin_display_coffin }
+    \box_set_eq:NN \l__coffin_display_coffin \l__coffin_aligned_coffin
   }
 \cs_new_protected:Npn \coffin_show_structure:N #1
   {
-    \coffin_if_exist:NT #1
+    \__coffin_if_exist:NT #1
       {
-        \msg_aux_show:Nnx #1 { coffins }
+        \__msg_show_variable:Nnn #1 { coffins }
           {
             \prop_map_function:cN
-              { l_coffin_poles_ \int_value:w #1 _prop }
-              \msg_aux_show_unbraced:nn
+              { l__coffin_poles_ \__int_value:w #1 _prop }
+              \__msg_show_item_unbraced:nn
           }
       }
   }
 \cs_generate_variant:Nn \coffin_show_structure:N { c }
-\msg_kernel_new:nnnn { coffins } { no-pole-intersection }
+\__msg_kernel_new:nnnn { kernel } { no-pole-intersection }
   { No~intersection~between~coffin~poles. }
   {
     \c_msg_coding_error_text_tl
@@ -1087,17 +858,17 @@
     but~they~do~not~have~a~unique~meeting~point:~
     the~value~(0~pt,~0~pt)~will~be~used.
   }
-\msg_kernel_new:nnnn { coffins } { unknown-coffin }
+\__msg_kernel_new:nnnn { kernel } { unknown-coffin }
   { Unknown~coffin~'#1'. }
   { The~coffin~'#1'~was~never~defined. }
-\msg_kernel_new:nnnn { coffins } { unknown-coffin-pole }
+\__msg_kernel_new:nnnn { kernel } { unknown-coffin-pole }
   { Pole~'#1'~unknown~for~coffin~'#2'. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~was~asked~to~find~a~typesetting~pole~for~a~coffin,~
     but~either~the~coffin~does~not~exist~or~the~pole~name~is~wrong.
   }
-\msg_kernel_new:nnn { coffins } { show }
+\__msg_kernel_new:nnn { kernel } { show-coffins }
   {
     Size~of~coffin~\token_to_str:N #1 : \\
     > ~ ht~=~\dim_use:N \box_ht:N #1 \\
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3color.sty b/Master/texmf-dist/tex/latex/l3kernel/l3color.sty
index 989061981f4..5ea45852215 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3color.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3color.sty
@@ -13,7 +13,7 @@
 %% 
 %% Do not distribute a modified version of this file.
 %% 
-%% File: l3color.dtx Copyright(C) 2011 The LaTeX3 Project
+%% File: l3color.dtx Copyright(C) 2011,2012 The LaTeX3 Project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -47,18 +47,30 @@
 %% -----------------------------------------------------------------------
 %%
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3color.dtx 2776 2011-09-07 18:33:19Z joseph $
+\GetIdInfo$Id: l3color.dtx 3986 2012-07-15 19:23:51Z joseph $
   {L3 Experimental colour support}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 \cs_new_eq:NN \color_group_begin: \group_begin:
 \cs_new_protected_nopar:Npn \color_group_end:
   {
       \tex_par:D
     \group_end:
   }
-\cs_new_protected_nopar:Npn \color_ensure_current: { \set@color }
+\cs_new_protected_nopar:Npn \color_ensure_current: { }
+\AtBeginDocument
+  {
+    \cs_if_exist:NTF \__driver_color_ensure_current:
+      {
+        \cs_set_protected_nopar:Npn \color_ensure_current:
+          { \__driver_color_ensure_current: }
+      }
+      {
+        \cs_if_exist:NT \set@color
+          { \cs_set_protected_nopar:Npn \color_ensure_current: { \set@color } }
+      }
+  }
 %% 
 %%
 %% End of file `l3color.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3doc.cls b/Master/texmf-dist/tex/latex/l3kernel/l3doc.cls
index b79ca0bb135..c1adee8c71f 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3doc.cls
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3doc.cls
@@ -4,7 +4,7 @@
 %%
 %% The original source files were:
 %%
-%% l3doc.dtx  (with options: `class')
+%% l3doc.dtx  (with options: `class,cfg')
 %% 
 %% 
 %% EXPERIMENTAL CODE
@@ -15,7 +15,7 @@
 %% Do not distribute a modified version of this file.
 %% 
 %% 
-%% File: l3doc.dtx Copyright (C) 1990-2011 The LaTeX3 project
+%% File: l3doc.dtx Copyright (C) 1990-2012 The LaTeX3 project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -47,12 +47,12 @@
 %%   prior consultation with the LaTeX3 Project.
 %%
 %% -----------------------------------------------------------------------
-\RequirePackage{expl3,xparse,calc}
 \let        \filenameOld        \ExplFileName
 \let        \filedateOld        \ExplFileDate
 \let     \fileversionOld        \ExplFileVersion
 \let \filedescriptionOld        \ExplFileDescription
-\GetIdInfo$Id: l3doc.dtx 3491 2012-03-04 06:13:18Z bruno $
+\RequirePackage{expl3,xparse,calc}
+\GetIdInfo$Id: l3doc.dtx 3989 2012-07-16 01:15:43Z bruno $
           {L3 Experimental documentation class}
 \ProvidesExplClass
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -60,12 +60,6 @@
 \let        \ExplFileDate        \filedateOld
 \let        \ExplFileVersion     \fileversionOld
 \let        \ExplFileDescription \filedescriptionOld
-\cs_new_nopar:Npn\Team{%
-  The~\LaTeX3~Project\thanks{%
-  Frank~Mittelbach,~Denys~Duchier,~Chris~Rowley,~
-  Rainer~Sch\"opf,~Johannes~Braams,~Michael~Downes,~
-  David~Carlisle,~Alan~Jeffrey,~Morten~H\o{}gholm,~Thomas~Lotze,~
-  Javier~Bezos,~Will~Robertson,~Joseph~Wright,~Bruno~Le~Floch}}
 \coffin_new:N \l_doc_output_box
 \coffin_new:N \l_doc_names_coffin
 \coffin_new:N \l_doc_descr_coffin
@@ -95,12 +89,17 @@
 \bool_new:N \g_doc_lmodern_bool
 \bool_new:N \g_doc_checkfunc_bool
 \bool_new:N \g_doc_checktest_bool
+\seq_new:N \g_doc_tmpa_seq
+\tl_new:N \l_doc_tmpa_tl
+\tl_new:N \l_doc_tmpb_tl
+\int_new:N \l_doc_tmpa_int
+\bool_new:N \l_doc_tested_bool
 \cs_set_protected_nopar:Npn \coffin_gset_eq:NN #1#2
   {
     \coffin_if_exist:NT #1
       {
         \box_gset_eq:NN #1 #2
-        \coffin_gset_eq_structure:NN #1 #2
+        \__coffin_gset_eq_structure:NN #1 #2
       }
   }
 \cs_generate_variant:Nn \coffin_gset_eq:NN { c , Nc , cc }
@@ -115,13 +114,15 @@
 \DeclareOption{lm-default}{ \bool_set_true:N \g_doc_lmodern_bool }
 \DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}}
 \ExecuteOptions{full,a4paper,nocheck,nochecktest,lm-default}
-\InputIfFileExists{l3doc.cfg}
+\msg_new:nnn {l3doc} {input-cfg}
   {
-    \typeout{*************************************^^J
-             *~Local~config~file~l3doc.cfg~used   ^^J
-             *************************************}
+    Local~config~file~l3doc.cfg~loaded.
+  }
+\file_if_exist:nT {l3doc.cfg}
+  {
+    \file_input:n {l3doc.cfg}
+    \msg_info:nn {l3doc} {input-cfg}
   }
-  { \@input{l3doc.ltx} }
 \ProcessOptions
 \LoadClass{article}
 \RequirePackage{doc}
@@ -129,6 +130,7 @@
   {
     array,
     alphalph,
+    amsmath,
     booktabs,
     color,
     colortbl,
@@ -182,9 +184,9 @@
 }
 \setcounter{StandardModuleDepth}{1}
 \@addtoreset{CodelineNo}{part}
-\cs_set_nopar:Npn \theCodelineNo {
-  \textcolor[gray]{0.5}{ \sffamily\tiny\arabic{CodelineNo} }
-}
+\tl_replace_once:Nnn \theCodelineNo
+ { \HDorg@theCodelineNo }
+ { \textcolor[gray]{0.5} { \sffamily\tiny\arabic{CodelineNo} } }
 \setlength   \textwidth      { 385pt }
 \addtolength \marginparwidth {  30pt }
 \addtolength \oddsidemargin  {  20pt }
@@ -226,9 +228,18 @@
   \cs_new_protected_nopar:Npn \XeTeX
     {X\kern-.125em\lower.5ex\hbox{\reflectbox{E}}\kern-.1667em\TeX}
 }
-\cs_set_nopar:Npn \cmd #1 { \cs{\expandafter\cmd@to@cs\string#1} }
-\cs_set_nopar:Npn \cmd@to@cs #1#2 { \char\number`#2\relax }
-\DeclareRobustCommand \cs [1] { \texttt { \char`\\ #1 } }
+\cs_set_nopar:Npn \cmd #1 { \cs{\expandafter \doc_cmd_to_cs:w \string#1} }
+\cs_set_nopar:Npn \doc_cmd_to_cs:w #1#2 { \char\number`#2\relax }
+\DeclareRobustCommand \cs [1]
+  {
+    \tl_set_rescan:Nnn \l_doc_tmpb_tl { } { _ }
+    \tl_set:Nn \l_doc_tmpa_tl {#1}
+    \tl_replace_all:NVn \l_doc_tmpa_tl \l_doc_tmpb_tl { _ }
+    \doc_replace_at_at:N \l_doc_tmpa_tl
+    \tl_replace_all:NnV \l_doc_tmpa_tl { _ } \l_doc_tmpb_tl
+    \texttt { \char`\\ \tl_use:N \l_doc_tmpa_tl}
+  }
+\cs_generate_variant:Nn \tl_replace_all:Nnn { NV , NnV }
 \providecommand\marg[1]{ \texttt{\char`\{} \meta{#1} \texttt{\char`\}} }
 \providecommand\oarg[1]{ \texttt[ \meta{#1} \texttt] }
 \providecommand\parg[1]{ \texttt( \meta{#1} \texttt) }
@@ -249,7 +260,7 @@
           \string\TeX{}~and~\string\LaTeXe{}~commands:\levelchar
           #1\actualchar{\string\ttfamily\string\bslash{}#1}}}
 \cs_new:Npn \doc_implementation: {
-  \cs_set:Npn \variable {\macro[var]}
+  \DeclareDocumentCommand {\variable} { O{} } { \doc_macro:n { var , ##1 } }
   \cs_set_eq:NN \endvariable \endmacro
 }
 \cs_new:Npn \doc_docu: {
@@ -333,8 +344,9 @@
     \char_set_catcode_ignore:N \ % space
     \char_set_catcode_ignore:N \^^M
     \char_set_catcode_ignore:N \^^I
-
-    \function_aux:n
+    \exp_after:wN
+  \group_end:
+  \function_aux:n
   }
   {
     \vcoffin_set_end:
@@ -381,8 +393,6 @@
 \cs_set_eq:NN \endvariabledoc \endfunction
 \cs_set_nopar:Npn \function_aux:n #1 {
 
-  \group_end:
-
   \tl_set:Nn \l_doc_function_input_tl {#1}
 
   \dim_zero:N \l_doc_trial_width_dim
@@ -428,22 +438,22 @@
   % finally, for regular old csnames:
 \exp_args:NNf \prop_get:NnNTF
   \l_doc_functions_block_prop
-  { \cs_get_function_name:N #1 } \l_doc_tmp_tl
+  { \__cs_get_function_name:N #1 } \l_doc_tmpb_tl
 {
 \prop_put:Nxx \l_doc_functions_block_prop
-{ \cs_get_function_name:N #1 }
+{ \__cs_get_function_name:N #1 }
 {
-  \l_doc_tmp_tl ,
-  {\cs_get_arg_count_from_signature:N #1}
-  {\cs_get_function_signature:N #1}
+  \l_doc_tmpb_tl ,
+  {\__cs_count_signature:N #1}
+  {\__cs_get_function_signature:N #1}
 }
 }
 {
 \prop_put:Nxx \l_doc_functions_block_prop
-{ \cs_get_function_name:N #1 }
+{ \__cs_get_function_name:N #1 }
 {
-  {\cs_get_arg_count_from_signature:N #1}
-  {\cs_get_function_signature:N #1}
+  {\__cs_count_signature:N #1}
+  {\__cs_get_function_signature:N #1}
 }
 }
 }
@@ -452,20 +462,20 @@
       {
         % for now don't bother splitting into variants:
         \tl_gclear:N \l_doc_function_name_prefix_tl
-\prop_put:Nxx \l_doc_functions_block_prop { #1 } { {-1} {} }
+\prop_put:Nxx \l_doc_functions_block_prop { \tl_to_str:n {#1} } { {-1} {} }
       }
   }
 
 \cs_new:Nn \doc_typeset_functions:nn
   {
     \clist_gset:Nn \l_doc_variants_clist {#2}
-    \clist_gpop:NN \l_doc_variants_clist \l_doc_tmp_tl
+    \clist_gpop:NN \l_doc_variants_clist \l_doc_tmpb_tl
     \exp_args:Nc \doc_typeset_functions_aux:N
       {
          #1
-         \int_compare:nT { \exp_after:wN \use_i:nn \l_doc_tmp_tl > -1 } {:}
-         \int_compare:nT { \exp_after:wN \use_i:nn \l_doc_tmp_tl >  0 }
-           { \exp_after:wN \use_ii:nn \l_doc_tmp_tl }
+         \int_compare:nT { \exp_after:wN \use_i:nn \l_doc_tmpb_tl > -1 } {:}
+         \int_compare:nT { \exp_after:wN \use_i:nn \l_doc_tmpb_tl >  0 }
+           { \exp_after:wN \use_ii:nn \l_doc_tmpb_tl }
       }
     \\
   }
@@ -473,18 +483,22 @@
 \cs_new_nopar:Nn \doc_typeset_functions_aux:N
 {
   \bool_if:NT \l_doc_meta_pTF_bool {
+    \tl_set:Nx \l_doc_pTF_name_tl
+      { \l_doc_function_name_prefix_tl \doc_predicate_from_base:N #1 }
+    \doc_special_main_index:o { \l_doc_pTF_name_tl }
+    \seq_gput_right:Nx \g_doc_functions_seq
+      { \tl_to_str:N \l_doc_pTF_name_tl }
     \tl_set:Nx \l_doc_pTF_name_tl { \doc_predicate_from_base:N #1 }
-    \doc_special_main_index:o { \tl_to_str:N \l_doc_pTF_name_tl }
-    \seq_gput_right:Nx \g_doc_functions_seq { \l_doc_function_name_prefix_tl \l_doc_pTF_name_tl }
   }
 
-  \bool_if:NTF \l_doc_meta_TF_bool {
-    \doc_special_main_index:o { \token_to_str:N #1 TF }
-    \seq_gput_right:Nx \g_doc_functions_seq { \token_to_str:N #1 TF }
-  }{
-    \doc_special_main_index:o { \token_to_str:N #1 }
-    \seq_gput_right:Nx \g_doc_functions_seq { \tl_to_str:n {#1}  }
-  }
+  \tl_set:Nx \l_doc_tmpa_tl
+    {
+      \l_doc_function_name_prefix_tl
+      \cs_to_str:N #1
+      \bool_if:NT \l_doc_meta_TF_bool { \tl_to_str:n {TF} }
+    }
+  \doc_special_main_index:o { \l_doc_tmpa_tl }
+  \seq_gput_right:No \g_doc_functions_seq { \l_doc_tmpa_tl }
 
   \bool_if:NTF \l_doc_meta_pTF_bool {
 
@@ -502,24 +516,19 @@
   }
 }
 \cs_set_nopar:Nn \doc_typeset_function_block:N {
-  \tl_gset:Nx \l_doc_function_name_tl { \cs_get_function_name:N #1 }
-  \tl_gset:Nx \l_doc_function_sig_tl { \cs_get_function_signature:N #1 }
+  \tl_gset:Nx \l_doc_function_name_tl { \__cs_get_function_name:N #1 }
+  \tl_gset:Nx \l_doc_function_sig_tl { \__cs_get_function_signature:N #1 }
   \tl_gset:Nx \g_doc_macro_tl { \l_doc_function_name_prefix_tl \l_doc_function_name_tl }
 
   \doc_typeset_function_basename:N #1
   \bool_if:NT \l_doc_meta_TF_bool { \doc_typeset_TF: }
   \doc_typeset_expandability:
   \clist_if_empty:NF \l_doc_variants_clist { \doc_typeset_variants: }
-  \bool_if:NT \g_doc_full_bool { \doc_label_function: }
+  \bool_if:NT \g_doc_full_bool { \doc_label_function:N #1 }
 
 }
 \cs_set:Nn \doc_typeset_function_basename:N
-  {
-    \g_doc_macro_tl
-    \int_compare:nT { \cs_get_arg_count_from_signature:N #1 >  -1 } { : }
-    \int_compare:nT { \cs_get_arg_count_from_signature:N #1 >   0 }
-      { \l_doc_function_sig_tl }
-  }
+  { \l_doc_function_name_prefix_tl \cs_to_str:N #1 }
 \cs_set:Nn \doc_typeset_expandability:
   {
     &
@@ -536,12 +545,12 @@
   {
     \\
     \doc_typeset_aux:n \g_doc_macro_tl :
-    \int_compare:nTF { \clist_length:N \l_doc_variants_clist == 1 }
+    \int_compare:nTF { \clist_count:N \l_doc_variants_clist == 1 }
       { \exp_after:wN \use_ii:nn \l_doc_variants_clist }
       {
         \textrm(
-          \clist_pop:NN \l_doc_variants_clist \l_doc_tmp_tl
-          \exp_after:wN \use_ii:nn \l_doc_tmp_tl
+          \clist_pop:NN \l_doc_variants_clist \l_doc_tmpb_tl
+          \exp_after:wN \use_ii:nn \l_doc_tmpb_tl
           \clist_map_inline:Nn \l_doc_variants_clist {\textrm| \use_ii:nn ##1}
         \textrm)
       }
@@ -556,15 +565,12 @@
       \hyperlink{rexpstar} {\ding{73}} % hollow star
     }
   }
-\cs_set:Nn \doc_label_function:
+\cs_set:Nn \doc_label_function:N
   {
-    \exp_args:NNf \tl_replace_all:Nnn \g_doc_macro_tl {\token_to_str:N _} {/}
-    \exp_args:NNf \tl_replace_all:Nnn \g_doc_macro_tl {\@backslashchar} {}
-    \exp_args:Nx \label
-      {
-        doc/function//\g_doc_macro_tl
-        \tl_if_empty:NF \l_doc_function_sig_tl { : \l_doc_function_sig_tl }
-      }
+    \tl_set:Nx \l_doc_tmpa_tl { \l_doc_function_name_prefix_tl \cs_to_str:N #1 }
+    \exp_args:NNf \tl_replace_all:Nnn \l_doc_tmpa_tl {\token_to_str:N _} {/}
+    \exp_args:NNf \tl_remove_all:Nn \l_doc_tmpa_tl {\@backslashchar}
+    \exp_args:Nx \label {doc/function//\l_doc_tmpa_tl}
   }
 \cs_set_nopar:Nn \doc_show_macro_unusual:N {
   \tl_gset:Nx \g_doc_macro_tl { \token_to_str:N #1}
@@ -665,8 +671,11 @@
       { \bool_set_true:N \l_doc_macro_TF_bool } ,
     pTF .code:n =
       { \bool_set_true:N \l_doc_macro_pTF_bool } ,
+    tested .code:n =
+      { } ,
   }
-\renewcommand \macro [1][] {
+\RenewDocumentCommand { \macro } { O{} } { \doc_macro:n {#1} }
+\cs_new_protected:Npn \doc_macro:n #1 {
 
   \int_compare:nNnTF \currentgrouplevel=2
     { \int_gzero:N \g_doc_nested_macro_int }
@@ -727,15 +736,18 @@
 }
 \cs_set:Nn \doc_predicate_from_base:N
   {
-    \cs_get_function_name:N #1 _p: \cs_get_function_signature:N #1
+    \__cs_get_function_name:N #1 _p: \__cs_get_function_signature:N #1
   }
 \cs_set:Npn \doc_predicate_from_base:w #1 : #2 \q_nil
   {
     #1 _p: #2
   }
+\tl_new:N \l_doc_at_replaced_macro_tl
 \cs_set_nopar:Npn \doc_macro_single:n #1 {
   \int_incr:N \l_doc_macro_int
-  \tl_set:Nx \saved@macroname { \token_to_str:N #1 }
+  \tl_set:Nx \l_doc_at_replaced_macro_tl { \token_to_str:N #1 }
+  \doc_replace_at_at:N \l_doc_at_replaced_macro_tl
+  \tl_set_eq:NN \saved@macroname \l_doc_at_replaced_macro_tl
   \topsep\MacroTopsep
   \trivlist
   \cs_set_nopar:Npn \makelabel ##1 { \llap{##1} }
@@ -762,33 +774,33 @@
   }
 
   \bool_if:NF \l_doc_macro_aux_bool {
-    \tl_gset:Nx \l_doc_macro_tl { \tl_to_str:n {#1} }
+    \tl_gset:Nx \l_doc_macro_tl { \tl_to_str:N \l_doc_at_replaced_macro_tl }
     \exp_args:NNf \tl_greplace_all:Nnn \l_doc_macro_tl {\token_to_str:N _} {/}
     \exp_args:NNf \tl_greplace_all:Nnn \l_doc_macro_tl {\@backslashchar} {}
   }
 
   \use:x {
     \exp_not:N \item [ \exp_not:N \doc_print_macroname:n {
-      \tl_to_str:n {#1}
+      \tl_to_str:N \l_doc_at_replaced_macro_tl
     }]
   }
   \global\advance \c@CodelineNo \@ne
 
   \bool_if:NF \l_doc_macro_aux_bool {
     \bool_if:NTF \l_doc_macro_TF_bool {
-      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:n { #1 TF } }
-      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:n { #1 T  } }
-      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:n { #1 F  } }
+      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:N \l_doc_at_replaced_macro_tl \tl_to_str:n {TF} }
+      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:N \l_doc_at_replaced_macro_tl \tl_to_str:n {T } }
+      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:N \l_doc_at_replaced_macro_tl \tl_to_str:n { F} }
     }{
-      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:n {#1} }
+      \seq_gput_right:Nx \g_doc_macros_seq { \tl_to_str:N \l_doc_at_replaced_macro_tl }
     }
   }
   \bool_if:NTF \l_doc_macro_TF_bool {
-    \SpecialMainIndex{#1 TF}\nobreak
-    \DoNotIndex{#1 TF}
+    \exp_args:Nx \SpecialMainIndex{ \tl_to_str:N \l_doc_at_replaced_macro_tl TF}\nobreak
+    \exp_args:Nx \DoNotIndex{ \tl_to_str:N \l_doc_at_replaced_macro_tl TF}
   }{
-    \SpecialMainIndex{#1}\nobreak
-    \DoNotIndex{#1}
+    \exp_args:Nx \SpecialMainIndex{ \tl_to_str:N \l_doc_at_replaced_macro_tl }\nobreak
+    \exp_args:Nx \DoNotIndex{ \tl_to_str:N \l_doc_at_replaced_macro_tl }
   }
 
   \global\advance \c@CodelineNo \m@ne
@@ -797,7 +809,8 @@
 \tl_clear:N \l_doc_macro_tl
 \cs_set_nopar:Npn \doc_print_macroname:n #1 {
   \strut
-  \int_compare:nTF { \tl_length:n {#1} <= 28 }
+  \HD@target
+  \int_compare:nTF { \tl_count:n {#1} <= 28 }
     { \MacroFont } { \MacroLongFont }
 
   % INEFFICIENT: (!)
@@ -853,19 +866,42 @@
 \DeclareDocumentCommand \TestMissing {m} {
   \prop_if_in:NVTF \g_doc_missing_tests_prop \l_doc_macro_input_clist
   {
-    \prop_get:NVN \g_doc_missing_tests_prop \l_doc_macro_input_clist \l_tmpa_tl
+    \prop_get:NVN \g_doc_missing_tests_prop \l_doc_macro_input_clist \l_doc_tmpa_tl
     \prop_gput:NVx \g_doc_missing_tests_prop \l_doc_macro_input_clist
     {
-      *~ \l_tmpa_tl
+      *~ \l_doc_tmpa_tl
       ^^J \exp_not:n {\space\space\space\space\space\space}
       *~ #1
     }
   }
   { \prop_gput:NVn \g_doc_missing_tests_prop \l_doc_macro_input_clist {#1} }
 }
-\cs_set:Nn \doc_macro_wrap:n
+\tl_new:N \g_doc_module_name_tl
+\cs_new_protected:Npn \doc_replace_at_at:N #1 {
+    \tl_if_empty:NF \g_doc_module_name_tl
+      {
+        \tl_replace_all:Non #1 { \token_to_str:N @ } { @ }
+        \tl_replace_all:Non #1 { \token_to_str:N _ } { _ }
+        \tl_replace_all:Nox #1 { _@@ } { __ \g_doc_module_name_tl }
+        \tl_replace_all:Nox #1 { @@ } { __ \g_doc_module_name_tl }
+      }
+}
+\cs_generate_variant:Nn \tl_replace_all:Nnn { Non, Nox }
+\cs_new_protected:Nn \doc_endmacro_build_seq:N
+  {
+    \seq_gclear:N #1
+    \clist_map_inline:Nn \l_doc_macro_input_clist
+      {
+        \tl_set:Nn \l_doc_tmpa_tl {##1}
+        \doc_replace_at_at:N \l_doc_tmpa_tl
+        \seq_gput_right:No #1 { \l_doc_tmpa_tl }
+      }
+  }
+\cs_set_protected:Nn \doc_endmacro_wrap_each:N
   {
-    #1 \bool_if:NT \l_doc_macro_TF_bool {TF}
+    \bool_if:NTF \l_doc_macro_TF_bool
+      { \seq_gset_map:NNn #1 #1 { \exp_not:N \texttt { ##1 TF } } }
+      { \seq_gset_map:NNn #1 #1 { \exp_not:N \texttt { ##1 } } }
   }
 \cs_set:Nn \doc_texttt_comma:n {\,,~\texttt{#1}}
 \cs_set:Npn \endmacro {
@@ -873,29 +909,14 @@
   {
   \par\nobreak\noindent{\footnotesize(\emph{
     End~ definition~ for~
-    \prg_case_int:nnn { \clist_length:N \l_doc_macro_input_clist }
-    {
-      {1} { \texttt{ \doc_macro_wrap:n { \clist_use:N \l_doc_macro_input_clist } }. }
-      {2}
+    \doc_endmacro_build_seq:N \g_doc_tmpa_seq
+    \doc_endmacro_wrap_each:N \g_doc_tmpa_seq
+    \int_compare:nTF { \seq_count:N \g_doc_tmpa_seq <= 3 }
       {
-        \tl_set:Nx \l_clist_first_tl { \clist_item:Nn \l_doc_macro_input_clist {0} }
-        \tl_set:Nx \l_clist_last_tl { \clist_item:Nn \l_doc_macro_input_clist {1} }
-        \texttt{\doc_macro_wrap:n\l_clist_first_tl}\,~ and~ \texttt{\doc_macro_wrap:n\l_clist_last_tl}\,.
+        \seq_use:Nnnn \g_doc_tmpa_seq
+          { \,~and~ } { \,,~ } { \,,~and~ }
       }
-      {3}
-      {
-        \tl_set:Nx \l_clist_first_tl { \clist_item:Nn \l_doc_macro_input_clist {0} }
-        \tl_set:Nx \l_clist_mid_tl   { \clist_item:Nn \l_doc_macro_input_clist {1} }
-        \tl_set:Nx \l_clist_last_tl  { \clist_item:Nn \l_doc_macro_input_clist {2} }
-        \texttt{\doc_macro_wrap:n\l_clist_first_tl}\,,~
-        \texttt{\doc_macro_wrap:n\l_clist_mid_tl}\,,~
-        and~ \texttt{\doc_macro_wrap:n\l_clist_last_tl}\,.
-      }
-    }
-    {
-      \tl_set:Nx \l_clist_first_tl { \clist_item:Nn \l_doc_macro_input_clist {0} }
-      \texttt{\doc_macro_wrap:n\l_clist_first_tl}\,~and~others.
-    }
+      { \seq_item:Nn \g_doc_tmpa_seq {1}\,~and~others. }
     \bool_if:nT {
       !\l_doc_macro_aux_bool &&
       !\l_doc_macro_internal_bool &&
@@ -918,12 +939,59 @@
   {
     \seq_gput_right:Nx \g_doc_not_tested_seq
     {
-      \l_doc_macro_input_clist
+      \seq_use:Nnnn \g_doc_tmpa_seq { , } { , } { , }
       \bool_if:NT \l_doc_macro_pTF_bool {~(pTF)}
       \bool_if:NT \l_doc_macro_TF_bool {~(TF)}
     }
   }
 }
+\group_begin:
+  \char_set_catcode_escape:N \/
+  \char_set_catcode_other:N \^^A
+  \char_set_catcode_active:N \^^S
+  \char_set_catcode_active:N \^^B
+  \char_set_catcode_other:N \^^L
+  \char_set_catcode_other:N \^^R
+  \char_set_lccode:nn { `\^^A } { `\% }
+  \char_set_lccode:nn { `\^^S } { `\  }
+  \char_set_lccode:nn { `\^^B } { `\\ }
+  \char_set_lccode:nn { `\^^L } { `\{ }
+  \char_set_lccode:nn { `\^^R } { `\} }
+  \tl_to_lowercase:n
+    {
+      \group_end:
+      \cs_set_protected:Npn \xmacro@code
+          #1 ^^A ^^S^^S^^S^^S ^^Bend ^^Lmacrocode^^R
+        { \doc_xmacro_code:n {#1} /end{macrocode} }
+    }
+\group_begin:
+  \char_set_catcode_active:N \<
+  \char_set_catcode_active:N \>
+  \cs_new_protected:Npn \doc_xmacro_code:n #1
+    {
+      \tl_if_in:nnTF {#1} { < @ @ = }
+        { \doc_xmacro_code:w #1 \q_stop }
+        {
+          \tl_set:Nn \l_doc_tmpa_tl {#1}
+          \doc_replace_at_at:N \l_doc_tmpa_tl
+          \tl_use:N \l_doc_tmpa_tl
+        }
+    }
+  \cs_new_protected:Npn \doc_xmacro_code:w #1 < @ @ = #2 > #3 \q_stop
+    {
+      \tl_set:Nn \l_doc_tmpa_tl {#1}
+      \doc_replace_at_at:N \l_doc_tmpa_tl
+
+      \tl_gset:Nn \g_doc_module_name_tl {#2}
+      \tl_put_right:Nn \l_doc_tmpa_tl { < @ @ = #2 > }
+
+      \tl_set:Nn \l_doc_tmpb_tl {#3}
+      \doc_replace_at_at:N \l_doc_tmpb_tl
+      \tl_put_right:No \l_doc_tmpa_tl { \l_doc_tmpb_tl }
+
+      \tl_use:N \l_doc_tmpa_tl
+    }
+\group_end:
 \newcommand*{\DescribeOption}{
  \leavevmode
  \@bsphack
@@ -1138,48 +1206,52 @@
   }
   \cs_set_eq:NN \@evenfoot \@oddfoot
 }
-\iow_open:Nn \g_write_func_stream { \jobname.cmds }
+\iow_new:N \g_doc_func_iow
 \cs_new_nopar:Npn \doc_show_functions_defined: {
   \bool_if:nT { \g_doc_implementation_bool && \g_doc_checkfunc_bool } {
     \typeout{ ======================================== ^^J }
+    \iow_open:Nn \g_doc_func_iow { \c_job_name_tl .cmds }
 
-    \tl_clear:N \l_tmpa_tl
+    \tl_clear:N \l_doc_tmpa_tl
     \seq_map_inline:Nn \g_doc_functions_seq {
       \seq_if_in:NnT \g_doc_macros_seq {##1} {
-        \tl_put_right:Nn \l_tmpa_tl { ##1 ^^J }
-        \iow_now:Nn \g_write_func_stream { ##1 }
+        \tl_put_right:Nn \l_doc_tmpa_tl { ##1 ^^J }
+        \iow_now:Nn \g_doc_func_iow { > ~ ##1 }
       }
     }
-    \iow_close:N \g_write_func_stream
+
     \doc_functions_typeout:n {
       Functions~both~documented~and~defined:^^J (In~order~of~being~documented)
     }
 
     \seq_map_inline:Nn \g_doc_functions_seq {
       \seq_if_in:NnF \g_doc_macros_seq {##1} {
-        \tl_put_right:Nn \l_tmpa_tl { ##1 ^^J }
+        \tl_put_right:Nn \l_doc_tmpa_tl { ##1 ^^J }
+        \iow_now:Nn \g_doc_func_iow { ! ~ ##1}
       }
     }
     \doc_functions_typeout:n { Functions~documented~but~not~defined: }
 
     \seq_map_inline:Nn \g_doc_macros_seq {
       \seq_if_in:NnF \g_doc_functions_seq {##1} {
-        \tl_put_right:Nn \l_tmpa_tl { ##1 ^^J }
+        \tl_put_right:Nn \l_doc_tmpa_tl { ##1 ^^J }
+        \iow_now:Nn \g_doc_func_iow { ? ~ ##1}
       }
     }
     \doc_functions_typeout:n { Functions~defined~but~not~documented: }
 
+    \iow_close:N \g_doc_func_iow
     \typeout{ ======================================== }
   }
 }
 \AtEndDocument{ \doc_show_functions_defined: }
 \cs_set_nopar:Npn \doc_functions_typeout:n #1 {
-  \tl_if_empty:NF \l_tmpa_tl {
+  \tl_if_empty:NF \l_doc_tmpa_tl {
     \typeout{
       -------------------------------------- ^^J #1 ^^J
-      -------------------------------------- ^^J \l_tmpa_tl
+      -------------------------------------- ^^J \l_doc_tmpa_tl
     }
-    \tl_clear:N \l_tmpa_tl
+    \tl_clear:N \l_doc_tmpa_tl
   }
 }
 \cs_new:Npn \doc_show_not_tested: {
@@ -1188,23 +1260,23 @@
     \bool_if:nT { !(\seq_if_empty_p:N  \g_doc_not_tested_seq) ||
                   !(\prop_if_empty_p:N \g_doc_missing_tests_prop) }
     {
-      \tl_clear:N \l_tmpa_tl
+      \tl_clear:N \l_doc_tmpa_tl
       \prop_if_empty:NF \g_doc_missing_tests_prop
       {
-        \tl_put_right:Nn \l_tmpa_tl
+        \tl_put_right:Nn \l_doc_tmpa_tl
         {
           ^^J^^JThe~ following~ macro(s)~ have~ incomplete~ tests:^^J
         }
         \prop_map_inline:Nn \g_doc_missing_tests_prop
         {
-          \tl_put_right:Nn \l_tmpa_tl
+          \tl_put_right:Nn \l_doc_tmpa_tl
           {^^J\space\space\space\space ##1
            ^^J\space\space\space\space\space\space ##2}
         }
       }
       \seq_if_empty:NF \g_doc_not_tested_seq
       {
-        \tl_put_right:Nn \l_tmpa_tl
+        \tl_put_right:Nn \l_doc_tmpa_tl
         {
           ^^J^^J
           The~ following~ macro(s)~ do~ not~ have~ any~ tests:^^J
@@ -1213,12 +1285,12 @@
         {
           \clist_map_inline:nn {##1}
           {
-            \tl_put_right:Nn \l_tmpa_tl {^^J\space\space\space\space ####1}
+            \tl_put_right:Nn \l_doc_tmpa_tl {^^J\space\space\space\space ####1}
           }
         }
         \int_set:Nn \l_tmpa_int {\etex_interactionmode:D}
         \errorstopmode
-        \ClassError{l3doc}{\l_tmpa_tl}{}
+        \ClassError{l3doc}{\l_doc_tmpa_tl}{}
         \int_set:Nn \etex_interactionmode:D {\l_tmpa_int}
       }
     }
@@ -1239,42 +1311,34 @@
 }
 
