expl3 1981 (11jul10)

git-svn-id: svn://tug.org/texlive/trunk@19383 c570f23f-e606-0410-a88d-b1316a301751

13 files changed, 3595 insertions, 20 deletions

diff --git a/Master/texmf-dist/doc/latex/expl3/expl3.pdf b/Master/texmf-dist/doc/latex/expl3/expl3.pdf
index 5c3f8c38a8d..10f3d53602f 100644
--- a/Master/texmf-dist/doc/latex/expl3/expl3.pdf
+++ b/Master/texmf-dist/doc/latex/expl3/expl3.pdf
diff --git a/Master/texmf-dist/doc/latex/expl3/source3.pdf b/Master/texmf-dist/doc/latex/expl3/source3.pdf
index f8bbfe4a5c3..5bedd54b62a 100644
--- a/Master/texmf-dist/doc/latex/expl3/source3.pdf
+++ b/Master/texmf-dist/doc/latex/expl3/source3.pdf
diff --git a/Master/texmf-dist/source/latex/expl3/expl3.dtx b/Master/texmf-dist/source/latex/expl3/expl3.dtx
index 63fb9616c72..b063be947dc 100644
--- a/Master/texmf-dist/source/latex/expl3/expl3.dtx
+++ b/Master/texmf-dist/source/latex/expl3/expl3.dtx
@@ -37,7 +37,7 @@
 \RequirePackage{l3names}
 %</driver|package>
 %\fi
-\GetIdInfo$Id: expl3.dtx 1905 2010-05-19 07:45:31Z joseph $
+\GetIdInfo$Id: expl3.dtx 1955 2010-06-15 06:04:59Z joseph $
        {L3 Experimental code bundle wrapper}%
 %\iffalse
 %<*driver>
@@ -919,7 +919,8 @@
   l3precom,
   l3calc,
   l3xref,
-  l3file
+  l3file, 
+  l3fp,
 }
 %    \end{macrocode}
 %    
diff --git a/Master/texmf-dist/source/latex/expl3/l3candidates.dtx b/Master/texmf-dist/source/latex/expl3/l3candidates.dtx
index 2c8d8968e6c..8051fb7f340 100644
--- a/Master/texmf-dist/source/latex/expl3/l3candidates.dtx
+++ b/Master/texmf-dist/source/latex/expl3/l3candidates.dtx
@@ -37,7 +37,7 @@
 %</driver|package>
 %\fi
 \errorcontextlines=999
-\GetIdInfo$Id$
+\GetIdInfo$Id: l3candidates.dtx 1957 2010-06-15 06:33:43Z mittelba $
           {L3 Experimental 'extras' module}
 %\iffalse
 %<*driver>
diff --git a/Master/texmf-dist/source/latex/expl3/l3expan.dtx b/Master/texmf-dist/source/latex/expl3/l3expan.dtx
index 1a77ea97d71..e28b81baa32 100644
--- a/Master/texmf-dist/source/latex/expl3/l3expan.dtx
+++ b/Master/texmf-dist/source/latex/expl3/l3expan.dtx
@@ -36,7 +36,7 @@
 \RequirePackage{l3names}
 %</driver|package>
 %\fi
-\GetIdInfo$Id: l3expan.dtx 1873 2010-03-24 08:32:54Z joseph $
+\GetIdInfo$Id: l3expan.dtx 1948 2010-06-10 18:53:09Z joseph $
        {L3 Experimental Argument Expansion module}
 %\iffalse
 %<*driver>
@@ -440,10 +440,12 @@
 % \begin{function}{
 %   \exp_last_unbraced:Nf|
 %   \exp_last_unbraced:NV|
+%   \exp_last_unbraced:No|
 %   \exp_last_unbraced:Nv|
 %   \exp_last_unbraced:NcV|
-%   \exp_last_unbraced:NNo|
 %   \exp_last_unbraced:NNV|
+%   \exp_last_unbraced:NNo|
+%   \exp_last_unbraced:NNNV|
 %   \exp_last_unbraced:NNNo|
 %   }
 % \begin{syntax}
@@ -1165,25 +1167,31 @@
 %\end{macro}
 %
 %\begin{macro}{\exp_last_unbraced:NV}
+%\begin{macro}{\exp_last_unbraced:No}
 %\begin{macro}{\exp_last_unbraced:Nv}
 %\begin{macro}{\exp_last_unbraced:Nf}
 %\begin{macro}{\exp_last_unbraced:NcV}
-%\begin{macro}{\exp_last_unbraced:NNo}
 %\begin{macro}{\exp_last_unbraced:NNV}
+%\begin{macro}{\exp_last_unbraced:NNo}
+%\begin{macro}{\exp_last_unbraced:NNNV}
 %\begin{macro}{\exp_last_unbraced:NNNo}
 % Now the business end.