 \cs_set_nopar:Npn \doc_special_main_index:n #1 {
+  \HD@target
   \index{
     \@gobble#1
     \actualchar
     \string\verb\quotechar*\verbatimchar#1\verbatimchar
     \encapchar
-    hdpgindex{\thepage}{usage}
+    hdclindex{\the\c@HD@hypercount}{usage}
   }
 }
-\cs_set_nopar:Npn \doc_special_main_index:o { \exp_args:No \doc_special_main_index:n }
-\cs_set_nopar:Npn \hdpgindex #1#2#3 {
-  \csname\ifx\\#2\\relax\else#2\fi\endcsname{
-    \hyperlink{page.#1}{#3}
+\cs_generate_variant:Nn \doc_special_main_index:n { o , x }
+\msg_new:nnn {l3doc} {print-index-howto}
+  {
+    Generate~the~index~by~executing\\
+    \iow_indent:n { makeindex~-s~l3doc.ist~-o~\c_job_name_tl .ind~\c_job_name_tl .idx }
   }
-}
-\g@addto@macro \PrintIndex { \AtEndDocument{ \typeout{^^J
-  ========================================^^J
-  Generate~the~index~by~executing^^J
-  \c_space_tl \c_space_tl \c_space_tl \c_space_tl
-  makeindex~-s~l3doc.ist~-o~\jobname.ind~\jobname.idx^^J
-  ========================================^^J
-  }}
-}
+\tl_gput_right:Nn \PrintIndex { \AtEndDocument{ \msg_info:nn {l3doc} {print-index-howto} } }
 \GlossaryPrologue{
   \part*{Change~History}
   {\GlossaryParms\ttfamily\hyphenchar\font=`\-}
   \markboth{Change~History}{Change~History}
   \addcontentsline{toc}{part}{Change~History}
 }
-\g@addto@macro \PrintChanges { \AtEndDocument{ \typeout{^^J
-  ========================================^^J
-  Generate~the~change~list~by~executing^^J
-  \c_space_tl \c_space_tl \c_space_tl \c_space_tl
-   makeindex~-s~gglo.ist~~-o~\jobname.gls~\jobname.glo^^J
-  ========================================^^J
-  }}
-}
+\msg_new:nnn {l3doc} {print-changes-howto}
+  {
+    Generate~the~change~list~by~executing\\
+    \iow_indent:n { makeindex~-s~gglo.ist~-o~\c_job_name_tl .gls~\c_job_name_tl .glo }
+  }
+\tl_gput_right:Nn \PrintChanges { \AtEndDocument{ \msg_info:nn {l3doc} {print-changes-howto} } }
 \bool_if:NTF \g_doc_full_bool {
   \RecordChanges
   \CodelineIndex
@@ -1285,6 +1349,40 @@
   \DisableCrossrefs
   \OnlyDescription
 }
+\cs_new_nopar:Npn\Team{%
+  The~\LaTeX3~Project\thanks{%
+  Frank~Mittelbach,~Denys~Duchier,~Chris~Rowley,~
+  Rainer~Sch\"opf,~Johannes~Braams,~Michael~Downes,~
+  David~Carlisle,~Alan~Jeffrey,~Morten~H\o{}gholm,~Thomas~Lotze,~
+  Javier~Bezos,~Will~Robertson,~Joseph~Wright,~Bruno~Le~Floch}}
+\NewDocumentCommand{\ExplMakeTitle}{mm}
+ {
+   \title
+     {
+        The~\pkg{#1}~package \\ #2
+        \thanks{This~file~describes~v\ExplFileVersion,~
+          last~revised~\ExplFileDate.}
+     }
+   \author{The~\LaTeX3~Project\thanks{E-mail:~
+     \href{mailto:latex-l@listserv.uni-heidelberg.de}
+          {latex-l@listserv.uni-heidelberg.de}}}
+   \date{Released~\ExplFileDate}
+   \maketitle
+ }
+\DeclareDocumentCommand\ie{}{\emph{i.e.}}
+\DeclareDocumentCommand\eg{}{\emph{e.g.}}
+\DeclareDocumentCommand\Ie{}{\emph{I.e.}}
+\DeclareDocumentCommand\Eg{}{\emph{E.g.}}
+\AtBeginDocument
+  {
+    \clist_map_inline:nn
+      {
+        asin, acos, atan, acot,
+        asinh, acosh, atanh, acoth, round, floor, ceil
+      }
+      { \exp_args:Nc \DeclareMathOperator{#1}{#1} }
+  }
+\NewDocumentCommand { \nan } { } { \text { \texttt { nan } } }
 %% 
 %%
 %% End of file `l3doc.cls'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3docstrip.tex b/Master/texmf-dist/tex/latex/l3kernel/l3docstrip.tex
new file mode 100644
index 00000000000..a8d05a96841
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3docstrip.tex
@@ -0,0 +1,106 @@
+%%
+%% This is file `l3docstrip.tex',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% l3docstrip.dtx  (with options: `program')
+%% 
+%% EXPERIMENTAL CODE
+%% 
+%% Do not distribute this file without also distributing the
+%% source files specified above.
+%% 
+%% Do not distribute a modified version of this file.
+%% 
+%% File l3dosctrip.dtx Copyright (C) 2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\def\ExplFileDate{2012/06/08}
+\def\ExplFileName{l3docstrip}
+\def\ExplFileVersion{3787}
+\input docstrip %
+\def\checkOption<#1{%
+  \ifcase
+    \ifx*#10\else \ifx/#11\else
+    \ifx+#12\else \ifx-#13\else
+    \ifx<#14\else \ifx @#15\else 6\fi\fi\fi\fi\fi\fi\relax
+  \expandafter\starOption\or
+  \expandafter\slashOption\or
+  \expandafter\plusOption\or
+  \expandafter\minusOption\or
+  \expandafter\verbOption\or
+  \expandafter\moduleOption\or
+  \expandafter\doOption\fi
+  #1%
+}
+\def\moduleOption @@=#1>#2\endLine{%
+  \maybeMsg{<@@=#1>}%
+  \prepareActiveModule{#1}%
+}
+\begingroup
+  \catcode`\_ = 12 %
+  \long\gdef\prepareActiveModule#1{%
+    \ifx\relax#1\relax
+       \let\replaceModuleInLine\empty
+    \else
+      \def\replaceModuleInLine{%
+        \replaceAllIn\inLine{__@@}{__#1}%
+        \replaceAllIn\inLine{_@@}{__#1}%
+        \replaceAllIn\inLine{@@}{__#1}%
+      }%
+    \fi
+  }
+\endgroup
+\let\replaceModuleInLine\empty
+\long\def\replaceAllIn#1#2#3{%
+  \long\def\tempa##1##2#2{%
+    ##2\qMark\replaceAllInAuxIII#3##1%
+  }%
+  \edef#1{\expandafter\replaceAllInAuxI#1\qMark#2\qStop}%
+}
+\def\replaceAllInAuxI{%
+  \expandafter\replaceAllInAuxII\tempa\replaceAllInAuxI\empty
+}
+\long\def\replaceAllInAuxII#1\qMark#2{#1}
+\long\def\replaceAllInAuxIII#1\qStop{}
+\def\normalLine#1\endLine{%
+  \maybeMsg{.}%
+  \def\inLine{#1}%
+  \replaceModuleInLine
+  \let\do\putline@do
+  \activefiles
+}
+%% 
+%%
+%% End of file `l3docstrip.tex'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3expan.sty b/Master/texmf-dist/tex/latex/l3kernel/l3expan.sty
index d6463b70fac..234f1e45a27 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3expan.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3expan.sty
@@ -46,63 +46,63 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3expan.dtx 3460 2012-02-26 12:16:41Z will $
-  {L3 Experimental argument expansion}
+\GetIdInfo$Id: l3expan.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Argument expansion}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
-\cs_new_nopar:Npn \l_exp_internal_tl { }
-\cs_new:Npn \exp_arg_next:nnn #1#2#3 { #2 \::: { #3 {#1} } }
-\cs_new:Npn \exp_arg_next:Nnn #1#2#3 { #2 \::: { #3 #1 } }
+\__expl_package_check:
+\cs_new_nopar:Npn \l__exp_internal_tl { }
+\cs_new:Npn \__exp_arg_next:nnn #1#2#3 { #2 \::: { #3 {#1} } }
+\cs_new:Npn \__exp_arg_next:Nnn #1#2#3 { #2 \::: { #3 #1 } }
 \cs_new:Npn \::: #1 {#1}
 \cs_new:Npn \::n #1 \::: #2#3 { #1 \::: { #2 {#3} } }
 \cs_new:Npn \::N #1 \::: #2#3 { #1 \::: {#2#3} }
 \cs_new:Npn \::c #1 \::: #2#3
-  { \exp_after:wN \exp_arg_next:Nnn \cs:w #3 \cs_end: {#1} {#2} }
+  { \exp_after:wN \__exp_arg_next:Nnn \cs:w #3 \cs_end: {#1} {#2} }
 \cs_new:Npn \::o #1 \::: #2#3
-  { \exp_after:wN \exp_arg_next:nnn \exp_after:wN {#3} {#1} {#2} }
+  { \exp_after:wN \__exp_arg_next:nnn \exp_after:wN {#3} {#1} {#2} }
 \cs_new:Npn \::f #1 \::: #2#3
   {
-    \exp_after:wN \exp_arg_next:nnn
+    \exp_after:wN \__exp_arg_next:nnn
       \exp_after:wN { \tex_romannumeral:D -`0 #3 }
       {#1} {#2}
   }
 \use:nn { \cs_new_eq:NN \exp_stop_f: } { ~ }
 \cs_new_protected:Npn \::x #1 \::: #2#3
   {
-    \cs_set_nopar:Npx \l_exp_internal_tl { {#3} }
-    \exp_after:wN \exp_arg_next:nnn \l_exp_internal_tl {#1} {#2}
+    \cs_set_nopar:Npx \l__exp_internal_tl { {#3} }
+    \exp_after:wN \__exp_arg_next:nnn \l__exp_internal_tl {#1} {#2}
   }
 \cs_new:Npn \::V #1 \::: #2#3
   {
-    \exp_after:wN \exp_arg_next:nnn
-      \exp_after:wN { \tex_romannumeral:D \exp_eval_register:N #3 }
+    \exp_after:wN \__exp_arg_next:nnn
+      \exp_after:wN { \tex_romannumeral:D \__exp_eval_register:N #3 }
       {#1} {#2}
 }
 \cs_new:Npn \::v # 1\::: #2#3
   {
-    \exp_after:wN \exp_arg_next:nnn
-      \exp_after:wN { \tex_romannumeral:D \exp_eval_register:c {#3} }
+    \exp_after:wN \__exp_arg_next:nnn
+      \exp_after:wN { \tex_romannumeral:D \__exp_eval_register:c {#3} }
       {#1} {#2}
   }
-\cs_new:Npn \exp_eval_register:N #1
+\cs_new:Npn \__exp_eval_register:N #1
   {
     \exp_after:wN \if_meaning:w \exp_not:N #1 #1
       \if_meaning:w \scan_stop: #1
-        \exp_eval_error_msg:w
+        \__exp_eval_error_msg:w
       \fi:
     \else:
       \exp_after:wN \use_i_ii:nnn
     \fi:
     \exp_after:wN \c_zero \tex_the:D #1
   }
-\cs_new:Npn \exp_eval_register:c #1
-  { \exp_after:wN \exp_eval_register:N \cs:w #1 \cs_end: }
-\cs_new:Npn \exp_eval_error_msg:w #1 \tex_the:D #2
+\cs_new:Npn \__exp_eval_register:c #1
+  { \exp_after:wN \__exp_eval_register:N \cs:w #1 \cs_end: }
+\cs_new:Npn \__exp_eval_error_msg:w #1 \tex_the:D #2
   {
       \fi:
     \fi:
-    \msg_expandable_kernel_error:nnn { kernel } { bad-var } {#2}
+    \__msg_kernel_expandable_error:nnn { kernel } { bad-variable } {#2}
     \c_zero
   }
 \cs_new:Npn \exp_args:No #1#2 { \exp_after:wN #1 \exp_after:wN {#2} }
@@ -128,12 +128,12 @@
 \cs_new:Npn \exp_args:Nv #1#2
   {
     \exp_after:wN #1 \exp_after:wN
-      { \tex_romannumeral:D \exp_eval_register:c {#2} }
+      { \tex_romannumeral:D \__exp_eval_register:c {#2} }
   }
 \cs_new:Npn \exp_args:NV #1#2
   {
     \exp_after:wN #1 \exp_after:wN
-      { \tex_romannumeral:D \exp_eval_register:N #2 }
+      { \tex_romannumeral:D \__exp_eval_register:N #2 }
   }
 \cs_new:Npn \exp_args:NNf #1#2#3
   {
@@ -145,13 +145,13 @@
   {
     \exp_after:wN #1
     \exp_after:wN #2
-    \exp_after:wN { \tex_romannumeral:D \exp_eval_register:c {#3} }
+    \exp_after:wN { \tex_romannumeral:D \__exp_eval_register:c {#3} }
   }
 \cs_new:Npn \exp_args:NNV #1#2#3
   {
     \exp_after:wN #1
     \exp_after:wN #2
-    \exp_after:wN { \tex_romannumeral:D \exp_eval_register:N #3 }
+    \exp_after:wN { \tex_romannumeral:D \__exp_eval_register:N #3 }
   }
 \cs_new:Npn \exp_args:Nco #1#2#3
   {
@@ -169,15 +169,15 @@
   {
     \exp_after:wN #1
     \exp_after:wN { \tex_romannumeral:D \exp_after:wN
-      \exp_eval_register:N \exp_after:wN #2 \exp_after:wN }
-    \exp_after:wN { \tex_romannumeral:D \exp_eval_register:N #3 }
+      \__exp_eval_register:N \exp_after:wN #2 \exp_after:wN }
+    \exp_after:wN { \tex_romannumeral:D \__exp_eval_register:N #3 }
   }
 \cs_new:Npn \exp_args:NNNV #1#2#3#4
   {
     \exp_after:wN #1
     \exp_after:wN #2
     \exp_after:wN #3
-    \exp_after:wN { \tex_romannumeral:D \exp_eval_register:N #4 }
+    \exp_after:wN { \tex_romannumeral:D \__exp_eval_register:N #4 }
   }
 \cs_new:Npn \exp_args:NcNc #1#2#3#4
   {
@@ -228,33 +228,33 @@
 \cs_new_protected_nopar:Npn \exp_args:Nccx { \::c \::c \::x \::: }
 \cs_new_protected_nopar:Npn \exp_args:Ncnx { \::c \::n \::x \::: }
 \cs_new_protected_nopar:Npn \exp_args:Noox { \::o \::o \::x \::: }
-\cs_new:Npn \exp_arg_last_unbraced:nn #1#2 { #2#1 }
+\cs_new:Npn \__exp_arg_last_unbraced:nn #1#2 { #2#1 }
 \cs_new:Npn \::f_unbraced \::: #1#2
   {
-    \exp_after:wN \exp_arg_last_unbraced:nn
+    \exp_after:wN \__exp_arg_last_unbraced:nn
       \exp_after:wN { \tex_romannumeral:D -`0 #2 } {#1}
   }
 \cs_new:Npn \::o_unbraced \::: #1#2
-  { \exp_after:wN \exp_arg_last_unbraced:nn \exp_after:wN {#2} {#1} }
+  { \exp_after:wN \__exp_arg_last_unbraced:nn \exp_after:wN {#2} {#1} }
 \cs_new:Npn \::V_unbraced \::: #1#2
   {
-    \exp_after:wN \exp_arg_last_unbraced:nn
-      \exp_after:wN { \tex_romannumeral:D \exp_eval_register:N #2 } {#1}
+    \exp_after:wN \__exp_arg_last_unbraced:nn
+      \exp_after:wN { \tex_romannumeral:D \__exp_eval_register:N #2 } {#1}
   }
 \cs_new:Npn \::v_unbraced \::: #1#2
   {
-    \exp_after:wN \exp_arg_last_unbraced:nn
-      \exp_after:wN { \tex_romannumeral:D \exp_eval_register:c {#2} } {#1}
+    \exp_after:wN \__exp_arg_last_unbraced:nn
+      \exp_after:wN { \tex_romannumeral:D \__exp_eval_register:c {#2} } {#1}
   }
 \cs_new_protected:Npn \::x_unbraced \::: #1#2
   {
-    \cs_set_nopar:Npx \l_exp_internal_tl { \exp_not:n {#1} #2 }
-    \l_exp_internal_tl
+    \cs_set_nopar:Npx \l__exp_internal_tl { \exp_not:n {#1} #2 }
+    \l__exp_internal_tl
   }
 \cs_new:Npn \exp_last_unbraced:NV #1#2
-  { \exp_after:wN #1 \tex_romannumeral:D \exp_eval_register:N #2 }
+  { \exp_after:wN #1 \tex_romannumeral:D \__exp_eval_register:N #2 }
 \cs_new:Npn \exp_last_unbraced:Nv #1#2
-  { \exp_after:wN #1 \tex_romannumeral:D \exp_eval_register:c {#2} }
+  { \exp_after:wN #1 \tex_romannumeral:D \__exp_eval_register:c {#2} }
 \cs_new:Npn \exp_last_unbraced:No #1#2 { \exp_after:wN #1 #2 }
 \cs_new:Npn \exp_last_unbraced:Nf #1#2
   { \exp_after:wN #1 \tex_romannumeral:D -`0 #2 }
@@ -264,13 +264,13 @@
   {
     \exp_after:wN #1
     \cs:w #2 \exp_after:wN \cs_end:
-    \tex_romannumeral:D \exp_eval_register:N #3
+    \tex_romannumeral:D \__exp_eval_register:N #3
   }
 \cs_new:Npn \exp_last_unbraced:NNV #1#2#3
   {
     \exp_after:wN #1
     \exp_after:wN #2
-    \tex_romannumeral:D \exp_eval_register:N #3
+    \tex_romannumeral:D \__exp_eval_register:N #3
   }
 \cs_new:Npn \exp_last_unbraced:NNo #1#2#3
   { \exp_after:wN #1 \exp_after:wN #2 #3 }
@@ -279,7 +279,7 @@
     \exp_after:wN #1
     \exp_after:wN #2
     \exp_after:wN #3
-    \tex_romannumeral:D \exp_eval_register:N #4
+    \tex_romannumeral:D \__exp_eval_register:N #4
   }
 \cs_new:Npn \exp_last_unbraced:NNNo #1#2#3#4
   { \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN #3 #4 }
@@ -289,8 +289,8 @@
 \cs_new_nopar:Npn \exp_last_unbraced:NnNo { \::n \::N \::o_unbraced \::: }
 \cs_new_protected_nopar:Npn \exp_last_unbraced:Nx { \::x_unbraced \::: }
 \cs_new:Npn \exp_last_two_unbraced:Noo #1#2#3
-  { \exp_after:wN \exp_last_two_unbraced_aux:noN \exp_after:wN {#3} {#2} #1 }
-\cs_new:Npn \exp_last_two_unbraced_aux:noN #1#2#3
+  { \exp_after:wN \__exp_last_two_unbraced:noN \exp_after:wN {#3} {#2} #1 }
+\cs_new:Npn \__exp_last_two_unbraced:noN #1#2#3
    { \exp_after:wN #3 #2 #1 }
 \cs_new:Npn \exp_not:o #1 { \etex_unexpanded:D \exp_after:wN {#1} }
 \cs_new:Npn \exp_not:c #1 { \exp_after:wN \exp_not:N \cs:w #1 \cs_end: }
@@ -299,55 +299,90 @@
 \cs_new:Npn \exp_not:V #1
   {
     \etex_unexpanded:D \exp_after:wN
-      { \tex_romannumeral:D \exp_eval_register:N #1 }
+      { \tex_romannumeral:D \__exp_eval_register:N #1 }
   }
 \cs_new:Npn \exp_not:v #1
   {
     \etex_unexpanded:D \exp_after:wN
-      { \tex_romannumeral:D \exp_eval_register:c {#1} }
+      { \tex_romannumeral:D \__exp_eval_register:c {#1} }
   }
-\cs_new_protected:Npn \cs_generate_variant:Nn #1
+\cs_new_protected:Npn \cs_generate_variant:Nn #1#2
   {
-    \chk_if_exist_cs:N #1
-    \cs_generate_variant_aux:N #1
-    \cs_split_function:NN #1 \cs_generate_variant_aux:nnNNn
-    #1
+    \__chk_if_exist_cs:N #1
+    \__cs_generate_variant:N #1
+    \exp_after:wN \__cs_split_function:NN
+    \exp_after:wN #1
+    \exp_after:wN \__cs_generate_variant:nnNN
+    \exp_after:wN #1
+    \etex_detokenize:D {#2} , ? , \q_recursion_stop
   }
-\cs_new_protected:Npn \cs_generate_variant_aux:nnNNn #1#2#3#4#5
-  { \cs_generate_variant_aux:Nnnw #4 {#1}{#2} #5 , ? , \q_recursion_stop }
-\cs_new_protected:Npn \cs_generate_variant_aux:Nnnw #1#2#3#4 ,
+\group_begin:
+  \tex_lccode:D `\Z = `\d \scan_stop:
+  \tex_lccode:D `\? =`\\ \scan_stop:
+  \tex_catcode:D `\P = 12 \scan_stop:
+  \tex_catcode:D `\R = 12 \scan_stop:
+  \tex_catcode:D `\O = 12 \scan_stop:
+  \tex_catcode:D `\T = 12 \scan_stop:
+  \tex_catcode:D `\E = 12 \scan_stop:
+  \tex_catcode:D `\C = 12 \scan_stop:
+  \tex_catcode:D `\Z = 12 \scan_stop:
+\tex_lowercase:D
+  {
+    \group_end:
+    \cs_new_protected:Npn \__cs_generate_variant:N #1
+      {
+        \exp_after:wN \__cs_generate_variant:w
+          \token_to_meaning:N #1
+          \q_mark \cs_new_protected_nopar:Npx
+          ? PROTECTEZ
+          \q_mark \cs_new_nopar:Npx
+          \q_stop
+      }
+    \cs_new_protected:Npn \__cs_generate_variant:w
+        #1 ? PROTECTEZ #2 \q_mark #3 #4 \q_stop
+      {
+        \cs_set_eq:NN \__cs_tmp:w #3
+      }
+  }
+\cs_new_protected:Npn \__cs_generate_variant:nnNN #1#2#3#4
+  { \__cs_generate_variant:Nnnw #4 {#1}{#2} }
+\cs_new_protected:Npn \__cs_generate_variant:Nnnw #1#2#3#4 ,
   {
     \if:w ? #4
       \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
     \fi:
-    \exp_args:NNc \cs_generate_variant_aux:NNn
-      #1
-      {
-        #2 : #4
-        \exp_after:wN \use_i_delimit_by_q_stop:nw
-        \use_none:nnnnnnnnn #4
-        \use_none:nnnnnnnnn
-        \use_none:nnnnnnnn
-        \use_none:nnnnnnn
-        \use_none:nnnnnn
-        \use_none:nnnnn
-        \use_none:nnnn
-        \use_none:nnn
-        \use_none:nn
-        \use_none:n
-        { }
+    \exp_after:wN \__cs_generate_variant:NNn
+    \exp_after:wN #1
+      \cs:w
+        #2 :
+        \__cs_generate_variant_loop:NwN
+          ? #3
+          \q_mark #4 \__cs_generate_variant_loop_end:w
+          \q_mark \__cs_generate_variant_loop_error:wnNNnn
         \q_stop
-        #3
-      }
+      \cs_end:
       {#4}
-    \cs_generate_variant_aux:Nnnw #1 {#2} {#3}
+    \__cs_generate_variant:Nnnw #1 {#2} {#3}
   }
-\cs_new_protected:Npn \cs_generate_variant_aux:NNn #1 #2 #3
+\cs_new:Npn \__cs_generate_variant_loop:NwN #1 #2 \q_mark #3
+  { #3 \__cs_generate_variant_loop:NwN #2 \q_mark }
+\cs_new:Npn \__cs_generate_variant_loop_end:w #1#2 \q_mark #3 \q_stop {#2}
+\cs_new:Npn \__cs_generate_variant_loop_error:wnNNnn
+    #1 \q_stop \cs_end: #2 #3#4#5#6
+  {
+    \cs_end: {#2}
+    \__msg_kernel_error:nnxx { kernel } { variant-too-long }
+      { \tl_to_str:n {#2} } { \token_to_str:N #4 }
+    #3 #4 {#5} {#6}
+  }
+\cs_new_protected:Npn \__cs_generate_variant:NNn #1 #2 #3
   {
     \cs_if_free:NTF #2
       {
-        \cs_tmp:w #2 { \exp_not:c { exp_args:N #3 } \exp_not:N #1 }
-        \cs_generate_internal_variant:n {#3}
+        \group_begin:
+          \__cs_generate_internal_variant:n {#3}
+          \__cs_tmp:w #2 { \exp_not:c { exp_args:N #3 } \exp_not:N #1 }
+        \group_end:
       }
       {
         \iow_log:x
@@ -359,48 +394,35 @@
       }
   }
 \group_begin:
-  \tex_lccode:D `\Z = `\d \scan_stop:
-  \tex_lccode:D `\? =`\\ \scan_stop:
-  \tex_catcode:D `\P = 12 \scan_stop:
-  \tex_catcode:D `\R = 12 \scan_stop:
-  \tex_catcode:D `\O = 12 \scan_stop:
-  \tex_catcode:D `\T = 12 \scan_stop:
-  \tex_catcode:D `\E = 12 \scan_stop:
-  \tex_catcode:D `\C = 12 \scan_stop:
-  \tex_catcode:D `\Z = 12 \scan_stop:
+  \tex_catcode:D `\X = 12 \scan_stop:
+  \tex_lccode:D `\N = `\N \scan_stop:
 \tex_lowercase:D
   {
     \group_end:
-    \cs_new_protected:Npn \cs_generate_variant_aux:N #1
+    \cs_new_protected:Npn \__cs_generate_internal_variant:n #1
       {
-        \exp_after:wN \cs_generate_variant_aux:w
-          \token_to_meaning:N #1
-          \q_mark \cs_new_protected_nopar:Npx
-          ? PROTECTEZ
-          \q_mark \cs_new_nopar:Npx
-          \q_stop
-      }
-    \cs_new_protected:Npn \cs_generate_variant_aux:w
-        #1 ? PROTECTEZ #2 \q_mark #3 #4 \q_stop
-      {
-        \cs_set_eq:NN \cs_tmp:w #3
+        \__cs_generate_internal_variant:wwnNwnn
+          #1 \q_mark
+            { \cs_set_eq:NN \__cs_tmp:w \cs_new_protected_nopar:Npx }
+            \cs_new_protected_nopar:cpx
+          X \q_mark
+            { }
+            \cs_new_nopar:cpx
+        \q_stop
+          { exp_args:N #1 }
+          { \__cs_generate_internal_variant_loop:n #1 { : \use_i:nn } }
       }
-  }
-\cs_new_protected:Npn \cs_generate_internal_variant:n #1
-  {
-    \cs_if_free:cT { exp_args:N #1 }
+    \cs_new_protected:Npn \__cs_generate_internal_variant:wwnNwnn
+        #1 X #2 \q_mark #3 #4 #5 \q_stop #6 #7
       {
-        \cs_new:cpx { exp_args:N #1 }
-          { \cs_generate_internal_variant_aux:N #1 : }
+        #3
+        \cs_if_free:cT {#6} { #4 {#6} {#7} }
       }
   }
-\cs_new:Npn \cs_generate_internal_variant_aux:N #1
+\cs_new:Npn \__cs_generate_internal_variant_loop:n #1
   {
-    \exp_not:c { :: #1 }
-    \if_meaning:w : #1
-      \exp_after:wN \use_none:n
-    \fi:
-    \cs_generate_internal_variant_aux:N
+    \exp_after:wN \exp_not:N \cs:w :: #1 \cs_end:
+    \__cs_generate_internal_variant_loop:n
   }
 \cs_generate_variant:Nn \str_if_eq_p:nn {  V ,  o }
 \cs_generate_variant:Nn \str_if_eq_p:nn { nV , no , VV }
@@ -410,6 +432,7 @@
 \cs_generate_variant:Nn \str_if_eq:nnF  { nV , no , VV }
 \cs_generate_variant:Nn \str_if_eq:nnTF {  V ,  o }
 \cs_generate_variant:Nn \str_if_eq:nnTF { nV , no , VV }
+\cs_generate_variant:Nn \str_case:nnn { o }
 %% 
 %%
 %% End of file `l3expan.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3file.sty b/Master/texmf-dist/tex/latex/l3kernel/l3file.sty
index a86de65f88f..e0642b967a3 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3file.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3file.sty
@@ -46,121 +46,142 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3file.dtx 3520 2012-03-09 19:34:07Z joseph $
-  {L3 Experimental file and I/O operations}
+\GetIdInfo$Id: l3file.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 File and I/O operations}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 \tl_new:N \g_file_current_name_tl
 \tl_gset_eq:NN \g_file_current_name_tl \@currname
-\seq_new:N \g_file_stack_seq
-\seq_new:N \g_file_record_seq
-\tl_new:N \l_file_internal_name_tl
-\seq_new:N \l_file_search_path_seq
-\seq_new:N \l_file_internal_saved_path_seq
-\seq_new:N \l_file_internal_seq
-\cs_new_protected:Npn \file_name_sanitize:nn #1#2
+\seq_new:N \g__file_stack_seq
+\seq_new:N \g__file_record_seq
+\tl_new:N \l__file_internal_name_tl
+\seq_new:N \l__file_search_path_seq
+\seq_new:N \l__file_saved_search_path_seq
+\seq_new:N \l__file_internal_seq
+\cs_new_protected:Npn \__file_name_sanitize:nn #1#2
   {
     \group_begin:
       \seq_map_inline:Nn \l_char_active_seq
         { \cs_set_nopar:Npx ##1 { \token_to_str:N ##1 } }
-      \tl_set:Nx \l_file_internal_name_tl {#1}
-      \tl_set:Nx \l_file_internal_name_tl
-        { \tl_to_str:N \l_file_internal_name_tl }
-      \tl_if_in:NnTF \l_file_internal_name_tl { ~ }
+      \tl_set:Nx \l__file_internal_name_tl {#1}
+      \tl_set:Nx \l__file_internal_name_tl
+        { \tl_to_str:N \l__file_internal_name_tl }
+      \tl_if_in:NnT \l__file_internal_name_tl { ~ }
         {
-          \msg_kernel_error:nnx { file } { space-in-file-name }
-            { \l_file_internal_name_tl }
+          \__msg_kernel_error:nnx { kernel } { space-in-file-name }
+            { \l__file_internal_name_tl }
+          \tl_remove_all:Nn \l__file_internal_name_tl { ~ }
         }
       \use:x
         {
           \group_end:
-          \exp_not:n {#2} { \l_file_internal_name_tl }
+          \exp_not:n {#2} { \l__file_internal_name_tl }
         }
   }
 \cs_new_protected:Npn \file_add_path:nN #1
-  { \file_name_sanitize:nn {#1} { \file_add_path_aux:nN } }
-\cs_new_protected:Npn \file_add_path_aux:nN #1#2
+  { \__file_name_sanitize:nn {#1} { \__file_add_path:nN } }
+\cs_new_protected:Npn \__file_add_path:nN #1#2
   {
-    \ior_open_unsafe:Nn \g_file_internal_ior {#1}
-    \ior_if_eof:NTF \g_file_internal_ior
-      { \file_add_path_search:nN {#1} #2 }
-      {
-        \ior_close:N \g_file_internal_ior
-        \tl_set:Nn #2 {#1}
-      }
+    \__ior_open:Nn \g__file_internal_ior {#1}
+    \ior_if_eof:NTF \g__file_internal_ior
+      { \__file_add_path_search:nN {#1} #2 }
+      { \tl_set:Nn #2 {#1} }
+    \ior_close:N \g__file_internal_ior
   }
-\cs_new_protected:Npn \file_add_path_search:nN #1#2
+\cs_new_protected:Npn \__file_add_path_search:nN #1#2
   {
-    \tl_set:Nn #2 { \q_no_value }
+    \tl_set:Nn #2 { \q_no_value  }
     \cs_if_exist:NT \input@path
       {
-        \seq_set_eq:NN \l_file_internal_saved_path_seq \l_file_search_path_seq
-        \seq_set_from_clist:NN \l_file_internal_seq \input@path
-        \seq_concat:NNN \l_file_search_path_seq
-          \l_file_search_path_seq \l_file_internal_seq
+        \seq_set_eq:NN \l__file_saved_search_path_seq \l__file_search_path_seq
+        \seq_set_split:NnV \l__file_internal_seq { , } \input@path
+        \seq_concat:NNN \l__file_search_path_seq
+          \l__file_search_path_seq \l__file_internal_seq
       }
-    \seq_map_inline:Nn \l_file_search_path_seq
+    \seq_map_inline:Nn \l__file_search_path_seq
       {
-        \ior_open_unsafe:Nn \g_file_internal_ior { ##1 #1 }
-        \ior_if_eof:NF \g_file_internal_ior
+        \__ior_open:Nn \g__file_internal_ior { ##1 #1 }
+        \ior_if_eof:NF \g__file_internal_ior
           {
             \tl_set:Nx #2 { ##1 #1 }
             \seq_map_break:
           }
       }
     \cs_if_exist:NT \input@path
-      { \seq_set_eq:NN \l_file_search_path_seq \l_file_internal_saved_path_seq }
-    \ior_close:N \g_file_internal_ior
+      { \seq_set_eq:NN \l__file_search_path_seq \l__file_saved_search_path_seq }
   }
 \prg_new_protected_conditional:Npnn \file_if_exist:n #1 { T , F , TF }
   {
-    \file_add_path:nN {#1} \l_file_internal_name_tl
-    \quark_if_no_value:NTF \l_file_internal_name_tl
+    \file_add_path:nN {#1} \l__file_internal_name_tl
+    \quark_if_no_value:NTF \l__file_internal_name_tl
       { \prg_return_false: }
       { \prg_return_true: }
   }
 \cs_new_protected:Npn \file_input:n #1
   {
-    \file_add_path:nN {#1} \l_file_internal_name_tl
-    \quark_if_no_value:NTF \l_file_internal_name_tl
-      { \file_name_sanitize:nn {#1} { \file_input_error:n } }
-      { \file_input_aux:V \l_file_internal_name_tl }
+    \file_add_path:nN {#1} \l__file_internal_name_tl
+    \quark_if_no_value:NTF \l__file_internal_name_tl
+      {
+        \__file_name_sanitize:nn {#1}
+          { \__msg_kernel_error:nnx { kernel } { file-not-found } }
+      }
+      { \__file_input:V \l__file_internal_name_tl }
   }
-\cs_new_protected:Npn \file_input_aux:n #1
+\cs_new_protected:Npn \__file_input:n #1
   {
-    \@addtofilelist {#1}
-    \seq_gpush:Nn \g_file_stack_seq \g_file_current_name_tl
+    \quark_if_nil:oTF { \__file_input_aux:w #1 . \q_nil . \q_stop }
+      { \__file_input_aux:o { \tl_to_str:n { #1 .tex } } }
+      { \__file_input_aux:n {#1} }
+  }
+\cs_generate_variant:Nn \__file_input:n { V }
+\cs_new:Npn \__file_input_aux:w #1 . #2 . #3 \q_stop { #2 }
+\cs_new_protected:Npn \__file_input_aux:n #1
+  {
+    \clist_if_exist:NTF \@filelist
+      { \@addtofilelist {#1} }
+      { \seq_gput_right:Nn \g__file_record_seq {#1} }
+    \seq_gpush:Nn \g__file_stack_seq \g_file_current_name_tl
     \tl_gset:Nn \g_file_current_name_tl {#1}
     \tex_input:D #1 \c_space_tl
-    \seq_gpop:NN \g_file_stack_seq \g_file_current_name_tl
+    \seq_gpop:NN \g__file_stack_seq \g_file_current_name_tl
   }
-\cs_generate_variant:Nn \file_input_aux:n { V }
-\cs_new_protected:Npn \file_input_error:n #1
-  { \msg_kernel_error:nnx { file } { file-not-found } {#1} }
+\cs_generate_variant:Nn \__file_input_aux:n { o }
 \cs_new_protected:Npn \file_path_include:n #1
+  { \__file_name_sanitize:nn {#1} { \__file_path_include:n } }
+\cs_new_protected:Npn \__file_path_include:n #1
   {
-    \seq_if_in:NnF  \l_file_search_path_seq {#1}
-      { \seq_put_right:Nn \l_file_search_path_seq {#1} }
+    \seq_if_in:NnF \l__file_search_path_seq {#1}
+      { \seq_put_right:Nn \l__file_search_path_seq {#1} }
   }
 \cs_new_protected:Npn \file_path_remove:n #1
-  { \seq_remove_all:Nn \l_file_search_path_seq {#1} }
+  {
+    \__file_name_sanitize:nn {#1}
+      { \seq_remove_all:Nn \l__file_search_path_seq }
+  }
 \cs_new_protected_nopar:Npn \file_list:
   {
-    \seq_remove_duplicates:N \g_file_record_seq
+    \seq_set_eq:NN \l__file_internal_seq \g__file_record_seq
+    \clist_if_exist:NT \@filelist
+      {
+        \clist_map_inline:Nn \@filelist
+          {
+            \seq_put_right:No \l__file_internal_seq
+              { \tl_to_str:n {##1} }
+          }
+      }
+    \seq_remove_duplicates:N \l__file_internal_seq
     \iow_log:n { *~File~List~* }
-    \seq_map_inline:Nn \g_file_record_seq { \iow_log:n {##1} }
+    \seq_map_inline:Nn \l__file_internal_seq { \iow_log:n {##1} }
     \iow_log:n { ************* }
   }
 \AtBeginDocument
   {
-    \seq_set_from_clist:NN \l_file_internal_seq \@filelist
-    \seq_gconcat:NNN \g_file_record_seq \g_file_record_seq \l_file_internal_seq
+    \clist_map_inline:Nn \@filelist
+      { \seq_gput_right:No \g__file_record_seq { \tl_to_str:n {#1} } }
   }
 \cs_new_eq:NN \c_term_ior \c_sixteen
-\cs_new_eq:NN \c_log_iow  \c_minus_one
-\cs_new_eq:NN \c_term_iow \c_sixteen
-\tl_const:Nn \c_iow_streams_tl
+\tl_const:Nn \c__ior_streams_tl
   {
     \c_zero
     \c_one
@@ -179,232 +200,243 @@
     \c_fourteen
     \c_fifteen
   }
-\cs_new_eq:NN \c_ior_streams_tl \c_iow_streams_tl
-\prop_new:N \g_iow_streams_prop
-\prop_new:N \g_ior_streams_prop
-\prop_put:Nnn \g_iow_streams_prop { 0 } { LaTeX2e~reserved }
-\prop_put:Nnn \g_iow_streams_prop { 1 } { LaTeX2e~reserved }
-\prop_put:Nnn \g_iow_streams_prop { 2 } { LaTeX2e~reserved }
-\prop_put:Nnn \g_ior_streams_prop { 0 } { LaTeX2e~reserved }
-\int_new:N \l_iow_stream_int
-\cs_new_eq:NN \l_ior_stream_int \l_iow_stream_int
-\cs_set_eq:NN \iow_raw_new:N \newwrite
-\cs_set_eq:NN \ior_raw_new:N \newread
-\cs_generate_variant:Nn \ior_raw_new:N { c }
-\cs_generate_variant:Nn \iow_raw_new:N { c }
+\prop_new:N \g__ior_streams_prop
+\prop_put:Nnn \g__ior_streams_prop { 0 } { LaTeX2e~reserved }
+\int_new:N \l__ior_stream_int
+\cs_set_eq:NN \__ior_new:N \newread
+\cs_generate_variant:Nn \__ior_new:N { c }
 \cs_new_protected:Npn \ior_new:N #1 { \cs_new_eq:NN #1 \c_term_ior }
 \cs_generate_variant:Nn \ior_new:N { c }
-\cs_new_protected:Npn \iow_new:N #1 { \cs_new_eq:NN #1 \c_term_iow }
-\cs_generate_variant:Nn \iow_new:N { c }
-\ior_new:N \g_file_internal_ior
+\ior_new:N \g__file_internal_ior
 \cs_new_protected:Npn \ior_open:Nn #1#2
-  { \file_name_sanitize:nn {#2} { \ior_open_aux:Nn #1 } }
+  { \__file_name_sanitize:nn {#2} { \__ior_open_aux:Nn #1 } }
 \cs_generate_variant:Nn \ior_open:Nn { c }
-\cs_new_protected:Npn \iow_open:Nn #1#2
-  { \file_name_sanitize:nn {#2} { \iow_open_unsafe:Nn #1 } }
-\cs_generate_variant:Nn \iow_open:Nn { c }
-\cs_new_protected:Npn \ior_open_aux:Nn #1#2
+\cs_new_protected:Npn \__ior_open_aux:Nn #1#2
   {
-    \file_add_path:nN {#2} \l_file_internal_name_tl
-    \quark_if_no_value:NTF \l_file_internal_name_tl
-      { \file_input_error:n {#2} }
-      { \ior_open_unsafe:No #1 \l_file_internal_name_tl }
+    \file_add_path:nN {#2} \l__file_internal_name_tl
+    \quark_if_no_value:NTF \l__file_internal_name_tl
+      { \__msg_kernel_error:nnx { kernel } { file-not-found } {#2} }
+      { \__ior_open:No #1 \l__file_internal_name_tl }
   }
 \prg_new_protected_conditional:Npnn \ior_open:Nn #1#2 { T , F , TF }
-  { \file_name_sanitize:nn {#2} { \ior_open_aux:NnTF #1 } }
-\cs_new_protected:Npn \ior_open_aux:NnTF #1#2
+  { \__file_name_sanitize:nn {#2} { \__ior_open_aux:NnTF #1 } }
+\cs_new_protected:Npn \__ior_open_aux:NnTF #1#2
   {
-    \file_add_path:nN {#2} \l_file_internal_name_tl
-    \quark_if_no_value:NTF \l_file_internal_name_tl
+    \file_add_path:nN {#2} \l__file_internal_name_tl
+    \quark_if_no_value:NTF \l__file_internal_name_tl
       { \prg_return_false: }
       {
-        \ior_open_unsafe:No #1 \l_file_internal_name_tl
+        \__ior_open:No #1 \l__file_internal_name_tl
         \prg_return_true:
       }
   }
 \cs_generate_variant:Nn \ior_open:NnT  { c }
 \cs_generate_variant:Nn \ior_open:NnF  { c }
 \cs_generate_variant:Nn \ior_open:NnTF { c }
-\cs_new_protected:Npn \ior_open_unsafe:Nn #1#2
+\cs_new_protected:Npn \__ior_open:Nn #1#2
   {
     \ior_close:N #1
-    \int_set:Nn \l_ior_stream_int \c_sixteen
-    \tl_map_function:NN \c_ior_streams_tl \ior_alloc_read:n
-    \int_compare:nNnTF \l_ior_stream_int = \c_sixteen
-      { \msg_kernel_fatal:nn { ior } { streams-exhausted } }
+    \int_set_eq:NN \l__ior_stream_int \c_sixteen
+    \tl_map_function:NN \c__ior_streams_tl \__ior_alloc:n
+    \int_compare:nNnTF \l__ior_stream_int = \c_sixteen
+      { \__msg_kernel_fatal:nn { kernel } { input-streams-exhausted } }
       {
-        \ior_stream_alloc:N #1
-        \prop_gput:NVn \g_ior_streams_prop \l_ior_stream_int {#2}
+        \__ior_alloc:N #1
+        \prop_gput:NVn \g__ior_streams_prop \l__ior_stream_int {#2}
         \tex_openin:D #1#2 \scan_stop:
       }
   }
-\cs_generate_variant:Nn \ior_open_unsafe:Nn { No }
-\cs_new_protected:Npn \iow_open_unsafe:Nn #1#2
+\cs_generate_variant:Nn \__ior_open:Nn { No }
+\cs_new_protected:Npn \__ior_alloc:n #1
   {
-    \iow_close:N #1
-    \int_set:Nn \l_iow_stream_int \c_sixteen
-    \tl_map_function:NN \c_iow_streams_tl \iow_alloc_write:n
-    \int_compare:nNnTF \l_iow_stream_int = \c_sixteen
-      { \msg_kernel_fatal:nn { iow } { streams-exhausted } }
+    \prop_if_in:NnF \g__ior_streams_prop {#1}
       {
-        \iow_stream_alloc:N #1
-        \prop_gput:NVn \g_iow_streams_prop \l_iow_stream_int {#2}
-        \tex_immediate:D \tex_openout:D #1#2 \scan_stop:
+        \int_set:Nn \l__ior_stream_int {#1}
+        \tl_map_break:
       }
   }
-\cs_new_protected:Npn \iow_alloc_write:n #1
+\ior_new:N \g__ior_internal_ior
+\cs_new_protected:Npn \__ior_alloc:N #1
   {
-    \prop_if_in:NnF \g_iow_streams_prop {#1}
+    \cs_if_exist:cF { g_ior_ \int_use:N \l__ior_stream_int _ior }
       {
-        \int_set:Nn \l_iow_stream_int {#1}
-        \tl_map_break:
+        \__ior_alloc:
+        \int_compare:nNnT \l__ior_stream_int = \c_sixteen
+          {
+            \__ior_new:N \g__ior_internal_ior
+            \int_set:Nn \l__ior_stream_int { \g__ior_internal_ior }
+            \cs_gset_eq:cN
+              { g_ior_ \int_use:N \l__ior_stream_int _ior } \g__ior_internal_ior
+          }
       }
+    \cs_gset_eq:Nc #1 { g_ior_ \int_use:N \l__ior_stream_int _ior }
   }
-\cs_new_protected:Npn \ior_alloc_read:n #1
+\cs_new_protected_nopar:Npn \__ior_alloc:
   {
-    \prop_if_in:NnF \g_iow_streams_prop {#1}
+    \int_incr:N \l__ior_stream_int
+    \int_compare:nNnT \l__ior_stream_int < \c_sixteen
       {
-        \int_set:Nn \l_ior_stream_int {#1}
-        \tl_map_break:
+        \cs_if_exist:cTF { g_ior_ \int_use:N \l__ior_stream_int _ior }
+          {
+            \prop_if_in:NVT \g__ior_streams_prop \l__ior_stream_int
+              { \__ior_alloc: }
+          }
+          { \__ior_alloc: }
       }
   }
-\iow_new:N \g_iow_internal_iow
-\ior_new:N \g_ior_internal_ior
-\cs_new_protected:Npn \iow_stream_alloc:N #1
+\cs_new_protected:Npn \ior_close:N #1
   {
-    \cs_if_exist:cF { g_iow_ \int_use:N \l_iow_stream_int _iow }
+    \__chk_if_exist_cs:N #1
+    \int_compare:nNnF #1 < \c_zero
       {
-        \iow_stream_alloc_aux:
-        \int_compare:nNnT \l_iow_stream_int = \c_sixteen
+        \int_compare:nNnF #1 > \c_fifteen
           {
-            \iow_raw_new:N \g_iow_internal_iow
-            \int_set:Nn \l_iow_stream_int { \g_iow_internal_iow }
-            \cs_gset_eq:cN
-              { g_iow_ \int_use:N \l_iow_stream_int _iow } \g_iow_internal_iow
+            \tex_closein:D #1
+            \prop_gremove:NV \g__ior_streams_prop #1
+            \cs_gset_eq:NN #1 \c_term_ior
           }
       }
-    \cs_gset_eq:Nc #1 { g_iow_ \int_use:N \l_iow_stream_int _iow }
   }
-\cs_new_protected_nopar:Npn \iow_stream_alloc_aux:
+\cs_generate_variant:Nn \ior_close:N { c }
+\cs_new_protected_nopar:Npn \ior_list_streams:
+  { \__ior_list_streams:Nn \g__ior_streams_prop { input } }
+\cs_new_protected:Npn \__ior_list_streams:Nn #1#2
   {
-    \int_incr:N \l_iow_stream_int
-    \int_compare:nNnT \l_iow_stream_int < \c_sixteen
+    \__msg_term:nnn { LaTeX / kernel }
+      { \prop_if_empty:NTF #1 { show-no-stream } { show-open-streams } }
+      {#2}
+    \__msg_show_variable:x
+      { \prop_map_function:NN #1 \__msg_show_item_unbraced:nn }
+  }
+\cs_new_eq:NN \if_eof:w \tex_ifeof:D
+\prg_new_conditional:Nnn \ior_if_eof:N { p , T , F , TF }
+  {
+    \cs_if_exist:NTF #1
       {
-        \cs_if_exist:cTF { g_iow_ \int_use:N \l_iow_stream_int _iow }
-          {
-            \prop_if_in:NVT \g_iow_streams_prop \l_iow_stream_int
-              { \iow_stream_alloc_aux: }
-          }
-          { \iow_stream_alloc_aux: }
+        \if_int_compare:w #1 = \c_sixteen
+          \prg_return_true:
+        \else:
+          \if_eof:w #1
+            \prg_return_true:
+          \else:
+            \prg_return_false:
+          \fi:
+        \fi:
       }
+      { \prg_return_true: }
   }
-\cs_new_protected:Npn \ior_stream_alloc:N #1
+\cs_new_protected:Npn \ior_get:NN #1#2
+  { \tex_read:D #1 to #2 }
+\cs_new_protected:Npn \ior_get_str:NN #1#2
+  { \etex_readline:D #1 to #2 }
+\cs_new_eq:NN \c_log_iow  \c_minus_one
+\cs_new_eq:NN \c_term_iow \c_sixteen
+\cs_new_eq:NN \c__iow_streams_tl \c__ior_streams_tl
+\prop_new:N \g__iow_streams_prop
+\prop_put:Nnn \g__iow_streams_prop { 0 } { LaTeX2e~reserved }
+\prop_put:Nnn \g__iow_streams_prop { 1 } { LaTeX2e~reserved }
+\prop_put:Nnn \g__iow_streams_prop { 2 } { LaTeX2e~reserved }
+\cs_new_eq:NN \l__iow_stream_int \l__ior_stream_int
+\cs_set_eq:NN \__iow_new:N \newwrite
+\cs_generate_variant:Nn \__iow_new:N { c }
+\cs_new_protected:Npn \iow_new:N #1 { \cs_new_eq:NN #1 \c_term_iow }
+\cs_generate_variant:Nn \iow_new:N { c }
+\cs_new_protected:Npn \iow_open:Nn #1#2
+  { \__file_name_sanitize:nn {#2} { \__iow_open:Nn #1 } }
+\cs_generate_variant:Nn \iow_open:Nn { c }
+\cs_new_protected:Npn \__iow_open:Nn #1#2
   {
-    \cs_if_exist:cF { g_ior_ \int_use:N \l_ior_stream_int _ior }
+    \iow_close:N #1
+    \int_set_eq:NN \l__iow_stream_int \c_sixteen
+    \tl_map_function:NN \c__iow_streams_tl \__iow_alloc:n
+    \int_compare:nNnTF \l__iow_stream_int = \c_sixteen
+      { \__msg_kernel_fatal:nn { kernel } { output-streams-exhausted } }
       {
-        \ior_stream_alloc_aux:
-        \int_compare:nNnT \l_ior_stream_int = \c_sixteen
-          {
-            \ior_raw_new:N \g_ior_internal_ior
-            \int_set:Nn \l_ior_stream_int { \g_ior_internal_ior }
-            \cs_gset_eq:cN
-              { g_ior_ \int_use:N \l_iow_stream_int _ior } \g_ior_internal_ior
-          }
+        \__iow_alloc:N #1
+        \prop_gput:NVn \g__iow_streams_prop \l__iow_stream_int {#2}
+        \tex_immediate:D \tex_openout:D #1#2 \scan_stop:
+      }
+  }
+\cs_new_protected:Npn \__iow_alloc:n #1
+  {
+    \prop_if_in:NnF \g__iow_streams_prop {#1}
+      {
+        \int_set:Nn \l__iow_stream_int {#1}
+        \tl_map_break:
       }
-    \cs_gset_eq:Nc #1 { g_ior_ \int_use:N \l_ior_stream_int _ior }
   }
-\cs_new_protected_nopar:Npn \ior_stream_alloc_aux:
+\iow_new:N \g__iow_internal_iow
+\cs_new_protected:Npn \__iow_alloc:N #1
   {
-    \int_incr:N \l_ior_stream_int
-    \int_compare:nNnT \l_ior_stream_int < \c_sixteen
+    \cs_if_exist:cF { g_iow_ \int_use:N \l__iow_stream_int _iow }
       {
-        \cs_if_exist:cTF { g_ior_ \int_use:N \l_ior_stream_int _ior }
+        \__iow_alloc:
+        \int_compare:nNnT \l__iow_stream_int = \c_sixteen
           {
-            \prop_if_in:NVT \g_ior_streams_prop \l_ior_stream_int
-              { \ior_stream_alloc_aux: }
+            \__iow_new:N \g__iow_internal_iow
+            \int_set:Nn \l__iow_stream_int { \g__iow_internal_iow }
+            \cs_gset_eq:cN
+              { g_iow_ \int_use:N \l__iow_stream_int _iow } \g__iow_internal_iow
           }
-          { \ior_stream_alloc_aux: }
       }
+    \cs_gset_eq:Nc #1 { g_iow_ \int_use:N \l__iow_stream_int _iow }
   }
-\cs_new_protected:Npn \ior_close:N #1
+\cs_new_protected_nopar:Npn \__iow_alloc:
   {
-    \cs_if_exist:NT #1
+    \int_incr:N \l__iow_stream_int
+    \int_compare:nNnT \l__iow_stream_int < \c_sixteen
       {
-        \int_compare:nNnF #1 = \c_minus_one
+        \cs_if_exist:cTF { g_iow_ \int_use:N \l__iow_stream_int _iow }
           {
-            \int_compare:nNnF #1 = \c_sixteen
-              { \tex_closein:D #1 }
-            \prop_gdel:NV \g_ior_streams_prop #1
-            \cs_gset_eq:NN #1 \c_term_ior
+            \prop_if_in:NVT \g__iow_streams_prop \l__iow_stream_int
+              { \__iow_alloc: }
           }
+          { \__iow_alloc: }
       }
   }
 \cs_new_protected:Npn \iow_close:N #1
   {
-    \cs_if_exist:NT #1
+    \__chk_if_exist_cs:N #1
+    \int_compare:nNnF #1 < \c_zero
       {
-        \int_compare:nNnF #1 = \c_minus_one
+        \int_compare:nNnF #1 > \c_fifteen
           {
-            \int_compare:nNnF #1 = \c_sixteen
-              { \tex_closein:D #1 }
-            \prop_gdel:NV \g_iow_streams_prop #1
+            \tex_closeout:D #1
+            \prop_gremove:NV \g__iow_streams_prop #1
             \cs_gset_eq:NN #1 \c_term_iow
           }
       }
   }
-\cs_generate_variant:Nn \ior_close:N { c }
 \cs_generate_variant:Nn \iow_close:N { c }
-\cs_new_protected_nopar:Npn \ior_list_streams:
-  { \ior_list_streams_aux:Nn \g_ior_streams_prop { ior } }
 \cs_new_protected_nopar:Npn \iow_list_streams:
-  { \ior_list_streams_aux:Nn \g_iow_streams_prop { iow } }
-\cs_new_protected:Npn \ior_list_streams_aux:Nn #1#2
-  {
-    \msg_aux_use:nn { LaTeX / #2 }
-      { \prop_if_empty:NTF #1 { show-no-stream } { show-open-streams } }
-    \msg_aux_show:x
-      { \prop_map_function:NN #1 \msg_aux_show_unbraced:nn }
-  }
-\msg_kernel_new:nnnn { iow } { streams-exhausted }
-  { Output~streams~exhausted }
-  {
-    TeX~can~only~open~up~to~16~output~streams~at~one~time.\\
-    All~16 are currently~in~use,~and~something~wanted~to~open
-    another~one.
-  }
-\msg_kernel_new:nnnn { ior } { streams-exhausted }
-  { Input~streams~exhausted }
-  {
-    TeX~can~only~open~up~to~16~input~streams~at~one~time.\\
-    All~16 are currently~in~use,~and~something~wanted~to~open
-    another~one.
-  }
+  { \__iow_list_streams:Nn \g__iow_streams_prop { output } }
+\cs_new_eq:NN \__iow_list_streams:Nn \__ior_list_streams:Nn
 \cs_new_eq:NN \iow_shipout_x:Nn \tex_write:D
 \cs_generate_variant:Nn \iow_shipout_x:Nn { Nx }
 \cs_new_protected:Npn \iow_shipout:Nn #1#2
   { \iow_shipout_x:Nn #1 { \exp_not:n {#2} } }
 \cs_generate_variant:Nn \iow_shipout:Nn { Nx }
-\cs_new_protected_nopar:Npn \iow_now:Nx { \tex_immediate:D \iow_shipout_x:Nn }
 \cs_new_protected:Npn \iow_now:Nn #1#2
-  { \iow_now:Nx #1 { \exp_not:n {#2} } }
+  { \tex_immediate:D \iow_shipout_x:Nn #1 { \exp_not:n {#2} } }
+\cs_generate_variant:Nn \iow_now:Nn { Nx }
 \cs_set_protected_nopar:Npn \iow_log:x  { \iow_now:Nx \c_log_iow  }
 \cs_new_protected_nopar:Npn \iow_log:n  { \iow_now:Nn \c_log_iow  }
 \cs_set_protected_nopar:Npn \iow_term:x { \iow_now:Nx \c_term_iow }
 \cs_new_protected_nopar:Npn \iow_term:n { \iow_now:Nn \c_term_iow }
 \cs_new_nopar:Npn \iow_newline: { ^^J }
 \cs_new_eq:NN \iow_char:N \cs_to_str:N
-\int_new:N  \l_iow_line_length_int
-\int_set:Nn \l_iow_line_length_int { 78 }
-\int_new:N \l_iow_target_length_int
-\int_new:N \l_iow_current_line_int
-\int_new:N \l_iow_current_word_int
-\int_new:N \l_iow_current_indentation_int
-\tl_new:N \l_iow_current_line_tl
-\tl_new:N \l_iow_current_word_tl
-\tl_new:N \l_iow_current_indentation_tl
-\tl_new:N \l_iow_wrap_tl
-\tl_new:N \l_iow_wrapped_tl
-\bool_new:N \l_iow_line_start_bool
+\int_new:N  \l_iow_line_count_int
+\int_set:Nn \l_iow_line_count_int { 78 }
+\int_new:N \l__iow_target_count_int
+\int_new:N \l__iow_current_line_int
+\int_new:N \l__iow_current_word_int
+\int_new:N \l__iow_current_indentation_int
+\tl_new:N \l__iow_current_line_tl
+\tl_new:N \l__iow_current_word_tl
+\tl_new:N \l__iow_current_indentation_tl
+\tl_new:N \l__iow_wrap_tl
+\tl_new:N \l__iow_newline_tl
+\bool_new:N \l__iow_line_start_bool
 \group_begin:
   \char_set_catcode_other:N \*
   \char_set_lccode:nn {`\*} {`\ }
@@ -412,41 +444,31 @@
 \group_end:
 \group_begin:
   \int_set_eq:NN \tex_escapechar:D \c_minus_one
-  \tl_const:Nx \c_iow_wrap_marker_tl
+  \tl_const:Nx \c__iow_wrap_marker_tl
     { \tl_to_str:n { \^^I \^^O \^^W \^^_ \^^W \^^R \^^A \^^P } }
-  \cs_set:Npn \iow_wrap_new_marker:n #1
-    {
-      \tl_const:cx { c_iow_wrap_ #1 _marker_tl }
-        {
-          \c_catcode_other_space_tl
-          \c_iow_wrap_marker_tl
-          \c_catcode_other_space_tl
-          #1
-          \c_catcode_other_space_tl
-        }
-    }
-  \iow_wrap_new_marker:n { end }
-  \iow_wrap_new_marker:n { newline }
-  \iow_wrap_new_marker:n { indent }
-  \iow_wrap_new_marker:n { unindent }
 \group_end:
+\tl_map_inline:nn
+  { { end } { newline } { indent } { unindent } }
+  {
+    \tl_const:cx { c__iow_wrap_ #1 _marker_tl }
+      {
+        \c_catcode_other_space_tl
+        \c__iow_wrap_marker_tl
+        \c_catcode_other_space_tl
+        #1
+        \c_catcode_other_space_tl
+      }
+  }
 \cs_new_protected:Npn \iow_indent:n #1 { }
-\cs_new:Npx \iow_indent_expandable:n #1
+\cs_new:Npx \__iow_indent:n #1
   {
-    \c_iow_wrap_indent_marker_tl
+    \c__iow_wrap_indent_marker_tl
     #1
-    \c_iow_wrap_unindent_marker_tl
+    \c__iow_wrap_unindent_marker_tl
   }
-\cs_new_protected:Npn \iow_wrap:xnnnN #1#2#3#4#5
+\cs_new_protected:Npn \iow_wrap:nnnN #1#2#3#4
   {
     \group_begin:
-      \int_set:Nn \l_iow_target_length_int { \l_iow_line_length_int - ( #3 ) }
-      \int_zero:N \l_iow_current_indentation_int
-      \tl_clear:N \l_iow_current_indentation_tl
-      \int_zero:N \l_iow_current_line_int
-      \tl_clear:N \l_iow_current_line_tl
-      \tl_clear:N \l_iow_wrap_tl
-      \bool_set_true:N \l_iow_line_start_bool
       \int_set_eq:NN \tex_escapechar:D \c_minus_one
       \cs_set_nopar:Npx \{ { \token_to_str:N \{ }
       \cs_set_nopar:Npx \# { \token_to_str:N \# }
@@ -454,186 +476,162 @@
       \cs_set_nopar:Npx \% { \token_to_str:N \% }
       \cs_set_nopar:Npx \~ { \token_to_str:N \~ }
       \int_set:Nn \tex_escapechar:D { 92 }
-      \cs_set_eq:NN \\ \c_iow_wrap_newline_marker_tl
+      \cs_set_eq:NN \\ \c__iow_wrap_newline_marker_tl
       \cs_set_eq:NN \  \c_catcode_other_space_tl
-      \cs_set_eq:NN \iow_indent:n \iow_indent_expandable:n
-      #4
-      \protected@edef \l_iow_wrap_tl {#1}
-      \cs_set:Npn \\ { \iow_newline: #2 }
+      \cs_set_eq:NN \iow_indent:n \__iow_indent:n
+      #3
+      \protected@edef \l__iow_wrap_tl {#1}
+      \tl_set:Nx \l__iow_newline_tl { \iow_newline: #2 }
+      \tl_set:Nx \l__iow_newline_tl { \tl_to_str:N \l__iow_newline_tl }
+      \tl_replace_all:Nnn \l__iow_newline_tl { ~ } { \c_space_tl }
+      \int_set:Nn \l__iow_target_count_int
+        { \l_iow_line_count_int - \tl_count:N \l__iow_newline_tl + \c_one }
+      \int_zero:N \l__iow_current_indentation_int
+      \tl_clear:N \l__iow_current_indentation_tl
+      \int_zero:N \l__iow_current_line_int
+      \tl_clear:N \l__iow_current_line_tl
+      \bool_set_true:N \l__iow_line_start_bool
       \use:x
         {
-          \iow_wrap_loop:w
-          \tl_to_str:N \l_iow_wrap_tl
-          \tl_to_str:N \c_iow_wrap_end_marker_tl
+          \exp_not:n { \tl_clear:N \l__iow_wrap_tl }
+          \__iow_wrap_loop:w
+          \tl_to_str:N \l__iow_wrap_tl
+          \tl_to_str:N \c__iow_wrap_end_marker_tl
           \c_space_tl \c_space_tl
           \exp_not:N \q_stop
         }
     \exp_args:NNo \group_end:
-    #5 \l_iow_wrapped_tl
+    #4 \l__iow_wrap_tl
   }
-\cs_new_protected:Npn \iow_wrap_loop:w #1 ~ %
+\cs_new_protected:Npn \__iow_wrap_loop:w #1 ~ %
   {
-    \tl_set:Nn \l_iow_current_word_tl {#1}
-    \tl_if_eq:NNTF \l_iow_current_word_tl \c_iow_wrap_marker_tl
-      { \iow_wrap_special:w }
-      { \iow_wrap_word: }
+    \tl_set:Nn \l__iow_current_word_tl {#1}
+    \tl_if_eq:NNTF \l__iow_current_word_tl \c__iow_wrap_marker_tl
+      { \__iow_wrap_special:w }
+      { \__iow_wrap_word: }
   }
-\cs_new_protected_nopar:Npn \iow_wrap_word:
+\cs_new_protected_nopar:Npn \__iow_wrap_word:
   {
-    \int_set:Nn \l_iow_current_word_int
-      { \str_length_skip_spaces:N \l_iow_current_word_tl }
-    \int_add:Nn \l_iow_current_line_int { \l_iow_current_word_int }
-    \int_compare:nNnTF \l_iow_current_line_int < \l_iow_target_length_int
-      { \iow_wrap_word_fits: }
-      { \iow_wrap_word_newline: }
-    \iow_wrap_loop:w
+    \int_set:Nn \l__iow_current_word_int
+      { \__str_count_ignore_spaces:N \l__iow_current_word_tl }
+    \int_add:Nn \l__iow_current_line_int { \l__iow_current_word_int }
+    \int_compare:nNnTF \l__iow_current_line_int < \l__iow_target_count_int
+      { \__iow_wrap_word_fits: }
+      { \__iow_wrap_word_newline: }
+    \__iow_wrap_loop:w
   }
-\cs_new_protected_nopar:Npn \iow_wrap_word_fits:
+\cs_new_protected_nopar:Npn \__iow_wrap_word_fits:
   {
-    \bool_if:NTF \l_iow_line_start_bool
+    \bool_if:NTF \l__iow_line_start_bool
       {
-        \bool_set_false:N \l_iow_line_start_bool
-        \tl_put_right:Nx \l_iow_current_line_tl
-          { \l_iow_current_indentation_tl \l_iow_current_word_tl }
-        \int_add:Nn \l_iow_current_line_int
-          { \l_iow_current_indentation_int }
+        \bool_set_false:N \l__iow_line_start_bool
+        \tl_put_right:Nx \l__iow_current_line_tl
+          { \l__iow_current_indentation_tl \l__iow_current_word_tl }
+        \int_add:Nn \l__iow_current_line_int
+          { \l__iow_current_indentation_int }
       }
       {
-        \tl_put_right:Nx \l_iow_current_line_tl
-          { ~ \l_iow_current_word_tl }
-        \int_incr:N \l_iow_current_line_int
+        \tl_put_right:Nx \l__iow_current_line_tl
+          { ~ \l__iow_current_word_tl }
+        \int_incr:N \l__iow_current_line_int
       }
   }
-\cs_new_protected_nopar:Npn \iow_wrap_word_newline:
+\cs_new_protected_nopar:Npn \__iow_wrap_word_newline:
   {
-    \tl_put_right:Nx \l_iow_wrapped_tl
-      { \l_iow_current_line_tl \\ }
-    \int_set:Nn \l_iow_current_line_int
+    \tl_put_right:Nx \l__iow_wrap_tl
+      { \l__iow_current_line_tl \l__iow_newline_tl }
+    \int_set:Nn \l__iow_current_line_int
       {
-        \l_iow_current_word_int
-        + \l_iow_current_indentation_int
+        \l__iow_current_word_int
+        + \l__iow_current_indentation_int
       }
-    \tl_set:Nx \l_iow_current_line_tl
-      { \l_iow_current_indentation_tl \l_iow_current_word_tl }
+    \tl_set:Nx \l__iow_current_line_tl
+      { \l__iow_current_indentation_tl \l__iow_current_word_tl }
   }
-\cs_new_protected:Npn \iow_wrap_special:w #1 ~ #2 ~ #3 ~ %
+\cs_new_protected:Npn \__iow_wrap_special:w #1 ~ #2 ~ #3 ~ %
   {
-    \use:c { iow_wrap_#1: }
-    \str_if_eq:xxTF { #2~#3 } { ~ \c_iow_wrap_marker_tl }
-      { \iow_wrap_special:w }
-      { \iow_wrap_loop:w #2 ~ #3 ~ }
+    \use:c { __iow_wrap_#1: }
+    \str_if_eq_x:nnTF { #2~#3 } { ~ \c__iow_wrap_marker_tl }
+      { \__iow_wrap_special:w }
+      { \__iow_wrap_loop:w #2 ~ #3 ~ }
   }
-\cs_new_protected_nopar:Npn \iow_wrap_newline:
+\cs_new_protected_nopar:Npn \__iow_wrap_newline:
   {
-    \tl_put_right:Nx \l_iow_wrapped_tl
-      { \l_iow_current_line_tl \\ }
-    \int_zero:N \l_iow_current_line_int
-    \tl_clear:N \l_iow_current_line_tl
-    \bool_set_true:N \l_iow_line_start_bool
+    \tl_put_right:Nx \l__iow_wrap_tl
+      { \l__iow_current_line_tl \l__iow_newline_tl }
+    \int_zero:N \l__iow_current_line_int
+    \tl_clear:N \l__iow_current_line_tl
+    \bool_set_true:N \l__iow_line_start_bool
   }
-\cs_new_protected_nopar:Npx \iow_wrap_indent:
+\cs_new_protected_nopar:Npx \__iow_wrap_indent:
   {
-    \int_add:Nn \l_iow_current_indentation_int \c_four
-    \tl_put_right:Nx \exp_not:N \l_iow_current_indentation_tl
+    \int_add:Nn \l__iow_current_indentation_int \c_four
+    \tl_put_right:Nx \exp_not:N \l__iow_current_indentation_tl
       { \c_space_tl \c_space_tl \c_space_tl \c_space_tl }
   }
-\cs_new_protected_nopar:Npn \iow_wrap_unindent:
+\cs_new_protected_nopar:Npn \__iow_wrap_unindent:
   {
-    \int_sub:Nn \l_iow_current_indentation_int \c_four
-    \tl_set:Nx \l_iow_current_indentation_tl
-      { \prg_replicate:nn \l_iow_current_indentation_int { ~ } }
+    \int_sub:Nn \l__iow_current_indentation_int \c_four
+    \tl_set:Nx \l__iow_current_indentation_tl
+      { \prg_replicate:nn \l__iow_current_indentation_int { ~ } }
   }
-\cs_new_protected_nopar:Npn \iow_wrap_end:
+\cs_new_protected_nopar:Npn \__iow_wrap_end:
   {
-    \tl_put_right:Nx \l_iow_wrapped_tl
-      { \l_iow_current_line_tl }
+    \tl_put_right:Nx \l__iow_wrap_tl
+      { \l__iow_current_line_tl }
     \use_none_delimit_by_q_stop:w
   }
-\cs_new_nopar:Npn \str_length_skip_spaces:N
-  { \exp_args:No \str_length_skip_spaces:n }
-\cs_new:Npn \str_length_skip_spaces:n #1
+\cs_new_nopar:Npn \__str_count_ignore_spaces:N
+  { \exp_args:No \__str_count_ignore_spaces:n }
+\cs_new:Npn \__str_count_ignore_spaces:n #1
   {
-    \int_value:w \int_eval:w
-      \exp_after:wN \str_length_loop:NNNNNNNNN \tl_to_str:n {#1}
+    \__int_value:w \__int_eval:w
+      \exp_after:wN \__str_count_loop:NNNNNNNNN \tl_to_str:n {#1}
         { X8 } { X7 } { X6 } { X5 } { X4 } { X3 } { X2 } { X1 } { X0 } \q_stop
-    \int_eval_end:
+    \__int_eval_end:
   }
-\cs_new:Npn \str_length_loop:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+\cs_new:Npn \__str_count_loop:NNNNNNNNN #1#2#3#4#5#6#7#8#9
   {
     \if_catcode:w X #9
       \exp_after:wN \use_none_delimit_by_q_stop:w
     \else:
       9 +
-      \exp_after:wN \str_length_loop:NNNNNNNNN
+      \exp_after:wN \__str_count_loop:NNNNNNNNN
     \fi:
   }
-\cs_new_eq:NN \if_eof:w \tex_ifeof:D
-\prg_new_conditional:Nnn \ior_if_eof:N { p , T , F , TF }
-  {
-    \cs_if_exist:NTF #1
-      {
-        \if_int_compare:w #1 = \c_sixteen
-          \prg_return_true:
-        \else:
-          \if_eof:w #1
-            \prg_return_true:
-          \else:
-            \prg_return_false:
-          \fi:
-        \fi:
-      }
-      { \prg_return_true: }
-  }
-\cs_new_protected:Npn \ior_to:NN #1#2
-  { \tex_read:D #1 to #2 }
-\cs_new_protected:Npn \ior_gto:NN #1#2
-  { \tex_global:D \tex_read:D #1 to #2 }
-\cs_new_protected:Npn \ior_str_to:NN #1#2
-  { \etex_readline:D #1 to #2 }
-\cs_new_protected:Npn \ior_str_gto:NN #1#2
-  { \tex_global:D \etex_readline:D #1 to #2 }
-\cs_new_protected_nopar:Npn \ior_map_inline:Nn
-  { \ior_map_inline_aux:NNn \ior_to:NN }
-\cs_new_protected_nopar:Npn \ior_str_map_inline:Nn
-  { \ior_map_inline_aux:NNn \ior_str_to:NN }
-\cs_new_protected_nopar:Npn \ior_map_inline_aux:NNn
-  {
-    \exp_args:Nc \ior_map_inline_aux:NNNn
-      { ior_map_ \int_use:N \g_prg_map_int :n }
-  }
-\cs_new_protected:Npn \ior_map_inline_aux:NNNn #1#2#3#4
+\__msg_kernel_new:nnnn { kernel } { file-not-found }
+  { File~'#1'~not~found. }
   {
-    \cs_set:Npn #1 ##1 {#4}
-    \int_gincr:N \g_prg_map_int
-    \ior_if_eof:NF #3 { \ior_map_inline_loop:NNN #1#2#3 }
-    \prg_break_point:n { \int_gdecr:N \g_prg_map_int }
+    The~requested~file~could~not~be~found~in~the~current~directory,~
+    in~the~TeX~search~path~or~in~the~LaTeX~search~path.
   }
-\cs_new_protected:Npn \ior_map_inline_loop:NNN #1#2#3
+\__msg_kernel_new:nnnn { kernel } { input-streams-exhausted }
+  { Input~streams~exhausted }
   {
-    #2 #3 \l_ior_internal_tl
-    \ior_if_eof:NF #3
-      {
-        \exp_args:No #1 \l_ior_internal_tl
-        \ior_map_inline_loop:NNN #1#2#3
-      }
+    TeX~can~only~open~up~to~16~input~streams~at~one~time.\\
+    All~16~are~currently~in~use,~and~something~wanted~to~open~
+    another~one.
   }
-\tl_new:N  \l_ior_internal_tl
-\msg_kernel_new:nnnn { file } { file-not-found }
-  { File~'#1'~not~found. }
+\__msg_kernel_new:nnnn { kernel } { output-streams-exhausted }
+  { Output~streams~exhausted }
   {
-    The~requested~file~could~not~be~found~in~the~current~directory,~
-    in~the~TeX~search~path~or~in~the~LaTeX~search~path.
+    TeX~can~only~open~up~to~16~output~streams~at~one~time.\\
+    All~16~are~currently~in~use,~and~something~wanted~to~open~
+    another~one.
   }
-\msg_kernel_new:nnnn { file } { space-in-file-name }
+\__msg_kernel_new:nnnn { kernel } { space-in-file-name }
   { Space~in~file~name~'#1'. }
   {
     Spaces~are~not~permitted~in~files~loaded~by~LaTeX: \\
     Further~errors~may~follow!
   }
-\cs_new_protected:Npn \iow_now_when_avail:Nn #1
-  { \cs_if_free:NTF #1 { \use_none:n } { \iow_now:Nn #1 } }
-\cs_new_protected:Npn \iow_now_when_avail:Nx #1
-  { \cs_if_free:NTF #1 { \use_none:n } { \iow_now:Nx #1 } }
+\cs_new_protected:Npn \iow_wrap:xnnnN #1#2#3#4#5
+  { \iow_wrap:nnnN {#1} {#2} {#4} #5 }
+\cs_new_eq:NN \l_iow_line_length_int \l_iow_line_count_int
+\cs_new_eq:NN \ior_to:NN \ior_get:NN
+\cs_new_protected_nopar:Npn \ior_gto:NN { \tex_global:D \ior_to:NN }
+\cs_new_eq:NN \ior_str_to:NN \ior_get_str:NN
+\cs_new_protected_nopar:Npn \ior_str_gto:NN { \tex_global:D \ior_str_to:NN }
 %% 
 %%
 %% End of file `l3file.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty b/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty
index bb38caa64f6..a7680dc7803 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty
@@ -5,6 +5,18 @@
 %% The original source files were:
 %%
 %% l3fp.dtx  (with options: `package')
+%% l3fp-aux.dtx  (with options: `package')
+%% l3fp-traps.dtx  (with options: `package')
+%% l3fp-round.dtx  (with options: `package')
+%% l3fp-parse.dtx  (with options: `package')
+%% l3fp-logic.dtx  (with options: `package')
+%% l3fp-basics.dtx  (with options: `package')
+%% l3fp-extended.dtx  (with options: `package')
+%% l3fp-expo.dtx  (with options: `package')
+%% l3fp-trig.dtx  (with options: `package')
+%% l3fp-convert.dtx  (with options: `package')
+%% l3fp-assign.dtx  (with options: `package')
+%% l3fp-old.dtx  (with options: `package')
 %% 
 %% EXPERIMENTAL CODE
 %% 
@@ -13,7 +25,7 @@
 %% 
 %% Do not distribute a modified version of this file.
 %% 
-%% File: l3fp.dtx Copyright (C) 2010-2012 The LaTeX3 Project
+%% File: l3fp.dtx Copyright (C) 2011-2012 The LaTeX3 Project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -42,3386 +54,4527 @@
 %%   Snapshots taken from the repository represent work in progress and may
 %%   not work or may contain conflicting material!  We therefore ask
 %%   people _not_ to put them into distributions, archives, etc. without
-%%   prior consultation with the LaTeX3 Project.
+%%   prior consultation with the LaTeX3 Project Team.
 %%
 %% -----------------------------------------------------------------------
+%%
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3fp.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental floating-point operations}
+\GetIdInfo$Id: l3fp.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Floating points}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
-\int_const:Nn \c_forty_four { 44 }
-\int_const:Nn \c_one_million { 1 000 000 }
-\int_const:Nn \c_one_hundred_million { 100 000 000 }
-\int_const:Nn \c_five_hundred_million { 500 000 000 }
-\int_const:Nn \c_one_thousand_million { 1 000 000 000 }
-\int_new:N  \c_fp_pi_by_four_decimal_int
-\int_set:Nn \c_fp_pi_by_four_decimal_int { 785 398 158 }
-\int_new:N  \c_fp_pi_by_four_extended_int
-\int_set:Nn \c_fp_pi_by_four_extended_int { 897 448 310 }
-\int_new:N  \c_fp_pi_decimal_int
-\int_set:Nn \c_fp_pi_decimal_int { 141 592 653 }
-\int_new:N  \c_fp_pi_extended_int
-\int_set:Nn \c_fp_pi_extended_int { 589 793 238 }
-\int_new:N  \c_fp_two_pi_decimal_int
-\int_set:Nn \c_fp_two_pi_decimal_int { 283 185 307 }
-\int_new:N  \c_fp_two_pi_extended_int
-\int_set:Nn \c_fp_two_pi_extended_int { 179 586 477 }
-\tl_const:Nn \c_e_fp { + 2.718281828 e 0 }
-\tl_const:Nn \c_one_fp { + 1.000000000 e 0 }
-\tl_const:Nn \c_pi_fp { + 3.141592654 e 0 }
-\tl_const:Nn \c_undefined_fp { X 0.000000000 e 0 }
-\tl_const:Nn \c_zero_fp { + 0.000000000 e 0 }
-\tl_new:N \l_fp_arg_tl
-\int_new:N \l_fp_count_int
-\int_new:N \l_fp_div_offset_int
-\int_new:N \l_fp_exp_integer_int
-\int_new:N \l_fp_exp_decimal_int
-\int_new:N \l_fp_exp_extended_int
-\int_new:N \l_fp_exp_exponent_int
-\int_new:N \l_fp_input_a_sign_int
-\int_new:N \l_fp_input_a_integer_int
-\int_new:N \l_fp_input_a_decimal_int
-\int_new:N \l_fp_input_a_exponent_int
-\int_new:N \l_fp_input_b_sign_int
-\int_new:N \l_fp_input_b_integer_int
-\int_new:N \l_fp_input_b_decimal_int
-\int_new:N \l_fp_input_b_exponent_int
-\int_new:N \l_fp_input_a_extended_int
-\int_new:N \l_fp_input_b_extended_int
-\int_new:N \l_fp_mul_a_i_int
-\int_new:N \l_fp_mul_a_ii_int
-\int_new:N \l_fp_mul_a_iii_int
-\int_new:N \l_fp_mul_a_iv_int
-\int_new:N \l_fp_mul_a_v_int
-\int_new:N \l_fp_mul_a_vi_int
-\int_new:N \l_fp_mul_b_i_int
-\int_new:N \l_fp_mul_b_ii_int
-\int_new:N \l_fp_mul_b_iii_int
-\int_new:N \l_fp_mul_b_iv_int
-\int_new:N \l_fp_mul_b_v_int
-\int_new:N \l_fp_mul_b_vi_int
-\int_new:N \l_fp_mul_output_int
-\tl_new:N  \l_fp_mul_output_tl
-\int_new:N \l_fp_output_sign_int
-\int_new:N \l_fp_output_integer_int
-\int_new:N \l_fp_output_decimal_int
-\int_new:N \l_fp_output_exponent_int
-\int_new:N \l_fp_output_extended_int
-\bool_new:N \l_fp_round_carry_bool
-\tl_new:N \l_fp_round_decimal_tl
-\int_new:N \l_fp_round_position_int
-\int_new:N \l_fp_round_target_int
-\tl_new:N \l_fp_sign_tl
-\int_new:N \l_fp_split_sign_int
-\int_new:N \l_fp_internal_int
-\tl_new:N \l_fp_internal_tl
-\int_new:N \l_fp_trig_octant_int
-\int_new:N \l_fp_trig_sign_int
-\int_new:N \l_fp_trig_decimal_int
-\int_new:N \l_fp_trig_extended_int
-\cs_new_protected:Npn \fp_read:N #1
-  { \exp_after:wN \fp_read_aux:w #1 \q_stop }
-\cs_new_protected:Npn \fp_read_aux:w #1#2 . #3 e #4 \q_stop
-  {
-    \if:w #1 -
-      \l_fp_input_a_sign_int \c_minus_one
-    \else:
-      \l_fp_input_a_sign_int \c_one
-    \fi:
-    \l_fp_input_a_integer_int  #2 \scan_stop:
-    \l_fp_input_a_decimal_int  #3 \scan_stop:
-    \l_fp_input_a_exponent_int #4 \scan_stop:
-  }
-\cs_new_protected:Npn \fp_split:Nn #1#2
-  {
-    \tl_set:Nx \l_fp_internal_tl {#2}
-    \tl_set_rescan:Nno \l_fp_internal_tl { \char_set_catcode_ignore:n { 32 } }
-      { \l_fp_internal_tl }
-    \l_fp_split_sign_int \c_one
-    \fp_split_sign:
-    \use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int
-    \exp_after:wN \fp_split_exponent:w \l_fp_internal_tl e e \q_stop #1
-  }
-\cs_new_protected_nopar:Npn \fp_split_sign:
-  {
-    \if_int_compare:w \pdftex_strcmp:D
-      { \exp_after:wN \tl_head:w \l_fp_internal_tl ? \q_stop } { - }
-        = \c_zero
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \exp_after:wN
-            \tl_tail:w \l_fp_internal_tl \prg_do_nothing: \q_stop
-        }
-      \l_fp_split_sign_int -\l_fp_split_sign_int
-      \exp_after:wN \fp_split_sign:
+\__expl_package_check:
+%% File: l3fp-aux.dtx Copyright(C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\cs_new:Npn \__fp_use_none_stop_f:n #1 { \exp_stop_f: }
+\cs_new:Npn \__fp_use_s:n #1 { #1; }
+\cs_new:Npn \__fp_use_s:nn #1#2 { #1#2; }
+\cs_new:Npn \__fp_use_none_until_s:w #1; { }
+\cs_new:Npn \__fp_use_i_until_s:nw #1#2; {#1}
+\cs_new:Npn \__fp_use_ii_until_s:nnw #1#2#3; {#2}
+\cs_new:Npn \__fp_reverse_args:Nww #1 #2; #3; { #1 #3; #2; }
+\__scan_new:N \s__fp
+\cs_new_protected:Npn \__fp_chk:w #1 ;
+  {
+    \__msg_kernel_error:nnx { kernel } { misused-fp }
+      { \__fp_to_tl:w \s__fp \__fp_chk:w #1 ; }
+  }
+\__scan_new:N \s__fp_mark
+\__scan_new:N \s__fp_stop
+\__scan_new:N \s__fp_invalid
+\__scan_new:N \s__fp_underflow
+\__scan_new:N \s__fp_overflow
+\__scan_new:N \s__fp_division
+\__scan_new:N \s__fp_exact
+\tl_const:Nn \c_zero_fp       { \s__fp \__fp_chk:w 0 0 \s__fp_exact ; }
+\tl_const:Nn \c_minus_zero_fp { \s__fp \__fp_chk:w 0 2 \s__fp_exact ; }
+\tl_const:Nn \c_inf_fp        { \s__fp \__fp_chk:w 2 0 \s__fp_exact ; }
+\tl_const:Nn \c_minus_inf_fp  { \s__fp \__fp_chk:w 2 2 \s__fp_exact ; }
+\tl_const:Nn \c_nan_fp        { \s__fp \__fp_chk:w 3 1 \s__fp_exact ; }
+\int_const:Nn \c__fp_max_exponent_int { 10000 }
+\cs_new:Npn \__fp_zero_fp:N #1 { \s__fp \__fp_chk:w 0 #1 \s__fp_underflow ; }
+\cs_new:Npn \__fp_inf_fp:N #1  { \s__fp \__fp_chk:w 2 #1 \s__fp_overflow ; }
+\cs_new:Npn \__fp_min_fp:N #1
+  {
+    \s__fp \__fp_chk:w 1 #1
+      { \int_eval:n { - \c__fp_max_exponent_int } }
+      {1000} {0000} {0000} {0000} ;
+  }
+\cs_new:Npn \__fp_max_fp:N #1
+  {
+    \s__fp \__fp_chk:w 1 #1
+      { \int_use:N \c__fp_max_exponent_int }
+      {9999} {9999} {9999} {9999} ;
+  }
+\cs_new:Npn \__fp_exponent:w \s__fp \__fp_chk:w #1
+  {
+    \if_meaning:w 1 #1
+      \exp_after:wN \__fp_use_ii_until_s:nnw
     \else:
-      \if_int_compare:w \pdftex_strcmp:D
-        { \exp_after:wN \tl_head:w \l_fp_internal_tl ? \q_stop } { + }
-          = \c_zero
-        \tl_set:Nx \l_fp_internal_tl
-          {
-            \exp_after:wN
-              \tl_tail:w \l_fp_internal_tl \prg_do_nothing: \q_stop
-          }
-        \exp_after:wN \exp_after:wN \exp_after:wN \fp_split_sign:
-       \fi:
+      \exp_after:wN \__fp_use_i_until_s:nw
+      \exp_after:wN 0
     \fi:
   }
-\cs_new_protected:Npn \fp_split_exponent:w #1 e #2 e #3 \q_stop #4
+\cs_new:Npn \__fp_sanitize:Nw #1 #2;
   {
-    \use:c { l_fp_input_ #4 _exponent_int }
-      \int_eval:w 0 #2 \scan_stop:
-    \tex_afterassignment:D \fp_split_aux_i:w
-    \use:c { l_fp_input_ #4 _integer_int }
-      \int_eval:w 0 #1 . . \q_stop #4
+    \if_case:w \if_int_compare:w #2 > \c__fp_max_exponent_int \c_one \else:
+               \if_int_compare:w #2 < - \c__fp_max_exponent_int \c_two \else:
+               \if_meaning:w 1 #1 \c_three \else: \c_zero \fi: \fi: \fi:
+    \or: \exp_after:wN \__fp_overflow:w
+    \or: \exp_after:wN \__fp_underflow:w
+    \or: \exp_after:wN \__fp_sanitize_zero:w
+    \fi:
+    \s__fp \__fp_chk:w 1 #1 {#2}
   }
-\cs_new_protected:Npn \fp_split_aux_i:w #1 . #2 . #3 \q_stop
-  { \fp_split_aux_ii:w #2 000000000 \q_stop }
-\cs_new_protected:Npn \fp_split_aux_ii:w #1#2#3#4#5#6#7#8#9
-  { \fp_split_aux_iii:w {#1#2#3#4#5#6#7#8#9} }
-\cs_new_protected:Npn \fp_split_aux_iii:w #1#2 \q_stop
+\cs_new:Npn \__fp_sanitize:wN #1; #2 { \__fp_sanitize:Nw #2 #1; }
+\cs_new:Npn \__fp_sanitize_zero:w \s__fp \__fp_chk:w #1 #2 #3; { \c_zero_fp }
+\cs_new:Npn \__fp_exp_after_o:w \s__fp \__fp_chk:w #1
   {
-    \l_fp_internal_int 1 #1 \scan_stop:
-    \exp_after:wN \fp_split_decimal:w
-      \int_use:N \l_fp_internal_int 000000000 \q_stop
+    \if_meaning:w 1 #1
+      \exp_after:wN \__fp_exp_after_normal:nNNw
+    \else:
+      \exp_after:wN \__fp_exp_after_special:nNNw
+    \fi:
+    { }
+    #1
   }
-\cs_new_protected:Npn \fp_split_decimal:w #1#2#3#4#5#6#7#8#9
-  { \fp_split_decimal_aux:w {#2#3#4#5#6#7#8#9} }
-\cs_new_protected:Npn \fp_split_decimal_aux:w #1#2#3 \q_stop #4
+\cs_new:Npn \__fp_exp_after_o:nw #1 \s__fp \__fp_chk:w #2
   {
-    \use:c { l_fp_input_ #4 _decimal_int } #1#2 \scan_stop:
-    \if_int_compare:w
-      \int_eval:w
-        \use:c { l_fp_input_ #4 _integer_int } +
-        \use:c { l_fp_input_ #4 _decimal_int }
-      \scan_stop:
-        = \c_zero
-      \use:c { l_fp_input_ #4 _sign_int } \c_one
+    \if_meaning:w 1 #2
+      \exp_after:wN \__fp_exp_after_normal:nNNw
+    \else:
+      \exp_after:wN \__fp_exp_after_special:nNNw
     \fi:
-    \if_int_compare:w
-      \use:c { l_fp_input_ #4 _integer_int } < \c_one_thousand_million
+    { #1 }
+    #2
+  }
+\cs_new:Npn \__fp_exp_after_f:nw #1 \s__fp \__fp_chk:w #2
+  {
+    \if_meaning:w 1 #2
+      \exp_after:wN \__fp_exp_after_normal:nNNw
     \else:
-      \exp_after:wN \fp_overflow_msg:
+      \exp_after:wN \__fp_exp_after_special:nNNw
     \fi:
+    { \tex_romannumeral:D -`0 #1 }
+    #2
   }
-\cs_new_protected:Npn \fp_standardise:NNNN #1#2#3#4
+\cs_new:Npn \__fp_exp_after_special:nNNw #1#2#3#4;
   {
-    \if_int_compare:w
-      \int_eval:w #2 + #3 = \c_zero
-      #1 \c_one
-      #4 \c_zero
-      \exp_after:wN \use_none:nnnn
+    \exp_after:wN \s__fp
+    \exp_after:wN \__fp_chk:w
+    \exp_after:wN #2
+    \exp_after:wN #3
+    \exp_after:wN #4
+    \exp_after:wN ;
+    #1
+  }
+\cs_new:Npn \__fp_exp_after_normal:nNNw #1 1 #2 #3 #4#5#6#7;
+  {
+    \exp_after:wN \__fp_exp_after_normal:Nwwwww
+    \exp_after:wN #2
+    \__int_value:w #3   \exp_after:wN ;
+    \__int_value:w 1 #4 \exp_after:wN ;
+    \__int_value:w 1 #5 \exp_after:wN ;
+    \__int_value:w 1 #6 \exp_after:wN ;
+    \__int_value:w 1 #7 \exp_after:wN ; #1
+  }
+\cs_new:Npn \__fp_exp_after_normal:Nwwwww
+    #1 #2; 1 #3 ; 1 #4 ; 1 #5 ; 1 #6 ;
+  { \s__fp \__fp_chk:w 1 #1 {#2} {#3} {#4} {#5} {#6} ; }
+\int_const:Nn \c__fp_leading_shift_int  { - 5 0000 }
+\int_const:Nn \c__fp_middle_shift_int   { 5 0000 *  9999 }
+\int_const:Nn \c__fp_trailing_shift_int { 5 0000 * 10000 }
+\cs_new:Npn \__fp_pack:NNNNNw #1 #2#3#4#5 #6; { + #1#2#3#4#5 ; {#6} }
+\int_const:Nn \c__fp_big_leading_shift_int  { - 15 2374 }
+\int_const:Nn \c__fp_big_middle_shift_int   { 15 2374 *  9999 }
+\int_const:Nn \c__fp_big_trailing_shift_int { 15 2374 * 10000 }
+\cs_new:Npn \__fp_pack_big:NNNNNNw #1#2 #3#4#5#6 #7;
+  { + #1#2#3#4#5#6 ; {#7} }
+\cs_new:Npn \__fp_pack_twice_four:wNNNNNNNN #1; #2#3#4#5 #6#7#8#9
+  { #1 {#2#3#4#5} {#6#7#8#9} ; }
+\cs_new:Npn \__fp_decimate:nNnnnn #1
+  {
+    \cs:w
+      __fp_decimate_
+      \if_int_compare:w \__int_eval:w #1 > \c_sixteen
+        tiny
+      \else:
+        \tex_romannumeral:D \__int_eval:w #1
+      \fi:
+      :Nnnnn
+    \cs_end:
+  }
+\cs_new:Npn \__fp_decimate_:Nnnnn #1 #2#3#4#5
+  { #1 0 {#2#3} {#4#5} ; }
+\cs_new:Npn \__fp_decimate_tiny:Nnnnn #1 #2#3#4#5
+  { #1 1 { 0000 0000 } { 0000 0000 } 0 #2#3#4#5 ; }
+\cs_new:Npn \__fp_tmp:w #1 #2 #3
+  {
+    \cs_new:cpn { __fp_decimate_ #1 :Nnnnn } ##1 ##2##3##4##5
+      {
+        \exp_after:wN ##1
+        \__int_value:w
+          \exp_after:wN \__fp_decimate_round:Nw #2 ;
+        \__fp_decimate_pack:nnnnnnnnnnw #3 ;
+      }
+  }
+\__fp_tmp:w {i}   {\use_none:nnn      #50} {    0{#2}#3{#4}#5                }
+\__fp_tmp:w {ii}  {\use_none:nn       #5 } {    00{#2}#3{#4}#5               }
+\__fp_tmp:w {iii} {\use_none:n        #5 } {    000{#2}#3{#4}#5              }
+\__fp_tmp:w {iv}  {                   #5 } {   {0000}#2{#3}#4 #5             }
+\__fp_tmp:w {v}   {\use_none:nnn    #4#5 } {   0{0000}#2{#3}#4 #5            }
+\__fp_tmp:w {vi}  {\use_none:nn     #4#5 } {   00{0000}#2{#3}#4 #5           }
+\__fp_tmp:w {vii} {\use_none:n      #4#5 } {   000{0000}#2{#3}#4 #5          }
+\__fp_tmp:w {viii}{                 #4#5 } {  {0000}0000{#2}#3 #4 #5         }
+\__fp_tmp:w {ix}  {\use_none:nnn  #3#4+#5} {  0{0000}0000{#2}#3 #4 #5        }
+\__fp_tmp:w {x}   {\use_none:nn   #3#4+#5} {  00{0000}0000{#2}#3 #4 #5       }
+\__fp_tmp:w {xi}  {\use_none:n    #3#4+#5} {  000{0000}0000{#2}#3 #4 #5      }
+\__fp_tmp:w {xii} {               #3#4+#5} { {0000}0000{0000}#2 #3 #4 #5     }
+\__fp_tmp:w {xiii}{\use_none:nnn#2#3+#4#5} { 0{0000}0000{0000}#2 #3 #4 #5    }
+\__fp_tmp:w {xiv} {\use_none:nn #2#3+#4#5} { 00{0000}0000{0000}#2 #3 #4 #5   }
+\__fp_tmp:w {xv}  {\use_none:n  #2#3+#4#5} { 000{0000}0000{0000}#2 #3 #4 #5  }
+\__fp_tmp:w {xvi} {             #2#3+#4#5} {{0000}0000{0000}0000 #2 #3 #4 #5 }
+\cs_new:Npn \__fp_decimate_round:Nw #1 #2;
+  {
+    \if_int_odd:w \if_meaning:w 0 #1 \c_one \else:
+                  \if_meaning:w 5 #1 \c_one \else:
+                  \c_zero \fi: \fi:
+      \if_int_compare:w \__int_eval:w #2 > \c_zero
+        \__int_eval:w 1 +
+      \fi:
+    \fi:
+    #1
+  }
+\cs_new:Npn \__fp_decimate_pack:nnnnnnnnnnw #1#2#3#4#5
+  { \__fp_decimate_pack_ii:nnnnnnw { #1#2#3#4#5 } }
+\cs_new:Npn \__fp_decimate_pack_ii:nnnnnnw #1 #2#3#4#5#6
+  { {#1} {#2#3#4#5#6} }
+\cs_new:Npn \__fp_case_use:nw #1#2 \fi: #3 \s__fp { \fi: #1 \s__fp }
+\cs_new:Npn \__fp_case_return:nw #1#2 \fi: #3 ; { \fi: #1 }
+\cs_new:Npn \__fp_case_return_o:Nw #1#2 \fi: #3 \s__fp #4 ;
+  { \fi: \exp_after:wN #1 }
+\cs_new:Npn \__fp_case_return_same_o:w #1 \fi: #2 \s__fp
+  { \fi: \__fp_exp_after_o:w \s__fp }
+\cs_new:Npn \__fp_case_return_o:Nww #1#2 \fi: #3 \s__fp #4 ; #5 ;
+  { \fi: \exp_after:wN #1 }
+\cs_new:Npn \__fp_case_return_ii_o:ww #1 \fi: #2 \s__fp #3 ;
+  { \fi: \__fp_exp_after_o:w }
+\cs_new:Npn \__fp_small_int:wTF \s__fp \__fp_chk:w #1
+  {
+    \if_case:w #1 \exp_stop_f:
+           \__fp_case_return:nw { \__fp_small_int_true:wTF 0 ; }
+    \or:   \exp_after:wN \__fp_small_int_normal:NnwTF
+    \else: \__fp_case_return:nw \use_ii:nn
+    \fi:
+  }
+\cs_new:Npn \__fp_small_int_true:wTF #1; #2#3 { #2 {#1} }
+\cs_new:Npn \__fp_small_int_normal:NnwTF #1#2#3;
+  {
+    \if_int_compare:w #2 > \c_zero
+      \if_int_compare:w #2 > \c_eight
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \use_iii:nnn
+      \else:
+        \__fp_decimate:nNnnnn { \c_sixteen - #2 }
+          \__fp_small_int_test:NnnwNTF
+          #3 #1
+      \fi:
+    \else:
+      \exp_after:wN \use_iii:nnn
+    \fi:
+    ;
+  }
+\cs_new:Npn \__fp_small_int_test:NnnwNTF #1#2#3#4; #5
+  {
+    \if_meaning:w 0 #1
+      \exp_after:wN \__fp_small_int_true:wTF
+      \__int_value:w \if_meaning:w 2 #5 - \fi: #3
     \else:
-      \exp_after:wN \fp_standardise_aux:NNNN
+      \exp_after:wN \use_iii:nnn
     \fi:
-    #1#2#3#4
   }
-\cs_new_protected:Npn \fp_standardise_aux:NNNN #1#2#3#4
+\cs_new:Npn \__fp_array_count:w #1 @
   {
-    \cs_set_protected_nopar:Npn \fp_standardise_aux:
+    \int_use:N \__int_eval:w \c_zero
+      \__fp_array_count_loop:Nw #1 { ? \__prg_break: } ;
+      \__prg_break_point:
+    \__int_eval_end:
+  }
+\cs_new:Npn \__fp_array_count_loop:Nw #1#2;
+  { \use_none:n #1 + \c_one \__fp_array_count_loop:Nw }
+\__msg_kernel_new:nnnn { kernel } { misused-fp }
+  { A~floating~point~with~value~'#1'~was~misused. }
+  {
+    To~obtain~the~value~of~a~floating~point~variable,~use~
+    '\token_to_str:N \fp_to_decimal:N',~
+    '\token_to_str:N \fp_to_scientific:N',~or~other~
+    conversion~functions.
+  }
+%%
+%% File: l3fp-traps.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\cs_new_protected:Npn \__fp_flag_off:n #1
+  { \cs_set_eq:cN { l__fp_ #1 _flag_token } \c_undefined:D }
+\cs_new:Npn \__fp_flag_on:n #1
+  { \exp_args:Nc \use_none:n { l__fp_ #1 _flag_token } }
+\prg_new_conditional:Npnn \__fp_if_flag_on:n #1 { p , T , F , TF }
+  {
+    \if_cs_exist:w l__fp_ #1 _flag_token \cs_end:
+      \prg_return_true:
+    \else:
+      \prg_return_false:
+    \fi:
+  }
+\cs_new_eq:NN \l__fp_invalid_operation_flag_token \c_undefined:D
+\cs_new_eq:NN \l__fp_division_by_zero_flag_token \c_undefined:D
+\cs_new_eq:NN \l__fp_overflow_flag_token \c_undefined:D
+\cs_new_eq:NN \l__fp_underflow_flag_token \c_undefined:D
+\cs_new_protected:Npn \__fp_trap:nn #1#2
+  {
+    \cs_if_exist_use:cF { __fp_trap_#1_set_#2: }
       {
-        \if_int_compare:w #2 = \c_zero
-          \tex_advance:D #3 \c_one_thousand_million
-          \exp_after:wN \fp_standardise_aux:w
-            \int_use:N #3 \q_stop
-           \exp_after:wN \fp_standardise_aux:
-         \fi:
+        \clist_if_in:nnTF
+          { invalid_operation , division_by_zero , overflow , underflow }
+          {#1}
+          {
+            \__msg_kernel_error:nnxx { kernel }
+              { unknown-fpu-trap-type } {#1} {#2}
+          }
+          { \__msg_kernel_error:nnx { kernel } { unknown-fpu-exception } {#1} }
       }
-    \cs_set_protected:Npn
-      \fp_standardise_aux:w ##1##2##3##4##5##6##7##8##9 \q_stop
+  }
+\cs_new_protected_nopar:Npn \__fp_trap_invalid_operation_set_error:
+  { \__fp_trap_invalid_operation_set:N \prg_do_nothing: }
+\cs_new_protected_nopar:Npn \__fp_trap_invalid_operation_set_flag:
+  { \__fp_trap_invalid_operation_set:N \use_none:nn }
+\cs_new_protected_nopar:Npn \__fp_trap_invalid_operation_set_none:
+  { \__fp_trap_invalid_operation_set:N \use_none:nnnn }
+\cs_new_protected:Npn \__fp_trap_invalid_operation_set:N #1
+  {
+    \__fp_trap_invalid_operation_set:Nnn #1
+      { invalid_operation } { Invalid~operation~ }
+  }
+\cs_new_protected_nopar:Npn \__fp_trap_division_by_zero_set_error:
+  { \__fp_trap_division_by_zero_set:N \prg_do_nothing: }
+\cs_new_protected_nopar:Npn \__fp_trap_division_by_zero_set_flag:
+  { \__fp_trap_division_by_zero_set:N \use_none:nn }
+\cs_new_protected_nopar:Npn \__fp_trap_division_by_zero_set_none:
+  { \__fp_trap_division_by_zero_set:N \use_none:nnnn }
+\cs_new_protected:Npn \__fp_trap_division_by_zero_set:N #1
+  {
+    \__fp_trap_invalid_operation_set:Nnn #1
+      { division_by_zero } { Division~by~zero~in~ }
+  }
+\cs_new_protected:Npn \__fp_trap_invalid_operation_set:Nnn #1#2#3
+  {
+    \exp_args:Nno \use:n
+      { \cs_set:cpn { __fp_ #2 :Nnw } ##1##2##3; }
       {
-        #2 ##2 \scan_stop:
-        #3 ##3##4##5##6##7##8##9 0 \scan_stop:
-        \tex_advance:D #4 \c_minus_one
+        #1
+        \__fp_error:x { { #3 ##2 } ( \__fp_to_tl:w ##3; ) }
+        \__fp_flag_on:n {#2}
+        \exp_after:wN ##1
       }
-    \fp_standardise_aux:
-    \cs_set_protected_nopar:Npn \fp_standardise_aux:
+    \exp_args:Nno \use:n
+      { \cs_set:cpn { __fp_ #2 :Nnww } ##1##2##3; ##4; }
       {
-        \if_int_compare:w #2 > \c_nine
-          \tex_advance:D #2 \c_one_thousand_million
-          \exp_after:wN \use_i:nn \exp_after:wN
-            \fp_standardise_aux:w \int_use:N #2
-           \exp_after:wN \fp_standardise_aux:
-         \fi:
+        #1
+        \__fp_error:x
+          {
+            {#3}
+            \tl_if_single:nTF {##2}
+              { ( \__fp_to_tl:w ##3; ) ##2 ( \__fp_to_tl:w ##4; ) }
+              { { ##2 ( } \__fp_to_tl:w ##3; { , ~ } \__fp_to_tl:w ##4; ) }
+          }
+        \__fp_flag_on:n {#2}
+        \exp_after:wN ##1
       }
-    \cs_set_protected:Npn
-      \fp_standardise_aux:w ##1##2##3##4##5##6##7##8##9
+  }
+\cs_new_protected_nopar:Npn \__fp_trap_overflow_set_error:
+  { \__fp_trap_overflow_set:N \prg_do_nothing: }
+\cs_new_protected_nopar:Npn \__fp_trap_overflow_set_flag:
+  { \__fp_trap_overflow_set:N \use_none:nn }
+\cs_new_protected_nopar:Npn \__fp_trap_overflow_set_none:
+  { \__fp_trap_overflow_set:N \use_none:nnnn }
+\cs_new_protected:Npn \__fp_trap_overflow_set:N #1
+  { \__fp_trap_overflow_set:NnNn #1 { overflow } \__fp_inf_fp:N { inf } }
+\cs_new_protected_nopar:Npn \__fp_trap_underflow_set_error:
+  { \__fp_trap_underflow_set:N \prg_do_nothing: }
+\cs_new_protected_nopar:Npn \__fp_trap_underflow_set_flag:
+  { \__fp_trap_underflow_set:N \use_none:nn }
+\cs_new_protected_nopar:Npn \__fp_trap_underflow_set_none:
+  { \__fp_trap_underflow_set:N \use_none:nnnn }
+\cs_new_protected:Npn \__fp_trap_underflow_set:N #1
+  { \__fp_trap_overflow_set:NnNn #1 { underflow } \__fp_zero_fp:N { 0 } }
+\cs_new_protected:Npn \__fp_trap_overflow_set:NnNn #1#2#3#4
+  {
+    \exp_args:Nno \use:n
+      { \cs_set:cpn { __fp_ #2 :w } \s__fp \__fp_chk:w ##1##2##3; }
       {
-        #2 ##1##2##3##4##5##6##7##8 \scan_stop:
-        \tex_advance:D #3 \c_one_thousand_million
-        \tex_divide:D #3 \c_ten
-        \tl_set:Nx \l_fp_internal_tl
+        #1
+        \__fp_error:x
           {
-            ##9
-            \exp_after:wN \use_none:n \int_use:N #3
+            \token_if_eq_meaning:NNTF 1 ##1
+              {
+                \__fp_to_tl:w \s__fp \__fp_chk:w ##1##2##3; ~ #2 ed ~ to ~
+                \token_if_eq_meaning:NNF 0 ##2 { - } #4 .
+              }
+              { An~#2~occurred. }
           }
-        #3 \l_fp_internal_tl \scan_stop:
-        \tex_advance:D #4 \c_one
+        \__fp_flag_on:n {#2}
+        #3 ##2
       }
-    \fp_standardise_aux:
-    \if_int_compare:w #4 < \c_one_hundred
-      \if_int_compare:w #4 > -\c_one_hundred
-      \else:
-        #1 \c_one
-        #2 \c_zero
-        #3 \c_zero
-        #4 \c_zero
+  }
+\cs_new_protected_nopar:Npn \__fp_invalid_operation:Nnw { }
+\cs_new_protected_nopar:Npn \__fp_invalid_operation:Nnww { }
+\cs_new_protected_nopar:Npn \__fp_division_by_zero:Nnw { }
+\cs_new_protected_nopar:Npn \__fp_division_by_zero:Nnww { }
+\cs_new_protected_nopar:Npn \__fp_overflow:w { }
+\cs_new_protected_nopar:Npn \__fp_underflow:w { }
+\__fp_trap:nn { invalid_operation } { error }
+\__fp_trap:nn { division_by_zero } { flag }
+\__fp_trap:nn { overflow } { flag }
+\__fp_trap:nn { underflow } { flag }
+\cs_new_eq:NN \__fp_error:n \__msg_expandable_error:n
+\cs_new:Npn \__fp_error:x #1
+  {
+    \exp_args:Nf \__msg_expandable_error:n
+      {
+        \__fp_error_loop:nwnN { \exp_stop_f: } #1 \prg_do_nothing:
+        \s__fp_mark { } \__fp_error_loop:nwnN \s__fp_mark { } \__fp_error_end:nw
+      }
+  }
+\cs_new:Npn \__fp_error_end:nw #1#2 \__fp_error_end:nw { #1 }
+\cs_new:Npn \__fp_error_loop:nwnN #1#2 \s__fp_mark #3 #4
+  {
+    \exp_after:wN #4 \tex_romannumeral:D -`0
+    #2
+    \s__fp_mark { #3 #1 } #4
+  }
+\msg_new:nnnn { kernel } { unknown-fpu-exception }
+  { The~FPU~exception~'#1'~is~not~known:~that~trap~will~never~be~triggered. }
+  {
+    The~only~exceptions~to~which~traps~can~be~attached~are \\
+    \iow_indent:n
+      {
+        * ~ invalid_operation \\
+        * ~ division_by_zero \\
+        * ~ overflow \\
+        * ~ underflow
+      }
+  }
+\msg_new:nnnn { kernel } { unknown-fpu-trap-type }
+  { The~FPU~trap~type~'#2'~is~not~known. }
+  {
+    The~trap~type~must~be~one~of \\
+    \iow_indent:n
+      {
+        * ~ error \\
+        * ~ flag \\
+        * ~ none
+      }
+  }
+%% File: l3fp-round.dtx Copyright(C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\cs_new:Npn \__fp_round_return_one:
+  { \exp_after:wN \c_one \tex_romannumeral:D }
+\cs_new:Npn \__fp_round_to_ninf:NNN #1 #2 #3
+  {
+    \if_meaning:w 2 #1
+      \if_int_compare:w #3 > \c_zero
+        \__fp_round_return_one:
       \fi:
-    \else:
-      \exp_after:wN \fp_overflow_msg:
     \fi:
+    \c_zero
   }
-\cs_new_protected_nopar:Npn \fp_standardise_aux: { }
-\cs_new_protected_nopar:Npn \fp_standardise_aux:w { }
-\cs_new_protected_nopar:Npn \fp_level_input_exponents:
+\cs_new:Npn \__fp_round_to_zero:NNN #1 #2 #3 { \c_zero }
+\cs_new:Npn \__fp_round_to_pinf:NNN #1 #2 #3
   {
-    \if_int_compare:w \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
-      \exp_after:wN \fp_level_input_exponents_a:
+    \if_meaning:w 0 #1
+      \if_int_compare:w #3 > \c_zero
+        \__fp_round_return_one:
+      \fi:
+    \fi:
+    \c_zero
+  }
+\cs_new:Npn \__fp_round_to_nearest:NNN #1 #2 #3
+  {
+    \if_int_compare:w #3 > \c_five
+      \__fp_round_return_one:
     \else:
-      \exp_after:wN \fp_level_input_exponents_b:
+      \if_meaning:w 5 #3
+        \if_int_odd:w #2 \exp_stop_f:
+          \__fp_round_return_one:
+        \fi:
+      \fi:
     \fi:
+    \c_zero
+  }
+\cs_new_eq:NN \__fp_round:NNN \__fp_round_to_nearest:NNN
+\cs_new:Npn \__fp_round_s:NNNw #1 #2 #3 #4;
+  {
+    \exp_after:wN \__fp_round:NNN
+    \exp_after:wN #1
+    \exp_after:wN #2
+    \int_use:N \__int_eval:w
+      \if_int_odd:w 0 \if_meaning:w 0 #3 1 \fi:
+                      \if_meaning:w 5 #3 1 \fi:
+                \exp_stop_f:
+        \if_int_compare:w \__int_eval:w #4 > \c_zero
+          1 +
+        \fi:
+      \fi:
+      #3
+    ;
+  }
+\cs_new:Npn \__fp_round:NNNN #1 #2 #3 #4
+  {
+    \exp_after:wN \__fp_round:NNN
+    \exp_after:wN #1
+    \exp_after:wN #2
+    \int_use:N \__int_eval:w
+      \if_int_odd:w 0 \if_meaning:w 0 #3 1 \fi:
+                      \if_meaning:w 5 #3 1 \fi:
+                \exp_stop_f:
+        \if_int_compare:w #4 > \c_zero
+          1 +
+        \fi:
+      \fi:
+      #3
+    \__int_eval_end:
   }
-\cs_new_protected_nopar:Npn \fp_level_input_exponents_a:
+\cs_new:Npn \__fp_round_to_ninf_neg:NNN #1 #2 #3
   {
-    \if_int_compare:w \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
-      \tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million
-      \exp_after:wN \use_i:nn \exp_after:wN
-        \fp_level_input_exponents_a:NNNNNNNNN
-          \int_use:N \l_fp_input_b_integer_int
-      \exp_after:wN \fp_level_input_exponents_a:
+    \if_meaning:w 0 #1
+      \if_int_compare:w #3 > \c_zero
+        \__fp_round_return_one:
+      \fi:
     \fi:
+    \c_zero
   }
-\cs_new_protected:Npn \fp_level_input_exponents_a:NNNNNNNNN
-  #1#2#3#4#5#6#7#8#9
+\cs_new:Npn \__fp_round_to_zero_neg:NNN #1 #2 #3
   {
-    \l_fp_input_b_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
-    \tex_advance:D \l_fp_input_b_decimal_int \c_one_thousand_million
-    \tex_divide:D \l_fp_input_b_decimal_int \c_ten
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        #9
-        \exp_after:wN \use_none:n
-          \int_use:N \l_fp_input_b_decimal_int
-      }
-    \l_fp_input_b_decimal_int \l_fp_internal_tl \scan_stop:
-    \tex_advance:D \l_fp_input_b_exponent_int \c_one
+    \if_int_compare:w #3 > \c_zero
+      \__fp_round_return_one:
+    \fi:
+    \c_zero
   }
-\cs_new_protected_nopar:Npn \fp_level_input_exponents_b:
+\cs_new:Npn \__fp_round_to_pinf_neg:NNN #1 #2 #3
   {
-    \if_int_compare:w \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int
-      \tex_advance:D \l_fp_input_a_integer_int \c_one_thousand_million
-      \exp_after:wN \use_i:nn \exp_after:wN
-        \fp_level_input_exponents_b:NNNNNNNNN
-          \int_use:N \l_fp_input_a_integer_int
-      \exp_after:wN \fp_level_input_exponents_b:
+    \if_meaning:w 2 #1
+      \if_int_compare:w #3 > \c_zero
+        \__fp_round_return_one:
+      \fi:
     \fi:
+    \c_zero
   }
-\cs_new_protected:Npn \fp_level_input_exponents_b:NNNNNNNNN
-  #1#2#3#4#5#6#7#8#9
+\cs_new_eq:NN \__fp_round_to_nearest_neg:NNN \__fp_round_to_nearest:NNN
+\cs_new_eq:NN \__fp_round_neg:NNN \__fp_round_to_nearest_neg:NNN
+\cs_new:Npn \__fp_round:Nww #1#2 ; #3 ;
   {
-    \l_fp_input_a_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \tex_divide:D \l_fp_input_a_decimal_int \c_ten
-    \tl_set:Nx \l_fp_internal_tl
+    \__fp_small_int:wTF #3; { \__fp_round:Nwn #1#2; }
       {
-        #9
-        \exp_after:wN \use_none:n
-          \int_use:N \l_fp_input_a_decimal_int
+        \__fp_error:x { {round(x,n)~with~n=} \__fp_to_tl:w #3; }
+        \exp_after:wN \c_nan_fp
       }
-    \l_fp_input_a_decimal_int \l_fp_internal_tl \scan_stop:
-    \tex_advance:D \l_fp_input_a_exponent_int \c_one
   }
-\cs_new_protected:Npn \fp_tmp:w #1#2 { }
-\cs_new_protected:Npn \fp_new:N #1
+\cs_new:Npn \__fp_round:Nwn #1 \s__fp \__fp_chk:w #2#3#4; #5
   {
-    \tl_new:N #1
-    \tl_gset_eq:NN #1 \c_zero_fp
+    \if_meaning:w 1 #2
+      \exp_after:wN \__fp_round_normal:NwNNnw
+      \exp_after:wN #1
+      \__int_value:w #5
+    \else:
+      \exp_after:wN \__fp_exp_after_o:w
+    \fi:
+    \s__fp \__fp_chk:w #2#3#4;
   }
-\cs_generate_variant:Nn \fp_new:N { c }
-\cs_new_protected:Npn \fp_const:Nn #1#2
+\cs_new:Npn \__fp_round_normal:NwNNnw #1#2 \s__fp \__fp_chk:w 1#3#4#5;
   {
-    \fp_new:N #1
-    \fp_gset:Nn #1 {#2}
+    \__fp_decimate:nNnnnn { \c_sixteen - #4 - #2 }
+      \__fp_round_normal_ii:NnnwNNnn #5 #1 #3 {#4} {#2}
   }
-\cs_generate_variant:Nn \fp_const:Nn { c }
-\cs_new_protected:Npn \fp_zero:N #1
-  { \tl_set_eq:NN #1 \c_zero_fp }
-\cs_new_protected:Npn \fp_gzero:N #1
-  { \tl_gset_eq:NN #1 \c_zero_fp }
-\cs_generate_variant:Nn \fp_zero:N { c }
-\cs_generate_variant:Nn \fp_gzero:N { c }
-\cs_new_protected:Npn \fp_zero_new:N  #1
-  { \fp_if_exist:NTF #1 { \fp_zero:N #1 } { \fp_new:N #1 } }
-\cs_new_protected:Npn \fp_gzero_new:N #1
-  { \fp_if_exist:NTF #1 { \fp_gzero:N #1 } { \fp_new:N #1 } }
-\cs_generate_variant:Nn \fp_zero_new:N  { c }
-\cs_generate_variant:Nn \fp_gzero_new:N { c }
-\cs_new_protected_nopar:Npn \fp_set:Nn  { \fp_set_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gset:Nn { \fp_set_aux:NNn \tl_gset:Nn }
-\cs_new_protected:Npn \fp_set_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-                -
-              \else:
-                +
-              \fi:
-              \int_use:N \l_fp_input_a_integer_int
-              .
-              \exp_after:wN \use_none:n
-                \int_use:N \l_fp_input_a_decimal_int
-              e
-              \int_use:N \l_fp_input_a_exponent_int
-            }
-        }
-    \fp_tmp:w
-  }
-\cs_generate_variant:Nn \fp_set:Nn  { c }
-\cs_generate_variant:Nn \fp_gset:Nn { c }
-\cs_new_protected_nopar:Npn \fp_set_from_dim:Nn
-  { \fp_set_from_dim_aux:NNn \tl_set:Nx }
-\cs_new_protected_nopar:Npn \fp_gset_from_dim:Nn
-  { \fp_set_from_dim_aux:NNn \tl_gset:Nx }
-\cs_new_protected:Npn \fp_set_from_dim_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \l_fp_internal_skip \etex_glueexpr:D #3 \scan_stop:
-      \l_fp_internal_dim \l_fp_internal_skip
-      \fp_split:Nn a
-        {
-          \exp_after:wN \fp_set_from_dim_aux:w
-            \dim_use:N \l_fp_internal_dim
-        }
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-                -
-              \else:
-                +
-              \fi:
-              \int_use:N \l_fp_input_a_integer_int
-              .
-              \exp_after:wN \use_none:n
-                \int_use:N \l_fp_input_a_decimal_int
-              e
-              \int_use:N \l_fp_input_a_exponent_int
-            }
-        }
-    \fp_tmp:w
+\cs_new:Npn \__fp_round_normal_ii:NnnwNNnn #1#2#3#4; #5#6
+  {
+    \exp_after:wN \__fp_round_normal_iii:NNwNnn
+    \int_use:N \__int_eval:w
+      \if_int_compare:w #2 > \c_zero
+        1 \__int_value:w #2
+        \exp_after:wN \__fp_round_pack:Nw
+        \int_use:N \__int_eval:w 1#3 +
+      \else:
+        \if_int_compare:w #3 > \c_zero
+          1 \__int_value:w #3 +
+        \fi:
+      \fi:
+      \exp_after:wN #5
+      \exp_after:wN #6
+      \use_none:nnnnnnn #3
+      #1
+      \__int_eval_end:
+      0000 0000 0000 0000 ; #6
   }
-\cs_set_protected_nopar:Npx \fp_set_from_dim_aux:w
+\cs_new:Npn \__fp_round_pack:Nw #1
+  { \if_meaning:w 2 #1 + \c_one \fi: \__int_eval_end: }
+\cs_new:Npn \__fp_round_normal_iii:NNwNnn #1 #2
   {
-    \cs_set:Npn \exp_not:N \fp_set_from_dim_aux:w
-      ##1 \tl_to_str:n { pt } {##1}
+    \if_meaning:w 0 #2
+      \exp_after:wN \__fp_round_special:NwwNnn
+      \exp_after:wN #1
+    \fi:
+    \__fp_pack_twice_four:wNNNNNNNN
+    \__fp_pack_twice_four:wNNNNNNNN
+    \__fp_round_normal_end:wwNnn
+    ; #2
   }
-\fp_set_from_dim_aux:w
-\cs_generate_variant:Nn \fp_set_from_dim:Nn  { c }
-\cs_generate_variant:Nn \fp_gset_from_dim:Nn { c }
-\dim_new:N \l_fp_internal_dim
-\skip_new:N \l_fp_internal_skip
-\cs_new_eq:NN \fp_set_eq:NN  \tl_set_eq:NN
-\cs_new_eq:NN \fp_set_eq:cN  \tl_set_eq:cN
-\cs_new_eq:NN \fp_set_eq:Nc  \tl_set_eq:Nc
-\cs_new_eq:NN \fp_set_eq:cc  \tl_set_eq:cc
-\cs_new_eq:NN \fp_gset_eq:NN \tl_gset_eq:NN
-\cs_new_eq:NN \fp_gset_eq:cN \tl_gset_eq:cN
-\cs_new_eq:NN \fp_gset_eq:Nc \tl_gset_eq:Nc
-\cs_new_eq:NN \fp_gset_eq:cc \tl_gset_eq:cc
-\cs_new_eq:NN \fp_show:N \tl_show:N
-\cs_new_eq:NN \fp_show:c \tl_show:c
-\cs_new:Npn \fp_use:N #1
-  { \exp_after:wN \fp_use_aux:w #1 \q_stop }
-\cs_generate_variant:Nn \fp_use:N { c }
-\cs_new:Npn \fp_use_aux:w #1#2 e #3 \q_stop
+\cs_new:Npn \__fp_round_normal_end:wwNnn #1;#2;#3#4#5
   {
-    \if:w #1 -
-      -
+    \exp_after:wN \__fp_exp_after_o:w \tex_romannumeral:D -`0
+    \__fp_sanitize:Nw #3 #4 ; #1 ;
+  }
+\cs_new:Npn \__fp_round_special:NwwNnn #1#2;#3;#4#5#6
+  {
+    \if_meaning:w 0 #1
+      \__fp_case_return:nw
+        { \exp_after:wN \__fp_zero_fp:N \exp_after:wN #4 }
+    \else:
+      \exp_after:wN \__fp_round_special_aux:Nw
+      \exp_after:wN #4
+      \int_use:N \__int_eval:w \c_one
+        \if_meaning:w 1 #1 -#6 \else: +#5 \fi:
     \fi:
-    \if_int_compare:w #3 > \c_zero
-      \exp_after:wN \fp_use_large:w
+    ;
+  }
+\cs_new:Npn \__fp_round_special_aux:Nw #1#2;
+  {
+    \exp_after:wN \__fp_exp_after_o:w \tex_romannumeral:D -`0
+    \__fp_sanitize:Nw #1#2; {1000}{0000}{0000}{0000};
+  }
+%% File: l3fp-parse.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\cs_new:Npn \__fp_parse_expand:w #1 { -`0 #1 }
+\cs_new:Npn \__fp_parse_return_semicolon:w
+    #1 \fi: \__fp_parse_expand:w { \fi: ; #1 }
+\group_begin:
+\char_set_catcode_other:N \S
+\char_set_catcode_other:N \F
+\char_set_catcode_other:N \P
+\char_set_lccode:nn { `\- } { `\_ }
+\tl_to_lowercase:n
+  {
+    \group_end:
+    \cs_new:Npn \__fp_type_from_scan:N #1
+      {
+        \exp_after:wN \__fp_type_from_scan:w
+        \token_to_str:N #1 \q_mark S--FP \q_mark \q_stop
+      }
+    \cs_new:Npn \__fp_type_from_scan:w #1 S--FP #2 \q_mark #3 \q_stop {#2}
+  }
+\cs_set_protected:Npn \__fp_tmp:w #1 #2 #3
+  {
+    \cs_new:cpn { __fp_parse_digits_ #1 :N } ##1
+      {
+        \if_int_compare:w \c_nine < 1 \token_to_str:N ##1 \exp_stop_f:
+          \token_to_str:N ##1 \exp_after:wN #2 \tex_romannumeral:D
+        \else:
+          \__fp_parse_return_semicolon:w #3 ##1
+        \fi:
+        \__fp_parse_expand:w
+      }
+  }
+\__fp_tmp:w {vii}  \__fp_parse_digits_vi:N   { 0000000 ; 7 }
+\__fp_tmp:w {vi}   \__fp_parse_digits_v:N    { 000000 ; 6 }
+\__fp_tmp:w {v}    \__fp_parse_digits_iv:N   { 00000 ; 5 }
+\__fp_tmp:w {iv}   \__fp_parse_digits_iii:N  { 0000 ; 4 }
+\__fp_tmp:w {iii}  \__fp_parse_digits_ii:N   { 000 ; 3 }
+\__fp_tmp:w {ii}   \__fp_parse_digits_i:N    { 00 ; 2 }
+\__fp_tmp:w {i}    \__fp_parse_digits_:N     { 0 ; 1 }
+\cs_new_nopar:Npn \__fp_parse_digits_:N { ; ; 0 }
+\cs_new:Npn \__fp_parse_operand:Nw #1 #2
+  {
+    \if_catcode:w \tex_relax:D #2
+      \if_meaning:w \tex_relax:D #2
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__fp_parse_operand_relax:NN
+      \else:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__fp_parse_operand_register:NN
+      \fi:
     \else:
-      \if_int_compare:w #3 < \c_zero
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \fp_use_small:w
+      \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__fp_parse_operand_digit:NN
       \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN \fp_use_none:w
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__fp_parse_operand_other:NN
       \fi:
     \fi:
-    #2 e #3 \q_stop
+    #1 #2
   }
-\cs_new:Npn \fp_use_none:w #1 e #2 \q_stop {#1}
-\cs_new:Npn \fp_use_small:w #1 . #2 e #3 \q_stop
+\group_begin:
+\char_set_catcode_other:N \P
+\char_set_catcode_other:N \T
+\tl_to_lowercase:n
   {
-    0 .
-    \prg_replicate:nn { -#3 - 1 } { 0 }
-    #1#2
+    \group_end:
+    \cs_new:Npn \__fp_parse_operand_register:NN #1#2
+      {
+        \exp_after:wN \__fp_parse_infix_after_operand:NwN
+        \exp_after:wN #1
+        \tex_romannumeral:D -`0
+          \exp_after:wN \__fp_parse_operand_register_aux:www
+          \tex_the:D
+            \exp_after:wN #2
+            \exp_after:wN P
+            \exp_after:wN T
+            \exp_after:wN \q_stop
+          \__int_value:w \__fp_parse_exponent:N
+      }
+    \cs_new:Npn \__fp_parse_operand_register_aux:www #1 PT #2 \q_stop #3 ;
+      { \__fp_parse:n { #1 e #3 } }
+  }
+\cs_new:Npn \__fp_parse_operand_relax:NN #1#2
+  {
+      \__fp_parse_operand_relax_aux:wwnw
+        #2 \s__fp_mark
+          {
+            \__fp_exp_after_o:nw
+              {
+                \tex_romannumeral:D -`0
+                \exp_after:wN \__fp_parse_infix:NN
+                \exp_after:wN #1 \tex_romannumeral:D \__fp_parse_expand:w
+              }
+            \s__fp
+          }
+        \s__fp #2
+          {
+            \__fp_error:n { Premature~end~in~fp~expression. }
+            \exp_after:wN \c_nan_fp
+            \tex_romannumeral:D -`0
+              \__fp_parse_infix:NN #1
+              \s__fp_mark
+          }
+        \s__fp_mark
+          {
+            \__fp_error:n { Erroneous~variable~#2 used! }
+            \exp_after:wN \c_nan_fp
+            \tex_romannumeral:D -`0
+              \exp_after:wN \__fp_parse_infix:NN
+              \exp_after:wN #1
+              \tex_romannumeral:D \__fp_parse_expand:w
+          }
+        \s__fp_mark \s__fp_stop
   }
-\cs_new:Npn \fp_use_large:w #1 . #2 e #3 \q_stop
+\cs_new:Npn \__fp_parse_operand_relax_aux:wwnw
+    #1 \s__fp #2 \s__fp_mark #3 #4 \s__fp_mark \s__fp_stop { #3 }
+\cs_new:Npn \__fp_parse_operand_other:NN #1 #2
   {
-    \if_int_compare:w #3 < \c_ten
-      \exp_after:wN \fp_use_large_aux_i:w
+    \if_int_compare:w
+        \__int_eval:w \tex_uccode:D `#2 / 26 = \c_three
+      \exp_after:wN \__fp_parse_operand_other_word_aux:Nw
+      \exp_after:wN #1
+      \tex_romannumeral:D
+        \exp_after:wN \__fp_parse_letters:NN
+        \exp_after:wN #2
+        \tex_romannumeral:D
     \else:
-      \exp_after:wN \fp_use_large_aux_ii:w
+      \exp_after:wN \__fp_parse_operand_other_prefix_aux:NNN
+      \exp_after:wN #1
+      \exp_after:wN #2
+      \cs:w __fp_parse_prefix_#2:Nw \exp_after:wN \cs_end:
+      \tex_romannumeral:D
     \fi:
-    #1#2 e #3 \q_stop
+    \__fp_parse_expand:w
   }
-\cs_new:Npn \fp_use_large_aux_i:w #1#2 e #3 \q_stop
+
+\cs_new:Npn \__fp_parse_letters:NN #1#2
   {
-    #1
-    \use:c { fp_use_large_aux_ #3 :w } #2 \q_stop
-  }
-\cs_new:cpn { fp_use_large_aux_1:w } #1#2 \q_stop { #1 . #2 }
-\cs_new:cpn { fp_use_large_aux_2:w } #1#2#3 \q_stop
-  { #1#2 . #3 }
-\cs_new:cpn { fp_use_large_aux_3:w } #1#2#3#4 \q_stop
-  { #1#2#3 . #4 }
-\cs_new:cpn { fp_use_large_aux_4:w } #1#2#3#4#5 \q_stop
-  { #1#2#3#4 . #5 }
-\cs_new:cpn { fp_use_large_aux_5:w } #1#2#3#4#5#6 \q_stop
-  { #1#2#3#4#5 . #6 }
-\cs_new:cpn { fp_use_large_aux_6:w } #1#2#3#4#5#6#7 \q_stop
-  { #1#2#3#4#5#6 . #7 }
-\cs_new:cpn { fp_use_large_aux_7:w } #1#2#3#4#5#6#7#8 \q_stop
-  { #1#2#3#4#6#7 . #8 }
-\cs_new:cpn { fp_use_large_aux_8:w } #1#2#3#4#5#6#7#8#9 \q_stop
-  { #1#2#3#4#5#6#7#8 . #9 }
-\cs_new:cpn { fp_use_large_aux_9:w } #1 \q_stop { #1 . }
-\cs_new:Npn \fp_use_large_aux_ii:w #1 e #2 \q_stop
+    \exp_after:wN \c_zero
+    \exp_after:wN #1
+    \tex_romannumeral:D
+      \if_int_compare:w
+          \if_catcode:w \tex_relax:D #2
+            \c_zero
+          \else:
+            \__int_eval:w \tex_uccode:D `#2 / 26
+          \fi:
+          = \c_three
+        \exp_after:wN \__fp_parse_letters:NN
+        \exp_after:wN #2
+        \tex_romannumeral:D
+        \exp_after:wN \__fp_parse_expand:w
+      \else:
+        \exp_after:wN \c_zero
+        \exp_after:wN ;
+        \exp_after:wN #2
+      \fi:
+  }
+\cs_new:Npn \__fp_parse_operand_other_word_aux:Nw #1 #2;
   {
-    #1
-    \prg_replicate:nn { #2 - 9 } { 0 }
-    .
+    \cs_if_exist_use:cF { __fp_parse_word_#2:N }
+      {
+        \__msg_expandable_error:n { Unknown~word~#2. }
+        \exp_after:wN \c_nan_fp
+        \tex_romannumeral:D -`0
+          \__fp_parse_infix:NN
+      }
+      #1
   }
-\cs_new_eq:NN \fp_if_exist:NTF \cs_if_exist:NTF
-\cs_new_eq:NN \fp_if_exist:NT  \cs_if_exist:NT
-\cs_new_eq:NN \fp_if_exist:NF  \cs_if_exist:NF
-\cs_new_eq:NN \fp_if_exist_p:N \cs_if_exist_p:N
-\cs_new_eq:NN \fp_if_exist:cTF \cs_if_exist:cTF
-\cs_new_eq:NN \fp_if_exist:cT  \cs_if_exist:cT
-\cs_new_eq:NN \fp_if_exist:cF  \cs_if_exist:cF
-\cs_new_eq:NN \fp_if_exist_p:c \cs_if_exist_p:c
-\cs_new:Npn \fp_to_dim:N #1 { \fp_use:N #1 pt }
-\cs_generate_variant:Nn \fp_to_dim:N { c }
-\cs_new:Npn \fp_to_int:N #1
-  { \exp_after:wN \fp_to_int_aux:w #1 \q_stop }
-\cs_generate_variant:Nn \fp_to_int:N { c }
-\cs_new:Npn \fp_to_int_aux:w #1#2 e #3 \q_stop
+\cs_new_eq:NN \s__fp_unknown \tex_relax:D
+\cs_new:Npn \__fp_parse_operand_other_prefix_aux:NNN #1#2#3
   {
-    \if:w #1 -
-      -
+    \if_meaning:w \tex_relax:D #3
+      \exp_after:wN \__fp_parse_operand_other_prefix_unknown:NNN
+      \exp_after:wN #2
     \fi:
-    \if_int_compare:w #3 < \c_zero
-      \exp_after:wN \fp_to_int_small:w
-    \else:
-      \exp_after:wN \fp_to_int_large:w
-    \fi:
-    #2 e #3 \q_stop
+    #3 #1
+  }
+\cs_new:Npn \__fp_parse_operand_other_prefix_unknown:NNN #1#2#3
+  {
+    \cs_if_exist:cTF { __fp_parse_infix_#1:N }
+      {
+        \__fp_error:n { Missing~number~before~'#1'. }
+        \exp_after:wN \c_nan_fp
+        \tex_romannumeral:D -`0
+          \__fp_parse_infix:NN #3 #1
+      }
+      {
+        \__fp_error:n { Unknown~symbol~#1~ignored. }
+        \__fp_parse_operand:Nw #3
+      }
   }
-\cs_new:Npn \fp_to_int_small:w #1 . #2 e #3 \q_stop
+\cs_new:Npn \__fp_parse_operand_digit:NN #1
   {
-    \if_int_compare:w #3 > \c_one
+    \exp_after:wN \__fp_parse_infix_after_operand:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+      \exp_after:wN \__fp_sanitize:wN
+      \int_use:N \__int_eval:w \c_zero \__fp_parse_trim_zeros:N
+  }
+\cs_new:Npn \__fp_parse_trim_zeros:N #1
+  {
+    \if:w 0 #1
+      \exp_after:wN \__fp_parse_trim_zeros:N
+      \tex_romannumeral:D
     \else:
-      \if_int_compare:w #1 < \c_five
-        0
+      \if:w . #1
+        \exp_after:wN \__fp_parse_strim_zeros:N
+        \tex_romannumeral:D
       \else:
-        1
+        \__fp_parse_trim_end:w #1
       \fi:
     \fi:
+    \__fp_parse_expand:w
   }
-\cs_new:Npn \fp_to_int_large:w #1 . #2 e #3 \q_stop
+\cs_new:Npn \__fp_parse_trim_end:w #1 \fi: \fi: \__fp_parse_expand:w
   {
-    \if_int_compare:w #3 < \c_ten
-      \exp_after:wN \fp_to_int_large_aux_i:w
+      \fi:
+    \fi:
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+      \exp_after:wN \__fp_parse_large:N
     \else:
-      \exp_after:wN \fp_to_int_large_aux_ii:w
+      \exp_after:wN \__fp_parse_zero:
     \fi:
-    #1#2 e #3 \q_stop
+    #1
   }
-\cs_new:Npn \fp_to_int_large_aux_i:w #1#2 e #3 \q_stop
-  { \use:c { fp_to_int_large_aux_ #3 :w } #2 \q_stop {#1} }
-\cs_new:cpn { fp_to_int_large_aux_1:w } #1#2 \q_stop
-  { \fp_to_int_large_aux:nnn { #2 0 } {#1} }
-\cs_new:cpn { fp_to_int_large_aux_2:w } #1#2#3 \q_stop
-  { \fp_to_int_large_aux:nnn { #3 00 } {#1#2} }
-\cs_new:cpn { fp_to_int_large_aux_3:w } #1#2#3#4 \q_stop
-  { \fp_to_int_large_aux:nnn { #4 000 } {#1#2#3} }
-\cs_new:cpn { fp_to_int_large_aux_4:w } #1#2#3#4#5 \q_stop
-  { \fp_to_int_large_aux:nnn { #5 0000 } {#1#2#3#4} }
-\cs_new:cpn { fp_to_int_large_aux_5:w } #1#2#3#4#5#6 \q_stop
-  { \fp_to_int_large_aux:nnn { #6 00000 } {#1#2#3#4#5} }
-\cs_new:cpn { fp_to_int_large_aux_6:w } #1#2#3#4#5#6#7 \q_stop
-  { \fp_to_int_large_aux:nnn { #7 000000 } {#1#2#3#4#5#6} }
-\cs_new:cpn { fp_to_int_large_aux_7:w } #1#2#3#4#5#6#7#8 \q_stop
-  { \fp_to_int_large_aux:nnn { #8 0000000 } {#1#2#3#4#5#6#7} }
-\cs_new:cpn { fp_to_int_large_aux_8:w } #1#2#3#4#5#6#7#8#9 \q_stop
-  { \fp_to_int_large_aux:nnn { #9 00000000 } {#1#2#3#4#5#6#7#8} }
-\cs_new:cpn { fp_to_int_large_aux_9:w } #1 \q_stop {#1}
-\cs_new:Npn \fp_to_int_large_aux:nnn #1#2#3
+\cs_new:Npn \__fp_parse_strim_zeros:N #1
   {
-    \if_int_compare:w #1 < \c_five_hundred_million
-      #3#2
+    \if:w 0 #1
+      - \c_one
+      \exp_after:wN \__fp_parse_strim_zeros:N
+      \tex_romannumeral:D
     \else:
-      \int_value:w \int_eval:w #3#2 + 1 \int_eval_end:
+      \__fp_parse_strim_end:w #1
     \fi:
+    \__fp_parse_expand:w
   }
-\cs_new:Npn \fp_to_int_large_aux_ii:w #1 e #2 \q_stop
+\cs_new:Npn \__fp_parse_strim_end:w #1 \fi: \__fp_parse_expand:w
   {
-    #1
-    \prg_replicate:nn { #2 - 9 } { 0 }
-  }
-\cs_new:Npn \fp_to_tl:N #1
-  { \exp_after:wN \fp_to_tl_aux:w #1 \q_stop }
-\cs_generate_variant:Nn \fp_to_tl:N { c }
-\cs_new:Npn \fp_to_tl_aux:w #1#2 e #3 \q_stop
-  {
-    \if:w #1 -
-      -
     \fi:
-    \if_int_compare:w #3 < \c_zero
-      \exp_after:wN \fp_to_tl_small:w
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+      \exp_after:wN \__fp_parse_small:N
     \else:
-      \exp_after:wN \fp_to_tl_large:w
+      \exp_after:wN \__fp_parse_zero:
     \fi:
-    #2 e #3 \q_stop
+    #1
   }
-\cs_new:Npn \fp_to_tl_large:w #1 e #2 \q_stop
+\cs_new:Npn \__fp_parse_zero:
   {
-    \if_int_compare:w #2 < \c_ten
-      \exp_after:wN \fp_to_tl_large_aux_i:w
-    \else:
-      \exp_after:wN \fp_to_tl_large_aux_ii:w
-    \fi:
-    #1 e #2 \q_stop
+    \exp_after:wN ; \exp_after:wN 1
+    \__int_value:w \__fp_parse_exponent:N
   }
-\cs_new:Npn \fp_to_tl_large_aux_i:w #1 e #2 \q_stop
-  { \use:c { fp_to_tl_large_ #2 :w } #1 \q_stop }
-\cs_new:Npn \fp_to_tl_large_aux_ii:w #1 . #2 e #3 \q_stop
+\cs_new:Npn \__fp_parse_small:N #1
   {
-    #1
-    \fp_to_tl_large_zeros:NNNNNNNNN #2
-    e #3
+    \exp_after:wN \__fp_parse_pack_leading:NNNNNww
+    \int_use:N \__int_eval:w 1 \token_to_str:N #1
+      \exp_after:wN \__fp_parse_small_leading:wwNN
+      \__int_value:w 1
+        \exp_after:wN \__fp_parse_digits_vii:N
+        \tex_romannumeral:D \__fp_parse_expand:w
   }
-\cs_new:cpn { fp_to_tl_large_0:w } #1 . #2 \q_stop
+\cs_new:Npn \__fp_parse_small_leading:wwNN 1 #1 ; #2; #3 #4
   {
-    #1
-    \fp_to_tl_large_zeros:NNNNNNNNN #2
+    #1 #2
+    \exp_after:wN \__fp_parse_pack_trailing:NNNNNNww
+    \exp_after:wN \c_zero
+    \int_use:N \__int_eval:w 1
+      \if_int_compare:w \c_nine < 1 \token_to_str:N #4 \exp_stop_f:
+        \token_to_str:N #4
+        \exp_after:wN \__fp_parse_small_trailing:wwNN
+        \__int_value:w 1
+          \exp_after:wN \__fp_parse_digits_vi:N
+          \tex_romannumeral:D
+      \else:
+        0000 0000 \__fp_parse_exponent:Nw #4
+      \fi:
+      \__fp_parse_expand:w
   }
-\cs_new:cpn { fp_to_tl_large_1:w } #1 . #2#3 \q_stop
+\cs_new:Npn \__fp_parse_small_trailing:wwNN 1 #1 ; #2; #3 #4
   {
-    #1#2
-    \fp_to_tl_large_zeros:NNNNNNNNN #3 0
+    #1 #2
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #4 \exp_stop_f:
+      \token_to_str:N #4
+      \exp_after:wN \__fp_parse_small_round:NN
+      \exp_after:wN #4
+      \tex_romannumeral:D
+    \else:
+      0 \__fp_parse_exponent:Nw #4
+    \fi:
+    \__fp_parse_expand:w
   }
-\cs_new:cpn { fp_to_tl_large_2:w } #1 . #2#3#4 \q_stop
+\cs_new:Npn \__fp_parse_pack_trailing:NNNNNNww #1 #2 #3#4#5#6 #7; #8 ;
   {
-    #1#2#3
-    \fp_to_tl_large_zeros:NNNNNNNNN #4 00
+    \if_meaning:w 2 #2 + \c_one \fi:
+    ; #8 + #1 ; {#3#4#5#6} {#7};
   }
-\cs_new:cpn { fp_to_tl_large_3:w } #1 . #2#3#4#5 \q_stop
+\cs_new:Npn \__fp_parse_pack_leading:NNNNNww #1 #2#3#4#5 #6; #7;
   {
-    #1#2#3#4
-    \fp_to_tl_large_zeros:NNNNNNNNN #5 000
+    + #7
+    \if_meaning:w 2 #1 \__fp_parse_pack_carry:w \fi:
+    ; 0 {#2#3#4#5} {#6}
   }
-\cs_new:cpn { fp_to_tl_large_4:w } #1 . #2#3#4#5#6 \q_stop
+\cs_new:Npn \__fp_parse_pack_carry:w \fi: ; 0 #1
+  { \fi: + \c_one ; 0 {1000} }
+\cs_new:Npn \__fp_parse_large:N #1
   {
-    #1#2#3#4#5
-    \fp_to_tl_large_zeros:NNNNNNNNN #6 0000
+    \exp_after:wN \__fp_parse_large_leading:wwNN
+    \__int_value:w 1 \token_to_str:N #1
+      \exp_after:wN \__fp_parse_digits_vii:N
+      \tex_romannumeral:D \__fp_parse_expand:w
   }
-\cs_new:cpn { fp_to_tl_large_5:w } #1 . #2#3#4#5#6#7 \q_stop
+\cs_new:Npn \__fp_parse_large_leading:wwNN 1 #1 ; #2; #3 #4
   {
-    #1#2#3#4#5#6
-    \fp_to_tl_large_zeros:NNNNNNNNN #7 00000
+    + \c_eight - #3
+    \exp_after:wN \__fp_parse_pack_leading:NNNNNww
+    \int_use:N \__int_eval:w 1 #1
+      \if_int_compare:w \c_nine < 1 \token_to_str:N #4 \exp_stop_f:
+        \exp_after:wN \__fp_parse_large_trailing:wwNN
+        \__int_value:w 1 \token_to_str:N #4
+          \exp_after:wN \__fp_parse_digits_vi:N
+          \tex_romannumeral:D
+      \else:
+        \if:w . #4
+          \exp_after:wN \__fp_parse_small_leading:wwNN
+          \__int_value:w 1
+            \cs:w
+              __fp_parse_digits_
+              \tex_romannumeral:D #3
+              :N \exp_after:wN
+            \cs_end:
+            \tex_romannumeral:D
+        \else:
+          #2
+          \exp_after:wN \__fp_parse_pack_trailing:NNNNNNww
+          \exp_after:wN \c_zero
+          \__int_value:w 1 0000 0000
+          \__fp_parse_exponent:Nw #4
+        \fi:
+      \fi:
+      \__fp_parse_expand:w
   }
-\cs_new:cpn { fp_to_tl_large_6:w } #1 . #2#3#4#5#6#7#8 \q_stop
+\cs_new:Npn \__fp_parse_large_trailing:wwNN 1 #1 ; #2; #3 #4
   {
-    #1#2#3#4#5#6#7
-    \fp_to_tl_large_zeros:NNNNNNNNN #8 000000
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #4 \exp_stop_f:
+      \exp_after:wN \__fp_parse_pack_trailing:NNNNNNww
+      \exp_after:wN \c_eight
+      \int_use:N \__int_eval:w 1 #1 \token_to_str:N #4
+        \exp_after:wN \__fp_parse_large_round:NN
+        \exp_after:wN #4
+        \tex_romannumeral:D
+    \else:
+      \exp_after:wN \__fp_parse_pack_trailing:NNNNNNww
+      \int_use:N \__int_eval:w \c_seven - #3 \exp_stop_f:
+      \int_use:N \__int_eval:w 1 #1
+        \if:w . #4
+          \exp_after:wN \__fp_parse_small_trailing:wwNN
+          \__int_value:w 1
+            \cs:w
+              __fp_parse_digits_
+              \tex_romannumeral:D #3
+              :N \exp_after:wN
+            \cs_end:
+            \tex_romannumeral:D
+        \else:
+          #2 0 \__fp_parse_exponent:Nw #4
+        \fi:
+    \fi:
+    \__fp_parse_expand:w
   }
-\cs_new:cpn { fp_to_tl_large_7:w } #1 . #2#3#4#5#6#7#8#9 \q_stop
+\cs_new:Npn \__fp_parse_exponent:Nw #1 #2 \__fp_parse_expand:w
   {
-    #1#2#3#4#5#6#7#8
-    \fp_to_tl_large_zeros:NNNNNNNNN #9 0000000
+    \exp_after:wN ;
+    \__int_value:w #2 \__fp_parse_exponent:N #1
   }
-\cs_new:cpn { fp_to_tl_large_8:w } #1 .
+\cs_new:Npn \__fp_parse_exponent:N #1
   {
-    #1
-    \use:c { fp_to_tl_large_8_aux:w }
+    \if:w e #1
+      \exp_after:wN \__fp_parse_exponent_ii:N
+      \tex_romannumeral:D
+    \else:
+      0 \__fp_parse_return_semicolon:w #1
+    \fi:
+    \__fp_parse_expand:w
   }
-\cs_new:cpn { fp_to_tl_large_8_aux:w } #1#2#3#4#5#6#7#8#9 \q_stop
+\cs_new:Npn \__fp_parse_exponent_ii:N #1
   {
-    #1#2#3#4#5#6#7#8
-    \fp_to_tl_large_zeros:NNNNNNNNN #9 00000000
+    \if_int_compare:w \if_catcode:w \tex_relax:D #1
+                \c_zero \else: `#1 \fi: > `9 \exp_stop_f:
+      0 \exp_after:wN ; \exp_after:wN e
+    \else:
+      \exp_after:wN \__fp_parse_exponent_sign:N
+    \fi:
+    #1
   }
-\cs_new:cpn { fp_to_tl_large_9:w } #1 . #2 \q_stop {#1#2}
-\cs_new:Npn \fp_to_tl_small:w #1 e #2 \q_stop
+\cs_new:Npn \__fp_parse_exponent_sign:N #1
   {
-    \if_int_compare:w #2 = \c_minus_one
-      \exp_after:wN \fp_to_tl_small_one:w
+    \if:w + \if:w - #1 + \fi: \token_to_str:N #1
+      \exp_after:wN \__fp_parse_exponent_sign:N
+      \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
     \else:
-      \if_int_compare:w #2 = -\c_two
-        \exp_after:wN \exp_after:wN \exp_after:wN \fp_to_tl_small_two:w
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN \fp_to_tl_small_aux:w
-      \fi:
+      \exp_after:wN \__fp_parse_exponent_body:N
+      \exp_after:wN #1
     \fi:
-    #1 e #2 \q_stop
   }
-\cs_new:Npn \fp_to_tl_small_one:w #1 . #2 e #3 \q_stop
+\cs_new:Npn \__fp_parse_exponent_body:N #1
   {
-    \if_int_compare:w \fp_use_ix:NNNNNNNNN #2 > \c_four
-      \if_int_compare:w
-        \int_eval:w #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
-          < \c_one_thousand_million
-        0.
-        \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN
-          \int_value:w \int_eval:w
-              #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
-            \int_eval_end:
-      \else:
-        1
-      \fi:
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+      \token_to_str:N #1
+      \exp_after:wN \__fp_parse_exponent_digits:N
+      \tex_romannumeral:D
     \else:
-      0. #1
-      \fp_to_tl_small_zeros:NNNNNNNNN #2
+      \__fp_parse_exponent_keep:NTF #1
+        { \__fp_parse_return_semicolon:w #1 }
+        {
+          \exp_after:wN ;
+          \tex_romannumeral:D
+        }
     \fi:
+    \__fp_parse_expand:w
   }
-\cs_new:Npn \fp_to_tl_small_two:w #1 . #2 e #3 \q_stop
+\cs_new:Npn \__fp_parse_exponent_digits:N #1
   {
-    \if_int_compare:w \fp_use_iix_ix:NNNNNNNNN #2 > \c_forty_four
-      \if_int_compare:w
-        \int_eval:w #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
-          < \c_one_thousand_million
-        0.0
-        \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN
-          \int_value:w \int_eval:w
-              #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
-            \int_eval_end:
-      \else:
-        0.1
-      \fi:
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+      \token_to_str:N #1
+      \exp_after:wN \__fp_parse_exponent_digits:N
+      \tex_romannumeral:D
     \else:
-      0.0
-      #1
-      \fp_to_tl_small_zeros:NNNNNNNNN #2
+      \__fp_parse_return_semicolon:w #1
     \fi:
+    \__fp_parse_expand:w
   }
-\cs_new:Npn \fp_to_tl_small_aux:w #1 . #2 e #3 \q_stop
+\prg_new_conditional:Npnn \__fp_parse_exponent_keep:N #1 { TF }
   {
-    #1
-    \fp_to_tl_large_zeros:NNNNNNNNN #2
-    e #3
-  }
-\cs_new:Npn \fp_to_tl_large_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {
-    \if_int_compare:w #9 = \c_zero
-      \if_int_compare:w #8 = \c_zero
-        \if_int_compare:w #7 = \c_zero
-          \if_int_compare:w #6 = \c_zero
-            \if_int_compare:w #5 = \c_zero
-              \if_int_compare:w #4 = \c_zero
-                \if_int_compare:w #3 = \c_zero
-                  \if_int_compare:w #2 = \c_zero
-                    \if_int_compare:w #1 = \c_zero
-                    \else:
-                      . #1
-                    \fi:
-                  \else:
-                    . #1#2
-                  \fi:
-                \else:
-                  . #1#2#3
-                \fi:
-              \else:
-                . #1#2#3#4
-              \fi:
-            \else:
-              . #1#2#3#4#5
-            \fi:
-          \else:
-            . #1#2#3#4#5#6
-          \fi:
+    \if_catcode:w \tex_relax:D #1
+      \if_meaning:w \tex_relax:D #1
+        \if_int_compare:w \pdftex_strcmp:D { \s__fp } { #1 } = \c_zero
+          0 \__fp_error:n { Cannot~use~floating~point~after~'e'. }
+          \prg_return_true:
         \else:
-          . #1#2#3#4#5#6#7
+          0 \__fp_error:n { Erroneous~variable~#1 used. }
+          \prg_return_false:
         \fi:
       \else:
-         . #1#2#3#4#5#6#7#8
-      \fi:
-    \else:
-      . #1#2#3#4#5#6#7#8#9
-    \fi:
-  }
-\cs_new:Npn \fp_to_tl_small_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {
-    \if_int_compare:w #9 = \c_zero
-      \if_int_compare:w #8 = \c_zero
-        \if_int_compare:w #7 = \c_zero
-          \if_int_compare:w #6 = \c_zero
-            \if_int_compare:w #5 = \c_zero
-              \if_int_compare:w #4 = \c_zero
-                \if_int_compare:w #3 = \c_zero
-                  \if_int_compare:w #2 = \c_zero
-                    \if_int_compare:w #1 = \c_zero
-                    \else:
-                      #1
-                    \fi:
-                  \else:
-                    #1#2
-                  \fi:
-                \else:
-                  #1#2#3
-                \fi:
-              \else:
-                #1#2#3#4
-              \fi:
-            \else:
-              #1#2#3#4#5
-            \fi:
-          \else:
-            #1#2#3#4#5#6
-          \fi:
+        \if_int_compare:w
+            \pdftex_strcmp:D { \__int_value:w #1 } { \tex_the:D #1 }
+            = \c_zero
+          \__int_value:w #1
         \else:
-          #1#2#3#4#5#6#7
+          0 \__fp_error:n { Cannot~use~a~dimension~(#1)~after~'e'. }
         \fi:
-      \else:
-         #1#2#3#4#5#6#7#8
+        \prg_return_false:
       \fi:
     \else:
-      #1#2#3#4#5#6#7#8#9
+      0 \__fp_error:n { Missing~exponent~after~'e'. }
+      \prg_return_true:
     \fi:
   }
-\cs_new:Npn \fp_use_iix_ix:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {#8#9}
-\cs_new:Npn \fp_use_ix:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {#9}
-\cs_new:Npn \fp_use_i_to_vii:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {#1#2#3#4#5#6#7}
-\cs_new:Npn \fp_use_i_to_iix:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {#1#2#3#4#5#6#7#8}
-\cs_new_protected_nopar:Npn \fp_round_figures:Nn
-  { \fp_round_figures_aux:NNn \tl_set:Nn }
-\cs_generate_variant:Nn \fp_round_figures:Nn { c }
-\cs_new_protected_nopar:Npn \fp_ground_figures:Nn
-  { \fp_round_figures_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_ground_figures:Nn { c }
-\cs_new_protected:Npn \fp_round_figures_aux:NNn #1#2#3
+\cs_new:Npn \__fp_cfs_round_loop:N #1
   {
-    \group_begin:
-      \fp_read:N #2
-      \int_set:Nn \l_fp_round_target_int { #3 - 1 }
-      \if_int_compare:w \l_fp_round_target_int < \c_ten
-        \exp_after:wN \fp_round:
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+      + \c_one
+      \if:w 0 #1
+        \exp_after:wN \__fp_cfs_round_loop:N
+        \tex_romannumeral:D
+      \else:
+        \exp_after:wN \__fp_cfs_round_up:N
+        \tex_romannumeral:D
       \fi:
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-                -
-              \else:
-                +
-              \fi:
-              \int_use:N \l_fp_input_a_integer_int
-              .
-              \exp_after:wN \use_none:n
-                \int_use:N \l_fp_input_a_decimal_int
-              e
-              \int_use:N \l_fp_input_a_exponent_int
-            }
-        }
-    \fp_tmp:w
+    \else:
+      \__fp_parse_return_semicolon:w \c_zero #1
+    \fi:
+    \__fp_parse_expand:w
   }
-\cs_new_protected_nopar:Npn \fp_round_places:Nn
-  { \fp_round_places_aux:NNn \tl_set:Nn }
-\cs_generate_variant:Nn \fp_round_places:Nn { c }
-\cs_new_protected_nopar:Npn \fp_ground_places:Nn
-  { \fp_round_places_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_ground_places:Nn { c }
-\cs_new_protected:Npn \fp_round_places_aux:NNn #1#2#3
+\cs_new:Npn \__fp_cfs_round_up:N #1
   {
-    \group_begin:
-      \fp_read:N #2
-      \int_set:Nn \l_fp_round_target_int
-        { #3 + \l_fp_input_a_exponent_int }
-      \if_int_compare:w \l_fp_round_target_int < \c_ten
-        \exp_after:wN \fp_round:
-      \fi:
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-                -
-              \else:
-                +
-              \fi:
-              \int_use:N \l_fp_input_a_integer_int
-              .
-              \exp_after:wN \use_none:n
-                \int_use:N \l_fp_input_a_decimal_int
-              e
-              \int_use:N \l_fp_input_a_exponent_int
-            }
-        }
-    \fp_tmp:w
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
+      + 1
+      \exp_after:wN \__fp_cfs_round_up:N
+      \tex_romannumeral:D
+    \else:
+      \__fp_parse_return_semicolon:w \c_one #1
+    \fi:
+    \__fp_parse_expand:w
+  }
+\cs_new:Npn \__fp_parse_large_round:NN #1#2
+  {
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f:
+      +
+      \exp_after:wN \__fp_round_s:NNNw
+      \exp_after:wN 0
+      \exp_after:wN #1
+      \exp_after:wN #2
+      \int_use:N \__int_eval:w
+        \exp_after:wN \__fp_parse_large_round_after:wNN
+        \int_use:N \__int_eval:w \c_one
+          \exp_after:wN \__fp_cfs_round_loop:N
+    \else: %^^A could be dot, or e, or other
+      \exp_after:wN \__fp_parse_large_round_dot_test:NNw
+      \exp_after:wN #1
+      \exp_after:wN #2
+    \fi:
   }
-\cs_new_protected_nopar:Npn \fp_round:
+\cs_new:Npn \__fp_parse_large_round_dot_test:NNw #1#2
   {
-    \bool_set_false:N \l_fp_round_carry_bool
-    \l_fp_round_position_int \c_eight
-    \tl_clear:N \l_fp_round_decimal_tl
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \exp_after:wN \use_i:nn \exp_after:wN
-      \fp_round_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int
+    \if:w . #2
+      \exp_after:wN \__fp_parse_small_round:NN
+      \exp_after:wN #1
+      \tex_romannumeral:D
+    \else:
+      \__fp_parse_exponent:Nw #2
+    \fi:
+    \__fp_parse_expand:w
   }
-\cs_new_protected:Npn \fp_round_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+\cs_new:Npn \__fp_parse_large_round_after:wNN #1 ; #2 #3
   {
-    \fp_round_loop:N #9#8#7#6#5#4#3#2#1
-    \bool_if:NT \l_fp_round_carry_bool
-      { \tex_advance:D \l_fp_input_a_integer_int \c_one }
-    \l_fp_input_a_decimal_int \l_fp_round_decimal_tl \scan_stop:
-    \if_int_compare:w \l_fp_input_a_integer_int < \c_ten
+    \if:w . #3
+      \exp_after:wN \__fp_parse_large_round_after_ii:wN
+      \int_use:N \__int_eval:w #1 +
+        \c_zero * \__int_eval:w \c_zero
+          \exp_after:wN \__fp_cfs_round_loop:N
+          \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
+    \else:
+      + #2
+      \exp_after:wN ;
+      \int_use:N \__int_eval:w #1 +
+        \exp_after:wN \__fp_parse_exponent:N
+        \exp_after:wN #3
+    \fi:
+  }
+\cs_new:Npn \__fp_parse_large_round_after_ii:wN #1 ; #2
+  {
+    + #2
+    \exp_after:wN ;
+    \int_use:N \__int_eval:w #1 +
+      \__fp_parse_exponent:N
+  }
+\cs_new:Npn \__fp_parse_small_round:NN #1#2
+  {
+    \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f:
+      +
+      \exp_after:wN \__fp_round_s:NNNw
+      \exp_after:wN 0
+      \exp_after:wN #1
+      \exp_after:wN #2
+      \int_use:N \__int_eval:w
+        \exp_after:wN \__fp_parse_small_round_after:wN
+        \int_use:N \__int_eval:w \c_zero
+          \exp_after:wN \__fp_cfs_round_loop:N
+          \tex_romannumeral:D
     \else:
-      \l_fp_input_a_integer_int \c_one
-      \tex_divide:D \l_fp_input_a_decimal_int \c_ten
-      \tex_advance:D \l_fp_input_a_exponent_int \c_one
+      \__fp_parse_exponent:Nw #2
     \fi:
+    \__fp_parse_expand:w
   }
-\cs_new_protected:Npn \fp_round_loop:N #1
+\cs_new:Npn \__fp_parse_small_round_after:wN #1; #2
   {
-    \if_int_compare:w \l_fp_round_position_int < \l_fp_round_target_int
-      \bool_if:NTF \l_fp_round_carry_bool
-        { \l_fp_internal_int \int_eval:w #1 + \c_one \scan_stop: }
-        { \l_fp_internal_int \int_eval:w #1 \scan_stop: }
-      \if_int_compare:w \l_fp_internal_int = \c_ten
-        \l_fp_internal_int \c_zero
+    + #2 \exp_after:wN ;
+    \__int_value:w \__fp_parse_exponent:N
+  }
+\cs_new:Npn \__fp_parse:n #1
+  {
+    \tex_romannumeral:D
+      \exp_after:wN \__fp_parse_after:ww
+      \tex_romannumeral:D
+        \__fp_parse_until:Nw \c_minus_one
+        \__fp_parse_expand:w #1 \s__fp_mark
+      \s__fp_stop
+  }
+\cs_new:Npn \__fp_parse_after:ww #1@ #2 \s__fp_stop
+  {
+    \c_zero #1
+  }
+\cs_new:Npn \__fp_parse_until:Nw #1
+  {
+    -`0
+    \exp_after:wN \__fp_parse_until_test:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+    \exp_after:wN \__fp_parse_operand:Nw
+    \exp_after:wN #1
+    \tex_romannumeral:D
+  }
+\cs_new:Npn \__fp_parse_until_test:NwN #1 #2 @ #3 { #3 #1 #2 @ }
+\cs_new:Npn \__fp_parse_stop_until:N #1 { }
+\cs_new:Npn \__fp_parse_infix_after_operand:NwN #1 #2;
+  {
+    \__fp_exp_after_f:nw { \__fp_parse_infix:NN #1 }
+    #2;
+  }
+\group_begin:
+  \char_set_catcode_letter:N \*
+  \cs_new:Npn \__fp_parse_infix:NN #1 #2
+    {
+      \if_catcode:w \tex_relax:D #2
+        \if_int_compare:w
+            \pdftex_strcmp:D { \s__fp_mark } { #2 }
+            = \c_zero
+          \exp_after:wN \exp_after:wN
+          \exp_after:wN \__fp_parse_infix_end:N
+        \else:
+          \exp_after:wN \exp_after:wN
+          \exp_after:wN \__fp_parse_infix_juxtapose:N
+        \fi:
+      \else:
+        \if_int_compare:w
+            \__int_eval:w \tex_uccode:D `#2 / 26
+            = \c_three
+          \exp_after:wN \exp_after:wN
+          \exp_after:wN \__fp_parse_infix_juxtapose:N
+        \else:
+          \exp_after:wN \__fp_parse_infix_check:NNN
+          \cs:w
+            __fp_parse_infix_#2:N
+            \exp_after:wN \exp_after:wN \exp_after:wN
+          \cs_end:
+        \fi:
+      \fi:
+      #1
+      #2
+    }
+  \cs_new:Npn \__fp_parse_infix_check:NNN #1#2#3
+    {
+      \if_meaning:w \tex_relax:D #1
+        \__msg_expandable_error:n { Missing~*~inserted. }
+        \exp_after:wN \__fp_parse_infix_*:N
+        \exp_after:wN #2
+        \exp_after:wN #3
       \else:
-        \bool_set_false:N \l_fp_round_carry_bool
+        \exp_after:wN #1
+        \exp_after:wN #2
+        \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
       \fi:
-      \tl_set:Nx \l_fp_round_decimal_tl
-        { \int_use:N \l_fp_internal_int \l_fp_round_decimal_tl }
+    }
+\group_end:
+\cs_new:Npn \__fp_parse_apply_binary:NwNwN #1 #2#3@ #4 #5#6@ #7
+  {
+    \exp_after:wN \__fp_parse_until_test:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+      \cs:w
+        __fp
+        \__fp_type_from_scan:N #2
+        \__fp_type_from_scan:N #5
+        _ #4 _o:ww
+      \cs_end:
+      #2#3 #5#6
+    \tex_romannumeral:D -`0 #7 #1
+  }
+\cs_new:Npn \__fp_parse_apply_unary_array:NNwN #1#2#3@#4
+  {
+    #2 #3 @
+    \tex_romannumeral:D -`0 #4 #1
+  }
+\cs_new:Npn \__fp_parse_apply_unary:NNwN #1#2#3@#4
+  {
+    #2 #3
+    \tex_romannumeral:D -`0 #4 #1
+  }
+\cs_new:Npn \__fp_parse_unary_type:N #1
+  { \__fp_type_from_scan:N #1 :w \cs_end: #1 }
+\cs_set_protected:Npn \__fp_tmp:w #1 #2
+  {
+    \cs_new_nopar:cpn { __fp_parse_word_#1:N }
+      { \exp_after:wN #2 \tex_romannumeral:D -`0 \__fp_parse_infix:NN }
+  }
+\__fp_tmp:w { inf } \c_inf_fp
+\__fp_tmp:w { nan } \c_nan_fp
+\__fp_tmp:w { pi  } \c_pi_fp
+\__fp_tmp:w { deg } \c_one_degree_fp
+\__fp_tmp:w { true } \c_one_fp
+\__fp_tmp:w { false } \c_zero_fp
+\__fp_tmp:w { pt } \c_one_fp
+\cs_set_protected:Npn \__fp_tmp:w #1 #2
+  {
+    \cs_new_nopar:cpn { __fp_parse_word_#1:N }
+      {
+        \__fp_exp_after_f:nw { \__fp_parse_infix:NN }
+        \s__fp \__fp_chk:w 10 #2 ;
+      }
+  }
+\__fp_tmp:w {in} { {2} {7227} {0000} {0000} {0000} }
+\__fp_tmp:w {pc} { {2} {1200} {0000} {0000} {0000} }
+\__fp_tmp:w {cm} { {2} {2845} {2755} {9055} {1181} }
+\__fp_tmp:w {mm} { {1} {2845} {2755} {9055} {1181} }
+\__fp_tmp:w {dd} { {1} {1070} {0085} {6496} {0630} }
+\__fp_tmp:w {cc} { {2} {1284} {0102} {7795} {2756} }
+\__fp_tmp:w {nd} { {1} {1066} {9783} {4645} {6693} }
+\__fp_tmp:w {nc} { {2} {1280} {3740} {1574} {8031} }
+\__fp_tmp:w {bp} { {1} {1003} {7500} {0000} {0000} }
+\__fp_tmp:w {sp} { {-4} {1525} {8789} {0625} {0000} }
+\tl_map_inline:nn { {em} {ex} }
+  {
+    \cs_new_nopar:cpn { __fp_parse_word_#1:N }
+      {
+        \exp_after:wN \dim_to_fp:n \exp_after:wN
+          { \dim_use:N \__dim_eval:w 1 #1 \exp_after:wN }
+        \tex_romannumeral:D -`0 \__fp_parse_infix:NN
+      }
+  }
+\tl_map_inline:nn { {abs} {cos} {cot} {exp} {ln} {sin} {tan} }
+  {
+    \cs_new:cpn { __fp_parse_word_#1:N } ##1
+      {
+        \exp_after:wN \__fp_parse_apply_unary:NNwN
+        \exp_after:wN ##1
+        \cs:w __fp_ #1 \exp_after:wN \__fp_parse_unary_type:N
+        \tex_romannumeral:D
+        \__fp_parse_until:Nw \c_fifteen
+        \__fp_parse_expand:w
+      }
+  }
+\cs_set_protected:Npn \__fp_tmp:w #1#2
+  {
+    \cs_new:Npn #1 ##1
+      {
+        \exp_after:wN \__fp_parse_apply_unary_array:NNwN
+        \exp_after:wN ##1
+        \exp_after:wN #2
+        \tex_romannumeral:D
+        \__fp_parse_until:Nw \c_sixteen \__fp_parse_expand:w
+      }
+  }
+\__fp_tmp:w \__fp_parse_word_max:N \__fp_max:w
+\__fp_tmp:w \__fp_parse_word_min:N \__fp_min:w
+ % \__fp_tmp:w \__fp_parse_word_mod:N \__fp_mod:w %^^A todo: not implemented!
+\cs_new:Npn \__fp_parse_word_round:N #1#2
+  {
+    \if_meaning:w + #2
+      \__fp_parse_round:Nw \__fp_round_to_pinf:NNN
     \else:
-      \tl_set:Nx \l_fp_round_decimal_tl { 0 \l_fp_round_decimal_tl }
-      \if_int_compare:w \l_fp_round_position_int = \l_fp_round_target_int
-        \if_int_compare:w #1 > \c_four
-          \bool_set_true:N \l_fp_round_carry_bool
+      \if_meaning:w 0 #2
+        \__fp_parse_round:Nw \__fp_round_to_zero:NNN
+      \else:
+        \if_meaning:w - #2
+          \__fp_parse_round:Nw \__fp_round_to_ninf:NNN
         \fi:
       \fi:
     \fi:
-    \tex_advance:D \l_fp_round_position_int \c_minus_one
-    \if_int_compare:w \l_fp_round_position_int > \c_minus_one
-      \exp_after:wN \fp_round_loop:N
+    \exp_after:wN \__fp_parse_apply_round:NNwN
+    \exp_after:wN #1
+    \exp_after:wN \__fp_round_to_nearest:NNN
+    \tex_romannumeral:D
+    \__fp_parse_until:Nw \c_sixteen \__fp_parse_expand:w #2
+  }
+\cs_new:Npn \__fp_parse_round:Nw
+    #1 #2 \__fp_round_to_nearest:NNN #3 \__fp_parse_expand:w #4
+  { #2 #1 #3 \__fp_parse_expand:w }
+\cs_new:Npn \__fp_parse_apply_round:NNwN #1#2#3@#4
+  {
+    \if_case:w \__int_eval:w \__fp_array_count:w #3@ - \c_one \__int_eval_end:
+         \__fp_round:Nwn #2 #3 {0} \tex_romannumeral:D
+    \or: \__fp_round:Nww #2 #3 \tex_romannumeral:D
+    \else:
+      \__fp_error:n { round()~expects~1~or~2~arguments. }
+      \exp_after:wN \c_nan_fp \tex_romannumeral:D
     \fi:
+    -`0 #4 #1
   }
-\cs_new_protected_nopar:Npn \fp_abs:N  { \fp_abs_aux:NN \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gabs:N { \fp_abs_aux:NN \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_abs:N  { c }
-\cs_generate_variant:Nn \fp_gabs:N { c }
-\cs_new_protected:Npn \fp_abs_aux:NN #1#2
+\cs_new_eq:cN { __fp_parse_prefix_+:Nw } \__fp_parse_operand:Nw
+\cs_set_protected:Npn \__fp_tmp:w #1#2
   {
-    \group_begin:
-      \fp_read:N #2
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \cs_set_protected_nopar:Npx \fp_tmp:w
+    \cs_new:cpn { __fp_parse_prefix_#1:Nw } ##1
+      {
+        \exp_after:wN \__fp_parse_apply_unary:NNwN
+        \exp_after:wN ##1
+        \cs:w __fp_ #2 \exp_after:wN \__fp_parse_unary_type:N
+        \tex_romannumeral:D
+        \if_int_compare:w \c_twelve < ##1
+          \__fp_parse_until:Nw ##1
+        \else:
+          \__fp_parse_until:Nw \c_twelve
+        \fi:
+        \__fp_parse_expand:w
+      }
+  }
+\__fp_tmp:w - { neg }
+\__fp_tmp:w ! { not }
+\group_begin:
+  \char_set_catcode_letter:N \)
+  \cs_new:cpn { __fp_parse_prefix_(:Nw } #1
+    {
+      \exp_after:wN \__fp_parse_lparen_after:NwN
+      \exp_after:wN #1
+      \tex_romannumeral:D
+      \if_int_compare:w #1 = \c_sixteen
+        \__fp_parse_until:Nw \c_one
+      \else:
+        \__fp_parse_until:Nw \c_zero
+      \fi:
+      \__fp_parse_expand:w
+    }
+  \cs_new:Npn \__fp_parse_lparen_after:NwN #1#2@#3
+    {
+      \token_if_eq_meaning:NNTF #3 \__fp_parse_infix_):N
         {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              +
-              \int_use:N \l_fp_input_a_integer_int
-              .
-              \exp_after:wN \use_none:n
-                \int_use:N \l_fp_input_a_decimal_int
-              e
-              \int_use:N \l_fp_input_a_exponent_int
-            }
+          \__fp_parse_exp_after_array:wf #2 \s__fp_stop
+          \exp_after:wN \__fp_parse_infix:NN
+          \exp_after:wN #1
+          \tex_romannumeral:D \__fp_parse_expand:w
         }
-    \fp_tmp:w
-  }
-\cs_new_protected_nopar:Npn \fp_neg:N  { \fp_neg_aux:NN \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gneg:N { \fp_neg_aux:NN \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_neg:N  { c }
-\cs_generate_variant:Nn \fp_gneg:N { c }
-\cs_new_protected:Npn \fp_neg_aux:NN #1#2
-  {
-    \group_begin:
-      \fp_read:N #2
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \tl_set:Nx \l_fp_internal_tl
         {
-          \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-            +
-          \else:
-            -
-          \fi:
-          \int_use:N \l_fp_input_a_integer_int
-          .
-          \exp_after:wN \use_none:n
-            \int_use:N \l_fp_input_a_decimal_int
-          e
-          \int_use:N \l_fp_input_a_exponent_int
+          \__fp_error:n { Missing~')'~inserted. }
+          #2 @ \__fp_parse_stop_until:N #3
         }
-    \exp_after:wN \group_end: \exp_after:wN
-    #1 \exp_after:wN #2 \exp_after:wN { \l_fp_internal_tl }
-  }
-\cs_new_protected_nopar:Npn \fp_add:Nn  { \fp_add_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gadd:Nn { \fp_add_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_add:Nn   { c }
-\cs_generate_variant:Nn \fp_gadd:Nn  { c }
-\cs_new_protected:Npn \fp_add_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_read:N #2
-      \fp_split:Nn b {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_b_sign_int
-        \l_fp_input_b_integer_int
-        \l_fp_input_b_decimal_int
-        \l_fp_input_b_exponent_int
-      \fp_add_core:
-    \fp_tmp:w #1#2
-  }
-\cs_new_protected_nopar:Npn \fp_add_core:
-  {
-    \fp_level_input_exponents:
-    \if_int_compare:w
-      \int_eval:w
-        \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
-        > \c_zero
-      \exp_after:wN \fp_add_sum:
-    \else:
-      \exp_after:wN \fp_add_difference:
-    \fi:
-    \l_fp_output_exponent_int \l_fp_input_a_exponent_int
-    \fp_standardise:NNNN
-      \l_fp_output_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \cs_set_protected:Npx \fp_tmp:w ##1##2
+    }
+\group_end:
+\cs_new:Npn \__fp_parse_exp_after_array:wf #1
+  {
+    \cs:w __fp \__fp_type_from_scan:N #1 _exp_after_f:nw \cs_end:
+      { \__fp_parse_exp_after_array:wf }
+    #1
+  }
+\cs_new:Npn \__fp_stop_exp_after_f:nw #1#2 { }
+\cs_new:cpn {__fp_parse_prefix_.:Nw} #1
+  {
+    \exp_after:wN \__fp_parse_infix_after_operand:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+      \exp_after:wN \__fp_sanitize:wN
+      \int_use:N \__int_eval:w \c_zero \__fp_parse_strim_zeros:N
+  }
+\cs_set_protected:Npn \__fp_tmp:w #1#2#3#4
+  {
+    \cs_new:Npn #1 ##1
       {
-        \group_end:
-        ##1 ##2
-          {
-             \if_int_compare:w \l_fp_output_sign_int < \c_zero
-              -
-            \else:
-              +
-            \fi:
-            \int_use:N \l_fp_output_integer_int
-            .
-            \exp_after:wN \use_none:n
-              \int_value:w \int_eval:w
-                 \l_fp_output_decimal_int + \c_one_thousand_million
-            e
-            \int_use:N \l_fp_output_exponent_int
-          }
+        \if_int_compare:w ##1 < #3
+          \exp_after:wN @
+          \exp_after:wN \__fp_parse_apply_binary:NwNwN
+          \exp_after:wN #2
+          \tex_romannumeral:D
+          \__fp_parse_until:Nw #4
+          \exp_after:wN \__fp_parse_expand:w
+        \else:
+          \exp_after:wN @
+          \exp_after:wN \__fp_parse_stop_until:N
+          \exp_after:wN #1
+        \fi:
       }
   }
-\cs_new_protected_nopar:Npn \fp_add_sum:
-  {
-    \l_fp_output_sign_int \l_fp_input_a_sign_int
-    \l_fp_output_integer_int
-      \int_eval:w
-        \l_fp_input_a_integer_int + \l_fp_input_b_integer_int
-      \scan_stop:
-    \l_fp_output_decimal_int
-      \int_eval:w
-        \l_fp_input_a_decimal_int + \l_fp_input_b_decimal_int
-      \scan_stop:
-    \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
-    \else:
-      \tex_advance:D \l_fp_output_integer_int \c_one
-      \tex_advance:D \l_fp_output_decimal_int -\c_one_thousand_million
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_add_difference:
-  {
-    \l_fp_output_integer_int
-      \int_eval:w
-        \l_fp_input_a_integer_int - \l_fp_input_b_integer_int
-      \scan_stop:
-    \l_fp_output_decimal_int
-      \int_eval:w
-        \l_fp_input_a_decimal_int - \l_fp_input_b_decimal_int
-      \scan_stop:
-    \if_int_compare:w \l_fp_output_decimal_int < \c_zero
-      \tex_advance:D \l_fp_output_integer_int \c_minus_one
-      \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
-    \fi:
-    \if_int_compare:w \l_fp_output_integer_int < \c_zero
-      \l_fp_output_sign_int \l_fp_input_b_sign_int
-      \if_int_compare:w \l_fp_output_decimal_int = \c_zero
-        \l_fp_output_integer_int -\l_fp_output_integer_int
+\group_begin:
+  \char_set_catcode_other:N \&
+  \__fp_tmp:w \__fp_parse_infix_juxtapose:N * \c_thirty_two \c_thirty_two
+  \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_ / :N } / \c_ten \c_ten
+  \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_mul:N } * \c_ten \c_ten
+  \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_ - :N } - \c_nine \c_nine
+  \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_ + :N } + \c_nine \c_nine
+  \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_and:N } & \c_five \c_five
+  \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_ or:N } | \c_four \c_four
+\group_end:
+\group_begin:
+  \char_set_catcode_letter:N ^
+  \__fp_tmp:w \__fp_parse_infix_^:N ^ \c_fifteen \c_fourteen
+  \cs_new:cpn { __fp_parse_infix_*:N } #1#2
+    {
+      \if:w * #2
+        \exp_after:wN \__fp_parse_infix_^:N
+        \exp_after:wN #1
       \else:
-        \l_fp_output_decimal_int
-          \int_eval:w
-            \c_one_thousand_million - \l_fp_output_decimal_int
-          \scan_stop:
-        \l_fp_output_integer_int
-           \int_eval:w
-             - \l_fp_output_integer_int - \c_one
-           \scan_stop:
-      \fi:
-    \else:
-      \l_fp_output_sign_int \l_fp_input_a_sign_int
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_sub:Nn  { \fp_sub_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gsub:Nn { \fp_sub_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_sub:Nn   { c }
-\cs_generate_variant:Nn \fp_gsub:Nn  { c }
-\cs_new_protected:Npn \fp_sub_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_read:N #2
-      \fp_split:Nn b {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_b_sign_int
-        \l_fp_input_b_integer_int
-        \l_fp_input_b_decimal_int
-        \l_fp_input_b_exponent_int
-      \tex_multiply:D \l_fp_input_b_sign_int \c_minus_one
-      \fp_add_core:
-    \fp_tmp:w #1#2
-  }
-\cs_new_protected_nopar:Npn \fp_mul:Nn  { \fp_mul_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gmul:Nn { \fp_mul_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_mul:Nn  { c }
-\cs_generate_variant:Nn \fp_gmul:Nn { c }
-\cs_new_protected:Npn \fp_mul_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_read:N #2
-      \fp_split:Nn b {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_b_sign_int
-        \l_fp_input_b_integer_int
-        \l_fp_input_b_decimal_int
-        \l_fp_input_b_exponent_int
-      \fp_mul_internal:
-      \l_fp_output_exponent_int
-        \int_eval:w
-          \l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int
-        \scan_stop:
-      \fp_standardise:NNNN
-        \l_fp_output_sign_int
-        \l_fp_output_integer_int
-        \l_fp_output_decimal_int
-        \l_fp_output_exponent_int
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              \if_int_compare:w
-                \int_eval:w
-                  \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
-                  < \c_zero
-                \if_int_compare:w
-                  \int_eval:w
-                    \l_fp_output_integer_int + \l_fp_output_decimal_int
-                    = \c_zero
-                  +
-                \else:
-                  -
-                \fi:
-              \else:
-                +
-             \fi:
-              \int_use:N \l_fp_output_integer_int
-              .
-              \exp_after:wN \use_none:n
-                \int_value:w \int_eval:w
-                   \l_fp_output_decimal_int + \c_one_thousand_million
-              e
-              \int_use:N \l_fp_output_exponent_int
-            }
-        }
-    \fp_tmp:w
-  }
-\cs_new_protected_nopar:Npn \fp_mul_internal:
-  {
-    \fp_mul_split:NNNN \l_fp_input_a_decimal_int
-      \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
-    \fp_mul_split:NNNN \l_fp_input_b_decimal_int
-      \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
-    \l_fp_mul_output_int \c_zero
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_mul_b_i_int
-    \tex_divide:D \l_fp_mul_output_int \c_one_thousand
-    \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_input_b_integer_int
-    \fp_mul_end_level:
-    \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_input_b_integer_int
-    \fp_mul_end_level:
-    \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_input_b_integer_int
-    \fp_mul_end_level:
-    \l_fp_output_decimal_int 0 \l_fp_mul_output_tl \scan_stop:
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_input_b_integer_int
-    \fp_mul_end_level:
-    \l_fp_output_integer_int 0 \l_fp_mul_output_tl \scan_stop:
-  }
-\cs_new_protected:Npn \fp_mul_split:NNNN #1#2#3#4
-  {
-    \tex_advance:D #1 \c_one_thousand_million
-    \cs_set_protected:Npn \fp_mul_split_aux:w
-       ##1##2##3##4##5##6##7##8##9 \q_stop {
-        #2 ##2##3##4 \scan_stop:
-        #3 ##5##6##7 \scan_stop:
-        #4 ##8##9    \scan_stop:
-      }
-    \exp_after:wN \fp_mul_split_aux:w \int_use:N #1 \q_stop
-    \tex_advance:D #1 -\c_one_thousand_million
+        \exp_after:wN \__fp_parse_infix_mul:N
+        \exp_after:wN #1
+        \exp_after:wN #2
+      \fi:
+    }
+\group_end:
+\group_begin:
+  \char_set_catcode_letter:N \|
+  \char_set_catcode_letter:N \&
+  \cs_new:Npn \__fp_parse_infix_|:N #1#2
+    {
+      \if:w | #2
+        \exp_after:wN \__fp_parse_infix_|:N
+        \exp_after:wN #1
+        \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
+      \else:
+        \exp_after:wN \__fp_parse_infix_or:N
+        \exp_after:wN #1
+        \exp_after:wN #2
+      \fi:
+    }
+  \cs_new:Npn \__fp_parse_infix_&:N #1#2
+    {
+      \if:w & #2
+        \exp_after:wN \__fp_parse_infix_&:N
+        \exp_after:wN #1
+        \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
+      \else:
+        \exp_after:wN \__fp_parse_infix_and:N
+        \exp_after:wN #1
+        \exp_after:wN #2
+      \fi:
+    }
+\group_end:
+\cs_new:cpn { __fp_parse_infix_<:N } #1
+  {
+    \__fp_infix_compare:N #1 \c_one_fp
+      \c_zero_fp  \c_zero_fp \c_zero_fp \c_zero_fp <
   }
-\cs_new_protected:Npn \fp_mul_product:NN #1#2
+\cs_new:cpn { __fp_parse_infix_=:N } #1
   {
-    \l_fp_mul_output_int
-      \int_eval:w \l_fp_mul_output_int + #1 * #2 \scan_stop:
+    \__fp_infix_compare:N #1 \c_one_fp
+      \c_zero_fp \c_zero_fp \c_zero_fp \c_zero_fp =
   }
-\cs_new_protected_nopar:Npn \fp_mul_end_level:
+\cs_new:cpn { __fp_parse_infix_>:N } #1
   {
-    \tex_advance:D \l_fp_mul_output_int \c_one_thousand_million
-    \exp_after:wN \use_i:nn \exp_after:wN
-      \fp_mul_end_level:NNNNNNNNN \int_use:N \l_fp_mul_output_int
+    \__fp_infix_compare:N #1 \c_one_fp
+      \c_zero_fp \c_zero_fp \c_zero_fp \c_zero_fp >
   }
-\cs_new_protected:Npn \fp_mul_end_level:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+\cs_new:cpn { __fp_parse_infix_!:N } #1
   {
-    \tl_set:Nx \l_fp_mul_output_tl { #7#8#9 \l_fp_mul_output_tl }
-    \l_fp_mul_output_int #1#2#3#4#5#6 \scan_stop:
+    \exp_after:wN \__fp_parse_infix_excl_aux:NN
+    \exp_after:wN #1 \tex_romannumeral:D \__fp_parse_expand:w
   }
-\cs_new_protected_nopar:Npn \fp_div:Nn  { \fp_div_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gdiv:Nn { \fp_div_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_div:Nn  { c }
-\cs_generate_variant:Nn \fp_gdiv:Nn { c }
-\cs_new_protected:Npn \fp_div_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_read:N #2
-      \fp_split:Nn b {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_b_sign_int
-        \l_fp_input_b_integer_int
-        \l_fp_input_b_decimal_int
-        \l_fp_input_b_exponent_int
-      \if_int_compare:w
-        \int_eval:w
-          \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
-          = \c_zero
-        \cs_set_protected:Npx \fp_tmp:w ##1##2
-          {
-            \group_end:
-            #1 \exp_not:N #2 { \c_undefined_fp }
-          }
+\cs_new:Npn \__fp_parse_infix_excl_aux:NN #1#2
+  {
+    \if_catcode:w \tex_relax:D #2
+      \__fp_parse_infix_excl_error:
+    \else:
+      \if_int_compare:w `#2 > `? \exp_stop_f:
+        \__fp_parse_infix_excl_error:
       \else:
-        \if_int_compare:w
-          \int_eval:w
-            \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-            = \c_zero
-          \cs_set_protected:Npx \fp_tmp:w ##1##2
-            {
-              \group_end:
-              #1 \exp_not:N #2 { \c_zero_fp }
-            }
+        \if_int_compare:w `#2 < `< \exp_stop_f:
+          \__fp_parse_infix_excl_error:
+        \fi:
+      \fi:
+    \fi:
+    \__fp_infix_compare:N #1 \c_zero_fp
+      \c_one_fp \c_one_fp \c_one_fp \c_one_fp #2
+  }
+\cs_new:Npn \__fp_parse_infix_excl_error:
+  { \__msg_expandable_error:n { Missing~relation~symbol~after~'!'. } }
+\cs_new:Npn \__fp_infix_compare:N #1
+  {
+    \if_int_compare:w #1 < \c_seven
+      \exp_after:wN \__fp_parse_compare:NNNNNw
+    \else:
+      \exp_after:wN @
+      \exp_after:wN \__fp_parse_stop_until:N
+      \exp_after:wN \__fp_infix_compare:N
+    \fi:
+  }
+\cs_new:Npn \__fp_parse_compare:NNNNNw #1#2#3#4#5#6
+  {
+    \if_case:w
+          \if_catcode:w \tex_relax:D #6
+            \c_minus_one
+          \else:
+            \__int_eval:w `#6 - `< \__int_eval_end:
+          \fi:
+         \__fp_parse_compare_expand:NNNNNw #1#1#3#4#5
+    \or: \__fp_parse_compare_expand:NNNNNw #1#2#1#4#5
+    \or: \__fp_parse_compare_expand:NNNNNw #1#2#3#1#5
+    \or: \__fp_parse_compare_expand:NNNNNw #1#2#3#4#1
+    \else: \__fp_parse_compare_end:NNNN #2#3#4#5#6
+    \fi:
+  }
+\cs_new:Npn \__fp_parse_compare_expand:NNNNNw #1#2#3#4#5
+  {
+    \exp_after:wN \__fp_parse_compare:NNNNNw
+    \exp_after:wN #1
+    \exp_after:wN #2
+    \exp_after:wN #3
+    \exp_after:wN #4
+    \exp_after:wN #5
+    \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
+  }
+\cs_new:Npn \__fp_parse_compare_end:NNNN #1#2#3#4#5 \fi:
+  {
+    \fi:
+    \exp_after:wN @
+    \exp_after:wN \__fp_parse_apply_compare:NwNNNNwN
+    \exp_after:wN #1
+    \exp_after:wN #2
+    \exp_after:wN #3
+    \exp_after:wN #4
+    \tex_romannumeral:D
+    \__fp_parse_until:Nw \c_seven \__fp_parse_expand:w #5
+  }
+\cs_new:Npn \__fp_parse_apply_compare:NwNNNNwN #1 #2@ #3#4#5#6 #7@ #8
+  {
+    \exp_after:wN \__fp_parse_until_test:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+      \exp_after:wN \exp_after:wN
+      \exp_after:wN \exp_after:wN
+      \exp_after:wN \exp_after:wN
+      \if_case:w \__fp_compare:ww #2 #7 \exp_stop_f:
+             #4
+      \or:   #5
+      \or:   #6
+      \else: #3
+      \fi:
+    \tex_romannumeral:D -`0 #8 #1
+  }
+\group_begin:
+  \char_set_catcode_letter:N \?
+  \cs_new:Npn \__fp_parse_infix_?:N #1
+    {
+      \if_int_compare:w #1 < \c_three
+        \exp_after:wN @
+        \exp_after:wN \__fp_ternary:NwwN
+        \tex_romannumeral:D
+        \__fp_parse_until:Nw \c_three
+        \exp_after:wN \__fp_parse_expand:w
+      \else:
+        \exp_after:wN @
+        \exp_after:wN \__fp_parse_stop_until:N
+        \exp_after:wN \__fp_parse_infix_?:N
+      \fi:
+    }
+  \cs_new:Npn \__fp_parse_infix_::N #1
+    {
+      \if_int_compare:w #1 < \c_three
+        \__msg_expandable_error:n { Missing~'?'~inserted~for~'?:'. }
+        \exp_after:wN @
+        \exp_after:wN \__fp_ternary_ii:NwwN
+        \tex_romannumeral:D
+        \__fp_parse_until:Nw \c_two
+        \exp_after:wN \__fp_parse_expand:w
+      \else:
+        \exp_after:wN @
+        \exp_after:wN \__fp_parse_stop_until:N
+        \exp_after:wN \__fp_parse_infix_::N
+      \fi:
+    }
+\group_end:
+\group_begin:
+  \char_set_catcode_letter:N \)
+  \cs_new:Npn \__fp_parse_infix_):N #1
+    {
+      \if_int_compare:w #1 < \c_zero
+        \__fp_error:n { Extra~')'~ignored. }
+        \exp_after:wN \__fp_parse_infix:NN
+        \exp_after:wN #1
+        \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
+      \else:
+        \exp_after:wN @
+        \exp_after:wN \__fp_parse_stop_until:N
+        \exp_after:wN \__fp_parse_infix_):N
+      \fi:
+    }
+\group_end:
+\cs_new:Npn \__fp_parse_infix_end:N #1
+  { @ \__fp_parse_stop_until:N \__fp_parse_infix_end:N }
+\group_begin:
+  \char_set_catcode_letter:N \,
+  \cs_new:Npn \__fp_parse_infix_,:N #1
+    {
+      \if_int_compare:w #1 > \c_one
+        \exp_after:wN @
+        \exp_after:wN \__fp_parse_stop_until:N
+        \exp_after:wN \__fp_parse_infix_,:N
+      \else:
+        \if_int_compare:w #1 = \c_one
+          \exp_after:wN \__fp_parse_infix_comma:w
+          \tex_romannumeral:D
         \else:
-          \exp_after:wN \exp_after:wN \exp_after:wN \fp_div_internal:
+          \exp_after:wN \__fp_parse_infix_comma_gobble:w
+          \tex_romannumeral:D
         \fi:
+        \__fp_parse_until:Nw \c_one
+        \exp_after:wN \__fp_parse_expand:w
       \fi:
-    \fp_tmp:w #1#2
-  }
-\cs_new_protected_nopar:Npn \fp_div_internal: {
-  \l_fp_output_integer_int \c_zero
-  \l_fp_output_decimal_int \c_zero
-  \cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
-  \l_fp_div_offset_int \c_one_hundred_million
-  \fp_div_loop:
-  \l_fp_output_exponent_int
-    \int_eval:w
-      \l_fp_input_a_exponent_int - \l_fp_input_b_exponent_int
-    \scan_stop:
-  \fp_standardise:NNNN
-    \l_fp_output_sign_int
-    \l_fp_output_integer_int
-    \l_fp_output_decimal_int
-    \l_fp_output_exponent_int
-  \cs_set_protected:Npx \fp_tmp:w ##1##2
+    }
+  \cs_new:Npn \__fp_parse_infix_comma:w #1 @
+    { #1 @ \__fp_parse_stop_until:N }
+  \cs_new:Npn \__fp_parse_infix_comma_gobble:w #1 @
     {
-      \group_end:
-      ##1 ##2
-        {
-          \if_int_compare:w
-            \int_eval:w
-              \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
-              < \c_zero
-            \if_int_compare:w
-              \int_eval:w
-                \l_fp_output_integer_int + \l_fp_output_decimal_int
-                = \c_zero
-              +
-            \else:
-              -
-            \fi:
+      \__fp_error:n { Unexpected~comma:~extra~arguments~ignored. }
+      @ \__fp_parse_stop_until:N
+    }
+\group_end:
+%% File: l3fp-logic.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\cs_new_eq:NN \fp_if_exist:NTF \cs_if_exist:NTF
+\cs_new_eq:NN \fp_if_exist:NT  \cs_if_exist:NT
+\cs_new_eq:NN \fp_if_exist:NF  \cs_if_exist:NF
+\cs_new_eq:NN \fp_if_exist_p:N \cs_if_exist_p:N
+\cs_new_eq:NN \fp_if_exist:cTF \cs_if_exist:cTF
+\cs_new_eq:NN \fp_if_exist:cT  \cs_if_exist:cT
+\cs_new_eq:NN \fp_if_exist:cF  \cs_if_exist:cF
+\cs_new_eq:NN \fp_if_exist_p:c \cs_if_exist_p:c
+\cs_new:Npn \__fp_compare:ww \s__fp \__fp_chk:w #1#2#3; \s__fp \__fp_chk:w #4#5#6;
+  {
+    \__int_value:w
+      \if_meaning:w 3 #1 \exp_after:wN \__fp_compare_nan:w \fi:
+      \if_meaning:w 3 #4 \exp_after:wN \__fp_compare_nan:w \fi:
+      \if_meaning:w 2 #2 - \fi:
+      \if_meaning:w #2 #5
+        \if_meaning:w #1 #4
+          \if_meaning:w 1 #1
+            \__fp_compare_mantissa:ww #3; #6;
           \else:
-            +
+            0
           \fi:
-          \int_use:N \l_fp_output_integer_int
-          .
-          \exp_after:wN \use_none:n
-            \int_value:w \int_eval:w
-               \l_fp_output_decimal_int + \c_one_thousand_million
-             \int_eval_end:
-          e
-          \int_use:N \l_fp_output_exponent_int
-        }
-    }
-}
-\cs_new_protected_nopar:Npn \fp_div_loop:
-  {
-    \l_fp_count_int \c_zero
-    \fp_div_divide:
-    \fp_div_store:
-    \tex_multiply:D \l_fp_input_a_integer_int \c_ten
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \exp_after:wN \fp_div_loop_step:w
-      \int_use:N \l_fp_input_a_decimal_int \q_stop
-    \if_int_compare:w
-      \int_eval:w \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-        > \c_zero
-        \if_int_compare:w \l_fp_div_offset_int > \c_zero
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \fp_div_loop:
+        \else:
+          \if_int_compare:w #1 < #4 - \fi: 1
         \fi:
-    \fi:
+      \else:
+        \if_meaning:w 0 #1
+          \if_meaning:w 0 #4
+            0
+          \else:
+            1
+          \fi:
+        \else:
+          1
+        \fi:
+      \fi:
+    \exp_stop_f:
   }
-\cs_new_protected_nopar:Npn \fp_div_divide:
+\cs_new:Npn \__fp_compare_nan:w #1 \exp_stop_f: { \c_two }
+\cs_new:Npn \__fp_compare_mantissa:ww #1#2; #3#4;
   {
-    \if_int_compare:w \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
-      \exp_after:wN \fp_div_divide_aux:
+    \if_int_compare:w #1 = #3 \exp_stop_f:
+      \__fp_compare_mantissa:nnnnnnnn #2 #4
     \else:
-      \if_int_compare:w \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
-      \else:
-        \if_int_compare:w
-          \l_fp_input_a_decimal_int < \l_fp_input_b_decimal_int
+      \if_int_compare:w #1 < #3 - \fi: 1
+    \fi:
+  }
+\cs_new:Npn \__fp_compare_mantissa:nnnnnnnn #1#2#3#4#5#6#7#8
+  {
+    \if_int_compare:w #1 = #5 \exp_stop_f:
+      \if_int_compare:w #2 = #6 \exp_stop_f:
+        \if_int_compare:w #3 = #7 \exp_stop_f:
+          \if_int_compare:w #4 = #8 \exp_stop_f:
+            0
+          \else:
+            \if_int_compare:w #4 < #8 - \fi: 1
+          \fi:
         \else:
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \fp_div_divide_aux:
+          \if_int_compare:w #3 < #7 - \fi: 1
         \fi:
+      \else:
+        \if_int_compare:w #2 < #6 - \fi: 1
       \fi:
+    \else:
+      \if_int_compare:w #1 < #5 - \fi: 1
     \fi:
   }
-\cs_new_protected_nopar:Npn \fp_div_divide_aux:
+\prg_new_conditional:Npnn \fp_compare:nNn #1#2#3 { p , T , F , TF }
   {
-    \tex_advance:D \l_fp_count_int \c_one
-    \tex_advance:D \l_fp_input_a_integer_int -\l_fp_input_b_integer_int
-    \tex_advance:D \l_fp_input_a_decimal_int -\l_fp_input_b_decimal_int
-    \if_int_compare:w \l_fp_input_a_decimal_int < \c_zero
-      \tex_advance:D \l_fp_input_a_integer_int \c_minus_one
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \if_int_compare:w
+        \exp_after:wN \__fp_compare_aux:wn
+          \tex_romannumeral:D -`0 \__fp_parse:n {#3} {#1}
+        = \__int_eval:w `#2 - `= \__int_eval_end:
+      \prg_return_true:
+    \else:
+      \prg_return_false:
     \fi:
-    \fp_div_divide:
   }
-\cs_new_protected_nopar:Npn \fp_div_store: { }
-\cs_new_protected_nopar:Npn \fp_div_store_integer:
+\cs_new:Npn \__fp_compare_aux:wn #1; #2
   {
-    \l_fp_output_integer_int \l_fp_count_int
-    \cs_set_eq:NN \fp_div_store: \fp_div_store_decimal:
+    \exp_after:wN \__fp_compare:ww
+      \tex_romannumeral:D -`0 \__fp_parse:n {#2} #1;
   }
-\cs_new_protected_nopar:Npn \fp_div_store_decimal:
+\prg_new_conditional:Npnn \fp_compare:n #1 { p , T , F , TF }
   {
-    \l_fp_output_decimal_int
-      \int_eval:w
-        \l_fp_output_decimal_int +
-        \l_fp_count_int * \l_fp_div_offset_int
-      \int_eval_end:
-    \tex_divide:D \l_fp_div_offset_int \c_ten
+    \exp_after:wN \__fp_compare_aux:w
+    \tex_romannumeral:D -`0 \__fp_parse:n {#1}
   }
-\cs_new_protected:Npn \fp_div_loop_step:w #1#2#3#4#5#6#7#8#9 \q_stop
+\cs_new:Npn \__fp_compare_aux:w \s__fp \__fp_chk:w #1#2;
   {
-    \l_fp_input_a_integer_int
-      \int_eval:w #2 + \l_fp_input_a_integer_int  \int_eval_end:
-    \l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
+    \if_meaning:w 0 #1
+      \prg_return_false:
+    \else:
+      \prg_return_true:
+    \fi:
   }
-\cs_new_protected:Npn \fp_add:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+\cs_new:Npn \__fp_not:w \s__fp \__fp_chk:w #1#2;
   {
-    #7 \int_eval:w #1 + #4 \int_eval_end:
-    #8 \int_eval:w #2 + #5 \int_eval_end:
-    #9 \int_eval:w #3 + #6 \int_eval_end:
-    \if_int_compare:w #9 < \c_one_thousand_million
+    \if_meaning:w 0 #1
+      \exp_after:wN \exp_after:wN \exp_after:wN \c_one_fp
     \else:
-      \tex_advance:D #8 \c_one
-      \tex_advance:D #9 -\c_one_thousand_million
+      \exp_after:wN \exp_after:wN \exp_after:wN \c_zero_fp
     \fi:
-    \if_int_compare:w #8 < \c_one_thousand_million
+  }
+\cs_new:cpn { __fp_ \iow_char:N \& _o:ww } #1 \s__fp \__fp_chk:w #2#3;
+  {
+    \if_meaning:w 0 #2 #1
+      \__fp_and_return:wNw \s__fp \__fp_chk:w #2#3;
+    \fi:
+    \__fp_exp_after_o:w
+  }
+\cs_new_nopar:cpx { __fp_ \iow_char:N \| _o:ww }
+  { \exp_not:c { __fp_ \iow_char:N \& _o:ww } \exp_not:N \else: }
+\cs_new:Npn \__fp_and_return:wNw #1; \fi: #2#3; { \fi: #2 #1; }
+\cs_new:Npn \__fp_ternary:NwwN #1 #2@ #3@ #4
+  {
+    \if_meaning:w \__fp_parse_infix_::N #4
+      \__fp_ternary_loop:Nw
+        #2
+        \s__fp \__fp_chk:w { \__fp_ternary_loop_break:w } ;
+      \__fp_ternary_break_point:n { \exp_after:wN \__fp_ternary_i:NwwN }
+      \exp_after:wN #1
+      \tex_romannumeral:D -`0
+      \__fp_parse_exp_after_array:wf #3 \s__fp_stop
+      \exp_after:wN @
+      \tex_romannumeral:D
+        \__fp_parse_until:Nw \c_two
+        \__fp_parse_expand:w
     \else:
-      \tex_advance:D #7 \c_one
-      \tex_advance:D #8 -\c_one_thousand_million
+      \__fp_error:n { Missing~':'~clause~for~'?:'. }
+      \exp_after:wN \__fp_parse_until_test:NwN
+      \exp_after:wN #1
+      \tex_romannumeral:D -`0
+      \__fp_parse_exp_after_array:wf #3 \s__fp_stop
+      \exp_after:wN #4
+      \exp_after:wN #1
     \fi:
   }
-\cs_new_protected:Npn \fp_sub:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+\cs_new:Npn \__fp_ternary_loop_break:w #1 \fi: #2 \__fp_ternary_break_point:n #3
   {
-    #7 \int_eval:w #1 - #4 \int_eval_end:
-    #8 \int_eval:w #2 - #5 \int_eval_end:
-    #9 \int_eval:w #3 - #6 \int_eval_end:
-    \if_int_compare:w #9 < \c_zero
-      \tex_advance:D #8 \c_minus_one
-      \tex_advance:D #9 \c_one_thousand_million
-    \fi:
-    \if_int_compare:w #8 < \c_zero
-      \tex_advance:D #7 \c_minus_one
-      \tex_advance:D #8 \c_one_thousand_million
+    \c_zero = \c_zero \fi:
+    \exp_after:wN \__fp_ternary_ii:NwwN
+  }
+\cs_new:Npn \__fp_ternary_loop:Nw \s__fp \__fp_chk:w #1#2;
+  {
+    \if_int_compare:w #1 > \c_zero
+      \exp_after:wN \__fp_ternary_map_break:
     \fi:
-    \if_int_compare:w #7 < \c_zero
-      \if_int_compare:w \int_eval:w #8 + #9 = \c_zero
-        #7 -#7
-      \else:
-        \tex_advance:D #7 \c_one
-        #8 \int_eval:w \c_one_thousand_million - #8 \int_eval_end:
-        #9 \int_eval:w \c_one_thousand_million - #9 \int_eval_end:
-      \fi:
-    \fi:
-  }
-\cs_new_protected:Npn \fp_mul:NNNNNN #1#2#3#4#5#6
-  {
-    \fp_mul_split:NNNN #1
-      \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
-    \fp_mul_split:NNNN #2
-      \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
-    \fp_mul_split:NNNN #3
-      \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
-    \fp_mul_split:NNNN #4
-      \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int
-    \l_fp_mul_output_int \c_zero
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_vi_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_v_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int        \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_v_int         \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_vi_int        \l_fp_mul_b_i_int
-    \tex_divide:D \l_fp_mul_output_int \c_one_thousand
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_v_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_v_int        \l_fp_mul_b_i_int
-    \fp_mul_end_level:
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_i_int
-    \fp_mul_end_level:
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_i_int
-    \fp_mul_end_level:
-    #6 0 \l_fp_mul_output_tl \scan_stop:
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_i_int
-    \fp_mul_end_level:
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_i_int
-    \fp_mul_end_level:
-    \fp_mul_end_level:
-    #5 0 \l_fp_mul_output_tl \scan_stop:
-  }
-\cs_new_protected:Npn \fp_mul:NNNNNNNNN #1#2#3#4#5#6#7#8#9
-  {
-    \fp_mul_split:NNNN #2
-      \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
-    \fp_mul_split:NNNN #3
-      \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
-    \fp_mul_split:NNNN #5
-      \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
-    \fp_mul_split:NNNN #6
-      \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int
-    \l_fp_mul_output_int \c_zero
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_vi_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_v_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int        \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_v_int         \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_vi_int        \l_fp_mul_b_i_int
-    \tex_divide:D \l_fp_mul_output_int \c_one_thousand
-    \fp_mul_product:NN #1                       \l_fp_mul_b_vi_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_v_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_v_int        \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_vi_int       #4
-    \fp_mul_end_level:
-    \fp_mul_product:NN #1                       \l_fp_mul_b_v_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_v_int        #4
-    \fp_mul_end_level:
-    \fp_mul_product:NN #1                       \l_fp_mul_b_iv_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_iv_int       #4
-    \fp_mul_end_level:
-    #9 0 \l_fp_mul_output_tl \scan_stop:
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN #1                       \l_fp_mul_b_iii_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_iii_int      #4
-    \fp_mul_end_level:
-    \fp_mul_product:NN #1                       \l_fp_mul_b_ii_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_ii_int       #4
-    \fp_mul_end_level:
-    \fp_mul_product:NN #1                       \l_fp_mul_b_i_int
-    \fp_mul_product:NN \l_fp_mul_a_i_int        #4
-    \fp_mul_end_level:
-    #8 0 \l_fp_mul_output_tl \scan_stop:
-    \tl_clear:N \l_fp_mul_output_tl
-    \fp_mul_product:NN #1 #4
-    \fp_mul_end_level:
-    #7 0 \l_fp_mul_output_tl \scan_stop:
-  }
-\cs_new_protected:Npn \fp_div_integer:NNNNN #1#2#3#4#5
-  {
-    \l_fp_internal_int #1
-    \tex_divide:D \l_fp_internal_int #3
-    \l_fp_internal_int \int_eval:w #1 - \l_fp_internal_int * #3 \int_eval_end:
+    \__fp_ternary_loop:Nw
+  }
+\cs_new:Npn \__fp_ternary_map_break: #1 \__fp_ternary_break_point:n #2 {#2}
+\cs_new:Npn \__fp_ternary_i:NwwN #1#2@#3@#4
+  {
+    \exp_after:wN \__fp_parse_until_test:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+    \__fp_parse_exp_after_array:wf #2 \s__fp_stop
     #4 #1
-    \tex_divide:D #4 #3
-    #5 #2
-    \tex_divide:D #5 #3
-    \tex_multiply:D \l_fp_internal_int \c_one_thousand
-    \tex_divide:D \l_fp_internal_int #3
-    #5 \int_eval:w #5 + \l_fp_internal_int * \c_one_million \int_eval_end:
-    \if_int_compare:w #5 > \c_one_thousand_million
-      \tex_advance:D #4 \c_one
-      \tex_advance:D #5 -\c_one_thousand_million
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_extended_normalise:
-  {
-    \fp_extended_normalise_aux_i:
-    \fp_extended_normalise_aux_ii:
-  }
-\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_i:
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int > \c_zero
-      \tex_multiply:D \l_fp_input_a_integer_int \c_ten
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \exp_after:wN \fp_extended_normalise_aux_i:w
-        \int_use:N \l_fp_input_a_decimal_int \q_stop
-       \exp_after:wN \fp_extended_normalise_aux_i:
-     \fi:
-  }
-\cs_new_protected:Npn \fp_extended_normalise_aux_i:w
-  #1#2#3#4#5#6#7#8#9 \q_stop
-  {
-    \l_fp_input_a_integer_int
-      \int_eval:w \l_fp_input_a_integer_int + #2 \scan_stop:
-    \l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
-    \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
-    \exp_after:wN \fp_extended_normalise_aux_ii:w
-      \int_use:N \l_fp_input_a_extended_int \q_stop
-  }
-\cs_new_protected:Npn \fp_extended_normalise_aux_ii:w
-  #1#2#3#4#5#6#7#8#9 \q_stop
-  {
-    \l_fp_input_a_decimal_int
-      \int_eval:w \l_fp_input_a_decimal_int + #2 \scan_stop:
-    \l_fp_input_a_extended_int #3#4#5#6#7#8#9 0 \scan_stop:
-    \tex_advance:D \l_fp_input_a_exponent_int \c_minus_one
-  }
-\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_ii:
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int < \c_zero
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-      \exp_after:wN \use_i:nn \exp_after:wN
-        \fp_extended_normalise_ii_aux:NNNNNNNNN
-        \int_use:N \l_fp_input_a_decimal_int
-       \exp_after:wN \fp_extended_normalise_aux_ii:
-     \fi:
-  }
-\cs_new_protected:Npn \fp_extended_normalise_ii_aux:NNNNNNNNN
-  #1#2#3#4#5#6#7#8#9
-  {
-    \if_int_compare:w \l_fp_input_a_integer_int = \c_zero
-      \l_fp_input_a_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
-    \else:
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \int_use:N \l_fp_input_a_integer_int
-          #1#2#3#4#5#6#7#8
-        }
-      \l_fp_input_a_integer_int \c_zero
-      \l_fp_input_a_decimal_int \l_fp_internal_tl \scan_stop:
-    \fi:
-    \tex_divide:D \l_fp_input_a_extended_int \c_ten
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        #9
-        \int_use:N \l_fp_input_a_extended_int
-      }
-    \l_fp_input_a_extended_int \l_fp_internal_tl \scan_stop:
-    \tex_advance:D \l_fp_input_a_exponent_int \c_one
   }
-\cs_new_protected_nopar:Npn \fp_extended_normalise_output:
+\cs_new:Npn \__fp_ternary_ii:NwwN #1#2@#3@#4
   {
-    \if_int_compare:w \l_fp_output_integer_int > \c_nine
-      \tex_advance:D \l_fp_output_integer_int \c_one_thousand_million
-      \exp_after:wN \use_i:nn \exp_after:wN
-        \fp_extended_normalise_output_aux_i:NNNNNNNNN
-        \int_use:N \l_fp_output_integer_int
-      \exp_after:wN \fp_extended_normalise_output:
-    \fi:
+    \exp_after:wN \__fp_parse_until_test:NwN
+    \exp_after:wN #1
+    \tex_romannumeral:D -`0
+    \__fp_parse_exp_after_array:wf #3 \s__fp_stop
+    #4 #1
   }
-\cs_new_protected:Npn \fp_extended_normalise_output_aux_i:NNNNNNNNN
-  #1#2#3#4#5#6#7#8#9
+\cs_new:Npn \__fp_max:w #1@
   {
-    \l_fp_output_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
-    \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        #9
-        \exp_after:wN \use_none:n
-        \int_use:N \l_fp_output_decimal_int
-      }
-    \exp_after:wN \fp_extended_normalise_output_aux_ii:NNNNNNNNN
-      \l_fp_internal_tl
+    \exp_after:wN \__fp_minmax_loop:Nww
+    \exp_after:wN \c_minus_one
+    \c_minus_inf_fp
+    #1
+    \s__fp \__fp_chk:w { 3 \__fp_minmax_break:w } ;
   }
-\cs_new_protected:Npn \fp_extended_normalise_output_aux_ii:NNNNNNNNN
-  #1#2#3#4#5#6#7#8#9
+\cs_new:Npn \__fp_min:w #1@
   {
-    \l_fp_output_decimal_int #1#2#3#4#5#6#7#8#9 \scan_stop:
-    \fp_extended_normalise_output_aux:N
+    \exp_after:wN \__fp_minmax_loop:Nww
+    \exp_after:wN \c_one
+    \c_inf_fp
+    #1
+    \s__fp \__fp_chk:w { 3 \__fp_minmax_break:w } ;
   }
-\cs_new_protected:Npn \fp_extended_normalise_output_aux:N #1
+\cs_new:Npn \__fp_minmax_loop:Nww
+    #1 \s__fp \__fp_chk:w #2#3; \s__fp \__fp_chk:w #4#5;
   {
-    \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million
-    \tex_divide:D \l_fp_output_extended_int \c_ten
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        #1
-        \exp_after:wN \use_none:n
-          \int_use:N \l_fp_output_extended_int
-      }
-    \l_fp_output_extended_int \l_fp_internal_tl \scan_stop:
-    \tex_advance:D \l_fp_output_exponent_int \c_one
-  }
-\cs_new_protected_nopar:Npn \fp_trig_normalise:
-  {
-    \if_int_compare:w \l_fp_input_a_exponent_int < \c_ten
-      \l_fp_input_a_extended_int \c_zero
-      \fp_extended_normalise:
-      \fp_trig_normalise_aux:
-      \if_int_compare:w \l_fp_input_a_integer_int < \c_zero
-        \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
-      \fi:
-       \exp_after:wN \fp_trig_octant:
-    \else:
-      \l_fp_input_a_sign_int    \c_one
-      \l_fp_output_integer_int  \c_zero
-      \l_fp_output_decimal_int  \c_zero
-      \l_fp_output_exponent_int \c_zero
-      \exp_after:wN \fp_trig_overflow_msg:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_trig_normalise_aux:
-  {
-    \if_int_compare:w \l_fp_input_a_integer_int > \c_three
-      \fp_trig_sub:NNN
-        \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
-      \exp_after:wN \fp_trig_normalise_aux:
-    \else:
-      \if_int_compare:w \l_fp_input_a_integer_int > \c_two
-        \if_int_compare:w \l_fp_input_a_decimal_int > \c_fp_pi_decimal_int
-          \fp_trig_sub:NNN
-            \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \fp_trig_normalise_aux:
-          \fi:
+    \if_meaning:w 3 #4
+      \if_meaning:w 3 #2
+        \__fp_minmax_i:ww
+      \else:
+        \__fp_minmax_ii:ww
+      \fi:
+    \else:
+      \if_int_compare:w \__fp_compare:ww \s__fp \__fp_chk:w #2#3;
+                               \s__fp \__fp_chk:w #4#5; = #1
+        \__fp_minmax_ii:ww
+      \else:
+        \__fp_minmax_i:ww
       \fi:
     \fi:
-  }
-\cs_new_protected:Npn \fp_trig_sub:NNN #1#2#3
+    \__fp_minmax_loop:Nww #1
+      \s__fp \__fp_chk:w #2#3;
+      \s__fp \__fp_chk:w #4#5;
+  }
+\cs_new:Npn \__fp_minmax_i:ww
+    #1 \__fp_minmax_loop:Nww #2 \s__fp #3; \s__fp #4;
+  { #1 \__fp_minmax_loop:Nww #2 \s__fp #3; }
+\cs_new:Npn \__fp_minmax_ii:ww
+    #1 \__fp_minmax_loop:Nww #2 \s__fp #3; \s__fp #4;
+  { #1 \__fp_minmax_loop:Nww #2 \s__fp #4; }
+\cs_new:Npn \__fp_minmax_break:w #1 \__fp_minmax_loop:Nww #2 #3; #4;
   {
-    \l_fp_input_a_integer_int
-      \int_eval:w \l_fp_input_a_integer_int - #1 \int_eval_end:
-    \l_fp_input_a_decimal_int
-      \int_eval:w \l_fp_input_a_decimal_int - #2 \int_eval_end:
-    \l_fp_input_a_extended_int
-      \int_eval:w \l_fp_input_a_extended_int - #3 \int_eval_end:
-    \if_int_compare:w \l_fp_input_a_extended_int < \c_zero
-      \tex_advance:D \l_fp_input_a_decimal_int \c_minus_one
-      \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
     \fi:
-    \if_int_compare:w \l_fp_input_a_decimal_int < \c_zero
-      \tex_advance:D \l_fp_input_a_integer_int \c_minus_one
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \__fp_exp_after_o:w #3;
+  }
+%% File: l3fp-basics.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\cs_new:Npn \__fp_basics_pack_low:NNNNNw #1 #2#3#4#5 #6;
+  {
+    \if_meaning:w 2 #1
+      + \c_one
     \fi:
-    \if_int_compare:w \l_fp_input_a_integer_int < \c_zero
-      \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
-      \if_int_compare:w
-        \int_eval:w
-          \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
-        = \c_zero
-        \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
-      \else:
-        \l_fp_input_a_integer_int
-           \int_eval:w
-             - \l_fp_input_a_integer_int - \c_one
-           \int_eval_end:
-        \l_fp_input_a_decimal_int
-          \int_eval:w
-            \c_one_thousand_million - \l_fp_input_a_decimal_int
-          \int_eval_end:
-        \l_fp_input_a_extended_int
-          \int_eval:w
-            \c_one_thousand_million - \l_fp_input_a_extended_int
-          \int_eval_end:
-      \fi:
+    ; {#2#3#4#5} {#6} ;
+  }
+\cs_new:Npn \__fp_basics_pack_high:NNNNNw #1 #2#3#4#5 #6;
+  {
+    \if_meaning:w 2 #1
+      \__fp_basics_pack_high_carry:w
     \fi:
+    ; {#2#3#4#5} {#6}
   }
-\cs_new_protected_nopar:Npn \fp_trig_octant:
+\cs_new:Npn \__fp_basics_pack_high_carry:w \fi: ; #1
+  { \fi: + \c_one ; {1000} }
+\cs_new:Npn \__fp_basics_return_nan_nan:NNww #1#2 #3; #4;
+  { \__fp_exp_after_o:w \s__fp \__fp_chk:w 3 1 #3 ; }
+\cs_new:Npn \__fp_basics_return_zero:NNww #1#2 #3; #4;
   {
-    \l_fp_trig_octant_int \c_one
-    \fp_trig_octant_aux_i:
-    \if_int_compare:w \l_fp_input_a_decimal_int < \c_ten
-      \l_fp_input_a_decimal_int  \c_zero
-      \l_fp_input_a_extended_int \c_zero
+    \if_meaning:w #1 #2
+      \exp_after:wN \exp_after:wN \exp_after:wN \c_zero_fp
+    \else:
+      \exp_after:wN \exp_after:wN \exp_after:wN \c_minus_zero_fp
     \fi:
-    \if_int_odd:w \l_fp_trig_octant_int
+  }
+\cs_new:Npn \__fp_basics_return_inf:NNww #1#2 #3; #4;
+  {
+    \if_meaning:w #1 #2
+      \exp_after:wN \exp_after:wN \exp_after:wN \c_inf_fp
     \else:
-      \fp_sub:NNNNNNNNN
-        \c_zero \c_fp_pi_by_four_decimal_int \c_fp_pi_by_four_extended_int
-        \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-          \l_fp_input_a_extended_int
-        \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-          \l_fp_input_a_extended_int
+      \exp_after:wN \exp_after:wN \exp_after:wN \c_minus_inf_fp
     \fi:
   }
-\cs_new_protected_nopar:Npn \fp_trig_octant_aux_i:
+\cs_new:Npn \__fp_basics_return_i:NNNNww #1#2 #3#4 #5; #6;
+  { \__fp_exp_after_o:w \s__fp \__fp_chk:w #1 #3 #5; }
+\cs_new:Npn \__fp_basics_return_ii:NNNNww #1#2 #3#4 #5; #6;
+  { \__fp_exp_after_o:w \s__fp \__fp_chk:w #2 #4 #6; }
+\cs_new:Npn \__fp_basics_return_nan:NNww #1#2
   {
-    \if_int_compare:w \l_fp_trig_octant_int > \c_four
-      \l_fp_trig_octant_int \c_four
-      \l_fp_input_a_decimal_int  \c_fp_pi_by_four_decimal_int
-      \l_fp_input_a_extended_int \c_fp_pi_by_four_extended_int
+    \if_meaning:w 1 #1
+      \exp_after:wN \__fp_basics_return_i:NNNNww
     \else:
-      \exp_after:wN \fp_trig_octant_aux_ii:
+      \exp_after:wN \__fp_basics_return_ii:NNNNww
     \fi:
+    3 3 #1 #2
   }
-\cs_new_protected_nopar:Npn \fp_trig_octant_aux_ii:
+\cs_new:cpn { __fp_+_o:ww }
+    \s__fp \__fp_chk:w #1 #2 #3 ; \s__fp \__fp_chk:w #4 #5
+  { \__fp_add_cases:NN #1 #4 #2 #5 #3 ; }
+\cs_new:cpn { __fp_-_o:ww }
+    \s__fp \__fp_chk:w #1 #2 #3 ; \s__fp \__fp_chk:w #4 #5
   {
-    \if_int_compare:w \l_fp_input_a_integer_int > \c_zero
-      \fp_sub:NNNNNNNNN
-        \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-          \l_fp_input_a_extended_int
-        \c_zero \c_fp_pi_by_four_decimal_int \c_fp_pi_by_four_extended_int
-        \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-          \l_fp_input_a_extended_int
-      \tex_advance:D \l_fp_trig_octant_int \c_one
-      \exp_after:wN \fp_trig_octant_aux_i:
+    \exp_after:wN \__fp_add_cases:NN
+    \exp_after:wN #1
+    \exp_after:wN #4
+    \exp_after:wN #2
+    \int_use:N \__int_eval:w \c_two - #5 \__int_eval_end:
+    #3 ;
+  }
+\cs_new:Npn \__fp_add_cases:NN #1 #2