 %    \begin{macrocode}
 \cs_new_nopar:Npn \exp_last_unbraced:Nf { \::f_unbraced \::: }
 \cs_new_nopar:Npn \exp_last_unbraced:NV { \::V_unbraced \::: }
+\cs_new_nopar:Npn \exp_last_unbraced:No { \::o_unbraced \::: }
 \cs_new_nopar:Npn \exp_last_unbraced:Nv { \::v_unbraced \::: }
 \cs_new_nopar:Npn \exp_last_unbraced:NcV { 
   \::c \::V_unbraced \::: 
 }
+\cs_new_nopar:Npn \exp_last_unbraced:NNV { 
+  \::N \::V_unbraced \::: 
+}
 \cs_new:Npn \exp_last_unbraced:NNo #1#2#3 { 
   \exp_after:wN #1 \exp_after:wN #2 #3
 }
-\cs_new_nopar:Npn \exp_last_unbraced:NNV { 
-  \::N \::V_unbraced \::: 
+\cs_new_nopar:Npn \exp_last_unbraced:NNNV { 
+  \::N \::N \::V_unbraced \::: 
 }
 \cs_new:Npn \exp_last_unbraced:NNNo #1#2#3#4 { 
   \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN #3 #4
@@ -1196,6 +1204,8 @@
 %\end{macro}
 %\end{macro}
 %\end{macro}
+%\end{macro}
+%\end{macro}
 %
 %    \begin{macrocode}
 %</initex|package>
diff --git a/Master/texmf-dist/source/latex/expl3/l3fp.dtx b/Master/texmf-dist/source/latex/expl3/l3fp.dtx
new file mode 100644
index 00000000000..7b3b63ba16f
--- /dev/null
+++ b/Master/texmf-dist/source/latex/expl3/l3fp.dtx
@@ -0,0 +1,2393 @@
+% \iffalse
+%% File: l3fp.dtx Copyright (C) 2010 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 ``expl3 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}
+%</driver|package>
+%\fi
+\GetIdInfo$Id: l3fp.dtx 1979 2010-07-08 19:51:19Z joseph $
+  {L3 Experimental floating-point operations}
+%\iffalse
+%<*driver>
+%\fi
+\ProvidesFile{\filename.\filenameext}
+  [\filedate\space v\fileversion\space\filedescription]
+%\iffalse
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{l3fp.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \title{The \textsf{l3fp} package\thanks{This file
+%         has version number \fileversion, last
+%         revised \filedate.}\\
+% Fixed-point arithmetic}
+% \author{\Team}
+% \date{\filedate}
+% \maketitle
+%
+%\begin{documentation}
+%
+%\section{Fixed-point numbers}
+%
+% This module implements a fixed-point data type and arithmetic support.
+% Fixed-point numbers are real numbers with a fixed range of decimal
+% places available, in this case nine before and nine after the
+% decimal point. As this is a low-level module, error-checking is 
+% minimal.
+% 
+% 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 { - }
+%\end{verbatim} 
+% will all be interpreted as zero values without raising an error.
+% 
+% Number which are too large for the fixed-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.
+% 
+% Operations which give an undefined result (such as division by
+% \( 0 \)) or those which result in \( \pm \infty \) will not lead
+% to errors. Instead special marker values are returned, which
+% can be tested for using \cs{fp_if_undefined:N(TF)} and
+% \cs{fp_if_infinity:N(TF)}. In this way it is possible to work with
+% asymptopic functions without first checking the input. If these
+% special values are carried forward in calculations they will be
+% treated as \( 0 \).
+% 
+% Fixed-point numbers are stored in the \texttt{fp} fixed-point 
+% variable type. This has a standard range of functions for
+% variable management.
+% 
+%\subsection{Fixed-point variables}
+% 
+%\begin{function}{ 
+%  \fp_new:N |
+%  \fp_new:c |
+%}
+%  \begin{syntax}
+%    \cs{fp_new:N} \meta{fixed-point}
+%  \end{syntax}
+%  Creates a new \meta{fixed-point} or raises an error if the
+%  name is already taken. The declaration global. The 
+%  \meta{fixed-point} will initially be set to  "+0.000000000".
+%\end{function}
+%
+%\begin{function}{ 
+%  \fp_set_eq:NN |
+%  \fp_set_eq:cN |
+%  \fp_set_eq:Nc |
+%  \fp_set_eq:cc |
+%}
+%  \begin{syntax}
+%    \cs{fp_set_eq:NN} \meta{fp1} \meta{fp2}
+%  \end{syntax}
+%  Sets the value of \meta{fixed-point1} equal to that of
+%  \meta{fixed-point2}. This assignment is restricted to the 
+%  current \TeX\ group level.
+%\end{function}
+%
+%\begin{function}{ 
+%  \fp_gset_eq:NN |
+%  \fp_gset_eq:cN |
+%  \fp_gset_eq:Nc |
+%  \fp_gset_eq:cc |
+%}
+%  \begin{syntax}
+%    \cs{tl_gset_eq:NN} \meta{tl var1} \meta{tl var2}
+%  \end{syntax}
+%  Sets the value of \meta{fixed-point1} equal to that of
+%  \meta{fixed-point2}. This assignment is global and so is
+%  not limited by the current \TeX\ group level.
+%\end{function}
+%
+%\begin{function}{ 
+%  \fp_zero:N  |
+%  \fp_zero:c  |
+%}
+%  \begin{syntax}
+%    \cs{fp_zero:N} \meta{fixed-point}
+%  \end{syntax}
+%  Sets the \meta{fixed-point} to "+0.000000000" within the current 
+%  scope.
+%\end{function}
+%
+%\begin{function}{ 
+%  \fp_gzero:N  |
+%  \fp_gzero:c  |
+%}
+%  \begin{syntax}
+%    \cs{fp_gzero:N} \meta{fixed-point}
+%  \end{syntax}
+%  Sets the \meta{fixed-point} to "+0.000000000" globally.
+%\end{function}
+%
+%\begin{function}{ 
+%  \fp_set:Nn |
+%  \fp_set:cn |
+%}
+%  \begin{syntax}
+%    \cs{fp_set:Nn} \meta{fixed-point} \Arg{value}
+%  \end{syntax}
+%  Sets the \meta{fixed-point} variable to \meta{value} within
+%  the scope of the current \TeX\ group.
+%\end{function}
+%
+%\begin{function}{ 
+%  \fp_gset:Nn |
+%  \fp_gset:cn |
+%}
+%  \begin{syntax}
+%    \cs{fp_gset:Nn} \meta{fixed-point} \Arg{value}
+%  \end{syntax}
+%  Sets the \meta{fixed-point} variable to \meta{value} globally.
+%\end{function} 
+%
+%\begin{function}{ 
+%  \fp_set_from_dim:Nn |
+%  \fp_set_from_dim:cn |
+%}
+%  \begin{syntax}
+%    \cs{fp_set_from_dim:Nn} \meta{fixed-point} \Arg{dimexpr}
+%  \end{syntax}
+%  Sets the \meta{fixed-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{fixed-point}. The assignment
+%  is local.