+  {
+    \if_int_compare:w #1 = #2 \exp_stop_f:
+      \exp_after:wN \__fp_add_cases_eq:N
     \else:
-      \if_int_compare:w
-        \l_fp_input_a_decimal_int > \c_fp_pi_by_four_decimal_int
-        \fp_sub:NNNNNNNNN
-          \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-            \l_fp_input_a_extended_int
-          \c_zero \c_fp_pi_by_four_decimal_int
-            \c_fp_pi_by_four_extended_int
-          \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-            \l_fp_input_a_extended_int
-        \tex_advance:D \l_fp_trig_octant_int \c_one
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \fp_trig_octant_aux_i:
-      \fi:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_sin:Nn  { \fp_sin_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gsin:Nn { \fp_sin_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_sin:Nn   { c }
-\cs_generate_variant:Nn \fp_gsin:Nn  { c }
-\cs_new_protected:Npn \fp_sin_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \tl_set:Nx \l_fp_arg_tl
-        {
-          \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-            -
-          \else:
-            +
-          \fi:
-          \int_use:N \l_fp_input_a_integer_int
-          .
-          \exp_after:wN \use_none:n
-            \int_value:w \int_eval:w
-              \l_fp_input_a_decimal_int + \c_one_thousand_million
-          e
-          \int_use:N \l_fp_input_a_exponent_int
-        }
-      \if_int_compare:w \l_fp_input_a_exponent_int < -\c_five
-        \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2 { \l_fp_arg_tl }
-        }
+      \if_int_compare:w #1 < #2 \exp_stop_f:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__fp_basics_return_ii:NNNNww
       \else:
-        \if_cs_exist:w
-          c_fp_sin ( \l_fp_arg_tl ) _fp
-        \cs_end:
-        \else:
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \fp_sin_aux_i:
-        \fi:
-        \cs_set_protected_nopar:Npx \fp_tmp:w
-          {
-            \group_end:
-            #1 \exp_not:N #2
-              { \use:c { c_fp_sin ( \l_fp_arg_tl ) _fp } }
-          }
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__fp_basics_return_i:NNNNww
       \fi:
-    \fp_tmp:w
+      \exp_after:wN #1
+    \fi:
+    #2
   }
-\cs_new_protected_nopar:Npn \fp_sin_aux_i:
+\cs_new:Npn \__fp_add_cases_eq:N #1
   {
-    \fp_trig_normalise:
-    \fp_sin_aux_ii:
-    \if_int_compare:w \l_fp_output_integer_int = \c_one
-      \l_fp_output_exponent_int \c_zero
+    \if_case:w #1 \exp_stop_f:
+         \exp_after:wN \__fp_add_zeros:NNww
+    \or: \exp_after:wN \__fp_add_normal:NNww
+    \or: \exp_after:wN \__fp_add_inf:NNww
+    \or: \exp_after:wN \__fp_basics_return_nan_nan:NNww
+    \fi:
+  }
+\cs_new:Npn \__fp_add_zeros:NNww #1#2 #3;
+  {
+    \if_int_compare:w #1 #2 = 02 \exp_stop_f:
+      \__fp_case_return_o:Nw \c_zero_fp
     \else:
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-      \l_fp_output_decimal_int \l_fp_output_extended_int
-      \l_fp_output_exponent_int -\c_nine
+      \__fp_case_return_same_o:w
     \fi:
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \tl_new:c { c_fp_sin ( \l_fp_arg_tl ) _fp }
-    \tl_gset:cx { c_fp_sin ( \l_fp_arg_tl ) _fp }
-      {
-        \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-          +
-        \else:
-          -
-        \fi:
-        \int_use:N \l_fp_output_integer_int
-        .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_output_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_output_exponent_int
-      }
+    \s__fp \__fp_chk:w 0 #2
   }
-\cs_new_protected_nopar:Npn \fp_sin_aux_ii:
+\cs_new:Npn \__fp_add_inf:NNww #1#2 #3;
   {
-    \if_case:w \l_fp_trig_octant_int
-    \or:
-      \exp_after:wN \fp_trig_calc_sin:
-    \or:
-      \exp_after:wN \fp_trig_calc_cos:
-    \or:
-      \exp_after:wN \fp_trig_calc_cos:
-    \or:
-      \exp_after:wN \fp_trig_calc_sin:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_cos:Nn  { \fp_cos_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gcos:Nn { \fp_cos_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_cos:Nn   { c }
-\cs_generate_variant:Nn \fp_gcos:Nn  { c }
-\cs_new_protected:Npn \fp_cos_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \tl_set:Nx \l_fp_arg_tl
+    \if_meaning:w #1 #2
+      \__fp_case_return_same_o:w
+    \else:
+      \__fp_case_use:nw
         {
-          \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-            -
-          \else:
-            +
-          \fi:
-          \int_use:N \l_fp_input_a_integer_int
-          .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_input_a_decimal_int + \c_one_thousand_million
-          e
-          \int_use:N \l_fp_input_a_exponent_int
+          \__fp_invalid_operation:Nnww \c_nan_fp { + }
+            \s__fp \__fp_chk:w 2 #1 #3 ;
         }
-      \if_cs_exist:w c_fp_cos ( \l_fp_arg_tl ) _fp \cs_end:
+    \fi:
+    \s__fp \__fp_chk:w 2 #2
+  }
+\cs_new:Npn \__fp_add_normal:NNww #1#2
+  {
+    \if_meaning:w #1#2
+      \exp_after:wN \__fp_add_npos:Nnwnw
+    \else:
+      \exp_after:wN \__fp_sub_npos:Nnwnw
+    \fi:
+    #1
+  }
+\cs_new:Npn \__fp_add_npos:Nnwnw #1 #2#3; #4
+  {
+    \exp_after:wN \__fp_sanitize:Nw
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w
+      \if_int_compare:w #2 > #4 \exp_stop_f:
+        #2
+        \exp_after:wN \__fp_add_big_i:wNww \__int_value:w -
       \else:
-        \exp_after:wN \fp_cos_aux_i:
+        #4
+        \exp_after:wN \__fp_add_big_ii:wNww \__int_value:w
       \fi:
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            { \use:c { c_fp_cos ( \l_fp_arg_tl ) _fp } }
-        }
-    \fp_tmp:w
-  }
-\cs_new_protected_nopar:Npn \fp_cos_aux_i:
-  {
-    \fp_trig_normalise:
-    \fp_cos_aux_ii:
-    \if_int_compare:w \l_fp_output_integer_int = \c_one
-      \l_fp_output_exponent_int \c_zero
-    \else:
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-      \l_fp_output_decimal_int \l_fp_output_extended_int
-      \l_fp_output_exponent_int -\c_nine
-    \fi:
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \tl_new:c { c_fp_cos ( \l_fp_arg_tl ) _fp }
-    \tl_gset:cx { c_fp_cos ( \l_fp_arg_tl ) _fp }
-      {
-        \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-          +
-        \else:
-          -
-        \fi:
-        \int_use:N \l_fp_output_integer_int
-        .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_output_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_output_exponent_int
-      }
+      \__int_eval:w #4 - #2 ; #1 #3;
   }
-\cs_new_protected_nopar:Npn \fp_cos_aux_ii:
+\cs_new:Npn \__fp_add_big_i:wNww #1; #2 #3; #4;
   {
-    \if_case:w \l_fp_trig_octant_int
-    \or:
-      \exp_after:wN \fp_trig_calc_cos:
-    \or:
-      \exp_after:wN \fp_trig_calc_sin:
-    \or:
-      \exp_after:wN \fp_trig_calc_sin:
-    \or:
-      \exp_after:wN \fp_trig_calc_cos:
+    \__fp_decimate:nNnnnn {#1}
+      \__fp_add_mantissa:NnnwnnnnN
+      #4
+    #3
+    #2
+  }
+\cs_new:Npn \__fp_add_big_ii:wNww #1; #2 #3; #4;
+  {
+    \__fp_decimate:nNnnnn {#1}
+      \__fp_add_mantissa:NnnwnnnnN
+      #3
+    #4
+    #2
+  }
+\cs_new:Npn \__fp_add_mantissa:NnnwnnnnN #1 #2#3 #4; #5#6#7#8
+  {
+    \exp_after:wN \__fp_add_mantissa_test:N
+    \int_use:N \__int_eval:w 1#5#6 + #2
+      \exp_after:wN \__fp_add_mantissa_pack:NNNNNNN
+      \int_use:N \__int_eval:w 1#7#8 + #3 ; #1
+  }
+\cs_new:Npn \__fp_add_mantissa_pack:NNNNNNN #1 #2#3#4#5#6#7
+  {
+    \if:w 2 #1
+      + \c_one
     \fi:
-    \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-      \if_int_compare:w \l_fp_trig_octant_int > \c_two
-        \l_fp_input_a_sign_int \c_minus_one
-      \fi:
+    ; #2 #3 #4 #5 #6 #7 ;
+  }
+\cs_new:Npn \__fp_add_mantissa_test:N #1
+  {
+    \if:w 2 #1
+      \exp_after:wN \__fp_add_mantissa_carry:wwNNNN
     \else:
-      \if_int_compare:w \l_fp_trig_octant_int > \c_two
-      \else:
-        \l_fp_input_a_sign_int \c_one
-      \fi:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_trig_calc_cos:
-  {
-    \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
-      \l_fp_output_integer_int \c_one
-      \l_fp_output_decimal_int \c_zero
-    \else:
-      \l_fp_trig_sign_int \c_minus_one
-      \fp_mul:NNNNNN
-        \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-        \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-        \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \fp_div_integer:NNNNN
-        \l_fp_trig_decimal_int \l_fp_trig_extended_int
-        \c_two
-        \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \l_fp_count_int \c_three
-      \if_int_compare:w \l_fp_trig_extended_int = \c_zero
-        \if_int_compare:w \l_fp_trig_decimal_int = \c_zero
-          \l_fp_output_integer_int \c_one
-          \l_fp_output_decimal_int \c_zero
-          \l_fp_output_extended_int \c_zero
-        \else:
-          \l_fp_output_integer_int \c_zero
-          \l_fp_output_decimal_int \c_one_thousand_million
-          \l_fp_output_extended_int \c_zero
-        \fi:
+      \exp_after:wN \__fp_add_mantissa_no_carry:wwNNNN
+    \fi:
+  }
+\cs_new:Npn \__fp_add_mantissa_no_carry:wwNNNN
+    #1; #2; #3#4 ; #5#6
+  {
+    \exp_after:wN \__fp_basics_pack_high:NNNNNw
+    \int_use:N \__int_eval:w 1 #1
+      \exp_after:wN \__fp_basics_pack_low:NNNNNw
+      \int_use:N \__int_eval:w 1 #2 #3#4
+        + \__fp_round:NNN #6 #4 #5
+        \exp_after:wN ;
+  }
+\cs_new:Npn \__fp_add_mantissa_carry:wwNNNN
+    #1; #2; #3#4; #5#6
+  {
+    + \c_one
+    \exp_after:wN \__fp_add_mantissa_carry_pack:NNNNNNNNw
+    \int_use:N \__int_eval:w 1 #1
+      \exp_after:wN \__fp_add_mantissa_carry_pack_ii:NNNNw
+      \int_use:N \__int_eval:w 1 #2#3
+        + \__fp_round:NNNN #6 #3 #4 #5
+        \exp_after:wN ;
+  }
+\cs_new:Npn \__fp_add_mantissa_carry_pack_ii:NNNNw #1 #2#3#4 #5;
+  {
+    \if:w 2 #1
+      + \c_one
+    \fi:
+    \__int_eval_end:
+    #2#3#4; {#5} ;
+  }
+\cs_new:Npn \__fp_add_mantissa_carry_pack:NNNNNNNNw
+    #1#2#3#4 #5#6#7#8 #9; { ; {#1#2#3#4} {#5#6#7#8} {#9} }
+\cs_new:Npn \__fp_sub_npos:Nnwnw #1 #2#3; #4 #5;
+  {
+    \exp_after:wN \__fp_sanitize:wN
+    \int_use:N \__int_eval:w
+      \if_int_compare:w #2 > #4 \exp_stop_f:
+        #2
+        \exp_after:wN \__fp_sub_big_i:wNww \__int_value:w -
       \else:
-        \l_fp_output_integer_int \c_zero
-        \l_fp_output_decimal_int 999999999 \scan_stop:
-        \l_fp_output_extended_int \c_one_thousand_million
-      \fi:
-      \tex_advance:D \l_fp_output_extended_int -\l_fp_trig_extended_int
-      \tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int
-      \exp_after:wN \fp_trig_calc_Taylor:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_trig_calc_sin:
-  {
-    \l_fp_output_integer_int \c_zero
-    \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
-      \l_fp_output_decimal_int \c_zero
-    \else:
-      \l_fp_output_decimal_int \l_fp_input_a_decimal_int
-      \l_fp_output_extended_int \l_fp_input_a_extended_int
-      \l_fp_trig_sign_int \c_one
-      \l_fp_trig_decimal_int \l_fp_input_a_decimal_int
-      \l_fp_trig_extended_int \l_fp_input_a_extended_int
-      \l_fp_count_int \c_two
-      \exp_after:wN \fp_trig_calc_Taylor:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_trig_calc_Taylor:
-  {
-    \l_fp_trig_sign_int -\l_fp_trig_sign_int
-    \fp_mul:NNNNNN
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \fp_mul:NNNNNN
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \fp_div_integer:NNNNN
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \l_fp_count_int
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \tex_advance:D \l_fp_count_int \c_one
-    \fp_div_integer:NNNNN
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \l_fp_count_int
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \tex_advance:D \l_fp_count_int \c_one
-    \if_int_compare:w \l_fp_trig_decimal_int > \c_zero
-      \if_int_compare:w \l_fp_trig_sign_int > \c_zero
-        \tex_advance:D \l_fp_output_decimal_int \l_fp_trig_decimal_int
-        \tex_advance:D \l_fp_output_extended_int
-          \l_fp_trig_extended_int
-        \if_int_compare:w \l_fp_output_extended_int < \c_one_thousand_million
-        \else:
-          \tex_advance:D \l_fp_output_decimal_int \c_one
-          \tex_advance:D \l_fp_output_extended_int
-            -\c_one_thousand_million
-        \fi:
-        \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
+        #4
+        \if_int_compare:w #2 = #4 \exp_stop_f:
+          \__fp_sub_exponent_eq:nnnnnnnn #3 #5
         \else:
-          \tex_advance:D \l_fp_output_integer_int \c_one
-          \tex_advance:D \l_fp_output_decimal_int
-            -\c_one_thousand_million
-        \fi:
-      \else:
-        \tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int
-        \tex_advance:D \l_fp_output_extended_int
-          -\l_fp_input_a_extended_int
-        \if_int_compare:w \l_fp_output_extended_int < \c_zero
-          \tex_advance:D \l_fp_output_decimal_int \c_minus_one
-          \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million
-        \fi:
-        \if_int_compare:w \l_fp_output_decimal_int < \c_zero
-          \tex_advance:D \l_fp_output_integer_int \c_minus_one
-          \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+          \exp_after:wN \__fp_sub_big_ii:wNww \__int_value:w
         \fi:
       \fi:
-      \exp_after:wN \fp_trig_calc_Taylor:
-    \fi:
+      \__int_eval:w #4 - #2 ; #1 #3; #5;
   }
-\cs_new_protected_nopar:Npn \fp_tan:Nn  { \fp_tan_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gtan:Nn { \fp_tan_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_tan:Nn   { c }
-\cs_generate_variant:Nn \fp_gtan:Nn  { c }
-\cs_new_protected:Npn \fp_tan_aux:NNn #1#2#3
+\cs_new:Npn \__fp_sub_exponent_eq:nnnnnnnn #1#2#3#4 #5#6#7#8
   {
-    \group_begin:
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \tl_set:Nx \l_fp_arg_tl
-        {
-          \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-            -
-          \else:
-            +
-          \fi:
-          \int_use:N \l_fp_input_a_integer_int
-          .
-          \exp_after:wN \use_none:n
-            \int_value:w \int_eval:w
-              \l_fp_input_a_decimal_int + \c_one_thousand_million
-          e
-          \int_use:N \l_fp_input_a_exponent_int
-        }
-      \if_int_compare:w \l_fp_input_a_exponent_int < -\c_five
-        \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2 { \l_fp_arg_tl }
-        }
+    \if_int_compare:w #1#2 > #5#6 \exp_stop_f:
+      \exp_after:wN \__fp_sub_big_i:wNww \__int_value:w
+    \else:
+      \if_int_compare:w #1#2 < #5#6 \exp_stop_f:
+        \exp_after:wN \__fp_sub_big_ii:wNww \__int_value:w
       \else:
-        \if_cs_exist:w
-          c_fp_tan ( \l_fp_arg_tl ) _fp
-        \cs_end:
+        \if_int_compare:w #3#4 > #7#8 \exp_stop_f:
+          \exp_after:wN \__fp_sub_big_i:wNww \__int_value:w
         \else:
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \fp_tan_aux_i:
+          \if_int_compare:w #3#4 < #7#8 \exp_stop_f:
+            \exp_after:wN \__fp_sub_big_ii:wNww \__int_value:w
+          \else:
+            \exp_after:wN \__fp_sub_eq:wNww \__int_value:w
+          \fi:
         \fi:
-        \cs_set_protected_nopar:Npx \fp_tmp:w
-          {
-            \group_end:
-            #1 \exp_not:N #2
-              { \use:c { c_fp_tan ( \l_fp_arg_tl ) _fp } }
-          }
       \fi:
-    \fp_tmp:w
+    \fi:
   }
-\cs_new_protected_nopar:Npn \fp_tan_aux_i:
+\cs_new:Npn \__fp_sub_eq:wNww #1; #2 #3; #4;
+  { \exp_after:wN ; \exp_after:wN 1 \exp_after:wN ; }
+\cs_new:Npn \__fp_sub_big_i:wNww #1; #2 #3; #4;
+  {
+    \__fp_decimate:nNnnnn {#1}
+      \__fp_sub_back_mantissa:NnnwNnnnn
+      #4
+    #2
+    #3
+  }
+\cs_new:Npn \__fp_sub_big_ii:wNww #1; #2 #3; #4;
+  {
+    \exp_after:wN \__fp_sub_big_i:wNww
+    \__int_value:w #1 \exp_after:wN ;
+    \int_use:N \__int_eval:w 2 - #2 \__int_eval_end:
+    #4; #3;
+  }
+\cs_new:Npn \__fp_sub_back_mantissa:NnnwNnnnn #1 #2#3 #4; #5 #6#7#8#9
+  {
+    \exp_after:wN \__fp_sub_back_mantissa_i:NNwNNNNwN
+    \exp_after:wN #1
+    \exp_after:wN #5
+    \int_use:N \__int_eval:w 2#6#7 - #2 - \c_two +
+      \exp_after:wN \__fp_sub_back_mantissa_round:wNN
+      \int_use:N \__int_eval:w 2#8#9 - #3 ; #1 #5
+  }
+\cs_new:Npn \__fp_sub_back_mantissa_round:wNN #1; #2 #3
+  {
+    \exp_after:wN \__fp_sub_back_mantissa_iii:N
+    \__int_value:w
+        \exp_after:wN \__fp_round_neg:NNN
+        \exp_after:wN #3
+        \use_none:nnnnnnnn #1 #2
+      + #1
+    \exp_after:wN ;
+  }
+\cs_new:Npn \__fp_sub_back_mantissa_iii:N #1
+  {
+    \exp_after:wN \__fp_sub_back_mantissa_ii:NNNNNNw
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w
+      - #1
+  }
+\cs_new:Npn \__fp_sub_back_mantissa_ii:NNNNNNw #1 #2 #3#4#5#6 #7;
+  { #2 ; #1 {#3#4#5#6} {#7} ; }
+\cs_new:Npn \__fp_sub_back_mantissa_i:NNwNNNNwN #1#2 #3 #4#5#6#7 #8; #9
+  {
+    \if:w 0 #4
+      \exp_after:wN \__fp_sub_back_carry:NNwNnnnn
+      \exp_after:wN #1
+      \exp_after:wN #9
+    \fi:
+    ; #2
+    {#4#5#6#7} {#8}
+  }
+\cs_new:Npn \__fp_sub_back_carry:NNwNnnnn #1#2 ; #3 #4#5#6#7 ;
+  {
+    \exp_after:wN \__fp_sub_back_carry_i:wwN
+    \int_use:N \__int_eval:w #4 #5 - 1 + \exp_after:wN \__fp_use_s:n
+    \int_use:N \__int_eval:w 1 #6 #7 0 + #2 0 - #1 ; #3
+  }
+\cs_new:Npn \__fp_sub_back_carry_i:wwN #1 ;
   {
-    \if_int_compare:w \l_fp_input_a_exponent_int < \c_ten
-      \exp_after:wN \fp_tan_aux_ii:
+    \if:w 0 #1
+      - 8
+      \exp_after:wN \__fp_sub_back_carry_small:wN \__int_value:w
     \else:
-      \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
-        \c_zero_fp
-      \exp_after:wN \fp_trig_overflow_msg:
+      - \__fp_sub_back_carry_ii:NNNNNNNNw #1 1234567;
+      \exp_after:wN \__fp_sub_back_carry_large:NNNNNNNNw
+    \fi:
+    #1
+  }
+\cs_new:Npn \__fp_sub_back_carry_ii:NNNNNNNNw #1#2#3#4#5#6#7#8#9; {#8}
+\cs_new:Npn \__fp_sub_back_carry_large:NNNNNNNNw #1#2#3#4 #5#6#7#8 #9;
+  {
+    \__fp_sub_back_carry_large_ii:NNNNNNNNw
+    #9 000000 ; {#1#2#3#4} {#5#6#7#8}
+  }
+\cs_new:Npn \__fp_sub_back_carry_large_ii:NNNNNNNNw #1#2#3#4 #5#6#7#8 #9;
+  { \__fp_sub_back_carry_large_iii:nnnnN {#1#2#3#4} {#5#6#7#8} }
+\cs_new:Npn \__fp_sub_back_carry_large_iii:nnnnN #1#2 #3#4 #5
+  { ; #5 {#3}{#4} {#1}{#2} ; }
+\cs_new:Npn \__fp_sub_back_carry_small:wN #1;
+  {
+    - \exp_after:wN \__fp_use_i_until_s:nw
+      \use_none:nnnnnnnnn #1 012345678;
+    \__fp_sub_back_carry_small_ii:NNNNNNNN #1 00000000 ;
+  }
+\cs_new:Npn \__fp_sub_back_carry_small_ii:NNNNNNNN #1#2#3#4 #5#6#7#8
+  { \__fp_sub_back_carry_small_iii:nnNwN {#1#2#3#4} {#5#6#7#8} }
+\cs_new:Npn \__fp_sub_back_carry_small_iii:nnNwN #1 #2 #3 #4; #5
+  { ; #5 {#1} {#2} {#3000} {0000} ; }
+\cs_new:cpn { __fp_*_o:ww }
+    \s__fp \__fp_chk:w #1 #2 #3 ; \s__fp \__fp_chk:w #4 #5
+  { \__fp_mul_cases:NN #1 #4 #2 #5 #3 ; }
+\cs_new:Npn \__fp_mul_cases:NN #1 #2
+  {
+    \if_case:w \if_meaning:w 1 #1 #2 \else:
+               \if_meaning:w 1 #2 #1 \else:
+               \if_meaning:w #1#2 #1 \else:
+               \if_int_compare:w \__int_eval:w #1 + #2 > \c_two
+                 3 \else: 4 \fi: \fi: \fi: \fi:
+               \exp_stop_f:
+         \exp_after:wN \__fp_basics_return_zero:NNww
+    \or: \exp_after:wN \__fp_mul_normal:NNww
+    \or: \exp_after:wN \__fp_basics_return_inf:NNww
+    \or: \exp_after:wN \__fp_basics_return_nan:NNww
+    \or:
+      \exp_after:wN \__fp_mul_invalid:NNNNww
+      \exp_after:wN #1
+      \exp_after:wN #2
     \fi:
   }
-\cs_new_protected_nopar:Npn \fp_tan_aux_ii:
+\cs_new:Npn \__fp_mul_invalid:NNNNww #1#2#3#4#5; #6;
   {
-    \fp_trig_normalise:
-    \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-      \if_int_compare:w \l_fp_trig_octant_int > \c_two
-        \l_fp_output_sign_int \c_minus_one
-      \else:
-        \l_fp_output_sign_int \c_one
-      \fi:
+    \__fp_invalid_operation:Nnww \c_nan_fp { * }
+      \s__fp \__fp_chk:w #1 #3 #5 ;
+      \s__fp \__fp_chk:w #2 #4 #6 ;
+  }
+\cs_new:Npn \__fp_mul_normal:NNww #1#2
+  {
+    \if:w #1#2
+      \exp_after:wN \__fp_mul_npos:Nnwnw
+      \exp_after:wN 0
     \else:
-      \if_int_compare:w \l_fp_trig_octant_int > \c_two
-        \l_fp_output_sign_int \c_one
-      \else:
-        \l_fp_output_sign_int \c_minus_one
-      \fi:
+      \exp_after:wN \__fp_mul_npos:Nnwnw
+      \exp_after:wN 2
     \fi:
-    \fp_cos_aux_ii:
-    \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
-      \if_int_compare:w \l_fp_input_a_integer_int = \c_zero
-        \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
-          \c_undefined_fp
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \fp_tan_aux_iii:
-      \fi:
-    \else:
-      \exp_after:wN \fp_tan_aux_iii:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_tan_aux_iii:
-  {
-    \l_fp_input_b_integer_int \l_fp_output_decimal_int
-    \l_fp_input_b_decimal_int \l_fp_output_extended_int
-    \l_fp_input_b_exponent_int -\c_nine
-    \fp_standardise:NNNN
-      \l_fp_input_b_sign_int
-      \l_fp_input_b_integer_int
-      \l_fp_input_b_decimal_int
-      \l_fp_input_b_exponent_int
-    \fp_sin_aux_ii:
-    \l_fp_input_a_integer_int \l_fp_output_decimal_int
-    \l_fp_input_a_decimal_int \l_fp_output_extended_int
-    \l_fp_input_a_exponent_int -\c_nine
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int
-      \l_fp_input_a_decimal_int
-      \l_fp_input_a_exponent_int
-    \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
-      \if_int_compare:w \l_fp_input_a_integer_int = \c_zero
-        \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
-          \c_zero_fp
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN \fp_tan_aux_iv:
-      \fi:
-    \else:
-      \exp_after:wN \fp_tan_aux_iv:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_tan_aux_iv:
-  {
-    \l_fp_output_integer_int \c_zero
-    \l_fp_output_decimal_int \c_zero
-    \cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
-    \l_fp_div_offset_int \c_one_hundred_million
-    \fp_div_loop:
-    \l_fp_output_exponent_int
-      \int_eval:w
-        \l_fp_input_a_exponent_int - \l_fp_input_b_exponent_int
-      \int_eval_end:
-    \fp_standardise:NNNN
-      \l_fp_output_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \tl_new:c { c_fp_tan ( \l_fp_arg_tl ) _fp }
-    \tl_gset:cx { c_fp_tan ( \l_fp_arg_tl ) _fp }
-      {
-        \if_int_compare:w \l_fp_output_sign_int > \c_zero
-          +
-        \else:
-          -
-        \fi:
-        \int_use:N \l_fp_output_integer_int
-        .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_output_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_output_exponent_int
-      }
   }
-\tl_const:cn { c_fp_exp_1_tl }   { { 2 } { 718281828 } { 459045235 } { 0 } }
-\tl_const:cn { c_fp_exp_2_tl }   { { 7 } { 389056098 } { 930650227 } { 0 } }
-\tl_const:cn { c_fp_exp_3_tl }   { { 2 } { 008553692 } { 318766774 } { 1 } }
-\tl_const:cn { c_fp_exp_4_tl }   { { 5 } { 459815003 } { 314423908 } { 1 } }
-\tl_const:cn { c_fp_exp_5_tl }   { { 1 } { 484131591 } { 025766034 } { 2 } }
-\tl_const:cn { c_fp_exp_6_tl }   { { 4 } { 034287934 } { 927351226 } { 2 } }
-\tl_const:cn { c_fp_exp_7_tl }   { { 1 } { 096633158 } { 428458599 } { 3 } }
-\tl_const:cn { c_fp_exp_8_tl }   { { 2 } { 980957987 } { 041728275 } { 3 } }
-\tl_const:cn { c_fp_exp_9_tl }   { { 8 } { 103083927 } { 575384008 } { 3 } }
-\tl_const:cn { c_fp_exp_10_tl }  { { 2 } { 202646579 } { 480671652 } { 4 } }
-\tl_const:cn { c_fp_exp_20_tl }  { { 4 } { 851651954 } { 097902280 } { 8 } }
-\tl_const:cn { c_fp_exp_30_tl }  { { 1 } { 068647458 } { 152446215 } { 13 } }
-\tl_const:cn { c_fp_exp_40_tl }  { { 2 } { 353852668 } { 370199854 } { 17 } }
-\tl_const:cn { c_fp_exp_50_tl }  { { 5 } { 184705528 } { 587072464 } { 21 } }
-\tl_const:cn { c_fp_exp_60_tl }  { { 1 } { 142007389 } { 815684284 } { 26 } }
-\tl_const:cn { c_fp_exp_70_tl }  { { 2 } { 515438670 } { 919167006 } { 30 } }
-\tl_const:cn { c_fp_exp_80_tl }  { { 5 } { 540622384 } { 393510053 } { 34 } }
-\tl_const:cn { c_fp_exp_90_tl }  { { 1 } { 220403294 } { 317840802 } { 39 } }
-\tl_const:cn { c_fp_exp_100_tl } { { 2 } { 688117141 } { 816135448 } { 43 } }
-\tl_const:cn { c_fp_exp_200_tl } { { 7 } { 225973768 } { 125749258 } { 86 } }
-\tl_const:cn { c_fp_exp_-1_tl }   { { 3 } { 678794411 } { 71442322 }  { -1 } }
-\tl_const:cn { c_fp_exp_-2_tl }   { { 1 } { 353352832 } { 366132692 } { -1 } }
-\tl_const:cn { c_fp_exp_-3_tl }   { { 4 } { 978706836 } { 786394298 } { -2 } }
-\tl_const:cn { c_fp_exp_-4_tl }   { { 1 } { 831563888 } { 873418029 } { -2 } }
-\tl_const:cn { c_fp_exp_-5_tl }   { { 6 } { 737946999 } { 085467097 } { -3 } }
-\tl_const:cn { c_fp_exp_-6_tl }   { { 2 } { 478752176 } { 666358423 } { -3 } }
-\tl_const:cn { c_fp_exp_-7_tl }   { { 9 } { 118819655 } { 545162080 } { -4 } }
-\tl_const:cn { c_fp_exp_-8_tl }   { { 3 } { 354626279 } { 025118388 } { -4 } }
-\tl_const:cn { c_fp_exp_-9_tl }   { { 1 } { 234098040 } { 866795495 } { -4 } }
-\tl_const:cn { c_fp_exp_-10_tl }  { { 4 } { 539992976 } { 248451536 } { -5 } }
-\tl_const:cn { c_fp_exp_-20_tl }  { { 2 } { 061153622 } { 438557828 } { -9 } }
-\tl_const:cn { c_fp_exp_-30_tl }  { { 9 } { 357622968 } { 840174605 } { -14 } }
-\tl_const:cn { c_fp_exp_-40_tl }  { { 4 } { 248354255 } { 291588995 } { -18 } }
-\tl_const:cn { c_fp_exp_-50_tl }  { { 1 } { 928749847 } { 963917783 } { -22 } }
-\tl_const:cn { c_fp_exp_-60_tl }  { { 8 } { 756510762 } { 696520338 } { -27 } }
-\tl_const:cn { c_fp_exp_-70_tl }  { { 3 } { 975449735 } { 908646808 } { -31 } }
-\tl_const:cn { c_fp_exp_-80_tl }  { { 1 } { 804851387 } { 845415172 } { -35 } }
-\tl_const:cn { c_fp_exp_-90_tl }  { { 8 } { 194012623 } { 990515430 } { -40 } }
-\tl_const:cn { c_fp_exp_-100_tl } { { 3 } { 720075976 } { 020835963 } { -44 } }
-\tl_const:cn { c_fp_exp_-200_tl } { { 1 } { 383896526 } { 736737530 } { -87 } }
-\cs_new_protected_nopar:Npn \fp_exp:Nn  { \fp_exp_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gexp:Nn { \fp_exp_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_exp:Nn  { c }
-\cs_generate_variant:Nn \fp_gexp:Nn { c }
-\cs_new_protected:Npn \fp_exp_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \l_fp_input_a_extended_int \c_zero
-      \tl_set:Nx \l_fp_arg_tl
-        {
-          \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-            -
-          \else:
-            +
-          \fi:
-          \int_use:N \l_fp_input_a_integer_int
-          .
-          \exp_after:wN \use_none:n
-            \int_value:w \int_eval:w
-               \l_fp_input_a_decimal_int + \c_one_thousand_million
-          e
-          \int_use:N \l_fp_input_a_exponent_int
-        }
-      \if_cs_exist:w c_fp_exp ( \l_fp_arg_tl ) _fp \cs_end:
-      \else:
-        \exp_after:wN \fp_exp_internal:
-      \fi:
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            {
-              \if_cs_exist:w c_fp_exp ( \l_fp_arg_tl ) _fp
-                \cs_end:
-                \use:c { c_fp_exp ( \l_fp_arg_tl ) _fp }
-              \else:
-                \c_zero_fp
-              \fi:
-            }
-        }
-    \fp_tmp:w
+\cs_new:Npn \__fp_mul_npos:Nnwnw #1 #2#3; #4 #5;
+  {
+    \exp_after:wN \__fp_sanitize:Nw
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w
+      #2 + #4
+      \__fp_mul_mantissa:nnnnNnnnn #3 #1 #5
+    \exp_after:wN ;
+  }
+\cs_new:Npn \__fp_mul_mantissa:nnnnNnnnn #1#2#3#4 #5 #6#7#8#9
+  {
+    \exp_after:wN \__fp_mul_mantissa_after:NNN
+    \exp_after:wN #5
+    \int_use:N \__int_eval:w 99990000 + #1*#6 +
+      \exp_after:wN \__fp_mul_mantissa_keep:NNNNNw
+      \int_use:N \__int_eval:w 99990000 + #1*#7 + #2*#6 +
+        \exp_after:wN \__fp_mul_mantissa_keep:NNNNNw
+        \int_use:N \__int_eval:w 99990000 + #1*#8 + #2*#7 + #3*#6 +
+          \exp_after:wN \__fp_mul_mantissa_drop:NNNNNw
+          \int_use:N \__int_eval:w  99990000 + #1*#9 + #2*#8 + #3*#7 + #4*#6 +
+            \exp_after:wN \__fp_mul_mantissa_drop:NNNNNw
+            \int_use:N \__int_eval:w  99990000 + #2*#9 + #3*#8 + #4*#7 +
+              \exp_after:wN \__fp_mul_mantissa_drop:NNNNNw
+              \int_use:N \__int_eval:w  99990000 + #3*#9 + #4*#8 +
+                \exp_after:wN \__fp_mul_mantissa_drop:NNNNNw
+                \int_use:N \__int_eval:w 100000000 + #4*#9 \exp_after:wN ;
+  }
+\cs_new:Npn \__fp_mul_mantissa_drop:NNNNNw #1#2#3#4#5 #6;
+  { #1#2#3#4#5 ; + #6 }
+\cs_new:Npn \__fp_mul_mantissa_keep:NNNNNw #1#2#3#4#5 #6;
+  { #1#2#3#4#5 ; #6 ; }
+\cs_new:Npn \__fp_mul_mantissa_after:NNN #1 #2 #3
+  {
+    \if:w 0 #3
+      \exp_after:wN \__fp_mul_mantissa_small:NNwwwN
+    \else:
+      \exp_after:wN \__fp_mul_mantissa_large:NwwNNNN
+    \fi:
+    #1 #3
   }
-\cs_new_protected_nopar:Npn \fp_exp_internal:
+\cs_new:Npn \__fp_mul_mantissa_large:NwwNNNN #1 #2; #3; #4#5#6#7; +
   {
-    \if_int_compare:w \l_fp_input_a_exponent_int < \c_three
-      \fp_extended_normalise:
-      \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-        \if_int_compare:w \l_fp_input_a_integer_int < 230 \scan_stop:
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \fp_exp_aux:
-        \else:
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \fp_exp_overflow_msg:
+    \exp_after:wN \__fp_basics_pack_high:NNNNNw
+    \int_use:N \__int_eval:w 1#2
+      \exp_after:wN \__fp_basics_pack_low:NNNNNw
+      \int_use:N \__int_eval:w 1#3#4#5#6#7 + \__fp_round_s:NNNw #1 #7
+  }
+\cs_new:Npn \__fp_mul_mantissa_small:NNwwwN #1 #2#3; #4; #5; + #6
+  {
+    - \c_one
+    \exp_after:wN \__fp_basics_pack_high:NNNNNw
+    \int_use:N \__int_eval:w 1#3
+      \exp_after:wN \__fp_mul_mantissa_small_pack:NNNNNNw
+      \int_use:N \__int_eval:w 1#4#5#6 + \__fp_round_s:NNNw #1 #6
+  }
+\cs_new:Npn \__fp_mul_mantissa_small_pack:NNNNNNw #1#2 #3#4#5#6 #7;
+  {
+    #2
+    \if:w 2 #1
+      + \c_ten
+    \fi:
+    ; {#3#4#5#6} {#7} ;
+  }
+\cs_new:cpn { __fp_/_o:ww }
+    \s__fp \__fp_chk:w #1 #2 #3 ; \s__fp \__fp_chk:w #4 #5 #6 ;
+  { \__fp_div_back_cases:NN #4 #1 #5 #2 #6 ; #3 ; }
+\cs_new:Npn \__fp_div_back_cases:NN #1 #2
+  {
+    \if_case:w \if_int_compare:w #1 = #2 \exp_stop_f:
+                 #1 \exp_stop_f:
+               \else:
+                 \if_int_compare:w #1 < #2 \exp_stop_f:
+                   \if:w 3 #2 \c_four \else: \c_five \fi:
+                 \else:
+                   \if:w 3 #1 \c_six \else: \c_seven \fi:
+                 \fi:
+               \fi:
+         \exp_after:wN \__fp_div_back_invalid:NNNww \exp_after:wN 0
+    \or: \exp_after:wN \__fp_div_back_normal:NNww
+    \or: \exp_after:wN \__fp_div_back_invalid:NNNww \exp_after:wN 2
+    \or: \exp_after:wN \__fp_basics_return_nan_nan:NNww
+    \or:
+      \exp_after:wN \__fp_basics_return_ii:NNNNww
+      \exp_after:wN #1
+      \exp_after:wN #2
+    \or: \exp_after:wN \__fp_basics_return_inf:NNww
+    \or:
+      \exp_after:wN \__fp_basics_return_i:NNNNww
+      \exp_after:wN #1
+      \exp_after:wN #2
+    \or: \exp_after:wN \__fp_basics_return_zero:NNww
+    \fi:
+  }
+\cs_new:Npn \__fp_div_back_invalid:NNNww #1#2#3 #4; #5;
+  {
+    \__fp_invalid_operation:Nnww \c_nan_fp { / }
+      \s__fp \__fp_chk:w #1 #3 #5 ;
+      \s__fp \__fp_chk:w #1 #2 #4 ;
+  }
+\cs_new:Npn \__fp_div_back_normal:NNww #1#2
+  {
+    \if:w #1#2
+      \exp_after:wN \__fp_div_back_npos:Nnwnw
+      \exp_after:wN 0
+    \else:
+      \exp_after:wN \__fp_div_back_npos:Nnwnw
+      \exp_after:wN 2
+    \fi:
+  }
+\cs_new:Npn \__fp_div_back_npos:Nnwnw #1 #2 #3#4#5#6; #7 #8;
+  {
+    \exp_after:wN \__fp_sanitize:Nw
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w
+      #7 - #2
+      \__fp_div_mantissa_i:wNwnn #3; #4;
+      #8 {#3}{#4}{#5}{#6} #1
+  }
+\cs_new:Npn \__fp_div_mantissa_i:wNwnn #1; #2 #3; #4 #5
+  {
+    \exp_after:wN \__fp_div_mantissa_ii:ww
+    \int_use:N \__int_eval:w #1#2 + \c_one ;
+    #4 #5 ;
+  }
+\cs_new:Npn \__fp_div_mantissa_ii:ww #1; #2;
+  {
+    \exp_after:wN \__fp_div_mantissa_iii:www
+    \__int_value:w #1 \exp_after:wN ;
+    \__int_value:w
+      \exp_after:wN \__fp_div_mantissa_calc:Nwwnnnnnn
+      \int_use:N \__int_eval:w #20/#1 + 999999 ; #2 ;
+  }
+\cs_new:Npn \__fp_div_mantissa_calc:Nwwnnnnnn 1#1#2; #3;#4#5 #6#7#8#9
+  {
+    1 #1 #2 \exp_after:wN ;
+    \int_use:N \__int_eval:w
+      - 200000 + #3 - #2 * #6
+      \if_meaning:w 1 #1
+        - #6#70
+      \fi:
+      +
+      \exp_after:wN \__fp_div_mantissa_calc_last:NNNNNN
+      \int_use:N \__int_eval:w
+        1999800000 + #4 - #2*#7
+        \if_meaning:w 1 #1
+          - #80
+        \fi:
+        +
+        \exp_after:wN \__fp_div_mantissa_calc_pack:NNNNNNw
+        \int_use:N \__int_eval:w
+          1999800000 + #5 - #2*#8
+          \if_meaning:w 1 #1
+            - #90
           \fi:
+          +
+          \exp_after:wN \__fp_div_mantissa_calc_pack:NNNNNNw
+          \int_use:N \__int_eval:w 2000000000 - #2*#9 ;
+    {#6}{#7}{#8}{#9}
+  }
+\cs_new:Npn \__fp_div_mantissa_calc_pack:NNNNNNw #1#2#3#4#5#6 #7;
+  { #1#2#3#4#5#6 ; {#7} }
+\cs_new:Npn \__fp_div_mantissa_calc_last:NNNNNN #1#2#3#4#5#6
+  { #1#2#3#4#5#6 \__int_eval_end: }
+\cs_new:Npn \__fp_div_mantissa_iii:www #1; #2; #3;
+  {
+    \exp_after:wN \__fp_div_mantissa_iii_after:w
+    \int_use:N \__int_eval:w #2
+      \exp_after:wN \__fp_div_mantissa_iv:www
+      \__int_value:w #1 \exp_after:wN ;
+      \__int_value:w
+        \exp_after:wN \__fp_div_mantissa_calc:Nwwnnnnnn
+        \int_use:N \__int_eval:w #30/#1 + 999999 ;
+        #3 ;
+  }
+\cs_new:Npn \__fp_div_mantissa_iv:www #1; #2; #3;
+  {
+    \exp_after:wN \__fp_div_mantissa_pack:NNN
+    \int_use:N \__int_eval:w #2
+      \exp_after:wN \__fp_div_mantissa_v:www
+      \__int_value:w #1 \exp_after:wN ;
+      \__int_value:w
+        \exp_after:wN \__fp_div_mantissa_calc:Nwwnnnnnn
+        \int_use:N \__int_eval:w #30/#1 + 999999 ;
+        #3 ;
+  }
+\cs_new:Npn \__fp_div_mantissa_v:www #1; #2; #3;
+  {
+    \exp_after:wN \__fp_div_mantissa_pack:NNN
+    \int_use:N \__int_eval:w #2
+      \exp_after:wN \__fp_div_mantissa_vi:wwnnnn
+      \__int_value:w
+        \exp_after:wN \__fp_div_mantissa_calc:Nwwnnnnnn
+        \int_use:N \__int_eval:w #30/#1 + 999999 ;
+        #3 ;
+  }
+\cs_new:Npn \__fp_div_mantissa_vi:wwnnnn #1; #2;#3#4 #5#6
+  {
+    \exp_after:wN \__fp_div_mantissa_pack:NNN
+    \int_use:N \__int_eval:w #10
+      \exp_after:wN \__fp_div_mantissa_vii:wwnnnnnn
+      \int_use:N \__int_eval:w (\c_two*#2)/#5#6 ; % <- P
+      #2;{#3}{#4}
+      {#5}{#6}
+  }
+\cs_new:Npn \__fp_div_mantissa_vii:wwnnnnnn #1; #2;#3#4 #5#6#7#8
+  {
+    + \c_five * #1
+    \exp_after:wN \__fp_div_mantissa_ix:Nww
+    \int_use:N \__int_eval:w -20 + 2*#2 - #1*#5#6 +
+      \exp_after:wN \__fp_div_mantissa_viii:NNw
+      \int_use:N \__int_eval:w 199980 + 2*#3 - #1*#7 +
+        \exp_after:wN \__fp_div_mantissa_viii:NNw
+        \int_use:N \__int_eval:w 200000 + 2*#4 - #1*#8 ; ;
+  }
+\cs_new:Npn \__fp_div_mantissa_viii:NNw #1#2#3; { #1#2 ; + #3 }
+\cs_new:Npn \__fp_div_mantissa_ix:Nww #1#2;#3;
+  {
+    \if_meaning:w 0 #1
+      \exp_after:wN \__fp_div_mantissa_x:w
+      \int_use:N \__int_eval:w #3
+    \else:
+      \if_meaning:w - #1
+        -
       \else:
-        \if_int_compare:w \l_fp_input_a_integer_int < 230 \scan_stop:
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN  \fp_exp_aux:
-        \else:
-          \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
-            { \c_zero_fp }
-        \fi:
+        +
       \fi:
-    \else:
-      \exp_after:wN \fp_exp_overflow_msg:
+      \c_one
     \fi:
+    ;
   }
-\cs_new_protected_nopar:Npn \fp_exp_aux:
+\cs_new:Npn \__fp_div_mantissa_x:w #1;
   {
-    \if_int_compare:w \l_fp_input_a_integer_int > \c_zero
-      \exp_after:wN \fp_exp_integer:
+    \if_int_compare:w #1 > \c_zero
+      + \c_one
+    \fi:
+    ;
+  }
+\cs_new:Npn \__fp_div_mantissa_pack:NNN 1 #1 #2 { + #1 #2 ; }
+\cs_new:Npn \__fp_div_mantissa_iii_after:w 10 #1
+  {
+    \if_meaning:w 0 #1
+      \exp_after:wN \__fp_div_mantissa_small:wwwNNNNwN
     \else:
-      \l_fp_output_integer_int  \c_one
-      \l_fp_output_decimal_int  \c_zero
-      \l_fp_output_extended_int \c_zero
-      \l_fp_output_exponent_int \c_zero
-      \exp_after:wN \fp_exp_decimal:
+      \exp_after:wN \__fp_div_mantissa_large:wwwNNNNwN
     \fi:
+    #1
   }
-\cs_new_protected_nopar:Npn \fp_exp_integer:
+\cs_new:Npn \__fp_div_mantissa_small:wwwNNNNwN
+    0 #1; #2; #3; #4#5#6#7#8; #9
+  {
+    \exp_after:wN \__fp_basics_pack_high:NNNNNw
+    \int_use:N \__int_eval:w 1 #1#2
+      \exp_after:wN \__fp_basics_pack_low:NNNNNw
+      \int_use:N \__int_eval:w 1 #3#4#5#6#7
+        + \__fp_round:NNN #9 #7 #8
+        \exp_after:wN ;
+  }
+\cs_new:Npn \__fp_div_mantissa_large:wwwNNNNwN
+    #1; #2; #3; #4#5#6#7#8; #9
+  {
+    + \c_one
+    \exp_after:wN \__fp_div_mantissa_large_pack:NNNNNNNNw
+    \int_use:N \__int_eval:w 1 #1 #2 %<- 1+9d
+      \exp_after:wN \__fp_add_mantissa_carry_pack_ii:NNNNw
+      \int_use:N \__int_eval:w 1 #3 #4 #5 #6
+        + \__fp_round:NNNN #9 #6 #7 #8
+        \exp_after:wN ;
+  }
+\cs_new:Npn \__fp_div_mantissa_large_pack:NNNNNNNNw
+    1 #1#2#3#4 #5#6#7#8 #9; { ; {#1#2#3#4} {#5#6#7#8} {#9} }
+\cs_new:Npn \__fp_neg:w \s__fp \__fp_chk:w #1 #2
+  {
+    \exp_after:wN \__fp_exp_after_o:w
+    \exp_after:wN \s__fp
+    \exp_after:wN \__fp_chk:w
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w \c_two - #2 \__int_eval_end:
+  }
+\cs_new:Npn \__fp_abs:w \s__fp \__fp_chk:w #1 #2
+  { \__fp_exp_after_o:w \s__fp \__fp_chk:w #1 0 }
+%% File: l3fp-extended.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\tl_const:Nn \c__fp_one_fixed_tl
+  { {10000} {0000} {0000} {0000} {0000} {0000} }
+\cs_new:Npn \__fp_fixed_continue:wn #1; #2 { #2 #1; }
+\cs_new:Npn \__fp_fixed_div_int:wwN #1#2#3#4#5#6 ; #7 ; #8
+  {
+    \exp_after:wN \__fp_fixed_div_int_after:Nw
+    \exp_after:wN #8
+    \int_use:N \__int_eval:w \c_minus_one
+      \__fp_fixed_div_int_i:wnN
+      #1; {#7} \__fp_fixed_div_int_ii:wnn
+      #2; {#7} \__fp_fixed_div_int_ii:wnn
+      #3; {#7} \__fp_fixed_div_int_ii:wnn
+      #4; {#7} \__fp_fixed_div_int_ii:wnn
+      #5; {#7} \__fp_fixed_div_int_ii:wnn
+      #6; {#7} \__fp_fixed_div_int_end:wnn ;
+  }
+\cs_new:Npn \__fp_fixed_div_int_i:wnN #1; #2 #3
+  {
+    \exp_after:wN #3
+    \int_use:N \__int_eval:w #1 / #2 - \c_one ;
+    {#2}
+    {#1}
+  }
+\cs_new:Npn \__fp_fixed_div_int_ii:wnn #1; #2 #3
+  {
+    + #1
+    \exp_after:wN \__fp_fixed_div_int_pack:Nw
+    \int_use:N \__int_eval:w 9999
+      \exp_after:wN \__fp_fixed_div_int_i:wnN
+      \int_use:N \__int_eval:w #3 - #1*#2 \__int_eval_end:
+  }
+\cs_new:Npn \__fp_fixed_div_int_end:wnn #1; #2 #3 { + #1 + \c_two ; }
+\cs_new:Npn \__fp_fixed_div_int_pack:Nw #1 #2; { + #1; {#2} }
+\cs_new:Npn \__fp_fixed_div_int_after:Nw #1 #2; { #1 {#2} }
+\cs_new:Npn \__fp_fixed_add_one:wN #1#2; #3
+  {
+    \exp_after:wN #3 \exp_after:wN
+      { \int_use:N \__int_eval:w 10000 + #1 } #2 ;
+  }
+\cs_new_nopar:Npn \__fp_fixed_add:wwN { \__fp_fixed_add_i:NNnnnnwnn + + }
+\cs_new_nopar:Npn \__fp_fixed_sub:wwN { \__fp_fixed_add_i:NNnnnnwnn + - }
+\cs_new_nopar:Npn \__fp_fixed_sub_back:wwN { \__fp_fixed_add_i:NNnnnnwnn - + }
+\cs_new:Npn \__fp_fixed_add_i:NNnnnnwnn #1#2 #3#4#5#6 #7; #8#9
+  {
+    \exp_after:wN \__fp_fixed_add_after:NNNNNwN
+    \int_use:N \__int_eval:w 1 9999 9998 #1 #3#4 #2 #8#9
+      \exp_after:wN \__fp_fixed_add_pack:NNNNNwN
+      \int_use:N \__int_eval:w 1 9999 9998 #1 #5#6
+        \__fp_fixed_add_ii:NnnNnnnnw #1 #7 #2
+  }
+\cs_new:Npn \__fp_fixed_add_ii:NnnNnnnnw #1 #2#3 #4 #5#6 #7#8 ; #9
+  {
+    #4 #5#6
+    \exp_after:wN \__fp_fixed_add_pack:NNNNNwN
+    \int_use:N \__int_eval:w 2 0000 0000 #4 #7#8 #1 #2#3 ; #9 ;
+  }
+\cs_new:Npn \__fp_fixed_add_pack:NNNNNwN #1 #2#3#4#5 #6; #7
+  { + #1 ; #7 {#2#3#4#5} {#6} }
+\cs_new:Npn \__fp_fixed_add_after:NNNNNwN #1 #2#3#4#5 #6; #7
+  {
+    \exp_after:wN #7
+    \exp_after:wN { \int_use:N \__int_eval:w - 2 0000 + #1#2#3#4#5 }
+    {#6}
+  }
+\cs_new:Npn \__fp_fixed_mul:wwn #1#2#3#4 #5; #6#7#8#9
+  {
+    \exp_after:wN \__fp_fixed_mul_after:wwn
+    \int_use:N \__int_eval:w \c__fp_leading_shift_int
+      \exp_after:wN \__fp_pack:NNNNNw
+      \int_use:N \__int_eval:w \c__fp_middle_shift_int
+        + #1*#6
+        \exp_after:wN \__fp_pack:NNNNNw
+        \int_use:N \__int_eval:w \c__fp_middle_shift_int
+          + #1*#7 + #2*#6
+          \exp_after:wN \__fp_pack:NNNNNw
+          \int_use:N \__int_eval:w \c__fp_middle_shift_int
+            + #1*#8 + #2*#7 + #3*#6
+            \exp_after:wN \__fp_pack:NNNNNw
+            \int_use:N \__int_eval:w \c__fp_middle_shift_int
+              + #1*#9 + #2*#8 + #3*#7 + #4*#6
+              \exp_after:wN \__fp_pack:NNNNNw
+              \int_use:N \__int_eval:w \c__fp_trailing_shift_int
+                + #2*#9 + #3*#8 + #4*#7
+                + ( #3*#9 + #4*#8
+                  + \__fp_fixed_mul_i:nnnnnnnn #5 {#6}{#7}  {#1}{#2}
+  }
+\cs_new:Npn \__fp_fixed_mul_i:nnnnnnnn #1#2 #3#4 #5#6 #7#8
+  { #1*#4 + #2*#3 + #5*#8 + #6*#7 )/10000 + #1*#3 + #5*#7 ; }
+\cs_new:Npn \__fp_fixed_mul_pack:NNNNNw
+    #1 #2#3#4#5 #6; { + #1#2#3#4#5 ; {#6} }
+\cs_new:Npn \__fp_fixed_mul_after:wwn #1; #2; #3 { #3 {#1} #2 ; }
+\cs_new:Npn \__fp_fixed_one_minus_mul:wwn #1; #2#3#4#5;
+  {
+    \exp_after:wN \__fp_fixed_mul_after:wwn
+    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int + \c_ten_thousand
+      \exp_after:wN \__fp_pack_big:NNNNNNw
+      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
+        \__fp_fixed_mul_add_i:Nnwnnwnnn
+          - 00; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; - 00 ;
+  }
+\cs_new:Npn \__fp_fixed_mul_add:wwwn #1; #2#3#4#5; #6#7#8#9
+  {
+    \exp_after:wN \__fp_fixed_mul_after:wwn
+    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int + #6
+      \exp_after:wN \__fp_pack_big:NNNNNNw
+      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #7
+        \__fp_fixed_mul_add_i:Nnwnnwnnn
+          + {#8}{#9}; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; +
+  }
+\cs_new:Npn \__fp_fixed_mul_sub_back:wwwn #1; #2#3#4#5; #6#7#8#9
+  {
+    \exp_after:wN \__fp_fixed_mul_after:wwn
+    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int + #6
+      \exp_after:wN \__fp_pack_big:NNNNNNw
+      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #7
+        \__fp_fixed_mul_add_i:Nnwnnwnnn
+          - {#8}{#9}; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; -
+  }
+\cs_new:Npn \__fp_fixed_mul_add_i:Nnwnnwnnn #1 #2#3; #4#5#6; #7#8#9
+  { % sg z3z4; y1y2y3; x1x2x3  x4x5x6; y1y2y3y4y5y6; sg z5z6;
+        #1 #7*#4
+        \exp_after:wN \__fp_pack_big:NNNNNNw
+        \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #2
+          #1 #7*#5 #1 #8*#4
+          \exp_after:wN \__fp_pack_big:NNNNNNw
+          \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #3
+            #1 #7*#6 #1 #8*#5 #1 #9*#4
+            \exp_after:wN \__fp_pack_big:NNNNNNw
+            \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
+              #1 \__fp_fixed_mul_add_ii:nnnnwnnnn {#7}{#8}{#9}
+  }
+\cs_new:Npn \__fp_fixed_mul_add_ii:nnnnwnnnn #1#2#3#4#5; #6#7#8#9
+  { % x1x2x3x4 x5x6; y1y2y3y4  y5y6; sg z5z6;
+    ( #1*#9 + #2*#8 + #3*#7 + #4*#6 )
+    \exp_after:wN \__fp_pack_big:NNNNNNw
+    \int_use:N \__int_eval:w \c__fp_big_trailing_shift_int
+      \__fp_fixed_mul_add_iii:nnnnwnnwN
+        { #6 + #4*#7 + #3*#8 + #2*#9 + #1 }
+        { #7 + #4*#8 + #3*#9 + #2 }
+        {#1} #5;
+        {#6}
+  }
+\cs_new:Npn \__fp_fixed_mul_add_iii:nnnnwnnwN #1#2 #3#4#5; #6#7#8; #9
+  { % {y1+x4*y2+x3*y3+x2*y4+x1} {y2+x4*y3+x3*y4+x2}
+    % x1x5x6; y1y5y6; sg z5z6;
+    % =>
+    % sg (x5*y1+x4*y2+x3*y3+x2*y4+x1*y5)
+    % sg (x6*y1+x5*y2+x4*y3+x3*y4+x2*y5+x1*y6)/10000
+    % + z5z6;
+    #9 (#4* #1 *#7)
+    #9 (#5*#6+#4* #2 *#7+#3*#8) / \c_ten_thousand
+    + \__fp_use_s:nn
+  }
+\cs_new:Npn \__fp_fixed_to_float:Nw #1#2; { \__fp_fixed_to_float:wN #2; #1 }
+\cs_new:Npn \__fp_fixed_to_float:wN #1#2#3#4#5#6; #7
+  {
+    + \c_four % for the 8-digit-at-the-start thing.
+    \exp_after:wN \exp_after:wN
+    \exp_after:wN \__fp_fixed_to_loop:N
+    \exp_after:wN \use_none:n
+    \int_use:N \__int_eval:w
+      1 0000 0000 + #1   \exp_after:wN \__fp_use_none_stop_f:n
+      \__int_value:w   1#2 \exp_after:wN \__fp_use_none_stop_f:n
+      \__int_value:w 1#3#4 \exp_after:wN \__fp_use_none_stop_f:n
+      \__int_value:w 1#5#6
+    \exp_after:wN ;
+    \exp_after:wN ;
+  }
+\cs_new:Npn \__fp_fixed_to_loop:N #1
+  {
+    \if_meaning:w 0 #1
+      - \c_one
+      \exp_after:wN \__fp_fixed_to_loop:N
+    \else:
+      \exp_after:wN \__fp_fixed_to_loop_end:w
+      \exp_after:wN #1
+    \fi:
+  }
+\cs_new:Npn \__fp_fixed_to_loop_end:w #1 #2 ;
   {
-    \if_int_compare:w \l_fp_input_a_integer_int < \c_one_hundred
-      \l_fp_exp_integer_int  \c_one
-      \l_fp_exp_decimal_int  \c_zero
-      \l_fp_exp_extended_int \c_zero
-      \l_fp_exp_exponent_int \c_zero
-      \exp_after:wN \fp_exp_integer_tens:
+    \if_meaning:w ; #1
+      \exp_after:wN \__fp_fixed_to_float_zero:w
     \else:
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \exp_after:wN \use_i:nnn
-            \int_use:N \l_fp_input_a_integer_int
-        }
-      \l_fp_input_a_integer_int
-        \int_eval:w
-          \l_fp_input_a_integer_int - \l_fp_internal_tl 00
-        \int_eval_end:
-      \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
-        \if_int_compare:w \l_fp_output_integer_int > 200 \scan_stop:
-          \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
-            { \c_zero_fp }
-        \else:
-          \fp_exp_integer_const:n { - \l_fp_internal_tl 00 }
-          \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \fp_exp_integer_tens:
+      \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
+      \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
+      \exp_after:wN \__fp_fixed_to_float_pack:ww
+      \exp_after:wN ;
+    \fi:
+    #1 #2 0000 0000 0000 0000 ;
+  }
+\cs_new:Npn \__fp_fixed_to_float_zero:w ; 0000 0000 0000 0000 ;
+  {
+    - \c_two * \c__fp_max_exponent_int ;
+    {0000} {0000} {0000} {0000} ;
+  }
+\cs_new:Npn \__fp_fixed_to_float_pack:ww #1 ; #2#3 ; ;
+  {
+    \if_int_compare:w #2 > \c_four
+      \exp_after:wN \__fp_fixed_to_float_round_up:wnnnnw
+    \fi:
+    ; #1 ;
+  }
+\cs_new:Npn \__fp_fixed_to_float_round_up:wnnnnw ; #1#2#3#4 ;
+  {
+    \exp_after:wN \__fp_basics_pack_high:NNNNNw
+    \int_use:N \__int_eval:w 1 #1#2
+      \exp_after:wN \__fp_basics_pack_low:NNNNNw
+      \int_use:N \__int_eval:w 1 #3#4 + \c_one ;
+  }
+\cs_new:Npn \__fp_fixed_inv_to_float:wN #1#2; #3
+  {
+    - \__int_eval:w
+        \if_int_compare:w #1 < \c_one_thousand
+          \__fp_fixed_dtf_zeros:wNnnnnnn
         \fi:
-      \else:
-        \fp_exp_integer_const:n { \l_fp_internal_tl 00 }
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \fp_exp_integer_tens:
+        \__fp_fixed_dtf_no_zero:Nwn + {#1} #2 \s__fp
+        \__fp_fixed_dtf_approx:n
+        {10000} {0000} {0000} {0000} {0000} {0000} ;
+  }
+\cs_new:Npn \__fp_fixed_div_to_float:ww #1#2; #3#4;
+  {
+    \if_int_compare:w #1 < \c_one_thousand
+      \__fp_fixed_dtf_zeros:wNnnnnnn
+    \fi:
+    \__fp_fixed_dtf_no_zero:Nwn - {#1} #2 \s__fp
+    {
+      \if_int_compare:w #3 < \c_one_thousand
+        \__fp_fixed_dtf_zeros:wNnnnnnn
       \fi:
+      \__fp_fixed_dtf_no_zero:Nwn + {#3} #4 \s__fp
+      \__fp_fixed_dtf_approx:n
+    }
+  }
+\cs_new:Npn \__fp_fixed_dtf_no_zero:Nwn #1#2 \s__fp #3 { #3 #2; }
+\cs_new:Npn \__fp_fixed_dtf_zeros:wNnnnnnn
+    \fi: \__fp_fixed_dtf_no_zero:Nwn #1#2#3#4#5#6#7
+  {
     \fi:
+    #1 \c_minus_one
+    \exp_after:wN \use_i_ii:nnn
+    \exp_after:wN \__fp_fixed_dtf_zeros:NN
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w 10 0000 + #2 \__int_eval_end: #3#4#5#6#7
+    ; 1 ;
   }
-\cs_new_protected_nopar:Npn \fp_exp_integer_tens:
+\cs_new:Npn \__fp_fixed_dtf_zeros:NN #1#2
   {
-    \l_fp_output_integer_int  \l_fp_exp_integer_int
-    \l_fp_output_decimal_int  \l_fp_exp_decimal_int
-    \l_fp_output_extended_int \l_fp_exp_extended_int
-    \l_fp_output_exponent_int \l_fp_exp_exponent_int
-    \if_int_compare:w \l_fp_input_a_integer_int > \c_nine
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \exp_after:wN \use_i:nn
-            \int_use:N \l_fp_input_a_integer_int
-        }
-      \l_fp_input_a_integer_int
-        \int_eval:w
-          \l_fp_input_a_integer_int - \l_fp_internal_tl 0
-        \int_eval_end:
-      \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-        \fp_exp_integer_const:n { \l_fp_internal_tl 0 }
-      \else:
-        \fp_exp_integer_const:n { - \l_fp_internal_tl 0 }
-      \fi:
-      \fp_mul:NNNNNNNNN
-        \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-      \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
-      \fp_extended_normalise_output:
+    \if_meaning:w 0 #2
+      #1 \c_one
+    \else:
+      \__fp_fixed_dtf_zeros_end:wNww #2
     \fi:
-    \fp_exp_integer_units:
+    \__fp_fixed_dtf_zeros:NN #1
   }
-\cs_new_protected_nopar:Npn \fp_exp_integer_units:
+\cs_new:Npn \__fp_fixed_dtf_zeros_end:wNww
+    #1 \fi: \__fp_fixed_dtf_zeros:NN #2 #3; #4 \s__fp
   {
-    \if_int_compare:w \l_fp_input_a_integer_int > \c_zero
-      \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-        \fp_exp_integer_const:n { \int_use:N \l_fp_input_a_integer_int }
-      \else:
-        \fp_exp_integer_const:n
-          { - \int_use:N \l_fp_input_a_integer_int }
-      \fi:
-      \fp_mul:NNNNNNNNN
-        \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-      \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
-      \fp_extended_normalise_output:
     \fi:
-    \fp_exp_decimal:
+    \if_meaning:w ; #1
+      #2 \c_two * \c__fp_max_exponent_int
+      \use_i_ii:nnn
+    \fi:
+    \__fp_fixed_dtf_zeros_ii:ww
+    #1#3 0000 0000 0000 0000 0000 0000 ;
+  }
+\cs_new:Npn \__fp_fixed_dtf_zeros_ii:ww
+  {
+    \__fp_pack_twice_four:wNNNNNNNN
+    \__fp_pack_twice_four:wNNNNNNNN
+    \__fp_pack_twice_four:wNNNNNNNN
+    \__fp_fixed_dtf_zeros_iii:ww
+    ;
+  }
+\cs_new:Npn \__fp_fixed_dtf_zeros_iii:ww #1; #2; #3 { #3 #1; }
+\cs_new:Npn \__fp_fixed_dtf_approx:n #1
+  {
+    \exp_after:wN \__fp_fixed_dtf_approx_ii:wnn
+    \int_use:N \__int_eval:w 10 0000 0000 / ( #1 + \c_one ) ;
+    {#1}
+  }
+\cs_new:Npn \__fp_fixed_dtf_approx_ii:wnn #1; #2#3
+  {
+    \exp_after:wN \__fp_fixed_dtf_approx_iii:NNNNNw
+    \int_use:N \__int_eval:w 10 0000 0000 - 1750
+      + #1000 + (10 0000 0000/#2-#1) * (1000-#3/10) ;
+    {#2}{#3}
   }
-\cs_new_protected:Npn \fp_exp_integer_const:n #1
+\cs_new:Npn \__fp_fixed_dtf_approx_iii:NNNNNw 1#1#2#3#4#5#6; #7; #8;
   {
-    \exp_after:wN \exp_after:wN \exp_after:wN
-      \fp_exp_integer_const:nnnn
-      \cs:w c_fp_exp_ #1 _tl \cs_end:
+    + \c_four % because of the line below "dtf_epsilon" here.
+    \__fp_fixed_mul:wwn {000#1}{#2#3#4#5}{#6}{0000}{0000}{0000} ; #7;
+    \__fp_fixed_dtf_epsilon:wN
+    \__fp_fixed_mul:wwn {000#1}{#2#3#4#5}{#6}{0000}{0000}{0000} ;
+    \__fp_fixed_mul:wwn #8;
+    \__fp_fixed_to_float:wN ?
   }
-\cs_new_protected:Npn \fp_exp_integer_const:nnnn #1#2#3#4
+\cs_new:Npn \__fp_fixed_dtf_epsilon:wN #1#2#3#4#5#6;
   {
-    \l_fp_exp_integer_int  #1 \scan_stop:
-    \l_fp_exp_decimal_int  #2 \scan_stop:
-    \l_fp_exp_extended_int #3 \scan_stop:
-    \l_fp_exp_exponent_int #4 \scan_stop:
+    \exp_after:wN \__fp_fixed_dtf_epsilon_ii:NNNNNww
+    \int_use:N \__int_eval:w 1 9999 9998 - #3#4 +
+      \exp_after:wN \__fp_fixed_dtf_epsilon_pack:NNNNNw
+      \int_use:N \__int_eval:w 2 0000 0000 - #5#6 ; {0000} ;
   }
-\cs_new_protected_nopar:Npn \fp_exp_decimal:
+\cs_new:Npn \__fp_fixed_dtf_epsilon_pack:NNNNNw #1#2#3#4#5#6;
+  { #1 ; {#2#3#4#5} {#6} }
+\cs_new:Npn \__fp_fixed_dtf_epsilon_ii:NNNNNww #1#2#3#4#5#6; #7;
   {
-    \if_int_compare:w \l_fp_input_a_decimal_int > \c_zero
-      \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-        \l_fp_exp_integer_int  \c_one
-        \l_fp_exp_decimal_int  \l_fp_input_a_decimal_int
-        \l_fp_exp_extended_int \l_fp_input_a_extended_int
+    \__fp_fixed_mul:wwn %^^A todo: optimize to use \__fp_mul_mantissa.
+      {0000} {#2#3#4#5} {#6} #7 ;
+      {0000} {#2#3#4#5} {#6} #7 ;
+    \__fp_fixed_add_one:wN
+    \__fp_fixed_mul:wwn {10000} {#2#3#4#5} {#6} #7 ;
+  }
+%% File: l3fp-expo.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\tl_const:Nn \c__fp_ln_i_fixed_tl   { {0000}{0000}{0000}{0000}{0000}{0000} }
+\tl_const:Nn \c__fp_ln_ii_fixed_tl  { {6931}{4718}{0559}{9453}{0941}{7232} }
+\tl_const:Nn \c__fp_ln_iii_fixed_tl {{10986}{1228}{8668}{1096}{9139}{5245} }
+\tl_const:Nn \c__fp_ln_iv_fixed_tl  {{13862}{9436}{1119}{8906}{1883}{4464} }
+ % \tl_const:Nn \c__fp_ln_v_fixed_tl   {{16094}{3791}{2434}{1003}{7460}{0759} }
+\tl_const:Nn \c__fp_ln_vi_fixed_tl  {{17917}{5946}{9228}{0550}{0081}{2477} }
+\tl_const:Nn \c__fp_ln_vii_fixed_tl {{19459}{1014}{9055}{3133}{0510}{5353} }
+\tl_const:Nn \c__fp_ln_viii_fixed_tl{{20794}{4154}{1679}{8359}{2825}{1696} }
+\tl_const:Nn \c__fp_ln_ix_fixed_tl  {{21972}{2457}{7336}{2193}{8279}{0490} }
+\tl_const:Nn \c__fp_ln_x_fixed_tl   {{23025}{8509}{2994}{0456}{8401}{7991} }
+ %\tl_const:Nn \c__fp_ln_ten_fixed_tl {{23025}{8509}{2994}{0456}{8401}{7991} }
+\cs_new:Npn \__fp_ln:w \s__fp \__fp_chk:w #1 #2
+  {
+    \if_meaning:w 0 #1
+      \__fp_case_use:nw
+        { \__fp_division_by_zero:Nnw \c_minus_inf_fp { ln } }
+    \fi:
+    \if_meaning:w 2 #2
+      \__fp_case_use:nw
+        { \__fp_invalid_operation:Nnw \c_nan_fp { ln } }
+    \fi:
+    \if_meaning:w 1 #1 \else:
+      \__fp_case_return_same_o:w
+    \fi:
+    \__fp_ln_npos:w \s__fp \__fp_chk:w #1#2
+  }
+\cs_new:Npn \__fp_ln_npos:w \s__fp \__fp_chk:w 10#1#2#3;
+  { %^^A todo: ln(1) should be "exact zero", not "underflow"
+    \exp_after:wN \__fp_sanitize:Nw
+    \__int_value:w % for the overall sign
+      \if_int_compare:w #1 < \c_one
+        2
       \else:
-        \l_fp_exp_integer_int \c_zero
-        \if_int_compare:w \l_fp_exp_extended_int = \c_zero
-          \l_fp_exp_decimal_int
-            \int_eval:w
-              \c_one_thousand_million - \l_fp_input_a_decimal_int
-            \int_eval_end:
-          \l_fp_exp_extended_int \c_zero
+        0
+      \fi:
+      \exp_after:wN \exp_stop_f:
+      \int_use:N \__int_eval:w % for the exponent
+        \__fp_ln_significand:NNNNnnnN #2#3
+        \__fp_ln_exponent:wn {#1}
+  }
+\cs_new:Npn \__fp_ln_significand:NNNNnnnN #1#2#3#4
+  {
+    \exp_after:wN \__fp_ln_x_ii:wnnnn
+    \__int_value:w
+      \if_case:w #1 \exp_stop_f:
+      \or:
+        \if_int_compare:w #2 < \c_four
+          \__int_eval:w \c_ten - #2
         \else:
-          \l_fp_exp_decimal_int
-            \int_eval:w
-              999999999 - \l_fp_input_a_decimal_int
-            \scan_stop:
-          \l_fp_exp_extended_int
-            \int_eval:w
-              \c_one_thousand_million - \l_fp_input_a_extended_int
-            \int_eval_end:
+          6
         \fi:
+      \or: 4
+      \or: 3
+      \or: 2
+      \or: 2
+      \or: 2
+      \else: 1
       \fi:
-      \l_fp_input_b_sign_int     \l_fp_input_a_sign_int
-      \l_fp_input_b_decimal_int  \l_fp_input_a_decimal_int
-      \l_fp_input_b_extended_int \l_fp_input_a_extended_int
-      \l_fp_count_int \c_one
-      \fp_exp_Taylor:
-      \fp_mul:NNNNNNNNN
-        \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-    \fi:
-    \if_int_compare:w \l_fp_output_extended_int < \c_five_hundred_million
-    \else:
-      \tex_advance:D \l_fp_output_decimal_int \c_one
-      \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
-      \else:
-        \l_fp_output_decimal_int \c_zero
-        \tex_advance:D \l_fp_output_integer_int \c_one
-      \fi:
-    \fi:
-    \fp_standardise:NNNN
-      \l_fp_output_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+    ; { #1 #2 #3 #4 }
+  }
+\cs_new:Npn \__fp_ln_x_ii:wnnnn #1; #2#3#4#5
+  {
+    \exp_after:wN \__fp_ln_div_after:Nw
+    \cs:w c__fp_ln_ \tex_romannumeral:D #1 _fixed_tl \exp_after:wN \cs_end:
+    \__int_value:w
+      \exp_after:wN \__fp_ln_x_iv:nnnnnnnn
+      \tex_romannumeral:D -`0
+        \exp_after:wN \__fp_ln_x_iii_var:NNNNNw
+        \int_use:N \__int_eval:w 9999 9999 + #1*#2#3 +
+          \exp_after:wN \__fp_ln_x_iii:NNNNNw
+          \int_use:N \__int_eval:w 1 0000 0000 + #1*#4#5 ;
+    {20000} {0000} {0000} {0000}
+  } %^^A todo: reoptimize (a generalization attempt failed).
+\cs_new:Npn \__fp_ln_x_iii:NNNNNw #1 #2#3#4#5 #6; { #1; {#2#3#4#5} {#6} }
+\cs_new:Npn \__fp_ln_x_iii_var:NNNNNw #1 #2#3#4#5 #6; { {#1#2#3#4#5} {#6} }
+\cs_new:Npn \__fp_ln_x_iv:nnnnnnnn #1#2#3#4 #5#6#7#8
+  {
+    \exp_after:wN \__fp_ln_div_i:w
+    \int_use:N \__int_eval:w #1 + \c_one ;
+    #5 #6 ; {#7} {#8}
+    {#1} {#2} {#3} {#4}
+  }
+\cs_new:Npn \__fp_ln_div_i:w #1;
+  {
+    \exp_after:wN \__fp_ln_div_ii:www
+    \__int_value:w #1 \exp_after:wN ;
+    \__int_value:w
+      \exp_after:wN \__fp_div_mantissa_calc:Nwwnnnnnn
+      \int_use:N \__int_eval:w 999999 + 2 0000 0000 / #1 ; % Q1
+  }
+\cs_set_protected:Npn \__fp_tmp:w #1#2
+  {
+    \cs_new:Npn #1 ##1; ##2; ##3; % y; Q1; B1B2; <- for k=1
       {
-        +
-        \int_use:N \l_fp_output_integer_int
-        .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_output_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_output_exponent_int
+        \exp_after:wN \__fp_div_mantissa_pack:NNN
+        \int_use:N \__int_eval:w ##2
+          \exp_after:wN #2
+          \__int_value:w ##1 \exp_after:wN ;
+          \__int_value:w
+            \exp_after:wN \__fp_div_mantissa_calc:Nwwnnnnnn
+            \int_use:N \__int_eval:w 999999 + ##3 / ##1 ; % Q2
+            ##3 ;
       }
   }
-\cs_new_protected_nopar:Npn \fp_exp_Taylor:
-  {
-    \tex_advance:D \l_fp_count_int \c_one
-    \tex_multiply:D \l_fp_input_b_sign_int \l_fp_input_a_sign_int
-    \fp_mul:NNNNNN
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-      \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-    \fp_div_integer:NNNNN
-      \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-      \l_fp_count_int
-      \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-    \if_int_compare:w
-      \int_eval:w
-        \l_fp_input_b_decimal_int + \l_fp_input_b_extended_int
-        > \c_zero
-      \if_int_compare:w \l_fp_input_b_sign_int > \c_zero
-        \tex_advance:D \l_fp_exp_decimal_int \l_fp_input_b_decimal_int
-        \tex_advance:D \l_fp_exp_extended_int
-          \l_fp_input_b_extended_int
-        \if_int_compare:w \l_fp_exp_extended_int < \c_one_thousand_million
+\__fp_tmp:w \__fp_ln_div_ii:www \__fp_ln_div_iii:www
+\__fp_tmp:w \__fp_ln_div_iii:www \__fp_ln_div_iv:www
+\__fp_tmp:w \__fp_ln_div_iv:www \__fp_ln_div_v:www
+\__fp_tmp:w \__fp_ln_div_v:www \__fp_ln_div_vi:www
+\cs_new:Npn \__fp_ln_div_vi:www #1; #2; #3;#4#5 #6#7#8#9 %y;Q5;F1F2;F3F4x1x2x3x4
+  {
+    \exp_after:wN \__fp_div_mantissa_pack:NNN
+    \int_use:N \__int_eval:w #2
+      \exp_after:wN \__fp_div_mantissa_pack:NNN
+      \int_use:N \__int_eval:w 1000000 + #3 / #1 ; % Q6
+  }
+\cs_new:Npn \__fp_ln_div_after:Nw #1#2;
+  {
+    \if_meaning:w 0 #2
+      \exp_after:wN \__fp_ln_t_small:Nw
+    \else:
+      \exp_after:wN \__fp_ln_t_large:NNw
+      \exp_after:wN -
+    \fi:
+    #1
+  }
+\cs_new:Npn \__fp_ln_t_small:Nw #1 #2; #3; #4; #5; #6; #7;
+  {
+    \exp_after:wN \__fp_ln_t_large:NNw
+    \exp_after:wN + % <sign>
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w 9999 - #2 \exp_after:wN ;
+    \int_use:N \__int_eval:w 9999 - #3 \exp_after:wN ;
+    \int_use:N \__int_eval:w 9999 - #4 \exp_after:wN ;
+    \int_use:N \__int_eval:w 9999 - #5 \exp_after:wN ;
+    \int_use:N \__int_eval:w 9999 - #6 \exp_after:wN ;
+    \int_use:N \__int_eval:w 1 0000 - #7 ;
+  }
+\cs_new:Npn \__fp_ln_t_large:NNw #1 #2 #3; #4; #5; #6; #7; #8;
+  {
+    \exp_after:wN \__fp_ln_square_t_after:w
+    \int_use:N \__int_eval:w 9999 0000 + #3*#3
+      \exp_after:wN \__fp_ln_square_t_pack:NNNNNw
+      \int_use:N \__int_eval:w 9999 0000 + 2*#3*#4
+        \exp_after:wN \__fp_ln_square_t_pack:NNNNNw
+        \int_use:N \__int_eval:w 9999 0000 + 2*#3*#5 + #4*#4
+          \exp_after:wN \__fp_ln_square_t_pack:NNNNNw
+          \int_use:N \__int_eval:w 9999 0000 + 2*#3*#6 + 2*#4*#5
+            \exp_after:wN \__fp_ln_square_t_pack:NNNNNw
+            \int_use:N \__int_eval:w 1 0000 0000 + 2*#3*#7 + 2*#4*#6 + #5*#5
+              + (2*#3*#8 + 2*#4*#7 + 2*#5*#6) / 1 0000
+              % ; ; ;
+    \exp_after:wN \__fp_ln_twice_t_after:w
+    \int_use:N \__int_eval:w -1 + 2*#3
+      \exp_after:wN \__fp_ln_twice_t_pack:Nw
+      \int_use:N \__int_eval:w 9999 + 2*#4
+        \exp_after:wN \__fp_ln_twice_t_pack:Nw
+        \int_use:N \__int_eval:w 9999 + 2*#5
+          \exp_after:wN \__fp_ln_twice_t_pack:Nw
+          \int_use:N \__int_eval:w 9999 + 2*#6
+            \exp_after:wN \__fp_ln_twice_t_pack:Nw
+            \int_use:N \__int_eval:w 9999 + 2*#7
+              \exp_after:wN \__fp_ln_twice_t_pack:Nw
+              \int_use:N \__int_eval:w 10000 + 2*#8 ; ;
+    { \__fp_ln_c:NwNw #1 }
+    #2
+  }
+\cs_new:Npn \__fp_ln_twice_t_pack:Nw #1 #2; { + #1 ; {#2} }
+\cs_new:Npn \__fp_ln_twice_t_after:w #1; { ;;; {#1} }
+\cs_new:Npn \__fp_ln_square_t_pack:NNNNNw #1 #2#3#4#5 #6;
+  { + #1#2#3#4#5 ; {#6} }
+\cs_new:Npn \__fp_ln_square_t_after:w 1 0 #1#2#3 #4;
+  { \__fp_ln_Taylor:wwNw {0#1#2#3} {#4} }
+\cs_new:Npn \__fp_ln_Taylor:wwNw
+  { \__fp_ln_Taylor_loop:www 21 ; {0000}{0000}{0000}{0000}{0000}{0000} ; }
+\cs_new:Npn \__fp_ln_Taylor_loop:www #1; #2; #3;
+  {
+    \if_int_compare:w #1 = \c_one
+      \__fp_ln_Taylor_break:w
+    \fi:
+    \exp_after:wN \__fp_fixed_div_int:wwN \c__fp_one_fixed_tl ; #1;
+    \__fp_fixed_add:wwN #2;
+    \__fp_fixed_mul:wwn #3;
+    {
+      \exp_after:wN \__fp_ln_Taylor_loop:www
+      \int_use:N \__int_eval:w #1 - \c_two ;
+    }
+    #3;
+  }
+\cs_new:Npn \__fp_ln_Taylor_break:w \fi: #1 \__fp_fixed_add:wwN #2#3; #4 ;;
+  {
+    \fi:
+    \exp_after:wN \__fp_fixed_mul:wwn
+    \exp_after:wN { \int_use:N \__int_eval:w 10000 + #2 } #3;
+  }
+\cs_new:Npn \__fp_ln_c:NwNw #1 #2; #3
+  {
+    \if_meaning:w + #1
+      \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_sub:wwN
+    \else:
+      \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_add:wwN
+    \fi:
+    #3 ; #2 ;
+  }
+\cs_new:Npn \__fp_ln_exponent:wn #1; #2
+  {
+    \if_case:w #2 \exp_stop_f:
+      \c_zero \__fp_case_return:nw { \__fp_fixed_to_float:Nw 2 }
+    \or:
+      \exp_after:wN \__fp_ln_exponent_one:ww \__int_value:w
+    \else:
+      \if_int_compare:w #2 > \c_zero
+        \exp_after:wN \__fp_ln_exponent_small:NNww
+        \exp_after:wN 0
+        \exp_after:wN \__fp_fixed_sub:wwN \__int_value:w
       \else:
-          \tex_advance:D \l_fp_exp_decimal_int \c_one
-          \tex_advance:D \l_fp_exp_extended_int
-            -\c_one_thousand_million
-        \fi:
-        \if_int_compare:w \l_fp_exp_decimal_int < \c_one_thousand_million
-        \else:
-          \tex_advance:D \l_fp_exp_integer_int \c_one
-          \tex_advance:D \l_fp_exp_decimal_int
-            -\c_one_thousand_million
-        \fi:
+        \exp_after:wN \__fp_ln_exponent_small:NNww
+        \exp_after:wN 2
+        \exp_after:wN \__fp_fixed_add:wwN \__int_value:w -
+      \fi:
+    \fi:
+    #2; #1;
+  }
+\cs_new:Npn \__fp_ln_exponent_one:ww 1; #1;
+  {
+    \c_zero
+    \exp_after:wN \__fp_fixed_sub:wwN \c__fp_ln_x_fixed_tl ; #1;
+    \__fp_fixed_to_float:wN 0
+  }
+\cs_new:Npn \__fp_ln_exponent_small:NNww #1#2#3; #4#5#6#7#8#9;
+  {
+    \c_four
+    \exp_after:wN \__fp_fixed_mul:wwn
+      \c__fp_ln_x_fixed_tl ;
+      {#3}{0000}{0000}{0000}{0000}{0000} ;
+    #2
+      {0000}{#4}{#5}{#6}{#7}{#8};
+    \__fp_fixed_to_float:wN #1
+  }
+\cs_new:Npn \__fp_exp:w \s__fp \__fp_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+      \__fp_case_return_o:Nw \c_one_fp
+    \or:
+      \exp_after:wN \__fp_exp_normal:w
+    \or:
+      \if_meaning:w 0 #2
+        \exp_after:wN \__fp_case_return_o:Nw
+        \exp_after:wN \c_inf_fp
       \else:
-        \tex_advance:D \l_fp_exp_decimal_int -\l_fp_input_b_decimal_int
-        \tex_advance:D \l_fp_exp_extended_int
-          -\l_fp_input_a_extended_int
-        \if_int_compare:w \l_fp_exp_extended_int < \c_zero
-          \tex_advance:D \l_fp_exp_decimal_int \c_minus_one
-          \tex_advance:D \l_fp_exp_extended_int \c_one_thousand_million
-        \fi:
-        \if_int_compare:w \l_fp_exp_decimal_int < \c_zero
-          \tex_advance:D \l_fp_exp_integer_int \c_minus_one
-          \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
-        \fi:
+        \exp_after:wN \__fp_case_return_o:Nw
+        \exp_after:wN \c_zero_fp
       \fi:
-      \exp_after:wN \fp_exp_Taylor:
-    \fi:
-  }
-\cs_new_protected:Npn \fp_exp_const:Nx #1#2
-  {
-    \tl_new:N #1
-    \tl_gset:Nx #1 {#2}
-  }
-\cs_generate_variant:Nn \fp_exp_const:Nx { c }
-\tl_const:cn { c_fp_ln_10_1_tl } { { 2 } { 302585092 } { 994045684 } { 0 } }
-\tl_const:cn { c_fp_ln_10_2_tl } { { 4 } { 605170185 } { 988091368 } { 0 } }
-\tl_const:cn { c_fp_ln_10_3_tl } { { 6 } { 907755278 } { 982137052 } { 0 } }
-\tl_const:cn { c_fp_ln_10_4_tl } { { 9 } { 210340371 } { 976182736 } { 0 } }
-\tl_const:cn { c_fp_ln_10_5_tl } { { 1 } { 151292546 } { 497022842 } { 1 } }
-\tl_const:cn { c_fp_ln_10_6_tl } { { 1 } { 381551055 } { 796427410 } { 1 } }
-\tl_const:cn { c_fp_ln_10_7_tl } { { 1 } { 611809565 } { 095831979 } { 1 } }
-\tl_const:cn { c_fp_ln_10_8_tl } { { 1 } { 842068074 } { 395226547 } { 1 } }
-\tl_const:cn { c_fp_ln_10_9_tl } { { 2 } { 072326583 } { 694641116 } { 1 } }
-\tl_const:cn { c_fp_ln_2_1_tl } { { 0 } { 693147180 } { 559945309 } { 0 } }
-\tl_const:cn { c_fp_ln_2_2_tl } { { 1 } { 386294361 } { 119890618 } { 0 } }
-\tl_const:cn { c_fp_ln_2_3_tl } { { 2 } { 079441541 } { 679835928 } { 0 } }
-\cs_new_protected_nopar:Npn \fp_ln:Nn  { \fp_ln_aux:NNn \tl_set:Nn  }
-\cs_new_protected_nopar:Npn \fp_gln:Nn { \fp_ln_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_ln:Nn  { c }
-\cs_generate_variant:Nn \fp_gln:Nn { c }
-\cs_new_protected:Npn \fp_ln_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-        \if_int_compare:w
-          \int_eval:w
-            \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-            > \c_zero
-          \exp_after:wN \exp_after:wN \exp_after:wN \fp_ln_aux:
-        \else:
-          \cs_set_protected:Npx \fp_tmp:w ##1##2
-            {
-              \group_end:
-              ##1 \exp_not:N ##2 { \c_zero_fp }
-            }
-          \exp_after:wN \exp_after:wN \exp_after:wN \fp_ln_error_msg:
-        \fi:
+    \or:
+      \__fp_case_return_same_o:w
+    \fi:
+    \s__fp \__fp_chk:w #1#2
+  }
+\cs_new:Npn \__fp_exp_normal:w \s__fp \__fp_chk:w 1#1
+  {
+    \if_meaning:w 0 #1
+      \__fp_exp_pos:NNwnw + \__fp_fixed_to_float:wN
+    \else:
+      \__fp_exp_pos:NNwnw - \__fp_fixed_inv_to_float:wN
+    \fi:
+  }
+\cs_new:Npn \__fp_exp_pos:NNwnw #1#2#3 \fi: #4#5;
+  {
+    \fi:
+    \exp_after:wN \__fp_sanitize:Nw
+    \exp_after:wN 0
+    \__int_value:w #1 \__int_eval:w
+      \if_int_compare:w #4 < - \c_eight
+        \c_one
+        \exp_after:wN \__fp_add_big_i:wNww
+        \int_use:N \__int_eval:w \c_one - #4 ;
+        0 {1000}{0000}{0000}{0000} ; #5;
+        \tex_romannumeral:D
       \else:
-        \cs_set_protected:Npx \fp_tmp:w ##1##2
+        \if_int_compare:w #4 > \c_five % cf \c__fp_max_exponent_int
+          \exp_after:wN \__fp_exp_overflow:
+          \tex_romannumeral:D
+        \else:
+          \if_int_compare:w #4 < \c_zero
+            \exp_after:wN \use_i:nn
+          \else:
+            \exp_after:wN \use_ii:nn
+          \fi:
+          {
+            \c_zero
+            \__fp_decimate:nNnnnn { - #4 }
+              \__fp_exp_Taylor:Nnnwn
+          }
           {
-            \group_end:
-            ##1 \exp_not:N ##2 { \c_zero_fp }
+            \__fp_decimate:nNnnnn { \c_sixteen - #4 }
+              \__fp_exp_pos_large:NnnNwn
           }
-        \exp_after:wN \fp_ln_error_msg:
+          #5
+          {#4}
+          #2 0
+          \tex_romannumeral:D
+        \fi:
       \fi:
-    \fp_tmp:w #1 #2
+    \exp_after:wN \c_zero
   }
-\cs_new_protected_nopar:Npn \fp_ln_aux:
+\cs_new:Npn \__fp_exp_overflow:
+  { + \c_two * \c__fp_max_exponent_int ; {1000} {0000} {0000} {0000} ; }
+\cs_new:Npn \__fp_exp_Taylor:Nnnwn #1#2#3 #4; #5
   {
-    \tl_set:Nx \l_fp_arg_tl
-      {
-        +
-        \int_use:N \l_fp_input_a_integer_int
-        .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_input_a_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_input_a_exponent_int
-      }
-    \if_cs_exist:w c_fp_ln ( \l_fp_arg_tl ) _fp \cs_end:
+    \__fp_pack_twice_four:wNNNNNNNN
+    \__fp_pack_twice_four:wNNNNNNNN
+    \__fp_pack_twice_four:wNNNNNNNN
+    \__fp_exp_Taylor_ii:ww
+    ; #2#3#4 0000 0000 ;
+  }
+\cs_new:Npn \__fp_exp_Taylor_ii:ww #1; #2;
+  { \__fp_exp_Taylor_loop:www 10 ; #1 ; #1 ; \s__stop }
+\cs_new:Npn \__fp_exp_Taylor_loop:www #1; #2; #3;
+  {
+    \if_int_compare:w #1 = \c_one
+      \exp_after:wN \__fp_exp_Taylor_break:Nww
+    \fi:
+    \__fp_fixed_div_int:wwN #3 ; #1 ;
+    \__fp_fixed_add_one:wN
+    \__fp_fixed_mul:wwn #2 ;
+    {
+      \exp_after:wN \__fp_exp_Taylor_loop:www
+      \int_use:N \__int_eval:w #1 - 1 ;
+      #2 ;
+    }
+  }
+\cs_new:Npn \__fp_exp_Taylor_break:Nww #1 #2; #3 \s__stop
+  { \__fp_fixed_add_one:wN #2 ; }
+\cs_new:Npn \__fp_exp_pos_large:NnnNwn #1#2#3 #4#5; #6
+  {
+    \exp_after:wN \exp_after:wN
+    \cs:w __fp_exp_large_\tex_romannumeral:D #6:wN \exp_after:wN \cs_end:
+    \exp_after:wN \c__fp_one_fixed_tl
+    \exp_after:wN ;
+    \__int_value:w #3 #4 \exp_stop_f:
+    #5 00000 ;
+  }
+\cs_new:Npn \__fp_exp_large:w #1 \or: #2 \fi:
+  { \fi: \__fp_fixed_mul:wwn #1; }
+\cs_new:Npn \__fp_exp_large_v:wN #1; #2
+  {
+    \if_case:w #2 ~           \exp_after:wN \__fp_fixed_continue:wn  \or:
+      +  4343 \__fp_exp_large:w {8806}{8182}{2566}{2921}{5872}{6150} \or:
+      +  8686 \__fp_exp_large:w {7756}{0047}{2598}{6861}{0458}{3204} \or:
+      + 13029 \__fp_exp_large:w {6830}{5723}{7791}{4884}{1932}{7351} \or:
+      + 17372 \__fp_exp_large:w {6015}{5609}{3095}{3052}{3494}{7574} \or:
+      + 21715 \__fp_exp_large:w {5297}{7951}{6443}{0315}{3251}{3576} \or:
+      + 26058 \__fp_exp_large:w {4665}{6719}{0099}{3379}{5527}{2929} \or:
+      + 30401 \__fp_exp_large:w {4108}{9724}{3326}{3186}{5271}{5665} \or:
+      + 34744 \__fp_exp_large:w {3618}{6973}{3140}{0875}{3856}{4102} \or:
+      + 39087 \__fp_exp_large:w {3186}{9209}{6113}{3900}{6705}{9685} \or:
+    \fi:
+    #1;
+    \__fp_exp_large_iv:wN
+  }
+\cs_new:Npn \__fp_exp_large_iv:wN #1; #2
+  {
+    \if_case:w #2 ~          \exp_after:wN \__fp_fixed_continue:wn  \or:
+      +  435 \__fp_exp_large:w {1970}{0711}{1401}{7046}{9938}{8888} \or:
+      +  869 \__fp_exp_large:w {3881}{1801}{9428}{4368}{5764}{8232} \or:
+      + 1303 \__fp_exp_large:w {7646}{2009}{8905}{4704}{8893}{1073} \or:
+      + 1738 \__fp_exp_large:w {1506}{3559}{7005}{0524}{9009}{7592} \or:
+      + 2172 \__fp_exp_large:w {2967}{6283}{8402}{3667}{0689}{6630} \or:
+      + 2606 \__fp_exp_large:w {5846}{4389}{5650}{2114}{7278}{5046} \or:
+      + 3041 \__fp_exp_large:w {1151}{7900}{5080}{6878}{2914}{4154} \or:
+      + 3475 \__fp_exp_large:w {2269}{1083}{0850}{6857}{8724}{4002} \or:
+      + 3909 \__fp_exp_large:w {4470}{3047}{3316}{5442}{6408}{6591} \or:
+    \fi:
+    #1;
+    \__fp_exp_large_iii:wN
+  }
+\cs_new:Npn \__fp_exp_large_iii:wN #1; #2
+  {
+    \if_case:w #2 ~         \exp_after:wN \__fp_fixed_continue:wn  \or:
+      +  44 \__fp_exp_large:w {2688}{1171}{4181}{6135}{4484}{1263} \or:
+      +  87 \__fp_exp_large:w {7225}{9737}{6812}{5749}{2581}{7748} \or:
+      + 131 \__fp_exp_large:w {1942}{4263}{9524}{1255}{9365}{8421} \or:
+      + 174 \__fp_exp_large:w {5221}{4696}{8976}{4143}{9505}{8876} \or:
+      + 218 \__fp_exp_large:w {1403}{5922}{1785}{2837}{4107}{3977} \or:
+      + 261 \__fp_exp_large:w {3773}{0203}{0092}{9939}{8234}{0143} \or:
+      + 305 \__fp_exp_large:w {1014}{2320}{5473}{5004}{5094}{5533} \or:
+      + 348 \__fp_exp_large:w {2726}{3745}{7211}{2566}{5673}{6478} \or:
+      + 391 \__fp_exp_large:w {7328}{8142}{2230}{7421}{7051}{8866} \or:
+    \fi:
+    #1;
+    \__fp_exp_large_ii:wN
+  }
+\cs_new:Npn \__fp_exp_large_ii:wN #1; #2
+  {
+    \if_case:w #2 ~        \exp_after:wN \__fp_fixed_continue:wn  \or:
+      +  5 \__fp_exp_large:w {2202}{6465}{7948}{0671}{6516}{9579} \or:
+      +  9 \__fp_exp_large:w {4851}{6519}{5409}{7902}{7796}{9107} \or:
+      + 14 \__fp_exp_large:w {1068}{6474}{5815}{2446}{2146}{9905} \or:
+      + 18 \__fp_exp_large:w {2353}{8526}{6837}{0199}{8540}{7900} \or:
+      + 22 \__fp_exp_large:w {5184}{7055}{2858}{7072}{4640}{8745} \or:
+      + 27 \__fp_exp_large:w {1142}{0073}{8981}{5684}{2836}{6296} \or:
+      + 31 \__fp_exp_large:w {2515}{4386}{7091}{9167}{0062}{6578} \or:
+      + 35 \__fp_exp_large:w {5540}{6223}{8439}{3510}{0525}{7117} \or:
+      + 40 \__fp_exp_large:w {1220}{4032}{9431}{7840}{8020}{0271} \or:
+    \fi:
+    #1;
+    \__fp_exp_large_i:wN
+  }
+\cs_new:Npn \__fp_exp_large_i:wN #1; #2
+  {
+    \if_case:w #2 ~       \exp_after:wN \__fp_fixed_continue:wn  \or:
+      + 1 \__fp_exp_large:w {2718}{2818}{2845}{9045}{2353}{6029} \or:
+      + 1 \__fp_exp_large:w {7389}{0560}{9893}{0650}{2272}{3043} \or:
+      + 2 \__fp_exp_large:w {2008}{5536}{9231}{8766}{7740}{9285} \or:
+      + 2 \__fp_exp_large:w {5459}{8150}{0331}{4423}{9078}{1103} \or:
+      + 3 \__fp_exp_large:w {1484}{1315}{9102}{5766}{0342}{1116} \or:
+      + 3 \__fp_exp_large:w {4034}{2879}{3492}{7351}{2260}{8387} \or:
+      + 4 \__fp_exp_large:w {1096}{6331}{5842}{8458}{5992}{6372} \or:
+      + 4 \__fp_exp_large:w {2980}{9579}{8704}{1728}{2747}{4359} \or:
+      + 4 \__fp_exp_large:w {8103}{0839}{2757}{5384}{0077}{1000} \or:
+    \fi:
+    #1;
+    \__fp_exp_large_:wN
+  }
+\cs_new:Npn \__fp_exp_large_:wN #1; #2
+  {
+    \if_case:w #2 ~       \exp_after:wN \__fp_fixed_continue:wn  \or:
+      + 1 \__fp_exp_large:w {1105}{1709}{1807}{5647}{6248}{1171} \or:
+      + 1 \__fp_exp_large:w {1221}{4027}{5816}{0169}{8339}{2107} \or:
+      + 1 \__fp_exp_large:w {1349}{8588}{0757}{6003}{1039}{8374} \or:
+      + 1 \__fp_exp_large:w {1491}{8246}{9764}{1270}{3178}{2485} \or:
+      + 1 \__fp_exp_large:w {1648}{7212}{7070}{0128}{1468}{4865} \or:
+      + 1 \__fp_exp_large:w {1822}{1188}{0039}{0508}{9748}{7537} \or:
+      + 1 \__fp_exp_large:w {2013}{7527}{0747}{0476}{5216}{2455} \or:
+      + 1 \__fp_exp_large:w {2225}{5409}{2849}{2467}{6045}{7954} \or:
+      + 1 \__fp_exp_large:w {2459}{6031}{1115}{6949}{6638}{0013} \or:
+    \fi:
+    #1;
+    \__fp_exp_large_after:wwn
+  }
+\cs_new:Npn \__fp_exp_large_after:wwn #1; #2;
+  {
+    \__fp_exp_Taylor:Nnnwn ? { } { } 0 #2; {}
+    \__fp_fixed_mul:wwn #1;
+  }
+\cs_new:cpn { __fp_ \iow_char:N \^ _o:ww }
+    \s__fp \__fp_chk:w #1#2#3; \s__fp \__fp_chk:w #4#5#6;
+  {
+    \if_meaning:w 0 #4
+      \__fp_case_return_o:Nw \c_one_fp
+    \fi:
+    \if_case:w #2 \exp_stop_f:
+      \exp_after:wN \use_i:nn
+    \or:
+      \__fp_case_return_o:Nw \c_nan_fp
     \else:
-      \exp_after:wN \fp_ln_exponent:
+      \exp_after:wN \__fp_pow_neg:www
+      \tex_romannumeral:D -`0 \exp_after:wN \use:nn
     \fi:
-    \cs_set_protected:Npx \fp_tmp:w ##1##2
-      {
-        \group_end:
-        ##1 \exp_not:N ##2
-          { \use:c { c_fp_ln ( \l_fp_arg_tl ) _fp } }
-      }
+    {
+      \if_meaning:w 1 #1
+        \exp_after:wN \__fp_pow_normal:ww
+      \else:
+        \exp_after:wN \__fp_pow_zero_or_inf:ww
+      \fi:
+      \s__fp \__fp_chk:w #1#2#3;
+    }
+    { \s__fp \__fp_chk:w #4#5#6; \s__fp \__fp_chk:w #1#2#3; }
+    \s__fp \__fp_chk:w #4#5#6;
   }
-\cs_new_protected_nopar:Npn \fp_ln_exponent:
+\cs_new:Npn \__fp_pow_zero_or_inf:ww \s__fp \__fp_chk:w #1#2; \s__fp \__fp_chk:w #3#4
   {
-    \fp_ln_internal:
-    \if_int_compare:w \l_fp_output_extended_int < \c_five_hundred_million
+    \if_meaning:w 1 #4
+      \__fp_case_return_same_o:w
+    \fi:
+    \if_meaning:w #1 #4
+      \__fp_case_return_o:Nw \c_zero_fp
     \else:
-      \tex_advance:D \l_fp_output_decimal_int \c_one
-      \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
+      \__fp_case_return_o:Nw \c_inf_fp
+    \fi:
+    \s__fp \__fp_chk:w #3#4
+  }
+\cs_new:Npn \__fp_pow_normal:ww \s__fp \__fp_chk:w 1 #1#2#3; \s__fp \__fp_chk:w #4#5
+  {
+    \if_int_compare:w \pdftex_strcmp:D { #2 #3 }
+              { 1 {1000} {0000} {0000} {0000} } = \c_zero
+      \if_int_compare:w #4 #1 = 32 \exp_stop_f:
+        \exp_after:wN \__fp_case_return_ii_o:ww
+      \fi:
+      \__fp_case_return_o:Nww \c_one_fp
+    \fi:
+    \if_case:w #4 ~
+    \or:
+      \exp_after:wN \__fp_pow_npos:Nww
+      \exp_after:wN #5
+    \or:
+      \if_meaning:w 2 #5 \exp_after:wN \reverse_if:N \fi:
+      \if_int_compare:w #2 > \c_zero
+        \exp_after:wN \__fp_case_return_o:Nww
+        \exp_after:wN \c_inf_fp
       \else:
-        \l_fp_output_decimal_int \c_zero
-        \tex_advance:D \l_fp_output_integer_int \c_one
+        \exp_after:wN \__fp_case_return_o:Nww
+        \exp_after:wN \c_zero_fp
       \fi:
+    \or:
+      \__fp_case_return_ii_o:ww
     \fi:
-    \fp_standardise:NNNN
-      \l_fp_output_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \tl_const:cx { c_fp_ln ( \l_fp_arg_tl ) _fp }
-      {
-        \if_int_compare:w \l_fp_output_sign_int > \c_zero
-          +
-        \else:
-          -
-        \fi:
-        \int_use:N \l_fp_output_integer_int
-        .
-        \exp_after:wN \use_none:n
-          \int_value:w \int_eval:w
-             \l_fp_output_decimal_int + \c_one_thousand_million
-           \scan_stop:
-        e
-        \int_use:N \l_fp_output_exponent_int
-      }
+    \s__fp \__fp_chk:w 1 #1 {#2} #3 ;
+    \s__fp \__fp_chk:w #4 #5
   }
-\cs_new_protected_nopar:Npn \fp_ln_internal:
+\cs_new:Npn \__fp_pow_npos:Nww #1 \s__fp \__fp_chk:w 1#2#3
   {
-    \if_int_compare:w \l_fp_input_a_exponent_int < \c_zero
-      \l_fp_input_a_exponent_int -\l_fp_input_a_exponent_int
-      \l_fp_output_sign_int \c_minus_one
+    \exp_after:wN \__fp_sanitize:Nw
+    \exp_after:wN 0
+    \__int_value:w
+      \if:w #1 \if_int_compare:w #3 > \c_zero 0 \else: 2 \fi:
+        \exp_after:wN \__fp_pow_npos_aux:Nnww
+        \exp_after:wN \__fp_fixed_to_float:wN
+      \else:
+        -
+        \exp_after:wN \__fp_pow_npos_aux:Nnww
+        \exp_after:wN \__fp_fixed_inv_to_float:wN
+      \fi:
+      {#3}
+  }
+\cs_new:Npn \__fp_pow_npos_aux:Nnww #1#2#3#4; \s__fp \__fp_chk:w 1#5#6#7;
+  {
+    \__int_eval:w
+      \__fp_ln_significand:NNNNnnnN #3#4
+      \__fp_pow_exponent:wnN {#2}
+      \__fp_fixed_mul:wwn #7 {0000}{0000} ;
+      \__fp_pow_B:wwN #6;
+      #1 0 % fixed_to_float:wN
+  }
+\cs_new:Npn \__fp_pow_exponent:wnN #1; #2
+  {
+    \if_int_compare:w #2 > \c_zero
+      \exp_after:wN \__fp_pow_exponent:Nwnnnnnn % n\log 10 - (-\log x)
+      \exp_after:wN +
     \else:
-      \l_fp_output_sign_int \c_one
+      \exp_after:wN \__fp_pow_exponent:Nwnnnnnn % -( |n|\log 10 + (-\log x) )
+      \exp_after:wN -
     \fi:
-    \if_int_compare:w \l_fp_input_a_exponent_int > \c_nine
-      \exp_after:wN \fp_ln_exponent_tens:NN
-        \int_use:N \l_fp_input_a_exponent_int
+    #2; #1;
+  }
+\cs_new:Npn \__fp_pow_exponent:Nwnnnnnn #1#2; #3#4#5#6#7#8;
+  { %^^A todo: use that in ln. %^^A todo: log(1.00...) too inaccurate?
+    \exp_after:wN \__fp_fixed_mul_after:wwn
+    \int_use:N \__int_eval:w -5 0000
+      \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
+      \int_use:N \__int_eval:w 4 9995 0000 #1#2*23025 - #1 #3
+        \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
+        \int_use:N \__int_eval:w 4 9995 0000 #1 #2*8509 - #1 #4
+          \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
+          \int_use:N \__int_eval:w 4 9995 0000 #1 #2*2994 - #1 #5
+            \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
+            \int_use:N \__int_eval:w 4 9995 0000 #1 #2*0456 - #1 #6
+              \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
+              \int_use:N \__int_eval:w 5 0000 0000 #1 #2*8401 - #1 #7
+                #1 ( #2*7991 - #8 ) / 1 0000 ; ;
+  }
+\cs_new:Npn \__fp_pow_B:wwN #1#2#3#4#5#6; #7;
+  {
+    \if_int_compare:w #7 < \c_zero
+      \exp_after:wN \__fp_pow_C_neg:w \__int_value:w -
     \else:
-      \l_fp_output_integer_int  \c_zero
-      \l_fp_output_decimal_int  \c_zero
-      \l_fp_output_extended_int \c_zero
-      \l_fp_output_exponent_int \c_zero
+      \if_int_compare:w #7 < 22 \exp_stop_f:
+        \exp_after:wN \__fp_pow_C_pos:w \__int_value:w
+      \else:
+        \exp_after:wN \__fp_pow_C_overflow:w \__int_value:w
+      \fi:
     \fi:
-    \fp_ln_exponent_units:
+    #7 \exp_after:wN ;
+    \int_use:N \__int_eval:w 10 0000 + #1 \__int_eval_end:
+    #2#3#4#5#6 0000 0000 0000 0000 0000 0000 ; %^^A todo: how many 0?
   }
-\cs_new_protected:Npn \fp_ln_exponent_tens:NN #1 #2
+\cs_new:Npn \__fp_pow_C_overflow:w #1; #2;
   {
-    \l_fp_input_a_exponent_int #2 \scan_stop:
-    \fp_ln_const:nn { 10 } { #1 }
-    \tex_advance:D \l_fp_exp_exponent_int \c_one
-    \l_fp_output_integer_int  \l_fp_exp_integer_int
-    \l_fp_output_decimal_int  \l_fp_exp_decimal_int
-    \l_fp_output_extended_int \l_fp_exp_extended_int
-    \l_fp_output_exponent_int \l_fp_exp_exponent_int
+    + \c_two * \c__fp_max_exponent_int
+    \exp_after:wN \__fp_fixed_continue:wn \c__fp_one_fixed_tl ;
   }
-\cs_new_protected_nopar:Npn \fp_ln_exponent_units:
+\cs_new:Npn \__fp_pow_C_neg:w #1 ; 1
   {
-    \if_int_compare:w \l_fp_input_a_exponent_int > \c_zero
-      \fp_ln_const:nn { 10 } { \int_use:N \l_fp_input_a_exponent_int }
-      \fp_ln_normalise:
-      \fp_add:NNNNNNNNN
-        \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-        \l_fp_output_integer_int \l_fp_output_decimal_int
-          \l_fp_output_extended_int
-    \fi:
-    \fp_ln_mantissa:
+    \exp_after:wN \exp_after:wN \exp_after:wN \__fp_pow_C_pack:w
+    \prg_replicate:nn {#1} {0}
   }
-\cs_new_protected_nopar:Npn \fp_ln_normalise:
+\cs_new:Npn \__fp_pow_C_pos:w #1; 1
+  { \__fp_pow_C_pos_loop:wN #1; }
+\cs_new:Npn \__fp_pow_C_pos_loop:wN #1; #2
   {
-    \if_int_compare:w \l_fp_exp_exponent_int < \l_fp_output_exponent_int
-      \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
-      \exp_after:wN \use_i:nn \exp_after:wN
-        \fp_ln_normalise_aux:NNNNNNNNN
-        \int_use:N \l_fp_exp_decimal_int
-       \exp_after:wN \fp_ln_normalise:
+    \if_meaning:w 0 #1
+      \exp_after:wN \__fp_pow_C_pack:w
+      \exp_after:wN #2
     \else:
-      \l_fp_output_exponent_int \l_fp_exp_exponent_int
+      \if_meaning:w 0 #2
+        \exp_after:wN \__fp_pow_C_pos_loop:wN \__int_value:w
+      \else:
+        \exp_after:wN \__fp_pow_C_overflow:w \__int_value:w
+      \fi:
+      \__int_eval:w #1 - \c_one \exp_after:wN ;
     \fi:
   }
-\cs_new_protected:Npn \fp_ln_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+\cs_new:Npn \__fp_pow_C_pack:w
+  { \exp_after:wN \__fp_exp_large_v:wN \c__fp_one_fixed_tl ; }
+\cs_new:Npn \__fp_pow_neg:www \s__fp \__fp_chk:w #1#2; #3; #4;
   {
-    \if_int_compare:w \l_fp_exp_integer_int = \c_zero
-      \l_fp_exp_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
-    \else:
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \int_use:N \l_fp_exp_integer_int
-          #1#2#3#4#5#6#7#8
-        }
-      \l_fp_exp_integer_int \c_zero
-      \l_fp_exp_decimal_int \l_fp_internal_tl \scan_stop:
+    \if_case:w \__fp_pow_neg_case:w #4 ;
+      \exp_after:wN \__fp_pow_neg_neg:w
+    \or:
+      \if_int_compare:w \__int_eval:w #1 / \c_two = \c_one
+        \__fp_invalid_operation:Nnww \c_nan_fp { ^ } #3; #4;
+        \tex_romannumeral:D -`0
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__fp_use_none_until_s:w
+      \fi:
     \fi:
-    \tex_divide:D \l_fp_exp_extended_int \c_ten
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        #9
-        \int_use:N \l_fp_exp_extended_int
-      }
-    \l_fp_exp_extended_int \l_fp_internal_tl \scan_stop:
-    \tex_advance:D \l_fp_exp_exponent_int \c_one
-  }
-\cs_new_protected_nopar:Npn \fp_ln_mantissa:
-  {
-    \l_fp_count_int \c_zero
-    \l_fp_input_a_extended_int \c_zero
-    \fp_ln_mantissa_aux:
-    \if_int_compare:w \l_fp_count_int > \c_zero
-      \fp_ln_const:nn { 2 } { \int_use:N \l_fp_count_int }
-      \fp_ln_normalise:
-      \if_int_compare:w \l_fp_output_sign_int > \c_zero
-        \exp_after:wN \fp_add:NNNNNNNNN
+    \__fp_exp_after_o:w
+    \s__fp \__fp_chk:w #1#2;
+  }
+\cs_new:Npn \__fp_pow_neg_neg:w \__fp_exp_after_o:w \s__fp \__fp_chk:w #1#2
+  {
+    \exp_after:wN \__fp_exp_after_o:w
+    \exp_after:wN \s__fp
+    \exp_after:wN \__fp_chk:w
+    \exp_after:wN #1
+    \int_use:N \__int_eval:w \c_two - #2 \__int_eval_end:
+  }
+\cs_new:Npn \__fp_pow_neg_case:w \s__fp \__fp_chk:w #1#2#3;
+  {
+    \if_case:w #1 \exp_stop_f:
+           \c_minus_one
+    \or:   \__fp_pow_neg_case_aux:nnnnn #3
+    \else: \c_one
+    \fi:
+  }
+\cs_new:Npn \__fp_pow_neg_case_aux:nnnnn #1#2#3#4#5
+  {
+    \if_int_compare:w #1 > \c_eight
+      \if_int_compare:w #1 > \c_sixteen
+        \c_minus_one
       \else:
-        \exp_after:wN \fp_sub:NNNNNNNNN
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__fp_pow_neg_case_aux:NNNNNNNNw
+        \prg_replicate:nn { \c_sixteen - #1 } { 0 } #4#5 ;
       \fi:
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-      \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-    \fi:
-    \if_int_compare:w
-      \int_eval:w
-        \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int > \c_one
-      \exp_after:wN \fp_ln_Taylor:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_ln_mantissa_aux:
-  {
-    \if_int_compare:w \l_fp_input_a_integer_int > \c_one
-      \tex_advance:D \l_fp_count_int \c_one
-      \fp_ln_mantissa_divide_two:
-      \exp_after:wN \fp_ln_mantissa_aux:
-    \fi:
-  }
-\cs_new_protected_nopar:Npn \fp_ln_mantissa_divide_two:
-  {
-    \if_int_odd:w \l_fp_input_a_decimal_int
-      \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
-    \fi:
-    \if_int_odd:w \l_fp_input_a_integer_int
-      \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \fi:
-    \tex_divide:D \l_fp_input_a_integer_int  \c_two
-    \tex_divide:D \l_fp_input_a_decimal_int  \c_two
-    \tex_divide:D \l_fp_input_a_extended_int \c_two
-  }
-\cs_new_protected:Npn \fp_ln_const:nn #1#2
-  {
-    \exp_after:wN \exp_after:wN \exp_after:wN
-      \fp_exp_integer_const:nnnn
-      \cs:w c_fp_ln_ #1 _ #2 _tl \cs_end:
-  }
-\cs_new_protected_nopar:Npn \fp_ln_Taylor:
-  {
-    \group_begin:
-      \l_fp_input_a_integer_int \c_zero
-      \l_fp_input_a_exponent_int \c_zero
-      \l_fp_input_b_integer_int \c_two
-      \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
-      \l_fp_input_b_exponent_int \c_zero
-      \fp_div_internal:
-      \fp_ln_fixed:
-      \l_fp_input_a_integer_int  \l_fp_output_integer_int
-      \l_fp_input_a_decimal_int  \l_fp_output_decimal_int
-      \l_fp_input_a_extended_int \c_zero
-      \l_fp_input_a_exponent_int \l_fp_output_exponent_int
-      \l_fp_output_decimal_int \c_zero %^^A Bug?
-      \l_fp_output_decimal_int  \l_fp_input_a_decimal_int
-      \l_fp_output_extended_int \l_fp_input_a_extended_int
-      \fp_mul:NNNNNN
-        \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-        \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-        \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-      \l_fp_count_int \c_one
-      \fp_ln_Taylor_aux:
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          \l_fp_exp_integer_int \c_zero
-          \exp_not:N \l_fp_exp_decimal_int
-            \int_use:N \l_fp_output_decimal_int \scan_stop:
-          \exp_not:N \l_fp_exp_extended_int
-            \int_use:N \l_fp_output_extended_int \scan_stop:
-          \exp_not:N \l_fp_exp_exponent_int
-            \int_use:N \l_fp_output_exponent_int \scan_stop:
-        }
-    \fp_tmp:w
-    \tex_advance:D \l_fp_exp_decimal_int \l_fp_exp_decimal_int
-    \if_int_compare:w \l_fp_exp_extended_int < \c_five_hundred_million
     \else:
-      \tex_advance:D \l_fp_exp_extended_int -\c_five_hundred_million
-      \tex_advance:D \l_fp_exp_decimal_int \c_one
+      \if_int_compare:w #1 > \c_zero
+        \if_int_compare:w #4#5 = \c_zero
+          \exp_after:wN \exp_after:wN
+          \exp_after:wN \__fp_pow_neg_case_aux:NNNNNNNNw
+          \prg_replicate:nn { \c_eight - #1 } { 0 } #2#3 ;
+        \else:
+          \c_one
+        \fi:
+      \else:
+        \c_one
+      \fi:
     \fi:
-    \tex_advance:D \l_fp_exp_extended_int \l_fp_exp_extended_int
-    \fp_ln_normalise:
-    \if_int_compare:w \l_fp_output_sign_int > \c_zero
-      \exp_after:wN \fp_add:NNNNNNNNN
+  }
+\cs_new:Npn \__fp_pow_neg_case_aux:NNNNNNNNw #1#2#3#4#5#6#7#8#9;
+  {
+    \if_int_compare:w 0 #9 = \c_zero
+      \if_int_odd:w #8 \exp_stop_f:
+        \c_zero
+      \else:
+        \c_minus_one
+      \fi:
     \else:
-      \exp_after:wN \fp_sub:NNNNNNNNN
+      \c_one
     \fi:
-    \l_fp_output_integer_int \l_fp_output_decimal_int
-      \l_fp_output_extended_int
-    \c_zero \l_fp_exp_decimal_int \l_fp_exp_extended_int
-    \l_fp_output_integer_int \l_fp_output_decimal_int
-      \l_fp_output_extended_int
   }
-\cs_new_protected_nopar:Npn \fp_ln_fixed:
+%% File: l3fp-trig.dtx Copyright (C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\cs_new_nopar:Npx \__fp_one_over:w
   {
-    \if_int_compare:w \l_fp_output_exponent_int < \c_zero
-      \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
-      \exp_after:wN \use_i:nn \exp_after:wN
-        \fp_ln_fixed_aux:NNNNNNNNN
-        \int_use:N \l_fp_output_decimal_int
-       \exp_after:wN \fp_ln_fixed:
-     \fi:
+    \exp_not:N \exp_after:wN
+    \exp_not:c { __fp_/_o:ww }
+    \exp_not:N \c_one_fp
   }
-\cs_new_protected:Npn \fp_ln_fixed_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+\cs_new:Npn \__fp_sin:w \s__fp \__fp_chk:w #1#2
   {
-    \if_int_compare:w \l_fp_output_integer_int = \c_zero
-      \l_fp_output_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
-    \else:
-      \tl_set:Nx \l_fp_internal_tl
+    \if_case:w #1 \exp_stop_f:
+           \__fp_case_return_same_o:w
+    \or:
+      \exp_after:wN \__fp_trig_exponent:NNNNwn
+      \exp_after:wN \__fp_sin_series:NNwww
+      \exp_after:wN ?
+      \exp_after:wN #2
+      \exp_after:wN \c_zero
+    \or:
+      \__fp_case_use:nw
+        { \__fp_invalid_operation:Nnw \c_nan_fp { sin } }
+    \else: \__fp_case_return_same_o:w
+    \fi:
+    \s__fp \__fp_chk:w #1#2
+  }
+\cs_new:Npn \__fp_cos:w \s__fp \__fp_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+           \__fp_case_return_o:Nw \c_one_fp
+    \or:
+      \__fp_case_use:nw %^^A todo: is that faster than the exp_after route?
         {
-          \int_use:N \l_fp_output_integer_int
-          #1#2#3#4#5#6#7#8
+          \__fp_trig_exponent:NNNNwn
+          \__fp_sin_series:NNwww
+          ?
+          0
+          \c_two
         }
-      \l_fp_output_integer_int \c_zero
-      \l_fp_output_decimal_int \l_fp_internal_tl \scan_stop:
+    \or:
+      \__fp_case_use:nw
+        { \__fp_invalid_operation:Nnw \c_nan_fp { cos } }
+    \else: \__fp_case_return_same_o:w
     \fi:
-    \tex_advance:D \l_fp_output_exponent_int \c_one
+    \s__fp \__fp_chk:w #1#2
   }
-\cs_new_protected_nopar:Npn \fp_ln_Taylor_aux:
+\cs_new:Npn \__fp_tan:w \s__fp \__fp_chk:w #1#2
   {
-    \tex_advance:D \l_fp_count_int \c_two
-    \fp_mul:NNNNNN
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-    \if_int_compare:w
-      \int_eval:w
-        \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
-        > \c_zero
-      \fp_div_integer:NNNNN
-        \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-        \l_fp_count_int
-        \l_fp_exp_decimal_int \l_fp_exp_extended_int
-        \tex_advance:D \l_fp_output_decimal_int \l_fp_exp_decimal_int
-        \tex_advance:D \l_fp_output_extended_int \l_fp_exp_extended_int
-        \if_int_compare:w \l_fp_output_extended_int < \c_one_thousand_million
-        \else:
-          \tex_advance:D \l_fp_output_decimal_int \c_one
-          \tex_advance:D \l_fp_output_extended_int
-            -\c_one_thousand_million
-        \fi:
-        \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
-        \else:
-          \tex_advance:D \l_fp_output_integer_int \c_one
-          \tex_advance:D \l_fp_output_decimal_int
-            -\c_one_thousand_million
-        \fi:
-      \exp_after:wN \fp_ln_Taylor_aux:
+    \if_case:w #1 \exp_stop_f:
+           \__fp_case_return_same_o:w
+    \or:
+      \exp_after:wN \__fp_trig_exponent:NNNNwn
+      \exp_after:wN \__fp_tan_series:NNwww
+      \exp_after:wN 0
+      \exp_after:wN #2
+      \exp_after:wN \c_one
+    \or:
+      \__fp_case_use:nw
+        { \__fp_invalid_operation:Nnw \c_nan_fp { tan } }
+    \else: \__fp_case_return_same_o:w
     \fi:
+    \s__fp \__fp_chk:w #1#2
   }
-\cs_new_protected_nopar:Npn \fp_pow:Nn  { \fp_pow_aux:NNn \tl_set:Nn }
-\cs_new_protected_nopar:Npn \fp_gpow:Nn { \fp_pow_aux:NNn \tl_gset:Nn }
-\cs_generate_variant:Nn \fp_pow:Nn  { c }
-\cs_generate_variant:Nn \fp_gpow:Nn { c }
-\cs_new_protected:Npn \fp_pow_aux:NNn #1#2#3
-  {
-    \group_begin:
-      \fp_read:N #2
-      \l_fp_input_b_sign_int     \l_fp_input_a_sign_int
-      \l_fp_input_b_integer_int  \l_fp_input_a_integer_int
-      \l_fp_input_b_decimal_int  \l_fp_input_a_decimal_int
-      \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int
-      \fp_split:Nn a {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \if_int_compare:w
-        \int_eval:w
-          \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
-          = \c_zero
-         \if_int_compare:w
-           \int_eval:w
-             \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-             = \c_zero
-             \cs_set_protected:Npx \fp_tmp:w ##1##2
-               {
-                 \group_end:
-                 ##1 ##2 { \c_undefined_fp }
-               }
-           \else:
-             \cs_set_protected:Npx \fp_tmp:w ##1##2
-               {
-                 \group_end:
-                 ##1 ##2 { \c_zero_fp }
-               }
-          \fi:
-       \else:
-         \if_int_compare:w
-           \int_eval:w
-             \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-             = \c_zero
-             \cs_set_protected:Npx \fp_tmp:w ##1##2
-               {
-                 \group_end:
-                 ##1 ##2 { \c_one_fp }
-               }
-           \else:
-             \exp_after:wN \exp_after:wN \exp_after:wN
-               \fp_pow_aux_i:
-          \fi:
-       \fi:
-    \fp_tmp:w #1 #2
-}
-\cs_new_protected_nopar:Npn \fp_pow_aux_i:
-  {
-    \if_int_compare:w \l_fp_input_b_sign_int > \c_zero
-      \tl_set:Nn \l_fp_sign_tl { + }
-      \exp_after:wN \fp_pow_aux_ii:
-    \else:
-      \l_fp_input_a_extended_int \c_zero
-      \if_int_compare:w \l_fp_input_a_exponent_int < \c_ten
-        \group_begin:
-        \fp_extended_normalise:
-        \if_int_compare:w
-          \int_eval:w
-            \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
-            = \c_zero
-           \group_end:
-          \tl_set:Nn \l_fp_sign_tl { - }
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \fp_pow_aux_ii:
+\cs_new:Npn \__fp_cot:w \s__fp \__fp_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+           \exp_after:wN \__fp_one_over:w
+    \or:
+      \exp_after:wN \__fp_trig_exponent:NNNNwn
+      \exp_after:wN \__fp_tan_series:NNwww
+      \exp_after:wN 2
+      \exp_after:wN #2
+      \exp_after:wN \c_three
+    \or:
+      \__fp_case_use:nw
+        { \__fp_invalid_operation:Nnw \c_nan_fp { cot } }
+    \else: \__fp_case_return_same_o:w
+    \fi:
+    \s__fp \__fp_chk:w #1#2
+  }
+\cs_new:Npn \__fp_trig_exponent:NNNNwn #1#2#3#4 \s__fp \__fp_chk:w 1#5#6
+  {
+    \if_int_compare:w #6 > - \c_eight
+      \exp_after:wN #1
+      \exp_after:wN #2
+      \exp_after:wN #3
+      \int_use:N \__int_eval:w #4
+        \if_int_compare:w #6 > \c_zero
+          \exp_after:wN \__fp_trig_large:w \__int_value:w
         \else:
-          \group_end:
-          \cs_set_protected:Npx \fp_tmp:w ##1##2
-            {
-              \group_end:
-              ##1 ##2 { \c_undefined_fp }
-           }
+          \exp_after:wN \__fp_trig_small:w \__int_value:w
         \fi:
-      \else:
-        \cs_set_protected:Npx \fp_tmp:w ##1##2
-          {
-            \group_end:
-            ##1 ##2 { \c_undefined_fp }
-         }
+    \else:
+      \if_case:w #4
+             \__fp_sin_epsilon:w
+      \or:   \__fp_sin_epsilon:w
+      \or:   \__fp_cos_epsilon:w
+      \else: \__fp_cot_epsilon:w
       \fi:
+      #5
     \fi:
+    #6 ;
   }
-\cs_new_protected_nopar:Npn \fp_pow_aux_ii:
+\cs_new:Npn \__fp_sin_epsilon:w #1 \fi: #2 \fi: #3 ;
+  { \fi: \fi: \__fp_exp_after_o:w \s__fp \__fp_chk:w 1 #2 {#3} }
+\cs_new:Npn \__fp_cos_epsilon:w #1 \fi: #2 \fi: #3 ; #4 ;
+  { \fi: \fi: \exp_after:wN \c_one_fp }
+\cs_new:Npn \__fp_cot_epsilon:w \fi: #1 \fi: #2 ;
+  { \fi: \fi: \__fp_one_over:w \s__fp \__fp_chk:w 1 #1 {#2} }
+\cs_new:Npn \__fp_trig_small:w #1;
   {
-    \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-      \exp_after:wN \fp_pow_aux_iv:
-    \else:
-      \if_int_compare:w \l_fp_input_a_exponent_int < \c_ten
-        \group_begin:
-        \l_fp_input_a_extended_int \c_zero
-        \fp_extended_normalise:
-        \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
-          \if_int_compare:w \l_fp_input_a_integer_int > \c_ten
-            \group_end:
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-              \fp_pow_aux_iv:
-          \else:
-            \group_end:
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-              \exp_after:wN \fp_pow_aux_iii:
-          \fi:
+    \exp_after:wN \exp_after:wN \exp_after:wN \__fp_trig_small_aux:wwNN
+    \prg_replicate:nn { - #1 } { 0 } ;
+  }
+\cs_new:Npn \__fp_trig_small_aux:wwNN #1; #2#3#4#5;
+  {
+    \__fp_pack_twice_four:wNNNNNNNN
+    \__fp_pack_twice_four:wNNNNNNNN
+    \__fp_pack_twice_four:wNNNNNNNN
+    .
+    ;
+    #1#2#3#4#5 0000 0000;
+  }
+\cs_new:Npn \__fp_trig_large:w #1; #2#3;
+  { \__fp_trig_large_i:www #2; #3 ;  #1; }
+\cs_new:Npn \__fp_trig_large_i:www #1; #2; #3;
+  {
+    \if_meaning:w 0 #3 \__fp_trig_large_break:w \fi:
+    \exp_after:wN \__fp_trig_large_ii:wnnnnnn
+    \int_use:N \__int_eval:w ( #1 - 3141 ) / 6283 ;
+    {#1} #2;
+    \int_use:N \__int_eval:w \c_minus_one + #3;
+  }
+\cs_new:Npn \__fp_trig_large_ii:wnnnnnn #1; #2#3#4#5;
+  {
+    \exp_after:wN \__fp_trig_large_i:www
+    \int_use:N \__int_eval:w -5 0000 + #20 - #1*62831
+      \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
+      \int_use:N \__int_eval:w 4 9995 0000 + #30 - #1*8530
+        \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
+        \int_use:N \__int_eval:w 4 9995 0000 + #40 - #1*7179
+          \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
+          \int_use:N \__int_eval:w 5 0000 0000 + #50 - #1*5880
+    \exp_after:wN ;
+    \exp_after:wN ;
+  }
+\cs_new:Npn \__fp_trig_large_break:w \fi: #1; #2;
+  { \fi: \__fp_trig_octant_loop:nw #2 {0000} {0000} ; }
+\cs_new:Npn \__fp_trig_octant_loop:nw #1#2;
+  {
+    \if_int_compare:w #1 < 15707 \exp_stop_f:
+      \__fp_trig_octant_break:w
+    \fi:
+    + \c_two
+    \__fp_fixed_sub_back:wwN
+      {15707} {9632} {6794} {8970} {0000} {0000} ;
+      {#1} #2;
+    \__fp_trig_octant_loop:nw
+  }
+\cs_new:Npn \__fp_trig_octant_break:w #1 \fi: + #2#3 #4; #5#6; #7;
+  {
+    \fi:
+    \if_int_compare:w #5 < 7854 \exp_stop_f:
+      \if_int_compare:w #5 < \c_zero
+        \exp_after:wN \__fp_trig_octant_neg:w
+      \fi:
+      \exp_after:wN \__fp_use_i_until_s:nw
+      \exp_after:wN .
+    \fi:
+    + \c_one
+    \__fp_fixed_sub:wwN
+    {15707} {9632} {6794} {8970} {0000} {0000} ;
+    {#5} #6 ; . ;
+  }
+\cs_new:Npn \__fp_trig_octant_neg:w #1\fi: #2; #3#4#5#6#7#8; #9
+  {
+    \fi:
+    + \c_seven
+    \exp_after:wN \__fp_fixed_add_after:NNNNNwN
+    \int_use:N \__int_eval:w 1 9999 9998 - #30000 - #4
+      \exp_after:wN \__fp_fixed_add_pack:NNNNNwN
+      \int_use:N \__int_eval:w 1 9999 9998 - #5#6
+        \exp_after:wN \__fp_fixed_add_pack:NNNNNwN
+        \int_use:N \__int_eval:w 2 0000 0000 - #7#8 ; {#9} ;
+  }
+\cs_new:Npn \__fp_sin_series:NNwww #1#2#3 . #4; #5;
+  {
+    \__fp_fixed_mul:wwn #4; #4;
+    {
+      \exp_after:wN \__fp_sin_series_aux:Nnww
+      \__int_value:w
+        \if_int_odd:w \__int_eval:w ( #3 + \c_two ) / \c_four \__int_eval_end:
+          #2
         \else:
-          \group_end:
-            \exp_after:wN \exp_after:wN \exp_after:wN
-            \exp_after:wN \exp_after:wN \exp_after:wN
-              \exp_after:wN \fp_pow_aux_iv:
+          \if_meaning:w #2 0 2 \else: 0 \fi:
         \fi:
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \fp_pow_aux_iv:
-      \fi:
+      {#3}
+    }
+    #4 ;
+  }
+\cs_new:Npn \__fp_sin_series_aux:Nnww #1#2 #3; #4;
+  {
+    \if_int_odd:w \__int_eval:w #2 / \c_two \__int_eval_end:
+      \exp_after:wN \use_i:nn
+    \else:
+      \exp_after:wN \use_ii:nn
     \fi:
-    \cs_set_protected:Npx \fp_tmp:w ##1##2
+    {
+      \__fp_fixed_continue:wn {0000}{0000}{0000}{0001}{5619}{2070}; % 1/18!
+      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0000}{0477}{9477}{3324};
+      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0011}{4707}{4559}{7730};
+      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{2087}{6756}{9878}{6810};
+      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0027}{5573}{1922}{3985}{8907};
+      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{2480}{1587}{3015}{8730}{1587};
+      \__fp_fixed_mul_sub_back:wwwn #3; {0013}{8888}{8888}{8888}{8888}{8889};
+      \__fp_fixed_mul_sub_back:wwwn #3; {0416}{6666}{6666}{6666}{6666}{6667};
+      \__fp_fixed_mul_sub_back:wwwn #3; {5000}{0000}{0000}{0000}{0000}{0000};
+      \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
+    }
+    {
+      \__fp_fixed_continue:wn {0000}{0000}{0000}{0028}{1145}{7254}; % 1/17!
+      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0000}{7647}{1637}{3182};
+      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0160}{5904}{3836}{8216};
+      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0002}{5052}{1083}{8544}{1719};
+      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0275}{5731}{9223}{9858}{9065};
+      \__fp_fixed_mul_sub_back:wwwn #3; {0001}{9841}{2698}{4126}{9841}{2698};
+      \__fp_fixed_mul_sub_back:wwwn #3; {0083}{3333}{3333}{3333}{3333}{3333};
+      \__fp_fixed_mul_sub_back:wwwn #3; {1666}{6666}{6666}{6666}{6666}{6667};
+      \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
+      \__fp_fixed_mul:wwn #4;
+    }
+    {
+      \exp_after:wN \__fp_sanitize:Nw
+      \exp_after:wN #1
+      \int_use:N \__int_eval:w \__fp_fixed_to_float:wN
+    }
+    #1
+  }
+\cs_new:Npn \__fp_tan_series:NNwww #1#2#3. #4; #5;
+  {
+    \__fp_fixed_mul:wwn #4; #4;
+    {
+      \exp_after:wN \__fp_tan_series_aux:Nnww
+      \__int_value:w
+        \if_int_odd:w \__int_eval:w #3 / \c_two \__int_eval_end:
+          \exp_after:wN \reverse_if:N
+        \fi:
+        \if_meaning:w #1#2 2 \else: 0 \fi:
+      {#3}
+    }
+    #4 ;
+  }
+\cs_new:Npn \__fp_tan_series_aux:Nnww #1 #2 #3; #4;
+  {
+    \__fp_fixed_continue:wn {0000}{0000}{1527}{3493}{0856}{7059};
+    \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0159}{6080}{0274}{5257}{6472};
+    \__fp_fixed_mul_sub_back:wwwn #3; {0002}{4571}{2320}{0157}{2558}{8481};
+    \__fp_fixed_mul_sub_back:wwwn #3; {0115}{5830}{7533}{5397}{3168}{2147};
+    \__fp_fixed_mul_sub_back:wwwn #3; {1929}{8245}{6140}{3508}{7719}{2982};
+    \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
+    \__fp_fixed_mul:wwn #4;
       {
-        \group_end:
-        ##1 ##2
+        \__fp_fixed_continue:wn {0000}{0007}{0258}{0681}{9408}{4706};
+        \__fp_fixed_mul_sub_back:wwwn #3; {0000}{2343}{7175}{1399}{6151}{7670};
+        \__fp_fixed_mul_sub_back:wwwn #3; {0019}{2638}{4588}{9232}{8861}{3691};
+        \__fp_fixed_mul_sub_back:wwwn #3; {0536}{6357}{0691}{4344}{6852}{4252};
+        \__fp_fixed_mul_sub_back:wwwn #3; {5263}{1578}{9473}{6842}{1052}{6315};
+        \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
           {
-            \l_fp_sign_tl
-            \int_use:N \l_fp_output_integer_int
-            .
-            \exp_after:wN \use_none:n
-              \int_value:w \int_eval:w
-                 \l_fp_output_decimal_int + \c_one_thousand_million
-            e
-            \int_use:N \l_fp_output_exponent_int
+            \exp_after:wN \__fp_sanitize:Nw
+            \exp_after:wN #1
+            \int_use:N \__int_eval:w
+              \reverse_if:N \if_int_odd:w
+                  \__int_eval:w (#2 - \c_one) / \c_two \__int_eval_end:
+                \exp_after:wN \__fp_reverse_args:Nww
+              \fi:
+              \__fp_fixed_div_to_float:ww
           }
       }
   }
-\cs_new_protected_nopar:Npn \fp_pow_aux_iii:
-  {
-    \l_fp_input_a_sign_int \c_one
-    \fp_pow_aux_iv:
-    \l_fp_input_a_integer_int  \c_one
-    \l_fp_input_a_decimal_int  \c_zero
-    \l_fp_input_a_exponent_int \c_zero
-    \l_fp_input_b_integer_int  \l_fp_output_integer_int
-    \l_fp_input_b_decimal_int  \l_fp_output_decimal_int
-    \l_fp_input_b_exponent_int \l_fp_output_exponent_int
-    \fp_div_internal:
-  }
-\cs_new_protected_nopar:Npn \fp_pow_aux_iv:
-  {
-    \group_begin:
-      \l_fp_input_a_integer_int  \l_fp_input_b_integer_int
-      \l_fp_input_a_decimal_int  \l_fp_input_b_decimal_int
-      \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int
-      \fp_ln_internal:
-      \cs_set_protected_nopar:Npx \fp_tmp:w
+%% File: l3fp-convert.dtx Copyright(C) 2011-2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\cs_new:Npn \__fp_trim_zeros:w #1 ;
+  {
+    \__fp_trim_zeros_loop:w #1
+      ; \__fp_trim_zeros_loop:w 0; \__fp_trim_zeros_dot:w .; \s__stop
+  }
+\cs_new:Npn \__fp_trim_zeros_loop:w #1 0; #2 { #2 #1 ; #2 }
+\cs_new:Npn \__fp_trim_zeros_dot:w #1 .; { \__fp_trim_zeros_end:w #1 ; }
+\cs_new:Npn \__fp_trim_zeros_end:w #1 ; #2 \s__stop { #1 }
+\tl_const:Nx \c__fp_scientific_inf_tl
+  { 1e \int_use:N \c__fp_max_exponent_int }
+\cs_new:Npn \fp_to_scientific:N #1 { \exp_after:wN \__fp_to_scientific:w #1 }
+\cs_generate_variant:Nn \fp_to_scientific:N { c }
+\cs_new:Npn \fp_to_scientific:n #1
+  {
+    \exp_after:wN \__fp_to_scientific:w
+    \tex_romannumeral:D -`0 \__fp_parse:n {#1}
+  }
+\cs_new:Npn \__fp_to_scientific:w \s__fp \__fp_chk:w #1#2#3 ;
+  {
+    \if_meaning:w 2 #2 \exp_after:wN - \tex_romannumeral:D -`0 \fi:
+    \if_case:w #1 \exp_stop_f:
+         \__fp_case_return:nw { \exp_after:wN 0 }
+    \or: \exp_after:wN \__fp_to_scientific_normal:wnnnnn
+    \or:
+      \__fp_case_use:nw
         {
-          \group_end:
-          \exp_not:N \l_fp_input_b_sign_int
-            \int_use:N \l_fp_output_sign_int \scan_stop:
-          \exp_not:N \l_fp_input_b_integer_int
-            \int_use:N \l_fp_output_integer_int \scan_stop:
-          \exp_not:N \l_fp_input_b_decimal_int
-            \int_use:N \l_fp_output_decimal_int \scan_stop:
-          \exp_not:N \l_fp_input_b_extended_int
-            \int_use:N \l_fp_output_extended_int \scan_stop:
-          \exp_not:N \l_fp_input_b_exponent_int
-            \int_use:N \l_fp_output_exponent_int \scan_stop:
+          \__fp_invalid_operation:Nnw
+            \c__fp_scientific_inf_tl { fp_to_scientific }
         }
-    \fp_tmp:w
-    \l_fp_input_a_extended_int  \c_zero
-    \fp_mul:NNNNNNNNN
-      \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-        \l_fp_input_a_extended_int
-      \l_fp_input_b_integer_int \l_fp_input_b_decimal_int
-        \l_fp_input_b_extended_int
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-    \l_fp_output_exponent_int
-      \int_eval:w
-        \l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int
-      \scan_stop:
-    \fp_extended_normalise_output:
-    \tex_multiply:D \l_fp_input_a_sign_int \l_fp_input_b_sign_int
-    \l_fp_input_a_integer_int  \l_fp_output_integer_int
-    \l_fp_input_a_decimal_int  \l_fp_output_decimal_int
-    \l_fp_input_a_extended_int \l_fp_output_extended_int
-    \l_fp_input_a_exponent_int \l_fp_output_exponent_int
-    \l_fp_output_integer_int  \c_zero
-    \l_fp_output_decimal_int  \c_zero
-    \l_fp_output_extended_int \c_zero
-    \l_fp_output_exponent_int \c_zero
-    \cs_set_eq:NN \fp_exp_const:Nx \use_none:nn
-    \fp_exp_internal:
+    \or:
+      \__fp_case_use:nw
+        { \__fp_invalid_operation:Nnw 0 { fp_to_scientific } }
+    \fi:
+    \s__fp \__fp_chk:w #1 #2 #3 ; \prg_do_nothing:
   }
-\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF }
+\cs_new:Npn \__fp_to_scientific_normal:wnnnnn
+    \s__fp \__fp_chk:w 1 #1 #2 #3#4#5#6 ; \prg_do_nothing:
   {
-    \if_meaning:w #1 \c_undefined_fp
-      \prg_return_true:
+    \if_int_compare:w #2 = \c_one
+      \exp_after:wN \__fp_to_scientific_normal:wNw
     \else:
-      \prg_return_false:
+      \exp_after:wN \__fp_to_scientific_normal:wNw
+      \exp_after:wN e
+      \int_use:N \__int_eval:w #2 - \c_one
     \fi:
+    ; #3 #4 #5 #6 ;
   }
-\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF }
+\cs_new:Npn \__fp_to_scientific_normal:wNw #1 ; #2#3;
+  { \__fp_trim_zeros:w #2.#3 ; #1 }
+\tl_const:Nn \c__fp_decimal_inf_tl
   {
-    \if_meaning:w #1 \c_zero_fp
-      \prg_return_true:
-    \else:
-      \prg_return_false:
+    \exp_after:wN \exp_after:wN \exp_after:wN 1
+    \prg_replicate:nn \c__fp_max_exponent_int 0
+  }
+\cs_new:Npn \fp_to_decimal:N #1 { \exp_after:wN \__fp_to_decimal:w #1 }
+\cs_generate_variant:Nn \fp_to_decimal:N { c }
+\cs_new_nopar:Npn \fp_to_decimal:n
+  {
+    \exp_after:wN \__fp_to_decimal:w
+    \tex_romannumeral:D -`0 \__fp_parse:n
+  }
+\cs_new:Npn \__fp_to_decimal:w \s__fp \__fp_chk:w #1#2#3 ;
+  {
+    \if_meaning:w 2 #2 \exp_after:wN - \tex_romannumeral:D -`0 \fi:
+    \if_case:w #1 \exp_stop_f:
+         \__fp_case_return:nw { \exp_after:wN 0 }
+    \or: \exp_after:wN \__fp_to_decimal_normal:wnnnnn
+    \or:
+      \__fp_case_use:nw
+        {
+          \__fp_invalid_operation:Nnw
+            \c__fp_decimal_inf_tl { fp_to_decimal }
+        }
+    \or:
+      \__fp_case_use:nw
+        { \__fp_invalid_operation:Nnw 0 { fp_to_decimal } }
     \fi:
+    \s__fp \__fp_chk:w #1 #2 #3 ; \prg_do_nothing:
   }
-\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3 { T , F , TF }
-  {
-    \group_begin:
-      \fp_split:Nn a {#1}
-      \fp_standardise:NNNN
-        \l_fp_input_a_sign_int
-        \l_fp_input_a_integer_int
-        \l_fp_input_a_decimal_int
-        \l_fp_input_a_exponent_int
-      \fp_split:Nn b {#3}
-      \fp_standardise:NNNN
-        \l_fp_input_b_sign_int
-        \l_fp_input_b_integer_int
-        \l_fp_input_b_decimal_int
-        \l_fp_input_b_exponent_int
-      \fp_compare_aux:N #2
-  }
-\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3 { T , F , TF }
-  {
-    \group_begin:
-      \fp_read:N #3
-      \l_fp_input_b_sign_int     \l_fp_input_a_sign_int
-      \l_fp_input_b_integer_int  \l_fp_input_a_integer_int
-      \l_fp_input_b_decimal_int  \l_fp_input_a_decimal_int
-      \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int
-      \fp_read:N #1
-      \fp_compare_aux:N #2
-  }
-\cs_new_protected:Npn \fp_compare_aux:N #1
-  {
-    \cs_if_exist:cTF { fp_compare_#1: }
-      { \use:c { fp_compare_#1: } }
+\cs_new:Npn \__fp_to_decimal_normal:wnnnnn
+    \s__fp \__fp_chk:w 1 #1 #2 #3#4#5#6 ; \prg_do_nothing:
+  {
+    \int_compare:nNnTF {#2} > \c_zero
       {
-        \group_end:
-        \prg_return_false:
+        \int_compare:nNnTF {#2} < \c_sixteen
+          {
+            \__fp_decimate:nNnnnn { \c_sixteen - #2 }
+              \__fp_to_decimal_large:Nnnw
+          }
+          {
+            \exp_after:wN \exp_after:wN
+            \exp_after:wN \__fp_to_decimal_huge:wnnnn
+            \prg_replicate:nn { #2 - \c_sixteen } { 0 } ;
+          }
+        {#3} {#4} {#5} {#6}
+      }
+      {
+        \exp_after:wN \__fp_trim_zeros:w
+        \exp_after:wN 0
+        \exp_after:wN .
+        \tex_romannumeral:D -`0 \prg_replicate:nn { - #2 } { 0 }
+        #3#4#5#6 ;
       }
   }
-\cs_new_protected_nopar:cpn { fp_compare_=: }
+\cs_new:Npn \__fp_to_decimal_large:Nnnw #1#2#3#4;
   {
-    \if_int_compare:w \l_fp_input_a_sign_int = \l_fp_input_b_sign_int
-      \if_int_compare:w \l_fp_input_a_integer_int = \l_fp_input_b_integer_int
-        \if_int_compare:w \l_fp_input_a_decimal_int = \l_fp_input_b_decimal_int
-          \if_int_compare:w
-            \l_fp_input_a_exponent_int = \l_fp_input_b_exponent_int
-            \group_end:
-            \prg_return_true:
-          \else:
-            \group_end:
-            \prg_return_false:
-          \fi:
-        \else:
-          \group_end:
-          \prg_return_false:
-        \fi:
-      \else:
-        \group_end:
-        \prg_return_false:
+    \exp_after:wN \__fp_trim_zeros:w \__int_value:w
+      \if_int_compare:w #2 > \c_zero
+        #2
       \fi:
-    \else:
-      \group_end:
-      \prg_return_false:
-    \fi:
+      \exp_stop_f:
+      #3.#4 ;
   }
-\cs_new_protected_nopar:cpn { fp_compare_>: }
+\cs_new:Npn \__fp_to_decimal_huge:wnnnn #1; #2#3#4#5 { #2#3#4#5 #1 }
+\cs_new:Npn \fp_to_tl:N #1 { \exp_after:wN \__fp_to_tl:w #1 }
+\cs_generate_variant:Nn \fp_to_tl:N { c }
+\cs_new_nopar:Npn \fp_to_tl:n
   {
-    \if_int_compare:w \int_eval:w
-      \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-      = \c_zero
-      \if_int_compare:w \int_eval:w
-        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
-        = \c_zero
-        \group_end:
-        \prg_return_false:
-      \else:
-        \if_int_compare:w \l_fp_input_b_sign_int > \c_zero
-          \group_end:
-          \prg_return_false:
-        \else:
-          \group_end:
-          \prg_return_true:
-        \fi:
-      \fi:
-    \else:
-      \if_int_compare:w \int_eval:w
-        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
-        = \c_zero
-        \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-          \group_end:
-          \prg_return_true:
-        \else:
-          \group_end:
-          \prg_return_false:
-        \fi:
-      \else:
-        \use:c { fp_compare_>_aux: }
-      \fi:
-    \fi:
+    \exp_after:wN \__fp_to_tl:w
+    \tex_romannumeral:D -`0 \__fp_parse:n
   }
-\cs_new_protected_nopar:cpn { fp_compare_>_aux: }
+\cs_new:Npn \__fp_to_tl:w \s__fp \__fp_chk:w #1#2
   {
-    \if_int_compare:w \l_fp_input_a_sign_int > \l_fp_input_b_sign_int
-      \group_end:
-      \prg_return_true:
-    \else:
-      \if_int_compare:w \l_fp_input_a_sign_int < \l_fp_input_b_sign_int
-        \group_end:
-        \prg_return_false:
-      \else:
-        \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
-          \use:c { fp_compare_absolute_a>b: }
-        \else:
-          \use:c { fp_compare_absolute_a<b: }
-        \fi:
-      \fi:
+    \if_meaning:w 2 #2 \exp_after:wN - \tex_romannumeral:D -`0 \fi:
+    \if_case:w #1 \exp_stop_f:
+           \__fp_case_return:nw { 0 }
+    \or:   \exp_after:wN \__fp_to_tl_normal:nnnnn
+    \or:   \__fp_case_return:nw { inf }
+    \else: \__fp_case_return:nw { nan }
     \fi:
   }
-\cs_new_protected_nopar:cpn { fp_compare_absolute_a>b: }
+\cs_new:Npn \__fp_to_tl_normal:nnnnn #1#2 ;
   {
-    \if_int_compare:w \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
-      \group_end:
-      \prg_return_true:
+    \if_int_compare:w #1 > \c_sixteen
+      \exp_after:wN \__fp_to_scientific_normal:wnnnnn
     \else:
-      \if_int_compare:w \l_fp_input_a_exponent_int < \l_fp_input_b_exponent_int
-        \group_end:
-        \prg_return_false:
+      \if_int_compare:w #1 < - \c_two
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__fp_to_scientific_normal:wnnnnn
       \else:
-        \if_int_compare:w \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
-          \group_end:
-          \prg_return_true:
-        \else:
-          \if_int_compare:w
-            \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
-            \group_end:
-            \prg_return_false:
-          \else:
-            \if_int_compare:w
-              \l_fp_input_a_decimal_int > \l_fp_input_b_decimal_int
-              \group_end:
-              \prg_return_true:
-            \else:
-              \group_end:
-              \prg_return_false:
-            \fi:
-          \fi:
-        \fi:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__fp_to_decimal_normal:wnnnnn
       \fi:
     \fi:
+    \s__fp \__fp_chk:w 1 0 {#1} #2 ; \prg_do_nothing:
   }
-\cs_new_protected_nopar:cpn { fp_compare_absolute_a<b: }
+\cs_new:Npn \fp_to_dim:N #1 { \fp_to_decimal:N #1 pt }
+\cs_generate_variant:Nn \fp_to_dim:N { c }
+\cs_new:Npn \fp_to_dim:n #1 { \fp_to_decimal:n {#1} pt }
+\cs_new:Npn \fp_to_int:N #1 { \exp_after:wN \__fp_to_int:w #1 }
+\cs_generate_variant:Nn \fp_to_int:N { c }
+\cs_new_nopar:Npn \fp_to_int:n
   {
-    \if_int_compare:w \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int
-      \group_end:
-      \prg_return_true:
-    \else:
-      \if_int_compare:w \l_fp_input_b_exponent_int < \l_fp_input_a_exponent_int
-        \group_end:
-        \prg_return_false:
-      \else:
-        \if_int_compare:w \l_fp_input_b_integer_int > \l_fp_input_a_integer_int
-          \group_end:
-          \prg_return_true:
-        \else:
-          \if_int_compare:w
-            \l_fp_input_b_integer_int < \l_fp_input_a_integer_int
-            \group_end:
-            \prg_return_false:
-          \else:
-            \if_int_compare:w
-              \l_fp_input_b_decimal_int > \l_fp_input_a_decimal_int
-              \group_end:
-              \prg_return_true:
-            \else:
-              \group_end:
-              \prg_return_false:
-            \fi:
-          \fi:
-        \fi:
-      \fi:
-    \fi:
+    \exp_after:wN \__fp_to_int:w
+    \tex_romannumeral:D -`0 \__fp_parse:n
   }
-\cs_new_protected_nopar:cpn { fp_compare_<: }
+\cs_new:Npn \__fp_to_int:w #1;
   {
-    \tl_set:Nx \l_fp_internal_tl
-      {
-        \int_set:Nn \exp_not:N \l_fp_input_a_sign_int
-          { \int_use:N \l_fp_input_b_sign_int }
-        \int_set:Nn \exp_not:N \l_fp_input_a_integer_int
-          { \int_use:N \l_fp_input_b_integer_int }
-        \int_set:Nn \exp_not:N \l_fp_input_a_decimal_int
-          { \int_use:N \l_fp_input_b_decimal_int }
-        \int_set:Nn \exp_not:N \l_fp_input_a_exponent_int
-          { \int_use:N \l_fp_input_b_exponent_int }
-        \int_set:Nn \exp_not:N \l_fp_input_b_sign_int
-          { \int_use:N \l_fp_input_a_sign_int }
-        \int_set:Nn \exp_not:N \l_fp_input_b_integer_int
-          { \int_use:N \l_fp_input_a_integer_int }
-        \int_set:Nn \exp_not:N \l_fp_input_b_decimal_int
-          { \int_use:N \l_fp_input_a_decimal_int }
-        \int_set:Nn \exp_not:N \l_fp_input_b_exponent_int
-          { \int_use:N \l_fp_input_a_exponent_int }
-      }
-    \l_fp_internal_tl
-    \use:c { fp_compare_>: }
+    \exp_after:wN \__fp_to_decimal:w \tex_romannumeral:D -`0
+    \__fp_round:Nwn \__fp_round_to_nearest:NNN #1; { 0 } \prg_do_nothing:
   }
-\prg_new_protected_conditional:Npnn \fp_compare:n #1 { T , F , TF }
+\cs_new:Npn \dim_to_fp:n #1
   {
-    \group_begin:
-      \tl_set:Nx \l_fp_internal_tl
-        {
-          \group_end:
-          \fp_compare_aux_i:w #1 \exp_not:n { == \q_nil == \q_stop }
-        }
-     \l_fp_internal_tl
+    \exp_after:wN \__fp_from_dim_test:N
+    \__int_value:w \etex_glueexpr:D #1 ;
   }
-\cs_new_protected:Npn \fp_compare_aux_i:w #1 == #2 == #3 \q_stop
+\cs_new:Npn \__fp_from_dim_test:N #1
   {
-    \quark_if_nil:nTF {#2}
-      { \fp_compare_aux_ii:w #1 != \q_nil != \q_stop }
-      { \fp_compare:nNnTF {#1} = {#2} \prg_return_true: \prg_return_false: }
+    \if_meaning:w 0 #1
+      \exp_after:wN \__fp_use_i_until_s:nw
+      \exp_after:wN \c_zero_fp
+    \else:
+      \if_meaning:w - #1
+        \exp_after:wN \__fp_from_dim:Nw
+        \exp_after:wN 2
+        \__int_value:w
+      \else:
+        \exp_after:wN \__fp_from_dim:Nw
+        \exp_after:wN 0
+        \__int_value:w #1
+      \fi:
+    \fi:
+  }
+\cs_new:Npn \__fp_from_dim:Nw #1 #2;
+  {
+    \__fp_pack_twice_four:wNNNNNNNN \__fp_from_dim_ii:wNNnnnnnn ;
+    #2 000 0000 00 {10}987654321; #1
   }
-\cs_new_protected:Npn \fp_compare_aux_ii:w #1 != #2 != #3 \q_stop
+\cs_new:Npn \__fp_from_dim_ii:wNNnnnnnn #1; #2#3#4#5#6#7#8#9
+  { \__fp_from_dim_iii:wnnnnwN #1 {#2#300} {0000} ; }
+\cs_new:Npn \__fp_from_dim_iii:wnnnnwN #1; #2#3#4#5#6; #7
   {
-    \quark_if_nil:nTF {#2}
-      { \fp_compare_aux_iii:w #1 <= \q_nil <= \q_stop }
-      { \fp_compare:nNnTF {#1} = {#2} \prg_return_false: \prg_return_true: }
+    \__fp_mul_npos:Nnwnw #7 {#5} #1 ;
+    {-4} {1525} {8789} {0625} {0000} ;
   }
-\cs_new_protected:Npn \fp_compare_aux_iii:w #1 <= #2 <= #3 \q_stop
+\cs_new_eq:NN \fp_use:N \fp_to_decimal:N
+\cs_generate_variant:Nn \fp_use:N { c }
+\cs_new_eq:NN \fp_eval:n \fp_to_decimal:n
+\cs_new:Npn \fp_abs:n #1 { \fp_to_decimal:n { abs ( #1 ) } }
+%%
+%% File: l3fp-assign.dtx Copyright (C) 2011-2012 The LaTeX3 project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\cs_new_protected:Npn \fp_new:N #1
+  { \cs_new_eq:NN #1 \c_zero_fp }
+\cs_generate_variant:Nn \fp_new:N {c}
+\cs_new_protected:Npn \fp_set:Nn   #1#2
+  { \tl_set:Nx #1 { \__fp_parse:n {#2} } }
+\cs_new_protected:Npn \fp_gset:Nn  #1#2
+  { \tl_gset:Nx #1 { \__fp_parse:n {#2} } }
+\cs_new_protected:Npn \fp_const:Nn #1#2
+  { \tl_const:Nx #1 { \__fp_parse:n {#2} } }
+\cs_generate_variant:Nn \fp_set:Nn {c}
+\cs_generate_variant:Nn \fp_gset:Nn {c}
+\cs_generate_variant:Nn \fp_const:Nn {c}
+\cs_new_eq:NN \fp_set_eq:NN  \tl_set_eq:NN
+\cs_new_eq:NN \fp_gset_eq:NN \tl_gset_eq:NN
+\cs_generate_variant:Nn \fp_set_eq:NN  { c , Nc , cc }
+\cs_generate_variant:Nn \fp_gset_eq:NN { c , Nc , cc }
+\cs_new_protected:Npn \fp_zero:N #1 { \fp_set_eq:NN #1 \c_zero_fp }
+\cs_new_protected:Npn \fp_gzero:N #1 { \fp_gset_eq:NN #1 \c_zero_fp }
+\cs_generate_variant:Nn \fp_zero:N  { c }
+\cs_generate_variant:Nn \fp_gzero:N { c }
+\cs_new_protected:Npn \fp_zero_new:N #1
+  { \fp_if_exist:NTF #1 { \fp_zero:N #1 } { \fp_new:N #1 } }
+\cs_new_protected:Npn \fp_gzero_new:N #1
+  { \fp_if_exist:NTF #1 { \fp_gzero:N #1 } { \fp_new:N #1 } }
+\cs_generate_variant:Nn \fp_zero_new:N  { c }
+\cs_generate_variant:Nn \fp_gzero_new:N { c }
+\cs_new_protected_nopar:Npn \fp_add:Nn  { \__fp_add:NNNn \fp_set:Nn  + }
+\cs_new_protected_nopar:Npn \fp_gadd:Nn { \__fp_add:NNNn \fp_gset:Nn + }
+\cs_new_protected_nopar:Npn \fp_sub:Nn  { \__fp_add:NNNn \fp_set:Nn  - }
+\cs_new_protected_nopar:Npn \fp_gsub:Nn { \__fp_add:NNNn \fp_gset:Nn - }
+\cs_new_protected:Npn \__fp_add:NNNn #1#2#3#4 { #1 #3 { #3 #2 (#4) } }
+\cs_generate_variant:Nn \fp_add:Nn  { c }
+\cs_generate_variant:Nn \fp_gadd:Nn { c }
+\cs_generate_variant:Nn \fp_sub:Nn  { c }
+\cs_generate_variant:Nn \fp_gsub:Nn { c }
+\cs_new_protected:Npn \fp_show:N #1
+  { \__msg_show_variable:x { > \fp_to_tl:N #1 } }
+\cs_new_protected:Npn \fp_show:n #1
+  { \__msg_show_variable:x { > \fp_to_tl:n {#1} } }
+\cs_generate_variant:Nn \fp_show:N { c }
+\fp_const:Nn \c_e_fp          { 2.718 2818 2845 9045 }
+\fp_const:Nn \c_one_fp        { 1 }
+\fp_const:Nn \c_pi_fp         { 3.141 5926 5358 9794 }
+\fp_const:Nn \c_one_degree_fp { 0.0 1745 3292 5199 4330 }
+\fp_new:N \l_tmpa_fp
+\fp_new:N \l_tmpb_fp
+\fp_new:N \g_tmpa_fp
+\fp_new:N \g_tmpb_fp
+%% File: l3fp-old.dtx Copyright (C) 2012 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX3 Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+\fp_const:Nn \c_undefined_fp { nan }
+\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF }
+  { \exp_after:wN \__fp_if_undefined:w #1 }
+\cs_new:Npn \__fp_if_undefined:w \s__fp \__fp_chk:w #1#2;
   {
-    \quark_if_nil:nTF {#2}
-      { \fp_compare_aux_iv:w #1 >= \q_nil >= \q_stop }
-      { \fp_compare:nNnTF {#1} > {#2} \prg_return_false: \prg_return_true: }
+    \if_int_compare:w #1 > \c_one
+      \prg_return_true: \else: \prg_return_false: \fi:
   }
-\cs_new_protected:Npn \fp_compare_aux_iv:w #1 >= #2 >= #3 \q_stop
+\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF }
+  { \exp_after:wN \__fp_if_zero:w #1 }
+\cs_new:Npn \__fp_if_zero:w \s__fp \__fp_chk:w #1#2;
+  { \if_meaning:w #1 0 \prg_return_true: \else: \prg_return_false: \fi: }
+\cs_new_protected_nopar:Npn \fp_abs:N  { \__fp_abs:NNN \tl_set:Nx  \__fp_abs:w }
+\cs_new_protected_nopar:Npn \fp_gabs:N { \__fp_abs:NNN \tl_gset:Nx \__fp_abs:w }
+\cs_new_protected_nopar:Npn \fp_neg:N  { \__fp_abs:NNN \tl_set:Nx  \__fp_neg:w }
+\cs_new_protected_nopar:Npn \fp_gneg:N { \__fp_abs:NNN \tl_gset:Nx \__fp_neg:w }
+\cs_new_protected:Npn \__fp_abs:NNN #1#2#3
+  { #1 #3 { \exp_after:wN #2 #3 \prg_do_nothing: } }
+\cs_generate_variant:Nn \fp_abs:N  { c }
+\cs_generate_variant:Nn \fp_gabs:N { c }
+\cs_generate_variant:Nn \fp_neg:N  { c }
+\cs_generate_variant:Nn \fp_gneg:N { c }
+\cs_new_protected_nopar:Npn \fp_mul:Nn  { \__fp_mul:NNNn \fp_set:Nn  * }
+\cs_new_protected_nopar:Npn \fp_gmul:Nn { \__fp_mul:NNNn \fp_gset:Nn * }
+\cs_new_protected_nopar:Npn \fp_div:Nn  { \__fp_mul:NNNn \fp_set:Nn  / }
+\cs_new_protected_nopar:Npn \fp_gdiv:Nn { \__fp_mul:NNNn \fp_gset:Nn / }
+\cs_new_protected_nopar:Npn \fp_pow:Nn  { \__fp_mul:NNNn \fp_set:Nn  ^ }
+\cs_new_protected_nopar:Npn \fp_gpow:Nn { \__fp_mul:NNNn \fp_gset:Nn ^ }
+\cs_new_protected:Npn \__fp_mul:NNNn #1#2#3#4 { #1 #3 { #3 #2 (#4) } }
+\cs_generate_variant:Nn \fp_mul:Nn  { c }
+\cs_generate_variant:Nn \fp_gmul:Nn { c }
+\cs_generate_variant:Nn \fp_div:Nn  { c }
+\cs_generate_variant:Nn \fp_gdiv:Nn { c }
+\cs_generate_variant:Nn \fp_pow:Nn  { c }
+\cs_generate_variant:Nn \fp_gpow:Nn { c }
+\cs_set_protected:Npn \__fp_tmp:w #1#2#3#4#5
   {
-    \quark_if_nil:nTF {#2}
-      { \fp_compare_aux_v:w #1 = \q_nil  \q_stop }
-      { \fp_compare:nNnTF {#1} < {#2} \prg_return_false: \prg_return_true: }
+    \cs_new_protected_nopar:Npn #1 { #5 {#4} \tl_set_eq:NN  #3 }
+    \cs_new_protected_nopar:Npn #2 { #5 {#4} \tl_gset_eq:NN #3 }
+    \cs_generate_variant:Nn #1 { c }
+    \cs_generate_variant:Nn #2 { c }
   }
-\cs_new_protected:Npn \fp_compare_aux_v:w #1 = #2 = #3 \q_stop
+\__fp_tmp:w \fp_exp:Nn \fp_gexp:Nn \__fp_exp:w {exp} \__fp_assign_to:nNNNn
+\__fp_tmp:w \fp_ln:Nn  \fp_gln:Nn  \__fp_ln:w  {ln } \__fp_assign_to:nNNNn
+\__fp_tmp:w \fp_sin:Nn \fp_gsin:Nn \__fp_sin:w {sin} \__fp_assign_to:nNNNn
+\__fp_tmp:w \fp_cos:Nn \fp_gcos:Nn \__fp_cos:w {cos} \__fp_assign_to:nNNNn
+\__fp_tmp:w \fp_tan:Nn \fp_gtan:Nn \__fp_tan:w {tan} \__fp_assign_to:nNNNn
+\cs_new_protected:Npn \__fp_assign_to:nNNNn #1#2#3#4#5
   {
-    \quark_if_nil:nTF {#2}
-      { \fp_compare_aux_vi:w #1 < \q_nil < \q_stop }
-      { \fp_compare:nNnTF {#1} = {#2} \prg_return_true: \prg_return_false: }
+    \exp_after:wN \__fp_assign_to_i:wNNNn
+    \tex_romannumeral:D -`0 \__fp_parse:n {#5} {#1} #2#3#4
   }
-\cs_new_protected:Npn \fp_compare_aux_vi:w #1 < #2 < #3 \q_stop
+\cs_new_protected:Npn \__fp_assign_to_i:wNNNn \s__fp \__fp_chk:w #1#2#3; #4
   {
-    \quark_if_nil:nTF {#2}
-      { \fp_compare_aux_vii:w #1 > \q_nil > \q_stop }
-      { \fp_compare:nNnTF {#1} < {#2} \prg_return_true: \prg_return_false: }
+    \exp_args:Nc \__fp_assign_to_ii:NnNNN
+      { c__fp_ #4 ( #2 \if_meaning:w 1 #1 #3 \fi: ) _fp }
+      { #1#2#3 }
   }
-\cs_new_protected:Npn \fp_compare_aux_vii:w #1 > #2 > #3 \q_stop
+\cs_new_protected:Npn \__fp_assign_to_ii:NnNNN #1#2#3#4#5
   {
-    \quark_if_nil:nTF {#2}
-      { \prg_return_false: }
-      { \fp_compare:nNnTF {#1} > {#2} \prg_return_true: \prg_return_false: }
+    \cs_if_exist:NF #1
+      { \tl_const:Nx #1 { #4 \s__fp \__fp_chk:w #2; } }
+    #3 #5 #1
   }
-\msg_kernel_new:nnnn { fpu } { overflow }
-  { Number~too~big. }
+\cs_new_protected_nopar:Npn \fp_compare:NNNTF { \fp_compare:nNnTF }
+\cs_new_protected_nopar:Npn \fp_compare:NNNT  { \fp_compare:nNnT  }
+\cs_new_protected_nopar:Npn \fp_compare:NNNF  { \fp_compare:nNnF  }
+\cs_new_protected_nopar:Npn \fp_compare_p:NNN { \fp_compare_p:nNn }
+\cs_new_protected_nopar:Npn \fp_round_places:Nn
+  { \__fp_round_places:NNn \tl_set:Nx }
+\cs_new_protected_nopar:Npn \fp_ground_places:Nn
+  { \__fp_round_places:NNn \tl_gset:Nx }
+\cs_new_protected:Npn \__fp_round_places:NNn #1#2#3
   {
-    The~input~given~is~too~big~for~the~LaTeX~floating~point~unit. \\
-    Further~errors~may~well~occur!
+    #1 #2
+      {
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__fp_round:Nwn
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__fp_round_to_nearest:NNN
+        \exp_after:wN #2
+        \exp_after:wN { \int_use:N \__int_eval:w #3 }
+      }
   }
-\cs_new_protected_nopar:Npn \fp_overflow_msg:
-  { \msg_kernel_error:nn { fpu } { overflow } }
-\msg_kernel_new:nnnn { fpu } { exponent-overflow }
-  { Number~too~big~for~exponent~unit. }
+\cs_generate_variant:Nn \fp_round_places:Nn { c }
+\cs_generate_variant:Nn \fp_ground_places:Nn { c }
+\cs_new_protected:Npn \fp_round_figures:Nn #1#2
   {
-    The~exponent~of~the~input~given~is~too~big~for~the~floating~point~
-    unit:~the~maximum~input~value~for~an~exponent~is~230.
+    \__fp_round_places:NNn \tl_set:Nx #1
+      { #2 - \exp_after:wN \__fp_exponent:w #1 }
   }
-\cs_new_protected_nopar:Npn \fp_exp_overflow_msg:
-  { \msg_kernel_error:nn { fpu } { exponent-overflow } }
-\msg_kernel_new:nnnn { fpu } { logarithm-input-error }
-  { Invalid~input~to~ln~function. }
-  { Logarithms~can~only~be~calculated~for~positive~numbers. }
-\cs_new_protected_nopar:Npn \fp_ln_error_msg: {
-  \msg_kernel_error:nn { fpu } { logarithm-input-error }
-}
-\msg_kernel_new:nnnn { fpu } { trigonometric-overflow }
-  { Number~too~big~for~trigonometry~unit. }
+\cs_new_protected:Npn \fp_ground_figures:Nn #1#2
   {
-    The~trigonometry~code~can~only~work~with~numbers~smaller~
-    than~1000000000.
+    \__fp_round_places:NNn \tl_gset:Nx #1
+      { #2 - \exp_after:wN \__fp_exponent:w #1 }
   }
-\cs_new_protected_nopar:Npn \fp_trig_overflow_msg:
-  { \msg_kernel_error:nn { fpu } { trigonometric-overflow } }
+\cs_generate_variant:Nn \fp_round_figures:Nn { c }
+\cs_generate_variant:Nn \fp_ground_figures:Nn { c }
 %% 
 %%
 %% End of file `l3fp.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3int.sty b/Master/texmf-dist/tex/latex/l3kernel/l3int.sty
index 76b61a861c6..f33a864bff7 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3int.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3int.sty
@@ -46,57 +46,56 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3int.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental integers}
+\GetIdInfo$Id: l3int.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Integers}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
-\cs_new_eq:NN \int_value:w   \tex_number:D
-\cs_new_eq:NN \int_eval:w    \etex_numexpr:D
-\cs_new_eq:NN \int_eval_end: \tex_relax:D
-\cs_new_eq:NN \if_num:w      \tex_ifnum:D
-\cs_new_eq:NN \if_int_odd:w  \tex_ifodd:D
-\cs_new_eq:NN \if_case:w     \tex_ifcase:D
-\cs_new:Npn \int_eval:n #1 { \int_value:w \int_eval:w #1 \int_eval_end: }
+\__expl_package_check:
+\cs_new_eq:NN \__int_value:w      \tex_number:D
+\cs_new_eq:NN \__int_eval:w       \etex_numexpr:D
+\cs_new_eq:NN \__int_eval_end:    \tex_relax:D
+\cs_new_eq:NN \if_int_odd:w     \tex_ifodd:D
+\cs_new_eq:NN \if_case:w        \tex_ifcase:D
+\cs_new:Npn \int_eval:n #1 { \__int_value:w \__int_eval:w #1 \__int_eval_end: }
 \cs_new:Npn \int_abs:n #1
   {
-    \int_value:w
-      \if_int_compare:w \int_eval:w #1 < \c_zero
+    \__int_value:w
+      \if_int_compare:w \__int_eval:w #1 < \c_zero
         -
       \fi:
-    \int_eval:w #1 \int_eval_end:
+    \__int_eval:w #1 \__int_eval_end:
   }
 \cs_new:Npn \int_max:nn #1#2
   {
-    \int_value:w \int_eval:w
+    \__int_value:w \__int_eval:w
       \if_int_compare:w
-        \int_eval:w #1 > \int_eval:w #2 \int_eval_end:
+        \__int_eval:w #1 > \__int_eval:w #2 \__int_eval_end:
         #1
       \else:
         #2
       \fi:
-    \int_eval_end:
+    \__int_eval_end:
   }
 \cs_new:Npn \int_min:nn #1#2
   {
-    \int_value:w \int_eval:w
+    \__int_value:w \__int_eval:w
       \if_int_compare:w
-        \int_eval:w #1 < \int_eval:w #2 \int_eval_end:
+        \__int_eval:w #1 < \__int_eval:w #2 \__int_eval_end:
         #1
       \else:
         #2
       \fi:
-    \int_eval_end:
+    \__int_eval_end:
   }
 \cs_new:Npn \int_div_truncate:nn #1#2
   {
-    \int_use:N \int_eval:w
-      \exp_after:wN \int_div_truncate_aux:NwNw
-      \int_use:N \int_eval:w #1 \exp_after:wN ;
-      \int_use:N \int_eval:w #2 ;
-    \int_eval_end:
+    \int_use:N \__int_eval:w
+      \exp_after:wN \__int_div_truncate:NwNw
+      \int_use:N \__int_eval:w #1 \exp_after:wN ;
+      \int_use:N \__int_eval:w #2 ;
+    \__int_eval_end:
   }
-\cs_new:Npn \int_div_truncate_aux:NwNw #1#2; #3#4;
+\cs_new:Npn \__int_div_truncate:NwNw #1#2; #3#4;
   {
     \if_meaning:w 0 #1
       \c_zero
@@ -112,13 +111,13 @@
 \cs_new:Npn \int_div_round:nn #1#2 { \int_eval:n { ( #1 ) / ( #2 ) } }
 \cs_new:Npn \int_mod:nn #1#2
   {
-    \int_value:w \int_eval:w
+    \__int_value:w \__int_eval:w
       #1 - \int_div_truncate:nn {#1} {#2} * ( #2 )
-    \int_eval_end:
+    \__int_eval_end:
   }
 \cs_new_protected:Npn \int_new:N #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \newcount #1
   }
 \cs_generate_variant:Nn \int_new:N { c }
@@ -126,15 +125,15 @@
   {
     \int_compare:nNnTF {#2} > \c_minus_one
       {
-        \int_compare:nNnTF {#2} > \c_max_const_int
+        \int_compare:nNnTF {#2} > \c__max_constdef_int
           {
             \int_new:N #1
             \int_gset:Nn #1 {#2}
           }
           {
-            \chk_if_free_cs:N #1
-            \tex_global:D \int_constdef:Nw #1 =
-              \int_eval:w #2 \int_eval_end:
+            \__chk_if_free_cs:N #1
+            \tex_global:D \__int_constdef:Nw #1 =
+              \__int_eval:w #2 \__int_eval_end:
           }
       }
       {
@@ -145,12 +144,12 @@
 \cs_generate_variant:Nn \int_const:Nn { c }
 \pdftex_if_engine:TF
   {
-    \cs_new_eq:NN \int_constdef:Nw \tex_mathchardef:D
-    \tex_mathchardef:D \c_max_const_int 32 767 ~
+    \cs_new_eq:NN \__int_constdef:Nw \tex_mathchardef:D
+    \tex_mathchardef:D \c__max_constdef_int 32 767 ~
   }
   {
-    \cs_new_eq:NN \int_constdef:Nw \tex_chardef:D
-    \tex_chardef:D \c_max_const_int 1 114 111 ~
+    \cs_new_eq:NN \__int_constdef:Nw \tex_chardef:D
+    \tex_chardef:D \c__max_constdef_int 1 114 111 ~
   }
 \cs_new_protected:Npn \int_zero:N  #1 { #1 = \c_zero }
 \cs_new_protected:Npn \int_gzero:N #1 { \tex_global:D #1 = \c_zero }
@@ -177,9 +176,9 @@
 \cs_new_eq:NN \int_if_exist:cF  \cs_if_exist:cF
 \cs_new_eq:NN \int_if_exist_p:c \cs_if_exist_p:c
 \cs_new_protected:Npn \int_add:Nn #1#2
-  { \tex_advance:D #1 by \int_eval:w #2 \int_eval_end: }
+  { \tex_advance:D #1 by \__int_eval:w #2 \__int_eval_end: }
 \cs_new_protected:Npn \int_sub:Nn #1#2
-  { \tex_advance:D #1 by - \int_eval:w #2 \int_eval_end: }
+  { \tex_advance:D #1 by - \__int_eval:w #2 \__int_eval_end: }
 \cs_new_protected_nopar:Npn \int_gadd:Nn
   { \tex_global:D \int_add:Nn }
 \cs_new_protected_nopar:Npn \int_gsub:Nn
@@ -201,70 +200,84 @@
 \cs_generate_variant:Nn \int_gincr:N { c }
 \cs_generate_variant:Nn \int_gdecr:N { c }
 \cs_new_protected:Npn \int_set:Nn #1#2
-  { #1 ~ \int_eval:w #2\int_eval_end: }
+  { #1 ~ \__int_eval:w #2\__int_eval_end: }
 \cs_new_protected_nopar:Npn \int_gset:Nn { \tex_global:D \int_set:Nn }
 \cs_generate_variant:Nn \int_set:Nn  { c }
 \cs_generate_variant:Nn \int_gset:Nn { c }
 \cs_new_eq:NN \int_use:N \tex_the:D
 \cs_new:Npn \int_use:c #1 { \int_use:N \cs:w #1 \cs_end: }
-\cs_new_protected_nopar:Npn \kernel_compare_error:
+\cs_new_protected_nopar:Npn \__prg_compare_error:
   {
-    \if_num:w \c_zero \c_zero \fi:
+    \if_int_compare:w \c_zero \c_zero \fi:
     =
-    \kernel_compare_error:
+    \__prg_compare_error:
   }
-\cs_new:Npn \kernel_compare_error:Nw
+\cs_new:Npn \__prg_compare_error:Nw
     #1#2 \prg_return_true: \else: \prg_return_false: \fi:
   {
-    \msg_expandable_kernel_error:nnn
+    \__msg_kernel_expandable_error:nnn
       { kernel } { unknown-comparison } {#1}
     \prg_return_false:
   }
 \prg_new_conditional:Npnn \int_compare:n #1 { p , T , F , TF }
   {
-    \exp_after:wN \int_compare_aux:Nw \int_use:N \int_eval:w #1
-        \kernel_compare_error: \int_eval_end:
+    \exp_after:wN \__int_compare_aux:Nw \int_use:N \__int_eval:w #1
+        \__prg_compare_error: \__int_eval_end:
       \prg_return_true:
     \else:
       \prg_return_false:
     \fi:
   }
-\cs_new:Npn \int_compare_aux:Nw #1#2 \kernel_compare_error:
+\cs_new:Npn \__int_compare_aux:Nw #1#2 \__prg_compare_error:
   {
-    \exp_after:wN \int_compare_aux:NNw
-      \int_to_roman:w - 0 #2 ?? \q_mark
+    \exp_after:wN \__int_compare_aux:NNw
+      \__int_to_roman:w - 0 #2 ?? \q_mark
     #1#2
   }
-\cs_new:Npn \int_compare_aux:NNw #1#2#3 \q_mark
-  {
-    \use:c { int_compare_  #1  \if_meaning:w = #2 =  \fi: :NNw }
-      \kernel_compare_error:Nw #1
-  }
-\cs_new:cpn { int_compare_=:NNw } #1#2#3 =
-  { \if_int_compare:w #3 = \int_eval:w }
-\cs_new:cpn { int_compare_<:NNw } #1#2#3 <
-  { \if_int_compare:w #3 < \int_eval:w }
-\cs_new:cpn { int_compare_>:NNw } #1#2#3 >
-  { \if_int_compare:w #3 > \int_eval:w }
-\cs_new:cpn { int_compare_==:NNw } #1#2#3 ==
-  { \if_int_compare:w #3 = \int_eval:w }
-\cs_new:cpn { int_compare_!=:NNw } #1#2#3 !=
-  { \reverse_if:N \if_int_compare:w #3 = \int_eval:w }
-\cs_new:cpn { int_compare_<=:NNw } #1#2#3 <=
-  { \reverse_if:N \if_int_compare:w #3 > \int_eval:w }
-\cs_new:cpn { int_compare_>=:NNw } #1#2#3 >=
-  { \reverse_if:N \if_int_compare:w #3 < \int_eval:w }
-\prg_new_conditional:Npnn \int_compare:nNn #1#2#3 { p , T , F , TF}
-  {
-    \if_int_compare:w \int_eval:w #1 #2 \int_eval:w #3 \int_eval_end:
+\cs_new:Npn \__int_compare_aux:NNw #1#2#3 \q_mark
+  {
+    \use:c { __int_compare_  #1  \if_meaning:w = #2 =  \fi: :NNw }
+      \__prg_compare_error:Nw #1
+  }
+\cs_new:cpn { __int_compare_=:NNw } #1#2#3 =
+  { \if_int_compare:w #3 = \__int_eval:w }
+\cs_new:cpn { __int_compare_<:NNw } #1#2#3 <
+  { \if_int_compare:w #3 < \__int_eval:w }
+\cs_new:cpn { __int_compare_>:NNw } #1#2#3 >
+  { \if_int_compare:w #3 > \__int_eval:w }
+\cs_new:cpn { __int_compare_==:NNw } #1#2#3 ==
+  { \if_int_compare:w #3 = \__int_eval:w }
+\cs_new:cpn { __int_compare_!=:NNw } #1#2#3 !=
+  { \reverse_if:N \if_int_compare:w #3 = \__int_eval:w }
+\cs_new:cpn { __int_compare_<=:NNw } #1#2#3 <=
+  { \reverse_if:N \if_int_compare:w #3 > \__int_eval:w }
+\cs_new:cpn { __int_compare_>=:NNw } #1#2#3 >=
+  { \reverse_if:N \if_int_compare:w #3 < \__int_eval:w }
+\prg_new_conditional:Npnn \int_compare:nNn #1#2#3 { p , T , F , TF }
+  {
+    \if_int_compare:w \__int_eval:w #1 #2 \__int_eval:w #3 \__int_eval_end:
       \prg_return_true:
     \else:
       \prg_return_false:
     \fi:
   }
+\cs_new:Npn \int_case:nnn #1
+  {
+    \tex_romannumeral:D
+    \exp_args:Nf \__int_case:nnn { \int_eval:n {#1} }
+  }
+\cs_new:Npn \__int_case:nnn #1#2#3
+  { \__int_case:nw {#1} #2 {#1} {#3} \q_recursion_stop }
+\cs_new:Npn \__int_case:nw #1#2#3
+  {
+    \int_compare:nNnTF {#1} = {#2}
+      { \__int_case_end:nw {#3} }
+      { \__int_case:nw {#1} }
+  }
+\cs_new_eq:NN \__int_case_end:nw \__prg_case_end:nw
 \prg_new_conditional:Npnn \int_if_odd:n #1 { p , T , F , TF}
   {
-    \if_int_odd:w \int_eval:w #1 \int_eval_end:
+    \if_int_odd:w \__int_eval:w #1 \__int_eval_end:
       \prg_return_true:
     \else:
       \prg_return_false:
@@ -272,7 +285,7 @@
   }
 \prg_new_conditional:Npnn \int_if_even:n #1 { p , T , F , TF}
   {
-    \if_int_odd:w \int_eval:w #1 \int_eval_end:
+    \if_int_odd:w \__int_eval:w #1 \__int_eval_end:
       \prg_return_false:
     \else:
       \prg_return_true:
@@ -334,22 +347,70 @@
     \int_compare:nNnF {#1} #2 {#3}
       { \int_do_until:nNnn {#1} #2 {#3} {#4} }
   }
+\cs_new:Npn \int_step_function:nnnN #1#2#3#4
+  {
+    \int_compare:nNnTF {#2} > \c_zero
+      { \exp_args:NNf \__int_step:NnnnN > }
+      {
+        \int_compare:nNnTF {#2} = \c_zero
+          {
+            \__msg_kernel_expandable_error:nnn { kernel } { zero-step } {#4}
+            \use_none:nnnn
+          }
+          { \exp_args:NNf \__int_step:NnnnN < }
+      }
+      { \int_eval:n {#1} } {#2} {#3} #4
+  }
+\cs_new:Npn \__int_step:NnnnN #1#2#3#4#5
+  {
+    \int_compare:nNnF {#2} #1 {#4}
+      {
+        #5 {#2}
+        \exp_args:NNf \__int_step:NnnnN
+          #1 { \int_eval:n { #2 + #3 } } {#3} {#4} #5
+      }
+  }
+\cs_new_protected_nopar:Npn \int_step_inline:nnnn
+  {
+    \int_gincr:N \g__prg_map_int
+    \exp_args:NNc \__int_step:NNnnnn
+      \cs_gset_nopar:Npn
+      { __prg_map_ \int_use:N \g__prg_map_int :w }
+  }
+\cs_new_protected:Npn \int_step_variable:nnnNn #1#2#3#4#5
+  {
+    \int_gincr:N \g__prg_map_int
+    \exp_args:NNc \__int_step:NNnnnn
+      \cs_gset_nopar:Npx
+      { __prg_map_ \int_use:N \g__prg_map_int :w }
+      {#1}{#2}{#3}
+      {
+        \tl_set:Nn \exp_not:N #4 {##1}
+        \exp_not:n {#5}
+      }
+  }
+\cs_new_protected:Npn \__int_step:NNnnnn #1#2#3#4#5#6
+  {
+    #1 #2 ##1 {#6}
+    \int_step_function:nnnN {#3} {#4} {#5} #2
+    \__prg_break_point:Nn \scan_stop: { \int_gdecr:N \g__prg_map_int }
+  }
 \cs_new:Npn \int_to_arabic:n #1 { \int_eval:n {#1} }
 \cs_new:Npn \int_to_symbols:nnn #1#2#3
   {
     \int_compare:nNnTF {#1} > {#2}
       {
-        \exp_args:NNo \exp_args:No \int_to_symbols_aux:nnnn
+        \exp_args:NNo \exp_args:No \__int_to_symbols:nnnn
           {
-            \prg_case_int:nnn
+            \int_case:nnn
               { 1 + \int_mod:nn { #1 - 1 } {#2} }
               {#3} { }
           }
           {#1} {#2} {#3}
       }
-      { \prg_case_int:nnn {#1} {#3} { } }
+      { \int_case:nnn {#1} {#3} { } }
   }
-\cs_new:Npn \int_to_symbols_aux:nnnn #1#2#3#4
+\cs_new:Npn \__int_to_symbols:nnnn #1#2#3#4
   {
     \exp_args:Nf \int_to_symbols:nnn
       { \int_div_truncate:nn { #2 - 1 } {#3} } {#3} {#4}
@@ -420,37 +481,37 @@
       }
   }
 \cs_new:Npn \int_to_base:nn #1
-  { \exp_args:Nf \int_to_base_aux_i:nn { \int_eval:n {#1} } }
-\cs_new:Npn \int_to_base_aux_i:nn #1#2
+  { \exp_args:Nf \__int_to_base:nn { \int_eval:n {#1} } }
+\cs_new:Npn \__int_to_base:nn #1#2
   {
     \int_compare:nNnTF {#1} < \c_zero
-      { \exp_args:No \int_to_base_aux_ii:nnN { \use_none:n #1 } {#2} - }
-      { \int_to_base_aux_ii:nnN {#1} {#2} \c_empty_tl }
+      { \exp_args:No \__int_to_base:nnN { \use_none:n #1 } {#2} - }
+      { \__int_to_base:nnN {#1} {#2} \c_empty_tl }
   }
-\cs_new:Npn \int_to_base_aux_ii:nnN #1#2#3
+\cs_new:Npn \__int_to_base:nnN #1#2#3
   {
     \int_compare:nNnTF {#1} < {#2}
-      { \exp_last_unbraced:Nf #3 { \int_to_letter:n {#1} } }
+      { \exp_last_unbraced:Nf #3 { \__int_to_letter:n {#1} } }
       {
-        \exp_args:Nf \int_to_base_aux_iii:nnnN
-          { \int_to_letter:n { \int_mod:nn {#1} {#2} } }
+        \exp_args:Nf \__int_to_base:nnnN
+          { \__int_to_letter:n { \int_mod:nn {#1} {#2} } }
           {#1}
           {#2}
           #3
       }
   }
-\cs_new:Npn \int_to_base_aux_iii:nnnN #1#2#3#4
+\cs_new:Npn \__int_to_base:nnnN #1#2#3#4
   {
-    \exp_args:Nf \int_to_base_aux_ii:nnN
+    \exp_args:Nf \__int_to_base:nnN
       { \int_div_truncate:nn {#2} {#3} }
       {#3}
       #4
     #1
   }
-\cs_new:Npn \int_to_letter:n #1
+\cs_new:Npn \__int_to_letter:n #1
   {
     \exp_after:wN \exp_after:wN
-    \if_case:w \int_eval:w #1 - \c_ten \int_eval_end:
+    \if_case:w \__int_eval:w #1 - \c_ten \__int_eval_end:
          A
     \or: B
     \or: C
@@ -477,7 +538,7 @@
     \or: X
     \or: Y
     \or: Z
-    \else: \int_value:w \int_eval:w #1 \exp_after:wN \int_eval_end:
+    \else: \__int_value:w \__int_eval:w #1 \exp_after:wN \__int_eval_end:
     \fi:
   }
 \cs_new:Npn \int_to_binary:n #1
@@ -488,117 +549,117 @@
   { \int_to_base:nn {#1} { 8 } }
 \cs_new:Npn \int_to_roman:n #1
   {
-    \exp_after:wN \int_to_roman_aux:N
-      \int_to_roman:w \int_eval:n {#1} Q
+    \exp_after:wN \__int_to_roman:N
+      \__int_to_roman:w \int_eval:n {#1} Q
   }
-\cs_new:Npn \int_to_roman_aux:N #1
+\cs_new:Npn \__int_to_roman:N #1
   {
-    \use:c { int_to_roman_ #1 :w }
-    \int_to_roman_aux:N
+    \use:c { __int_to_roman_ #1 :w }
+    \__int_to_roman:N
   }
 \cs_new:Npn \int_to_Roman:n #1
   {
-    \exp_after:wN \int_to_Roman_aux:N
-      \int_to_roman:w \int_eval:n {#1} Q
-  }
-\cs_new:Npn \int_to_Roman_aux:N #1
-  {
-    \use:c { int_to_Roman_ #1 :w }
-    \int_to_Roman_aux:N
-  }
-\cs_new_nopar:Npn \int_to_roman_i:w { i }
-\cs_new_nopar:Npn \int_to_roman_v:w { v }
-\cs_new_nopar:Npn \int_to_roman_x:w { x }
-\cs_new_nopar:Npn \int_to_roman_l:w { l }
-\cs_new_nopar:Npn \int_to_roman_c:w { c }
-\cs_new_nopar:Npn \int_to_roman_d:w { d }
-\cs_new_nopar:Npn \int_to_roman_m:w { m }
-\cs_new_nopar:Npn \int_to_roman_Q:w #1 { }
-\cs_new_nopar:Npn \int_to_Roman_i:w { I }
-\cs_new_nopar:Npn \int_to_Roman_v:w { V }
-\cs_new_nopar:Npn \int_to_Roman_x:w { X }
-\cs_new_nopar:Npn \int_to_Roman_l:w { L }
-\cs_new_nopar:Npn \int_to_Roman_c:w { C }
-\cs_new_nopar:Npn \int_to_Roman_d:w { D }
-\cs_new_nopar:Npn \int_to_Roman_m:w { M }
-\cs_new:Npn \int_to_Roman_Q:w #1 { }
-\cs_new:Npn \int_get_sign:n #1
-  {
-    \int_get_sign_and_digits_aux:nNNN {#1}
+    \exp_after:wN \__int_to_Roman_aux:N
+      \__int_to_roman:w \int_eval:n {#1} Q
+  }
+\cs_new:Npn \__int_to_Roman_aux:N #1
+  {
+    \use:c { __int_to_Roman_ #1 :w }
+    \__int_to_Roman_aux:N
+  }
+\cs_new_nopar:Npn \__int_to_roman_i:w { i }
+\cs_new_nopar:Npn \__int_to_roman_v:w { v }
+\cs_new_nopar:Npn \__int_to_roman_x:w { x }
+\cs_new_nopar:Npn \__int_to_roman_l:w { l }
+\cs_new_nopar:Npn \__int_to_roman_c:w { c }
+\cs_new_nopar:Npn \__int_to_roman_d:w { d }
+\cs_new_nopar:Npn \__int_to_roman_m:w { m }
+\cs_new_nopar:Npn \__int_to_roman_Q:w #1 { }
+\cs_new_nopar:Npn \__int_to_Roman_i:w { I }
+\cs_new_nopar:Npn \__int_to_Roman_v:w { V }
+\cs_new_nopar:Npn \__int_to_Roman_x:w { X }
+\cs_new_nopar:Npn \__int_to_Roman_l:w { L }
+\cs_new_nopar:Npn \__int_to_Roman_c:w { C }
+\cs_new_nopar:Npn \__int_to_Roman_d:w { D }
+\cs_new_nopar:Npn \__int_to_Roman_m:w { M }
+\cs_new:Npn \__int_to_Roman_Q:w #1 { }
+\cs_new:Npn \__int_get_sign:n #1
+  {
+    \__int_get_sign_and_digits:nNNN {#1}
       \c_true_bool \c_true_bool \c_false_bool
   }
-\cs_new:Npn \int_get_digits:n #1
+\cs_new:Npn \__int_get_digits:n #1
   {
-    \int_get_sign_and_digits_aux:nNNN {#1}
+    \__int_get_sign_and_digits:nNNN {#1}
       \c_true_bool \c_false_bool \c_true_bool
   }
-\cs_new:Npn \int_get_sign_and_digits_aux:nNNN #1#2#3#4
+\cs_new:Npn \__int_get_sign_and_digits:nNNN #1#2#3#4
   {
     \exp_args:Nf \tl_if_head_eq_charcode:nNTF {#1} -
       {
         \bool_if:NTF #2
           {
-            \int_get_sign_and_digits_aux:oNNN
+            \__int_get_sign_and_digits:oNNN
               { \use_none:n #1 } \c_false_bool #3#4
           }
           {
-            \int_get_sign_and_digits_aux:oNNN
+            \__int_get_sign_and_digits:oNNN
               { \use_none:n #1 } \c_true_bool #3#4
           }
       }
       {
         \exp_args:Nf \tl_if_head_eq_charcode:nNTF {#1} +
-          { \int_get_sign_and_digits_aux:oNNN { \use_none:n #1 } #2#3#4 }
+          { \__int_get_sign_and_digits:oNNN { \use_none:n #1 } #2#3#4 }
           {
             \bool_if:NT #3 { \bool_if:NF #2 - }
             \bool_if:NT #4 {#1}
           }
       }
   }
-\cs_generate_variant:Nn \int_get_sign_and_digits_aux:nNNN { o }
+\cs_generate_variant:Nn \__int_get_sign_and_digits:nNNN { o }
 \cs_new:Npn \int_from_alph:n #1
   {
     \int_eval:n
       {
-        \int_get_sign:n {#1}
-        \exp_args:Nf \int_from_alph_aux:n { \int_get_digits:n {#1} }
+        \__int_get_sign:n {#1}
+        \exp_args:Nf \__int_from_alph:n { \__int_get_digits:n {#1} }
       }
   }
-\cs_new:Npn \int_from_alph_aux:n #1
-  { \int_from_alph_aux:nN { 0 } #1 \q_nil }
-\cs_new:Npn \int_from_alph_aux:nN #1#2
+\cs_new:Npn \__int_from_alph:n #1
+  { \__int_from_alph:nN { 0 } #1 \q_nil }
+\cs_new:Npn \__int_from_alph:nN #1#2
   {
     \quark_if_nil:NTF #2
       {#1}
       {
-        \exp_args:Nf \int_from_alph_aux:nN
-          { \int_eval:n { #1 * 26 + \int_from_alph_aux:N #2 } }
+        \exp_args:Nf \__int_from_alph:nN
+          { \int_eval:n { #1 * 26 + \__int_from_alph:N #2 } }
       }
   }
-\cs_new:Npn \int_from_alph_aux:N #1
+\cs_new:Npn \__int_from_alph:N #1
   { \int_eval:n { `#1 - \int_compare:nNnTF { `#1 } < { 91 } { 64 } { 96 } } }
 \cs_new:Npn \int_from_base:nn #1#2
   {
     \int_eval:n
       {
-        \int_get_sign:n {#1}
-        \exp_args:Nf \int_from_base_aux:nn
-          { \int_get_digits:n {#1} } {#2}
+        \__int_get_sign:n {#1}
+        \exp_args:Nf \__int_from_base:nn
+          { \__int_get_digits:n {#1} } {#2}
       }
   }
-\cs_new:Npn \int_from_base_aux:nn #1#2
-  { \int_from_base_aux:nnN { 0 } { #2 } #1 \q_nil }
-\cs_new:Npn \int_from_base_aux:nnN #1#2#3
+\cs_new:Npn \__int_from_base:nn #1#2
+  { \__int_from_base:nnN { 0 } { #2 } #1 \q_nil }
+\cs_new:Npn \__int_from_base:nnN #1#2#3
   {
     \quark_if_nil:NTF #3
       {#1}
       {
-        \exp_args:Nf \int_from_base_aux:nnN
-          { \int_eval:n { #1 * #2 + \int_from_base_aux:N #3 } }
+        \exp_args:Nf \__int_from_base:nnN
+          { \int_eval:n { #1 * #2 + \__int_from_base:N #3 } }
           {#2}
       }
   }
-\cs_new:Npn \int_from_base_aux:N #1
+\cs_new:Npn \__int_from_base:N #1
   {
     \int_compare:nNnTF { `#1 } < { 58 }
       {#1}
@@ -613,70 +674,70 @@
   { \int_from_base:nn {#1} \c_sixteen }
 \cs_new:Npn \int_from_octal:n #1
   { \int_from_base:nn {#1} \c_eight }
-\int_const:cn { c_int_from_roman_i_int } { 1 }
-\int_const:cn { c_int_from_roman_v_int } { 5 }
-\int_const:cn { c_int_from_roman_x_int } { 10 }
-\int_const:cn { c_int_from_roman_l_int } { 50 }
-\int_const:cn { c_int_from_roman_c_int } { 100 }
-\int_const:cn { c_int_from_roman_d_int } { 500 }
-\int_const:cn { c_int_from_roman_m_int } { 1000 }
-\int_const:cn { c_int_from_roman_I_int } { 1 }
-\int_const:cn { c_int_from_roman_V_int } { 5 }
-\int_const:cn { c_int_from_roman_X_int } { 10 }
-\int_const:cn { c_int_from_roman_L_int } { 50 }
-\int_const:cn { c_int_from_roman_C_int } { 100 }
-\int_const:cn { c_int_from_roman_D_int } { 500 }
-\int_const:cn { c_int_from_roman_M_int } { 1000 }
+\int_const:cn { c__int_from_roman_i_int } { 1 }
+\int_const:cn { c__int_from_roman_v_int } { 5 }
+\int_const:cn { c__int_from_roman_x_int } { 10 }
+\int_const:cn { c__int_from_roman_l_int } { 50 }
+\int_const:cn { c__int_from_roman_c_int } { 100 }
+\int_const:cn { c__int_from_roman_d_int } { 500 }
+\int_const:cn { c__int_from_roman_m_int } { 1000 }
+\int_const:cn { c__int_from_roman_I_int } { 1 }
+\int_const:cn { c__int_from_roman_V_int } { 5 }
+\int_const:cn { c__int_from_roman_X_int } { 10 }
+\int_const:cn { c__int_from_roman_L_int } { 50 }
+\int_const:cn { c__int_from_roman_C_int } { 100 }
+\int_const:cn { c__int_from_roman_D_int } { 500 }
+\int_const:cn { c__int_from_roman_M_int } { 1000 }
 \cs_new:Npn \int_from_roman:n #1
   {
     \tl_if_blank:nF {#1}
       {
-        \exp_after:wN \int_from_roman_end:w
-          \int_value:w \int_eval:w
-            \int_from_roman_aux:NN #1 Q \q_stop
+        \exp_after:wN \__int_from_roman_end:w
+          \__int_value:w \__int_eval:w
+            \__int_from_roman:NN #1 Q \q_stop
       }
   }
-\cs_new:Npn \int_from_roman_aux:NN #1#2
+\cs_new:Npn \__int_from_roman:NN #1#2
   {
     \str_if_eq:nnTF {#1} { Q }
       {#1#2}
       {
         \str_if_eq:nnTF {#2} { Q }
           {
-            \int_if_exist:cF { c_int_from_roman_ #1 _int }
-              { \int_from_roman_clean_up:w }
+            \int_if_exist:cF { c__int_from_roman_ #1 _int }
+              { \__int_from_roman_clean_up:w }
             +
-            \use:c { c_int_from_roman_ #1 _int }
+            \use:c { c__int_from_roman_ #1 _int }
             #2
           }
           {
-            \int_if_exist:cF { c_int_from_roman_ #1 _int }
-              { \int_from_roman_clean_up:w }
-            \int_if_exist:cF { c_int_from_roman_ #2 _int }
-              { \int_from_roman_clean_up:w }
+            \int_if_exist:cF { c__int_from_roman_ #1 _int }
+              { \__int_from_roman_clean_up:w }
+            \int_if_exist:cF { c__int_from_roman_ #2 _int }
+              { \__int_from_roman_clean_up:w }
             \int_compare:nNnTF
-              { \use:c { c_int_from_roman_ #1 _int } }
+              { \use:c { c__int_from_roman_ #1 _int } }
               <
-              { \use:c { c_int_from_roman_ #2 _int  } }
+              { \use:c { c__int_from_roman_ #2 _int  } }
               {
-                + \use:c { c_int_from_roman_ #2 _int }
-                - \use:c { c_int_from_roman_ #1 _int }
-                \int_from_roman_aux:NN
+                + \use:c { c__int_from_roman_ #2 _int }
+                - \use:c { c__int_from_roman_ #1 _int }
+                \__int_from_roman:NN
               }
               {
-                + \use:c { c_int_from_roman_ #1 _int }
-                \int_from_roman_aux:NN #2
+                + \use:c { c__int_from_roman_ #1 _int }
+                \__int_from_roman:NN #2
               }
           }
       }
   }
-\cs_new:Npn \int_from_roman_end:w #1 Q #2 \q_stop
+\cs_new:Npn \__int_from_roman_end:w #1 Q #2 \q_stop
   { \tl_if_empty:nTF {#2} {#1} {#2} }
-\cs_new:Npn \int_from_roman_clean_up:w #1 Q { + 0 Q -1 }
-\cs_new_eq:NN \int_show:N \kernel_register_show:N
-\cs_new_eq:NN \int_show:c \kernel_register_show:c
+\cs_new:Npn \__int_from_roman_clean_up:w #1 Q { + 0 Q -1 }
+\cs_new_eq:NN \int_show:N \__kernel_register_show:N
+\cs_new_eq:NN \int_show:c \__kernel_register_show:c
 \cs_new_protected:Npn \int_show:n #1
-  { \tex_showthe:D \int_eval:w #1 \int_eval_end: }
+  { \etex_showtokens:D \exp_after:wN { \int_use:N \__int_eval:w #1 } }
 \int_const:Nn \c_one      {  1 }
 \int_const:Nn \c_two      {  2 }
 \int_const:Nn \c_three    {  3 }
@@ -698,9 +759,13 @@
 \int_const:Nn \c_max_int { 2 147 483 647 }
 \int_new:N \l_tmpa_int
 \int_new:N \l_tmpb_int
-\int_new:N \l_tmpc_int
 \int_new:N \g_tmpa_int
 \int_new:N \g_tmpb_int
+\cs_new_eq:NN \if_num:w \if_int_compare:w
+\int_new:N \l_tmpc_int
+\cs_new_eq:NN \int_eval:w    \__int_eval:w
+\cs_new_eq:NN \int_eval_end: \__int_eval_end:
+\cs_new_eq:NN \int_value:w \__int_value:w
 %% 
 %%
 %% End of file `l3int.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3keys.sty b/Master/texmf-dist/tex/latex/l3kernel/l3keys.sty
index a0ae5751eb3..3d1a698da0b 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3keys.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3keys.sty
@@ -13,7 +13,7 @@
 %% 
 %% Do not distribute a modified version of this file.
 %% 
-%% File: l3keys.dtx Copyright (C) 2006-2011 The LaTeX3 Project
+%% File: l3keys.dtx Copyright (C) 2006-2012 The LaTeX3 Project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -46,16 +46,16 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3keys.dtx 3487 2012-03-03 19:36:51Z bruno $
+\GetIdInfo$Id: l3keys.dtx 3986 2012-07-15 19:23:51Z joseph $
   {L3 Experimental key-value interfaces}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
-\int_new:N \g_keyval_level_int
-\tl_new:N \l_keyval_key_tl
-\tl_new:N \l_keyval_value_tl
-\tl_new:N \l_keyval_sanitise_tl
-\tl_new:N \l_keyval_parse_tl
+\__expl_package_check:
+\int_new:N \g__keyval_level_int
+\tl_new:N \l__keyval_key_tl
+\tl_new:N \l__keyval_value_tl
+\tl_new:N \l__keyval_sanitise_tl
+\tl_new:N \l__keyval_parse_tl
 \group_begin:
   \char_set_catcode_active:n { `\= }
   \char_set_catcode_active:n { `\, }
@@ -64,585 +64,599 @@
 \tl_to_lowercase:n
   {
     \group_end:
-    \cs_new_protected:Npn \keyval_parse:n #1
+    \cs_new_protected:Npn \__keyval_parse:n #1
       {
         \group_begin:
-          \tl_clear:N \l_keyval_sanitise_tl
-          \tl_set:Nn \l_keyval_sanitise_tl {#1}
-          \tl_replace_all:Nnn \l_keyval_sanitise_tl { = } { 8 }
-          \tl_replace_all:Nnn \l_keyval_sanitise_tl { , } { 9 }
-          \tl_clear:N \l_keyval_parse_tl
-          \exp_after:wN \keyval_parse_elt:w \exp_after:wN
-            \q_no_value \l_keyval_sanitise_tl 9 \q_nil 9
+          \tl_clear:N \l__keyval_sanitise_tl
+          \tl_set:Nn \l__keyval_sanitise_tl {#1}
+          \tl_replace_all:Nnn \l__keyval_sanitise_tl { = } { 8 }
+          \tl_replace_all:Nnn \l__keyval_sanitise_tl { , } { 9 }
+          \tl_clear:N \l__keyval_parse_tl
+          \exp_after:wN \__keyval_parse_elt:w \exp_after:wN
+            \q_no_value \l__keyval_sanitise_tl 9 \q_nil 9
         \exp_after:wN \group_end:
-        \l_keyval_parse_tl
+        \l__keyval_parse_tl
       }
   }
-\cs_new_protected:Npn \keyval_parse_elt:w #1 ,
+\cs_new_protected:Npn \__keyval_parse_elt:w #1 ,
   {
     \tl_if_blank:oTF { \use_none:n #1 }
-      { \keyval_parse_elt:w \q_no_value }
+      { \__keyval_parse_elt:w \q_no_value }
       {
         \quark_if_nil:oF { \use_ii:nn #1 }
           {
-            \keyval_split_key_value:w #1 = = \q_stop
-            \keyval_parse_elt:w \q_no_value
+            \__keyval_split_key_value:w #1 = = \q_stop
+            \__keyval_parse_elt:w \q_no_value
           }
       }
   }
-\cs_new_protected:Npn \keyval_split_key_value:w #1 = #2 \q_stop
+\cs_new_protected:Npn \__keyval_split_key_value:w #1 = #2 \q_stop
   {
-    \keyval_split_key:w #1 \q_stop
+    \__keyval_split_key:w #1 \q_stop
     \str_if_eq:nnTF {#2} { = }
       {
-        \tl_put_right:Nx \l_keyval_parse_tl
+        \tl_put_right:Nx \l__keyval_parse_tl
           {
             \exp_not:c
-              { keyval_key_no_value_elt_ \int_use:N \g_keyval_level_int :n }
-              { \exp_not:o \l_keyval_key_tl }
+              { __keyval_key_no_value_elt_ \int_use:N \g__keyval_level_int :n }
+              { \exp_not:o \l__keyval_key_tl }
           }
       }
       {
-        \keyval_split_key_value_aux:wTF #2 \q_no_value \q_stop
-          { \keyval_split_value:w \q_nil #2 }
-          { \msg_kernel_error:nn { keyval } { misplaced-equals-sign } }
+        \__keyval_split_key_value:wTF #2 \q_no_value \q_stop
+          { \__keyval_split_value:w \q_nil #2 }
+          { \__msg_kernel_error:nn { kernel } { misplaced-equals-sign } }
       }
   }
-\cs_new:Npn \keyval_split_key_value_aux:wTF #1 = #2#3 \q_stop
+\cs_new:Npn \__keyval_split_key_value:wTF #1 = #2#3 \q_stop
   { \tl_if_head_eq_meaning:nNTF {#3} \q_no_value }
-\cs_new_protected:Npn \keyval_split_key:w #1 \q_stop
+\cs_new_protected:Npn \__keyval_split_key:w #1 \q_stop
   {
-    \tl_set:Nx \l_keyval_key_tl
+    \tl_set:Nx \l__keyval_key_tl
       { \exp_after:wN \tl_trim_spaces:n \exp_after:wN { \use_none:n #1 } }
   }
-\cs_new_protected:Npn \keyval_split_value:w #1 = =
+\cs_new_protected:Npn \__keyval_split_value:w #1 = =
   {
-    \tl_put_right:Nx \l_keyval_parse_tl
+    \tl_put_right:Nx \l__keyval_parse_tl
       {
         \exp_not:c
-          { keyval_key_value_elt_ \int_use:N \g_keyval_level_int :nn }
-          { \exp_not:o \l_keyval_key_tl }
+          { __keyval_key_value_elt_ \int_use:N \g__keyval_level_int :nn }
+          { \exp_not:o \l__keyval_key_tl }
       }
-    \tl_set:Nx \l_keyval_value_tl
+    \tl_set:Nx \l__keyval_value_tl
       { \exp_not:o { \use_none:nnn #1 \q_nil \q_nil } }
-    \tl_if_empty:NTF \l_keyval_value_tl
-      { \tl_put_right:Nn \l_keyval_parse_tl { { } } }
+    \tl_if_empty:NTF \l__keyval_value_tl
+      { \tl_put_right:Nn \l__keyval_parse_tl { { } } }
       {
-        \quark_if_nil:NTF \l_keyval_value_tl
+        \quark_if_nil:NTF \l__keyval_value_tl
           {
-            \tl_put_right:Nx \l_keyval_parse_tl
+            \tl_put_right:Nx \l__keyval_parse_tl
               { { \exp_not:o { \use_ii:nnn #1 \q_nil } } }
           }
-          { \keyval_split_value_aux:w #1 \q_stop }
+          { \__keyval_split_value_aux:w #1 \q_stop }
       }
   }
-\cs_new_protected:Npn \keyval_split_value_aux:w \q_nil #1 \q_stop
+\cs_new_protected:Npn \__keyval_split_value_aux:w \q_nil #1 \q_stop
   {
-    \tl_set:Nx \l_keyval_value_tl { \tl_trim_spaces:n {#1} }
-    \tl_put_right:Nx \l_keyval_parse_tl
-      { { \exp_not:o \l_keyval_value_tl } }
+    \tl_set:Nx \l__keyval_value_tl { \tl_trim_spaces:n {#1} }
+    \tl_put_right:Nx \l__keyval_parse_tl
+      { { \exp_not:o \l__keyval_value_tl } }
   }
 \cs_new_protected:Npn \keyval_parse:NNn #1#2#3
   {
-    \int_gincr:N \g_keyval_level_int
+    \int_gincr:N \g__keyval_level_int
     \cs_gset_eq:cN
-      { keyval_key_no_value_elt_ \int_use:N \g_keyval_level_int :n } #1
+      { __keyval_key_no_value_elt_ \int_use:N \g__keyval_level_int :n } #1
     \cs_gset_eq:cN
-      { keyval_key_value_elt_ \int_use:N \g_keyval_level_int :nn }   #2
-    \keyval_parse:n {#3}
-    \int_gdecr:N \g_keyval_level_int
+      { __keyval_key_value_elt_ \int_use:N \g__keyval_level_int :nn }   #2
+    \__keyval_parse:n {#3}
+    \int_gdecr:N \g__keyval_level_int
   }
-\msg_kernel_new:nnnn { keyval } { misplaced-equals-sign }
+\__msg_kernel_new:nnnn { kernel } { misplaced-equals-sign }
   { Misplaced~equals~sign~in~key-value~input~\msg_line_number: }
   {
     LaTeX~is~attempting~to~parse~some~key-value~input~but~found~
     two~equals~signs~not~separated~by~a~comma.
   }
-\tl_const:Nn \c_keys_code_root_tl { key~code~>~ }
-\tl_const:Nn \c_keys_vars_root_tl { key~var~>~ }
-\tl_const:Nn \c_keys_props_root_tl { key~prop~>~ }
-\tl_const:Nn \c_keys_value_forbidden_tl { forbidden }
-\tl_const:Nn \c_keys_value_required_tl  { required }
+\tl_const:Nn \c__keys_code_root_tl { key~code~>~ }
+\tl_const:Nn \c__keys_vars_root_tl { key~var~>~ }
+\tl_const:Nn \c__keys_props_root_tl { key~prop~>~ }
+\tl_const:Nn \c__keys_value_forbidden_tl { forbidden }
+\tl_const:Nn \c__keys_value_required_tl  { required }
 \int_new:N \l_keys_choice_int
-\tl_new:N \l_keys_choices_tl
+\tl_new:N \l_keys_choice_tl
 \tl_new:N \l_keys_key_tl
-\tl_new:N \l_keys_module_tl
-\bool_new:N \l_keys_no_value_bool
+\tl_new:N \l__keys_module_tl
+\bool_new:N \l__keys_no_value_bool
 \tl_new:N \l_keys_path_tl
-\tl_new:N \l_keys_property_tl
-\tl_new:N \l_keys_unknown_clist
+\tl_new:N \l__keys_property_tl
+\tl_new:N \l__keys_unknown_clist
 \tl_new:N \l_keys_value_tl
 \cs_new_protected:Npn \keys_define:nn
-  { \keys_define_aux:onn \l_keys_module_tl }
-\cs_new_protected:Npn \keys_define_aux:nnn #1#2#3
+  { \__keys_define:onn \l__keys_module_tl }
+\cs_new_protected:Npn \__keys_define:nnn #1#2#3
   {
-    \tl_set:Nx \l_keys_module_tl { \tl_to_str:n {#2} }
-    \keyval_parse:NNn \keys_define_elt:n \keys_define_elt:nn {#3}
-    \tl_set:Nn \l_keys_module_tl {#1}
+    \tl_set:Nx \l__keys_module_tl { \tl_to_str:n {#2} }
+    \keyval_parse:NNn \__keys_define_elt:n \__keys_define_elt:nn {#3}
+    \tl_set:Nn \l__keys_module_tl {#1}
   }
-\cs_generate_variant:Nn \keys_define_aux:nnn { o }
-\cs_new_protected:Npn \keys_define_elt:n #1
+\cs_generate_variant:Nn \__keys_define:nnn { o }
+\cs_new_protected:Npn \__keys_define_elt:n #1
   {
-    \bool_set_true:N \l_keys_no_value_bool
-    \keys_define_elt_aux:nn {#1} { }
+    \bool_set_true:N \l__keys_no_value_bool
+    \__keys_define_elt_aux:nn {#1} { }
   }
-\cs_new_protected:Npn \keys_define_elt:nn #1#2
+\cs_new_protected:Npn \__keys_define_elt:nn #1#2
   {
-    \bool_set_false:N \l_keys_no_value_bool
-    \keys_define_elt_aux:nn {#1} {#2}
+    \bool_set_false:N \l__keys_no_value_bool
+    \__keys_define_elt_aux:nn {#1} {#2}
   }
-\cs_new_protected:Npn \keys_define_elt_aux:nn #1#2
+\cs_new_protected:Npn \__keys_define_elt_aux:nn #1#2
   {
-    \keys_property_find:n {#1}
-    \cs_if_exist:cTF { \c_keys_props_root_tl \l_keys_property_tl }
-      { \keys_define_key:n {#2} }
+    \__keys_property_find:n {#1}
+    \cs_if_exist:cTF { \c__keys_props_root_tl \l__keys_property_tl }
+      { \__keys_define_key:n {#2} }
       {
-        \msg_kernel_error:nnxx { keys } { property-unknown }
-          { \l_keys_property_tl } { \l_keys_path_tl }
+        \__msg_kernel_error:nnxx { kernel } { property-unknown }
+          { \l__keys_property_tl } { \l_keys_path_tl }
       }
   }
-\cs_new_protected:Npn \keys_property_find:n #1
+\cs_new_protected:Npn \__keys_property_find:n #1
   {
-    \tl_set:Nx \l_keys_path_tl { \l_keys_module_tl / }
+    \tl_set:Nx \l_keys_path_tl { \l__keys_module_tl / }
     \tl_if_in:nnTF {#1} { . }
-      { \keys_property_find_aux:w #1 \q_stop }
-      { \msg_kernel_error:nnx { keys } { key-no-property } {#1} }
+      { \__keys_property_find:w #1 \q_stop }
+      { \__msg_kernel_error:nnx { kernel } { key-no-property } {#1} }
   }
-\cs_new_protected:Npn \keys_property_find_aux:w #1 . #2 \q_stop
+\cs_new_protected:Npn \__keys_property_find:w #1 . #2 \q_stop
   {
     \tl_set:Nx \l_keys_path_tl { \l_keys_path_tl \tl_to_str:n {#1} }
     \tl_if_in:nnTF {#2} { . }
       {
         \tl_set:Nx \l_keys_path_tl { \l_keys_path_tl . }
-        \keys_property_find_aux:w #2 \q_stop
+        \__keys_property_find:w #2 \q_stop
       }
-      { \tl_set:Nn \l_keys_property_tl { . #2 } }
+      { \tl_set:Nn \l__keys_property_tl { . #2 } }
   }
-\cs_new_protected:Npn \keys_define_key:n #1
+\cs_new_protected:Npn \__keys_define_key:n #1
   {
-    \bool_if:NTF \l_keys_no_value_bool
+    \bool_if:NTF \l__keys_no_value_bool
       {
-        \exp_after:wN \keys_define_key_aux:w
-          \l_keys_property_tl \q_stop
-          { \use:c { \c_keys_props_root_tl \l_keys_property_tl } }
+        \exp_after:wN \__keys_define_key:w
+          \l__keys_property_tl \q_stop
+          { \use:c { \c__keys_props_root_tl \l__keys_property_tl } }
           {
-            \msg_kernel_error:nnxx { keys }
-              { property-requires-value } { \l_keys_property_tl }
+            \__msg_kernel_error:nnxx { kernel }
+              { property-requires-value } { \l__keys_property_tl }
               { \l_keys_path_tl }
             }
       }
-      { \use:c { \c_keys_props_root_tl \l_keys_property_tl } {#1} }
+      { \use:c { \c__keys_props_root_tl \l__keys_property_tl } {#1} }
   }
-\cs_new_protected:Npn \keys_define_key_aux:w #1 : #2 \q_stop
+\cs_new_protected:Npn \__keys_define_key:w #1 : #2 \q_stop
   { \tl_if_empty:nTF {#2} }
-\cs_new:Npn \keys_bool_set:NN #1#2
+\cs_new:Npn \__keys_bool_set:NN #1#2
   {
     \bool_if_exist:NF #1 { \bool_new:N #1 }
-    \keys_choice_make:
-    \keys_cmd_set:nx { \l_keys_path_tl / true }
+    \__keys_choice_make:
+    \__keys_cmd_set:nx { \l_keys_path_tl / true }
       { \exp_not:c { bool_ #2 set_true:N } \exp_not:N #1 }
-    \keys_cmd_set:nx { \l_keys_path_tl / false }
+    \__keys_cmd_set:nx { \l_keys_path_tl / false }
       { \exp_not:c { bool_ #2 set_false:N } \exp_not:N #1 }
-    \keys_cmd_set:nn { \l_keys_path_tl / unknown }
+    \__keys_cmd_set:nn { \l_keys_path_tl / unknown }
       {
-        \msg_kernel_error:nnx { keys } { boolean-values-only }
+        \__msg_kernel_error:nnx { kernel } { boolean-values-only }
           { \l_keys_key_tl }
       }
-    \keys_default_set:n { true }
+    \__keys_default_set:n { true }
   }
-\cs_new:Npn \keys_bool_set_inverse:NN #1#2
+\cs_new:Npn \__keys_bool_set_inverse:NN #1#2
   {
     \bool_if_exist:NF #1 { \bool_new:N #1 }
-    \keys_choice_make:
-    \keys_cmd_set:nx { \l_keys_path_tl / true }
+    \__keys_choice_make:
+    \__keys_cmd_set:nx { \l_keys_path_tl / true }
       { \exp_not:c { bool_ #2 set_false:N } \exp_not:N #1 }
-    \keys_cmd_set:nx { \l_keys_path_tl / false }
+    \__keys_cmd_set:nx { \l_keys_path_tl / false }
       { \exp_not:c { bool_ #2 set_true:N } \exp_not:N #1 }
-    \keys_cmd_set:nn { \l_keys_path_tl / unknown }
+    \__keys_cmd_set:nn { \l_keys_path_tl / unknown }
       {
-        \msg_kernel_error:nnx { keys } { boolean-values-only }
+        \__msg_kernel_error:nnx { kernel } { boolean-values-only }
           { \l_keys_key_tl }
       }
-    \keys_default_set:n { true }
+    \__keys_default_set:n { true }
   }
-\cs_new_protected_nopar:Npn \keys_choice_make:
+\cs_new_protected_nopar:Npn \__keys_choice_make:
   {
-    \keys_cmd_set:nn { \l_keys_path_tl }
-      { \keys_choice_find:n {##1} }
-    \keys_cmd_set:nn { \l_keys_path_tl / unknown }
+    \__keys_cmd_set:nn { \l_keys_path_tl }
+      { \__keys_choice_find:n {##1} }
+    \__keys_cmd_set:nn { \l_keys_path_tl / unknown }
       {
-        \msg_kernel_error:nnxx { keys } { choice-unknown }
+        \__msg_kernel_error:nnxx { kernel } { key-choice-unknown }
           { \l_keys_path_tl } {##1}
       }
   }
-\cs_new_protected:Npn \keys_choices_make:nn #1#2
+\cs_new_protected:Npn \__keys_choices_make:nn #1#2
   {
-    \keys_choice_make:
+    \__keys_choice_make:
     \int_zero:N \l_keys_choice_int
     \clist_map_inline:nn {#1}
       {
-        \keys_cmd_set:nx { \l_keys_path_tl / ##1 }
+        \int_incr:N \l_keys_choice_int
+        \__keys_cmd_set:nx { \l_keys_path_tl / ##1 }
           {
             \tl_set:Nn \exp_not:N \l_keys_choice_tl {##1}
             \int_set:Nn \exp_not:N \l_keys_choice_int
               { \int_use:N \l_keys_choice_int }
             \exp_not:n {#2}
           }
-        \int_incr:N \l_keys_choice_int
       }
   }
-\cs_new_protected:Npn \keys_choices_generate:n #1
+\cs_new_protected:Npn \__keys_choices_generate:n #1
   {
     \cs_if_exist:cTF
-      { \c_keys_vars_root_tl \l_keys_path_tl .choice~code }
+      { \c__keys_vars_root_tl \l_keys_path_tl .choice~code }
       {
-        \keys_choice_make:
+        \__keys_choice_make:
         \int_zero:N \l_keys_choice_int
-        \clist_map_function:nN {#1} \keys_choices_generate_aux:n
+        \clist_map_function:nN {#1} \__keys_choices_generate_aux:n
       }
       {
-        \msg_kernel_error:nnx { keys }
+        \__msg_kernel_error:nnx { kernel }
           { generate-choices-before-code } { \l_keys_path_tl }
       }
   }
-\cs_new_protected:Npn \keys_choices_generate_aux:n #1
+\cs_new_protected:Npn \__keys_choices_generate_aux:n #1
   {
-    \keys_cmd_set:nx { \l_keys_path_tl / #1 }
+    \int_incr:N \l_keys_choice_int
+    \__keys_cmd_set:nx { \l_keys_path_tl / #1 }
       {
         \tl_set:Nn \exp_not:N \l_keys_choice_tl {#1}
         \int_set:Nn \exp_not:N \l_keys_choice_int
           { \int_use:N \l_keys_choice_int }
         \exp_not:v
-          { \c_keys_vars_root_tl \l_keys_path_tl .choice~code }
+          { \c__keys_vars_root_tl \l_keys_path_tl .choice~code }
       }
-    \int_incr:N \l_keys_choice_int
   }
-\cs_new_protected:Npn \keys_choice_code_store:x #1
+\cs_new_protected:Npn \__keys_choice_code_store:n #1
   {
     \cs_if_exist:cF
-      { \c_keys_vars_root_tl \l_keys_path_tl .choice~code }
+      { \c__keys_vars_root_tl \l_keys_path_tl .choice~code }
       {
         \tl_new:c
-          { \c_keys_vars_root_tl \l_keys_path_tl .choice~code }
+          { \c__keys_vars_root_tl \l_keys_path_tl .choice~code }
       }
-    \tl_set:cx { \c_keys_vars_root_tl \l_keys_path_tl .choice~code }
+    \tl_set:cn { \c__keys_vars_root_tl \l_keys_path_tl .choice~code }
       {#1}
   }
-\cs_new_protected:Npn \keys_cmd_set:nn #1#2
+\cs_generate_variant:Nn \__keys_choice_code_store:n { x }
+\cs_new_protected:Npn \__keys_cmd_set:nn #1#2
+  {
+    \__keys_cmd_set:n {#1}
+    \cs_set:cpn { \c__keys_code_root_tl #1 } ##1 {#2}
+  }
+\cs_new_protected:Npn \__keys_cmd_set:nx #1#2
   {
-    \keys_cmd_set_aux:n {#1}
-    \cs_set:cpn { \c_keys_code_root_tl #1 } ##1 {#2}
+    \__keys_cmd_set:n {#1}
+    \cs_set:cpx { \c__keys_code_root_tl #1 } ##1 {#2}
   }
-\cs_new_protected:Npn \keys_cmd_set:nx #1#2
+\cs_generate_variant:Nn \__keys_cmd_set:nn { Vo }
+\cs_new_protected:Npn \__keys_cmd_set:n #1
   {
-    \keys_cmd_set_aux:n {#1}
-    \cs_set:cpx { \c_keys_code_root_tl #1 } ##1 {#2}
+    \tl_clear_new:c { \c__keys_vars_root_tl #1 .default }
+    \tl_set:cn { \c__keys_vars_root_tl #1 .default } { \q_no_value }
+    \tl_clear_new:c { \c__keys_vars_root_tl #1 .req }
   }
-\cs_new_protected:Npn \keys_cmd_set_aux:n #1
+\cs_new_protected:Npn \__keys_default_set:n #1
+  { \tl_set:cn { \c__keys_vars_root_tl \l_keys_path_tl .default } {#1} }
+\cs_generate_variant:Nn \__keys_default_set:n { V }
+\cs_new_protected:Npn \__keys_initialise:n #1
   {
-    \tl_clear_new:c { \c_keys_vars_root_tl #1 .default }
-    \tl_set:cn { \c_keys_vars_root_tl #1 .default } { \q_no_value }
-    \tl_clear_new:c { \c_keys_vars_root_tl #1 .req }
+    \use:x
+      { \exp_after:wN \__keys_initialise:wn \l_keys_path_tl \q_stop {#1} }
   }
-\cs_new_protected:Npn \keys_default_set:n #1
-  { \tl_set:cn { \c_keys_vars_root_tl \l_keys_path_tl .default } {#1} }
-\cs_generate_variant:Nn \keys_default_set:n { V }
-\cs_new_protected:Npn \keys_meta_make:n #1
+\cs_generate_variant:Nn \__keys_initialise:n { V }
+\cs_new:Npn \__keys_initialise:wn #1 / #2 \q_stop #3
+  { \keys_set:nn {#1} { #2 = \exp_not:n { {#3} } } }
+\cs_new_protected:Npn \__keys_meta_make:n #1
   {
-    \exp_args:NNo \keys_cmd_set:nn \l_keys_path_tl
-      { \exp_after:wN \keys_set:nn \exp_after:wN { \l_keys_module_tl } {#1} }
+    \__keys_cmd_set:Vo \l_keys_path_tl
+      { \exp_after:wN \keys_set:nn \exp_after:wN { \l__keys_module_tl } {#1} }
   }
-\cs_new_protected:Npn \keys_meta_make:x #1
+\cs_new_protected:Npn \__keys_meta_make:x #1
   {
-    \keys_cmd_set:nx { \l_keys_path_tl }
-      { \exp_not:N \keys_set:nn { \l_keys_module_tl } {#1} }
+    \__keys_cmd_set:nx { \l_keys_path_tl }
+      { \exp_not:N \keys_set:nn { \l__keys_module_tl } {#1} }
   }
-\cs_new:Npn \keys_multichoice_find:n #1
-  { \clist_map_function:nN {#1} \keys_choice_find:n }
-\cs_new_protected_nopar:Npn \keys_multichoice_make:
+\cs_new:Npn \__keys_multichoice_find:n #1
+  { \clist_map_function:nN {#1} \__keys_choice_find:n }
+\cs_new_protected_nopar:Npn \__keys_multichoice_make:
   {
-    \keys_cmd_set:nn { \l_keys_path_tl }
-      { \keys_multichoice_find:n {##1} }
-    \keys_cmd_set:nn { \l_keys_path_tl / unknown }
+    \__keys_cmd_set:nn { \l_keys_path_tl }
+      { \__keys_multichoice_find:n {##1} }
+    \__keys_cmd_set:nn { \l_keys_path_tl / unknown }
       {
-        \msg_kernel_error:nnxx { keys } { choice-unknown }
+        \__msg_kernel_error:nnxx { kernel } { key-choice-unknown }
           { \l_keys_path_tl } {##1}
       }
   }
-\cs_new_protected:Npn \keys_multichoices_make:nn #1#2
+\cs_new_protected:Npn \__keys_multichoices_make:nn #1#2
   {
-    \keys_multichoice_make:
+    \__keys_multichoice_make:
     \int_zero:N \l_keys_choice_int
     \clist_map_inline:nn {#1}
       {
-        \keys_cmd_set:nx { \l_keys_path_tl / ##1 }
+        \int_incr:N \l_keys_choice_int
+        \__keys_cmd_set:nx { \l_keys_path_tl / ##1 }
           {
             \tl_set:Nn \exp_not:N \l_keys_choice_tl {##1}
             \int_set:Nn \exp_not:N \l_keys_choice_int
               { \int_use:N \l_keys_choice_int }
             \exp_not:n {#2}
           }
-        \int_incr:N \l_keys_choice_int
       }
   }
-\cs_new_protected:Npn \keys_value_requirement:n #1
+\cs_new_protected:Npn \__keys_value_requirement:n #1
   {
     \tl_set_eq:cc
-      { \c_keys_vars_root_tl \l_keys_path_tl .req }
-      { c_keys_value_ #1 _tl }
+      { \c__keys_vars_root_tl \l_keys_path_tl .req }
+      { c__keys_value_ #1 _tl }
   }
-\cs_new_protected:Npn \keys_variable_set:NnNN #1#2#3#4
+\cs_new_protected:Npn \__keys_variable_set:NnNN #1#2#3#4
   {
     \use:c { #2_if_exist:NF } #1 { \use:c { #2 _new:N } #1 }
-    \keys_cmd_set:nx { \l_keys_path_tl }
+    \__keys_cmd_set:nx { \l_keys_path_tl }
       { \exp_not:c { #2 _ #3 set:N #4 } \exp_not:N #1 {##1} }
   }
-\cs_new_protected:Npn \keys_variable_set:NnN #1#2#3
-  { \keys_variable_set:NnNN #1 {#2} { } #3 }
-\cs_generate_variant:Nn \keys_variable_set:NnNN { c }
-\cs_generate_variant:Nn \keys_variable_set:NnN  { c }
-\cs_new_protected:cpn { \c_keys_props_root_tl .bool_set:N } #1
-  { \keys_bool_set:NN #1 { } }
-\cs_new_protected:cpn { \c_keys_props_root_tl .bool_gset:N } #1
-  { \keys_bool_set:NN #1 g }
-\cs_new_protected:cpn { \c_keys_props_root_tl .bool_set_inverse:N } #1
-  { \keys_bool_set_inverse:NN #1 { } }
-\cs_new_protected:cpn { \c_keys_props_root_tl .bool_gset_inverse:N } #1
-  { \keys_bool_set_inverse:NN #1 g }
-\cs_new_protected_nopar:cpn { \c_keys_props_root_tl .choice: }
-  { \keys_choice_make: }
-\cs_new_protected:cpn { \c_keys_props_root_tl .choices:nn } #1
-  { \keys_choices_make:nn #1 }
-\cs_new_protected:cpn { \c_keys_props_root_tl .code:n } #1
-  { \keys_cmd_set:nn { \l_keys_path_tl } {#1} }
-\cs_new_protected:cpn { \c_keys_props_root_tl .code:x } #1
-  { \keys_cmd_set:nx { \l_keys_path_tl } {#1} }
-\cs_new_protected:cpn { \c_keys_props_root_tl .choice_code:n } #1
-  { \keys_choice_code_store:x { \exp_not:n {#1} } }
-\cs_new_protected:cpn { \c_keys_props_root_tl .choice_code:x } #1
-  { \keys_choice_code_store:x {#1} }
-\cs_new_protected:cpn { \c_keys_props_root_tl .clist_set:N } #1
-  { \keys_variable_set:NnN #1 { clist } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .clist_set:c } #1
-  { \keys_variable_set:cnN {#1} { clist } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .clist_gset:N } #1
-  { \keys_variable_set:NnNN #1 { clist } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .clist_gset:c } #1
-  { \keys_variable_set:cnNN {#1} { clist } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .default:n } #1
-  { \keys_default_set:n {#1} }
-\cs_new_protected:cpn { \c_keys_props_root_tl .default:V } #1
-  { \keys_default_set:V #1 }
-\cs_new_protected:cpn { \c_keys_props_root_tl .dim_set:N } #1
-  { \keys_variable_set:NnN #1 { dim } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .dim_set:c } #1
-  { \keys_variable_set:cnN {#1} { dim } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .dim_gset:N } #1
-  { \keys_variable_set:NnNN #1 { dim } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .dim_gset:c } #1
-  { \keys_variable_set:cnNN {#1} { dim } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .fp_set:N } #1
-  { \keys_variable_set:NnN #1 { fp } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .fp_set:c } #1
-  { \keys_variable_set:cnN {#1} { fp } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .fp_gset:N } #1
-  { \keys_variable_set:NnNN #1 { fp } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .fp_gset:c } #1
-  { \keys_variable_set:cnNN {#1} { fp } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .generate_choices:n } #1
-  { \keys_choices_generate:n {#1} }
-\cs_new_protected:cpn { \c_keys_props_root_tl .int_set:N } #1
-  { \keys_variable_set:NnN #1 { int } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .int_set:c } #1
-  { \keys_variable_set:cnN {#1} { int } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .int_gset:N } #1
-  { \keys_variable_set:NnNN #1 { int } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .int_gset:c } #1
-  { \keys_variable_set:cnNN {#1} { int } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .meta:n } #1
-  { \keys_meta_make:n {#1} }
-\cs_new_protected:cpn { \c_keys_props_root_tl .meta:x } #1
-  { \keys_meta_make:x {#1} }
-\cs_new_protected_nopar:cpn { \c_keys_props_root_tl .multichoice: }
-  { \keys_multichoice_make: }
-\cs_new_protected:cpn { \c_keys_props_root_tl .multichoices:nn } #1
-  { \keys_multichoices_make:nn #1 }
-\cs_new_protected:cpn { \c_keys_props_root_tl .skip_set:N } #1
-  { \keys_variable_set:NnN #1 { skip } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .skip_set:c } #1
-  { \keys_variable_set:cnN {#1} { skip } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .skip_gset:N } #1
-  { \keys_variable_set:NnNN #1 { skip } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .skip_gset:c } #1
-  { \keys_variable_set:cnNN {#1} { skip } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_set:N } #1
-   { \keys_variable_set:NnN #1 { tl } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_set:c } #1
-  { \keys_variable_set:cnN {#1} { tl } n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_set_x:N } #1
-  { \keys_variable_set:NnN #1 { tl } x }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_set_x:c } #1
-  { \keys_variable_set:cnN {#1} { tl } x }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_gset:N } #1
-  { \keys_variable_set:NnNN #1 { tl } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_gset:c } #1
-  { \keys_variable_set:cnNN {#1} { tl } g n }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_gset_x:N } #1
-  { \keys_variable_set:NnNN #1 { tl } g x }
-\cs_new_protected:cpn { \c_keys_props_root_tl .tl_gset_x:c } #1
-  { \keys_variable_set:cnNN {#1} { tl } g x }
-\cs_new_protected_nopar:cpn { \c_keys_props_root_tl .value_forbidden: }
-  { \keys_value_requirement:n { forbidden } }
-\cs_new_protected_nopar:cpn { \c_keys_props_root_tl .value_required: }
-  { \keys_value_requirement:n { required } }
+\cs_new_protected:Npn \__keys_variable_set:NnN #1#2#3
+  { \__keys_variable_set:NnNN #1 {#2} { } #3 }
+\cs_generate_variant:Nn \__keys_variable_set:NnNN { c }
+\cs_generate_variant:Nn \__keys_variable_set:NnN  { c }
+\cs_new_protected:cpn { \c__keys_props_root_tl .bool_set:N } #1
+  { \__keys_bool_set:NN #1 { } }
+\cs_new_protected:cpn { \c__keys_props_root_tl .bool_gset:N } #1
+  { \__keys_bool_set:NN #1 g }
+\cs_new_protected:cpn { \c__keys_props_root_tl .bool_set_inverse:N } #1
+  { \__keys_bool_set_inverse:NN #1 { } }
+\cs_new_protected:cpn { \c__keys_props_root_tl .bool_gset_inverse:N } #1
+  { \__keys_bool_set_inverse:NN #1 g }
+\cs_new_protected_nopar:cpn { \c__keys_props_root_tl .choice: }
+  { \__keys_choice_make: }
+\cs_new_protected:cpn { \c__keys_props_root_tl .choices:nn } #1
+  { \__keys_choices_make:nn #1 }
+\cs_new_protected:cpn { \c__keys_props_root_tl .code:n } #1
+  { \__keys_cmd_set:nn { \l_keys_path_tl } {#1} }
+\cs_new_protected:cpn { \c__keys_props_root_tl .code:x } #1
+  { \__keys_cmd_set:nx { \l_keys_path_tl } {#1} }
+\cs_new_protected:cpn { \c__keys_props_root_tl .choice_code:n } #1
+  { \__keys_choice_code_store:n {#1} }
+\cs_new_protected:cpn { \c__keys_props_root_tl .choice_code:x } #1
+  { \__keys_choice_code_store:x {#1} }
+\cs_new_protected:cpn { \c__keys_props_root_tl .clist_set:N } #1
+  { \__keys_variable_set:NnN #1 { clist } n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .clist_set:c } #1
+  { \__keys_variable_set:cnN {#1} { clist } n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .clist_gset:N } #1
+  { \__keys_variable_set:NnNN #1 { clist } g n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .clist_gset:c } #1
+  { \__keys_variable_set:cnNN {#1} { clist } g n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .default:n } #1
+  { \__keys_default_set:n {#1} }
+\cs_new_protected:cpn { \c__keys_props_root_tl .default:V } #1
+  { \__keys_default_set:V #1 }
+\cs_new_protected:cpn { \c__keys_props_root_tl .dim_set:N } #1
+  { \__keys_variable_set:NnN #1 { dim } n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .dim_set:c } #1
+  { \__keys_variable_set:cnN {#1} { dim } n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .dim_gset:N } #1
+  { \__keys_variable_set:NnNN #1 { dim } g n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .dim_gset:c } #1
+  { \__keys_variable_set:cnNN {#1} { dim } g n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .fp_set:N } #1
+  { \__keys_variable_set:NnN #1 { fp } n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .fp_set:c } #1
+  { \__keys_variable_set:cnN {#1} { fp } n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .fp_gset:N } #1
+  { \__keys_variable_set:NnNN #1 { fp } g n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .fp_gset:c } #1
+  { \__keys_variable_set:cnNN {#1} { fp } g n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .generate_choices:n } #1
+  { \__keys_choices_generate:n {#1} }
+\cs_new_protected:cpn { \c__keys_props_root_tl .initial:n } #1
+  { \__keys_initialise:n {#1} }
+\cs_new_protected:cpn { \c__keys_props_root_tl .initial:V } #1
+  { \__keys_initialise:V #1 }
+\cs_new_protected:cpn { \c__keys_props_root_tl .int_set:N } #1
+  { \__keys_variable_set:NnN #1 { int } n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .int_set:c } #1
+  { \__keys_variable_set:cnN {#1} { int } n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .int_gset:N } #1
+  { \__keys_variable_set:NnNN #1 { int } g n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .int_gset:c } #1
+  { \__keys_variable_set:cnNN {#1} { int } g n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .meta:n } #1
+  { \__keys_meta_make:n {#1} }
+\cs_new_protected:cpn { \c__keys_props_root_tl .meta:x } #1
+  { \__keys_meta_make:x {#1} }
+\cs_new_protected_nopar:cpn { \c__keys_props_root_tl .multichoice: }
+  { \__keys_multichoice_make: }
+\cs_new_protected:cpn { \c__keys_props_root_tl .multichoices:nn } #1
+  { \__keys_multichoices_make:nn #1 }
+\cs_new_protected:cpn { \c__keys_props_root_tl .skip_set:N } #1
+  { \__keys_variable_set:NnN #1 { skip } n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .skip_set:c } #1
+  { \__keys_variable_set:cnN {#1} { skip } n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .skip_gset:N } #1
+  { \__keys_variable_set:NnNN #1 { skip } g n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .skip_gset:c } #1
+  { \__keys_variable_set:cnNN {#1} { skip } g n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .tl_set:N } #1
+   { \__keys_variable_set:NnN #1 { tl } n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .tl_set:c } #1
+  { \__keys_variable_set:cnN {#1} { tl } n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .tl_set_x:N } #1
+  { \__keys_variable_set:NnN #1 { tl } x }
+\cs_new_protected:cpn { \c__keys_props_root_tl .tl_set_x:c } #1
+  { \__keys_variable_set:cnN {#1} { tl } x }
+\cs_new_protected:cpn { \c__keys_props_root_tl .tl_gset:N } #1
+  { \__keys_variable_set:NnNN #1 { tl } g n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .tl_gset:c } #1
+  { \__keys_variable_set:cnNN {#1} { tl } g n }
+\cs_new_protected:cpn { \c__keys_props_root_tl .tl_gset_x:N } #1
+  { \__keys_variable_set:NnNN #1 { tl } g x }
+\cs_new_protected:cpn { \c__keys_props_root_tl .tl_gset_x:c } #1
+  { \__keys_variable_set:cnNN {#1} { tl } g x }
+\cs_new_protected_nopar:cpn { \c__keys_props_root_tl .value_forbidden: }
+  { \__keys_value_requirement:n { forbidden } }
+\cs_new_protected_nopar:cpn { \c__keys_props_root_tl .value_required: }
+  { \__keys_value_requirement:n { required } }
 \cs_new_protected:Npn \keys_set:nn
-  { \keys_set_aux:onn { \l_keys_module_tl } }
-\cs_new_protected:Npn \keys_set_aux:nnn #1#2#3
+  { \__keys_set:onn { \l__keys_module_tl } }
+\cs_new_protected:Npn \__keys_set:nnn #1#2#3
   {
-    \tl_set:Nx \l_keys_module_tl { \tl_to_str:n {#2} }
-    \keyval_parse:NNn \keys_set_elt:n \keys_set_elt:nn {#3}
-    \tl_set:Nn \l_keys_module_tl {#1}
+    \tl_set:Nx \l__keys_module_tl { \tl_to_str:n {#2} }
+    \keyval_parse:NNn \__keys_set_elt:n \__keys_set_elt:nn {#3}
+    \tl_set:Nn \l__keys_module_tl {#1}
   }
 \cs_generate_variant:Nn \keys_set:nn { nV , nv , no }
-\cs_generate_variant:Nn \keys_set_aux:nnn { o }
+\cs_generate_variant:Nn \__keys_set:nnn { o }
 \cs_new_protected:Npn \keys_set_known:nnN
-  { \keys_set_known_aux:onnN { \l_keys_module_tl } }
-\cs_new_protected:Npn \keys_set_known_aux:nnnN #1#2#3#4
+  { \__keys_set_known:onnN { \l__keys_module_tl } }
+\cs_new_protected:Npn \__keys_set_known:nnnN #1#2#3#4
   {
-    \tl_set:Nx \l_keys_module_tl { \tl_to_str:n {#2} }
-    \clist_clear:N \l_keys_unknown_clist
-    \cs_set_eq:NN \keys_execute_unknown: \keys_execute_unknown_alt:
-    \keyval_parse:NNn \keys_set_elt:n \keys_set_elt:nn {#3}
-    \cs_set_eq:NN \keys_execute_unknown: \keys_execute_unknown_std:
-    \tl_set:Nn \l_keys_module_tl {#1}
-    \clist_set_eq:NN #4 \l_keys_unknown_clist
+    \tl_set:Nx \l__keys_module_tl { \tl_to_str:n {#2} }
+    \clist_clear:N \l__keys_unknown_clist
+    \cs_set_eq:NN \__keys_execute_unknown: \__keys_execute_unknown_alt:
+    \keyval_parse:NNn \__keys_set_elt:n \__keys_set_elt:nn {#3}
+    \cs_set_eq:NN \__keys_execute_unknown: \__keys_execute_unknown_std:
+    \tl_set:Nn \l__keys_module_tl {#1}
+    \clist_set_eq:NN #4 \l__keys_unknown_clist
   }
 \cs_generate_variant:Nn \keys_set_known:nnN { nV , nv , no }
-\cs_generate_variant:Nn \keys_set_known_aux:nnnN { o }
-\cs_new_protected:Npn \keys_set_elt:n #1
+\cs_generate_variant:Nn \__keys_set_known:nnnN { o }
+\cs_new_protected:Npn \__keys_set_elt:n #1
   {
-    \bool_set_true:N \l_keys_no_value_bool
-    \keys_set_elt_aux:nn {#1} { }
+    \bool_set_true:N \l__keys_no_value_bool
+    \__keys_set_elt_aux:nn {#1} { }
   }
-\cs_new_protected:Npn \keys_set_elt:nn #1#2
+\cs_new_protected:Npn \__keys_set_elt:nn #1#2
   {
-    \bool_set_false:N \l_keys_no_value_bool
-    \keys_set_elt_aux:nn {#1} {#2}
+    \bool_set_false:N \l__keys_no_value_bool
+    \__keys_set_elt_aux:nn {#1} {#2}
   }
-\cs_new_protected:Npn \keys_set_elt_aux:nn #1#2
+\cs_new_protected:Npn \__keys_set_elt_aux:nn #1#2
   {
     \tl_set:Nx \l_keys_key_tl { \tl_to_str:n {#1} }
-    \tl_set:Nx \l_keys_path_tl { \l_keys_module_tl / \l_keys_key_tl }
-    \keys_value_or_default:n {#2}
+    \tl_set:Nx \l_keys_path_tl { \l__keys_module_tl / \l_keys_key_tl }
+    \__keys_value_or_default:n {#2}
     \bool_if:nTF
       {
-        \keys_if_value_p:n { required } &&
-        \l_keys_no_value_bool
+        \__keys_if_value_p:n { required } &&
+        \l__keys_no_value_bool
       }
       {
-        \msg_kernel_error:nnx { keys } { value-required }
+        \__msg_kernel_error:nnx { kernel } { value-required }
           { \l_keys_path_tl }
       }
       {
         \bool_if:nTF
           {
-              \keys_if_value_p:n { forbidden } &&
-            ! \l_keys_no_value_bool
+              \__keys_if_value_p:n { forbidden } &&
+            ! \l__keys_no_value_bool
           }
           {
-            \msg_kernel_error:nnxx { keys } { value-forbidden }
+            \__msg_kernel_error:nnxx { kernel } { value-forbidden }
               { \l_keys_path_tl } { \l_keys_value_tl }
           }
-          { \keys_execute: }
+          { \__keys_execute: }
       }
   }
-\cs_new_protected:Npn \keys_value_or_default:n #1
+\cs_new_protected:Npn \__keys_value_or_default:n #1
   {
     \tl_set:Nn \l_keys_value_tl {#1}
-    \bool_if:NT \l_keys_no_value_bool
+    \bool_if:NT \l__keys_no_value_bool
       {
-        \quark_if_no_value:cF { \c_keys_vars_root_tl \l_keys_path_tl .default }
+        \quark_if_no_value:cF { \c__keys_vars_root_tl \l_keys_path_tl .default }
           {
-            \cs_if_exist:cT { \c_keys_vars_root_tl \l_keys_path_tl .default }
+            \cs_if_exist:cT { \c__keys_vars_root_tl \l_keys_path_tl .default }
               {
                 \tl_set_eq:Nc \l_keys_value_tl
-                  { \c_keys_vars_root_tl \l_keys_path_tl .default }
+                  { \c__keys_vars_root_tl \l_keys_path_tl .default }
               }
           }
       }
   }
-\prg_new_conditional:Npnn \keys_if_value:n #1 { p }
+\prg_new_conditional:Npnn \__keys_if_value:n #1 { p }
   {
-    \tl_if_eq:ccTF { c_keys_value_ #1 _tl }
-      { \c_keys_vars_root_tl \l_keys_path_tl .req }
+    \tl_if_eq:ccTF { c__keys_value_ #1 _tl }
+      { \c__keys_vars_root_tl \l_keys_path_tl .req }
       { \prg_return_true: }
       { \prg_return_false: }
   }
-\cs_new_nopar:Npn \keys_execute:
-  { \keys_execute:nn { \l_keys_path_tl } { \keys_execute_unknown: } }
-\cs_new_nopar:Npn \keys_execute_unknown:
+\cs_new_nopar:Npn \__keys_execute:
+  { \__keys_execute:nn { \l_keys_path_tl } { \__keys_execute_unknown: } }
+\cs_new_nopar:Npn \__keys_execute_unknown:
   {
-    \keys_execute:nn { \l_keys_module_tl / unknown }
+    \__keys_execute:nn { \l__keys_module_tl / unknown }
       {
-        \msg_kernel_error:nnxx { keys } { key-unknown }
-          { \l_keys_path_tl } { \l_keys_module_tl }
+        \__msg_kernel_error:nnxx { kernel } { key-unknown }
+          { \l_keys_path_tl } { \l__keys_module_tl }
       }
   }
-\cs_new_eq:NN \keys_execute_unknown_std: \keys_execute_unknown:
-\cs_new_nopar:Npn \keys_execute_unknown_alt:
+\cs_new_eq:NN \__keys_execute_unknown_std: \__keys_execute_unknown:
+\cs_new_nopar:Npn \__keys_execute_unknown_alt:
   {
-    \clist_put_right:Nx \l_keys_unknown_clist
+    \clist_put_right:Nx \l__keys_unknown_clist
       {
         \exp_not:o \l_keys_key_tl
-        \bool_if:NF \l_keys_no_value_bool
+        \bool_if:NF \l__keys_no_value_bool
           { = { \exp_not:o \l_keys_value_tl } }
       }
   }
-\cs_new:Npn \keys_execute:nn #1#2
+\cs_new:Npn \__keys_execute:nn #1#2
   {
-    \cs_if_exist:cTF { \c_keys_code_root_tl #1 }
+    \cs_if_exist:cTF { \c__keys_code_root_tl #1 }
       {
-        \exp_args:Nc \exp_args:No { \c_keys_code_root_tl #1 }
+        \exp_args:Nc \exp_args:No { \c__keys_code_root_tl #1 }
           \l_keys_value_tl
       }
       {#2}
   }
-\cs_new:Npn \keys_choice_find:n #1
+\cs_new:Npn \__keys_choice_find:n #1
   {
-    \keys_execute:nn { \l_keys_path_tl / \tl_to_str:n {#1} }
-      { \keys_execute:nn { \l_keys_path_tl / unknown } { } }
+    \__keys_execute:nn { \l_keys_path_tl / \tl_to_str:n {#1} }
+      { \__keys_execute:nn { \l_keys_path_tl / unknown } { } }
   }
 \prg_new_conditional:Npnn \keys_if_exist:nn #1#2 { p , T , F , TF }
   {
-    \cs_if_exist:cTF { \c_keys_code_root_tl #1 / #2 }
+    \cs_if_exist:cTF { \c__keys_code_root_tl #1 / #2 }
       { \prg_return_true: }
       { \prg_return_false: }
   }
 \prg_new_conditional:Npnn \keys_if_choice_exist:nnn #1#2#3 { p , T , F , TF }
   {
-    \cs_if_exist:cTF { \c_keys_code_root_tl #1 / #2 / #3 }
+    \cs_if_exist:cTF { \c__keys_code_root_tl #1 / #2 / #3 }
       { \prg_return_true: }
       { \prg_return_false: }
   }
 \cs_new:Npn \keys_show:nn #1#2
-  { \cs_show:c { \c_keys_code_root_tl #1 / \tl_to_str:n {#2} } }
-\msg_kernel_new:nnnn { keys } { boolean-values-only }
+  { \cs_show:c { \c__keys_code_root_tl #1 / \tl_to_str:n {#2} } }
+\__msg_kernel_new:nnnn { kernel } { boolean-values-only }
   { Key~'#1'~accepts~boolean~values~only. }
   { The~key~'#1'~only~accepts~the~values~'true'~and~'false'. }
-\msg_kernel_new:nnnn { keys } { choice-unknown }
+\__msg_kernel_new:nnnn { kernel } { choice-unknown }
   { Choice~'#2'~unknown~for~key~'#1'. }
   {
     The~key~'#1'~takes~a~limited~number~of~values.\\
     The~input~given,~'#2',~is~not~on~the~list~accepted.
   }
-\msg_kernel_new:nnnn { keys } { generate-choices-before-code }
+\__msg_kernel_new:nnnn { kernel } { generate-choices-before-code }
   { No~code~available~to~generate~choices~for~key~'#1'. }
   {
     \c_msg_coding_error_text_tl
     Before~using~.generate_choices:n~the~code~should~be~defined~
     with~'.choice_code:n'~or~'.choice_code:x'.
   }
-\msg_kernel_new:nnnn { keys } { key-no-property }
+\__msg_kernel_new:nnnn { kernel } { key-no-property }
   { No~property~given~in~definition~of~key~'#1'. }
   {
     \c_msg_coding_error_text_tl
@@ -651,44 +665,39 @@
     ~ ~ #1 .<property> \\
     LaTeX~did~not~find~a~'.'~to~indicate~the~start~of~a~property.
   }
-\msg_kernel_new:nnnn { keys } { key-unknown }
+\__msg_kernel_new:nnnn { kernel } { key-unknown }
   { The~key~'#1'~is~unknown~and~is~being~ignored. }
   {
     The~module~'#2'~does~not~have~a~key~called~#1'.\\
     Check~that~you~have~spelled~the~key~name~correctly.
   }
-\msg_kernel_new:nnnn { keys } { option-unknown }
-  { Unknown~option~'#1'~for~package~#2. }
-  {
-    LaTeX~has~been~asked~to~set~an~option~called~'#1'~
-    but~the~#2~package~has~not~created~an~option~with~this~name.
-  }
-\msg_kernel_new:nnnn { keys } { property-requires-value }
+\__msg_kernel_new:nnnn { kernel } { property-requires-value }
   { The~property~'#1'~requires~a~value. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~was~asked~to~set~property~'#2'~for~key~'#1'.\\
     No~value~was~given~for~the~property,~and~one~is~required.
   }
-\msg_kernel_new:nnnn { keys } { property-unknown }
+\__msg_kernel_new:nnnn { kernel } { property-unknown }
   { The~key~property~'#1'~is~unknown. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~has~been~asked~to~set~the~property~'#1'~for~key~'#2':~
     this~property~is~not~defined.
   }
-\msg_kernel_new:nnnn { keys } { value-forbidden }
+\__msg_kernel_new:nnnn { kernel } { value-forbidden }
   { The~key~'#1'~does~not~taken~a~value. }
   {
     The~key~'#1'~should~be~given~without~a~value.\\
     LaTeX~will~ignore~the~given~value~'#2'.
   }
-\msg_kernel_new:nnnn { keys } { value-required }
+\__msg_kernel_new:nnnn { kernel } { value-required }
   { The~key~'#1'~requires~a~value. }
   {
     The~key~'#1'~must~have~a~value.\\
     No~value~was~present:~the~key~will~be~ignored.
   }
+\cs_new_eq:NN \c_keys_code_root_tl \c__keys_code_root_tl
 %% 
 %%
 %% End of file `l3keys.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3luatex.sty b/Master/texmf-dist/tex/latex/l3kernel/l3luatex.sty
index 7655ba4ae08..c6050b44f98 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3luatex.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3luatex.sty
@@ -46,17 +46,11 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3luatex.dtx 3355 2012-02-09 07:18:22Z joseph $
+\GetIdInfo$Id: l3luatex.dtx 3986 2012-07-15 19:23:51Z joseph $
   {L3 Experimental LuaTeX-specific functions}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
-\msg_kernel_new:nnnn { luatex } { bad-engine }
-  { LuaTeX~engine~not~in~use!~Ignoring~#1. }
-  {
-    The~feature~you~are~using~is~only~available~
-    with~the~LuaTeX~engine.~LaTeX3~ignored~`#1#2'.
-  }
+\__expl_package_check:
 \luatex_if_engine:TF
   {
     \cs_new_eq:NN \lua_now:x       \luatex_directlua:D
@@ -65,13 +59,13 @@
   {
     \cs_new:Npn \lua_now:x #1
       {
-        \msg_expandable_kernel_error:nnn
-          { luatex } { bad-engine } { \lua_now:x }
+        \__msg_kernel_expandable_error:nnn
+          { kernel } { bad-engine } { \lua_now:x }
       }
     \cs_new_protected:Npn \lua_shipout_x:n #1
       {
-        \msg_expandable_kernel_error:nnn
-          { luatex } { bad-engine } { \lua_shipout_x:n }
+        \__msg_kernel_expandable_error:nnn
+          { kernel } { bad-engine } { \lua_shipout_x:n }
       }
   }
 \cs_new:Npn \lua_now:n #1
@@ -80,27 +74,27 @@
 \cs_new_protected:Npn \lua_shipout:n #1
   { \lua_shipout_x:n { \exp_not:n {#1} } }
 \cs_generate_variant:Nn \lua_shipout:n { x }
-\int_new:N  \g_cctab_allocate_int
-\int_set:Nn \g_cctab_allocate_int { \c_minus_one }
-\int_new:N \g_cctab_stack_int
-\seq_new:N \g_cctab_stack_seq
+\int_new:N  \g__cctab_allocate_int
+\int_set:Nn \g__cctab_allocate_int { \c_minus_one }
+\int_new:N \g__cctab_stack_int
+\seq_new:N \g__cctab_stack_seq
 \cs_new_protected:Npn \cctab_new:N #1
   {
-    \chk_if_free_cs:N #1
-    \int_gadd:Nn \g_cctab_allocate_int { \c_two }
+    \__chk_if_free_cs:N #1
+    \int_gadd:Nn \g__cctab_allocate_int { \c_two }
     \int_compare:nNnTF
-      \g_cctab_allocate_int <  { \c_max_register_int + \c_one }
+      \g__cctab_allocate_int <  { \c_max_register_int + \c_one }
        {
-         \tex_global:D \tex_chardef:D #1 \g_cctab_allocate_int
+         \tex_global:D \tex_chardef:D #1 \g__cctab_allocate_int
          \luatex_initcatcodetable:D #1
        }
-       { \msg_kernel_fatal:nnx { kernel } { out-of-registers } { cctab } }
+       { \__msg_kernel_fatal:nnx { kernel } { out-of-registers } { cctab } }
   }
 \luatex_if_engine:F
   {
     \cs_set_protected:Npn \cctab_new:N #1
       {
-        \msg_kernel_error:nnx { luatex } { bad-engine }
+        \__msg_kernel_error:nnx { kernel } { bad-engine }
           { \exp_not:N \cctab_new:N }
       }
   }
@@ -108,39 +102,39 @@
   {
     \cs_set_protected:Npn \cctab_new:N #1
       {
-        \chk_if_free_cs:N #1
+        \__chk_if_free_cs:N #1
         \newcatcodetable #1
         \luatex_initcatcodetable:D #1
       }
   }
 \cs_new_protected:Npn \cctab_begin:N #1
   {
-    \seq_gpush:Nx \g_cctab_stack_seq { \tex_the:D \luatex_catcodetable:D }
+    \seq_gpush:Nx \g__cctab_stack_seq { \tex_the:D \luatex_catcodetable:D }
     \luatex_catcodetable:D #1
-    \int_gadd:Nn \g_cctab_stack_int { \c_two }
-    \int_compare:nNnT \g_cctab_stack_int > \c_max_register_int
-      { \msg_kernel_fatal:nn { code } { cctab-stack-full } }
-    \luatex_savecatcodetable:D \g_cctab_stack_int
-    \luatex_catcodetable:D \g_cctab_stack_int
+    \int_gadd:Nn \g__cctab_stack_int { \c_two }
+    \int_compare:nNnT \g__cctab_stack_int > \c_max_register_int
+      { \__msg_kernel_fatal:nn { kernel } { cctab-stack-full } }
+    \luatex_savecatcodetable:D \g__cctab_stack_int
+    \luatex_catcodetable:D \g__cctab_stack_int
   }
 \cs_new_protected_nopar:Npn \cctab_end:
   {
-    \int_gsub:Nn \g_cctab_stack_int { \c_two }
-    \seq_if_empty:NTF \g_cctab_stack_seq
-      { \tl_set:Nn \l_cctab_internal_tl { 0 } }
-      { \seq_gpop:NN \g_cctab_stack_seq \l_cctab_internal_tl }
-    \luatex_catcodetable:D \l_cctab_internal_tl \scan_stop:
+    \int_gsub:Nn \g__cctab_stack_int { \c_two }
+    \seq_if_empty:NTF \g__cctab_stack_seq
+      { \tl_set:Nn \l__cctab_internal_tl { 0 } }
+      { \seq_gpop:NN \g__cctab_stack_seq \l__cctab_internal_tl }
+    \luatex_catcodetable:D \l__cctab_internal_tl \scan_stop:
   }
 \luatex_if_engine:F
   {
     \cs_set_protected:Npn \cctab_begin:N #1
       {
-        \msg_kernel_error:nnxx { luatex } { bad-engine }
+        \__msg_kernel_error:nnxx { kernel } { bad-engine }
           { \exp_not:N \cctab_begin:N } {#1}
       }
     \cs_set_protected_nopar:Npn \cctab_end:
       {
-        \msg_kernel_error:nnx { luatex } { bad-engine }
+        \__msg_kernel_error:nnx { kernel } { bad-engine }
           { \exp_not:N \cctab_end: }
       }
   }
@@ -149,7 +143,7 @@
     \cs_set_protected:Npn \cctab_begin:N #1 { \BeginCatcodeRegime #1 }
     \cs_set_protected_nopar:Npn \cctab_end: { \EndCatcodeRegime }
   }
-\tl_new:N \l_cctab_internal_tl
+\tl_new:N \l__cctab_internal_tl
 \cs_new_protected:Npn \cctab_gset:Nn #1#2
   {
     \group_begin:
@@ -161,7 +155,7 @@
   {
     \cs_set_protected:Npn \cctab_gset:Nn #1#2
       {
-        \msg_kernel_error:nnxx { luatex } { bad-engine }
+        \__msg_kernel_error:nnxx { kernel } { bad-engine }
           { \exp_not:N \cctab_gset:Nn } { #1 {#2} }
       }
   }
@@ -177,7 +171,18 @@
     \cs_new_eq:NN \c_other_cctab    \CatcodeTableOther
     \cs_new_eq:NN \c_str_cctab      \CatcodeTableString
   }
-\cs_new_eq:NN \c_string_cctab \c_str_cctab
+\__msg_kernel_new:nnnn { kernel } { bad-engine }
+  { LuaTeX~engine~not~in~use!~Ignoring~#1. }
+  {
+    The~feature~you~are~using~is~only~available~
+    with~the~LuaTeX~engine.~LaTeX3~ignored~`#1#2'.
+  }
+\__msg_kernel_new:nnnn { kernel } { cctab-stack-full }
+  { The~category~code~table~stack~is~exhausted. }
+  {
+    LaTeX~has~been~asked~to~switch~to~a~new~category~code~table,~
+    but~there~is~no~more~space~to~do~this!
+  }
 %% 
 %%
 %% End of file `l3luatex.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3msg.sty b/Master/texmf-dist/tex/latex/l3kernel/l3msg.sty
index 2e5ae99d6a4..bfce368f0d0 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3msg.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3msg.sty
@@ -46,59 +46,59 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3msg.dtx 3568 2012-04-23 13:23:58Z joseph $
-  {L3 Experimental messages}
+\GetIdInfo$Id: l3msg.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Messages}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
-\tl_new:N \l_msg_internal_tl
-\tl_const:Nn \c_msg_text_prefix_tl      { msg~text~>~ }
-\tl_const:Nn \c_msg_more_text_prefix_tl { msg~extra~text~>~ }
+\__expl_package_check:
+\tl_new:N \l__msg_internal_tl
+\tl_const:Nn \c__msg_text_prefix_tl      { msg~text~>~ }
+\tl_const:Nn \c__msg_more_text_prefix_tl { msg~extra~text~>~ }
 \prg_new_conditional:Npnn \msg_if_exist:nn #1#2 { p , T , F , TF }
   {
-    \cs_if_exist:cTF { \c_msg_text_prefix_tl #1 / #2 }
+    \cs_if_exist:cTF { \c__msg_text_prefix_tl #1 / #2 }
       { \prg_return_true: } { \prg_return_false: }
   }
-\cs_new_protected:Npn \chk_if_free_msg:nn #1#2
+\cs_new_protected:Npn \__chk_if_free_msg:nn #1#2
   {
     \msg_if_exist:nnT {#1} {#2}
       {
-        \msg_kernel_error:nnxx { msg } { message-already-defined }
+        \__msg_kernel_error:nnxx { kernel } { message-already-defined }
           {#1} {#2}
       }
   }
 \tex_ifodd:D \l@expl@log@functions@bool
-  \cs_gset_protected:Npn \chk_if_free_msg:nn #1#2
+  \cs_gset_protected:Npn \__chk_if_free_msg:nn #1#2
     {
       \msg_if_exist:nnT {#1} {#2}
         {
-          \msg_kernel_error:nnxx { msg } { message-already-defined }
+          \__msg_kernel_error:nnxx { kernel } { message-already-defined }
             {#1} {#2}
         }
-      \iow_log:x { Defining~message~#1/#2~ \msg_line_context: }
+      \iow_log:x { Defining~message~ #1 / #2 ~\msg_line_context: }
     }
 \fi:
 \cs_new_protected:Npn \msg_new:nnnn #1#2
   {
-    \chk_if_free_msg:nn {#1} {#2}
+    \__chk_if_free_msg:nn {#1} {#2}
     \msg_gset:nnnn {#1} {#2}
   }
 \cs_new_protected:Npn \msg_new:nnn #1#2#3
   { \msg_new:nnnn {#1} {#2} {#3} { } }
 \cs_new_protected:Npn \msg_set:nnnn #1#2#3#4
   {
-    \cs_set:cpn { \c_msg_text_prefix_tl #1 / #2 }
+    \cs_set:cpn { \c__msg_text_prefix_tl #1 / #2 }
       ##1##2##3##4 {#3}
-    \cs_set:cpn { \c_msg_more_text_prefix_tl #1 / #2 }
+    \cs_set:cpn { \c__msg_more_text_prefix_tl #1 / #2 }
       ##1##2##3##4 {#4}
   }
 \cs_new_protected:Npn \msg_set:nnn #1#2#3
   { \msg_set:nnnn {#1} {#2} {#3} { } }
 \cs_new_protected:Npn \msg_gset:nnnn #1#2#3#4
   {
-    \cs_gset:cpn { \c_msg_text_prefix_tl #1 / #2 }
+    \cs_gset:cpn { \c__msg_text_prefix_tl #1 / #2 }
       ##1##2##3##4 {#3}
-    \cs_gset:cpn { \c_msg_more_text_prefix_tl #1 / #2 }
+    \cs_gset:cpn { \c__msg_more_text_prefix_tl #1 / #2 }
       ##1##2##3##4 {#4}
   }
 \cs_new_protected:Npn \msg_gset:nnn #1#2#3
@@ -135,8 +135,6 @@
     More~errors~will~almost~certainly~follow: \\
     the~LaTeX~run~should~be~aborted.
   }
-\cs_new_nopar:Npn \msg_newline: { ^^J }
-\cs_new_nopar:Npn \msg_two_newlines: { ^^J ^^J }
 \cs_new_nopar:Npn \msg_line_number: { \int_use:N \tex_inputlineno:D }
 \cs_gset_nopar:Npn \msg_line_context:
   {
@@ -144,24 +142,24 @@
     \c_space_tl
     \msg_line_number:
   }
-\cs_new_protected:Npn \msg_interrupt:xxx #1#2#3
+\cs_new_protected:Npn \msg_interrupt:nnn #1#2#3
   {
     \tl_if_empty:nTF {#3}
       {
-        \msg_interrupt_wrap:xx { \\ \c_msg_no_info_text_tl }
+        \__msg_interrupt_wrap:nn { \\ \c_msg_no_info_text_tl }
           {#1 \\\\ #2 \\\\ \c_msg_continue_text_tl }
       }
       {
-        \msg_interrupt_wrap:xx { \\ #3 }
+        \__msg_interrupt_wrap:nn { \\ #3 }
           {#1 \\\\ #2 \\\\ \c_msg_help_text_tl }
       }
   }
-\cs_new_protected:Npn \msg_interrupt_wrap:xx #1#2
+\cs_new_protected:Npn \__msg_interrupt_wrap:nn #1#2
   {
-    \iow_wrap:xnnnN {#1} { | ~ } { 2 } { } \msg_interrupt_more_text:n
-    \iow_wrap:xnnnN {#2} { ! ~ } { 2 } { } \msg_interrupt_text:n
+    \iow_wrap:nnnN {#1} { | ~ } { } \__msg_interrupt_more_text:n
+    \iow_wrap:nnnN {#2} { ! ~ } { } \__msg_interrupt_text:n
   }
-\cs_new_protected:Npn \msg_interrupt_more_text:n #1
+\cs_new_protected:Npn \__msg_interrupt_more_text:n #1
   {
     \exp_args:Nx \tex_errhelp:D
       {
@@ -175,13 +173,10 @@
   \char_set_lccode:nn {`\}} {`\ }
   \char_set_lccode:nn {`\&} {`\!}
   \char_set_catcode_active:N \&
-  \char_set_catcode_letter:N \.
-  \tl_new:N
-    \c_msg_hide_tl............................................
 \tl_to_lowercase:n
   {
     \group_end:
-    \cs_new_protected:Npn \msg_interrupt_text:n #1
+    \cs_new_protected:Npn \__msg_interrupt_text:n #1
       {
         \iow_term:x
           {
@@ -196,7 +191,8 @@
               \tex_errmessage:D
                 {
                   #1
-                  \c_msg_hide_tl............................................
+                  \use_none:n
+                    { ............................................ }
                 }
             }
           \exp_after:wN
@@ -204,347 +200,314 @@
         &
       }
   }
-\cs_new_protected:Npn \msg_log:x #1
+\cs_new_protected:Npn \msg_log:n #1
   {
-    \iow_log:x { ................................................. }
-    \iow_wrap:xnnnN { . ~ #1} { . ~ } { 2 } { }
-      \iow_log:x
-    \iow_log:x { ................................................. }
+    \iow_log:n { ................................................. }
+    \iow_wrap:nnnN { . ~ #1} { . ~ } { } \iow_log:n
+    \iow_log:n { ................................................. }
   }
-\cs_new_protected:Npn \msg_term:x #1
+\cs_new_protected:Npn \msg_term:n #1
   {
-    \iow_term:x { ************************************************* }
-    \iow_wrap:xnnnN { * ~ #1} { * ~ } { 2 } { }
-      \iow_term:x
-    \iow_term:x { ************************************************* }
+    \iow_term:n { ************************************************* }
+    \iow_wrap:nnnN { * ~ #1} { * ~ } { } \iow_term:n
+    \iow_term:n { ************************************************* }
   }
-\int_gset:Nn \tex_errorcontextlines:D { -1 }
 \cs_new:Npn \msg_fatal_text:n #1 { Fatal~#1~error }
 \cs_new:Npn \msg_critical_text:n #1 { Critical~#1~error }
 \cs_new:Npn \msg_error_text:n #1 { #1~error }
 \cs_new:Npn \msg_warning_text:n #1 { #1~warning }
 \cs_new:Npn \msg_info_text:n #1 { #1~info }
 \cs_new:Npn \msg_see_documentation_text:n #1
-  { \\ \\ See~the~#1~documentation~for~further~information. }
-\cs_new_protected:Npn \msg_class_set:nn #1#2
-  {
-    \prop_clear_new:c { l_msg_redirect_ #1 _prop }
-    \cs_set_protected:cpn { msg_ #1 :nnxxxx } ##1##2##3##4##5##6
-      { \msg_use:nnnnxxxx {#1} {#2} {##1} {##2} {##3} {##4} {##5} {##6} }
-    \cs_set_protected:cpx { msg_ #1 :nnxxx } ##1##2##3##4##5
-      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} {##5} { } }
-    \cs_set_protected:cpx { msg_ #1 :nnxx } ##1##2##3##4
-      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} { } { } }
-    \cs_set_protected:cpx { msg_ #1 :nnx } ##1##2##3
-      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} { } { } { } }
-    \cs_set_protected:cpx { msg_ #1 :nn } ##1##2
-      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} { } { } { } { } }
-  }
-\prg_new_conditional:Npnn \msg_if_more_text:N #1 { p , T , F , TF }
-  {
-    \cs_if_eq:NNTF #1 \msg_no_more_text:xxxx
-      { \prg_return_false:  }
-      { \prg_return_true: }
-  }
-\cs_new:Npn \msg_no_more_text:xxxx #1#2#3#4 { }
-\cs_generate_variant:Nn \msg_if_more_text_p:N { c }
-\cs_generate_variant:Nn \msg_if_more_text:NT  { c }
-\cs_generate_variant:Nn \msg_if_more_text:NF  { c }
-\cs_generate_variant:Nn \msg_if_more_text:NTF { c }
-\msg_class_set:nn { fatal }
   {
-    \msg_interrupt:xxx
-      { \msg_fatal_text:n {#1} : ~ "#2" }
-      {
-        \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
-        \msg_see_documentation_text:n {#1}
-      }
-      { \c_msg_fatal_text_tl }
-    \tex_end:D
+    \\ \\ See~the~
+    \str_if_eq:nnTF {#1} { LaTeX } { LaTeX3 } {#1} ~
+    documentation~for~further~information.
   }
-\msg_class_set:nn { critical }
+\group_begin:
+  \cs_set_protected:Npn \__msg_class_new:nn #1#2
+    {
+      \prop_new:c { l__msg_redirect_ #1 _prop }
+      \cs_new_protected:cpn { __msg_ #1 _code:nnnnnn } ##1##2##3##4##5##6 {#2}
+      \cs_new_protected:cpn { msg_ #1 :nnnnnn } ##1##2##3##4##5##6
+        {
+          \__msg_use:nnnnnnn {#1} {##1} {##2}
+            { \tl_to_str:n {##3} } { \tl_to_str:n {##4} }
+            { \tl_to_str:n {##5} } { \tl_to_str:n {##6} }
+        }
+      \cs_new_protected:cpx { msg_ #1 :nnnnn } ##1##2##3##4##5
+        { \exp_not:c { msg_ #1 :nnnnnn } {##1} {##2} {##3} {##4} {##5} { } }
+      \cs_new_protected:cpx { msg_ #1 :nnnn } ##1##2##3##4
+        { \exp_not:c { msg_ #1 :nnnnnn } {##1} {##2} {##3} {##4} { } { } }
+      \cs_new_protected:cpx { msg_ #1 :nnn } ##1##2##3
+        { \exp_not:c { msg_ #1 :nnnnnn } {##1} {##2} {##3} { } { } { } }
+      \cs_new_protected:cpx { msg_ #1 :nn } ##1##2
+        { \exp_not:c { msg_ #1 :nnnnnn } {##1} {##2} { } { } { } { } }
+      \cs_new_protected:cpn { msg_ #1 :nnxxxx } ##1##2##3##4##5##6
+        {
+          \use:x
+            {
+              \__msg_use:nnnnnnn
+                { \exp_not:n {#1} } { \exp_not:n {##1} } { \exp_not:n {##2} }
+                {##3} {##4} {##5} {##6}
+            }
+        }
+      \cs_new_protected:cpx { msg_ #1 :nnxxx } ##1##2##3##4##5
+        { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} {##5} { } }
+      \cs_new_protected:cpx { msg_ #1 :nnxx } ##1##2##3##4
+        { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} { } { } }
+      \cs_new_protected:cpx { msg_ #1 :nnx } ##1##2##3
+        { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} { } { } { } }
+    }
+  \__msg_class_new:nn { fatal }
+    {
+      \msg_interrupt:nnn
+        { \msg_fatal_text:n {#1} : ~ "#2" }
+        {
+          \use:c { \c__msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
+          \msg_see_documentation_text:n {#1}
+        }
+        { \c_msg_fatal_text_tl }
+      \tex_end:D
+    }
+  \__msg_class_new:nn { critical }
+    {
+      \msg_interrupt:nnn
+        { \msg_critical_text:n {#1} : ~ "#2" }
+        {
+          \use:c { \c__msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
+          \msg_see_documentation_text:n {#1}
+        }
+        { \c_msg_critical_text_tl }
+      \tex_endinput:D
+    }
+  \__msg_class_new:nn { error }
+    {
+      \__msg_error:cnnnnn
+        { \c__msg_more_text_prefix_tl #1 / #2 }
+        {#3} {#4} {#5} {#6}
+        {
+          \msg_interrupt:nnn
+            { \msg_error_text:n {#1} : ~ "#2" }
+            {
+              \use:c { \c__msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
+              \msg_see_documentation_text:n {#1}
+            }
+       }
+    }
+  \cs_new_protected:Npn \__msg_error:cnnnnn #1#2#3#4#5#6
+    {
+      \cs_if_eq:cNTF {#1} \__msg_no_more_text:nnnn
+        { #6 { } }
+        { #6 { \use:c {#1} {#2} {#3} {#4} {#5} } }
+    }
+  \cs_new:Npn \__msg_no_more_text:nnnn #1#2#3#4 { }
+  \__msg_class_new:nn { warning }
+    {
+      \msg_term:n
+        {
+          \msg_warning_text:n {#1} : ~ "#2" \\ \\
+          \use:c { \c__msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
+        }
+    }
+  \__msg_class_new:nn { info }
+    {
+      \msg_log:n
+        {
+          \msg_info_text:n {#1} : ~ "#2" \\ \\
+          \use:c { \c__msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
+        }
+    }
+  \__msg_class_new:nn { log }
+    {
+      \iow_wrap:nnnN
+        { \use:c { \c__msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6} }
+        { } { } \iow_log:n
+    }
+  \__msg_class_new:nn { none } { }
+\group_end:
+\cs_new:Npn \__msg_class_chk_exist:nT #1
   {
-    \msg_interrupt:xxx
-      { \msg_critical_text:n {#1} : ~ "#2" }
-      {
-        \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
-        \msg_see_documentation_text:n {#1}
-      }
-      { \c_msg_critical_text_tl }
-    \tex_endinput:D
+    \cs_if_free:cTF { __msg_ #1 _code:nnnnnn }
+      { \__msg_kernel_error:nnx { kernel } { message-class-unknown } {#1} }
   }
-\msg_class_set:nn { error }
+\tl_new:N \l__msg_class_tl
+\tl_new:N \l__msg_current_class_tl
+\prop_new:N \l__msg_redirect_prop
+\seq_new:N \l__msg_hierarchy_seq
+\seq_new:N \l__msg_class_loop_seq
+\cs_new_protected:Npn \__msg_use:nnnnnnn #1#2#3#4#5#6#7
   {
-    \msg_if_more_text:cTF { \c_msg_more_text_prefix_tl #1 / #2 }
+    \msg_if_exist:nnTF {#2} {#3}
       {
-        \msg_interrupt:xxx
-          { \msg_error_text:n {#1} : ~ "#2" }
+        \__msg_class_chk_exist:nT {#1}
           {
-            \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
-            \msg_see_documentation_text:n {#1}
-          }
-          { \use:c { \c_msg_more_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6} }
-     }
-     {
-        \msg_interrupt:xxx
-          { \msg_error_text:n {#1} : ~ "#2" }
-          {
-            \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
-            \msg_see_documentation_text:n {#1}
+            \tl_set:Nn \l__msg_current_class_tl {#1}
+            \cs_set_protected_nopar:Npx \__msg_use_code:
+              {
+                \exp_not:n
+                  {
+                    \use:c { __msg_ \l__msg_class_tl _code:nnnnnn }
+                      {#2} {#3} {#4} {#5} {#6} {#7}
+                  }
+              }
+            \__msg_use_redirect_name:n { #2 / #3 }
           }
-          { }
-     }
-  }
-\msg_class_set:nn { warning }
-  {
-    \msg_term:x
-      {
-        \msg_warning_text:n {#1} : ~ "#2" \\ \\
-        \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
       }
+      { \__msg_kernel_error:nnxx { kernel } { message-unknown } {#2} {#3} }
   }
-\msg_class_set:nn { info }
+\cs_new_protected_nopar:Npn \__msg_use_code: { }
+\cs_new_protected:Npn \__msg_use_redirect_name:n #1
   {
-    \msg_log:x
+    \prop_get:NnNTF \l__msg_redirect_prop { / #1 } \l__msg_class_tl
+      { \__msg_use_code: }
       {
-        \msg_info_text:n {#1} : ~ "#2" \\ \\
-        \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6}
+        \seq_clear:N \l__msg_hierarchy_seq
+        \__msg_use_hierarchy:nwwN { }
+          #1 \q_mark \__msg_use_hierarchy:nwwN
+          /  \q_mark \use_none_delimit_by_q_stop:w
+          \q_stop
+        \__msg_use_redirect_module:n { }
       }
   }
-\msg_class_set:nn { log }
+\cs_new_protected:Npn \__msg_use_hierarchy:nwwN #1#2 / #3 \q_mark #4
   {
-    \msg_log:x
-      { \use:c { \c_msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6} }
+    \seq_put_left:Nn \l__msg_hierarchy_seq {#1}
+    #4 { #1 / #2 } #3 \q_mark #4
   }
-\msg_class_set:nn { none } { }
-\tl_new:N \l_msg_class_tl
-\tl_new:N \l_msg_current_class_tl
-\prop_new:N \l_msg_redirect_classes_prop
-\prop_new:N \l_msg_redirect_names_prop
-\prop_new:N \l_msg_redirect_prop
-\bool_new:N \l_msg_use_direct_bool
-\cs_new_protected:Npn \msg_use:nnnnxxxx #1#2#3#4#5#6#7#8
+\cs_new_protected:Npn \__msg_use_redirect_module:n #1
   {
-    \msg_if_exist:nnTF {#3} {#4}
+    \seq_map_inline:Nn \l__msg_hierarchy_seq
       {
-        \cs_if_exist:cTF { msg_ #1 :nnxxxx }
+        \prop_get:cnNTF { l__msg_redirect_ \l__msg_current_class_tl _prop }
+          {##1} \l__msg_class_tl
           {
-            \tl_set:Nn \l_msg_current_class_tl {#1}
-            \cs_set_protected_nopar:Npx \msg_use_code: { \exp_not:n {#2} }
-            \cs_set_protected_nopar:Npn \msg_use_or_change_class:
+            \seq_map_break:n
               {
-                \tl_if_eq:NNTF \l_msg_current_class_tl \l_msg_class_tl
-                  { \msg_use_code: }
+                \tl_if_eq:NNTF \l__msg_current_class_tl \l__msg_class_tl
+                  { \__msg_use_code: }
                   {
-                    \use:c { msg_ \l_msg_class_tl :nnxxxx }
-                      {#3} {#4} {#5} {#6} {#7} {#8}
+                    \tl_set_eq:NN \l__msg_current_class_tl \l__msg_class_tl
+                    \__msg_use_redirect_module:n {##1}
                   }
               }
-            \bool_if:NTF \l_msg_use_direct_bool
+          }
+          {
+            \str_if_eq:nnT {##1} {#1}
               {
-                \bool_set_false:N \l_msg_use_direct_bool
-                \msg_use_code:
+                \tl_set_eq:NN \l__msg_class_tl \l__msg_current_class_tl
+                \seq_map_break:n { \__msg_use_code: }
               }
-              { \msg_use_aux_i:nn {#3} {#4} }
           }
-          { \msg_kernel_error:nnx { msg } { message-class-unknown } {#1} }
       }
-      { \msg_kernel_error:nnxx { msg } { message-unknown } {#3} {#4} }
   }
-\cs_new_protected_nopar:Npn \msg_use_code: { }
-\cs_new_protected_nopar:Npn \msg_use_or_change_class: { }
-\cs_new_protected:Npn \msg_use_aux_i:nn #1#2
+\cs_new_protected:Npn \msg_redirect_name:nnn #1#2#3
   {
-    \prop_get:NnNTF \l_msg_redirect_prop { #1 / #2 } \l_msg_class_tl
+    \tl_if_empty:nTF {#3}
+      { \prop_remove:Nn \l__msg_redirect_prop { / #1 / #2 } }
       {
-        \bool_set_true:N \l_msg_use_direct_bool
-        \msg_use_or_change_class:
+        \__msg_class_chk_exist:nT {#3}
+          { \prop_put:Nnn \l__msg_redirect_prop { / #1 / #2 } {#3} }
       }
-      { \msg_use_aux_ii:nn {#1} {#2} }
   }
-\cs_new_protected:Npn \msg_use_aux_ii:nn #1#2
+\cs_new_protected_nopar:Npn \msg_redirect_class:nn
+  { \__msg_redirect:nnn { } }
+\cs_new_protected:Npn \msg_redirect_module:nnn #1
+  { \__msg_redirect:nnn { / #1 } }
+\cs_new_protected:Npn \__msg_redirect:nnn #1#2#3
   {
-    \prop_get:coNTF { l_msg_redirect_ \l_msg_current_class_tl _ prop }
-      { \msg_use_aux_iii:w #1 / #2 / \q_stop } \l_msg_class_tl
-      { \msg_use_or_change_class: }
+    \__msg_class_chk_exist:nT {#2}
       {
-        \prop_get:coNTF { l_msg_redirect_ \l_msg_current_class_tl _ prop }
-          { \msg_use_aux_iv:w #1 / #2 \q_stop } \l_msg_class_tl
-        { \msg_use_or_change_class: }
-        { \msg_use_aux_v: }
-      }
-  }
-\cs_new:Npn \msg_use_aux_iii:w  #1 / #2 / #3 \q_stop { #1 / #2 }
-\cs_new:Npn \msg_use_aux_iv:w #1 / #2 \q_stop { #1 }
-\cs_new_protected:Npn \msg_use_aux_v:
-  {
-    \prop_get:cnNF { l_msg_redirect_ \l_msg_current_class_tl _ prop }
-      { * } \l_msg_class_tl
-      { \tl_set_eq:NN \l_msg_class_tl \l_msg_current_class_tl }
-    \msg_use_or_change_class:
-  }
-\cs_new_protected:Npn \msg_redirect_class:nn #1#2
-  {
-    \cs_if_exist:cTF { msg_ #1 :nnxxxx }
-      {
-        \cs_if_exist:cTF { msg_ #2 :nnxxxx }
+        \tl_if_empty:nTF {#3}
+          { \prop_remove:cn { l__msg_redirect_ #2 _prop } {#1} }
           {
-            \tl_set:Nn \l_msg_current_class_tl {#1}
-            \msg_redirect_class_aux:nnn {#1} {#2} {#2}
+            \__msg_class_chk_exist:nT {#3}
+              {
+                \prop_put:cnn { l__msg_redirect_ #2 _prop } {#1} {#3}
+                \tl_set:Nn \l__msg_current_class_tl {#2}
+                \seq_clear:N \l__msg_class_loop_seq
+                \__msg_redirect_loop_chk:nnn {#2} {#3} {#1}
+              }
           }
-          { \msg_kernel_error:nnx { msg } { message-class-unknown } {#2} }
       }
-      { \msg_kernel_error:nnx { msg } { message-class-unknown } {#1} }
   }
-\cs_new_protected:Npn \msg_redirect_class_aux:nnn #1#2#3
+\cs_new_protected:Npn \__msg_redirect_loop_chk:nnn #1#2#3
   {
-    \prop_get:cnNTF { l_msg_redirect_ #2 _prop } { * } \l_msg_class_tl
+    \seq_put_right:Nn \l__msg_class_loop_seq {#1}
+    \prop_get:cnNT { l__msg_redirect_ #1 _prop } {#3} \l__msg_class_tl
       {
-        \tl_if_eq:NNTF \l_msg_class_tl \l_msg_current_class_tl
-          { \msg_kernel_error:nnxx { msg } { message-loop } {#1} {#3} }
-          { \msg_redirect_class_aux:nVn {#1} \l_msg_class_tl {#3} }
-      }
-      { \prop_put:cnn { l_msg_redirect_ #1 _prop } { * } {#3} }
-  }
-\cs_generate_variant:Nn \msg_redirect_class_aux:nnn { nV }
-\cs_new_protected:Npn \msg_redirect_module:nnn #1#2#3
-  {
-    \cs_if_exist:cTF { msg_ #2 :nnxxxx }
-      {
-        \cs_if_exist:cTF { msg_ #3 :nnxxxx }
+        \str_if_eq_x:nnF { \l__msg_class_tl } {#1}
           {
-            \tl_set:Nn \l_msg_current_class_tl {#1}
-            \msg_redirect_module_aux:nnnn {#1} {#2} {#3} {#3}
+            \tl_if_eq:NNTF \l__msg_class_tl \l__msg_current_class_tl
+              {
+                \prop_put:cnn { l__msg_redirect_ #2 _prop } {#3} {#2}
+                \__msg_kernel_warning:nnxxxx { kernel } { message-redirect-loop }
+                  { \seq_item:Nn \l__msg_class_loop_seq { \c_one } }
+                  { \seq_item:Nn \l__msg_class_loop_seq { \c_two } }
+                  {#3}
+                  {
+                    \seq_map_function:NN \l__msg_class_loop_seq
+                      \__msg_redirect_loop_list:n
+                    { \seq_item:Nn \l__msg_class_loop_seq { \c_one } }
+                  }
+              }
+              { \__msg_redirect_loop_chk:onn \l__msg_class_tl {#2} {#3} }
           }
-          { \msg_kernel_error:nnx { msg } { message-class-unknown } {#3} }
-      }
-      { \msg_kernel_error:nnx { msg } { message-class-unknown } {#2} }
-  }
-\cs_new_protected:Npn \msg_redirect_module_aux:nnnn #1#2#3#4
-  {
-    \prop_get:cnNTF { l_msg_redirect_ #3 _prop } {#1} \l_msg_class_tl
-      {
-        \tl_if_eq:NNTF \l_msg_class_tl \l_msg_current_class_tl
-          { \msg_kernel_error:nnxx { msg } { message-loop } {#2} {#4} }
-          { \msg_redirect_moduel_aux:nVn {#1} {#2} \l_msg_class_tl {#4} }
       }
-      { \prop_put:cnn { l_msg_redirect_ #2 _prop } {#1} {#4} }
-  }
-\cs_generate_variant:Nn \msg_redirect_module_aux:nnnn { nnV }
-\cs_new_protected:Npn \msg_redirect_name:nnn #1#2#3
-  {
-    \cs_if_exist:cTF { msg_ #3 :nnxxxx }
-      { \prop_put:Nnn \l_msg_redirect_prop { #1 / #2 } {#3} }
-      { \msg_kernel_error:nnx { msg } { message-class-unknown } {#3} }
   }
-\cs_new_protected:Npn \msg_kernel_new:nnnn #1#2
+\cs_generate_variant:Nn \__msg_redirect_loop_chk:nnn { o }
+\cs_new:Npn \__msg_redirect_loop_list:n #1 { {#1} ~ => ~ }
+\cs_new_protected:Npn \__msg_kernel_new:nnnn #1#2
   { \msg_new:nnnn { LaTeX } { #1 / #2 } }
-\cs_new_protected:Npn \msg_kernel_new:nnn #1#2
+\cs_new_protected:Npn \__msg_kernel_new:nnn #1#2
   { \msg_new:nnn { LaTeX } { #1 / #2 } }
-\cs_new_protected:Npn \msg_kernel_set:nnnn #1#2
+\cs_new_protected:Npn \__msg_kernel_set:nnnn #1#2
   { \msg_set:nnnn { LaTeX } { #1 / #2 } }
-\cs_new_protected:Npn \msg_kernel_set:nnn #1#2
+\cs_new_protected:Npn \__msg_kernel_set:nnn #1#2
   { \msg_set:nnn { LaTeX } { #1 / #2 } }
-\cs_new_protected:Npn \msg_kernel_fatal:nnxxxx #1#2#3#4#5#6
-  {
-    \msg_interrupt:xxx
-      { \msg_fatal_text:n { LaTeX } : ~ "#1 / #2" }
-      {
-        \use:c { \c_msg_text_prefix_tl LaTeX / #1 / #2 }
-          {#3} {#4} {#5} {#6}
-        \msg_see_documentation_text:n { LaTeX3 }
-      }
-      { \c_msg_fatal_text_tl }
-    \tex_end:D
-  }
-\cs_new_protected:Npn \msg_kernel_fatal:nnxxx #1#2#3#4#5
-  {\msg_kernel_fatal:nnxxxx {#1} {#2} {#3} {#4} {#5} { } }
-\cs_new_protected:Npn \msg_kernel_fatal:nnxx #1#2#3#4
-  { \msg_kernel_fatal:nnxxxx {#1} {#2} {#3} {#4} { } { } }
-\cs_new_protected:Npn \msg_kernel_fatal:nnx #1#2#3
-  { \msg_kernel_fatal:nnxxxx {#1} {#2} {#3} { } { } { } }
-\cs_new_protected:Npn \msg_kernel_fatal:nn #1#2
-  { \msg_kernel_fatal:nnxxxx {#1} {#2} { } { } { } { } }
-\cs_new_protected:Npn \msg_kernel_error:nnxxxx #1#2#3#4#5#6
-  {
-    \msg_if_more_text:cTF { \c_msg_more_text_prefix_tl LaTeX / #1 / #2 }
-      {
-        \msg_interrupt:xxx
-          { \msg_error_text:n { LaTeX } : ~ " #1 / #2 " }
-          {
-            \use:c { \c_msg_text_prefix_tl LaTeX / #1 / #2 }
-              {#3} {#4} {#5} {#6}
-            \msg_see_documentation_text:n { LaTeX3 }
-          }
-          {
-            \use:c { \c_msg_more_text_prefix_tl LaTeX / #1 / #2 }
-              {#3} {#4} {#5} {#6}
-          }
-      }
-      {
-        \msg_interrupt:xxx
-          { \msg_error_text:n { LaTeX } : ~ " #1 / #2 " }
-          {
-            \use:c { \c_msg_text_prefix_tl LaTeX / #1 / #2 }
-              {#3} {#4} {#5} {#6}
-            \msg_see_documentation_text:n { LaTeX3 }
-          }
-          { }
-      }
-  }
-\cs_new_protected:Npn \msg_kernel_error:nnxxx #1#2#3#4#5
-  {\msg_kernel_error:nnxxxx {#1} {#2} {#3} {#4} {#5} { } }
-\cs_gset_protected:Npn \msg_kernel_error:nnxx #1#2#3#4
-  { \msg_kernel_error:nnxxxx {#1} {#2} {#3} {#4} { } { } }
-\cs_gset_protected:Npn \msg_kernel_error:nnx #1#2#3
-  { \msg_kernel_error:nnxxxx {#1} {#2} {#3} { } { } { } }
-\cs_gset_protected:Npn \msg_kernel_error:nn #1#2
-  { \msg_kernel_error:nnxxxx {#1} {#2} { } { } { } { } }
-\prop_new:N \l_msg_redirect_kernel_warning_prop
-\cs_new_protected:Npn \msg_kernel_warning:nnxxxx #1#2#3#4#5#6
-  {
-    \msg_use:nnnnxxxx { warning }
-      {
-        \msg_term:x
-          {
-            \msg_warning_text:n { LaTeX } : ~ " #1 / #2 " \\ \\
-            \use:c { \c_msg_text_prefix_tl LaTeX / #1 / #2 }
-              {#3} {#4} {#5} {#6}
-          }
-      }
-      { LaTeX } { #1 / #2 } {#3} {#4} {#5} {#6}
-  }
-\cs_new_protected:Npn \msg_kernel_warning:nnxxx #1#2#3#4#5
-  { \msg_kernel_warning:nnxxxx {#1} {#2} {#3} {#4} {#5} { } }
-\cs_new_protected:Npn \msg_kernel_warning:nnxx #1#2#3#4
-  { \msg_kernel_warning:nnxxxx {#1} {#2} {#3} {#4} { } { } }
-\cs_new_protected:Npn \msg_kernel_warning:nnx #1#2#3
-  { \msg_kernel_warning:nnxxxx {#1} {#2} {#3} { } { } { } }
-\cs_new_protected:Npn \msg_kernel_warning:nn #1#2
-  { \msg_kernel_warning:nnxxxx {#1} {#2} { } { } { } { } }
-\prop_new:N \l_msg_redirect_kernel_info_prop
-\cs_new_protected:Npn \msg_kernel_info:nnxxxx #1#2#3#4#5#6
-  {
-    \msg_use:nnnnxxxx { info }
-      {
-        \msg_log:x
-          {
-            \msg_info_text:n { LaTeX } : ~ " #1 / #2 " \\ \\
-            \use:c { \c_msg_text_prefix_tl LaTeX / #1 / #2 }
-              {#3} {#4} {#5} {#6}
-          }
-      }
-      { LaTeX } { #1 / #2 } {#3} {#4} {#5} {#6}
-  }
-\cs_new_protected:Npn \msg_kernel_info:nnxxx #1#2#3#4#5
-  { \msg_kernel_info:nnxxxx {#1} {#2} {#3} {#4} {#5} { } }
-\cs_new_protected:Npn \msg_kernel_info:nnxx #1#2#3#4
-  { \msg_kernel_info:nnxxxx {#1} {#2} {#3} {#4} { } { } }
-\cs_new_protected:Npn \msg_kernel_info:nnx #1#2#3
-  { \msg_kernel_info:nnxxxx {#1} {#2} {#3} { } { } { } }
-\cs_new_protected:Npn \msg_kernel_info:nn #1#2
-  { \msg_kernel_info:nnxxxx {#1} {#2} { } { } { } { } }
-\msg_kernel_new:nnnn { msg } { message-already-defined }
+\group_begin:
+  \cs_set_protected:Npn \__msg_kernel_class_new:nn #1
+    { \__msg_kernel_class_new_aux:nn { kernel_ #1 } }
+  \cs_set_protected:Npn \__msg_kernel_class_new_aux:nn #1#2
+    {
+      \cs_new_protected:cpn { __msg_ #1 :nnnnnn } ##1##2 {#2}
+      \cs_new_protected:cpx { __msg_ #1 :nnnnn } ##1##2##3##4##5
+        { \exp_not:c { __msg_ #1 :nnnnnn } {##1} {##2} {##3} {##4} {##5} { } }
+      \cs_new_protected:cpx { __msg_ #1 :nnnn } ##1##2##3##4
+        { \exp_not:c { __msg_ #1 :nnnnnn } {##1} {##2} {##3} {##4} { } { } }
+      \cs_new_protected:cpx { __msg_ #1 :nnn } ##1##2##3
+        { \exp_not:c { __msg_ #1 :nnnnnn } {##1} {##2} {##3} { } { } { } }
+      \cs_new_protected:cpx { __msg_ #1 :nn } ##1##2
+        { \exp_not:c { __msg_ #1 :nnnnnn } {##1} {##2} { } { } { } { } }
+      \cs_new_protected:cpx { __msg_ #1 :nnxxxx } ##1##2##3##4##5##6
+        {
+          \use:x
+            {
+              \exp_not:c { __msg_ #1 :nnnnnn }
+                { \exp_not:N \exp_not:n {##1} }
+                { \exp_not:N \exp_not:n {##2} }
+                {##3} {##4} {##5} {##6}
+            }
+        }
+      \cs_new_protected:cpx { __msg_ #1 :nnxxx } ##1##2##3##4##5
+        { \exp_not:c { __msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} {##5} { } }
+      \cs_new_protected:cpx { __msg_ #1 :nnxx } ##1##2##3##4
+        { \exp_not:c { __msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} { } { } }
+      \cs_new_protected:cpx { __msg_ #1 :nnx } ##1##2##3
+        { \exp_not:c { __msg_ #1 :nnxxxx } {##1} {##2} {##3} { } { } { } }
+    }
+  \__msg_kernel_class_new:nn { fatal }
+    { \__msg_fatal_code:nnnnnn { LaTeX } { #1 / #2 } }
+  \cs_undefine:N \__msg_kernel_error:nnxx
+  \cs_undefine:N \__msg_kernel_error:nnx
+  \cs_undefine:N \__msg_kernel_error:nn
+  \__msg_kernel_class_new:nn { error }
+    { \__msg_error_code:nnnnnn { LaTeX } { #1 / #2 } }
+  \__msg_kernel_class_new:nn { warning }
+    { \msg_warning:nnxxxx { LaTeX } { #1 / #2 } }
+  \__msg_kernel_class_new:nn { info }
+    { \msg_info:nnxxxx { LaTeX } { #1 / #2 } }
+\group_end:
+\__msg_kernel_new:nnnn { kernel } { message-already-defined }
   { Message~'#2'~for~module~'#1'~already~defined. }
   {
     \c_msg_coding_error_text_tl
@@ -552,37 +515,41 @@
     by~the~module~'#1':~this~message~already~exists.
     \c_msg_return_text_tl
   }
-\msg_kernel_new:nnnn { msg } { message-unknown }
+\__msg_kernel_new:nnnn { kernel } { message-unknown }
   { Unknown~message~'#2'~for~module~'#1'. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~was~asked~to~display~a~message~called~'#2'\\
-    by~the~module~'#1'~module:~this~message~does~not~exist.
+    by~the~module~'#1':~this~message~does~not~exist.
     \c_msg_return_text_tl
   }
-\msg_kernel_new:nnnn { msg } { message-class-unknown }
+\__msg_kernel_new:nnnn { kernel } { message-class-unknown }
   { Unknown~message~class~'#1'. }
   {
     LaTeX~has~been~asked~to~redirect~messages~to~a~class~'#1':\\
     this~was~never~defined.
     \c_msg_return_text_tl
   }
-\msg_kernel_new:nnnn { msg } { redirect-loop }
-  { Message~redirection~loop~for~message~class~'#1'. }
+\__msg_kernel_new:nnnn { kernel } { message-redirect-loop }
   {
-    LaTeX~has~been~asked~to~redirect~messages~in~an~infinite~loop.\\
-    The~original~message~here~has~been~lost.
-    \c_msg_return_text_tl
+    Message~redirection~loop~caused~by~ {#1} ~=>~ {#2}
+    \tl_if_empty:nF {#3} { ~for~module~' \use_none:n #3 ' } .
+  }
+  {
+    Adding~the~message~redirection~ {#1} ~=>~ {#2}
+    \tl_if_empty:nF {#3} { ~for~the~module~' \use_none:n #3 ' } ~
+    created~an~infinite~loop\\\\
+    \iow_indent:n { #4 \\\\ }
   }
-\msg_kernel_new:nnnn { kernel } { bad-number-of-arguments }
+\__msg_kernel_new:nnnn { kernel } { bad-number-of-arguments }
   { Function~'#1'~cannot~be~defined~with~#2~arguments. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~has~been~asked~to~define~a~function~'#1'~with~
-    #2~arguments. \\
+    #2~arguments.~
     TeX~allows~between~0~and~9~arguments~for~a~single~function.
   }
-\msg_kernel_new:nnnn { kernel } { command-already-defined }
+\__msg_kernel_new:nnnn { kernel } { command-already-defined }
   { Control~sequence~#1~already~defined. }
   {
     \c_msg_coding_error_text_tl
@@ -591,192 +558,239 @@
     The~current~meaning~is:\\
     \ \ #2
   }
-\msg_kernel_new:nnnn { kernel } { command-not-defined }
+\__msg_kernel_new:nnnn { kernel } { command-not-defined }
   { Control~sequence~#1~undefined. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~has~been~asked~to~use~a~command~#1,~but~this~has~not~
     been~defined~yet.
   }
-\msg_kernel_new:nnnn { kernel } { out-of-registers }
+\__msg_kernel_new:nnnn { kernel } { empty-search-pattern }
+  { Empty~search~pattern. }
+  {
+    \c_msg_coding_error_text_tl
+    LaTeX~has~been~asked~to~replace~an~empty~pattern~by~'#1':~that~
+    would~lead~to~an~infinite~loop!
+  }
+\__msg_kernel_new:nnnn { kernel } { out-of-registers }
   { No~room~for~a~new~#1. }
   {
     TeX~only~supports~\int_use:N \c_max_register_int \
     of~each~type.~All~the~#1~registers~have~been~used.~
     This~run~will~be~aborted~now.
   }
-\msg_kernel_new:nnnn { kernel } { variable-not-defined }
-  { Variable~#1~undefined. }
+\__msg_kernel_new:nnnn { kernel } { missing-colon }
+  { Function~'#1'~contains~no~':'. }
   {
     \c_msg_coding_error_text_tl
-    LaTeX~has~been~asked~to~show~a~variable~#1,~but~this~has~not~
-    been~defined~yet.
+    Code-level~functions~must~contain~':'~to~separate~the~
+    argument~specification~from~the~function~name.~This~is~
+    needed~when~defining~conditionals~or~when~building~a~
+    parameter~text~from~the~number~of~arguments~of~the~function.
   }
-\msg_kernel_new:nnnn { seq } { empty-sequence }
-  { Empty~sequence~#1. }
+\__msg_kernel_new:nnnn { kernel } { protected-predicate }
+  { Predicate~'#1'~must~be~expandable. }
   {
     \c_msg_coding_error_text_tl
-    LaTeX~has~been~asked~to~recover~an~entry~from~a~sequence~that~
-    has~no~content:~that~cannot~happen!
+    LaTeX~has~been~asked~to~define~'#1'~as~a~protected~predicate.~
+    Only~expandable~tests~can~have~a~predicate~version.
   }
-\msg_kernel_new:nnnn { tl } { empty-search-pattern }
-  { Empty~search~pattern. }
+\__msg_kernel_new:nnnn { kernel } { conditional-form-unknown }
+  { Conditional~form~'#1'~for~function~'#2'~unknown. }
   {
     \c_msg_coding_error_text_tl
-    LaTeX~has~been~asked~to~replace~an~empty~pattern~by~'#1':~that~%
-    would~lead~to~an~infinite~loop!
+    LaTeX~has~been~asked~to~define~the~conditional~form~'#1'~of~
+    the~function~'#2',~but~only~'TF',~'T',~'F',~and~'p'~forms~exist.
   }
-\msg_kernel_new:nnnn { scan } { already-defined }
+\__msg_kernel_new:nnnn { kernel } { scanmark-already-defined }
   { Scan~mark~#1~already~defined. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~has~been~asked~to~create~a~new~scan~mark~'#1'~
     but~this~name~has~already~been~used~for~a~scan~mark.
   }
-\msg_kernel_new:nnn { seq } { misused }
-  { A~sequence~was~misused. }
-\msg_kernel_new:nnn { kernel } { bad-var }
+\__msg_kernel_new:nnnn { kernel } { variable-not-defined }
+  { Variable~#1~undefined. }
+  {
+    \c_msg_coding_error_text_tl
+    LaTeX~has~been~asked~to~show~a~variable~#1,~but~this~has~not~
+    been~defined~yet.
+  }
+\__msg_kernel_new:nnnn { kernel } { variant-too-long }
+  { Variant~form~'#1'~longer~than~base~signature~of~'#2'. }
+  {
+    \c_msg_coding_error_text_tl
+    LaTeX~has~been~asked~to~create~a~variant~of~the~function~'#2'~
+    with~a~signature~starting~with~'#1',~but~that~is~longer~than~
+    the~signature~(part~after~the~colon)~of~'#2'.
+  }
+\__msg_kernel_new:nnn { kernel } { bad-variable }
   { Erroneous~variable~#1 used! }
-\msg_kernel_new:nnn { prg } { zero-step }
-  { Zero~step~size~for~stepwise~function~#1. }
-\msg_kernel_new:nnn { prg } { replicate-neg }
+\__msg_kernel_new:nnn { kernel } { misused-sequence }
+  { A~sequence~was~misused. }
+\__msg_kernel_new:nnn { kernel } { negative-replication }
   { Negative~argument~for~\prg_replicate:nn. }
-\msg_kernel_new:nnn { kernel } { unknown-comparison }
+\__msg_kernel_new:nnn { kernel } { unknown-comparison }
   { Relation~symbol~'#1'~unknown:~use~=,~<,~>,~==,~!=,~<=,~>=. }
-\msg_kernel_new:nnn { seq } { show }
+\__msg_kernel_new:nnn { kernel } { zero-step }
+  { Zero~step~size~for~step~function~#1. }
+\__msg_kernel_new:nnn { kernel } { show-clist }
   {
-    The~sequence~\token_to_str:N #1~
-    \seq_if_empty:NTF #1
+    The~comma~list~
+    \str_if_eq:nnF {#1} { \l__clist_internal_clist } { \token_to_str:N #1~}
+    \clist_if_empty:NTF #1
       { is~empty }
       { contains~the~items~(without~outer~braces): }
   }
-\msg_kernel_new:nnn { prop } { show }
+\__msg_kernel_new:nnn { kernel } { show-prop }
   {
     The~property~list~\token_to_str:N #1~
     \prop_if_empty:NTF #1
       { is~empty }
       { contains~the~pairs~(without~outer~braces): }
   }
-\msg_kernel_new:nnn { clist } { show }
+\__msg_kernel_new:nnn { kernel } { show-seq }
   {
-    The~comma~list~
-    \str_if_eq:nnF {#1} { \l_clist_internal_clist } { \token_to_str:N #1~}
-    \clist_if_empty:NTF #1
+    The~sequence~\token_to_str:N #1~
+    \seq_if_empty:NTF #1
       { is~empty }
       { contains~the~items~(without~outer~braces): }
   }
-\msg_kernel_new:nnn { ior } { show-no-stream }
-  { No~input~streams~are~open }
-\msg_kernel_new:nnn { ior } { show-open-streams }
-  { The~following~input~streams~are~in~use: }
-\msg_kernel_new:nnn { iow } { show-no-stream }
-  { No~output~streams~are~open }
-\msg_kernel_new:nnn { iow } { show-open-streams }
-  { The~following~output~streams~are~in~use: }
+\__msg_kernel_new:nnn { kernel } { show-no-stream }
+  { No~ #1 ~streams~are~open }
+\__msg_kernel_new:nnn { kernel } { show-open-streams }
+  { The~following~ #1 ~streams~are~in~use: }
 \group_begin:
 \char_set_catcode_math_superscript:N \^
-\char_set_lccode:nn {`^} {`\ }
-\char_set_lccode:nn {`L} {`L}
-\char_set_lccode:nn {`T} {`T}
-\char_set_lccode:nn {`X} {`X}
+\char_set_lccode:nn { `^ } { `\  }
+\char_set_lccode:nn { `L } { `L }
+\char_set_lccode:nn { `T } { `T }
+\char_set_lccode:nn { `X } { `X }
 \tl_to_lowercase:n
   {
-    \cs_new:Npx \msg_expandable_error:n #1
+    \cs_new:Npx \__msg_expandable_error:n #1
       {
         \exp_not:n
           {
             \tex_romannumeral:D
             \exp_after:wN \exp_after:wN
-            \exp_after:wN \msg_expandable_error_aux:w
+            \exp_after:wN \__msg_expandable_error:w
             \exp_after:wN \exp_after:wN
             \exp_after:wN \c_zero
           }
         \exp_not:N \use:n { \exp_not:c { LaTeX3~error: } ^ #1 } ^
       }
-    \cs_new:Npn \msg_expandable_error_aux:w #1 ^ #2 ^ { #1 }
+    \cs_new:Npn \__msg_expandable_error:w #1 ^ #2 ^ { #1 }
   }
 \group_end:
-\cs_new:Npn \msg_expandable_kernel_error:nnnnnn #1#2#3#4#5#6
+\cs_new:Npn \__msg_kernel_expandable_error:nnnnnn #1#2#3#4#5#6
   {
-    \exp_args:Nf \msg_expandable_error:n
+    \exp_args:Nf \__msg_expandable_error:n
       {
         \exp_args:NNc \exp_after:wN \exp_stop_f:
-          { \c_msg_text_prefix_tl LaTeX / #1 / #2 }
+          { \c__msg_text_prefix_tl LaTeX / #1 / #2 }
           {#3} {#4} {#5} {#6}
       }
   }
-\cs_new:Npn \msg_expandable_kernel_error:nnnnn #1#2#3#4#5
+\cs_new:Npn \__msg_kernel_expandable_error:nnnnn #1#2#3#4#5
   {
-    \msg_expandable_kernel_error:nnnnnn
+    \__msg_kernel_expandable_error:nnnnnn
       {#1} {#2} {#3} {#4} {#5} { }
   }
-\cs_new:Npn \msg_expandable_kernel_error:nnnn #1#2#3#4
+\cs_new:Npn \__msg_kernel_expandable_error:nnnn #1#2#3#4
   {
-    \msg_expandable_kernel_error:nnnnnn
+    \__msg_kernel_expandable_error:nnnnnn
       {#1} {#2} {#3} {#4} { } { }
   }
-\cs_new:Npn \msg_expandable_kernel_error:nnn #1#2#3
+\cs_new:Npn \__msg_kernel_expandable_error:nnn #1#2#3
   {
-    \msg_expandable_kernel_error:nnnnnn
+    \__msg_kernel_expandable_error:nnnnnn
       {#1} {#2} {#3} { } { } { }
   }
-\cs_new:Npn \msg_expandable_kernel_error:nn #1#2
+\cs_new:Npn \__msg_kernel_expandable_error:nn #1#2
   {
-    \msg_expandable_kernel_error:nnnnnn
+    \__msg_kernel_expandable_error:nnnnnn
       {#1} {#2} { } { } { } { }
   }
-\cs_new_protected:Npn \msg_aux_use:nn #1#2
-  { \msg_aux_use:nnxxxx {#1} {#2} { } { } { } { } }
-\cs_new_protected:Npn \msg_aux_use:nnxxxx #1#2#3#4#5#6
+\cs_new_protected:Npn \__msg_term:nnnnnn #1#2#3#4#5#6
   {
-    \iow_wrap:xnnnN
-      {
-        \use:c { \c_msg_text_prefix_tl #1 / #2 }
-          {#3} {#4} {#5} {#6}
-      }
-      { } \c_zero { } \iow_term:x
+    \iow_wrap:nnnN
+      { \use:c { \c__msg_text_prefix_tl #1 / #2 } {#3} {#4} {#5} {#6} }
+      { } { } \iow_term:n
   }
-\cs_new_protected:Npn \msg_aux_show:Nnx #1#2#3
+\cs_generate_variant:Nn \__msg_term:nnnnnn { nnnnnV }
+\cs_new_protected:Npn \__msg_term:nnnnn #1#2#3#4#5
+  { \__msg_term:nnnnnn {#1} {#2} {#3} {#4} {#5} { } }
+\cs_new_protected:Npn \__msg_term:nnn #1#2#3
+  { \__msg_term:nnnnnn {#1} {#2} {#3} { } { } { } }
+\cs_new_protected:Npn \__msg_term:nn #1#2
+  { \__msg_term:nnnnnn {#1} {#2} { } { } { } { } }
+\cs_new_protected:Npn \__msg_show_variable:Nnn #1#2#3
   {
     \cs_if_exist:NTF #1
       {
-        \msg_aux_use:nnxxxx { LaTeX / #2 } { show } {#1} { } { } { }
-        \msg_aux_show:x {#3}
+        \__msg_term:nnn { LaTeX / kernel } { show- #2 } {#1}
+        \__msg_show_variable:x {#3}
       }
       {
-        \msg_kernel_error:nnx { kernel } { variable-not-defined }
+        \__msg_kernel_error:nnx { kernel } { variable-not-defined }
           { \token_to_str:N #1 }
       }
   }
-\cs_new_protected:Npn \msg_aux_show:x #1
+\cs_generate_variant:Nn \__msg_show_variable:Nnn { Nnx }
+\cs_new_protected:Npn \__msg_show_variable:n #1
   {
-    \tl_set:Nx \l_msg_internal_tl {#1}
-    \tl_if_empty:NT \l_msg_internal_tl
-      { \tl_set:Nx \l_msg_internal_tl { > } }
-    \exp_args:Nf \etex_showtokens:D
+    \tl_set:Nn \l__msg_internal_tl {#1}
+    \tl_if_empty:NTF \l__msg_internal_tl
+      { \etex_showtokens:D \exp_after:wN { } }
       {
-        \exp_after:wN \exp_after:wN
-        \exp_after:wN \msg_aux_show:w
-        \exp_after:wN \l_msg_internal_tl
-        \exp_after:wN
+        \exp_args:Nf \etex_showtokens:D
+          {
+            \exp_after:wN \exp_after:wN
+            \exp_after:wN \__msg_show_variable:w
+            \exp_after:wN \l__msg_internal_tl
+          }
       }
-    \prg_do_nothing:
   }
-\cs_new:Npn \msg_aux_show:w #1 > { }
-\cs_new:Npn \msg_aux_show:n #1
+\cs_generate_variant:Nn \__msg_show_variable:n { x }
+\cs_new:Npn \__msg_show_variable:w #1 > { }
+\cs_new:Npn \__msg_show_item:n #1
   {
     \iow_newline: > \c_space_tl \c_space_tl { \exp_not:n {#1} }
   }
-\cs_new:Npn \msg_aux_show:nn #1#2
+\cs_new:Npn \__msg_show_item:nn #1#2
   {
     \iow_newline: > \c_space_tl \c_space_tl { \exp_not:n {#1} }
     \c_space_tl \c_space_tl => \c_space_tl \c_space_tl { \exp_not:n {#2} }
   }
-\cs_new:Npn \msg_aux_show_unbraced:nn #1#2
+\cs_new:Npn \__msg_show_item_unbraced:nn #1#2
   {
     \iow_newline: > \c_space_tl \c_space_tl \exp_not:n {#1}
     \c_space_tl \c_space_tl => \c_space_tl \c_space_tl \exp_not:n {#2}
   }
+\cs_new_nopar:Npn \msg_newline: { ^^J }
+\cs_new_nopar:Npn \msg_two_newlines: { ^^J ^^J }
+\cs_generate_variant:Nn \msg_log:n { x }
+\cs_generate_variant:Nn \msg_term:n { x }
+\cs_generate_variant:Nn \msg_interrupt:nnn { xxx }
+\cs_new_protected:Npn \msg_class_set:nn #1#2
+  {
+    \cs_if_exist:cTF { __msg_ #1 _code:nnnnnn }
+      \cs_set_protected:cpn
+      \cs_new_protected:cpn
+        { __msg_ #1 _code:nnnnnn } ##1##2##3##4##5##6 {#2}
+    \prop_clear_new:c { l__msg_redirect_ #1 _prop }
+    \cs_set_protected_nopar:cpn { msg_ #1 :nnxxxx }
+      { \__msg_use:nnnnnnn {#1} }
+    \cs_set_protected:cpx { msg_ #1 :nnxxx } ##1##2##3##4##5
+      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} {##5} { } }
+    \cs_set_protected:cpx { msg_ #1 :nnxx } ##1##2##3##4
+      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} {##4} { } { } }
+    \cs_set_protected:cpx { msg_ #1 :nnx } ##1##2##3
+      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} {##3} { } { } { } }
+    \cs_set_protected:cpx { msg_ #1 :nn } ##1##2
+      { \exp_not:c { msg_ #1 :nnxxxx } {##1} {##2} { } { } { } { } }
+  }
 %% 
 %%
 %% End of file `l3msg.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3names.sty b/Master/texmf-dist/tex/latex/l3kernel/l3names.sty
index fee26c9e876..660aa9e659b 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3names.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3names.sty
@@ -13,7 +13,7 @@
 %% 
 %% Do not distribute a modified version of this file.
 %% 
-%% File: l3names.dtx Copyright (C) 1990-2011 The LaTeX3 project
+%% File: l3names.dtx Copyright (C) 1990-2012 The LaTeX3 project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -45,443 +45,443 @@
 %%   prior consultation with the LaTeX3 Project.
 %%
 %% -----------------------------------------------------------------------
-\RequirePackage{l3bootstrap}[2011-12-29]
-\GetIdInfo$Id: l3names.dtx 3494 2012-03-04 09:58:29Z joseph $
-  {L3 Experimental namespace for primitives}
+\RequirePackage{l3bootstrap}[2012/07/15]
+\GetIdInfo$Id: l3names.dtx 3990 2012-07-16 07:46:03Z joseph $
+  {L3 Namespace for primitives}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
 \let \tex_global:D \global
 \let \tex_let:D    \let
 \begingroup
-  \long \def \name_primitive:NN #1#2
+  \long \def \__expl_primitive:NN #1#2
     {
       \tex_global:D \tex_let:D #2 #1
     }
-  \name_primitive:NN \                      \tex_space:D
-  \name_primitive:NN \/                     \tex_italiccor:D
-  \name_primitive:NN \-                     \tex_hyphen:D
-  \name_primitive:NN \let                   \tex_let:D
-  \name_primitive:NN \def                   \tex_def:D
-  \name_primitive:NN \edef                  \tex_edef:D
-  \name_primitive:NN \gdef                  \tex_gdef:D
-  \name_primitive:NN \xdef                  \tex_xdef:D
-  \name_primitive:NN \chardef               \tex_chardef:D
-  \name_primitive:NN \countdef              \tex_countdef:D
-  \name_primitive:NN \dimendef              \tex_dimendef:D
-  \name_primitive:NN \skipdef               \tex_skipdef:D
-  \name_primitive:NN \muskipdef             \tex_muskipdef:D
-  \name_primitive:NN \mathchardef           \tex_mathchardef:D
-  \name_primitive:NN \toksdef               \tex_toksdef:D
-  \name_primitive:NN \futurelet             \tex_futurelet:D
-  \name_primitive:NN \advance               \tex_advance:D
-  \name_primitive:NN \divide                \tex_divide:D
-  \name_primitive:NN \multiply              \tex_multiply:D
-  \name_primitive:NN \font                  \tex_font:D
-  \name_primitive:NN \fam                   \tex_fam:D
-  \name_primitive:NN \global                \tex_global:D
-  \name_primitive:NN \long                  \tex_long:D
-  \name_primitive:NN \outer                 \tex_outer:D
-  \name_primitive:NN \setlanguage           \tex_setlanguage:D
-  \name_primitive:NN \globaldefs            \tex_globaldefs:D
-  \name_primitive:NN \afterassignment       \tex_afterassignment:D
-  \name_primitive:NN \aftergroup            \tex_aftergroup:D
-  \name_primitive:NN \expandafter           \tex_expandafter:D
-  \name_primitive:NN \noexpand              \tex_noexpand:D
-  \name_primitive:NN \begingroup            \tex_begingroup:D
-  \name_primitive:NN \endgroup              \tex_endgroup:D
-  \name_primitive:NN \halign                \tex_halign:D
-  \name_primitive:NN \valign                \tex_valign:D
-  \name_primitive:NN \cr                    \tex_cr:D
-  \name_primitive:NN \crcr                  \tex_crcr:D
-  \name_primitive:NN \noalign               \tex_noalign:D
-  \name_primitive:NN \omit                  \tex_omit:D
-  \name_primitive:NN \span                  \tex_span:D
-  \name_primitive:NN \tabskip               \tex_tabskip:D
-  \name_primitive:NN \everycr               \tex_everycr:D
-  \name_primitive:NN \if                    \tex_if:D
-  \name_primitive:NN \ifcase                \tex_ifcase:D
-  \name_primitive:NN \ifcat                 \tex_ifcat:D
-  \name_primitive:NN \ifnum                 \tex_ifnum:D
-  \name_primitive:NN \ifodd                 \tex_ifodd:D
-  \name_primitive:NN \ifdim                 \tex_ifdim:D
-  \name_primitive:NN \ifeof                 \tex_ifeof:D
-  \name_primitive:NN \ifhbox                \tex_ifhbox:D
-  \name_primitive:NN \ifvbox                \tex_ifvbox:D
-  \name_primitive:NN \ifvoid                \tex_ifvoid:D
-  \name_primitive:NN \ifx                   \tex_ifx:D
-  \name_primitive:NN \iffalse               \tex_iffalse:D
-  \name_primitive:NN \iftrue                \tex_iftrue:D
-  \name_primitive:NN \ifhmode               \tex_ifhmode:D
-  \name_primitive:NN \ifmmode               \tex_ifmmode:D
-  \name_primitive:NN \ifvmode               \tex_ifvmode:D
-  \name_primitive:NN \ifinner               \tex_ifinner:D
-  \name_primitive:NN \else                  \tex_else:D
-  \name_primitive:NN \fi                    \tex_fi:D
-  \name_primitive:NN \or                    \tex_or:D
-  \name_primitive:NN \immediate             \tex_immediate:D
-  \name_primitive:NN \closeout              \tex_closeout:D
-  \name_primitive:NN \openin                \tex_openin:D
-  \name_primitive:NN \openout               \tex_openout:D
-  \name_primitive:NN \read                  \tex_read:D
-  \name_primitive:NN \write                 \tex_write:D
-  \name_primitive:NN \closein               \tex_closein:D
-  \name_primitive:NN \newlinechar           \tex_newlinechar:D
-  \name_primitive:NN \input                 \tex_input:D
-  \name_primitive:NN \endinput              \tex_endinput:D
-  \name_primitive:NN \inputlineno           \tex_inputlineno:D
-  \name_primitive:NN \errmessage            \tex_errmessage:D
-  \name_primitive:NN \message               \tex_message:D
-  \name_primitive:NN \show                  \tex_show:D
-  \name_primitive:NN \showthe               \tex_showthe:D
-  \name_primitive:NN \showbox               \tex_showbox:D
-  \name_primitive:NN \showlists             \tex_showlists:D
-  \name_primitive:NN \errhelp               \tex_errhelp:D
-  \name_primitive:NN \errorcontextlines     \tex_errorcontextlines:D
-  \name_primitive:NN \tracingcommands       \tex_tracingcommands:D
-  \name_primitive:NN \tracinglostchars      \tex_tracinglostchars:D
-  \name_primitive:NN \tracingmacros         \tex_tracingmacros:D
-  \name_primitive:NN \tracingonline         \tex_tracingonline:D
-  \name_primitive:NN \tracingoutput         \tex_tracingoutput:D
-  \name_primitive:NN \tracingpages          \tex_tracingpages:D
-  \name_primitive:NN \tracingparagraphs     \tex_tracingparagraphs:D
-  \name_primitive:NN \tracingrestores       \tex_tracingrestores:D
-  \name_primitive:NN \tracingstats          \tex_tracingstats:D
-  \name_primitive:NN \pausing               \tex_pausing:D
-  \name_primitive:NN \showboxbreadth        \tex_showboxbreadth:D
-  \name_primitive:NN \showboxdepth          \tex_showboxdepth:D
-  \name_primitive:NN \batchmode             \tex_batchmode:D
-  \name_primitive:NN \errorstopmode         \tex_errorstopmode:D
-  \name_primitive:NN \nonstopmode           \tex_nonstopmode:D
-  \name_primitive:NN \scrollmode            \tex_scrollmode:D
-  \name_primitive:NN \end                   \tex_end:D
-  \name_primitive:NN \csname                \tex_csname:D
-  \name_primitive:NN \endcsname             \tex_endcsname:D
-  \name_primitive:NN \ignorespaces          \tex_ignorespaces:D
-  \name_primitive:NN \relax                 \tex_relax:D
-  \name_primitive:NN \the                   \tex_the:D
-  \name_primitive:NN \mag                   \tex_mag:D
-  \name_primitive:NN \language              \tex_language:D
-  \name_primitive:NN \mark                  \tex_mark:D
-  \name_primitive:NN \topmark               \tex_topmark:D
-  \name_primitive:NN \firstmark             \tex_firstmark:D
-  \name_primitive:NN \botmark               \tex_botmark:D
-  \name_primitive:NN \splitfirstmark        \tex_splitfirstmark:D
-  \name_primitive:NN \splitbotmark          \tex_splitbotmark:D
-  \name_primitive:NN \fontname              \tex_fontname:D
-  \name_primitive:NN \escapechar            \tex_escapechar:D
-  \name_primitive:NN \endlinechar           \tex_endlinechar:D
-  \name_primitive:NN \mathchoice            \tex_mathchoice:D
-  \name_primitive:NN \delimiter             \tex_delimiter:D
-  \name_primitive:NN \mathaccent            \tex_mathaccent:D
-  \name_primitive:NN \mathchar              \tex_mathchar:D
-  \name_primitive:NN \mskip                 \tex_mskip:D
-  \name_primitive:NN \radical               \tex_radical:D
-  \name_primitive:NN \vcenter               \tex_vcenter:D
-  \name_primitive:NN \mkern                 \tex_mkern:D
-  \name_primitive:NN \above                 \tex_above:D
-  \name_primitive:NN \abovewithdelims       \tex_abovewithdelims:D
-  \name_primitive:NN \atop                  \tex_atop:D
-  \name_primitive:NN \atopwithdelims        \tex_atopwithdelims:D
-  \name_primitive:NN \over                  \tex_over:D
-  \name_primitive:NN \overwithdelims        \tex_overwithdelims:D
-  \name_primitive:NN \displaystyle          \tex_displaystyle:D
-  \name_primitive:NN \textstyle             \tex_textstyle:D
-  \name_primitive:NN \scriptstyle           \tex_scriptstyle:D
-  \name_primitive:NN \scriptscriptstyle     \tex_scriptscriptstyle:D
-  \name_primitive:NN \nonscript             \tex_nonscript:D
-  \name_primitive:NN \eqno                  \tex_eqno:D
-  \name_primitive:NN \leqno                 \tex_leqno:D
-  \name_primitive:NN \abovedisplayshortskip \tex_abovedisplayshortskip:D
-  \name_primitive:NN \abovedisplayskip      \tex_abovedisplayskip:D
-  \name_primitive:NN \belowdisplayshortskip \tex_belowdisplayshortskip:D
-  \name_primitive:NN \belowdisplayskip      \tex_belowdisplayskip:D
-  \name_primitive:NN \displaywidowpenalty   \tex_displaywidowpenalty:D
-  \name_primitive:NN \displayindent         \tex_displayindent:D
-  \name_primitive:NN \displaywidth          \tex_displaywidth:D
-  \name_primitive:NN \everydisplay          \tex_everydisplay:D
-  \name_primitive:NN \predisplaysize        \tex_predisplaysize:D
-  \name_primitive:NN \predisplaypenalty     \tex_predisplaypenalty:D
-  \name_primitive:NN \postdisplaypenalty    \tex_postdisplaypenalty:D
-  \name_primitive:NN \mathbin               \tex_mathbin:D
-  \name_primitive:NN \mathclose             \tex_mathclose:D
-  \name_primitive:NN \mathinner             \tex_mathinner:D
-  \name_primitive:NN \mathop                \tex_mathop:D
-  \name_primitive:NN \displaylimits         \tex_displaylimits:D
-  \name_primitive:NN \limits                \tex_limits:D
-  \name_primitive:NN \nolimits              \tex_nolimits:D
-  \name_primitive:NN \mathopen              \tex_mathopen:D
-  \name_primitive:NN \mathord               \tex_mathord:D
-  \name_primitive:NN \mathpunct             \tex_mathpunct:D
-  \name_primitive:NN \mathrel               \tex_mathrel:D
-  \name_primitive:NN \overline              \tex_overline:D
-  \name_primitive:NN \underline             \tex_underline:D
-  \name_primitive:NN \left                  \tex_left:D
-  \name_primitive:NN \right                 \tex_right:D
-  \name_primitive:NN \binoppenalty          \tex_binoppenalty:D
-  \name_primitive:NN \relpenalty            \tex_relpenalty:D
-  \name_primitive:NN \delimitershortfall    \tex_delimitershortfall:D
-  \name_primitive:NN \delimiterfactor       \tex_delimiterfactor:D
-  \name_primitive:NN \nulldelimiterspace    \tex_nulldelimiterspace:D
-  \name_primitive:NN \everymath             \tex_everymath:D
-  \name_primitive:NN \mathsurround          \tex_mathsurround:D
-  \name_primitive:NN \medmuskip             \tex_medmuskip:D
-  \name_primitive:NN \thinmuskip            \tex_thinmuskip:D
-  \name_primitive:NN \thickmuskip           \tex_thickmuskip:D
-  \name_primitive:NN \scriptspace           \tex_scriptspace:D
-  \name_primitive:NN \noboundary            \tex_noboundary:D
-  \name_primitive:NN \accent                \tex_accent:D
-  \name_primitive:NN \char                  \tex_char:D
-  \name_primitive:NN \discretionary         \tex_discretionary:D
-  \name_primitive:NN \hfil                  \tex_hfil:D
-  \name_primitive:NN \hfilneg               \tex_hfilneg:D
-  \name_primitive:NN \hfill                 \tex_hfill:D
-  \name_primitive:NN \hskip                 \tex_hskip:D
-  \name_primitive:NN \hss                   \tex_hss:D