+%\end{function}
+%
+%\begin{function}{ 
+%  \fp_gset_from_dim:Nn |
+%  \fp_gset_from_dim:cn |
+%}
+%  \begin{syntax}
+%    \cs{fp_gset_from_dim:Nn} \meta{fixed-point} \Arg{dimexpr}
+%  \end{syntax}
+%  Sets the \meta{fixed-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{fixed-point}. The assignment
+%  is global.
+%\end{function}
+%
+%\begin{function}{
+%  \fp_show:N |
+%  \fp_show:c |
+%}
+%  \begin{syntax}
+%    \cs{fp_show:N} \meta{fixed-point}
+%  \end{syntax}
+%  Displays the content of the \meta{fixed-point} on the
+%  terminal.
+%\end{function}
+%
+%\subsection{Unary operations}
+%
+% The unary operations alter the value stored within an \texttt{fp}
+% variable.
+%
+%\begin{function}{
+%  \fp_abs:N |
+%  \fp_abs:c |
+%}
+%  \begin{syntax}
+%    \cs{fp_abs:N} \meta{fixed-point} 
+%  \end{syntax}
+%  Converts the \meta{fixed-point} to its absolute value, assigning 
+%  the result within the current \TeX\ group.
+%\end{function}
+%
+%\begin{function}{
+%  \fp_gabs:N |
+%  \fp_gabs:c |
+%}
+%  \begin{syntax}
+%    \cs{fp_gabs:N} \meta{fixed-point} 
+%  \end{syntax}
+%  Converts the \meta{fixed-point} to its absolute value, assigning 
+%  the result globally.
+%\end{function}
+%
+%\begin{function}{
+%  \fp_neg:N |
+%  \fp_neg:c |
+%}
+%  \begin{syntax}
+%    \cs{fp_neg:N} \meta{fixed-point} 
+%  \end{syntax}
+%  Reverse the sign of the \meta{fixed-point}, assigning the result
+%  within the current \TeX\ group.
+%\end{function}
+%
+%\begin{function}{
+%  \fp_gneg:N |
+%  \fp_gneg:c |
+%}
+%  \begin{syntax}
+%    \cs{fp_gneg:N} \meta{fixed-point} 
+%  \end{syntax}
+%  Reverse the sign of the \meta{fixed-point}, assigning the result
+%  globally.
+%\end{function}
+%
+%\subsection{Transferring \texttt{fp} to \texttt{tl} data}
+%
+% The highly-structured internal format used for \texttt{fp} data
+% will not generally be desirable for use in user output. As a result,
+% the module provides a set of intermediate level functions to convert
+% \texttt{fp} into \texttt{tl} material. This process is governed by
+% a number of settings, which determine how the output is rounded and
+% how trailing zeros are handled.
+% 
+%\begin{function}{
+%  \fp_to_tl:NN |
+%  \fp_to_tl:Nc |
+%  \fp_to_tl:cN |
+%  \fp_to_tl:cc |
+%}
+%  \begin{syntax}
+%    \cs{fp_to_tl:NN} \meta{fixed-point} \meta{token list variable}
+%  \end{syntax}
+%  Transfers the content of the \meta{fixed-point} into the
+%  \meta{token list variable}, formatting according to the currently
+%  prevailing formatting settings. The \meta{token list variable} is
+%  set within the current \TeX\ group.
+%\end{function}
+%
+%\begin{function}{
+%  \fp_gto_tl:NN |
+%  \fp_gto_tl:Nc |
+%  \fp_gto_tl:cN |
+%  \fp_gto_tl:cc |
+%}
+%  \begin{syntax}
+%    \cs{fp_gto_tl:NN} \meta{fixed-point} \meta{token list variable}
+%  \end{syntax}
+%  Transfers the content of the \meta{fixed-point} into the
+%  \meta{token list variable}, formatting according to the currently
+%  prevailing formatting settings. The \meta{token list variable} is
+%  set globally.
+%\end{function}
+%
+% The exact behaviour of the transfer process is governed by a small
+% family of key--value settings. These are accessible using the
+% \cs{keys_set:nn} function in the \texttt{fp} path:
+%\begin{verbatim}
+%  \keys_set:nn { fp } {
+%    % Settings here
+%  }
+%\end{verbatim} 
+%
+%\DescribeOption{remove-trailing-zeros}
+% The Boolean setting \texttt{remove-trailing-zeros} is used to govern
+% whether trailing zeros in the decimal part of the \texttt{fp} are
+% removed.
+%\begin{verbatim}
+%  \fp_new:N \l_test_fp 
+%  \tl_new:N \l_test_tl
+%  \fp_set:Nn \l_test_fp { 1.234 }
+%  \keys_set:nn { fp } { remove-trailing-zeros = false }
+%  \fp_to_tl \l_test_fp \l_test_tl % => '1.234000000'
+%  \keys_set:nn { fp } { remove-trailing-zeros = true }
+%  \fp_to_tl \l_test_fp \l_test_tl % => '1.234'
+%\end{verbatim}
+% Removing trailing zeros will always leave the result as a real number:
+%\begin{verbatim}
+%  \fp_set:Nn \l_test_fp { 1.0 }
+%  \keys_set:nn { fp } { remove-trailing-zeros = true }
+%  \fp_to_tl \l_test_fp \l_test_tl % => '1.0'
+%\end{verbatim}
+%
+%\DescribeOption{round-mode}
+%\DescribeOption{precision}
+% The two options \texttt{round-mode} and \texttt{precision} determine
+% whether any rounding takes place for the decimal part of the output, 
+% and if so how many significant output digits are retained. The
+% \texttt{precision} option indicates how many decimal digits should
+% be retained in the output, and therefore takes numerical values
+% only. The \texttt{round-mode} option takes one of the values 
+% \texttt{none}, \texttt{truncate}, \texttt{half-from-zero} and 
+% \texttt{half-even}. The \texttt{none} setting completely disables any 
+% rounding, and therefore does not interact at all with 
+% \texttt{precision}. The number of digits in the \texttt{tl} will 
+% therefore depend only on the values in the \texttt{fp}, and whether
+% \texttt{remove-trailing-zeros} is active
+%\begin{verbatim}
+%  \fp_set:Nn \l_test_fp { 1.234 }
+%  \keys_set:nn { fp } { 
+%    round-mode            = none  ,
+%    remove-trailing-zeros = false , 
+%  }
+%  \fp_to_tl \l_test_fp \l_test_tl % => '1.234000000'
+%  \keys_set:nn { fp } { 
+%    round-mode            = none ,
+%    remove-trailing-zeros = true ,
+%  }
+%  \fp_to_tl \l_test_fp \l_test_tl % => '1.234'
+%\end{verbatim}
+% In all other cases (\texttt{truncate}, \texttt{half-from-zero}
+% and \texttt{half-even}) modification of the \texttt{fp} value will
+% always provide the number of decimal digits specified by
+% \texttt{precision}. This includes trailing zeros if they fall within
+% the \texttt{precision} requested. The \texttt{truncate} setting will 
+% cause the transfer to simply discard excess decimal digits. 
+%\begin{verbatim}
+%  \keys_set:nn { fp } { 
+%    precision             = 3        ,
+%    remove-trailing-zeros = true     ,
+%    round-mode            = truncate ,
+%  }
+%  \fp_set:Nn \l_test_fp { 1.23556 }
+%  \fp_to_tl \l_test_fp \l_test_tl % => 1.235
+%  \fp_set:Nn \l_test_fp { 1.2 }
+%  \fp_to_tl \l_test_fp \l_test_tl % => 1.200
+%\end{verbatim}
+% The \texttt{half-from-zero} setting will round the number such that
+% if the digit to be rounded is \( 5 \) then rounding will occur
+% away from zero (increasing the absolute value).