-  \name_primitive:NN \vfil                  \tex_vfil:D
-  \name_primitive:NN \vfilneg               \tex_vfilneg:D
-  \name_primitive:NN \vfill                 \tex_vfill:D
-  \name_primitive:NN \vskip                 \tex_vskip:D
-  \name_primitive:NN \vss                   \tex_vss:D
-  \name_primitive:NN \unskip                \tex_unskip:D
-  \name_primitive:NN \kern                  \tex_kern:D
-  \name_primitive:NN \unkern                \tex_unkern:D
-  \name_primitive:NN \hrule                 \tex_hrule:D
-  \name_primitive:NN \vrule                 \tex_vrule:D
-  \name_primitive:NN \leaders               \tex_leaders:D
-  \name_primitive:NN \cleaders              \tex_cleaders:D
-  \name_primitive:NN \xleaders              \tex_xleaders:D
-  \name_primitive:NN \lastkern              \tex_lastkern:D
-  \name_primitive:NN \lastskip              \tex_lastskip:D
-  \name_primitive:NN \indent                \tex_indent:D
-  \name_primitive:NN \par                   \tex_par:D
-  \name_primitive:NN \noindent              \tex_noindent:D
-  \name_primitive:NN \vadjust               \tex_vadjust:D
-  \name_primitive:NN \baselineskip          \tex_baselineskip:D
-  \name_primitive:NN \lineskip              \tex_lineskip:D
-  \name_primitive:NN \lineskiplimit         \tex_lineskiplimit:D
-  \name_primitive:NN \clubpenalty           \tex_clubpenalty:D
-  \name_primitive:NN \widowpenalty          \tex_widowpenalty:D
-  \name_primitive:NN \exhyphenpenalty       \tex_exhyphenpenalty:D
-  \name_primitive:NN \hyphenpenalty         \tex_hyphenpenalty:D
-  \name_primitive:NN \linepenalty           \tex_linepenalty:D
-  \name_primitive:NN \doublehyphendemerits  \tex_doublehyphendemerits:D
-  \name_primitive:NN \finalhyphendemerits   \tex_finalhyphendemerits:D
-  \name_primitive:NN \adjdemerits           \tex_adjdemerits:D
-  \name_primitive:NN \hangafter             \tex_hangafter:D
-  \name_primitive:NN \hangindent            \tex_hangindent:D
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-  \name_primitive:NN \hsize                 \tex_hsize:D
-  \name_primitive:NN \lefthyphenmin         \tex_lefthyphenmin:D
-  \name_primitive:NN \righthyphenmin        \tex_righthyphenmin:D
-  \name_primitive:NN \leftskip              \tex_leftskip:D
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-  \name_primitive:NN \looseness             \tex_looseness:D
-  \name_primitive:NN \parskip               \tex_parskip:D
-  \name_primitive:NN \parindent             \tex_parindent:D
-  \name_primitive:NN \uchyph                \tex_uchyph:D
-  \name_primitive:NN \emergencystretch      \tex_emergencystretch:D
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-  \name_primitive:NN \tolerance             \tex_tolerance:D
-  \name_primitive:NN \spaceskip             \tex_spaceskip:D
-  \name_primitive:NN \xspaceskip            \tex_xspaceskip:D
-  \name_primitive:NN \parfillskip           \tex_parfillskip:D
-  \name_primitive:NN \everypar              \tex_everypar:D
-  \name_primitive:NN \prevgraf              \tex_prevgraf:D
-  \name_primitive:NN \spacefactor           \tex_spacefactor:D
-  \name_primitive:NN \shipout               \tex_shipout:D
-  \name_primitive:NN \vsize                 \tex_vsize:D
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-  \name_primitive:NN \brokenpenalty         \tex_brokenpenalty:D
-  \name_primitive:NN \topskip               \tex_topskip:D
-  \name_primitive:NN \maxdeadcycles         \tex_maxdeadcycles:D
-  \name_primitive:NN \maxdepth              \tex_maxdepth:D
-  \name_primitive:NN \output                \tex_output:D
-  \name_primitive:NN \deadcycles            \tex_deadcycles:D
-  \name_primitive:NN \pagedepth             \tex_pagedepth:D
-  \name_primitive:NN \pagestretch           \tex_pagestretch:D
-  \name_primitive:NN \pagefilstretch        \tex_pagefilstretch:D
-  \name_primitive:NN \pagefillstretch       \tex_pagefillstretch:D
-  \name_primitive:NN \pagefilllstretch      \tex_pagefilllstretch:D
-  \name_primitive:NN \pageshrink            \tex_pageshrink:D
-  \name_primitive:NN \pagegoal              \tex_pagegoal:D
-  \name_primitive:NN \pagetotal             \tex_pagetotal:D
-  \name_primitive:NN \outputpenalty         \tex_outputpenalty:D
-  \name_primitive:NN \hoffset               \tex_hoffset:D
-  \name_primitive:NN \voffset               \tex_voffset:D
-  \name_primitive:NN \insert                \tex_insert:D
-  \name_primitive:NN \holdinginserts        \tex_holdinginserts:D
-  \name_primitive:NN \floatingpenalty       \tex_floatingpenalty:D
-  \name_primitive:NN \insertpenalties       \tex_insertpenalties:D
-  \name_primitive:NN \lower                 \tex_lower:D
-  \name_primitive:NN \moveleft              \tex_moveleft:D
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-  \name_primitive:NN \raise                 \tex_raise:D
-  \name_primitive:NN \copy                  \tex_copy:D
-  \name_primitive:NN \lastbox               \tex_lastbox:D
-  \name_primitive:NN \vsplit                \tex_vsplit:D
-  \name_primitive:NN \unhbox                \tex_unhbox:D
-  \name_primitive:NN \unhcopy               \tex_unhcopy:D
-  \name_primitive:NN \unvbox                \tex_unvbox:D
-  \name_primitive:NN \unvcopy               \tex_unvcopy:D
-  \name_primitive:NN \setbox                \tex_setbox:D
-  \name_primitive:NN \hbox                  \tex_hbox:D
-  \name_primitive:NN \vbox                  \tex_vbox:D
-  \name_primitive:NN \vtop                  \tex_vtop:D
-  \name_primitive:NN \prevdepth             \tex_prevdepth:D
-  \name_primitive:NN \badness               \tex_badness:D
-  \name_primitive:NN \hbadness              \tex_hbadness:D
-  \name_primitive:NN \vbadness              \tex_vbadness:D
-  \name_primitive:NN \hfuzz                 \tex_hfuzz:D
-  \name_primitive:NN \vfuzz                 \tex_vfuzz:D
-  \name_primitive:NN \overfullrule          \tex_overfullrule:D
-  \name_primitive:NN \boxmaxdepth           \tex_boxmaxdepth:D
-  \name_primitive:NN \splitmaxdepth         \tex_splitmaxdepth:D
-  \name_primitive:NN \splittopskip          \tex_splittopskip:D
-  \name_primitive:NN \everyhbox             \tex_everyhbox:D
-  \name_primitive:NN \everyvbox             \tex_everyvbox:D
-  \name_primitive:NN \nullfont              \tex_nullfont:D
-  \name_primitive:NN \textfont              \tex_textfont:D
-  \name_primitive:NN \scriptfont            \tex_scriptfont:D
-  \name_primitive:NN \scriptscriptfont      \tex_scriptscriptfont:D
-  \name_primitive:NN \fontdimen             \tex_fontdimen:D
-  \name_primitive:NN \hyphenchar            \tex_hyphenchar:D
-  \name_primitive:NN \skewchar              \tex_skewchar:D
-  \name_primitive:NN \defaulthyphenchar     \tex_defaulthyphenchar:D
-  \name_primitive:NN \defaultskewchar       \tex_defaultskewchar:D
-  \name_primitive:NN \number                \tex_number:D
-  \name_primitive:NN \romannumeral          \tex_romannumeral:D
-  \name_primitive:NN \string                \tex_string:D
-  \name_primitive:NN \lowercase             \tex_lowercase:D
-  \name_primitive:NN \uppercase             \tex_uppercase:D
-  \name_primitive:NN \meaning               \tex_meaning:D
-  \name_primitive:NN \penalty               \tex_penalty:D
-  \name_primitive:NN \unpenalty             \tex_unpenalty:D
-  \name_primitive:NN \lastpenalty           \tex_lastpenalty:D
-  \name_primitive:NN \special               \tex_special:D
-  \name_primitive:NN \dump                  \tex_dump:D
-  \name_primitive:NN \patterns              \tex_patterns:D
-  \name_primitive:NN \hyphenation           \tex_hyphenation:D
-  \name_primitive:NN \time                  \tex_time:D
-  \name_primitive:NN \day                   \tex_day:D
-  \name_primitive:NN \month                 \tex_month:D
-  \name_primitive:NN \year                  \tex_year:D
-  \name_primitive:NN \jobname               \tex_jobname:D
-  \name_primitive:NN \everyjob              \tex_everyjob:D
-  \name_primitive:NN \count                 \tex_count:D
-  \name_primitive:NN \dimen                 \tex_dimen:D
-  \name_primitive:NN \skip                  \tex_skip:D
-  \name_primitive:NN \toks                  \tex_toks:D
-  \name_primitive:NN \muskip                \tex_muskip:D
-  \name_primitive:NN \box                   \tex_box:D
-  \name_primitive:NN \wd                    \tex_wd:D
-  \name_primitive:NN \ht                    \tex_ht:D
-  \name_primitive:NN \dp                    \tex_dp:D
-  \name_primitive:NN \catcode               \tex_catcode:D
-  \name_primitive:NN \delcode               \tex_delcode:D
-  \name_primitive:NN \sfcode                \tex_sfcode:D
-  \name_primitive:NN \lccode                \tex_lccode:D
-  \name_primitive:NN \uccode                \tex_uccode:D
-  \name_primitive:NN \mathcode              \tex_mathcode:D
-  \name_primitive:NN \ifdefined             \etex_ifdefined:D
-  \name_primitive:NN \ifcsname              \etex_ifcsname:D
-  \name_primitive:NN \unless                \etex_unless:D
-  \name_primitive:NN \eTeXversion           \etex_eTeXversion:D
-  \name_primitive:NN \eTeXrevision          \etex_eTeXrevision:D
-  \name_primitive:NN \marks                 \etex_marks:D
-  \name_primitive:NN \topmarks              \etex_topmarks:D
-  \name_primitive:NN \firstmarks            \etex_firstmarks:D
-  \name_primitive:NN \botmarks              \etex_botmarks:D
-  \name_primitive:NN \splitfirstmarks       \etex_splitfirstmarks:D
-  \name_primitive:NN \splitbotmarks         \etex_splitbotmarks:D
-  \name_primitive:NN \unexpanded            \etex_unexpanded:D
-  \name_primitive:NN \detokenize            \etex_detokenize:D
-  \name_primitive:NN \scantokens            \etex_scantokens:D
-  \name_primitive:NN \showtokens            \etex_showtokens:D
-  \name_primitive:NN \readline              \etex_readline:D
-  \name_primitive:NN \tracingassigns        \etex_tracingassigns:D
-  \name_primitive:NN \tracingscantokens     \etex_tracingscantokens:D
-  \name_primitive:NN \tracingnesting        \etex_tracingnesting:D
-  \name_primitive:NN \tracingifs            \etex_tracingifs:D
-  \name_primitive:NN \currentiflevel        \etex_currentiflevel:D
-  \name_primitive:NN \currentifbranch       \etex_currentifbranch:D
-  \name_primitive:NN \currentiftype         \etex_currentiftype:D
-  \name_primitive:NN \tracinggroups         \etex_tracinggroups:D
-  \name_primitive:NN \currentgrouplevel     \etex_currentgrouplevel:D
-  \name_primitive:NN \currentgrouptype      \etex_currentgrouptype:D
-  \name_primitive:NN \showgroups            \etex_showgroups:D
-  \name_primitive:NN \showifs               \etex_showifs:D
-  \name_primitive:NN \interactionmode       \etex_interactionmode:D
-  \name_primitive:NN \lastnodetype          \etex_lastnodetype:D
-  \name_primitive:NN \iffontchar            \etex_iffontchar:D
-  \name_primitive:NN \fontcharht            \etex_fontcharht:D
-  \name_primitive:NN \fontchardp            \etex_fontchardp:D
-  \name_primitive:NN \fontcharwd            \etex_fontcharwd:D
-  \name_primitive:NN \fontcharic            \etex_fontcharic:D
-  \name_primitive:NN \parshapeindent        \etex_parshapeindent:D
-  \name_primitive:NN \parshapelength        \etex_parshapelength:D
-  \name_primitive:NN \parshapedimen         \etex_parshapedimen:D
-  \name_primitive:NN \numexpr               \etex_numexpr:D
-  \name_primitive:NN \dimexpr               \etex_dimexpr:D
-  \name_primitive:NN \glueexpr              \etex_glueexpr:D
-  \name_primitive:NN \muexpr                \etex_muexpr:D
-  \name_primitive:NN \gluestretch           \etex_gluestretch:D
-  \name_primitive:NN \glueshrink            \etex_glueshrink:D
-  \name_primitive:NN \gluestretchorder      \etex_gluestretchorder:D
-  \name_primitive:NN \glueshrinkorder       \etex_glueshrinkorder:D
-  \name_primitive:NN \gluetomu              \etex_gluetomu:D
-  \name_primitive:NN \mutoglue              \etex_mutoglue:D
-  \name_primitive:NN \lastlinefit           \etex_lastlinefit:D
-  \name_primitive:NN \interlinepenalties    \etex_interlinepenalties:D
-  \name_primitive:NN \clubpenalties         \etex_clubpenalties:D
-  \name_primitive:NN \widowpenalties        \etex_widowpenalties:D
-  \name_primitive:NN \displaywidowpenalties \etex_displaywidowpenalties:D
-  \name_primitive:NN \middle                \etex_middle:D
-  \name_primitive:NN \savinghyphcodes       \etex_savinghyphcodes:D
-  \name_primitive:NN \savingvdiscards       \etex_savingvdiscards:D
-  \name_primitive:NN \pagediscards          \etex_pagediscards:D
-  \name_primitive:NN \splitdiscards         \etex_splitdiscards:D
-  \name_primitive:NN \TeXXeTstate           \etex_TeXXeTstate:D
-  \name_primitive:NN \beginL                \etex_beginL:D
-  \name_primitive:NN \endL                  \etex_endL:D
-  \name_primitive:NN \beginR                \etex_beginR:D
-  \name_primitive:NN \endR                  \etex_endR:D
-  \name_primitive:NN \predisplaydirection   \etex_predisplaydirection:D
-  \name_primitive:NN \everyeof              \etex_everyeof:D
-  \name_primitive:NN \protected             \etex_protected:D
-  \name_primitive:NN \pdfcreationdate       \pdftex_pdfcreationdate:D
-  \name_primitive:NN \pdfcolorstack         \pdftex_pdfcolorstack:D
-  \name_primitive:NN \pdfcompresslevel      \pdftex_pdfcompresslevel:D
-  \name_primitive:NN \pdfdecimaldigits      \pdftex_pdfdecimaldigits:D
-  \name_primitive:NN \pdfhorigin            \pdftex_pdfhorigin:D
-  \name_primitive:NN \pdfinfo               \pdftex_pdfinfo:D
-  \name_primitive:NN \pdflastxform          \pdftex_pdflastxform:D
-  \name_primitive:NN \pdfliteral            \pdftex_pdfliteral:D
-  \name_primitive:NN \pdfminorversion       \pdftex_pdfminorversion:D
-  \name_primitive:NN \pdfobjcompresslevel   \pdftex_pdfobjcompresslevel:D
-  \name_primitive:NN \pdfoutput             \pdftex_pdfoutput:D
-  \name_primitive:NN \pdfrefxform           \pdftex_pdfrefxform:D
-  \name_primitive:NN \pdfrestore            \pdftex_pdfrestore:D
-  \name_primitive:NN \pdfsave               \pdftex_pdfsave:D
-  \name_primitive:NN \pdfsetmatrix          \pdftex_pdfsetmatrix:D
-  \name_primitive:NN \pdfpkresolution       \pdftex_pdfpkresolution:D
-  \name_primitive:NN \pdftexrevision        \pdftex_pdftextrevision:D
-  \name_primitive:NN \pdfvorigin            \pdftex_pdfvorigin:D
-  \name_primitive:NN \pdfxform              \pdftex_pdfxform:D
-  \name_primitive:NN \pdfstrcmp             \pdftex_strcmp:D
-  \name_primitive:NN \XeTeXversion          \xetex_XeTeXversion:D
-  \name_primitive:NN \catcodetable          \luatex_catcodetable:D
-  \name_primitive:NN \directlua             \luatex_directlua:D
-  \name_primitive:NN \initcatcodetable      \luatex_initcatcodetable:D
-  \name_primitive:NN \latelua               \luatex_latelua:D
-  \name_primitive:NN \luatexversion         \luatex_luatexversion:D
-  \name_primitive:NN \savecatcodetable      \luatex_savecatcodetable:D
+  \__expl_primitive:NN \                      \tex_space:D
+  \__expl_primitive:NN \/                     \tex_italiccorrection:D
+  \__expl_primitive:NN \-                     \tex_hyphen:D
+  \__expl_primitive:NN \let                   \tex_let:D
+  \__expl_primitive:NN \def                   \tex_def:D
+  \__expl_primitive:NN \edef                  \tex_edef:D
+  \__expl_primitive:NN \gdef                  \tex_gdef:D
+  \__expl_primitive:NN \xdef                  \tex_xdef:D
+  \__expl_primitive:NN \chardef               \tex_chardef:D
+  \__expl_primitive:NN \countdef              \tex_countdef:D
+  \__expl_primitive:NN \dimendef              \tex_dimendef:D
+  \__expl_primitive:NN \skipdef               \tex_skipdef:D
+  \__expl_primitive:NN \muskipdef             \tex_muskipdef:D
+  \__expl_primitive:NN \mathchardef           \tex_mathchardef:D
+  \__expl_primitive:NN \toksdef               \tex_toksdef:D
+  \__expl_primitive:NN \futurelet             \tex_futurelet:D
+  \__expl_primitive:NN \advance               \tex_advance:D
+  \__expl_primitive:NN \divide                \tex_divide:D
+  \__expl_primitive:NN \multiply              \tex_multiply:D
+  \__expl_primitive:NN \font                  \tex_font:D
+  \__expl_primitive:NN \fam                   \tex_fam:D
+  \__expl_primitive:NN \global                \tex_global:D
+  \__expl_primitive:NN \long                  \tex_long:D
+  \__expl_primitive:NN \outer                 \tex_outer:D
+  \__expl_primitive:NN \setlanguage           \tex_setlanguage:D
+  \__expl_primitive:NN \globaldefs            \tex_globaldefs:D
+  \__expl_primitive:NN \afterassignment       \tex_afterassignment:D
+  \__expl_primitive:NN \aftergroup            \tex_aftergroup:D
+  \__expl_primitive:NN \expandafter           \tex_expandafter:D
+  \__expl_primitive:NN \noexpand              \tex_noexpand:D
+  \__expl_primitive:NN \begingroup            \tex_begingroup:D
+  \__expl_primitive:NN \endgroup              \tex_endgroup:D
+  \__expl_primitive:NN \halign                \tex_halign:D
+  \__expl_primitive:NN \valign                \tex_valign:D
+  \__expl_primitive:NN \cr                    \tex_cr:D
+  \__expl_primitive:NN \crcr                  \tex_crcr:D
+  \__expl_primitive:NN \noalign               \tex_noalign:D
+  \__expl_primitive:NN \omit                  \tex_omit:D
+  \__expl_primitive:NN \span                  \tex_span:D
+  \__expl_primitive:NN \tabskip               \tex_tabskip:D
+  \__expl_primitive:NN \everycr               \tex_everycr:D
+  \__expl_primitive:NN \if                    \tex_if:D
+  \__expl_primitive:NN \ifcase                \tex_ifcase:D
+  \__expl_primitive:NN \ifcat                 \tex_ifcat:D
+  \__expl_primitive:NN \ifnum                 \tex_ifnum:D
+  \__expl_primitive:NN \ifodd                 \tex_ifodd:D
+  \__expl_primitive:NN \ifdim                 \tex_ifdim:D
+  \__expl_primitive:NN \ifeof                 \tex_ifeof:D
+  \__expl_primitive:NN \ifhbox                \tex_ifhbox:D
+  \__expl_primitive:NN \ifvbox                \tex_ifvbox:D
+  \__expl_primitive:NN \ifvoid                \tex_ifvoid:D
+  \__expl_primitive:NN \ifx                   \tex_ifx:D
+  \__expl_primitive:NN \iffalse               \tex_iffalse:D
+  \__expl_primitive:NN \iftrue                \tex_iftrue:D
+  \__expl_primitive:NN \ifhmode               \tex_ifhmode:D
+  \__expl_primitive:NN \ifmmode               \tex_ifmmode:D
+  \__expl_primitive:NN \ifvmode               \tex_ifvmode:D
+  \__expl_primitive:NN \ifinner               \tex_ifinner:D
+  \__expl_primitive:NN \else                  \tex_else:D
+  \__expl_primitive:NN \fi                    \tex_fi:D
+  \__expl_primitive:NN \or                    \tex_or:D
+  \__expl_primitive:NN \immediate             \tex_immediate:D
+  \__expl_primitive:NN \closeout              \tex_closeout:D
+  \__expl_primitive:NN \openin                \tex_openin:D
+  \__expl_primitive:NN \openout               \tex_openout:D
+  \__expl_primitive:NN \read                  \tex_read:D
+  \__expl_primitive:NN \write                 \tex_write:D
+  \__expl_primitive:NN \closein               \tex_closein:D
+  \__expl_primitive:NN \newlinechar           \tex_newlinechar:D
+  \__expl_primitive:NN \input                 \tex_input:D
+  \__expl_primitive:NN \endinput              \tex_endinput:D
+  \__expl_primitive:NN \inputlineno           \tex_inputlineno:D
+  \__expl_primitive:NN \errmessage            \tex_errmessage:D
+  \__expl_primitive:NN \message               \tex_message:D
+  \__expl_primitive:NN \show                  \tex_show:D
+  \__expl_primitive:NN \showthe               \tex_showthe:D
+  \__expl_primitive:NN \showbox               \tex_showbox:D
+  \__expl_primitive:NN \showlists             \tex_showlists:D
+  \__expl_primitive:NN \errhelp               \tex_errhelp:D
+  \__expl_primitive:NN \errorcontextlines     \tex_errorcontextlines:D
+  \__expl_primitive:NN \tracingcommands       \tex_tracingcommands:D
+  \__expl_primitive:NN \tracinglostchars      \tex_tracinglostchars:D
+  \__expl_primitive:NN \tracingmacros         \tex_tracingmacros:D
+  \__expl_primitive:NN \tracingonline         \tex_tracingonline:D
+  \__expl_primitive:NN \tracingoutput         \tex_tracingoutput:D
+  \__expl_primitive:NN \tracingpages          \tex_tracingpages:D
+  \__expl_primitive:NN \tracingparagraphs     \tex_tracingparagraphs:D
+  \__expl_primitive:NN \tracingrestores       \tex_tracingrestores:D
+  \__expl_primitive:NN \tracingstats          \tex_tracingstats:D
+  \__expl_primitive:NN \pausing               \tex_pausing:D
+  \__expl_primitive:NN \showboxbreadth        \tex_showboxbreadth:D
+  \__expl_primitive:NN \showboxdepth          \tex_showboxdepth:D
+  \__expl_primitive:NN \batchmode             \tex_batchmode:D
+  \__expl_primitive:NN \errorstopmode         \tex_errorstopmode:D
+  \__expl_primitive:NN \nonstopmode           \tex_nonstopmode:D
+  \__expl_primitive:NN \scrollmode            \tex_scrollmode:D
+  \__expl_primitive:NN \end                   \tex_end:D
+  \__expl_primitive:NN \csname                \tex_csname:D
+  \__expl_primitive:NN \endcsname             \tex_endcsname:D
+  \__expl_primitive:NN \ignorespaces          \tex_ignorespaces:D
+  \__expl_primitive:NN \relax                 \tex_relax:D
+  \__expl_primitive:NN \the                   \tex_the:D
+  \__expl_primitive:NN \mag                   \tex_mag:D
+  \__expl_primitive:NN \language              \tex_language:D
+  \__expl_primitive:NN \mark                  \tex_mark:D
+  \__expl_primitive:NN \topmark               \tex_topmark:D
+  \__expl_primitive:NN \firstmark             \tex_firstmark:D
+  \__expl_primitive:NN \botmark               \tex_botmark:D
+  \__expl_primitive:NN \splitfirstmark        \tex_splitfirstmark:D
+  \__expl_primitive:NN \splitbotmark          \tex_splitbotmark:D
+  \__expl_primitive:NN \fontname              \tex_fontname:D
+  \__expl_primitive:NN \escapechar            \tex_escapechar:D
+  \__expl_primitive:NN \endlinechar           \tex_endlinechar:D
+  \__expl_primitive:NN \mathchoice            \tex_mathchoice:D
+  \__expl_primitive:NN \delimiter             \tex_delimiter:D
+  \__expl_primitive:NN \mathaccent            \tex_mathaccent:D
+  \__expl_primitive:NN \mathchar              \tex_mathchar:D
+  \__expl_primitive:NN \mskip                 \tex_mskip:D
+  \__expl_primitive:NN \radical               \tex_radical:D
+  \__expl_primitive:NN \vcenter               \tex_vcenter:D
+  \__expl_primitive:NN \mkern                 \tex_mkern:D
+  \__expl_primitive:NN \above                 \tex_above:D
+  \__expl_primitive:NN \abovewithdelims       \tex_abovewithdelims:D
+  \__expl_primitive:NN \atop                  \tex_atop:D
+  \__expl_primitive:NN \atopwithdelims        \tex_atopwithdelims:D
+  \__expl_primitive:NN \over                  \tex_over:D
+  \__expl_primitive:NN \overwithdelims        \tex_overwithdelims:D
+  \__expl_primitive:NN \displaystyle          \tex_displaystyle:D
+  \__expl_primitive:NN \textstyle             \tex_textstyle:D
+  \__expl_primitive:NN \scriptstyle           \tex_scriptstyle:D
+  \__expl_primitive:NN \scriptscriptstyle     \tex_scriptscriptstyle:D
+  \__expl_primitive:NN \nonscript             \tex_nonscript:D
+  \__expl_primitive:NN \eqno                  \tex_eqno:D
+  \__expl_primitive:NN \leqno                 \tex_leqno:D
+  \__expl_primitive:NN \abovedisplayshortskip \tex_abovedisplayshortskip:D
+  \__expl_primitive:NN \abovedisplayskip      \tex_abovedisplayskip:D
+  \__expl_primitive:NN \belowdisplayshortskip \tex_belowdisplayshortskip:D
+  \__expl_primitive:NN \belowdisplayskip      \tex_belowdisplayskip:D
+  \__expl_primitive:NN \displaywidowpenalty   \tex_displaywidowpenalty:D
+  \__expl_primitive:NN \displayindent         \tex_displayindent:D
+  \__expl_primitive:NN \displaywidth          \tex_displaywidth:D
+  \__expl_primitive:NN \everydisplay          \tex_everydisplay:D
+  \__expl_primitive:NN \predisplaysize        \tex_predisplaysize:D
+  \__expl_primitive:NN \predisplaypenalty     \tex_predisplaypenalty:D
+  \__expl_primitive:NN \postdisplaypenalty    \tex_postdisplaypenalty:D
+  \__expl_primitive:NN \mathbin               \tex_mathbin:D
+  \__expl_primitive:NN \mathclose             \tex_mathclose:D
+  \__expl_primitive:NN \mathinner             \tex_mathinner:D
+  \__expl_primitive:NN \mathop                \tex_mathop:D
+  \__expl_primitive:NN \displaylimits         \tex_displaylimits:D
+  \__expl_primitive:NN \limits                \tex_limits:D
+  \__expl_primitive:NN \nolimits              \tex_nolimits:D
+  \__expl_primitive:NN \mathopen              \tex_mathopen:D
+  \__expl_primitive:NN \mathord               \tex_mathord:D
+  \__expl_primitive:NN \mathpunct             \tex_mathpunct:D
+  \__expl_primitive:NN \mathrel               \tex_mathrel:D
+  \__expl_primitive:NN \overline              \tex_overline:D
+  \__expl_primitive:NN \underline             \tex_underline:D
+  \__expl_primitive:NN \left                  \tex_left:D
+  \__expl_primitive:NN \right                 \tex_right:D
+  \__expl_primitive:NN \binoppenalty          \tex_binoppenalty:D
+  \__expl_primitive:NN \relpenalty            \tex_relpenalty:D
+  \__expl_primitive:NN \delimitershortfall    \tex_delimitershortfall:D
+  \__expl_primitive:NN \delimiterfactor       \tex_delimiterfactor:D
+  \__expl_primitive:NN \nulldelimiterspace    \tex_nulldelimiterspace:D
+  \__expl_primitive:NN \everymath             \tex_everymath:D
+  \__expl_primitive:NN \mathsurround          \tex_mathsurround:D
+  \__expl_primitive:NN \medmuskip             \tex_medmuskip:D
+  \__expl_primitive:NN \thinmuskip            \tex_thinmuskip:D
+  \__expl_primitive:NN \thickmuskip           \tex_thickmuskip:D
+  \__expl_primitive:NN \scriptspace           \tex_scriptspace:D
+  \__expl_primitive:NN \noboundary            \tex_noboundary:D
+  \__expl_primitive:NN \accent                \tex_accent:D
+  \__expl_primitive:NN \char                  \tex_char:D
+  \__expl_primitive:NN \discretionary         \tex_discretionary:D
+  \__expl_primitive:NN \hfil                  \tex_hfil:D
+  \__expl_primitive:NN \hfilneg               \tex_hfilneg:D
+  \__expl_primitive:NN \hfill                 \tex_hfill:D
+  \__expl_primitive:NN \hskip                 \tex_hskip:D
+  \__expl_primitive:NN \hss                   \tex_hss:D
+  \__expl_primitive:NN \vfil                  \tex_vfil:D
+  \__expl_primitive:NN \vfilneg               \tex_vfilneg:D
+  \__expl_primitive:NN \vfill                 \tex_vfill:D
+  \__expl_primitive:NN \vskip                 \tex_vskip:D
+  \__expl_primitive:NN \vss                   \tex_vss:D
+  \__expl_primitive:NN \unskip                \tex_unskip:D
+  \__expl_primitive:NN \kern                  \tex_kern:D
+  \__expl_primitive:NN \unkern                \tex_unkern:D
+  \__expl_primitive:NN \hrule                 \tex_hrule:D
+  \__expl_primitive:NN \vrule                 \tex_vrule:D
+  \__expl_primitive:NN \leaders               \tex_leaders:D
+  \__expl_primitive:NN \cleaders              \tex_cleaders:D
+  \__expl_primitive:NN \xleaders              \tex_xleaders:D
+  \__expl_primitive:NN \lastkern              \tex_lastkern:D
+  \__expl_primitive:NN \lastskip              \tex_lastskip:D
+  \__expl_primitive:NN \indent                \tex_indent:D
+  \__expl_primitive:NN \par                   \tex_par:D
+  \__expl_primitive:NN \noindent              \tex_noindent:D
+  \__expl_primitive:NN \vadjust               \tex_vadjust:D
+  \__expl_primitive:NN \baselineskip          \tex_baselineskip:D
+  \__expl_primitive:NN \lineskip              \tex_lineskip:D
+  \__expl_primitive:NN \lineskiplimit         \tex_lineskiplimit:D
+  \__expl_primitive:NN \clubpenalty           \tex_clubpenalty:D
+  \__expl_primitive:NN \widowpenalty          \tex_widowpenalty:D
+  \__expl_primitive:NN \exhyphenpenalty       \tex_exhyphenpenalty:D
+  \__expl_primitive:NN \hyphenpenalty         \tex_hyphenpenalty:D
+  \__expl_primitive:NN \linepenalty           \tex_linepenalty:D
+  \__expl_primitive:NN \doublehyphendemerits  \tex_doublehyphendemerits:D
+  \__expl_primitive:NN \finalhyphendemerits   \tex_finalhyphendemerits:D
+  \__expl_primitive:NN \adjdemerits           \tex_adjdemerits:D
+  \__expl_primitive:NN \hangafter             \tex_hangafter:D
+  \__expl_primitive:NN \hangindent            \tex_hangindent:D
+  \__expl_primitive:NN \parshape              \tex_parshape:D
+  \__expl_primitive:NN \hsize                 \tex_hsize:D
+  \__expl_primitive:NN \lefthyphenmin         \tex_lefthyphenmin:D
+  \__expl_primitive:NN \righthyphenmin        \tex_righthyphenmin:D
+  \__expl_primitive:NN \leftskip              \tex_leftskip:D
+  \__expl_primitive:NN \rightskip             \tex_rightskip:D
+  \__expl_primitive:NN \looseness             \tex_looseness:D
+  \__expl_primitive:NN \parskip               \tex_parskip:D
+  \__expl_primitive:NN \parindent             \tex_parindent:D
+  \__expl_primitive:NN \uchyph                \tex_uchyph:D
+  \__expl_primitive:NN \emergencystretch      \tex_emergencystretch:D
+  \__expl_primitive:NN \pretolerance          \tex_pretolerance:D
+  \__expl_primitive:NN \tolerance             \tex_tolerance:D
+  \__expl_primitive:NN \spaceskip             \tex_spaceskip:D
+  \__expl_primitive:NN \xspaceskip            \tex_xspaceskip:D
+  \__expl_primitive:NN \parfillskip           \tex_parfillskip:D
+  \__expl_primitive:NN \everypar              \tex_everypar:D
+  \__expl_primitive:NN \prevgraf              \tex_prevgraf:D
+  \__expl_primitive:NN \spacefactor           \tex_spacefactor:D
+  \__expl_primitive:NN \shipout               \tex_shipout:D
+  \__expl_primitive:NN \vsize                 \tex_vsize:D
+  \__expl_primitive:NN \interlinepenalty      \tex_interlinepenalty:D
+  \__expl_primitive:NN \brokenpenalty         \tex_brokenpenalty:D
+  \__expl_primitive:NN \topskip               \tex_topskip:D
+  \__expl_primitive:NN \maxdeadcycles         \tex_maxdeadcycles:D
+  \__expl_primitive:NN \maxdepth              \tex_maxdepth:D
+  \__expl_primitive:NN \output                \tex_output:D
+  \__expl_primitive:NN \deadcycles            \tex_deadcycles:D
+  \__expl_primitive:NN \pagedepth             \tex_pagedepth:D
+  \__expl_primitive:NN \pagestretch           \tex_pagestretch:D
+  \__expl_primitive:NN \pagefilstretch        \tex_pagefilstretch:D
+  \__expl_primitive:NN \pagefillstretch       \tex_pagefillstretch:D
+  \__expl_primitive:NN \pagefilllstretch      \tex_pagefilllstretch:D
+  \__expl_primitive:NN \pageshrink            \tex_pageshrink:D
+  \__expl_primitive:NN \pagegoal              \tex_pagegoal:D
+  \__expl_primitive:NN \pagetotal             \tex_pagetotal:D
+  \__expl_primitive:NN \outputpenalty         \tex_outputpenalty:D
+  \__expl_primitive:NN \hoffset               \tex_hoffset:D
+  \__expl_primitive:NN \voffset               \tex_voffset:D
+  \__expl_primitive:NN \insert                \tex_insert:D
+  \__expl_primitive:NN \holdinginserts        \tex_holdinginserts:D
+  \__expl_primitive:NN \floatingpenalty       \tex_floatingpenalty:D
+  \__expl_primitive:NN \insertpenalties       \tex_insertpenalties:D
+  \__expl_primitive:NN \lower                 \tex_lower:D
+  \__expl_primitive:NN \moveleft              \tex_moveleft:D
+  \__expl_primitive:NN \moveright             \tex_moveright:D
+  \__expl_primitive:NN \raise                 \tex_raise:D
+  \__expl_primitive:NN \copy                  \tex_copy:D
+  \__expl_primitive:NN \lastbox               \tex_lastbox:D
+  \__expl_primitive:NN \vsplit                \tex_vsplit:D
+  \__expl_primitive:NN \unhbox                \tex_unhbox:D
+  \__expl_primitive:NN \unhcopy               \tex_unhcopy:D
+  \__expl_primitive:NN \unvbox                \tex_unvbox:D
+  \__expl_primitive:NN \unvcopy               \tex_unvcopy:D
+  \__expl_primitive:NN \setbox                \tex_setbox:D
+  \__expl_primitive:NN \hbox                  \tex_hbox:D
+  \__expl_primitive:NN \vbox                  \tex_vbox:D
+  \__expl_primitive:NN \vtop                  \tex_vtop:D
+  \__expl_primitive:NN \prevdepth             \tex_prevdepth:D
+  \__expl_primitive:NN \badness               \tex_badness:D
+  \__expl_primitive:NN \hbadness              \tex_hbadness:D
+  \__expl_primitive:NN \vbadness              \tex_vbadness:D
+  \__expl_primitive:NN \hfuzz                 \tex_hfuzz:D
+  \__expl_primitive:NN \vfuzz                 \tex_vfuzz:D
+  \__expl_primitive:NN \overfullrule          \tex_overfullrule:D
+  \__expl_primitive:NN \boxmaxdepth           \tex_boxmaxdepth:D
+  \__expl_primitive:NN \splitmaxdepth         \tex_splitmaxdepth:D
+  \__expl_primitive:NN \splittopskip          \tex_splittopskip:D
+  \__expl_primitive:NN \everyhbox             \tex_everyhbox:D
+  \__expl_primitive:NN \everyvbox             \tex_everyvbox:D
+  \__expl_primitive:NN \nullfont              \tex_nullfont:D
+  \__expl_primitive:NN \textfont              \tex_textfont:D
+  \__expl_primitive:NN \scriptfont            \tex_scriptfont:D
+  \__expl_primitive:NN \scriptscriptfont      \tex_scriptscriptfont:D
+  \__expl_primitive:NN \fontdimen             \tex_fontdimen:D
+  \__expl_primitive:NN \hyphenchar            \tex_hyphenchar:D
+  \__expl_primitive:NN \skewchar              \tex_skewchar:D
+  \__expl_primitive:NN \defaulthyphenchar     \tex_defaulthyphenchar:D
+  \__expl_primitive:NN \defaultskewchar       \tex_defaultskewchar:D
+  \__expl_primitive:NN \number                \tex_number:D
+  \__expl_primitive:NN \romannumeral          \tex_romannumeral:D
+  \__expl_primitive:NN \string                \tex_string:D
+  \__expl_primitive:NN \lowercase             \tex_lowercase:D
+  \__expl_primitive:NN \uppercase             \tex_uppercase:D
+  \__expl_primitive:NN \meaning               \tex_meaning:D
+  \__expl_primitive:NN \penalty               \tex_penalty:D
+  \__expl_primitive:NN \unpenalty             \tex_unpenalty:D
+  \__expl_primitive:NN \lastpenalty           \tex_lastpenalty:D
+  \__expl_primitive:NN \special               \tex_special:D
+  \__expl_primitive:NN \dump                  \tex_dump:D
+  \__expl_primitive:NN \patterns              \tex_patterns:D
+  \__expl_primitive:NN \hyphenation           \tex_hyphenation:D
+  \__expl_primitive:NN \time                  \tex_time:D
+  \__expl_primitive:NN \day                   \tex_day:D
+  \__expl_primitive:NN \month                 \tex_month:D
+  \__expl_primitive:NN \year                  \tex_year:D
+  \__expl_primitive:NN \jobname               \tex_jobname:D
+  \__expl_primitive:NN \everyjob              \tex_everyjob:D
+  \__expl_primitive:NN \count                 \tex_count:D
+  \__expl_primitive:NN \dimen                 \tex_dimen:D
+  \__expl_primitive:NN \skip                  \tex_skip:D
+  \__expl_primitive:NN \toks                  \tex_toks:D
+  \__expl_primitive:NN \muskip                \tex_muskip:D
+  \__expl_primitive:NN \box                   \tex_box:D
+  \__expl_primitive:NN \wd                    \tex_wd:D
+  \__expl_primitive:NN \ht                    \tex_ht:D
+  \__expl_primitive:NN \dp                    \tex_dp:D
+  \__expl_primitive:NN \catcode               \tex_catcode:D
+  \__expl_primitive:NN \delcode               \tex_delcode:D
+  \__expl_primitive:NN \sfcode                \tex_sfcode:D
+  \__expl_primitive:NN \lccode                \tex_lccode:D
+  \__expl_primitive:NN \uccode                \tex_uccode:D
+  \__expl_primitive:NN \mathcode              \tex_mathcode:D
+  \__expl_primitive:NN \ifdefined             \etex_ifdefined:D
+  \__expl_primitive:NN \ifcsname              \etex_ifcsname:D
+  \__expl_primitive:NN \unless                \etex_unless:D
+  \__expl_primitive:NN \eTeXversion           \etex_eTeXversion:D
+  \__expl_primitive:NN \eTeXrevision          \etex_eTeXrevision:D
+  \__expl_primitive:NN \marks                 \etex_marks:D
+  \__expl_primitive:NN \topmarks              \etex_topmarks:D
+  \__expl_primitive:NN \firstmarks            \etex_firstmarks:D
+  \__expl_primitive:NN \botmarks              \etex_botmarks:D
+  \__expl_primitive:NN \splitfirstmarks       \etex_splitfirstmarks:D
+  \__expl_primitive:NN \splitbotmarks         \etex_splitbotmarks:D
+  \__expl_primitive:NN \unexpanded            \etex_unexpanded:D
+  \__expl_primitive:NN \detokenize            \etex_detokenize:D
+  \__expl_primitive:NN \scantokens            \etex_scantokens:D
+  \__expl_primitive:NN \showtokens            \etex_showtokens:D
+  \__expl_primitive:NN \readline              \etex_readline:D
+  \__expl_primitive:NN \tracingassigns        \etex_tracingassigns:D
+  \__expl_primitive:NN \tracingscantokens     \etex_tracingscantokens:D
+  \__expl_primitive:NN \tracingnesting        \etex_tracingnesting:D
+  \__expl_primitive:NN \tracingifs            \etex_tracingifs:D
+  \__expl_primitive:NN \currentiflevel        \etex_currentiflevel:D
+  \__expl_primitive:NN \currentifbranch       \etex_currentifbranch:D
+  \__expl_primitive:NN \currentiftype         \etex_currentiftype:D
+  \__expl_primitive:NN \tracinggroups         \etex_tracinggroups:D
+  \__expl_primitive:NN \currentgrouplevel     \etex_currentgrouplevel:D
+  \__expl_primitive:NN \currentgrouptype      \etex_currentgrouptype:D
+  \__expl_primitive:NN \showgroups            \etex_showgroups:D
+  \__expl_primitive:NN \showifs               \etex_showifs:D
+  \__expl_primitive:NN \interactionmode       \etex_interactionmode:D
+  \__expl_primitive:NN \lastnodetype          \etex_lastnodetype:D
+  \__expl_primitive:NN \iffontchar            \etex_iffontchar:D
+  \__expl_primitive:NN \fontcharht            \etex_fontcharht:D
+  \__expl_primitive:NN \fontchardp            \etex_fontchardp:D
+  \__expl_primitive:NN \fontcharwd            \etex_fontcharwd:D
+  \__expl_primitive:NN \fontcharic            \etex_fontcharic:D
+  \__expl_primitive:NN \parshapeindent        \etex_parshapeindent:D
+  \__expl_primitive:NN \parshapelength        \etex_parshapelength:D
+  \__expl_primitive:NN \parshapedimen         \etex_parshapedimen:D
+  \__expl_primitive:NN \numexpr               \etex_numexpr:D
+  \__expl_primitive:NN \dimexpr               \etex_dimexpr:D
+  \__expl_primitive:NN \glueexpr              \etex_glueexpr:D
+  \__expl_primitive:NN \muexpr                \etex_muexpr:D
+  \__expl_primitive:NN \gluestretch           \etex_gluestretch:D
+  \__expl_primitive:NN \glueshrink            \etex_glueshrink:D
+  \__expl_primitive:NN \gluestretchorder      \etex_gluestretchorder:D
+  \__expl_primitive:NN \glueshrinkorder       \etex_glueshrinkorder:D
+  \__expl_primitive:NN \gluetomu              \etex_gluetomu:D
+  \__expl_primitive:NN \mutoglue              \etex_mutoglue:D
+  \__expl_primitive:NN \lastlinefit           \etex_lastlinefit:D
+  \__expl_primitive:NN \interlinepenalties    \etex_interlinepenalties:D
+  \__expl_primitive:NN \clubpenalties         \etex_clubpenalties:D
+  \__expl_primitive:NN \widowpenalties        \etex_widowpenalties:D
+  \__expl_primitive:NN \displaywidowpenalties \etex_displaywidowpenalties:D
+  \__expl_primitive:NN \middle                \etex_middle:D
+  \__expl_primitive:NN \savinghyphcodes       \etex_savinghyphcodes:D
+  \__expl_primitive:NN \savingvdiscards       \etex_savingvdiscards:D
+  \__expl_primitive:NN \pagediscards          \etex_pagediscards:D
+  \__expl_primitive:NN \splitdiscards         \etex_splitdiscards:D
+  \__expl_primitive:NN \TeXXeTstate           \etex_TeXXeTstate:D
+  \__expl_primitive:NN \beginL                \etex_beginL:D
+  \__expl_primitive:NN \endL                  \etex_endL:D
+  \__expl_primitive:NN \beginR                \etex_beginR:D
+  \__expl_primitive:NN \endR                  \etex_endR:D
+  \__expl_primitive:NN \predisplaydirection   \etex_predisplaydirection:D
+  \__expl_primitive:NN \everyeof              \etex_everyeof:D
+  \__expl_primitive:NN \protected             \etex_protected:D
+  \__expl_primitive:NN \pdfcreationdate       \pdftex_pdfcreationdate:D
+  \__expl_primitive:NN \pdfcolorstack         \pdftex_pdfcolorstack:D
+  \__expl_primitive:NN \pdfcompresslevel      \pdftex_pdfcompresslevel:D
+  \__expl_primitive:NN \pdfdecimaldigits      \pdftex_pdfdecimaldigits:D
+  \__expl_primitive:NN \pdfhorigin            \pdftex_pdfhorigin:D
+  \__expl_primitive:NN \pdfinfo               \pdftex_pdfinfo:D
+  \__expl_primitive:NN \pdflastxform          \pdftex_pdflastxform:D
+  \__expl_primitive:NN \pdfliteral            \pdftex_pdfliteral:D
+  \__expl_primitive:NN \pdfminorversion       \pdftex_pdfminorversion:D
+  \__expl_primitive:NN \pdfobjcompresslevel   \pdftex_pdfobjcompresslevel:D
+  \__expl_primitive:NN \pdfoutput             \pdftex_pdfoutput:D
+  \__expl_primitive:NN \pdfrefxform           \pdftex_pdfrefxform:D
+  \__expl_primitive:NN \pdfrestore            \pdftex_pdfrestore:D
+  \__expl_primitive:NN \pdfsave               \pdftex_pdfsave:D
+  \__expl_primitive:NN \pdfsetmatrix          \pdftex_pdfsetmatrix:D
+  \__expl_primitive:NN \pdfpkresolution       \pdftex_pdfpkresolution:D
+  \__expl_primitive:NN \pdftexrevision        \pdftex_pdftextrevision:D
+  \__expl_primitive:NN \pdfvorigin            \pdftex_pdfvorigin:D
+  \__expl_primitive:NN \pdfxform              \pdftex_pdfxform:D
+  \__expl_primitive:NN \pdfstrcmp             \pdftex_strcmp:D
+  \__expl_primitive:NN \XeTeXversion          \xetex_XeTeXversion:D
+  \__expl_primitive:NN \catcodetable          \luatex_catcodetable:D
+  \__expl_primitive:NN \directlua             \luatex_directlua:D
+  \__expl_primitive:NN \initcatcodetable      \luatex_initcatcodetable:D
+  \__expl_primitive:NN \latelua               \luatex_latelua:D
+  \__expl_primitive:NN \luatexversion         \luatex_luatexversion:D
+  \__expl_primitive:NN \savecatcodetable      \luatex_savecatcodetable:D
 \tex_endgroup:D
 \tex_let:D \tex_end:D               \@@end
 \tex_let:D \tex_everydisplay:D      \frozen@everydisplay
 \tex_let:D \tex_everymath:D         \frozen@everymath
 \tex_let:D \tex_hyphen:D            \@@hyph
 \tex_let:D \tex_input:D             \@@input
-\tex_let:D \tex_italic_correction:D \@@italiccorr
+\tex_let:D \tex_italiccorrection:D  \@@italiccorr
 \tex_let:D \tex_underline:D         \@@underline
 \tex_let:D \luatex_catcodetable:D      \luatexcatcodetable
 \tex_let:D \luatex_initcatcodetable:D  \luatexinitcatcodetable
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3prg.sty b/Master/texmf-dist/tex/latex/l3kernel/l3prg.sty
index 51b98fabb03..6433a8eb325 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3prg.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3prg.sty
@@ -13,7 +13,7 @@
 %% 
 %% Do not distribute a modified version of this file.
 %% 
-%% File: l3prg.dtx Copyright (C) 2005-2011 The LaTeX3 Project
+%% File: l3prg.dtx Copyright (C) 2005-2012 The LaTeX3 Project
 %%
 %% It may be distributed and/or modified under the conditions of the
 %% LaTeX Project Public License (LPPL), either version 1.3c of this
@@ -46,12 +46,12 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3prg.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental control structures}
+\GetIdInfo$Id: l3prg.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Control structures}
 %%
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 \tex_let:D \if_bool:N          \tex_ifodd:D
 \tex_let:D \if_predicate:w     \tex_ifodd:D
 \cs_new_protected:Npn \bool_new:N #1 { \cs_new_eq:NN #1 \c_false_bool }
@@ -99,19 +99,21 @@
     \bool_if_exist:NTF #1
       { \bool_show:n {#1} }
       {
-        \msg_kernel_error:nnx { kernel } { variable-not-defined }
+        \__msg_kernel_error:nnx { kernel } { variable-not-defined }
           { \token_to_str:N #1 }
       }
   }
 \cs_new_protected:Npn \bool_show:n #1
   {
     \bool_if:nTF {#1}
-      { \msg_aux_show:x { > true } }
-      { \msg_aux_show:x { > false } }
+      { \__msg_show_variable:x { > true } }
+      { \__msg_show_variable:x { > false } }
   }
 \cs_generate_variant:Nn \bool_show:N { c }
 \bool_new:N \l_tmpa_bool
+\bool_new:N \l_tmpb_bool
 \bool_new:N \g_tmpa_bool
+\bool_new:N \g_tmpb_bool
 \cs_new_eq:NN \bool_if_exist:NTF \cs_if_exist:NTF
 \cs_new_eq:NN \bool_if_exist:NT  \cs_if_exist:NT
 \cs_new_eq:NN \bool_if_exist:NF  \cs_if_exist:NF
@@ -131,126 +133,75 @@
 \cs_new:Npn \bool_if_p:n #1
   {
     \group_align_safe_begin:
-    \bool_get_next:N ( #1 ) S
+    \__bool_if_left_parentheses:wwwn \q_nil
+      #1 \q_mark { }
+      (  \q_mark { \__bool_if_right_parentheses:wwwn \q_nil }
+      )  \q_mark { \__bool_if_or:wwwn \q_nil }
+      || \q_mark \__bool_if_parse:NNNww
+    \q_stop
   }
-\cs_new:Npn \bool_get_next:N #1
+\cs_new:Npn \__bool_if_left_parentheses:wwwn #1 \q_nil #2 ( #3 \q_mark #4
+  { #4 \__bool_if_left_parentheses:wwwn #1 #2 (( \q_nil #3 \q_mark {#4} }
+\cs_new:Npn \__bool_if_right_parentheses:wwwn #1 \q_nil #2 ) #3 \q_mark #4
+  { #4 \__bool_if_right_parentheses:wwwn #1 #2 )) \q_nil #3 \q_mark {#4} }
+\cs_new:Npn \__bool_if_or:wwwn #1 \q_nil #2 || #3 \q_mark #4
+  { #4 \__bool_if_or:wwwn #1 #2 )||( \q_nil #3 \q_mark {#4} }
+\cs_new:Npn \__bool_if_parse:NNNww #1#2#3#4 \q_mark #5 \q_stop
   {
-    \use:c
-      {
-        bool_
-        \if_meaning:w !#1 ! \else: \if_meaning:w (#1 ( \else: p \fi: \fi:
-        :w
-      }
-      #1
+    \__bool_get_next:NN \use_i:nn (( #4 )) S
   }
-\cs_new:Npn \bool_get_not_next:N #1
+\cs_new:Npn \__bool_get_next:NN #1#2
   {
     \use:c
       {
-      bool_not_
-      \if_meaning:w !#1 ! \else: \if_meaning:w (#1 ( \else: p \fi: \fi:
-      :w
+        __bool_
+        \if_meaning:w !#2 ! \else: \if_meaning:w (#2 ( \else: p \fi: \fi:
+        :Nw
       }
-        #1
-  }
-\cs_new:Npn \bool_get_next:NN #1#2 { \bool_get_next:N #2 }
-\cs_new:Npn \bool_get_not_next:NN #1#2 { \bool_get_not_next:N #2 }
-\cs_new:cpn { bool_!:w } #1#2
-  {
-    \if_meaning:w ( #2
-      \exp_after:wN \bool_Not:w
-    \else:
-      \if_meaning:w ! #2
-        \exp_after:wN \exp_after:wN \exp_after:wN \bool_get_next:NN
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN \bool_Not:N
-      \fi:
-    \fi:
-    #2
-  }
-\cs_new:cpn { bool_not_!:w } #1#2
-  {
-    \if_meaning:w ( #2
-      \exp_after:wN \bool_not_Not:w
-    \else:
-      \if_meaning:w ! #2
-        \exp_after:wN \exp_after:wN \exp_after:wN \bool_get_not_next:NN
-      \else:
-        \exp_after:wN \exp_after:wN \exp_after:wN \bool_not_Not:N
-      \fi:
-    \fi:
-    #2
+      #1 #2
   }
-\cs_new:Npn \bool_Not:w { \exp_after:wN \int_value:w \bool_get_not_next:N }
-\cs_new:Npn \bool_not_Not:w { \exp_after:wN \int_value:w \bool_get_next:N }
-\cs_new:Npn \bool_Not:N #1
+\cs_new:cpn { __bool_!:Nw } #1#2
+  { \exp_after:wN \__bool_get_next:NN #1 \use_ii:nn \use_i:nn }
+\cs_new:cpn { __bool_(:Nw } #1#2
   {
-    \exp_after:wN \bool_p:w
-    \if_meaning:w #1 \c_true_bool
-      \c_false_bool
-    \else:
-      \c_true_bool
-    \fi:
+    \exp_after:wN \__bool_choose:NNN \exp_after:wN #1
+    \__int_value:w \__bool_get_next:NN \use_i:nn
   }
-\cs_new:Npn \bool_not_Not:N #1
+\cs_new:cpn { __bool_p:Nw } #1
+  { \exp_after:wN \__bool_choose:NNN \exp_after:wN #1 \__int_value:w }
+\cs_new:Npn \__bool_choose:NNN #1#2#3
   {
-    \exp_after:wN \bool_p:w
-    \if_meaning:w #1 \c_true_bool
-      \c_true_bool
-    \else:
-      \c_false_bool
-    \fi:
-  }
-\cs_new:cpn { bool_(:w } #1
-  { \exp_after:wN  \bool_cleanup:N \int_value:w \bool_get_next:N }
-\cs_new:cpn { bool_not_(:w } #1
-  { \exp_after:wN  \bool_not_cleanup:N \int_value:w \bool_get_next:N }
-\cs_new:cpn { bool_p:w } { \exp_after:wN \bool_cleanup:N \int_value:w  }
-\cs_new:cpn { bool_not_p:w } {\exp_after:wN \bool_not_cleanup:N \int_value:w }
-\cs_new:Npn \bool_cleanup:N #1
-  {
-    \exp_after:wN \bool_choose:NN \exp_after:wN #1
-    \int_to_roman:w - `\q
-  }
-\cs_new:Npn \bool_not_cleanup:N #1
-  {
-    \exp_after:wN \bool_not_choose:NN \exp_after:wN #1
-    \int_to_roman:w - `\q
+    \use:c
+      {
+        __bool_ #3 _
+        #1 #2 { \if_meaning:w 0 #2 1 \else: 0 \fi: }
+        :w
+      }
   }
-\cs_new:Npn \bool_choose:NN #1#2 { \use:c { bool_ #2 _ #1 :w } }
-\cs_new:Npn \bool_not_choose:NN #1#2 { \use:c { bool_not_ #2 _ #1 :w } }
-\cs_new_nopar:cpn { bool_&_1:w } & { \bool_get_next:N }
-\cs_new_nopar:cpn { bool_|_0:w } | { \bool_get_next:N }
-\cs_new_nopar:cpn { bool_not_&_0:w } & { \bool_get_next:N }
-\cs_new_nopar:cpn { bool_not_|_1:w } | { \bool_get_next:N }
-\cs_new_nopar:cpn { bool_)_0:w } { \c_false_bool }
-\cs_new_nopar:cpn { bool_)_1:w } { \c_true_bool }
-\cs_new_nopar:cpn { bool_not_)_0:w } { \c_true_bool }
-\cs_new_nopar:cpn { bool_not_)_1:w } { \c_false_bool }
-\cs_new_nopar:cpn { bool_S_0:w } { \group_align_safe_end: \c_false_bool }
-\cs_new_nopar:cpn { bool_S_1:w } { \group_align_safe_end: \c_true_bool }
-\cs_new_nopar:cpn { bool_&_0:w } & { \bool_eval_skip_to_end:Nw \c_false_bool }
-\cs_new_nopar:cpn { bool_|_1:w } | { \bool_eval_skip_to_end:Nw \c_true_bool }
-\cs_new_nopar:cpn { bool_not_&_1:w } &
-  { \bool_eval_skip_to_end:Nw \c_false_bool }
-\cs_new_nopar:cpn { bool_not_|_0:w } |
-  { \bool_eval_skip_to_end:Nw \c_true_bool }
+\cs_new_nopar:cpn { __bool_)_0:w } { \c_false_bool }
+\cs_new_nopar:cpn { __bool_)_1:w } { \c_true_bool }
+\cs_new_nopar:cpn { __bool_S_0:w } { \group_align_safe_end: \c_false_bool }
+\cs_new_nopar:cpn { __bool_S_1:w } { \group_align_safe_end: \c_true_bool }
+\cs_new_nopar:cpn { __bool_&_1:w } & { \__bool_get_next:NN \use_i:nn }
+\cs_new_nopar:cpn { __bool_|_0:w } | { \__bool_get_next:NN \use_i:nn }
+\cs_new_nopar:cpn { __bool_&_0:w } & { \__bool_eval_skip_to_end:Nw \c_false_bool }
+\cs_new_nopar:cpn { __bool_|_1:w } | { \__bool_eval_skip_to_end:Nw \c_true_bool }
 %% (
-\cs_new:Npn \bool_eval_skip_to_end:Nw #1#2 )
+\cs_new:Npn \__bool_eval_skip_to_end:Nw #1#2 )
   {
-    \bool_eval_skip_to_end_aux:Nw #1#2 ( % )
+    \__bool_eval_skip_to_end_ii:Nw #1#2 ( % )
     \q_no_value \q_stop
     {#2}
   }
-\cs_new:Npn \bool_eval_skip_to_end_aux:Nw #1#2 ( #3#4 \q_stop #5 % )
+\cs_new:Npn \__bool_eval_skip_to_end_ii:Nw #1#2 ( #3#4 \q_stop #5 % )
   {
     \quark_if_no_value:NTF #3
     {#1}
-    { \bool_eval_skip_to_end_aux_ii:Nw #1 #5 }
+    { \__bool_eval_skip_to_end_iii:Nw #1 #5 }
   }
-\cs_new:Npn \bool_eval_skip_to_end_aux_ii:Nw #1#2 ( #3 )
+\cs_new:Npn \__bool_eval_skip_to_end_iii:Nw #1#2 ( #3 )
   { % (
-    \bool_eval_skip_to_end:Nw #1#3 )
+    \__bool_eval_skip_to_end:Nw #1#3 )
   }
 \cs_new:Npn \bool_not_p:n #1 { \bool_if_p:n { ! ( #1 ) } }
 \cs_new:Npn \bool_xor_p:nn #1#2
@@ -297,161 +248,50 @@
     #2
     \bool_if:nF {#1} { \bool_do_until:nn {#1} {#2}  }
   }
-\cs_new:Npn \prg_case_end:nw #1 #2 \q_recursion_stop { \c_zero #1 }
-\cs_new:Npn \prg_case_int:nnn #1
-  {
-    \tex_romannumeral:D
-    \exp_args:Nf \prg_case_int_aux:nnn { \int_eval:n {#1} }
-  }
-\cs_new:Npn \prg_case_int_aux:nnn #1 #2 #3
-  { \prg_case_int_aux:nw {#1} #2 {#1} {#3} \q_recursion_stop }
-\cs_new:Npn \prg_case_int_aux:nw #1#2#3
-  {
-    \int_compare:nNnTF {#1} = {#2}
-      { \prg_case_end:nw {#3} }
-      { \prg_case_int_aux:nw {#1} }
-  }
-\cs_new:Npn \prg_case_dim:nnn #1
-  {
-    \tex_romannumeral:D
-    \exp_args:Nf \prg_case_dim_aux:nnn { \dim_eval:n {#1} }
-  }
-\cs_new:Npn \prg_case_dim_aux:nnn #1 #2 #3
-  { \prg_case_dim_aux:nw {#1} #2 {#1} {#3} \q_recursion_stop }
-\cs_new:Npn \prg_case_dim_aux:nw #1#2#3
-  {
-    \dim_compare:nNnTF {#1} = {#2}
-      { \prg_case_end:nw {#3} }
-      { \prg_case_dim_aux:nw {#1} }
-  }
-\cs_new:Npn \prg_case_str:nnn #1#2#3
-  {
-    \tex_romannumeral:D
-    \prg_case_str_aux:nw {#1} #2 {#1} {#3} \q_recursion_stop
-  }
-\cs_new:Npn \prg_case_str_aux:nw #1#2#3
-  {
-    \str_if_eq:nnTF {#1} {#2}
-      { \prg_case_end:nw {#3} }
-      { \prg_case_str_aux:nw {#1} }
-  }
-\cs_generate_variant:Nn \prg_case_str:nnn { o }
-\cs_new:Npn \prg_case_str:xxn #1#2#3
-  {
-    \tex_romannumeral:D
-    \prg_case_str_x_aux:nw {#1} #2 {#1} {#3} \q_recursion_stop
-  }
-\cs_new:Npn \prg_case_str_x_aux:nw #1#2#3
-  {
-    \str_if_eq:xxTF {#1} {#2}
-      { \prg_case_end:nw {#3} }
-      { \prg_case_str_x_aux:nw {#1} }
-  }
-\cs_new:Npn \prg_case_tl:Nnn #1#2#3
-  {
-    \tex_romannumeral:D
-    \prg_case_tl_aux:Nw #1 #2 #1 {#3} \q_recursion_stop
-  }
-\cs_new:Npn \prg_case_tl_aux:Nw #1#2#3
-  {
-    \tl_if_eq:NNTF #1 #2
-      { \prg_case_end:nw {#3} }
-      { \prg_case_tl_aux:Nw #1 }
-  }
-\cs_generate_variant:Nn \prg_case_tl:Nnn { c }
 \cs_new:Npn \prg_replicate:nn #1
   {
-    \int_to_roman:w
-      \exp_after:wN \prg_replicate_first_aux:N
-        \int_value:w \int_eval:w #1 \int_eval_end:
+    \__int_to_roman:w
+      \exp_after:wN \__prg_replicate_first:N
+        \__int_value:w \__int_eval:w #1 \__int_eval_end:
       \cs_end:
   }
-\cs_new:Npn \prg_replicate_aux:N #1
-  { \cs:w prg_replicate_#1 :n \prg_replicate_aux:N }
-\cs_new:Npn \prg_replicate_first_aux:N #1
-  { \cs:w prg_replicate_first_ #1 :n \prg_replicate_aux:N }
-\cs_new:Npn \prg_replicate_ :n #1 { \cs_end: }
-\cs_new:cpn { prg_replicate_0:n } #1 { \cs_end: {#1#1#1#1#1#1#1#1#1#1} }
-\cs_new:cpn { prg_replicate_1:n } #1 { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1 }
-\cs_new:cpn { prg_replicate_2:n } #1 { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1 }
-\cs_new:cpn { prg_replicate_3:n } #1
+\cs_new:Npn \__prg_replicate:N #1
+  { \cs:w __prg_replicate_#1 :n \__prg_replicate:N }
+\cs_new:Npn \__prg_replicate_first:N #1
+  { \cs:w __prg_replicate_first_ #1 :n \__prg_replicate:N }
+\cs_new:Npn \__prg_replicate_ :n #1 { \cs_end: }
+\cs_new:cpn { __prg_replicate_0:n } #1 { \cs_end: {#1#1#1#1#1#1#1#1#1#1} }
+\cs_new:cpn { __prg_replicate_1:n } #1 { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1 }
+\cs_new:cpn { __prg_replicate_2:n } #1 { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1 }
+\cs_new:cpn { __prg_replicate_3:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1 }
-\cs_new:cpn { prg_replicate_4:n } #1
+\cs_new:cpn { __prg_replicate_4:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1#1 }
-\cs_new:cpn { prg_replicate_5:n } #1
+\cs_new:cpn { __prg_replicate_5:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_6:n } #1
+\cs_new:cpn { __prg_replicate_6:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_7:n } #1
+\cs_new:cpn { __prg_replicate_7:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_8:n } #1
+\cs_new:cpn { __prg_replicate_8:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_9:n } #1
+\cs_new:cpn { __prg_replicate_9:n } #1
   { \cs_end: {#1#1#1#1#1#1#1#1#1#1} #1#1#1#1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_first_-:n } #1
-  { \c_zero \msg_expandable_kernel_error:nn { prg } { replicate-neg } }
-\cs_new:cpn { prg_replicate_first_0:n } #1 { \c_zero }
-\cs_new:cpn { prg_replicate_first_1:n } #1 { \c_zero #1 }
-\cs_new:cpn { prg_replicate_first_2:n } #1 { \c_zero #1#1 }
-\cs_new:cpn { prg_replicate_first_3:n } #1 { \c_zero #1#1#1 }
-\cs_new:cpn { prg_replicate_first_4:n } #1 { \c_zero #1#1#1#1 }
-\cs_new:cpn { prg_replicate_first_5:n } #1 { \c_zero #1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_first_6:n } #1 { \c_zero #1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_first_7:n } #1 { \c_zero #1#1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_first_8:n } #1 { \c_zero #1#1#1#1#1#1#1#1 }
-\cs_new:cpn { prg_replicate_first_9:n } #1 { \c_zero #1#1#1#1#1#1#1#1#1 }
-\cs_new:Npn \prg_stepwise_function:nnnN #1#2#3#4
-  {
-    \prg_stepwise_aux:nnnN {#1} {#2} {#3} #4
-    \prg_break_point:n { }
-  }
-\cs_new:Npn \prg_stepwise_aux:nnnN #1#2#3#4
-  {
-    \int_compare:nNnTF {#2} > \c_zero
-      { \exp_args:NNf \prg_stepwise_aux:NnnnN > }
-      {
-        \int_compare:nNnTF {#2} = \c_zero
-          {
-            \msg_expandable_kernel_error:nnn { prg } { zero-step } {#4}
-            \prg_map_break:
-          }
-          { \exp_args:NNf \prg_stepwise_aux:NnnnN < }
-      }
-      { \int_eval:n {#1} } {#2} {#3} #4
-  }
-\cs_new:Npn \prg_stepwise_aux:NnnnN #1#2#3#4#5
-  {
-    \int_compare:nNnF {#2} #1 {#4}
-      {
-        #5 {#2}
-        \exp_args:NNf \prg_stepwise_aux:NnnnN
-          #1 { \int_eval:n { #2 + #3 } } {#3} {#4} #5
-      }
-  }
-\cs_new_protected:Npn \prg_stepwise_inline:nnnn
-  {
-    \exp_args:NNc \prg_stepwise_aux:NNnnnn
-      \cs_gset_nopar:Npn
-      { g_prg_stepwise_ \int_use:N \g_prg_map_int :n }
-  }
-\cs_new_protected:Npn \prg_stepwise_variable:nnnNn #1#2#3#4#5
-  {
-    \exp_args:NNc \prg_stepwise_aux:NNnnnn
-      \cs_gset_nopar:Npx
-      { g_prg_stepwise_ \int_use:N \g_prg_map_int :n }
-      {#1}{#2}{#3}
-      {
-        \tl_set:Nn \exp_not:N #4 {##1}
-        \exp_not:n {#5}
-      }
-  }
-\cs_new_protected:Npn \prg_stepwise_aux:NNnnnn #1#2#3#4#5#6
-  {
-    #1 #2 ##1 {#6}
-    \int_gincr:N \g_prg_map_int
-    \prg_stepwise_aux:nnnN {#3} {#4} {#5} #2
-    \prg_break_point:n { \int_gdecr:N \g_prg_map_int }
-  }
+\cs_new:cpn { __prg_replicate_first_-:n } #1
+  {
+    \c_zero
+    \__msg_kernel_expandable_error:nn { kernel } { negative-replication }
+  }
+\cs_new:cpn { __prg_replicate_first_0:n } #1 { \c_zero }
+\cs_new:cpn { __prg_replicate_first_1:n } #1 { \c_zero #1 }
+\cs_new:cpn { __prg_replicate_first_2:n } #1 { \c_zero #1#1 }
+\cs_new:cpn { __prg_replicate_first_3:n } #1 { \c_zero #1#1#1 }
+\cs_new:cpn { __prg_replicate_first_4:n } #1 { \c_zero #1#1#1#1 }
+\cs_new:cpn { __prg_replicate_first_5:n } #1 { \c_zero #1#1#1#1#1 }
+\cs_new:cpn { __prg_replicate_first_6:n } #1 { \c_zero #1#1#1#1#1#1 }
+\cs_new:cpn { __prg_replicate_first_7:n } #1 { \c_zero #1#1#1#1#1#1#1 }
+\cs_new:cpn { __prg_replicate_first_8:n } #1 { \c_zero #1#1#1#1#1#1#1#1 }
+\cs_new:cpn { __prg_replicate_first_9:n } #1 { \c_zero #1#1#1#1#1#1#1#1#1 }
 \prg_new_conditional:Npnn \mode_if_vertical: { p , T , F , TF }
   { \if_mode_vertical: \prg_return_true: \else: \prg_return_false: \fi: }
 \prg_new_conditional:Npnn \mode_if_horizontal: { p , T , F , TF }
@@ -466,117 +306,51 @@
   { \if_int_compare:w `{ = \c_zero } \fi: }
 \cs_new_protected_nopar:Npn \scan_align_safe_stop: { }
 \group_begin:
-  \tex_lccode:D `\& = `\g \scan_stop:
-  \tex_catcode:D `\& = \c_twelve
+  \tex_lccode:D `* = `g \scan_stop:
+  \tex_catcode:D `* = \c_twelve
 \tl_to_lowercase:n
   {
     \group_end:
-    \cs_new:Npn \prg_variable_get_scope:N #1
+    \cs_new:Npn \__prg_variable_get_scope:N #1
       {
         \exp_after:wN \exp_after:wN
-        \exp_after:wN \prg_variable_get_scope_aux:w
+        \exp_after:wN \__prg_variable_get_scope:w
           \cs_to_str:N #1 \exp_stop_f: \q_stop
       }
-    \cs_new:Npn \prg_variable_get_scope_aux:w #1#2 \q_stop
-      { \token_if_eq_meaning:NNT & #1 { g } }
+    \cs_new:Npn \__prg_variable_get_scope:w #1#2 \q_stop
+      { \token_if_eq_meaning:NNT * #1 { g } }
   }
 \group_begin:
-  \tex_lccode:D `\& = `\_ \scan_stop:
-  \tex_catcode:D `\& = \c_twelve
+  \tex_lccode:D `* = `_ \scan_stop:
+  \tex_catcode:D `* = \c_twelve
 \tl_to_lowercase:n
   {
     \group_end:
-    \cs_new:Npn \prg_variable_get_type:N #1
+    \cs_new:Npn \__prg_variable_get_type:N #1
       {
-        \exp_after:wN \prg_variable_get_type_aux:w
-          \token_to_str:N #1 & a \q_stop
+        \exp_after:wN \__prg_variable_get_type:w
+          \token_to_str:N #1 * a \q_stop
       }
-    \cs_new:Npn \prg_variable_get_type_aux:w #1 & #2#3 \q_stop
+    \cs_new:Npn \__prg_variable_get_type:w #1 * #2#3 \q_stop
       {
         \token_if_eq_meaning:NNTF a #2
           {#1}
-          { \prg_variable_get_type_aux:w #2#3 \q_stop }
+          { \__prg_variable_get_type:w #2#3 \q_stop }
       }
   }
-\int_new:N \g_prg_map_int
-\cs_new_protected:Npn \prg_define_quicksort:nnn #1#2#3 {
-  \cs_set:cpx{#1_quicksort:n}##1{
-    \exp_not:c{#1_quicksort_start_partition:w} ##1
-    \exp_not:n{#2\q_nil#3\q_stop}
-  }
-  \cs_set:cpx{#1_quicksort_braced:n}##1{
-    \exp_not:c{#1_quicksort_start_partition_braced:n} ##1
-    \exp_not:N\q_nil\exp_not:N\q_stop
-  }
-  \cs_set:cpx {#1_quicksort_start_partition:w} #2 ##1 #3{
-    \exp_not:N \quark_if_nil:nT {##1}\exp_not:N \use_none_delimit_by_q_stop:w
-    \exp_not:c{#1_quicksort_do_partition_i:nnnw} {##1}{}{}
-  }
-  \cs_set:cpx {#1_quicksort_start_partition_braced:n} ##1 {
-    \exp_not:N \quark_if_nil:nT {##1}\exp_not:N \use_none_delimit_by_q_stop:w
-    \exp_not:c{#1_quicksort_do_partition_i_braced:nnnn} {##1}{}{}
-  }
-  \cs_set:cpx {#1_quicksort_do_partition_i:nnnw} ##1##2##3 #2 ##4 #3 {
-    \exp_not:N \quark_if_nil:nTF {##4} \exp_not:c {#1_do_quicksort_braced:nnnnw}
-    {
-      \exp_not:c{#1_quicksort_compare:nnTF}{##1}{##4}
-      \exp_not:c{#1_quicksort_partition_greater_ii:nnnn}
-      \exp_not:c{#1_quicksort_partition_less_ii:nnnn}
-    }
-    {##1}{##2}{##3}{##4}
-  }
-  \cs_set:cpx {#1_quicksort_do_partition_i_braced:nnnn} ##1##2##3##4 {
-    \exp_not:N \quark_if_nil:nTF {##4} \exp_not:c {#1_do_quicksort_braced:nnnnw}
-    {
-      \exp_not:c{#1_quicksort_compare:nnTF}{##1}{##4}
-      \exp_not:c{#1_quicksort_partition_greater_ii_braced:nnnn}
-      \exp_not:c{#1_quicksort_partition_less_ii_braced:nnnn}
-    }
-    {##1}{##2}{##3}{##4}
-  }
-  \cs_set:cpx {#1_quicksort_do_partition_ii:nnnw} ##1##2##3 #2 ##4 #3 {
-    \exp_not:N \quark_if_nil:nTF {##4} \exp_not:c {#1_do_quicksort_braced:nnnnw}
-    {
-      \exp_not:c{#1_quicksort_compare:nnTF}{##4}{##1}
-      \exp_not:c{#1_quicksort_partition_less_i:nnnn}
-      \exp_not:c{#1_quicksort_partition_greater_i:nnnn}
-    }
-    {##1}{##2}{##3}{##4}
-  }
-  \cs_set:cpx {#1_quicksort_do_partition_ii_braced:nnnn} ##1##2##3##4 {
-    \exp_not:N \quark_if_nil:nTF {##4} \exp_not:c {#1_do_quicksort_braced:nnnnw}
-    {
-      \exp_not:c{#1_quicksort_compare:nnTF}{##4}{##1}
-      \exp_not:c{#1_quicksort_partition_less_i_braced:nnnn}
-      \exp_not:c{#1_quicksort_partition_greater_i_braced:nnnn}
-    }
-    {##1}{##2}{##3}{##4}
-  }
-  \cs_set:cpx {#1_quicksort_partition_less_i:nnnn} ##1##2##3##4{
-    \exp_not:c{#1_quicksort_do_partition_i:nnnw}{##1}{##2}{{##4}##3}}
-  \cs_set:cpx {#1_quicksort_partition_less_ii:nnnn} ##1##2##3##4{
-    \exp_not:c{#1_quicksort_do_partition_ii:nnnw}{##1}{##2}{##3{##4}}}
-  \cs_set:cpx {#1_quicksort_partition_greater_i:nnnn} ##1##2##3##4{
-    \exp_not:c{#1_quicksort_do_partition_i:nnnw}{##1}{{##4}##2}{##3}}
-  \cs_set:cpx {#1_quicksort_partition_greater_ii:nnnn} ##1##2##3##4{
-    \exp_not:c{#1_quicksort_do_partition_ii:nnnw}{##1}{##2{##4}}{##3}}
-  \cs_set:cpx {#1_quicksort_partition_less_i_braced:nnnn} ##1##2##3##4{
-    \exp_not:c{#1_quicksort_do_partition_i_braced:nnnn}{##1}{##2}{{##4}##3}}
-  \cs_set:cpx {#1_quicksort_partition_less_ii_braced:nnnn} ##1##2##3##4{
-    \exp_not:c{#1_quicksort_do_partition_ii_braced:nnnn}{##1}{##2}{##3{##4}}}
-  \cs_set:cpx {#1_quicksort_partition_greater_i_braced:nnnn} ##1##2##3##4{
-    \exp_not:c{#1_quicksort_do_partition_i_braced:nnnn}{##1}{{##4}##2}{##3}}
-  \cs_set:cpx {#1_quicksort_partition_greater_ii_braced:nnnn} ##1##2##3##4{
-    \exp_not:c{#1_quicksort_do_partition_ii_braced:nnnn}{##1}{##2{##4}}{##3}}
-  \cs_set:cpx {#1_do_quicksort_braced:nnnnw} ##1##2##3##4\q_stop {
-    \exp_not:c{#1_quicksort_braced:n}{##2}
-    \exp_not:c{#1_quicksort_function:n}{##1}
-    \exp_not:c{#1_quicksort_braced:n}{##3}
-  }
-}
-\prg_define_quicksort:nnn {prg}{}{}
-\cs_set:Npn \prg_quicksort_function:n {\ERROR}
-\cs_set:Npn \prg_quicksort_compare:nnTF {\ERROR}
+\int_new:N \g__prg_map_int
+\cs_new_eq:NN \__prg_break_point: \prg_do_nothing:
+\cs_new:Npn \__prg_break: #1 \__prg_break_point: { }
+\cs_new:Npn \__prg_break:n #1#2 \__prg_break_point: {#1}
+\cs_new_eq:NN \prg_case_int:nnn \int_case:nnn
+\cs_new_eq:NN \prg_case_str:nnn \str_case:nnn
+\cs_new_eq:NN \prg_case_str:onn \str_case:onn
+\cs_new_eq:NN \prg_case_str:xxn \str_case_x:nnn
+\cs_new_eq:NN \prg_case_tl:Nnn  \tl_case:Nnn
+\cs_new_eq:NN \prg_case_tl:cnn  \tl_case:cnn
+\cs_new_eq:NN \prg_stepwise_function:nnnN  \int_step_function:nnnN
+\cs_new_eq:NN \prg_stepwise_inline:nnnn    \int_step_inline:nnnn
+\cs_new_eq:NN \prg_stepwise_variable:nnnNn \int_step_variable:nnnNn
 %% 
 %%
 %% End of file `l3prg.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3prop.sty b/Master/texmf-dist/tex/latex/l3kernel/l3prop.sty
index 539f1539352..5699c49cc37 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3prop.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3prop.sty
@@ -46,20 +46,19 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3prop.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental property lists}
-%%
+\GetIdInfo$Id: l3prop.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Property lists}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
-\quark_new:N \q_prop
-\tl_const:Nn \c_empty_prop { \q_prop }
+\__expl_package_check:
+\quark_new:N \q__prop
+\tl_const:Nn \c_empty_prop { \q__prop }
 \cs_new_protected:Npn \prop_new:N #1 { \cs_new_eq:NN  #1  \c_empty_prop }
 \cs_new_protected:Npn \prop_new:c #1 { \cs_new_eq:cN {#1} \c_empty_prop }
 \cs_new_protected:Npn \prop_clear:N #1  { \cs_set_eq:NN   #1  \c_empty_prop }
-\cs_new_protected:Npn \prop_clear:c #1  { \cs_set_eq:cN  {#1} \c_empty_prop }
+\cs_generate_variant:Nn \prop_clear:N { c }
 \cs_new_protected:Npn \prop_gclear:N #1 { \cs_gset_eq:NN  #1  \c_empty_prop }
-\cs_new_protected:Npn \prop_gclear:c #1 { \cs_gset_eq:cN {#1} \c_empty_prop }
+\cs_generate_variant:Nn \prop_gclear:N { c }
 \cs_new_protected:Npn \prop_clear_new:N #1
   { \prop_if_exist:NTF #1 { \prop_clear:N #1 } { \prop_new:N #1 } }
 \cs_generate_variant:Nn \prop_clear_new:N { c }
@@ -74,57 +73,55 @@
 \cs_new_eq:NN \prop_gset_eq:Nc \tl_gset_eq:Nc
 \cs_new_eq:NN \prop_gset_eq:cN \tl_gset_eq:cN
 \cs_new_eq:NN \prop_gset_eq:cc \tl_gset_eq:cc
-\cs_new_protected:Npn \prop_split:NnTF #1#2
-  { \exp_args:NNo \prop_split_aux:NnTF #1 { \tl_to_str:n {#2} } }
-\cs_new_protected:Npn \prop_split_aux:NnTF #1#2
-  {
-    \cs_set_protected:Npn \prop_split_aux:w
-      ##1 \q_prop #2 \q_prop ##2 ##3 ##4 \q_mark ##5 \q_stop
-      { \prop_split_aux:nnnn ##3 { {##1 \q_prop } {##2} {##4} } }
-    \exp_after:wN \prop_split_aux:w #1 \q_mark
-         \q_prop #2 \q_prop { } { ? \use_ii:nn { } } \q_mark \q_stop
-  }
-\cs_new:Npn \prop_split_aux:nnnn #1#2#3#4 { #3 #2 }
-\cs_new_protected:Npn \prop_split_aux:w { }
-\cs_new_protected:Npn \prop_split:Nnn #1#2#3
+\prop_new:N \l_tmpa_prop
+\prop_new:N \l_tmpb_prop
+\prop_new:N \g_tmpa_prop
+\prop_new:N \g_tmpb_prop
+\cs_new_protected:Npn \__prop_split:NnTF #1#2
+  { \exp_args:NNo \__prop_split_aux:NnTF #1 { \tl_to_str:n {#2} } }
+\cs_new_protected:Npn \__prop_split_aux:NnTF #1#2
   {
-    \prop_split:NnTF #1 {#2}
-    {#3}
-    { \exp_args:Nno \use:n {#3} {#1} { \q_no_value } { } }
+    \cs_set_protected:Npn \__prop_split_aux:w
+      ##1 \q__prop #2 \q__prop ##2 ##3 ##4 \q_mark ##5 \q_stop
+      { \__prop_split_aux:nnnn ##3 { {##1 \q__prop } {##2} {##4} } }
+    \exp_after:wN \__prop_split_aux:w #1 \q_mark
+         \q__prop #2 \q__prop { } { ? \use_ii:nn { } } \q_mark \q_stop
   }
-\cs_new_protected:Npn \prop_del:Nn #1#2
-  { \prop_split:NnTF #1 {#2} { \prop_del_aux:NNnnn \tl_set:Nn #1 } { } }
-\cs_new_protected:Npn \prop_gdel:Nn #1#2
-  { \prop_split:NnTF #1 {#2} { \prop_del_aux:NNnnn \tl_gset:Nn #1 } { } }
-\cs_new_protected:Npn \prop_del_aux:NNnnn #1#2#3#4#5
+\cs_new:Npn \__prop_split_aux:nnnn #1#2#3#4 { #3 #2 }
+\cs_new_protected:Npn \__prop_split_aux:w { }
+\cs_new_protected:Npn \prop_remove:Nn #1#2
+  { \__prop_split:NnTF #1 {#2} { \__prop_remove:NNnnn \tl_set:Nn #1 } { } }
+\cs_new_protected:Npn \prop_gremove:Nn #1#2
+  { \__prop_split:NnTF #1 {#2} { \__prop_remove:NNnnn \tl_gset:Nn #1 } { } }
+\cs_new_protected:Npn \__prop_remove:NNnnn #1#2#3#4#5
   { #1 #2 { #3 #5 } }
-\cs_generate_variant:Nn \prop_del:Nn  {     NV }
-\cs_generate_variant:Nn \prop_del:Nn  { c , cV }
-\cs_generate_variant:Nn \prop_gdel:Nn {     NV }
-\cs_generate_variant:Nn \prop_gdel:Nn { c , cV }
+\cs_generate_variant:Nn \prop_remove:Nn  {     NV }
+\cs_generate_variant:Nn \prop_remove:Nn  { c , cV }
+\cs_generate_variant:Nn \prop_gremove:Nn {     NV }
+\cs_generate_variant:Nn \prop_gremove:Nn { c , cV }
 \cs_new_protected:Npn \prop_get:NnN #1#2#3
   {
-    \prop_split:NnTF #1 {#2}
-      { \prop_get_aux:Nnnn #3 }
+    \__prop_split:NnTF #1 {#2}
+      { \__prop_get:Nnnn #3 }
       { \tl_set:Nn #3 { \q_no_value } }
   }
-\cs_new_protected:Npn \prop_get_aux:Nnnn #1#2#3#4
+\cs_new_protected:Npn \__prop_get:Nnnn #1#2#3#4
   { \tl_set:Nn #1 {#3} }
 \cs_generate_variant:Nn \prop_get:NnN {     NV , No }
 \cs_generate_variant:Nn \prop_get:NnN { c , cV , co }
 \cs_new_protected:Npn \prop_pop:NnN #1#2#3
   {
-    \prop_split:NnTF #1 {#2}
-      { \prop_pop_aux:NNNnnn \tl_set:Nn #1 #3 }
+    \__prop_split:NnTF #1 {#2}
+      { \__prop_pop:NNNnnn \tl_set:Nn #1 #3 }
       { \tl_set:Nn #3 { \q_no_value } }
   }
 \cs_new_protected:Npn \prop_gpop:NnN #1#2#3
   {
-    \prop_split:NnTF #1 {#2}
-      { \prop_pop_aux:NNNnnn \tl_gset:Nn #1 #3 }
+    \__prop_split:NnTF #1 {#2}
+      { \__prop_pop:NNNnnn \tl_gset:Nn #1 #3 }
       { \tl_set:Nn #3 { \q_no_value } }
   }
-\cs_new_protected:Npn \prop_pop_aux:NNNnnn #1#2#3#4#5#6
+\cs_new_protected:Npn \__prop_pop:NNNnnn #1#2#3#4#5#6
   {
     \tl_set:Nn #3 {#5}
     #1 #2 { #4 #6 }
@@ -133,18 +130,47 @@
 \cs_generate_variant:Nn \prop_pop:NnN  { c , co }
 \cs_generate_variant:Nn \prop_gpop:NnN {     No }
 \cs_generate_variant:Nn \prop_gpop:NnN { c , co }
-\cs_new_protected:Npn \prop_put:Nnn { \prop_put_aux:NNnn \tl_set:Nx }
-\cs_new_protected:Npn \prop_gput:Nnn { \prop_put_aux:NNnn \tl_gset:Nx }
-\cs_new_protected:Npn \prop_put_aux:NNnn #1#2#3#4
+\prg_new_protected_conditional:Npnn \prop_pop:NnN #1#2#3 { T , F , TF }
+  {
+    \__prop_split:NnTF #1 {#2}
+      { \__prop_pop_true:NNNnnn \tl_set:Nn #1 #3 }
+      { \prg_return_false: }
+  }
+\prg_new_protected_conditional:Npnn \prop_gpop:NnN #1#2#3 { T , F , TF }
+  {
+    \__prop_split:NnTF #1 {#2}
+      { \__prop_pop_true:NNNnnn \tl_gset:Nn #1 #3 }
+      { \prg_return_false: }
+  }
+\cs_new_protected:Npn \__prop_pop_true:NNNnnn #1#2#3#4#5#6
+  {
+    \tl_set:Nn #3 {#5}
+    #1 #2 { #4 #6 }
+    \prg_return_true:
+  }
+\cs_generate_variant:Nn \prop_pop:NnNT   { c }
+\cs_generate_variant:Nn \prop_pop:NnNF   { c }
+\cs_generate_variant:Nn \prop_pop:NnNTF  { c }
+\cs_generate_variant:Nn \prop_gpop:NnNT  { c }
+\cs_generate_variant:Nn \prop_gpop:NnNF  { c }
+\cs_generate_variant:Nn \prop_gpop:NnNTF { c }
+\cs_new_protected:Npn \prop_put:Nnn
+  { \__prop_put:NNNnn \tl_set:Nx \tl_put_right:Nx }
+\cs_new_protected:Npn \prop_gput:Nnn
+  { \__prop_put:NNNnn \tl_gset:Nx \tl_gput_right:Nx }
+\cs_new_protected:Npn \__prop_put:NNNnn #1#2#3#4#5
   {
-    \prop_split:Nnn #2 {#3} { \prop_put_aux:NNnnnnn #1 #2 {#3} {#4} }
+    \__prop_split:NnTF #3 {#4}
+      { \__prop_put:NNnnnnn #1 #3 {#4} {#5} }
+      { #2 #3 { \tl_to_str:n {#4} \exp_not:n { \q__prop {#5} \q__prop } } }
   }
-\cs_new_protected:Npn \prop_put_aux:NNnnnnn #1#2#3#4#5#6#7
+\cs_new_protected:Npn \__prop_put:NNnnnnn #1#2#3#4#5#6#7
   {
     #1 #2
       {
-        \exp_not:n { #5 #7 }
-        \tl_to_str:n {#3} \exp_not:n { \q_prop {#4} \q_prop }
+        \exp_not:n {#5}
+        \tl_to_str:n {#3} \exp_not:n { \q__prop {#4} \q__prop }
+        \exp_not:n {#7}
       }
   }
 \cs_generate_variant:Nn \prop_put:Nnn
@@ -156,16 +182,16 @@
 \cs_generate_variant:Nn \prop_gput:Nnn
   { c , cnV , cno , cnx , cV , cVV , co , coo }
 \cs_new_protected_nopar:Npn \prop_put_if_new:Nnn
-  { \prop_put_if_new_aux:NNnn \tl_put_right:Nx }
+  { \__prop_put_if_new:NNnn \tl_put_right:Nx }
 \cs_new_protected_nopar:Npn \prop_gput_if_new:Nnn
-  { \prop_put_if_new_aux:NNnn \tl_gput_right:Nx }
-\cs_new_protected:Npn \prop_put_if_new_aux:NNnn #1#2#3#4
+  { \__prop_put_if_new:NNnn \tl_gput_right:Nx }
+\cs_new_protected:Npn \__prop_put_if_new:NNnn #1#2#3#4
   {
-    \prop_split:NnTF #2 {#3}
+    \__prop_split:NnTF #2 {#3}
       { \use_none:nnn }
       {
         #1 #2
-          { \tl_to_str:n {#3} \exp_not:n { \q_prop {#4} \q_prop } }
+          { \tl_to_str:n {#3} \exp_not:n { \q__prop {#4} \q__prop } }
       }
   }
 \cs_generate_variant:Nn \prop_put_if_new:Nnn  { c }
@@ -192,26 +218,26 @@
 \cs_generate_variant:Nn \prop_if_empty:NF  {c}
 \prg_new_conditional:Npnn \prop_if_in:Nn #1#2 { p , T , F , TF }
   {
-    \exp_last_unbraced:Noo \prop_if_in_aux:nwn
+    \exp_last_unbraced:Noo \__prop_if_in:nwn
       { \tl_to_str:n {#2} } #1
-      \tl_to_str:n {#2} \q_prop { }
-    \q_recursion_tail
-    \prg_break_point:n { }
+      \tl_to_str:n {#2} \q__prop { }
+    \q_recursion_tail % could be any cs != \q__prop
+    \__prg_break_point:
   }
-\cs_new:Npn \prop_if_in_aux:nwn #1 \q_prop #2 \q_prop #3
+\cs_new:Npn \__prop_if_in:nwn #1 \q__prop #2 \q__prop #3
   {
-    \str_if_eq:xxTF {#1} {#2}
-      { \prop_if_in_aux:N }
-      { \prop_if_in_aux:nwn {#1} }
+    \str_if_eq_x:nnTF {#1} {#2}
+      { \__prop_if_in:N }
+      { \__prop_if_in:nwn {#1} }
   }
-\cs_new:Npn \prop_if_in_aux:N #1
+\cs_new:Npn \__prop_if_in:N #1
   {
-    \if_meaning:w \q_prop #1
+    \if_meaning:w \q__prop #1
       \prg_return_true:
     \else:
       \prg_return_false:
     \fi:
-    \prop_map_break:
+    \__prg_break:
   }
 \cs_generate_variant:Nn \prop_if_in_p:Nn {     NV , No }
 \cs_generate_variant:Nn \prop_if_in_p:Nn { c , cV , co }
@@ -223,11 +249,11 @@
 \cs_generate_variant:Nn \prop_if_in:NnTF { c , cV , co }
 \prg_new_protected_conditional:Npnn \prop_get:NnN #1#2#3 { T , F , TF }
   {
-    \prop_split:NnTF #1 {#2}
-      { \prop_get_aux_true:Nnnn #3 }
+    \__prop_split:NnTF #1 {#2}
+      { \__prop_get_true:Nnnn #3 }
       { \prg_return_false: }
   }
-\cs_new_protected:Npn \prop_get_aux_true:Nnnn #1#2#3#4
+\cs_new_protected:Npn \__prop_get_true:Nnnn #1#2#3#4
   {
     \tl_set:Nn #1 {#3}
     \prg_return_true:
@@ -240,95 +266,49 @@
 \cs_generate_variant:Nn \prop_get:NnNTF { c , cV , co }
 \cs_new:Npn \prop_map_function:NN #1#2
   {
-    \exp_last_unbraced:NNo \prop_map_function_aux:Nwn #2
-      #1 \q_recursion_tail \q_prop { }
-    \prg_break_point:n { }
+    \exp_last_unbraced:NNo \__prop_map_function:Nwn #2
+      #1 \q_recursion_tail \q__prop { }
+    \__prg_break_point:Nn \prop_map_break: { }
   }
-\cs_new:Npn \prop_map_function_aux:Nwn #1 \q_prop #2 \q_prop #3
+\cs_new:Npn \__prop_map_function:Nwn #1 \q__prop #2 \q__prop #3
   {
-    \if_meaning:w \q_recursion_tail #2
-      \exp_after:wN \prop_map_break:
-    \fi:
+    \__quark_if_recursion_tail_break:nN {#2} \prop_map_break:
     #1 {#2} {#3}
-    \prop_map_function_aux:Nwn #1
+    \__prop_map_function:Nwn #1
   }
 \cs_generate_variant:Nn \prop_map_function:NN {     Nc }
 \cs_generate_variant:Nn \prop_map_function:NN { c , cc }
 \cs_new_protected:Npn \prop_map_inline:Nn #1#2
   {
-    \int_gincr:N \g_prg_map_int
-    \cs_gset:cpn { prop_map_inline_ \int_use:N \g_prg_map_int :nn }
-      ##1##2 {#2}
-    \exp_last_unbraced:Nco \prop_map_function_aux:Nwn
-      { prop_map_inline_ \int_use:N \g_prg_map_int :nn }
+    \int_gincr:N \g__prg_map_int
+    \cs_gset:cpn { __prg_map_ \int_use:N \g__prg_map_int :w } ##1##2 {#2}
+    \exp_last_unbraced:Nco \__prop_map_function:Nwn
+      { __prg_map_ \int_use:N \g__prg_map_int :w }
       #1
-      \q_recursion_tail \q_prop { }
-    \prg_break_point:n { \int_gdecr:N \g_prg_map_int }
+      \q_recursion_tail \q__prop { }
+    \__prg_break_point:Nn \prop_map_break: { \int_gdecr:N \g__prg_map_int }
   }
 \cs_generate_variant:Nn \prop_map_inline:Nn { c }
-\cs_new_eq:NN \prop_map_break:  \prg_map_break:
-\cs_new_eq:NN \prop_map_break:n \prg_map_break:n
+\cs_new_nopar:Npn \prop_map_break:
+  { \__prg_map_break:Nn \prop_map_break: { } }
+\cs_new_nopar:Npn \prop_map_break:n
+  { \__prg_map_break:Nn \prop_map_break: }
 \cs_new_protected:Npn \prop_show:N #1
   {
-    \msg_aux_show:Nnx
+    \__msg_show_variable:Nnn
       #1
       { prop }
-      { \prop_map_function:NN #1 \msg_aux_show:nn }
+      { \prop_map_function:NN #1 \__msg_show_item:nn }
   }
 \cs_generate_variant:Nn \prop_show:N { c }
-\prg_new_protected_conditional:Npnn \prop_pop:NnN #1#2#3 { T , F , TF }
-  {
-    \prop_split:NnTF #1 {#2}
-      { \prop_pop_aux_true:NNNnnn \tl_set:Nn #1 #3 }
-      { \prg_return_false: }
-  }
-\prg_new_protected_conditional:Npnn \prop_gpop:NnN #1#2#3 { T , F , TF }
-  {
-    \prop_split:NnTF #1 {#2}
-      { \prop_pop_aux_true:NNNnnn \tl_gset:Nn #1 #3 }
-      { \prg_return_false: }
-  }
-\cs_new_protected:Npn \prop_pop_aux_true:NNNnnn #1#2#3#4#5#6
-  {
-    \tl_set:Nn #3 {#5}
-    #1 #2 { #4 #6 }
-    \prg_return_true:
-  }
-\cs_generate_variant:Nn \prop_pop:NnNT   { c }
-\cs_generate_variant:Nn \prop_pop:NnNF   { c }
-\cs_generate_variant:Nn \prop_pop:NnNTF  { c }
-\cs_generate_variant:Nn \prop_gpop:NnNT  { c }
-\cs_generate_variant:Nn \prop_gpop:NnNF  { c }
-\cs_generate_variant:Nn \prop_gpop:NnNTF { c }
-\cs_new:Npn \prop_map_tokens:Nn #1#2
-  {
-    \exp_last_unbraced:Nno \prop_map_tokens_aux:nwn {#2} #1
-    \q_recursion_tail \q_prop { }
-    \prg_break_point:n { }
-  }
-\cs_new:Npn \prop_map_tokens_aux:nwn #1 \q_prop #2 \q_prop #3
-  {
-    \if_meaning:w \q_recursion_tail #2
-       \exp_after:wN \prop_map_break:
-    \fi:
-    \use:n {#1} {#2} {#3}
-    \prop_map_tokens_aux:nwn {#1}
-  }
-\cs_generate_variant:Nn \prop_map_tokens:Nn { c }
-\cs_new:Npn \prop_get:Nn #1#2
-  {
-    \exp_last_unbraced:Noo \prop_get_Nn_aux:nwn
-      { \tl_to_str:n {#2} } #1
-      \tl_to_str:n {#2} \q_prop { }
-    \prg_break_point:n { }
-  }
-\cs_new:Npn \prop_get_Nn_aux:nwn #1 \q_prop #2 \q_prop #3
-  {
-    \str_if_eq:xxTF {#1} {#2}
-      { \prg_map_break:n { \exp_not:n {#3} } }
-      { \prop_get_Nn_aux:nwn {#1} }
-  }
-\cs_generate_variant:Nn \prop_get:Nn { c }
+\cs_new_eq:NN \prop_del:Nn \prop_remove:Nn
+\cs_new_eq:NN \prop_del:NV \prop_remove:NV
+\cs_new_eq:NN \prop_del:cn \prop_remove:cn
+\cs_new_eq:NN \prop_del:cV \prop_remove:cV
+\cs_new_eq:NN \prop_gdel:Nn \prop_gremove:Nn
+\cs_new_eq:NN \prop_gdel:NV \prop_gremove:NV
+\cs_new_eq:NN \prop_gdel:cn \prop_gremove:cn
+\cs_new_eq:NN \prop_gdel:cV \prop_gremove:cV
 %% 
 %%
 %% End of file `l3prop.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3quark.sty b/Master/texmf-dist/tex/latex/l3kernel/l3quark.sty
index e22e215617a..deaf7d4699d 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3quark.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3quark.sty
@@ -46,11 +46,11 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3quark.dtx 3384 2012-02-12 13:13:11Z will $
-  {L3 Experimental quarks}
+\GetIdInfo$Id: l3quark.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Quarks}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 \cs_new_protected:Npn \quark_new:N #1 { \tl_const:Nn #1 {#1} }
 \quark_new:N \q_nil
 \quark_new:N \q_mark
@@ -90,17 +90,17 @@
   }
 \cs_generate_variant:Nn \quark_if_recursion_tail_stop:n { o }
 \cs_generate_variant:Nn \quark_if_recursion_tail_stop_do:nn { o }
-\cs_new:Npn \quark_if_recursion_tail_break:N #1
+\cs_new:Npn \__quark_if_recursion_tail_break:NN #1#2
   {
     \if_meaning:w \q_recursion_tail #1
-      \exp_after:wN \prg_map_break:
+      \exp_after:wN #2
     \fi:
   }
-\cs_new:Npn \quark_if_recursion_tail_break:n #1
+\cs_new:Npn \__quark_if_recursion_tail_break:nN #1#2
   {
     \if_int_compare:w \pdftex_strcmp:D
       { \exp_not:N \q_recursion_tail } { \exp_not:n {#1} } = \c_zero
-      \exp_after:wN \prg_map_break:
+      \exp_after:wN #2
     \fi:
   }
 \prg_new_conditional:Nnn \quark_if_nil:N { p, T , F , TF }
@@ -145,23 +145,27 @@
 \cs_generate_variant:Nn \quark_if_nil:nTF { V , o }
 \cs_generate_variant:Nn \quark_if_nil:nT  { V , o }
 \cs_generate_variant:Nn \quark_if_nil:nF  { V , o }
-\quark_new:N \q_tl_act_mark
-\quark_new:N \q_tl_act_stop
-\tl_new:N \g_scan_marks_tl
-\cs_new_protected:Npn \scan_new:N #1
+\quark_new:N \q__tl_act_mark
+\quark_new:N \q__tl_act_stop
+\tl_new:N \g__scan_marks_tl
+\cs_new_protected:Npn \__scan_new:N #1
   {
-    \tl_if_in:NnTF \g_scan_marks_tl { #1 }
+    \tl_if_in:NnTF \g__scan_marks_tl { #1 }
       {
-        \msg_kernel_error:nnx { scan } { already-defined }
+        \__msg_kernel_error:nnx { kernel } { scanmark-already-defined }
           { \token_to_str:N #1 }
       }
       {
-        \tl_gput_right:Nn \g_scan_marks_tl {#1}
+        \tl_gput_right:Nn \g__scan_marks_tl {#1}
         \cs_new_eq:NN #1 \scan_stop:
       }
   }
-\scan_new:N \s_stop
-\cs_new:Npn \use_none_delimit_by_s_stop:w #1 \s_stop { }
+\__scan_new:N \s__stop
+\cs_new:Npn \__use_none_delimit_by_s__stop:w #1 \s__stop { }
+\cs_new:Npn \quark_if_recursion_tail_break:N #1
+  { \__quark_if_recursion_tail_break:NN #1 \prg_break: }
+\cs_new:Npn \quark_if_recursion_tail_break:n #1
+  { \__quark_if_recursion_tail_break:nN {#1} \prg_break: }
 %% 
 %%
 %% End of file `l3quark.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3seq.sty b/Master/texmf-dist/tex/latex/l3kernel/l3seq.sty
index 6de7e2ea1ed..e5a270b01d7 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3seq.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3seq.sty
@@ -46,18 +46,19 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3seq.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental sequences and stacks}
+\GetIdInfo$Id: l3seq.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Sequences and stacks}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
-\cs_new:Npn \seq_item:n
+\__expl_package_check:
+\cs_new:Npn \__seq_item:n
   {
-    \msg_expandable_kernel_error:nn { seq } { misused }
+    \__msg_kernel_expandable_error:nn { kernel } { misused-sequence }
     \use_none:n
   }
-\tl_new:N \l_seq_internal_a_tl
-\tl_new:N \l_seq_internal_b_tl
+\tl_new:N \l__seq_internal_a_tl
+\tl_new:N \l__seq_internal_b_tl
+\cs_new_eq:NN \c_empty_seq \c_empty_tl
 \cs_new_eq:NN \seq_new:N \tl_new:N
 \cs_new_eq:NN \seq_new:c \tl_new:c
 \cs_new_eq:NN \seq_clear:N  \tl_clear:N
@@ -77,37 +78,39 @@
 \cs_new_eq:NN \seq_gset_eq:cN \tl_gset_eq:cN
 \cs_new_eq:NN \seq_gset_eq:cc \tl_gset_eq:cc
 \cs_new_protected_nopar:Npn \seq_set_split:Nnn
-  { \seq_set_split_aux:NNnn \tl_set:Nx }
+  { \__seq_set_split:NNnn \tl_set:Nx }
 \cs_new_protected_nopar:Npn \seq_gset_split:Nnn
-  { \seq_set_split_aux:NNnn \tl_gset:Nx }
-\cs_new_protected:Npn \seq_set_split_aux:NNnn #1 #2 #3 #4
+  { \__seq_set_split:NNnn \tl_gset:Nx }
+\cs_new_protected:Npn \__seq_set_split:NNnn #1 #2 #3 #4
   {
     \tl_if_empty:nTF {#3}
-      { #1 #2 { \tl_map_function:nN {#4} \seq_wrap_item:n } }
+      { #1 #2 { \tl_map_function:nN {#4} \__seq_wrap_item:n } }
       {
-        \tl_set:Nn \l_seq_internal_a_tl
+        \tl_set:Nn \l__seq_internal_a_tl
           {
-            \seq_set_split_aux_i:w \prg_do_nothing:
+            \__seq_set_split_i:w \prg_do_nothing:
             #4
-            \seq_set_split_aux_end:
+            \__seq_set_split_end:
           }
-        \tl_replace_all:Nnn \l_seq_internal_a_tl { #3 }
+        \tl_replace_all:Nnn \l__seq_internal_a_tl { #3 }
           {
-            \seq_set_split_aux_end:
-            \seq_set_split_aux_i:w \prg_do_nothing:
+            \__seq_set_split_end:
+            \__seq_set_split_i:w \prg_do_nothing:
           }
-        \tl_set:Nx \l_seq_internal_a_tl { \l_seq_internal_a_tl }
-        #1 #2 { \l_seq_internal_a_tl }
+        \tl_set:Nx \l__seq_internal_a_tl { \l__seq_internal_a_tl }
+        #1 #2 { \l__seq_internal_a_tl }
       }
   }
-\cs_new:Npn \seq_set_split_aux_i:w #1 \seq_set_split_aux_end:
+\cs_new:Npn \__seq_set_split_i:w #1 \__seq_set_split_end:
   {
-    \exp_not:N \seq_set_split_aux_ii:w
+    \exp_not:N \__seq_set_split_ii:w
     \exp_args:No \tl_trim_spaces:n {#1}
-    \exp_not:N \seq_set_split_aux_end:
+    \exp_not:N \__seq_set_split_end:
   }
-\cs_new:Npn \seq_set_split_aux_ii:w #1 \seq_set_split_aux_end:
-  { \seq_wrap_item:n {#1} }
+\cs_new:Npn \__seq_set_split_ii:w #1 \__seq_set_split_end:
+  { \__seq_wrap_item:n {#1} }
+\cs_generate_variant:Nn \seq_set_split:Nnn  { NnV }
+\cs_generate_variant:Nn \seq_gset_split:Nnn { NnV }
 \cs_new_protected:Npn \seq_concat:NNN #1#2#3
   { \tl_set:Nx #1 { \exp_not:o {#2} \exp_not:o {#3} } }
 \cs_new_protected:Npn \seq_gconcat:NNN #1#2#3
@@ -123,62 +126,62 @@
 \cs_new_eq:NN \seq_if_exist:cF  \cs_if_exist:cF
 \cs_new_eq:NN \seq_if_exist_p:c \cs_if_exist_p:c
 \cs_new_protected:Npn \seq_put_left:Nn #1#2
-  { \tl_put_left:Nn #1 { \seq_item:n {#2} } }
+  { \tl_put_left:Nn #1 { \__seq_item:n {#2} } }
 \cs_new_protected:Npn \seq_put_right:Nn #1#2
-  { \tl_put_right:Nn #1 { \seq_item:n {#2} } }
+  { \tl_put_right:Nn #1 { \__seq_item:n {#2} } }
 \cs_generate_variant:Nn \seq_put_left:Nn  {     NV , Nv , No , Nx }
 \cs_generate_variant:Nn \seq_put_left:Nn  { c , cV , cv , co , cx }
 \cs_generate_variant:Nn \seq_put_right:Nn {     NV , Nv , No , Nx }
 \cs_generate_variant:Nn \seq_put_right:Nn { c , cV , cv , co , cx }
 \cs_new_protected:Npn \seq_gput_left:Nn #1#2
-  { \tl_gput_left:Nn #1 { \seq_item:n {#2} } }
+  { \tl_gput_left:Nn #1 { \__seq_item:n {#2} } }
 \cs_new_protected:Npn \seq_gput_right:Nn #1#2
-  { \tl_gput_right:Nn #1 { \seq_item:n {#2} } }
+  { \tl_gput_right:Nn #1 { \__seq_item:n {#2} } }
 \cs_generate_variant:Nn \seq_gput_left:Nn  {     NV , Nv , No , Nx }
 \cs_generate_variant:Nn \seq_gput_left:Nn  { c , cV , cv , co , cx }
 \cs_generate_variant:Nn \seq_gput_right:Nn {     NV , Nv , No , Nx }
 \cs_generate_variant:Nn \seq_gput_right:Nn { c , cV , cv , co , cx }
-\cs_new:Npn \seq_wrap_item:n #1 { \exp_not:n { \seq_item:n {#1} } }
-\seq_new:N \l_seq_internal_remove_seq
+\cs_new:Npn \__seq_wrap_item:n #1 { \exp_not:n { \__seq_item:n {#1} } }
+\seq_new:N \l__seq_remove_seq
 \cs_new_protected:Npn \seq_remove_duplicates:N
-  { \seq_remove_duplicates_aux:NN \seq_set_eq:NN }
+  { \__seq_remove_duplicates:NN \seq_set_eq:NN }
 \cs_new_protected:Npn \seq_gremove_duplicates:N
-  { \seq_remove_duplicates_aux:NN \seq_gset_eq:NN }
-\cs_new_protected:Npn \seq_remove_duplicates_aux:NN #1#2
+  { \__seq_remove_duplicates:NN \seq_gset_eq:NN }
+\cs_new_protected:Npn \__seq_remove_duplicates:NN #1#2
   {
-    \seq_clear:N \l_seq_internal_remove_seq
+    \seq_clear:N \l__seq_remove_seq
     \seq_map_inline:Nn #2
       {
-        \seq_if_in:NnF \l_seq_internal_remove_seq {##1}
-          { \seq_put_right:Nn \l_seq_internal_remove_seq {##1} }