+%\begin{verbatim}
+%  \keys_set:nn { fp } { 
+%    precision             = 3              ,
+%    remove-trailing-zeros = true           ,
+%    round-mode            = half-from-zero ,
+%  }
+%  \fp_set:Nn \l_test_fp { 1.23556 }
+%  \fp_to_tl \l_test_fp \l_test_tl % => 1.236
+%  \fp_set:Nn \l_test_fp { 1.2358 }
+%  \fp_to_tl \l_test_fp \l_test_tl % => 1.236
+%  \fp_set:Nn \l_test_fp { 1.23505 }
+%  \fp_to_tl \l_test_fp \l_test_tl % => 1.235
+%  \fp_set:Nn \l_test_fp { -1.23556 }
+%  \fp_to_tl \l_test_fp \l_test_tl % => -1.236
+%  \fp_set:Nn \l_test_fp { -1.23 }
+%  \fp_to_tl \l_test_fp \l_test_tl % => -1.230
+%\end{verbatim}
+% The alternative \texttt{half-even} setting behaves indentically to
+% \texttt{half-from-zero} apart from the case where the discarded number
+% is exctly half. In this special case the result is rounded to the 
+% nearest even number in the final digit. This form of rounding is
+% sometimes used as it is does not add any bias to the final result.
+%\begin{verbatim}
+%  \keys_set:nn { fp } { 
+%    precision             = 3         ,
+%    remove-trailing-zeros = true      ,
+%    round-mode            = half-even ,
+%  }
+%  \fp_set:Nn \l_test_fp { 1.23556 }
+%  \fp_to_tl \l_test_fp \l_test_tl % => 1.236
+%  \fp_set:Nn \l_test_fp { 1.23550 }
+%  \fp_to_tl \l_test_fp \l_test_tl % => 1.236
+%  \fp_set:Nn \l_test_fp { 1.23450 }
+%  \fp_to_tl \l_test_fp \l_test_tl % => 1.234
+%  \fp_set:Nn \l_test_fp { 1.234500001 }
+%  \fp_to_tl \l_test_fp \l_test_tl % => 1.235
+%\end{verbatim}
+%
+%\subsection{Constants}
+%
+%\begin{variable}{ \c_zero_fp }
+% A permanently zero fixed-point variable.
+%\end{variable}
+%
+%\begin{variable}{ \c_undefined_fp }
+% A special marker fixed-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_infinity_fp }
+% A special marker fixed-point variable representing \( \infty \).
+%\end{variable}
+%
+%\begin{variable}{ \c_minus_infinity_fp }
+% A special marker fixed-point variable representing \( -\infty \).
+%\end{variable}
+%
+%\subsection{Tests on fixed-point values}
+%
+%\begin{function}{ 
+%  \fp_if_infinite_p:N / (EXP)      |
+%  \fp_if_infinite:N   / (EXP) (TF) |
+%}
+%  \begin{syntax}
+%    \cs{fp_if_infinite_p:N} \meta{fixed-point}
+%    \cs{fp_if_infinite:NTF} \meta{fixed-point} 
+%    ~~\Arg{true code} \Arg{false code}
+%  \end{syntax}
+%  Tests if \meta{fixed-point} is infinite (\emph{i.e}.~equal to the
+%  either of the special marker variables \cs{c_infinity_fp} or
+%  \cs{c_minus_infinity_fp}). The branching versions then leave either
+%  \meta{true code} or \meta{false code} in the input stream, as 
+%  appropriate to the truth of the test and the variant of the 
+%  function chosen. The logical truth of the test is left in the input
+%  stream by the predicate version. 
+%\end{function}
+%
+%\begin{function}{ 
+%  \fp_if_plus_infinity_p:N / (EXP)      |
+%  \fp_if_plus_infinity:N   / (EXP) (TF) |
+%}
+%  \begin{syntax}
+%    \cs{fp_if_plus_infinity_p:N} \meta{fixed-point}
+%    \cs{fp_if_plus_infinity:NTF} \meta{fixed-point} 
+%    ~~\Arg{true code} \Arg{false code}
+%  \end{syntax}
+%  Tests if \meta{fixed-point} is \( +\infty \) (\emph{i.e}.~equal to 
+%  the special \cs{c_infinity_fp} variable). The branching versions then
+%  leave either \meta{true code} or \meta{false code} in the input 
+%  stream, as appropriate to the truth of the test and the variant of 
+%  the function chosen. The logical truth of the test is left in the 
+%  input stream by the predicate version. 
+%\end{function}
+%
+%\begin{function}{ 
+%  \fp_if_minus_infinity_p:N / (EXP)      |
+%  \fp_if_minus_infinity:N   / (EXP) (TF) |
+%}
+%  \begin{syntax}
+%    \cs{fp_if_minus_infinity_p:N} \meta{fixed-point}
+%    \cs{fp_if_minus_infinity:NTF} \meta{fixed-point} 
+%    ~~\Arg{true code} \Arg{false code}
+%  \end{syntax}
+%  Tests if \meta{fixed-point} is \( +\infty \) (\emph{i.e}.~equal to 
+%  the special \cs{c_minus_infinity_fp} variable). The branching 
+%  versions then leave either \meta{true code} or \meta{false code} in
+%  the input stream, as appropriate to the truth of the test and the 
+%  variant of the function chosen. The logical truth of the test is left
+%  in the input stream by the predicate version. 
+%\end{function}
+%
+%\begin{function}{ 
+%  \fp_if_undefined_p:N / (EXP)      |
+%  \fp_if_undefined:N   / (EXP) (TF) |
+%}
+%  \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}
+%  \end{syntax}
+%  Tests if \meta{fixed-point} is undefined (\emph{i.e}.~equal to the
+%  special \cs{c_undefined_fp} variable). The branching versions then
+%  leave either \meta{true code} or \meta{false code} in the input 
+%  stream, as appropriate to the truth of the test and the variant of 
+%  the function chosen. The logical truth of the test is left in the 
+%  input stream by the predicate version. 
+%\end{function}
+%
+%\begin{function}{ 
+%  \fp_if_zero_p:N / (EXP)      |
+%  \fp_if_zero:N   / (EXP) (TF) |
+%}
+%  \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}
+%  \end{syntax}
+%  Tests if \meta{fixed-point} is equal to zero (\emph{i.e}.~equal to 
+%  the special \cs{c_zero_fp} variable). The branching versions then 
+%  leave either \meta{true code} or \meta{false code} in the input 
+%  stream, as appropriate to the truth of the test and the variant of 
+%  the function chosen. The logical truth of the test is left in the 
+%  input stream by the predicate version. 
+%\end{function}
+%
+%\begin{function}{ 
+%  \fp_compare:nNn / (TF) |
+%  \fp_compare:NNN / (TF) |
+%}
+%  \begin{syntax}
+%    \cs{fp_compare:nNnTF} \Arg{value1} \meta{relation} \Arg{value2}
+%    ~~\Arg{true code} \Arg{false code}
+%    \cs{fp_compare:NNNTF} \Arg{fp1} \meta{relation} \Arg{fp2}
+%    ~~\Arg{true code} \Arg{false code}
+%  \end{syntax}
+%  Compares the two \meta{values} or \meta{fixed-points} based on the
+%  \meta{relation} (\texttt{=}, \verb"<" or \verb">"), and leaves
+%  either the \meta{true code} or \meta{false code} in the input stream, 
+%  as appropriate to the truth of the test and the variant of the 
+%  function chosen. The tests treat undefined fixed-points
+%  as zero, as the comparison is intended for real numbers only.
+%\end{function}
+%
+%\subsection{Arithmetic operations}
+%
+% 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}.~\( -4.444 \)).