+        \seq_if_in:NnF \l__seq_remove_seq {##1}
+          { \seq_put_right:Nn \l__seq_remove_seq {##1} }
       }
-    #1 #2 \l_seq_internal_remove_seq
+    #1 #2 \l__seq_remove_seq
   }
 \cs_generate_variant:Nn \seq_remove_duplicates:N  { c }
 \cs_generate_variant:Nn \seq_gremove_duplicates:N { c }
 \cs_new_protected:Npn \seq_remove_all:Nn
-  { \seq_remove_all_aux:NNn \tl_set:Nx }
+  { \__seq_remove_all_aux:NNn \tl_set:Nx }
 \cs_new_protected:Npn \seq_gremove_all:Nn
-  { \seq_remove_all_aux:NNn \tl_gset:Nx }
-\cs_new_protected:Npn \seq_remove_all_aux:NNn #1#2#3
+  { \__seq_remove_all_aux:NNn \tl_gset:Nx }
+\cs_new_protected:Npn \__seq_remove_all_aux:NNn #1#2#3
   {
-    \seq_push_item_def:n
+    \__seq_push_item_def:n
       {
         \str_if_eq:nnT {##1} {#3}
           {
             \if_false: { \fi: }
-            \tl_set:Nn \l_seq_internal_b_tl {##1}
+            \tl_set:Nn \l__seq_internal_b_tl {##1}
             #1 #2
                { \if_false: } \fi:
                  \exp_not:o {#2}
-                 \tl_if_eq:NNT \l_seq_internal_a_tl \l_seq_internal_b_tl
+                 \tl_if_eq:NNT \l__seq_internal_a_tl \l__seq_internal_b_tl
                    { \use_none:nn }
           }
-        \seq_wrap_item:n {##1}
+        \__seq_wrap_item:n {##1}
       }
-    \tl_set:Nn \l_seq_internal_a_tl {#3}
+    \tl_set:Nn \l__seq_internal_a_tl {#3}
     #1 #2 {#2}
-    \seq_pop_item_def:
+    \__seq_pop_item_def:
   }
 \cs_generate_variant:Nn \seq_remove_all:Nn  { c }
 \cs_generate_variant:Nn \seq_gremove_all:Nn { c }
@@ -190,45 +193,63 @@
   { T , F , TF }
   {
     \group_begin:
-      \tl_set:Nn \l_seq_internal_a_tl {#2}
-      \cs_set_protected:Npn \seq_item:n ##1
+      \tl_set:Nn \l__seq_internal_a_tl {#2}
+      \cs_set_protected:Npn \__seq_item:n ##1
         {
-          \tl_set:Nn \l_seq_internal_b_tl {##1}
-          \if_meaning:w \l_seq_internal_a_tl \l_seq_internal_b_tl
-            \exp_after:wN \seq_if_in_aux:
+          \tl_set:Nn \l__seq_internal_b_tl {##1}
+          \if_meaning:w \l__seq_internal_a_tl \l__seq_internal_b_tl
+            \exp_after:wN \__seq_if_in:
           \fi:
         }
       #1
-      \seq_break:n { \prg_return_false: }
-    \prg_break_point:n { \group_end: }
+    \group_end:
+    \prg_return_false:
+    \__prg_break_point:
   }
-\cs_new_nopar:Npn \seq_if_in_aux: { \seq_break:n { \prg_return_true: } }
+\cs_new_nopar:Npn \__seq_if_in:
+  { \__prg_break:n { \group_end: \prg_return_true: } }
 \cs_generate_variant:Nn \seq_if_in:NnT  {     NV , Nv , No , Nx }
 \cs_generate_variant:Nn \seq_if_in:NnT  { c , cV , cv , co , cx }
 \cs_generate_variant:Nn \seq_if_in:NnF  {     NV , Nv , No , Nx }
 \cs_generate_variant:Nn \seq_if_in:NnF  { c , cV , cv , co , cx }
 \cs_generate_variant:Nn \seq_if_in:NnTF {     NV , Nv , No , Nx }
 \cs_generate_variant:Nn \seq_if_in:NnTF { c , cV , cv , co , cx }
+\cs_new_protected:Npn \__seq_pop:NNNN #1#2#3#4
+  {
+    \if_meaning:w #3 \c_empty_seq
+      \tl_set:Nn #4 { \q_no_value }
+    \else:
+      #1#2#3#4
+    \fi:
+  }
+\cs_new_protected:Npn \__seq_pop_TF:NNNN #1#2#3#4
+  {
+    \if_meaning:w #3 \c_empty_seq
+      % \tl_set:Nn #4 { \q_no_value }
+      \prg_return_false:
+    \else:
+      #1#2#3#4
+      \prg_return_true:
+    \fi:
+  }
 \cs_new_protected:Npn \seq_get_left:NN #1#2
   {
-    \seq_if_empty_err_break:N #1
-    \exp_after:wN \seq_get_left_aux:NnwN #1 \q_stop #2
-    \prg_break_point:n { }
+    \tl_set:Nx #2
+      {
+        \exp_after:wN \__seq_get_left:Nnw
+        #1 \__seq_item:n { \q_no_value } \q_stop
+      }
   }
-\cs_new_protected:Npn \seq_get_left_aux:NnwN \seq_item:n #1#2 \q_stop #3
-  { \tl_set:Nn #3 {#1} }
+\cs_new:Npn \__seq_get_left:Nnw \__seq_item:n #1#2 \q_stop
+  { \exp_not:n {#1} }
 \cs_generate_variant:Nn \seq_get_left:NN { c }
 \cs_new_protected_nopar:Npn \seq_pop_left:NN
-  { \seq_pop_left_aux:NNN \tl_set:Nn }
+  { \__seq_pop:NNNN \__seq_pop_left:NNN \tl_set:Nn }
 \cs_new_protected_nopar:Npn \seq_gpop_left:NN
-  { \seq_pop_left_aux:NNN \tl_gset:Nn }
-\cs_new_protected:Npn \seq_pop_left_aux:NNN #1#2#3
-  {
-    \seq_if_empty_err_break:N #2
-    \exp_after:wN \seq_pop_left_aux:NnwNNN #2 \q_stop #1#2#3
-    \prg_break_point:n { }
-  }
-\cs_new_protected:Npn \seq_pop_left_aux:NnwNNN \seq_item:n #1#2 \q_stop #3#4#5
+  { \__seq_pop:NNNN \__seq_pop_left:NNN \tl_gset:Nn }
+\cs_new_protected:Npn \__seq_pop_left:NNN #1#2#3
+  { \exp_after:wN \__seq_pop_left:NnwNNN #2 \q_stop #1#2#3 }
+\cs_new_protected:Npn \__seq_pop_left:NnwNNN \__seq_item:n #1#2 \q_stop #3#4#5
   {
     #3 #4 {#2}
     \tl_set:Nn #5 {#1}
@@ -237,121 +258,147 @@
 \cs_generate_variant:Nn \seq_gpop_left:NN { c }
 \cs_new_protected:Npn \seq_get_right:NN #1#2
   {
-    \seq_if_empty_err_break:N #1
-    \seq_get_right_aux:NN #1#2
-    \prg_break_point:n { }
+    \exp_after:wN \__seq_get_right_loop:nn
+    \exp_after:wN \q_no_value
+    #1
+    {
+      ??
+      \tex_afterassignment:D \use_none:n
+      \tl_set:Nn #2
+    }
   }
-\cs_new_protected:Npn \seq_get_right_aux:NN #1#2
-  {
-    \seq_push_item_def:n { }
-    \exp_after:wN \exp_after:wN \exp_after:wN \seq_get_right_loop:nn
-      \exp_after:wN \use_none:n #1
-      { \tl_set:Nn #2 }
-      { }
-      {
-        \seq_pop_item_def:
-        \seq_break:
-      }
-}
-\cs_new:Npn \seq_get_right_loop:nn #1#2
+\cs_new_protected:Npn \__seq_get_right_loop:nn #1#2
   {
-    #2 {#1}
-    \seq_get_right_loop:nn
+    \use_none:nn #2 {#1}
+    \__seq_get_right_loop:nn
   }
 \cs_generate_variant:Nn \seq_get_right:NN { c }
 \cs_new_protected_nopar:Npn \seq_pop_right:NN
-  { \seq_pop_right_aux:NNN \tl_set:Nx }
+  { \__seq_pop:NNNN \__seq_pop_right_aux:NNN \tl_set:Nx }
 \cs_new_protected_nopar:Npn \seq_gpop_right:NN
-  { \seq_pop_right_aux:NNN \tl_gset:Nx }
-\cs_new_protected:Npn \seq_pop_right_aux:NNN #1#2#3
-  {
-    \seq_if_empty_err_break:N #2
-    \seq_pop_right_aux_ii:NNN #1 #2 #3
-    \prg_break_point:n { }
-  }
-\cs_new_protected:Npn \seq_pop_right_aux_ii:NNN #1#2#3
-  {
-    \seq_push_item_def:n { \seq_wrap_item:n {##1} }
-    #1 #2 { \if_false: } \fi:
-      \exp_after:wN \exp_after:wN \exp_after:wN \seq_get_right_loop:nn
-         \exp_after:wN \use_none:n #2
+  { \__seq_pop:NNNN \__seq_pop_right_aux:NNN \tl_gset:Nx }
+\cs_new_protected:Npn \__seq_pop_right_aux:NNN #1#2#3
+  {
+    \cs_set_eq:NN \seq_tmp:w \__seq_item:n
+    \cs_set_eq:NN \__seq_item:n \scan_stop:
+    #1 #2
+      { \if_false: } \fi:
+        \exp_after:wN \exp_after:wN
+        \exp_after:wN \__seq_pop_right_loop:nn
+        \exp_after:wN \use_none:n
+        #2
         {
           \if_false: { \fi: }
-          \tl_set:Nn #3
-        }
-        { }
-        {
-          \seq_pop_item_def:
-          \seq_break:
+          \tex_afterassignment:D \use_none:n
+          \tl_set:Nx #3
         }
+    \cs_set_eq:NN \__seq_item:n \seq_tmp:w
   }
-\cs_generate_variant:Nn \seq_pop_right:NN  { c }
-\cs_generate_variant:Nn \seq_gpop_right:NN { c }
-\cs_new_eq:NN \seq_break:      \prg_map_break:
-\cs_new_eq:NN \seq_break:n     \prg_map_break:n
-\cs_new_eq:NN \seq_map_break:  \prg_map_break:
-\cs_new_eq:NN \seq_map_break:n \prg_map_break:n
-\cs_new_protected:Npn \seq_if_empty_err_break:N #1
+\cs_new:Npn \__seq_pop_right_loop:nn #1#2
   {
-    \if_meaning:w #1 \c_empty_tl
-      \msg_kernel_error:nnx { seq } { empty-sequence } { \token_to_str:N #1 }
-      \exp_after:wN \seq_break:
-    \fi:
+    #2 { \exp_not:n {#1} }
+    \__seq_pop_right_loop:nn
   }
+\cs_generate_variant:Nn \seq_pop_right:NN  { c }
+\cs_generate_variant:Nn \seq_gpop_right:NN { c }
+\prg_new_protected_conditional:Npnn \seq_get_left:NN #1#2 { T , F , TF }
+  { \__seq_pop_TF:NNNN \prg_do_nothing: \seq_get_left:NN #1#2 }
+\prg_new_protected_conditional:Npnn \seq_get_right:NN #1#2 { T , F , TF }
+  { \__seq_pop_TF:NNNN \prg_do_nothing: \seq_get_right:NN #1#2 }
+\cs_generate_variant:Nn \seq_get_left:NNT   { c }
+\cs_generate_variant:Nn \seq_get_left:NNF   { c }
+\cs_generate_variant:Nn \seq_get_left:NNTF  { c }
+\cs_generate_variant:Nn \seq_get_right:NNT  { c }
+\cs_generate_variant:Nn \seq_get_right:NNF  { c }
+\cs_generate_variant:Nn \seq_get_right:NNTF { c }
+\prg_new_protected_conditional:Npnn \seq_pop_left:NN #1#2 { T , F , TF }
+  { \__seq_pop_TF:NNNN \__seq_pop_left:NNN \tl_set:Nn #1 #2 }
+\prg_new_protected_conditional:Npnn \seq_gpop_left:NN #1#2 { T , F , TF }
+  { \__seq_pop_TF:NNNN \__seq_pop_left:NNN \tl_gset:Nn #1 #2 }
+\prg_new_protected_conditional:Npnn \seq_pop_right:NN #1#2 { T , F , TF }
+  { \__seq_pop_TF:NNNN \__seq_pop_right_aux:NNN \tl_set:Nx #1 #2 }
+\prg_new_protected_conditional:Npnn \seq_gpop_right:NN #1#2 { T , F , TF }
+  { \__seq_pop_TF:NNNN \__seq_pop_right_aux:NNN \tl_gset:Nx #1 #2 }
+\cs_generate_variant:Nn \seq_pop_left:NNT    { c }
+\cs_generate_variant:Nn \seq_pop_left:NNF    { c }
+\cs_generate_variant:Nn \seq_pop_left:NNTF   { c }
+\cs_generate_variant:Nn \seq_gpop_left:NNT   { c }
+\cs_generate_variant:Nn \seq_gpop_left:NNF   { c }
+\cs_generate_variant:Nn \seq_gpop_left:NNTF  { c }
+\cs_generate_variant:Nn \seq_pop_right:NNT   { c }
+\cs_generate_variant:Nn \seq_pop_right:NNF   { c }
+\cs_generate_variant:Nn \seq_pop_right:NNTF  { c }
+\cs_generate_variant:Nn \seq_gpop_right:NNT  { c }
+\cs_generate_variant:Nn \seq_gpop_right:NNF  { c }
+\cs_generate_variant:Nn \seq_gpop_right:NNTF { c }
+\cs_new_nopar:Npn \seq_map_break:
+  { \__prg_map_break:Nn \seq_map_break: { } }
+\cs_new_nopar:Npn \seq_map_break:n
+  { \__prg_map_break:Nn \seq_map_break: }
 \cs_new:Npn \seq_map_function:NN #1#2
   {
-    \exp_after:wN \seq_map_function_aux:NNn \exp_after:wN #2 #1
+    \exp_after:wN \__seq_map_function:NNn \exp_after:wN #2 #1
       { ? \seq_map_break: } { }
-    \prg_break_point:n { }
+    \__prg_break_point:Nn \seq_map_break: { }
   }
-\cs_new:Npn \seq_map_function_aux:NNn #1#2#3
+\cs_new:Npn \__seq_map_function:NNn #1#2#3
   {
     \use_none:n #2
     #1 {#3}
-    \seq_map_function_aux:NNn #1
+    \__seq_map_function:NNn #1
   }
 \cs_generate_variant:Nn \seq_map_function:NN { c }
-\cs_new_protected:Npn \seq_push_item_def:n
+\cs_new_protected:Npn \__seq_push_item_def:n
   {
-    \seq_push_item_def_aux:
-    \cs_gset:Npn \seq_item:n ##1
+    \__seq_push_item_def:
+    \cs_gset:Npn \__seq_item:n ##1
   }
-\cs_new_protected:Npn \seq_push_item_def:x
+\cs_new_protected:Npn \__seq_push_item_def:x
   {
-    \seq_push_item_def_aux:
-    \cs_gset:Npx \seq_item:n ##1
+    \__seq_push_item_def:
+    \cs_gset:Npx \__seq_item:n ##1
   }
-\cs_new_protected:Npn \seq_push_item_def_aux:
+\cs_new_protected:Npn \__seq_push_item_def:
   {
-    \cs_gset_eq:cN { seq_item_ \int_use:N \g_prg_map_int :n }
-      \seq_item:n
-    \int_gincr:N \g_prg_map_int
+    \int_gincr:N \g__prg_map_int
+    \cs_gset_eq:cN { __prg_map_ \int_use:N \g__prg_map_int :w }
+      \__seq_item:n
   }
-\cs_new_protected_nopar:Npn \seq_pop_item_def:
+\cs_new_protected_nopar:Npn \__seq_pop_item_def:
   {
-    \int_gdecr:N \g_prg_map_int
-    \cs_gset_eq:Nc \seq_item:n
-      { seq_item_ \int_use:N \g_prg_map_int :n }
+    \cs_gset_eq:Nc \__seq_item:n
+      { __prg_map_ \int_use:N \g__prg_map_int :w }
+    \int_gdecr:N \g__prg_map_int
   }
 \cs_new_protected:Npn \seq_map_inline:Nn #1#2
   {
-    \seq_push_item_def:n {#2}
+    \__seq_push_item_def:n {#2}
     #1
-    \prg_break_point:n { \seq_pop_item_def: }
+    \__prg_break_point:Nn \seq_map_break: { \__seq_pop_item_def: }
   }
 \cs_generate_variant:Nn \seq_map_inline:Nn { c }
 \cs_new_protected:Npn \seq_map_variable:NNn #1#2#3
   {
-    \seq_push_item_def:x
+    \__seq_push_item_def:x
       {
         \tl_set:Nn \exp_not:N #2 {##1}
         \exp_not:n {#3}
       }
     #1
-    \prg_break_point:n { \seq_pop_item_def: }
+    \__prg_break_point:Nn \seq_map_break: { \__seq_pop_item_def: }
   }
 \cs_generate_variant:Nn \seq_map_variable:NNn {     Nc }
 \cs_generate_variant:Nn \seq_map_variable:NNn { c , cc }
+\cs_new:Npn \seq_count:N #1
+  {
+    \int_eval:n
+      {
+        0
+        \seq_map_function:NN #1 \__seq_count:n
+      }
+  }
+\cs_new:Npn \__seq_count:n #1 { + \c_one }
+\cs_generate_variant:Nn \seq_count:N { c }
 \cs_new_eq:NN \seq_push:Nn  \seq_put_left:Nn
 \cs_new_eq:NN \seq_push:NV  \seq_put_left:NV
 \cs_new_eq:NN \seq_push:Nv  \seq_put_left:Nv
@@ -378,209 +425,28 @@
 \cs_new_eq:NN \seq_pop:cN \seq_pop_left:cN
 \cs_new_eq:NN \seq_gpop:NN \seq_gpop_left:NN
 \cs_new_eq:NN \seq_gpop:cN \seq_gpop_left:cN
+\prg_new_eq_conditional:NNn \seq_get:NN  \seq_get_left:NN  { T , F , TF }
+\prg_new_eq_conditional:NNn \seq_get:cN  \seq_get_left:cN  { T , F , TF }
+\prg_new_eq_conditional:NNn \seq_pop:NN  \seq_pop_left:NN  { T , F , TF }
+\prg_new_eq_conditional:NNn \seq_pop:cN  \seq_pop_left:cN  { T , F , TF }
+\prg_new_eq_conditional:NNn \seq_gpop:NN \seq_gpop_left:NN { T , F , TF }
+\prg_new_eq_conditional:NNn \seq_gpop:cN \seq_gpop_left:cN { T , F , TF }
 \cs_new_protected:Npn \seq_show:N #1
   {
-    \msg_aux_show:Nnx
+    \__msg_show_variable:Nnn
       #1
       { seq }
-      { \seq_map_function:NN #1 \msg_aux_show:n }
+      { \seq_map_function:NN #1 \__msg_show_item:n }
   }
 \cs_generate_variant:Nn \seq_show:N { c }
-\cs_new:Npn \seq_if_empty_break_return_false:N #1
-  {
-    \if_meaning:w #1 \c_empty_tl
-      \prg_return_false:
-      \exp_after:wN \seq_break:
-    \fi:
-  }
-\prg_new_protected_conditional:Npnn \seq_get_left:NN #1 #2 { T , F , TF }
-  {
-    \seq_if_empty_break_return_false:N #1
-    \exp_after:wN \seq_get_left_aux:Nw #1 \q_stop #2
-    \prg_return_true:
-    \seq_break:
-    \prg_break_point:n { }
-  }
-\prg_new_protected_conditional:Npnn \seq_get_right:NN #1#2 { T , F , TF }
-  {
-    \seq_if_empty_break_return_false:N #1
-    \seq_get_right_aux:NN #1#2
-    \prg_return_true: \seq_break:
-    \prg_break_point:n { }
-  }
-\cs_generate_variant:Nn \seq_get_left:NNT   { c }
-\cs_generate_variant:Nn \seq_get_left:NNF   { c }
-\cs_generate_variant:Nn \seq_get_left:NNTF  { c }
-\cs_generate_variant:Nn \seq_get_right:NNT  { c }
-\cs_generate_variant:Nn \seq_get_right:NNF  { c }
-\cs_generate_variant:Nn \seq_get_right:NNTF { c }
-\prg_new_protected_conditional:Npnn \seq_pop_left:NN #1#2 { T , F , TF }
-  {
-    \seq_if_empty_break_return_false:N #1
-    \exp_after:wN \seq_pop_left_aux:NnwNNN #1 \q_stop \tl_set:Nn #1#2
-    \prg_return_true: \seq_break:
-    \prg_break_point:n { }
-  }
-\prg_new_protected_conditional:Npnn \seq_gpop_left:NN #1#2 { T , F , TF }
-  {
-    \seq_if_empty_break_return_false:N #1
-    \exp_after:wN \seq_pop_left_aux:NnwNNN #1 \q_stop \tl_gset:Nn #1#2
-    \prg_return_true: \seq_break:
-    \prg_break_point:n { }
-  }
-\prg_new_protected_conditional:Npnn \seq_pop_right:NN #1#2 { T , F , TF }
-  {
-    \seq_if_empty_break_return_false:N #1
-    \seq_pop_right_aux_ii:NNN \tl_set:Nx #1 #2
-    \prg_return_true: \seq_break:
-    \prg_break_point:n { }
-  }
-\prg_new_protected_conditional:Npnn \seq_gpop_right:NN #1#2 { T , F , TF }
-  {
-    \seq_if_empty_break_return_false:N #1
-    \seq_pop_right_aux_ii:NNN \tl_gset:Nx #1 #2
-    \prg_return_true: \seq_break:
-    \prg_break_point:n { }
-  }
-\cs_generate_variant:Nn \seq_pop_left:NNT    { c }
-\cs_generate_variant:Nn \seq_pop_left:NNF    { c }
-\cs_generate_variant:Nn \seq_pop_left:NNTF   { c }
-\cs_generate_variant:Nn \seq_gpop_left:NNT   { c }
-\cs_generate_variant:Nn \seq_gpop_left:NNF   { c }
-\cs_generate_variant:Nn \seq_gpop_left:NNTF  { c }
-\cs_generate_variant:Nn \seq_pop_right:NNT   { c }
-\cs_generate_variant:Nn \seq_pop_right:NNF   { c }
-\cs_generate_variant:Nn \seq_pop_right:NNTF  { c }
-\cs_generate_variant:Nn \seq_gpop_right:NNT  { c }
-\cs_generate_variant:Nn \seq_gpop_right:NNF  { c }
-\cs_generate_variant:Nn \seq_gpop_right:NNTF { c }
-\cs_new:Npn \seq_length:N #1
-  {
-    \int_eval:n
-      {
-        0
-        \seq_map_function:NN #1 \seq_length_aux:n
-      }
-  }
-\cs_new:Npn \seq_length_aux:n #1 { +1 }
-\cs_generate_variant:Nn \seq_length:N { c }
-\cs_new:Npn \seq_item:Nn #1#2
-  {
-    \exp_last_unbraced:Nfo \seq_item_aux:nnn
-      {
-        \int_eval:n
-          {
-            \int_compare:nNnT {#2} < \c_zero
-              { \seq_length:N #1 + }
-            #2
-          }
-      }
-    #1
-    { ? \seq_break: }
-    { }
-    \prg_break_point:n { }
-  }
-\cs_new:Npn \seq_item_aux:nnn #1#2#3
-  {
-    \use_none:n #2
-    \int_compare:nNnTF {#1} = \c_zero
-      { \seq_break:n { \exp_not:n {#3} } }
-      { \exp_args:Nf \seq_item_aux:nnn { \int_eval:n { #1 - 1 } } }
-  }
-\cs_generate_variant:Nn \seq_item:Nn { c }
+\seq_new:N \l_tmpa_seq
+\seq_new:N \l_tmpb_seq
+\seq_new:N \g_tmpa_seq
+\seq_new:N \g_tmpb_seq
+\cs_new_eq:NN \seq_length:N \seq_count:N
+\cs_new_eq:NN \seq_length:c \seq_count:c
 \cs_new:Npn \seq_use:N #1 { \seq_map_function:NN #1 \use:n }
 \cs_generate_variant:Nn \seq_use:N { c }
-\cs_new:Npn \seq_mapthread_function:NNN #1#2#3
-  {
-    \exp_after:wN \seq_mapthread_function_aux:NN
-      \exp_after:wN #3
-      \exp_after:wN #1
-      #2
-      { ? \seq_break: } { }
-    \prg_break_point:n { }
-  }
-\cs_new:Npn \seq_mapthread_function_aux:NN #1#2
-  {
-    \exp_after:wN \seq_mapthread_function_aux:Nnnwnn
-      \exp_after:wN #1
-      #2
-      { ? \seq_break: } { }
-      \q_stop
-  }
-\cs_new:Npn \seq_mapthread_function_aux:Nnnwnn #1#2#3#4 \q_stop #5#6
-  {
-    \use_none:n #2
-    \use_none:n #5
-    #1 {#3} {#6}
-    \seq_mapthread_function_aux:Nnnwnn #1 #4 \q_stop
-  }
-\cs_generate_variant:Nn \seq_mapthread_function:NNN {     Nc }
-\cs_generate_variant:Nn \seq_mapthread_function:NNN { c , cc }
-\cs_new_protected:Npn \seq_set_from_clist:NN #1#2
-  {
-    \tl_set:Nx #1
-      { \clist_map_function:NN #2 \seq_wrap_item:n }
-  }
-\cs_new_protected:Npn \seq_set_from_clist:Nn #1#2
-  {
-    \tl_set:Nx #1
-      { \clist_map_function:nN {#2} \seq_wrap_item:n }
-  }
-\cs_new_protected:Npn \seq_gset_from_clist:NN #1#2
-  {
-    \tl_gset:Nx #1
-      { \clist_map_function:NN #2 \seq_wrap_item:n }
-  }
-\cs_new_protected:Npn \seq_gset_from_clist:Nn #1#2
-  {
-    \tl_gset:Nx #1
-      { \clist_map_function:nN {#2} \seq_wrap_item:n }
-  }
-\cs_generate_variant:Nn \seq_set_from_clist:NN  {     Nc }
-\cs_generate_variant:Nn \seq_set_from_clist:NN  { c , cc }
-\cs_generate_variant:Nn \seq_set_from_clist:Nn  { c      }
-\cs_generate_variant:Nn \seq_gset_from_clist:NN {     Nc }
-\cs_generate_variant:Nn \seq_gset_from_clist:NN { c , cc }
-\cs_generate_variant:Nn \seq_gset_from_clist:Nn { c      }
-\cs_new_protected_nopar:Npn \seq_tmp:w { }
-\cs_new_protected_nopar:Npn \seq_reverse:N
-  { \seq_reverse_aux:NN \tl_set:Nx }
-\cs_new_protected_nopar:Npn \seq_greverse:N
-  { \seq_reverse_aux:NN \tl_gset:Nx }
-\cs_new_protected:Npn \seq_reverse_aux:NN #1 #2
-  {
-    \cs_set_eq:NN \seq_tmp:w \seq_item:n
-    \cs_set_eq:NN \seq_item:n \seq_reverse_aux_item:nwn
-    #1 #2 { #2 \exp_not:n { } }
-    \cs_set_eq:NN \seq_item:n \seq_tmp:w
-  }
-\cs_new:Npn \seq_reverse_aux_item:nwn #1 #2 \exp_not:n #3
-  {
-    #2
-    \exp_not:n { \seq_item:n {#1} #3 }
-  }
-\cs_generate_variant:Nn \seq_reverse:N  { c }
-\cs_generate_variant:Nn \seq_greverse:N { c }
-\cs_new_protected_nopar:Npn \seq_set_filter:NNn
-  { \seq_set_filter_aux:NNNn \tl_set:Nx }
-\cs_new_protected_nopar:Npn \seq_gset_filter:NNn
-  { \seq_set_filter_aux:NNNn \tl_gset:Nx }
-\cs_new_protected:Npn \seq_set_filter_aux:NNNn #1#2#3#4
-  {
-    \seq_push_item_def:n { \bool_if:nT {#4} { \seq_wrap_item:n {##1} } }
-    #1 #2 { #3 \prg_break_point:n { } }
-    \seq_pop_item_def:
-  }
-\cs_new_protected_nopar:Npn \seq_set_map:NNn
-  { \seq_set_map_aux:NNNn \tl_set:Nx }
-\cs_new_protected_nopar:Npn \seq_gset_map:NNn
-  { \seq_set_map_aux:NNNn \tl_gset:Nx }
-\cs_new_protected:Npn \seq_set_map_aux:NNNn #1#2#3#4
-  {
-    \seq_push_item_def:n { \exp_not:N \seq_item:n {#4} }
-    #1 #2 { #3 }
-    \seq_pop_item_def:
-  }
 %% 
 %%
 %% End of file `l3seq.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3skip.sty b/Master/texmf-dist/tex/latex/l3kernel/l3skip.sty
index 671ce242540..b64003dfc27 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3skip.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3skip.sty
@@ -47,17 +47,17 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3skip.dtx 3499 2012-03-05 16:08:55Z bruno $
-  {L3 Experimental dimensions and skips}
+\GetIdInfo$Id: l3skip.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Dimensions and skips}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 \cs_new_eq:NN \if_dim:w      \tex_ifdim:D
-\cs_new_eq:NN \dim_eval:w    \etex_dimexpr:D
-\cs_new_eq:NN \dim_eval_end: \tex_relax:D
+\cs_new_eq:NN \__dim_eval:w      \etex_dimexpr:D
+\cs_new_eq:NN \__dim_eval_end:   \tex_relax:D
 \cs_new_protected:Npn \dim_new:N #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \newdimen #1
   }
 \cs_generate_variant:Nn \dim_new:N { c }
@@ -86,7 +86,7 @@
 \cs_new_eq:NN \dim_if_exist:cF  \cs_if_exist:cF
 \cs_new_eq:NN \dim_if_exist_p:c \cs_if_exist_p:c
 \cs_new_protected:Npn \dim_set:Nn #1#2
-  { #1 ~ \dim_eval:w #2 \dim_eval_end: }
+  { #1 ~ \__dim_eval:w #2 \__dim_eval_end: }
 \cs_new_protected:Npn \dim_gset:Nn { \tex_global:D \dim_set:Nn }
 \cs_generate_variant:Nn \dim_set:Nn  { c }
 \cs_generate_variant:Nn \dim_gset:Nn { c }
@@ -97,84 +97,98 @@
 \cs_generate_variant:Nn \dim_gset_eq:NN {       c }
 \cs_generate_variant:Nn \dim_gset_eq:NN { Nc , cc }
 \cs_new_protected_nopar:Npn \dim_set_max:Nn
-  { \dim_set_max_aux:NNNn < \dim_set:Nn }
+  { \__dim_set_max:NNNn < \dim_set:Nn }
 \cs_new_protected_nopar:Npn \dim_gset_max:Nn
-  { \dim_set_max_aux:NNNn < \dim_gset:Nn }
+  { \__dim_set_max:NNNn < \dim_gset:Nn }
 \cs_new_protected_nopar:Npn \dim_set_min:Nn
-  { \dim_set_max_aux:NNNn > \dim_set:Nn }
+  { \__dim_set_max:NNNn > \dim_set:Nn }
 \cs_new_protected_nopar:Npn \dim_gset_min:Nn
-  { \dim_set_max_aux:NNNn > \dim_gset:Nn }
-\cs_new_protected:Npn \dim_set_max_aux:NNNn #1#2#3#4
+  { \__dim_set_max:NNNn > \dim_gset:Nn }
+\cs_new_protected:Npn \__dim_set_max:NNNn #1#2#3#4
   { \dim_compare:nNnT {#3} #1 {#4} { #2 #3 {#4} } }
 \cs_generate_variant:Nn \dim_set_max:Nn  { c }
 \cs_generate_variant:Nn \dim_gset_max:Nn { c }
 \cs_generate_variant:Nn \dim_set_min:Nn  { c }
 \cs_generate_variant:Nn \dim_gset_min:Nn { c }
 \cs_new_protected:Npn \dim_add:Nn #1#2
-  { \tex_advance:D #1 by \dim_eval:w #2 \dim_eval_end: }
+  { \tex_advance:D #1 by \__dim_eval:w #2 \__dim_eval_end: }
 \cs_new_protected:Npn \dim_gadd:Nn { \tex_global:D \dim_add:Nn }
 \cs_generate_variant:Nn \dim_add:Nn  { c }
 \cs_generate_variant:Nn \dim_gadd:Nn { c }
 \cs_new_protected:Npn \dim_sub:Nn #1#2
-  { \tex_advance:D #1 by - \dim_eval:w #2 \dim_eval_end: }
+  { \tex_advance:D #1 by - \__dim_eval:w #2 \__dim_eval_end: }
 \cs_new_protected:Npn \dim_gsub:Nn { \tex_global:D \dim_sub:Nn }
 \cs_generate_variant:Nn \dim_sub:Nn  { c }
 \cs_generate_variant:Nn \dim_gsub:Nn { c }
 \cs_new:Npn \dim_abs:n #1
   {
     \dim_use:N
-      \dim_eval:w
-        \if_dim:w \dim_eval:w #1 < \c_zero_dim
+      \__dim_eval:w
+        \if_dim:w \__dim_eval:w #1 < \c_zero_dim
           -
         \fi:
-      \dim_eval:w #1 \dim_eval_end:
-    \dim_eval_end:
+      \__dim_eval:w #1 \__dim_eval_end:
+    \__dim_eval_end:
   }
 \cs_new:Npn \dim_ratio:nn #1#2
-  { \dim_ratio_aux:n {#1} / \dim_ratio_aux:n {#2} }
-\cs_new:Npn \dim_ratio_aux:n #1
-  { \int_value:w \dim_eval:w #1 \dim_eval_end: }
+  { \__dim_ratio:n {#1} / \__dim_ratio:n {#2} }
+\cs_new:Npn \__dim_ratio:n #1
+  { \__int_value:w \__dim_eval:w #1 \__dim_eval_end: }
 \prg_new_conditional:Npnn \dim_compare:nNn #1#2#3 { p , T , F , TF }
   {
-    \if_dim:w \dim_eval:w #1 #2 \dim_eval:w #3 \dim_eval_end:
+    \if_dim:w \__dim_eval:w #1 #2 \__dim_eval:w #3 \__dim_eval_end:
       \prg_return_true: \else: \prg_return_false: \fi:
   }
 \prg_new_conditional:Npnn \dim_compare:n #1 { p , T , F , TF }
   {
-    \exp_after:wN \dim_compare_aux:w \dim_use:N \dim_eval:w #1
-        \kernel_compare_error: \dim_eval_end:
+    \exp_after:wN \__dim_compare_aux:w \dim_use:N \__dim_eval:w #1
+        \__prg_compare_error: \__dim_eval_end:
       \prg_return_true:
     \else:
       \prg_return_false:
     \fi:
   }
 \exp_args:Nno \use:nn
-  { \cs_new:Npn \dim_compare_aux:w #1 }
+  { \cs_new:Npn \__dim_compare_aux:w #1 }
   { \tl_to_str:n { pt } }
-  #2 \kernel_compare_error:
+  #2 \__prg_compare_error:
   {
-    \exp_after:wN \dim_compare_aux:NNw #2 ?? \q_mark
+    \exp_after:wN \__dim_compare_aux:NNw #2 ?? \q_mark
     #1 pt #2
   }
-\cs_new:Npn \dim_compare_aux:NNw #1#2#3 \q_mark
+\cs_new:Npn \__dim_compare_aux:NNw #1#2#3 \q_mark
   {
-    \use:c { dim_compare_  #1  \if_meaning:w = #2 =  \fi: :NNw }
-      \kernel_compare_error:Nw #1
+    \use:c { __dim_compare_  #1  \if_meaning:w = #2 =  \fi: :NNw }
+      \__prg_compare_error:Nw #1
   }
-\cs_new:cpn { dim_compare_=:NNw } #1#2#3 =
-  { \if_dim:w #3 = \dim_eval:w }
-\cs_new:cpn { dim_compare_<:NNw } #1#2#3 <
-  { \if_dim:w #3 < \dim_eval:w }
-\cs_new:cpn { dim_compare_>:NNw } #1#2#3 >
-  { \if_dim:w #3 > \dim_eval:w }
-\cs_new:cpn { dim_compare_==:NNw } #1#2#3 ==
-  { \if_dim:w #3 = \dim_eval:w }
-\cs_new:cpn { dim_compare_!=:NNw } #1#2#3 !=
-  { \reverse_if:N \if_dim:w #3 = \dim_eval:w }
-\cs_new:cpn { dim_compare_<=:NNw } #1#2#3 <=
-  { \reverse_if:N \if_dim:w #3 > \dim_eval:w }
-\cs_new:cpn { dim_compare_>=:NNw } #1#2#3 >=
-  { \reverse_if:N \if_dim:w #3 < \dim_eval:w }
+\cs_new:cpn { __dim_compare_=:NNw } #1#2#3 =
+  { \if_dim:w #3 = \__dim_eval:w }
+\cs_new:cpn { __dim_compare_<:NNw } #1#2#3 <
+  { \if_dim:w #3 < \__dim_eval:w }
+\cs_new:cpn { __dim_compare_>:NNw } #1#2#3 >
+  { \if_dim:w #3 > \__dim_eval:w }
+\cs_new:cpn { __dim_compare_==:NNw } #1#2#3 ==
+  { \if_dim:w #3 = \__dim_eval:w }
+\cs_new:cpn { __dim_compare_!=:NNw } #1#2#3 !=
+  { \reverse_if:N \if_dim:w #3 = \__dim_eval:w }
+\cs_new:cpn { __dim_compare_<=:NNw } #1#2#3 <=
+  { \reverse_if:N \if_dim:w #3 > \__dim_eval:w }
+\cs_new:cpn { __dim_compare_>=:NNw } #1#2#3 >=
+  { \reverse_if:N \if_dim:w #3 < \__dim_eval:w }
+\cs_new:Npn \dim_case:nnn #1
+  {
+    \tex_romannumeral:D
+    \exp_args:Nf \__dim_case_aux:nnn { \dim_eval:n {#1} }
+  }
+\cs_new:Npn \__dim_case_aux:nnn #1#2#3
+  { \__dim_case_aux:nw {#1} #2 {#1} {#3} \q_recursion_stop }
+\cs_new:Npn \__dim_case_aux:nw #1#2#3
+  {
+    \dim_compare:nNnTF {#1} = {#2}
+      { \__dim_case_end:nw {#3} }
+      { \__dim_case_aux:nw {#1} }
+  }
+\cs_new_eq:NN \__dim_case_end:nw \__prg_case_end:nw
 \cs_set:Npn \dim_while_do:nn #1#2
   {
     \dim_compare:nT {#1}
@@ -232,17 +246,17 @@
       { \dim_do_until:nNnn {#1} #2 {#3} {#4} }
   }
 \cs_new:Npn \dim_eval:n #1
-  { \dim_use:N \dim_eval:w #1 \dim_eval_end: }
-\cs_new:Npn \dim_strip_bp:n #1
-  { \dim_strip_pt:n { 0.996 26 \dim_eval:w #1 \dim_eval_end: } }
-\cs_new:Npn \dim_strip_pt:n #1
+  { \dim_use:N \__dim_eval:w #1 \__dim_eval_end: }
+\cs_new:Npn \__dim_strip_bp:n #1
+  { \__dim_strip_pt:n { 0.996 26 \__dim_eval:w #1 \__dim_eval_end: } }
+\cs_new:Npn \__dim_strip_pt:n #1
   {
     \exp_after:wN
-      \dim_strip_pt:w \dim_use:N \dim_eval:w #1 \dim_eval_end: \q_stop
+      \__dim_strip_pt:w \dim_use:N \__dim_eval:w #1 \__dim_eval_end: \q_stop
   }
 \use:x
   {
-    \cs_new:Npn \exp_not:N \dim_strip_pt:w
+    \cs_new:Npn \exp_not:N \__dim_strip_pt:w
       ##1 . ##2 \tl_to_str:n { pt } ##3 \exp_not:N \q_stop
       {
         ##1
@@ -252,20 +266,19 @@
   }
 \cs_new_eq:NN \dim_use:N \tex_the:D
 \cs_generate_variant:Nn \dim_use:N { c }
-\cs_new_eq:NN  \dim_show:N \kernel_register_show:N
+\cs_new_eq:NN  \dim_show:N \__kernel_register_show:N
 \cs_generate_variant:Nn \dim_show:N { c }
 \cs_new_protected:Npn \dim_show:n #1
-  { \tex_showthe:D \dim_eval:w #1 \dim_eval_end: }
+  { \etex_showtokens:D \exp_after:wN { \dim_use:N \__dim_eval:w #1 } }
 \cs_new_eq:NN \c_zero_dim \z@
 \cs_new_eq:NN \c_max_dim  \maxdimen
 \dim_new:N \l_tmpa_dim
 \dim_new:N \l_tmpb_dim
-\dim_new:N \l_tmpc_dim
 \dim_new:N \g_tmpa_dim
 \dim_new:N \g_tmpb_dim
 \cs_new_protected:Npn \skip_new:N #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \newskip #1
   }
 \cs_generate_variant:Nn \skip_new:N { c }
@@ -324,19 +337,17 @@
         \prg_return_false:
     \fi:
   }
-\cs_set_protected:Npn \cs_tmp:w #1
+\cs_set_protected:Npn \__cs_tmp:w #1
   {
     \prg_new_conditional:Npnn \skip_if_finite:n ##1 { p , T , F , TF }
       {
-        \exp_after:wN \skip_if_finite_aux:wwNw
+        \exp_after:wN \__skip_if_finite:wwNw
         \skip_use:N \etex_glueexpr:D ##1 ; \prg_return_false:
         #1 ; \prg_return_true: \q_stop
       }
-    \cs_new:Npn \skip_if_finite_aux:wwNw ##1 #1 ##2 ; ##3 ##4 \q_stop {##3}
+    \cs_new:Npn \__skip_if_finite:wwNw ##1 #1 ##2 ; ##3 ##4 \q_stop {##3}
   }
-\exp_args:No \cs_tmp:w { \tl_to_str:n { fil } }
-\prg_new_conditional:Npnn \skip_if_infinite_glue:n #1 { p , T , F , TF }
-  { \skip_if_finite:nTF {#1} \prg_return_false: \prg_return_true: }
+\exp_args:No \__cs_tmp:w { \tl_to_str:n { fil } }
 \cs_new:Npn \skip_eval:n #1
   { \skip_use:N \etex_glueexpr:D #1 \scan_stop: }
 \cs_new_eq:NN \skip_use:N \tex_the:D
@@ -349,20 +360,19 @@
   { \skip_vertical:N \etex_glueexpr:D #1 \scan_stop: }
 \cs_generate_variant:Nn \skip_horizontal:N { c }
 \cs_generate_variant:Nn \skip_vertical:N { c }
-\cs_new_eq:NN  \skip_show:N \kernel_register_show:N
+\cs_new_eq:NN  \skip_show:N \__kernel_register_show:N
 \cs_generate_variant:Nn \skip_show:N { c }
 \cs_new_protected:Npn \skip_show:n #1
-  { \tex_showthe:D \etex_glueexpr:D #1 \scan_stop: }
+  { \etex_showtokens:D \exp_after:wN { \tex_the:D \etex_glueexpr:D #1 } }
 \cs_new_eq:NN \c_zero_skip \c_zero_dim
 \cs_new_eq:NN \c_max_skip  \c_max_dim
 \skip_new:N \l_tmpa_skip
 \skip_new:N \l_tmpb_skip
-\skip_new:N \l_tmpc_skip
 \skip_new:N \g_tmpa_skip
 \skip_new:N \g_tmpb_skip
 \cs_new_protected:Npn \muskip_new:N #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \newmuskip #1
   }
 \cs_generate_variant:Nn \muskip_new:N { c }
@@ -416,23 +426,21 @@
   { \muskip_use:N \etex_muexpr:D #1 \scan_stop: }
 \cs_new_eq:NN \muskip_use:N \tex_the:D
 \cs_generate_variant:Nn \muskip_use:N { c }
-\cs_new_eq:NN  \muskip_show:N \kernel_register_show:N
+\cs_new_eq:NN  \muskip_show:N \__kernel_register_show:N
 \cs_generate_variant:Nn \muskip_show:N { c }
 \cs_new_protected:Npn \muskip_show:n #1
-  { \tex_showthe:D \etex_muexpr:D #1 \scan_stop: }
-\cs_new:Npn \skip_split_finite_else_action:nnNN #1#2#3#4
-  {
-    \skip_if_finite:nTF {#1}
-      {
-        #3 = \etex_gluestretch:D #1 \scan_stop:
-        #4 = \etex_glueshrink:D  #1 \scan_stop:
-      }
-      {
-        #3 = \c_zero_skip
-        #4 = \c_zero_skip
-        #2
-      }
-  }
+  { \etex_showtokens:D \exp_after:wN { \tex_the:D \etex_muexpr:D #1 } }
+\muskip_const:Nn \c_zero_muskip { 0 mu }
+\muskip_const:Nn \c_max_muskip  { 16383.99999 mu }
+\muskip_new:N \l_tmpa_muskip
+\muskip_new:N \l_tmpb_muskip
+\muskip_new:N \g_tmpa_muskip
+\muskip_new:N \g_tmpb_muskip
+\prg_new_conditional:Npnn \skip_if_infinite_glue:n #1 { p , T , F , TF }
+  { \skip_if_finite:nTF {#1} \prg_return_false: \prg_return_true: }
+\cs_new_eq:NN \prg_case_dim:nnn \dim_case:nnn
+\cs_new_eq:NN \dim_eval:w    \__dim_eval:w
+\cs_new_eq:NN \dim_eval_end: \__dim_eval_end:
 %% 
 %%
 %% End of file `l3skip.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3tl.sty b/Master/texmf-dist/tex/latex/l3kernel/l3tl.sty
index 763eba4d8a7..166552a8a71 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3tl.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3tl.sty
@@ -46,25 +46,25 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3tl.dtx 3490 2012-03-04 01:00:53Z bruno $
-  {L3 Experimental token lists}
+\GetIdInfo$Id: l3tl.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Token lists}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 \cs_new_protected:Npn \tl_new:N #1
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \cs_gset_eq:NN #1 \c_empty_tl
   }
 \cs_generate_variant:Nn \tl_new:N { c }
 \cs_new_protected:Npn \tl_const:Nn #1#2
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \cs_gset_nopar:Npx #1 { \exp_not:n {#2} }
   }
 \cs_new_protected:Npn \tl_const:Nx #1#2
   {
-    \chk_if_free_cs:N #1
+    \__chk_if_free_cs:N #1
     \cs_gset_nopar:Npx #1 {#2}
   }
 \cs_generate_variant:Nn \tl_const:Nn { c }
@@ -90,6 +90,12 @@
 \cs_new_eq:NN \tl_gset_eq:cN \cs_gset_eq:cN
 \cs_new_eq:NN \tl_gset_eq:Nc \cs_gset_eq:Nc
 \cs_new_eq:NN \tl_gset_eq:cc \cs_gset_eq:cc
+\cs_new_protected:Npn \tl_concat:NNN #1#2#3
+  { \tl_set:Nx #1 { \exp_not:o {#2} \exp_not:o {#3} } }
+\cs_new_protected:Npn \tl_gconcat:NNN #1#2#3
+  { \tl_gset:Nx #1 { \exp_not:o {#2} \exp_not:o {#3} } }
+\cs_generate_variant:Nn \tl_concat:NNN  { ccc }
+\cs_generate_variant:Nn \tl_gconcat:NNN { ccc }
 \cs_new_eq:NN \tl_if_exist:NTF \cs_if_exist:NTF
 \cs_new_eq:NN \tl_if_exist:NT  \cs_if_exist:NT
 \cs_new_eq:NN \tl_if_exist:NF  \cs_if_exist:NF
@@ -98,6 +104,8 @@
 \cs_new_eq:NN \tl_if_exist:cT  \cs_if_exist:cT
 \cs_new_eq:NN \tl_if_exist:cF  \cs_if_exist:cF
 \cs_new_eq:NN \tl_if_exist_p:c \cs_if_exist_p:c
+\tl_const:Nx \c_job_name_tl { \tex_jobname:D }
+\tl_const:Nn \c_space_tl { ~ }
 \cs_new_protected:Npn \tl_set:Nn #1#2
   { \cs_set_nopar:Npx #1 { \exp_not:n {#2} } }
 \cs_new_protected:Npn \tl_set:No #1#2
@@ -172,18 +180,18 @@
 \tex_lowercase:D
   {
     \group_end:
-    \tl_const:Nn \c_tl_rescan_marker_tl { A B }
+    \tl_const:Nn \c__tl_rescan_marker_tl { A B }
   }
 \cs_new_protected_nopar:Npn \tl_set_rescan:Nnn
-  { \tl_set_rescan_aux:NNnn \tl_set:Nn }
+  { \__tl_set_rescan:NNnn \tl_set:Nn }
 \cs_new_protected_nopar:Npn \tl_gset_rescan:Nnn
-  { \tl_set_rescan_aux:NNnn \tl_gset:Nn }
+  { \__tl_set_rescan:NNnn \tl_gset:Nn }
 \cs_new_protected_nopar:Npn \tl_rescan:nn
-  { \tl_set_rescan_aux:NNnn \prg_do_nothing: \use:n }
-\cs_new_protected:Npn \tl_set_rescan_aux:NNnn #1#2#3#4
+  { \__tl_set_rescan:NNnn \prg_do_nothing: \use:n }
+\cs_new_protected:Npn \__tl_set_rescan:NNnn #1#2#3#4
   {
     \group_begin:
-      \exp_args:No \etex_everyeof:D { \c_tl_rescan_marker_tl \exp_not:N }
+      \exp_args:No \etex_everyeof:D { \c__tl_rescan_marker_tl \exp_not:N }
       \tex_endlinechar:D \c_minus_one
       \tex_newlinechar:D \c_minus_one
       #3
@@ -192,7 +200,7 @@
           \group_end:
           #1 \exp_not:N #2
             {
-              \exp_after:wN \tl_rescan_aux:w
+              \exp_after:wN \__tl_rescan:w
               \exp_after:wN \prg_do_nothing:
               \etex_scantokens:D {#4}
             }
@@ -200,8 +208,8 @@
   }
 \use:x
   {
-    \cs_new:Npn \exp_not:N \tl_rescan_aux:w ##1
-      \c_tl_rescan_marker_tl
+    \cs_new:Npn \exp_not:N \__tl_rescan:w ##1
+      \c__tl_rescan_marker_tl
       { \exp_not:N \exp_not:o { ##1 } }
   }
 \cs_generate_variant:Nn \tl_set_rescan:Nnn  {     Nno , Nnx }
@@ -211,27 +219,27 @@
 \cs_new_eq:NN \tl_to_lowercase:n \tex_lowercase:D
 \cs_new_eq:NN \tl_to_uppercase:n \tex_uppercase:D
 \cs_new_protected_nopar:Npn \tl_replace_once:Nnn
-  { \tl_replace_aux:NNNnn \tl_replace_once_aux: \tl_set:Nx }
+  { \__tl_replace:NNNnn \__tl_replace_once: \tl_set:Nx }
 \cs_new_protected_nopar:Npn \tl_greplace_once:Nnn
-  { \tl_replace_aux:NNNnn \tl_replace_once_aux: \tl_gset:Nx }
+  { \__tl_replace:NNNnn \__tl_replace_once: \tl_gset:Nx }
 \cs_new_protected_nopar:Npn \tl_replace_all:Nnn
-  { \tl_replace_aux:NNNnn \tl_replace_all_aux: \tl_set:Nx }
+  { \__tl_replace:NNNnn \__tl_replace_all: \tl_set:Nx }
 \cs_new_protected_nopar:Npn \tl_greplace_all:Nnn
-  { \tl_replace_aux:NNNnn \tl_replace_all_aux: \tl_gset:Nx }
+  { \__tl_replace:NNNnn \__tl_replace_all: \tl_gset:Nx }
 \cs_generate_variant:Nn \tl_replace_once:Nnn  { c }
 \cs_generate_variant:Nn \tl_greplace_once:Nnn { c }
 \cs_generate_variant:Nn \tl_replace_all:Nnn   { c }
 \cs_generate_variant:Nn \tl_greplace_all:Nnn  { c }
-\cs_new_protected:Npn \tl_replace_aux:NNNnn #1#2#3#4#5
+\cs_new_protected:Npn \__tl_replace:NNNnn #1#2#3#4#5
   {
     \tl_if_empty:nTF {#4}
       {
-         \msg_kernel_error:nnx { tl } { empty-search-pattern }
+         \__msg_kernel_error:nnx { kernel } { empty-search-pattern }
            { \tl_to_str:n {#5} }
       }
       {
         \group_align_safe_begin:
-        \cs_set:Npx \tl_tmp:w ##1##2 #4
+        \cs_set:Npx \__tl_tmp:w ##1##2 #4
           {
             ##2
             \exp_not:N \q_mark
@@ -247,18 +255,18 @@
           }
       }
   }
-\cs_new:Npn \tl_replace_aux_ii:w #1 \q_mark #2 { \exp_not:o {#1} }
-\cs_new:Npn \tl_replace_all_aux:
+\cs_new:Npn \__tl_replace:w #1 \q_mark #2 { \exp_not:o {#1} }
+\cs_new_nopar:Npn \__tl_replace_all:
   {
-    \exp_after:wN \tl_replace_aux_ii:w
-    \tl_tmp:w \tl_replace_all_aux: \prg_do_nothing:
+    \exp_after:wN \__tl_replace:w
+    \__tl_tmp:w \__tl_replace_all: \prg_do_nothing:
   }
-\cs_new_nopar:Npn \tl_replace_once_aux:
+\cs_new_nopar:Npn \__tl_replace_once:
   {
-    \exp_after:wN \tl_replace_aux_ii:w
-    \tl_tmp:w { \tl_replace_once_aux_end:w \prg_do_nothing: } \prg_do_nothing:
+    \exp_after:wN \__tl_replace:w
+    \__tl_tmp:w { \__tl_replace_once_end:w \prg_do_nothing: } \prg_do_nothing:
   }
-\cs_new:Npn \tl_replace_once_aux_end:w #1 \q_mark #2 \q_stop
+\cs_new:Npn \__tl_replace_once_end:w #1 \q_mark #2 \q_stop
   { \exp_not:o {#1} }
 \cs_new_protected:Npn \tl_remove_once:Nn #1#2
   { \tl_replace_once:Nnn #1 {#2} { } }
@@ -273,7 +281,7 @@
 \cs_generate_variant:Nn \tl_remove_all:Nn  { c }
 \cs_generate_variant:Nn \tl_gremove_all:Nn { c }
 \prg_new_conditional:Npnn \tl_if_blank:n #1 { p , T , F , TF }
-  { \tl_if_empty_return:o { \use_none:n #1 ? } }
+  { \__tl_if_empty_return:o { \use_none:n #1 ? } }
 \cs_generate_variant:Nn \tl_if_blank_p:n { V }
 \cs_generate_variant:Nn \tl_if_blank:nT  { V }
 \cs_generate_variant:Nn \tl_if_blank:nF  { V }
@@ -306,7 +314,7 @@
 \cs_generate_variant:Nn \tl_if_empty:nTF { V }
 \cs_generate_variant:Nn \tl_if_empty:nT  { V }
 \cs_generate_variant:Nn \tl_if_empty:nF  { V }
-\cs_new:Npn \tl_if_empty_return:o #1
+\cs_new:Npn \__tl_if_empty_return:o #1
   {
     \exp_after:wN \if_meaning:w \exp_after:wN \q_nil
       \tl_to_str:n \exp_after:wN {#1} \q_nil
@@ -316,7 +324,7 @@
     \fi:
   }
 \prg_new_conditional:Npnn \tl_if_empty:o #1 { p , TF , T , F }
-  { \tl_if_empty_return:o {#1} }
+  { \__tl_if_empty_return:o {#1} }
 \prg_new_conditional:Npnn \tl_if_eq:NN #1#2 { p , T , F , TF }
   {
     \if_meaning:w #1 #2
@@ -352,173 +360,269 @@
 \cs_generate_variant:Nn \tl_if_in:NnTF { c }
 \prg_new_protected_conditional:Npnn \tl_if_in:nn #1#2 { T  , F , TF }
   {
-    \cs_set:Npn \tl_tmp:w ##1 #2 { }
-    \tl_if_empty:oTF { \tl_tmp:w #1 {} {} #2 }
+    \cs_set:Npn \__tl_tmp:w ##1 #2 { }
+    \tl_if_empty:oTF { \__tl_tmp:w #1 {} {} #2 }
       { \prg_return_false: } { \prg_return_true: }
   }
 \cs_generate_variant:Nn \tl_if_in:nnT  { V , o , no }
 \cs_generate_variant:Nn \tl_if_in:nnF  { V , o , no }
 \cs_generate_variant:Nn \tl_if_in:nnTF { V , o , no }
+\cs_new:Npn \tl_if_single_p:N { \exp_args:No \tl_if_single_p:n }
+\cs_new:Npn \tl_if_single:NT  { \exp_args:No \tl_if_single:nT  }
+\cs_new:Npn \tl_if_single:NF  { \exp_args:No \tl_if_single:nF  }
+\cs_new:Npn \tl_if_single:NTF { \exp_args:No \tl_if_single:nTF }
+\prg_new_conditional:Npnn \tl_if_single:n #1 { p , T , F , TF }
+  { \__str_if_eq_x_return:nn { \exp_not:o { \use_none:nn #1 ?? } } {?} }
+\cs_new:Npn \tl_case:Nnn #1#2#3
+  {
+    \tex_romannumeral:D
+    \__tl_case:Nw #1 #2 #1 {#3} \q_recursion_stop
+  }
+\cs_new:Npn \__tl_case:Nw #1#2#3
+  {
+    \tl_if_eq:NNTF #1 #2
+      { \__tl_case_end:nw {#3} }
+      { \__tl_case:Nw #1 }
+  }
+\cs_generate_variant:Nn \tl_case:Nnn { c }
+\cs_new_eq:NN \__tl_case_end:nw \__prg_case_end:nw
 \cs_new:Npn \tl_map_function:nN #1#2
   {
-    \tl_map_function_aux:Nn #2 #1
+    \__tl_map_function:Nn #2 #1
       \q_recursion_tail
-    \prg_break_point:n { }
+    \__prg_break_point:Nn \tl_map_break: { }
   }
 \cs_new_nopar:Npn \tl_map_function:NN
   { \exp_args:No \tl_map_function:nN }
-\cs_new:Npn \tl_map_function_aux:Nn #1#2
+\cs_new:Npn \__tl_map_function:Nn #1#2
   {
-    \quark_if_recursion_tail_break:n {#2}
-    #1 {#2} \tl_map_function_aux:Nn #1
+    \__quark_if_recursion_tail_break:nN {#2} \tl_map_break:
+    #1 {#2} \__tl_map_function:Nn #1
   }
 \cs_generate_variant:Nn \tl_map_function:NN { c }
 \cs_new_protected:Npn \tl_map_inline:nn #1#2
   {
-    \int_gincr:N \g_prg_map_int
-    \cs_gset:cpn { tl_map_inline_ \int_use:N \g_prg_map_int :n }
-      ##1 {#2}
-    \exp_args:Nc \tl_map_function_aux:Nn
-      { tl_map_inline_ \int_use:N \g_prg_map_int :n }
+    \int_gincr:N \g__prg_map_int
+    \cs_gset:cpn { __prg_map_ \int_use:N \g__prg_map_int :w } ##1 {#2}
+    \exp_args:Nc \__tl_map_function:Nn
+      { __prg_map_ \int_use:N \g__prg_map_int :w }
       #1 \q_recursion_tail
-    \prg_break_point:n { \int_gdecr:N \g_prg_map_int }
+    \__prg_break_point:Nn \tl_map_break: { \int_gdecr:N \g__prg_map_int }
   }
 \cs_new_protected:Npn \tl_map_inline:Nn
   { \exp_args:No \tl_map_inline:nn }
 \cs_generate_variant:Nn \tl_map_inline:Nn { c }
 \cs_new_protected:Npn \tl_map_variable:nNn #1#2#3
   {
-    \tl_map_variable_aux:Nnn #2 {#3} #1
+    \__tl_map_variable:Nnn #2 {#3} #1
       \q_recursion_tail
-    \prg_break_point:n { }
+    \__prg_break_point:Nn \tl_map_break: { }
   }
 \cs_new_protected_nopar:Npn \tl_map_variable:NNn
   { \exp_args:No \tl_map_variable:nNn }
-\cs_new_protected:Npn \tl_map_variable_aux:Nnn #1#2#3
+\cs_new_protected:Npn \__tl_map_variable:Nnn #1#2#3
   {
     \tl_set:Nn #1 {#3}
-    \quark_if_recursion_tail_break:N #1
+    \__quark_if_recursion_tail_break:NN #1 \tl_map_break:
     \use:n {#2}
-    \tl_map_variable_aux:Nnn #1 {#2}
+    \__tl_map_variable:Nnn #1 {#2}
   }
 \cs_generate_variant:Nn \tl_map_variable:NNn { c }
-\cs_new_eq:NN \tl_map_break:  \prg_map_break:
-\cs_new_eq:NN \tl_map_break:n \prg_map_break:n
+\cs_new_nopar:Npn \tl_map_break:
+  { \__prg_map_break:Nn \tl_map_break: { } }
+\cs_new_nopar:Npn \tl_map_break:n
+  { \__prg_map_break:Nn \tl_map_break: }
 \cs_new_eq:NN \tl_to_str:n \etex_detokenize:D
 \cs_new:Npn \tl_to_str:N #1 { \etex_detokenize:D \exp_after:wN {#1} }
 \cs_generate_variant:Nn \tl_to_str:N { c }
 \cs_new:Npn \tl_use:N #1
   {
     \tl_if_exist:NTF #1 {#1}
-      { \msg_expandable_kernel_error:nnn { kernel } { bad-var } {#1} }
+      { \__msg_kernel_expandable_error:nnn { kernel } { bad-variable } {#1} }
   }
 \cs_generate_variant:Nn \tl_use:N { c }
-\cs_new:Npn \tl_length:n #1
+\cs_new:Npn \tl_count:n #1
   {
     \int_eval:n
-      { 0 \tl_map_function:nN {#1} \tl_length_aux:n }
+      { 0 \tl_map_function:nN {#1} \__tl_count:n }
   }
-\cs_new:Npn \tl_length:N #1
+\cs_new:Npn \tl_count:N #1
   {
     \int_eval:n
-      { 0 \tl_map_function:NN #1 \tl_length_aux:n }
+      { 0 \tl_map_function:NN #1 \__tl_count:n }
   }
-\cs_new:Npn \tl_length_aux:n #1 { + \c_one }
-\cs_generate_variant:Nn \tl_length:n { V , o }
-\cs_generate_variant:Nn \tl_length:N { c }
+\cs_new:Npn \__tl_count:n #1 { + \c_one }
+\cs_generate_variant:Nn \tl_count:n { V , o }
+\cs_generate_variant:Nn \tl_count:N { c }
 \cs_new:Npn \tl_reverse_items:n #1
   {
-    \tl_reverse_items_aux:nwNwn #1 ?
-      \q_mark \tl_reverse_items_aux:nwNwn
-      \q_mark \tl_reverse_items_aux:wn
+    \__tl_reverse_items:nwNwn #1 ?
+      \q_mark \__tl_reverse_items:nwNwn
+      \q_mark \__tl_reverse_items:wn
       \q_stop { }
   }
-\cs_new:Npn \tl_reverse_items_aux:nwNwn #1 #2 \q_mark #3 #4 \q_stop #5
+\cs_new:Npn \__tl_reverse_items:nwNwn #1 #2 \q_mark #3 #4 \q_stop #5
   {
     #3 #2
-      \q_mark \tl_reverse_items_aux:nwNwn
-      \q_mark \tl_reverse_items_aux:wn
+      \q_mark \__tl_reverse_items:nwNwn
+      \q_mark \__tl_reverse_items:wn
       \q_stop { {#1} #5 }
   }
-\cs_new:Npn \tl_reverse_items_aux:wn #1 \q_stop #2
+\cs_new:Npn \__tl_reverse_items:wn #1 \q_stop #2
   { \exp_not:o { \use_none:nn #2 } }
-\cs_set:Npn \tl_tmp:w #1
+\cs_new:Npn \tl_trim_spaces:n #1
+  { \__tl_trim_spaces:nn { \q_mark #1 } \exp_not:o }
+\cs_new_protected:Npn \tl_trim_spaces:N #1
+  { \tl_set:Nx #1 { \exp_args:No \tl_trim_spaces:n {#1} } }
+\cs_new_protected:Npn \tl_gtrim_spaces:N #1
+  { \tl_gset:Nx #1 { \exp_args:No \tl_trim_spaces:n {#1} } }
+\cs_generate_variant:Nn \tl_trim_spaces:N  { c }
+\cs_generate_variant:Nn \tl_gtrim_spaces:N { c }
+\cs_set:Npn \__tl_tmp:w #1
   {
-    \cs_new:Npn \tl_trim_spaces:n ##1
+    \cs_new:Npn \__tl_trim_spaces:nn ##1
       {
-        \etex_unexpanded:D
-          \tl_trim_spaces_aux_i:w
-          \q_mark
+        \__tl_trim_spaces_i:w
           ##1
           \q_nil
           \q_mark #1 { }
-          \q_mark \tl_trim_spaces_aux_ii:w
-          \tl_trim_spaces_aux_iii:w
+          \q_mark \__tl_trim_spaces_ii:w
+          \__tl_trim_spaces_iii:w
           #1 \q_nil
-          \tl_trim_spaces_aux_iv:w
-          \q_stop
+          \__tl_trim_spaces_iv:w
+        \q_stop
       }
-    \cs_new:Npn \tl_trim_spaces_aux_i:w ##1 \q_mark #1 ##2 \q_mark ##3
+    \cs_new:Npn \__tl_trim_spaces_i:w ##1 \q_mark #1 ##2 \q_mark ##3
       {
         ##3
-        \tl_trim_spaces_aux_i:w
+        \__tl_trim_spaces_i:w
         \q_mark
         ##2
         \q_mark #1 {##1}
       }
-    \cs_new:Npn \tl_trim_spaces_aux_ii:w ##1 \q_mark \q_mark ##2
+    \cs_new:Npn \__tl_trim_spaces_ii:w
+        \__tl_trim_spaces_i:w \q_mark \q_mark ##1
       {
-        \tl_trim_spaces_aux_iii:w
-        ##2
+        \__tl_trim_spaces_iii:w
+        ##1
       }
-    \cs_new:Npn \tl_trim_spaces_aux_iii:w ##1 #1 \q_nil ##2
+    \cs_new:Npn \__tl_trim_spaces_iii:w ##1 #1 \q_nil ##2
       {
         ##2
         ##1 \q_nil
-        \tl_trim_spaces_aux_iii:w
+        \__tl_trim_spaces_iii:w
       }
-    \cs_new:Npn \tl_trim_spaces_aux_iv:w ##1 \q_nil ##2 \q_stop
-      { \exp_after:wN { \use_none:n ##1 } }
+    \cs_new:Npn \__tl_trim_spaces_iv:w ##1 \q_nil ##2 \q_stop ##3
+      { ##3 { \use_none:n ##1 } }
   }
-\tl_tmp:w { ~ }
-\cs_new_protected:Npn \tl_trim_spaces:N #1
-  { \tl_set:Nx #1 { \exp_after:wN \tl_trim_spaces:n \exp_after:wN {#1} } }
-\cs_new_protected:Npn \tl_gtrim_spaces:N #1
-  { \tl_gset:Nx #1 { \exp_after:wN \tl_trim_spaces:n \exp_after:wN {#1} } }
-\cs_generate_variant:Nn \tl_trim_spaces:N  { c }
-\cs_generate_variant:Nn \tl_gtrim_spaces:N { c }
+\__tl_tmp:w { ~ }
+\cs_new:Npn \__tl_act:NNNnn #1#2#3#4#5
+  {
+    \group_align_safe_begin:
+    \__tl_act_loop:w #5 \q__tl_act_mark \q__tl_act_stop
+    {#4} #1 #2 #3
+    \__tl_act_result:n { }
+  }
+\cs_new:Npn \__tl_act_loop:w #1 \q__tl_act_stop
+  {
+    \tl_if_head_is_N_type:nTF {#1}
+      { \__tl_act_normal:NwnNNN }
+      {
+        \tl_if_head_is_group:nTF {#1}
+          { \__tl_act_group:nwnNNN }
+          { \__tl_act_space:wwnNNN }
+      }
+    #1 \q__tl_act_stop
+  }
+\cs_new:Npn \__tl_act_normal:NwnNNN #1 #2 \q__tl_act_stop #3#4
+  {
+    \if_meaning:w \q__tl_act_mark #1
+      \exp_after:wN \__tl_act_end:wn
+    \fi:
+    #4 {#3} #1
+    \__tl_act_loop:w #2 \q__tl_act_stop
+    {#3} #4
+  }
+\cs_new:Npn \__tl_act_end:wn #1 \__tl_act_result:n #2
+  { \group_align_safe_end: \c_zero #2 }
+\cs_new:Npn \__tl_act_group:nwnNNN #1 #2 \q__tl_act_stop #3#4#5
+  {
+    #5 {#3} {#1}
+    \__tl_act_loop:w #2 \q__tl_act_stop
+    {#3} #4 #5
+  }
+\exp_last_unbraced:NNo
+  \cs_new:Npn \__tl_act_space:wwnNNN \c_space_tl #1 \q__tl_act_stop #2#3#4#5
+  {
+    #5 {#2}
+    \__tl_act_loop:w #1 \q__tl_act_stop
+    {#2} #3 #4 #5
+  }
+\cs_new:Npn \__tl_act_output:n #1 #2 \__tl_act_result:n #3
+  { #2 \__tl_act_result:n { #3 #1 } }
+\cs_new:Npn \__tl_act_reverse_output:n #1 #2 \__tl_act_result:n #3
+  { #2 \__tl_act_result:n { #1 #3 } }
+\cs_new:Npn \tl_reverse:n #1
+  {
+    \etex_unexpanded:D \exp_after:wN
+      {
+        \tex_romannumeral:D
+        \__tl_act:NNNnn
+          \__tl_reverse_normal:nN
+          \__tl_reverse_group_preserve:nn
+          \__tl_reverse_space:n
+          { }
+          {#1}
+      }
+  }
+\cs_generate_variant:Nn \tl_reverse:n { o , V }
+\cs_new:Npn \__tl_reverse_normal:nN #1#2
+  { \__tl_act_reverse_output:n {#2} }
+\cs_new:Npn \__tl_reverse_group_preserve:nn #1#2
+  { \__tl_act_reverse_output:n { {#2} } }
+\cs_new:Npn \__tl_reverse_space:n #1
+  { \__tl_act_reverse_output:n { ~ } }
+\cs_new_protected:Npn \tl_reverse:N #1
+  { \tl_set:Nx #1 { \exp_args:No \tl_reverse:n { #1 } } }
+\cs_new_protected:Npn \tl_greverse:N #1
+  { \tl_gset:Nx #1 { \exp_args:No \tl_reverse:n { #1 } } }
+\cs_generate_variant:Nn \tl_reverse:N  { c }
+\cs_generate_variant:Nn \tl_greverse:N { c }
 \cs_new:Npn \tl_head:w #1#2 \q_stop {#1}
 \cs_new:Npn \tl_tail:w #1#2 \q_stop {#2}
 \cs_new:Npn \tl_head:n #1
   { \etex_unexpanded:D \exp_after:wN { \tl_head:w #1 { } \q_stop } }
 \cs_new:Npn \tl_tail:n #1
-  { \etex_unexpanded:D \tl_tail_aux:w #1 \q_mark { } \q_mark \q_stop }
-\cs_new:Npn \tl_tail_aux:w #1 #2 \q_mark #3 \q_stop { {#2} }
+  { \etex_unexpanded:D \__tl_tail:w #1 \q_mark { } \q_mark \q_stop }
+\cs_new:Npn \__tl_tail:w #1 #2 \q_mark #3 \q_stop { {#2} }
 \cs_new_nopar:Npn \tl_head:N { \exp_args:No \tl_head:n }
 \cs_generate_variant:Nn \tl_head:n { V , v , f }
 \cs_new_nopar:Npn \tl_tail:N { \exp_args:No \tl_tail:n }
 \cs_generate_variant:Nn \tl_tail:n { V , v , f }
 \cs_new:Npn \str_head:n #1
   {
-    \exp_after:wN \str_head_aux:w
+    \exp_after:wN \__str_head:w
     \tl_to_str:n {#1}
     { { } } ~ \q_stop
   }
-\cs_new:Npn \str_head_aux:w #1 ~ %
+\cs_new:Npn \__str_head:w #1 ~ %
   { \tl_head:w #1 { ~ } }
 \cs_new:Npn \str_tail:n #1
   {
-    \exp_after:wN \str_tail_aux:w
+    \exp_after:wN \__str_tail:w
     \reverse_if:N \if_charcode:w
         \scan_stop: \tl_to_str:n {#1} X X \q_stop
   }
-\cs_new:Npn \str_tail_aux:w #1 X #2 \q_stop { \fi: #1 }
+\cs_new:Npn \__str_tail:w #1 X #2 \q_stop { \fi: #1 }
 \prg_new_conditional:Npnn \tl_if_head_eq_charcode:nN #1#2 { p , T , F , TF }
   {
     \if_charcode:w
         \exp_not:N #2
-        \tl_if_head_N_type:nTF { #1 ? }
-          { \exp_after:wN \exp_not:N \tl_head:w #1 \q_nil \q_stop }
+        \tl_if_head_is_N_type:nTF { #1 ? }
+          {
+            \exp_after:wN \exp_not:N
+            \tl_head:w #1 { ? \use_none:nn } \q_stop
+          }
           { \str_head:n {#1} }
       \prg_return_true:
     \else:
@@ -533,10 +637,13 @@
   {
     \if_catcode:w
         \exp_not:N #2
-        \tl_if_head_N_type:nTF { #1 ? }
-          { \exp_after:wN \exp_not:N \tl_head:w #1 \q_nil \q_stop }
+        \tl_if_head_is_N_type:nTF { #1 ? }
+          {
+            \exp_after:wN \exp_not:N
+            \tl_head:w #1 { ? \use_none:nn } \q_stop
+          }
           {
-            \tl_if_head_group:nTF {#1}
+            \tl_if_head_is_group:nTF {#1}
               { \c_group_begin_token }
               { \c_space_token }
           }
@@ -547,20 +654,21 @@
   }
 \prg_new_conditional:Npnn \tl_if_head_eq_meaning:nN #1#2 { p , T , F , TF }
   {
-    \tl_if_head_N_type:nTF { #1 ? }
-      { \tl_if_head_eq_meaning_aux_normal:nN }
-      { \tl_if_head_eq_meaning_aux_special:nN }
+    \tl_if_head_is_N_type:nTF { #1 ? }
+      { \__tl_if_head_eq_meaning_normal:nN }
+      { \__tl_if_head_eq_meaning_special:nN }
     {#1} #2
   }
-\cs_new:Npn \tl_if_head_eq_meaning_aux_normal:nN #1 #2
+\cs_new:Npn \__tl_if_head_eq_meaning_normal:nN #1 #2
   {
-    \exp_after:wN \if_meaning:w \tl_head:w #1 \q_nil \q_stop #2
+    \exp_after:wN \if_meaning:w
+        \tl_head:w #1 { ?? \use_none:nnn } \q_stop #2
       \prg_return_true:
     \else:
       \prg_return_false:
     \fi:
   }
-\cs_new:Npn \tl_if_head_eq_meaning_aux_special:nN #1 #2
+\cs_new:Npn \__tl_if_head_eq_meaning_special:nN #1 #2
   {
     \if_charcode:w \str_head:n {#1} \exp_not:N #2
       \exp_after:wN \use:n
@@ -570,7 +678,7 @@
     \fi:
     {
       \if_catcode:w \exp_not:N #2
-                    \tl_if_head_group:nTF {#1}
+                    \tl_if_head_is_group:nTF {#1}
                       { \c_group_begin_token }
                       { \c_space_token }
         \prg_return_true:
@@ -579,13 +687,13 @@
       \fi:
     }
   }
-\prg_new_conditional:Npnn \tl_if_head_N_type:n #1 { p , T , F , TF }
+\prg_new_conditional:Npnn \tl_if_head_is_N_type:n #1 { p , T , F , TF }
   {
-    \str_if_eq_return:xx
+    \__str_if_eq_x_return:nn
       { \exp_not:o { \use:n #1 { } } }
       { \exp_not:n { #1 { } } }
   }
-\prg_new_conditional:Npnn \tl_if_head_group:n #1 { p , T , F , TF }
+\prg_new_conditional:Npnn \tl_if_head_is_group:n #1 { p , T , F , TF }
   {
     \if_catcode:w *
         \exp_after:wN \use_none:n
@@ -600,12 +708,12 @@
       \prg_return_true:
     \fi:
   }
-\prg_new_conditional:Npnn \tl_if_head_space:n #1 { p , T , F , TF }
+\prg_new_conditional:Npnn \tl_if_head_is_space:n #1 { p , T , F , TF }
   {
     \tex_romannumeral:D \if_false: { \fi:
-      \tl_if_head_space_aux:w ? #1 ? ~ }
+      \__tl_if_head_is_space:w ? #1 ? ~ }
   }
-\cs_new:Npn \tl_if_head_space_aux:w #1 ~
+\cs_new:Npn \__tl_if_head_is_space:w #1 ~
   {
     \tl_if_empty:oTF { \use_none:n #1 }
       { \exp_after:wN \c_zero \exp_after:wN \prg_return_true: }
@@ -615,218 +723,24 @@
 \cs_new_protected:Npn \tl_show:N #1 { \cs_show:N #1 }
 \cs_generate_variant:Nn \tl_show:N { c }
 \cs_new_eq:NN \tl_show:n \etex_showtokens:D
-\tl_const:Nx \c_job_name_tl { \tex_jobname:D }
-\tl_const:Nn \c_space_tl { ~ }
 \tl_new:N \g_tmpa_tl
 \tl_new:N \g_tmpb_tl
 \tl_new:N \l_tmpa_tl
 \tl_new:N \l_tmpb_tl
-\cs_new:Npn \str_if_eq_return:xx #1 #2
-  {
-    \if_int_compare:w \pdftex_strcmp:D {#1} {#2} = \c_zero
-      \prg_return_true:
-    \else:
-      \prg_return_false:
-    \fi:
-  }
-\cs_new:Npn \tl_if_single_p:N { \exp_args:No \tl_if_single_p:n }
-\cs_new:Npn \tl_if_single:NT  { \exp_args:No \tl_if_single:nT  }
-\cs_new:Npn \tl_if_single:NF  { \exp_args:No \tl_if_single:nF  }
-\cs_new:Npn \tl_if_single:NTF { \exp_args:No \tl_if_single:nTF }
-\prg_new_conditional:Npnn \tl_if_single:n #1 { p , T , F , TF }
-  { \str_if_eq_return:xx { \exp_not:o { \use_none:nn #1 ?? } } {?} }
-\prg_new_conditional:Npnn \tl_if_single_token:n #1 { p , T , F , TF }
-  {
-    \tl_if_head_N_type:nTF {#1}
-      { \str_if_eq_return:xx { \exp_not:o { \use_none:n #1 } } { } }
-      { \str_if_eq_return:xx { \exp_not:n {#1} } { ~ } }
-  }
-\cs_new:Npn \tl_act:NNNnn { \tex_romannumeral:D \tl_act_aux:NNNnn }
-\cs_new:Npn \tl_act_aux:NNNnn #1 #2 #3 #4 #5
-  {
-    \group_align_safe_begin:
-    \tl_act_loop:w #5 \q_tl_act_mark \q_tl_act_stop
-    {#4} #1 #2 #3
-    \tl_act_result:n { }
-  }
-\cs_new:Npn \tl_act_loop:w #1 \q_tl_act_stop
-  {
-    \tl_if_head_N_type:nTF {#1}
-      { \tl_act_normal:NwnNNN }
-      {
-        \tl_if_head_group:nTF {#1}
-          { \tl_act_group:nwnNNN }
-          { \tl_act_space:wwnNNN }
-      }
-    #1 \q_tl_act_stop
-  }
-\cs_new:Npn \tl_act_normal:NwnNNN #1 #2 \q_tl_act_stop #3#4
-  {
-    \if_meaning:w \q_tl_act_mark #1
-      \exp_after:wN \tl_act_end:wn
-    \fi:
-    #4 {#3} #1
-    \tl_act_loop:w #2 \q_tl_act_stop
-    {#3} #4
-  }
-\cs_new:Npn \tl_act_end:wn #1 \tl_act_result:n #2
-  { \group_align_safe_end: \c_zero #2 }
-\cs_new:Npn \tl_act_group:nwnNNN #1 #2 \q_tl_act_stop #3#4#5
-  {
-    #5 {#3} {#1}
-    \tl_act_loop:w #2 \q_tl_act_stop
-    {#3} #4 #5
-  }
-\exp_last_unbraced:NNo
-  \cs_new:Npn \tl_act_space:wwnNNN \c_space_tl #1 \q_tl_act_stop #2#3#4#5
-  {
-    #5 {#2}
-    \tl_act_loop:w #1 \q_tl_act_stop
-    {#2} #3 #4 #5
-  }
-\cs_new:Npn \tl_act_output:n #1 #2 \tl_act_result:n #3
-  { #2 \tl_act_result:n { #3 #1 } }
-\cs_new:Npn \tl_act_reverse_output:n #1 #2 \tl_act_result:n #3
-  { #2 \tl_act_result:n { #1 #3 } }
-\cs_new:Npn \tl_act_group_recurse:Nnn #1#2#3
-  {
-    \exp_args:Nf #1
-      { \exp_after:wN \exp_after:wN \exp_after:wN { #2 {#3} } }
-  }
-\cs_new:Npn \tl_reverse_tokens:n #1
-  {
-    \etex_unexpanded:D \exp_after:wN
-      {
-        \tex_romannumeral:D
-        \tl_act_aux:NNNnn
-          \tl_act_reverse_normal:nN
-          \tl_act_reverse_group:nn
-          \tl_act_reverse_space:n
-          { }
-          {#1}
-      }
-  }
-\cs_new:Npn \tl_act_reverse_space:n #1
-  { \tl_act_reverse_output:n {~} }
-\cs_new:Npn \tl_act_reverse_normal:nN #1 #2
-  { \tl_act_reverse_output:n {#2} }
-\cs_new:Npn \tl_act_reverse_group:nn #1
-  {
-    \tl_act_group_recurse:Nnn
-      \tl_act_reverse_output:n
-      { \tl_reverse_tokens:n }
-  }
-\cs_new:Npn \tl_reverse:n #1
-  {
-    \etex_unexpanded:D \exp_after:wN
-      {
-        \tex_romannumeral:D
-        \tl_act_aux:NNNnn
-          \tl_act_reverse_normal:nN
-          \tl_act_reverse_group_preserve:nn
-          \tl_act_reverse_space:n
-          { }
-          {#1}
-      }
-  }
-\cs_new:Npn \tl_act_reverse_group_preserve:nn #1 #2
-  { \tl_act_reverse_output:n { {#2} } }
-\cs_generate_variant:Nn \tl_reverse:n { o , V }
-\cs_new_protected:Npn \tl_reverse:N #1
-  { \tl_set:Nx #1 { \exp_args:No \tl_reverse:n { #1 } } }
-\cs_new_protected:Npn \tl_greverse:N #1
-  { \tl_gset:Nx #1 { \exp_args:No \tl_reverse:n { #1 } } }
-\cs_generate_variant:Nn \tl_reverse:N  { c }
-\cs_generate_variant:Nn \tl_greverse:N { c }
-\cs_new:Npn \tl_length_tokens:n #1
-  {
-    \int_eval:n
-      {
-        \tl_act_aux:NNNnn
-          \tl_act_length_normal:nN
-          \tl_act_length_group:nn
-          \tl_act_length_space:n
-          { }
-          {#1}
-      }
-  }
-\cs_new:Npn \tl_act_length_normal:nN #1 #2 { 1 + }
-\cs_new:Npn \tl_act_length_space:n #1 { 1 + }
-\cs_new:Npn \tl_act_length_group:nn #1 #2
-  { 2 + \tl_length_tokens:n {#2} + }
-\tl_const:Nn \c_tl_act_uppercase_tl
-  {
-    aA bB cC dD eE fF gG hH iI jJ kK lL mM
-    nN oO pP qQ rR sS tT uU vV wW xX yY zZ
-  }
-\tl_const:Nn \c_tl_act_lowercase_tl
-  {
-    Aa Bb Cc Dd Ee Ff Gg Hh Ii Jj Kk Ll Mm
-    Nn Oo Pp Qq Rr Ss Tt Uu Vv Ww Xx Yy Zz
-  }
-\cs_new:Npn \tl_expandable_uppercase:n #1
-  {
-    \etex_unexpanded:D \exp_after:wN
-      {
-        \tex_romannumeral:D
-          \tl_act_case_aux:nn { \c_tl_act_uppercase_tl } {#1}
-      }
-  }
-\cs_new:Npn \tl_expandable_lowercase:n #1
-  {
-    \etex_unexpanded:D \exp_after:wN
-      {
-        \tex_romannumeral:D
-          \tl_act_case_aux:nn { \c_tl_act_lowercase_tl } {#1}
-      }
-  }
-\cs_new:Npn \tl_act_case_aux:nn
-  {
-    \tl_act_aux:NNNnn
-      \tl_act_case_normal:nN
-      \tl_act_case_group:nn
-      \tl_act_case_space:n
-  }
-\cs_new:Npn \tl_act_case_space:n #1 { \tl_act_output:n {~} }
-\cs_new:Npn \tl_act_case_normal:nN #1 #2
-  {
-    \exp_args:Nf \tl_act_output:n
-      {
-        \exp_args:NNo \prg_case_str:nnn #2 {#1}
-          { \exp_stop_f: #2 }
-      }
-  }
-\cs_new:Npn \tl_act_case_group:nn #1 #2
-  {
-    \exp_after:wN \tl_act_output:n \exp_after:wN
-      { \exp_after:wN { \tex_romannumeral:D \tl_act_case_aux:nn {#1} {#2} } }
-  }
-\cs_new:Npn \tl_item:nn #1#2
-  {
-    \exp_args:Nf \tl_item_aux:nn
-      {
-        \int_eval:n
-          {
-            \int_compare:nNnT {#2} < \c_zero
-              { \tl_length:n {#1} + }
-            #2
-          }
-      }
-    #1
-    \q_recursion_tail
-    \prg_break_point:n { }
-  }
-\cs_new:Npn \tl_item_aux:nn #1#2
-  {
-    \quark_if_recursion_tail_break:n {#2}
-    \int_compare:nNnTF {#1} = \c_zero
-      { \tl_map_break:n { \exp_not:n {#2} } }
-      { \exp_args:Nf \tl_item_aux:nn { \int_eval:n { #1 - 1 } } }
-  }
-\cs_new_nopar:Npn \tl_item:Nn { \exp_args:No \tl_item:nn }
-\cs_generate_variant:Nn \tl_item:Nn { c }
+\cs_new_eq:NN \tl_length_tokens:n \tl_count_tokens:n
+\cs_new_eq:NN \tl_length:N \tl_count:N
+\cs_new_eq:NN \tl_length:c \tl_count:c
+\cs_new_eq:NN \tl_length:n \tl_count:n
+\cs_new_eq:NN \tl_length:V \tl_count:V
+\cs_new_eq:NN \tl_length:o \tl_count:o
 \prg_new_conditional:Npnn \tl_if_empty:x #1 { p , T , F , TF }
-  { \str_if_eq_return:xx { } {#1} }
+  { \__str_if_eq_x_return:nn { } {#1} }
+\prg_new_eq_conditional:NNn \tl_if_head_group:n \tl_if_head_is_group:n
+  { p , T , F , TF }
+\prg_new_eq_conditional:NNn \tl_if_head_N_type:n \tl_if_head_is_N_type:n
+  { p , T , F , TF }
+\prg_new_eq_conditional:NNn \tl_if_head_space:n \tl_if_head_is_space:n
+  { p , T , F , TF }
 %% 
 %%
 %% End of file `l3tl.sty'.
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3token.sty b/Master/texmf-dist/tex/latex/l3kernel/l3token.sty
index cd05ac7b262..bac0b7a8832 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3token.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3token.sty
@@ -46,17 +46,17 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3token.dtx 3491 2012-03-04 06:13:18Z bruno $
+\GetIdInfo$Id: l3token.dtx 3986 2012-07-15 19:23:51Z joseph $
   {L3 Experimental token manipulation}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 \cs_new_protected:Npn \char_set_catcode:nn #1#2
-  { \tex_catcode:D #1 = \int_eval:w #2 \int_eval_end: }
+  { \tex_catcode:D #1 = \__int_eval:w #2 \__int_eval_end: }
 \cs_new:Npn \char_value_catcode:n #1
-  { \tex_the:D \tex_catcode:D \int_eval:w #1\int_eval_end: }
+  { \tex_the:D \tex_catcode:D \__int_eval:w #1\__int_eval_end: }
 \cs_new_protected:Npn \char_show_value_catcode:n #1
-  { \tex_showthe:D \tex_catcode:D \int_eval:w #1 \int_eval_end: }
+  { \tex_showthe:D \tex_catcode:D \__int_eval:w #1 \__int_eval_end: }
 \cs_new_protected:Npn \char_set_catcode_escape:N #1
   { \char_set_catcode:nn { `#1 } \c_zero }
 \cs_new_protected:Npn \char_set_catcode_group_begin:N #1
@@ -122,29 +122,29 @@
 \cs_new_protected:Npn \char_set_catcode_invalid:n #1
   { \char_set_catcode:nn {#1} \c_fifteen }
 \cs_new_protected:Npn \char_set_mathcode:nn #1#2
-  { \tex_mathcode:D #1 = \int_eval:w #2 \int_eval_end: }
+  { \tex_mathcode:D #1 = \__int_eval:w #2 \__int_eval_end: }
 \cs_new:Npn \char_value_mathcode:n #1
-  { \tex_the:D \tex_mathcode:D \int_eval:w #1\int_eval_end: }
+  { \tex_the:D \tex_mathcode:D \__int_eval:w #1\__int_eval_end: }
 \cs_new_protected:Npn \char_show_value_mathcode:n #1
-  { \tex_showthe:D \tex_mathcode:D \int_eval:w #1 \int_eval_end: }
+  { \tex_showthe:D \tex_mathcode:D \__int_eval:w #1 \__int_eval_end: }
 \cs_new_protected:Npn \char_set_lccode:nn #1#2
-  { \tex_lccode:D #1 = \int_eval:w #2 \int_eval_end: }
+  { \tex_lccode:D #1 = \__int_eval:w #2 \__int_eval_end: }
 \cs_new:Npn \char_value_lccode:n #1
-  { \tex_the:D \tex_lccode:D \int_eval:w #1\int_eval_end: }
+  { \tex_the:D \tex_lccode:D \__int_eval:w #1\__int_eval_end: }
 \cs_new_protected:Npn \char_show_value_lccode:n #1
-  { \tex_showthe:D \tex_lccode:D \int_eval:w #1 \int_eval_end: }
+  { \tex_showthe:D \tex_lccode:D \__int_eval:w #1 \__int_eval_end: }
 \cs_new_protected:Npn \char_set_uccode:nn #1#2
-  { \tex_uccode:D #1 = \int_eval:w #2 \int_eval_end: }
+  { \tex_uccode:D #1 = \__int_eval:w #2 \__int_eval_end: }
 \cs_new:Npn \char_value_uccode:n #1
-  { \tex_the:D \tex_uccode:D \int_eval:w #1\int_eval_end: }
+  { \tex_the:D \tex_uccode:D \__int_eval:w #1\__int_eval_end: }
 \cs_new_protected:Npn \char_show_value_uccode:n #1
-  { \tex_showthe:D \tex_uccode:D \int_eval:w #1 \int_eval_end: }
+  { \tex_showthe:D \tex_uccode:D \__int_eval:w #1 \__int_eval_end: }
 \cs_new_protected:Npn \char_set_sfcode:nn #1#2
-  { \tex_sfcode:D #1 = \int_eval:w #2 \int_eval_end: }
+  { \tex_sfcode:D #1 = \__int_eval:w #2 \__int_eval_end: }
 \cs_new:Npn \char_value_sfcode:n #1
-  { \tex_the:D \tex_sfcode:D \int_eval:w #1\int_eval_end: }
+  { \tex_the:D \tex_sfcode:D \__int_eval:w #1\__int_eval_end: }
 \cs_new_protected:Npn \char_show_value_sfcode:n #1
-  { \tex_showthe:D \tex_sfcode:D \int_eval:w #1 \int_eval_end: }
+  { \tex_showthe:D \tex_sfcode:D \__int_eval:w #1 \__int_eval_end: }
 \cs_new_protected:Npn \token_new:Nn #1#2 { \cs_new_eq:NN #1 #2 }
 \cs_new_eq:NN \c_group_begin_token {
 \cs_new_eq:NN \c_group_end_token }
@@ -178,13 +178,13 @@
     \use:nn
       {
         \group_end:
-        \seq_set_from_clist:Nn \l_char_active_seq
+        \seq_set_split:Nnn \l_char_active_seq { }
       }
   }
-    { { " , $ , & , ^ , _ , ~ } } %$
+    { { " $ & ^ _ ~ } } %$
 \seq_new:N \l_char_special_seq
-\seq_set_from_clist:Nn \l_char_special_seq
-  { \  , \" , \# , \$ , \% , \& , \\ , \^ , \_ , \{ , \} , \~ }
+\seq_set_split:Nnn \l_char_special_seq { }
+  { \  \" \# \$ \% \& \\ \^ \_ \{ \} \~ }
 \prg_new_conditional:Npnn \token_if_group_begin:N #1 { p , T ,  F , TF }
   {
     \if_catcode:w \exp_not:N #1 \c_group_begin_token
@@ -269,10 +269,10 @@
     \group_end:
     \prg_new_conditional:Npnn \token_if_macro:N #1 { p , T ,  F , TF }
       {
-        \exp_after:wN \token_if_macro_p_aux:w
+        \exp_after:wN \__token_if_macro_p:w
         \token_to_meaning:N #1 MA; \q_stop
       }
-    \cs_new:Npn \token_if_macro_p_aux:w #1 MA #2 ; #3 \q_stop
+    \cs_new:Npn \__token_if_macro_p:w #1 MA #2 ; #3 \q_stop
       {
         \if_int_compare:w \pdftex_strcmp:D { #2 } { cro } = \c_zero
             \prg_return_true:
@@ -288,12 +288,15 @@
   }
 \prg_new_conditional:Npnn \token_if_expandable:N #1 { p , T ,  F , TF }
   {
-    \cs_if_exist:NTF #1
-      {
-        \exp_after:wN \if_meaning:w \exp_not:N #1 #1
-          \prg_return_false: \else: \prg_return_true: \fi:
-      }
-      { \prg_return_false: }
+    \exp_after:wN \if_meaning:w \exp_not:N #1 #1
+      \prg_return_false:
+    \else:
+      \if_cs_exist:N #1
+        \prg_return_true:
+      \else:
+        \prg_return_false:
+      \fi:
+    \fi:
   }
 \group_begin:
   \char_set_lccode:nn { `T } { `T }
@@ -308,23 +311,23 @@
     \group_end:
     \prg_new_conditional:Npnn \token_if_chardef:N #1 { p , T ,  F , TF }
       {
-        \str_if_eq_return:xx
+        \__str_if_eq_x_return:nn
           {
-            \exp_after:wN \token_if_chardef_aux:w
+            \exp_after:wN \__token_if_chardef:w
               \token_to_meaning:N #1 CHAR" \q_stop
           }
           { \token_to_str:N \char }
       }
     \prg_new_conditional:Npnn \token_if_mathchardef:N #1 { p , T ,  F , TF }
       {
-        \str_if_eq_return:xx
+        \__str_if_eq_x_return:nn
           {
-            \exp_after:wN \token_if_chardef_aux:w
+            \exp_after:wN \__token_if_chardef:w
               \token_to_meaning:N #1 CHAR" \q_stop
           }
           { \token_to_str:N \mathchar }
       }
-    \cs_new:Npn \token_if_chardef_aux:w #1 CHAR" #2 \q_stop { #1 CHAR }
+    \cs_new:Npn \__token_if_chardef:w #1 CHAR" #2 \q_stop { #1 CHAR }
     \prg_new_conditional:Npnn \token_if_dim_register:N #1 { p , T ,  F , TF }
       {
         \if_meaning:w \tex_dimen:D #1
@@ -333,16 +336,16 @@
           \if_meaning:w \tex_dimendef:D #1
             \prg_return_false:
           \else:
-            \str_if_eq_return:xx
+            \__str_if_eq_x_return:nn
               {
-                \exp_after:wN \token_if_dim_register_aux:w
+                \exp_after:wN \__token_if_dim_register:w
                   \token_to_meaning:N #1 ZIMEX \q_stop
               }
               { \token_to_str:N \  }
           \fi:
         \fi:
       }
-    \cs_new:Npn \token_if_dim_register_aux:w #1 ZIMEX #2 \q_stop { #1 ~ }
+    \cs_new:Npn \__token_if_dim_register:w #1 ZIMEX #2 \q_stop { #1 ~ }
     \prg_new_conditional:Npnn \token_if_int_register:N #1 { p , T ,  F , TF }
       {
         % \token_if_chardef:NTF #1 { \prg_return_true: }
@@ -355,9 +358,9 @@
           \if_meaning:w \tex_countdef:D #1
             \prg_return_false:
           \else:
-            \str_if_eq_return:xx
+            \__str_if_eq_x_return:nn
               {
-                \exp_after:wN \token_if_int_register_aux:w
+                \exp_after:wN \__token_if_int_register:w
                   \token_to_meaning:N #1 COUXY \q_stop
               }
               { \token_to_str:N \  }
@@ -366,7 +369,7 @@
         %       }
         %   }
       }
-    \cs_new:Npn \token_if_int_register_aux:w #1 COUXY #2 \q_stop { #1 ~ }
+    \cs_new:Npn \__token_if_int_register:w #1 COUXY #2 \q_stop { #1 ~ }
     \prg_new_conditional:Npnn \token_if_muskip_register:N #1 { p , T ,  F , TF }
       {
         \if_meaning:w \tex_muskip:D #1
@@ -375,16 +378,16 @@
           \if_meaning:w \tex_muskipdef:D #1
             \prg_return_false:
           \else:
-            \str_if_eq_return:xx
+            \__str_if_eq_x_return:nn
               {
-                \exp_after:wN \token_if_muskip_register_aux:w
+                \exp_after:wN \__token_if_muskip_register:w
                   \token_to_meaning:N #1 MUSKIP \q_stop
               }
               { \token_to_str:N \  }
           \fi:
         \fi:
       }
-    \cs_new:Npn \token_if_muskip_register_aux:w #1 MUSKIP #2 \q_stop { #1 ~ }
+    \cs_new:Npn \__token_if_muskip_register:w #1 MUSKIP #2 \q_stop { #1 ~ }
     \prg_new_conditional:Npnn \token_if_skip_register:N #1 { p , T ,  F , TF }
       {
         \if_meaning:w \tex_skip:D #1
@@ -393,16 +396,16 @@
           \if_meaning:w \tex_skipdef:D #1
             \prg_return_false:
           \else:
-            \str_if_eq_return:xx
+            \__str_if_eq_x_return:nn
               {
-                \exp_after:wN \token_if_skip_register_aux:w
+                \exp_after:wN \__token_if_skip_register:w
                   \token_to_meaning:N #1 SKIP \q_stop
               }
               { \token_to_str:N \  }
           \fi:
         \fi:
       }
-    \cs_new:Npn \token_if_skip_register_aux:w #1 SKIP #2 \q_stop { #1 ~ }
+    \cs_new:Npn \__token_if_skip_register:w #1 SKIP #2 \q_stop { #1 ~ }
     \prg_new_conditional:Npnn \token_if_toks_register:N #1 { p , T ,  F , TF }
       {
         \if_meaning:w \tex_toks:D #1
@@ -411,33 +414,33 @@
           \if_meaning:w \tex_toksdef:D #1
             \prg_return_false:
           \else:
-            \str_if_eq_return:xx
+            \__str_if_eq_x_return:nn
               {
-                \exp_after:wN \token_if_toks_register_aux:w
+                \exp_after:wN \__token_if_toks_register:w
                   \token_to_meaning:N #1 YOKS \q_stop
               }
               { \token_to_str:N \  }
           \fi:
         \fi:
       }
-     \cs_new:Npn \token_if_toks_register_aux:w #1 YOKS #2 \q_stop { #1 ~ }
+     \cs_new:Npn \__token_if_toks_register:w #1 YOKS #2 \q_stop { #1 ~ }
     \prg_new_conditional:Npnn \token_if_protected_macro:N #1
       { p , T ,  F , TF }
       {
-        \str_if_eq_return:xx
+        \__str_if_eq_x_return:nn
           {
-            \exp_after:wN \token_if_protected_macro_aux:w
+            \exp_after:wN \__token_if_protected_macro:w
               \token_to_meaning:N #1 PROYECYEZ~MACRO \q_stop
           }
           { \token_to_str:N \  }
       }
-    \cs_new:Npn \token_if_protected_macro_aux:w
+    \cs_new:Npn \__token_if_protected_macro:w
       #1 PROYECYEZ~MACRO #2 \q_stop { #1 ~ }
     \prg_new_conditional:Npnn \token_if_long_macro:N #1 { p , T ,  F , TF }
       {
-        \str_if_eq_return:xx
+        \__str_if_eq_x_return:nn
           {
-            \exp_after:wN \token_if_long_macro_aux:w
+            \exp_after:wN \__token_if_long_macro:w
               \token_to_meaning:N #1 LOXG~MACRO \q_stop
           }
           { \token_to_str:N \  }
@@ -445,14 +448,14 @@
     \prg_new_conditional:Npnn \token_if_protected_long_macro:N #1
       { p , T ,  F , TF }
       {
-        \str_if_eq_return:xx
+        \__str_if_eq_x_return:nn
           {
-            \exp_after:wN \token_if_long_macro_aux:w
+            \exp_after:wN \__token_if_long_macro:w
               \token_to_meaning:N #1 LOXG~MACRO \q_stop
           }
           { \token_to_str:N \protected \token_to_str:N \  }
       }
-    \cs_new:Npn \token_if_long_macro_aux:w #1 LOXG~MACRO #2 \q_stop { #1 ~ }
+    \cs_new:Npn \__token_if_long_macro:w #1 LOXG~MACRO #2 \q_stop { #1 ~ }
   }
 \tex_chardef:D \c_token_A_int = `A ~ %
 \group_begin:
@@ -467,19 +470,19 @@
       \token_if_macro:NTF #1
         \prg_return_false:
         {
-          \exp_after:wN \token_if_primitive_aux:NNw
+          \exp_after:wN \__token_if_primitive:NNw
           \token_to_meaning:N #1 ; ; ; \q_stop #1
         }
     }
-  \cs_new:Npn \token_if_primitive_aux:NNw #1#2 #3 ; #4 \q_stop
+  \cs_new:Npn \__token_if_primitive:NNw #1#2 #3 ; #4 \q_stop
     {
-      \tl_if_empty:oTF { \token_if_primitive_aux_space:w #3 ~ }
-        { \token_if_primitive_aux_loop:N #3 ; \q_stop }
-        { \token_if_primitive_aux_nullfont:N }
+      \tl_if_empty:oTF { \__token_if_primitive_space:w #3 ~ }
+        { \__token_if_primitive_loop:N #3 ; \q_stop }
+        { \__token_if_primitive_nullfont:N }
     }
 }
-\cs_new:Npn \token_if_primitive_aux_space:w #1 ~ { }
-\cs_new:Npn \token_if_primitive_aux_nullfont:N #1
+\cs_new:Npn \__token_if_primitive_space:w #1 ~ { }
+\cs_new:Npn \__token_if_primitive_nullfont:N #1
   {
     \if_meaning:w \tex_nullfont:D #1
       \prg_return_true:
@@ -487,25 +490,25 @@
       \prg_return_false:
     \fi:
   }
-\cs_new:Npn \token_if_primitive_aux_loop:N #1
+\cs_new:Npn \__token_if_primitive_loop:N #1
   {
-    \if_num:w `#1 < \c_token_A_int %
-      \exp_after:wN \token_if_primitive_auxii:Nw
+    \if_int_compare:w `#1 < \c_token_A_int %
+      \exp_after:wN \__token_if_primitive:Nw
       \exp_after:wN #1
     \else:
-      \exp_after:wN \token_if_primitive_aux_loop:N
+      \exp_after:wN \__token_if_primitive_loop:N
     \fi:
   }
-\cs_new:Npn \token_if_primitive_auxii:Nw #1 #2 \q_stop
+\cs_new:Npn \__token_if_primitive:Nw #1 #2 \q_stop
   {
     \if:w : #1
-      \exp_after:wN \token_if_primitive_aux_undefined:N
+      \exp_after:wN \__token_if_primitive_undefined:N
     \else:
       \prg_return_false:
       \exp_after:wN \use_none:n
     \fi:
   }
-\cs_new:Npn \token_if_primitive_aux_undefined:N #1
+\cs_new:Npn \__token_if_primitive_undefined:N #1
   {
     \if_cs_exist:N #1
       \prg_return_true:
@@ -515,32 +518,32 @@
   }
 \cs_new_eq:NN \l_peek_token ?
 \cs_new_eq:NN \g_peek_token ?
-\cs_new_eq:NN \l_peek_search_token ?
-\tl_new:N \l_peek_search_tl
-\cs_new_nopar:Npn \peek_true:w  { }
-\cs_new_nopar:Npn \peek_true_aux:w  { }
-\cs_new_nopar:Npn \peek_false:w { }
-\cs_new:Npn \peek_tmp:w { }
+\cs_new_eq:NN \l__peek_search_token ?
+\tl_new:N \l__peek_search_tl
+\cs_new_nopar:Npn \__peek_true:w  { }
+\cs_new_nopar:Npn \__peek_true_aux:w  { }
+\cs_new_nopar:Npn \__peek_false:w { }
+\cs_new:Npn \__peek_tmp:w { }
 \cs_new_protected_nopar:Npn \peek_after:Nw
   { \tex_futurelet:D \l_peek_token }
 \cs_new_protected_nopar:Npn \peek_gafter:Nw
   { \tex_global:D \tex_futurelet:D \g_peek_token }
-\cs_new_protected:Npn \peek_true_remove:w
+\cs_new_protected:Npn \__peek_true_remove:w
   {
     \group_align_safe_end:
-    \tex_afterassignment:D \peek_true_aux:w
-    \cs_set_eq:NN \peek_tmp:w
+    \tex_afterassignment:D \__peek_true_aux:w
+    \cs_set_eq:NN \__peek_tmp:w
   }
-\cs_new_protected:Npn \peek_token_generic:NNTF #1#2#3#4
+\cs_new_protected:Npn \__peek_token_generic:NNTF #1#2#3#4
   {
-    \cs_set_eq:NN \l_peek_search_token #2
-    \tl_set:Nn \l_peek_search_tl {#2}
-    \cs_set_nopar:Npx \peek_true:w
+    \cs_set_eq:NN \l__peek_search_token #2
+    \tl_set:Nn \l__peek_search_tl {#2}
+    \cs_set_nopar:Npx \__peek_true:w
       {
         \exp_not:N \group_align_safe_end:
         \exp_not:n {#3}
       }
-    \cs_set_nopar:Npx \peek_false:w
+    \cs_set_nopar:Npx \__peek_false:w
       {
         \exp_not:N \group_align_safe_end:
         \exp_not:n {#4}
@@ -548,17 +551,17 @@
     \group_align_safe_begin:
       \peek_after:Nw #1
   }
-\cs_new_protected:Npn \peek_token_generic:NNT #1#2#3
-  { \peek_token_generic:NNTF #1 #2 {#3} { } }
-\cs_new_protected:Npn \peek_token_generic:NNF #1#2#3
-  { \peek_token_generic:NNTF #1 #2 { } {#3} }
-\cs_new_protected:Npn \peek_token_remove_generic:NNTF #1#2#3#4
-  {
-    \cs_set_eq:NN \l_peek_search_token #2
-    \tl_set:Nn \l_peek_search_tl {#2}
-    \cs_set_eq:NN \peek_true:w \peek_true_remove:w
-    \cs_set_nopar:Npx \peek_true_aux:w { \exp_not:n {#3} }
-    \cs_set_nopar:Npx \peek_false:w
+\cs_new_protected:Npn \__peek_token_generic:NNT #1#2#3
+  { \__peek_token_generic:NNTF #1 #2 {#3} { } }
+\cs_new_protected:Npn \__peek_token_generic:NNF #1#2#3
+  { \__peek_token_generic:NNTF #1 #2 { } {#3} }
+\cs_new_protected:Npn \__peek_token_remove_generic:NNTF #1#2#3#4
+  {
+    \cs_set_eq:NN \l__peek_search_token #2
+    \tl_set:Nn \l__peek_search_tl {#2}
+    \cs_set_eq:NN \__peek_true:w \__peek_true_remove:w
+    \cs_set_nopar:Npx \__peek_true_aux:w { \exp_not:n {#3} }
+    \cs_set_nopar:Npx \__peek_false:w
       {
         \exp_not:N \group_align_safe_end:
         \exp_not:n {#4}
@@ -566,28 +569,28 @@
     \group_align_safe_begin:
       \peek_after:Nw #1
   }
-\cs_new_protected:Npn \peek_token_remove_generic:NNT #1#2#3
-  { \peek_token_remove_generic:NNTF #1 #2 {#3} { } }
-\cs_new_protected:Npn \peek_token_remove_generic:NNF #1#2#3
-  { \peek_token_remove_generic:NNTF #1 #2 { } {#3} }
-\cs_new_nopar:Npn \peek_execute_branches_catcode:
+\cs_new_protected:Npn \__peek_token_remove_generic:NNT #1#2#3
+  { \__peek_token_remove_generic:NNTF #1 #2 {#3} { } }
+\cs_new_protected:Npn \__peek_token_remove_generic:NNF #1#2#3
+  { \__peek_token_remove_generic:NNTF #1 #2 { } {#3} }
+\cs_new_nopar:Npn \__peek_execute_branches_catcode:
   {
     \if_catcode:w
-      \exp_not:N \l_peek_token \exp_not:N \l_peek_search_token
-      \exp_after:wN \peek_true:w
+      \exp_not:N \l_peek_token \exp_not:N \l__peek_search_token
+      \exp_after:wN \__peek_true:w
     \else:
-      \exp_after:wN \peek_false:w
+      \exp_after:wN \__peek_false:w
     \fi:
   }
-\cs_new_nopar:Npn \peek_execute_branches_meaning:
+\cs_new_nopar:Npn \__peek_execute_branches_meaning:
   {
-    \if_meaning:w \l_peek_token \l_peek_search_token
-      \exp_after:wN \peek_true:w
+    \if_meaning:w \l_peek_token \l__peek_search_token
+      \exp_after:wN \__peek_true:w
     \else:
-      \exp_after:wN \peek_false:w
+      \exp_after:wN \__peek_false:w
     \fi:
   }
-\cs_new_nopar:Npn \peek_execute_branches_charcode:
+\cs_new_nopar:Npn \__peek_execute_branches_charcode:
   {
     \bool_if:nTF
       {
@@ -595,107 +598,107 @@
         || \token_if_eq_catcode_p:NN \l_peek_token \c_group_end_token
         || \token_if_eq_meaning_p:NN \l_peek_token \c_space_token
       }
-      { \peek_false:w }
+      { \__peek_false:w }
       {
-        \exp_after:wN \peek_execute_branches_charcode_aux:NN
-          \l_peek_search_tl
+        \exp_after:wN \__peek_execute_branches_charcode_aux:NN
+          \l__peek_search_tl
       }
   }
-\cs_new:Npn \peek_execute_branches_charcode_aux:NN #1#2
+\cs_new:Npn \__peek_execute_branches_charcode_aux:NN #1#2
   {
     \if:w \exp_not:N #1 \exp_not:N #2
-      \exp_after:wN \peek_true:w
+      \exp_after:wN \__peek_true:w
     \else:
-      \exp_after:wN \peek_false:w
+      \exp_after:wN \__peek_false:w
     \fi:
     #2
   }
-\cs_new_protected_nopar:Npn \peek_ignore_spaces_execute_branches:
+\cs_new_protected_nopar:Npn \__peek_ignore_spaces_execute_branches:
   {
     \token_if_eq_meaning:NNTF \l_peek_token \c_space_token
       {
-        \tex_afterassignment:D \peek_ignore_spaces_execute_branches_aux:
-        \cs_set_eq:NN \peek_tmp:w
+        \tex_afterassignment:D \__peek_ignore_spaces_execute_branches_aux:
+        \cs_set_eq:NN \__peek_tmp:w
       }
-      { \peek_execute_branches: }
+      { \__peek_execute_branches: }
   }
-\cs_new_protected_nopar:Npn \peek_ignore_spaces_execute_branches_aux:
-  { \peek_after:Nw \peek_ignore_spaces_execute_branches: }
+\cs_new_protected_nopar:Npn \__peek_ignore_spaces_execute_branches_aux:
+  { \peek_after:Nw \__peek_ignore_spaces_execute_branches: }
 \group_begin:
-  \cs_set:Npn \peek_def:nnnn #1#2#3#4
+  \cs_set:Npn \__peek_def:nnnn #1#2#3#4
     {
-      \peek_def_aux:nnnnn {#1} {#2} {#3} {#4} { TF }
-      \peek_def_aux:nnnnn {#1} {#2} {#3} {#4} { T }
-      \peek_def_aux:nnnnn {#1} {#2} {#3} {#4} { F }
+      \__peek_def:nnnnn {#1} {#2} {#3} {#4} { TF }
+      \__peek_def:nnnnn {#1} {#2} {#3} {#4} { T }
+      \__peek_def:nnnnn {#1} {#2} {#3} {#4} { F }
     }
-  \cs_set:Npn \peek_def_aux:nnnnn #1#2#3#4#5
+  \cs_set:Npn \__peek_def:nnnnn #1#2#3#4#5
     {
       \cs_new_nopar:cpx { #1 #5 }
         {
           \tl_if_empty:nF {#2}
-            { \exp_not:n { \cs_set_eq:NN \peek_execute_branches: #2 } }
+            { \exp_not:n { \cs_set_eq:NN \__peek_execute_branches: #2 } }
           \exp_not:c { #3 #5 }
           \exp_not:n {#4}
         }
     }
-  \peek_def:nnnn { peek_catcode:N }
+  \__peek_def:nnnn { peek_catcode:N }
     { }
-    { peek_token_generic:NN }
-    { \peek_execute_branches_catcode: }
-  \peek_def:nnnn { peek_catcode_ignore_spaces:N }
-    { \peek_execute_branches_catcode: }
-    { peek_token_generic:NN }
-    { \peek_ignore_spaces_execute_branches: }
-  \peek_def:nnnn { peek_catcode_remove:N }
+    { __peek_token_generic:NN }
+    { \__peek_execute_branches_catcode: }
+  \__peek_def:nnnn { peek_catcode_ignore_spaces:N }
+    { \__peek_execute_branches_catcode: }
+    { __peek_token_generic:NN }
+    { \__peek_ignore_spaces_execute_branches: }
+  \__peek_def:nnnn { peek_catcode_remove:N }
     { }
-    { peek_token_remove_generic:NN }
-    { \peek_execute_branches_catcode: }
-  \peek_def:nnnn { peek_catcode_remove_ignore_spaces:N }
-    { \peek_execute_branches_catcode: }
-    { peek_token_remove_generic:NN }
-    { \peek_ignore_spaces_execute_branches: }
-  \peek_def:nnnn { peek_charcode:N }
+    { __peek_token_remove_generic:NN }
+    { \__peek_execute_branches_catcode: }
+  \__peek_def:nnnn { peek_catcode_remove_ignore_spaces:N }
+    { \__peek_execute_branches_catcode: }
+    { __peek_token_remove_generic:NN }
+    { \__peek_ignore_spaces_execute_branches: }
+  \__peek_def:nnnn { peek_charcode:N }
     { }
-    { peek_token_generic:NN }
-    { \peek_execute_branches_charcode: }
-  \peek_def:nnnn { peek_charcode_ignore_spaces:N }
-    { \peek_execute_branches_charcode: }
-    { peek_token_generic:NN }
-    { \peek_ignore_spaces_execute_branches: }
-  \peek_def:nnnn { peek_charcode_remove:N }
+    { __peek_token_generic:NN }
+    { \__peek_execute_branches_charcode: }
+  \__peek_def:nnnn { peek_charcode_ignore_spaces:N }
+    { \__peek_execute_branches_charcode: }
+    { __peek_token_generic:NN }
+    { \__peek_ignore_spaces_execute_branches: }
+  \__peek_def:nnnn { peek_charcode_remove:N }
     { }
-    { peek_token_remove_generic:NN }
-    { \peek_execute_branches_charcode: }
-  \peek_def:nnnn { peek_charcode_remove_ignore_spaces:N }
-    { \peek_execute_branches_charcode: }
-    { peek_token_remove_generic:NN }
-    { \peek_ignore_spaces_execute_branches: }
-  \peek_def:nnnn { peek_meaning:N }
+    { __peek_token_remove_generic:NN }
+    { \__peek_execute_branches_charcode: }
+  \__peek_def:nnnn { peek_charcode_remove_ignore_spaces:N }
+    { \__peek_execute_branches_charcode: }
+    { __peek_token_remove_generic:NN }
+    { \__peek_ignore_spaces_execute_branches: }
+  \__peek_def:nnnn { peek_meaning:N }
     { }
-    { peek_token_generic:NN }
-    { \peek_execute_branches_meaning: }
-  \peek_def:nnnn { peek_meaning_ignore_spaces:N }
-    { \peek_execute_branches_meaning: }
-    { peek_token_generic:NN }
-    { \peek_ignore_spaces_execute_branches: }
-  \peek_def:nnnn { peek_meaning_remove:N }
+    { __peek_token_generic:NN }
+    { \__peek_execute_branches_meaning: }
+  \__peek_def:nnnn { peek_meaning_ignore_spaces:N }
+    { \__peek_execute_branches_meaning: }
+    { __peek_token_generic:NN }
+    { \__peek_ignore_spaces_execute_branches: }
+  \__peek_def:nnnn { peek_meaning_remove:N }
     { }
-    { peek_token_remove_generic:NN }
-    { \peek_execute_branches_meaning: }
-  \peek_def:nnnn { peek_meaning_remove_ignore_spaces:N }
-    { \peek_execute_branches_meaning: }
-    { peek_token_remove_generic:NN }
-    { \peek_ignore_spaces_execute_branches: }
+    { __peek_token_remove_generic:NN }
+    { \__peek_execute_branches_meaning: }
+  \__peek_def:nnnn { peek_meaning_remove_ignore_spaces:N }
+    { \__peek_execute_branches_meaning: }
+    { __peek_token_remove_generic:NN }
+    { \__peek_ignore_spaces_execute_branches: }
 \group_end:
 \exp_args:Nno \use:nn
-  { \cs_new:Npn \token_get_prefix_arg_replacement_aux:wN #1 }
+  { \cs_new:Npn \__peek_get_prefix_arg_replacement:wN #1 }
   { \tl_to_str:n { macro : } #2 -> #3 \q_stop #4 }
   { #4 {#1} {#2} {#3} }
 \cs_new:Npn \token_get_prefix_spec:N #1
   {
     \token_if_macro:NTF #1
       {
-        \exp_after:wN \token_get_prefix_arg_replacement_aux:wN
+        \exp_after:wN \__peek_get_prefix_arg_replacement:wN
           \token_to_meaning:N #1 \q_stop \use_i:nnn
       }
       { \scan_stop: }
@@ -704,7 +707,7 @@
   {
     \token_if_macro:NTF #1
       {
-        \exp_after:wN \token_get_prefix_arg_replacement_aux:wN
+        \exp_after:wN \__peek_get_prefix_arg_replacement:wN
           \token_to_meaning:N #1 \q_stop \use_ii:nnn
       }
       { \scan_stop: }
@@ -713,47 +716,11 @@
   {
     \token_if_macro:NTF #1
       {
-        \exp_after:wN \token_get_prefix_arg_replacement_aux:wN
+        \exp_after:wN \__peek_get_prefix_arg_replacement:wN
           \token_to_meaning:N #1 \q_stop \use_iii:nnn
       }
       { \scan_stop: }
   }
-\group_begin:
-  \char_set_catcode_active:N \^^@
-  \cs_set:Npn \char_tmp:NN #1#2
-    {
-      \cs_new:Npn #1 ##1
-        {
-          \char_set_catcode_active:n { `##1 }
-          \group_begin:
-          \char_set_lccode:nn { `\^^@ } { `##1 }
-          \tl_to_lowercase:n { \group_end: #2 ^^@ }
-        }
-    }
-  \char_tmp:NN \char_set_active:Npn    \cs_set:Npn
-  \char_tmp:NN \char_set_active:Npx    \cs_set:Npx
-  \char_tmp:NN \char_gset_active:Npn   \cs_gset:Npn
-  \char_tmp:NN \char_gset_active:Npx   \cs_gset:Npx
-  \char_tmp:NN \char_set_active_eq:NN  \cs_set_eq:NN
-  \char_tmp:NN \char_gset_active_eq:NN \cs_gset_eq:NN
-\group_end:
-\cs_new_protected_nopar:Npn \peek_execute_branches_N_type:
-  {
-    \bool_if:nTF
-      {
-        \token_if_eq_catcode_p:NN \l_peek_token \c_group_begin_token ||
-        \token_if_eq_catcode_p:NN \l_peek_token \c_group_end_token   ||
-        \token_if_eq_meaning_p:NN \l_peek_token \c_space_token
-      }
-      { \peek_false:w }
-      { \peek_true:w }
-  }
-\cs_new_protected_nopar:Npn \peek_N_type:TF
-  { \peek_token_generic:NNTF \peek_execute_branches_N_type: \scan_stop: }
-\cs_new_protected_nopar:Npn \peek_N_type:T
-  { \peek_token_generic:NNT  \peek_execute_branches_N_type: \scan_stop: }
-\cs_new_protected_nopar:Npn \peek_N_type:F
-  { \peek_token_generic:NNF  \peek_execute_branches_N_type: \scan_stop: }
 %% 
 %%
 %% End of file `l3token.sty'.