+%
+%\begin{function}{
+%  \fp_add:Nn |
+%  \fp_add:cn |
+%}
+%  \begin{syntax}
+%    \cs{fp_add:Nn} \meta{fixed-point} \Arg{value}
+%  \end{syntax}
+%  Adds the \meta{value} to the \meta{fixed-point}, making the
+%  assignment within the current \TeX\ group level.
+%\end{function}
+%
+%\begin{function}{
+%  \fp_gadd:Nn |
+%  \fp_gadd:cn |
+%}
+%  \begin{syntax}
+%    \cs{fp_gadd:Nn} \meta{fixed-point} \Arg{value}
+%  \end{syntax}
+%  Adds the \meta{value} to the \meta{fixed-point}, making the
+%  assignment globally.
+%\end{function}
+%
+%\begin{function}{
+%  \fp_sub:Nn |
+%  \fp_sub:cn |
+%}
+%  \begin{syntax}
+%    \cs{fp_sub:Nn} \meta{fixed-point} \Arg{value}
+%  \end{syntax}
+%  Subtracts the \meta{value} from the \meta{fixed-point}, making the
+%  assignment within the current \TeX\ group level.
+%\end{function}
+%
+%\begin{function}{
+%  \fp_gsub:Nn |
+%  \fp_gsub:cn |
+%}
+%  \begin{syntax}
+%    \cs{fp_gsub:Nn} \meta{fixed-point} \Arg{value}
+%  \end{syntax}
+%  Subtracts the \meta{value} from the \meta{fixed-point}, making the
+%  assignment globally.
+%\end{function}
+%
+%\begin{function}{
+%  \fp_mul:Nn |
+%  \fp_mul:cn |
+%}
+%  \begin{syntax}
+%    \cs{fp_mul:Nn} \meta{fixed-point} \Arg{value}
+%  \end{syntax}
+%  Multiples the \meta{fixed-point} by the \meta{value}, making the
+%  assignment within the current \TeX\ group level.
+%\end{function}
+%
+%\begin{function}{
+%  \fp_gmul:Nn |
+%  \fp_gmul:cn |
+%}
+%  \begin{syntax}
+%    \cs{fp_gmul:Nn} \meta{fixed-point} \Arg{value}
+%  \end{syntax}
+%  Multiples the \meta{fixed-point} by the \meta{value}, making the
+%  assignment globally.
+%\end{function}
+%
+%\begin{function}{
+%  \fp_div:Nn |
+%  \fp_div:cn |
+%}
+%  \begin{syntax}
+%    \cs{fp_div:Nn} \meta{fixed-point} \Arg{value}
+%  \end{syntax}
+%  Divides the \meta{fixed-point} by the \meta{value}, making the
+%  assignment within the current \TeX\ group level. If the \meta{value}
+%  is zero, the \meta{fixed-point} will be set to \cs{c_undefined_fp}.
+%\end{function}
+%
+%\begin{function}{
+%  \fp_gdiv:Nn |
+%  \fp_gdiv:cn |
+%}
+%  \begin{syntax}
+%    \cs{fp_gdiv:Nn} \meta{fixed-point} \Arg{value}
+%  \end{syntax}
+%  Divides the \meta{fixed-point} by the \meta{value}, making the
+%  assignment globally. If the \meta{value} is zero, the 
+%  \meta{fixed-point} will be set to \cs{c_undefined_fp}.
+%\end{function}
+%
+%\end{documentation}
+%
+%\begin{implementation}
+%
+%\section{Implementation}
+% 
+%    Announce and ensure that the required packages are loaded.
+%    \begin{macrocode}
+%<*package>
+\ProvidesExplPackage
+  {\filename}{\filedate}{\fileversion}{\filedescription}
+\package_check_loaded_expl:
+%</package>
+%<*initex|package>
+%    \end{macrocode}
+%    
+% Internally, a fixed-point number is a token list variable of the 
+% correct format. The first token in the variable is the sign: normally
+% this will be "+" or "-", but this token can also be used to indicate
+% a special state (for exampe if a calculation would give infinity as
+% a result). The main part of the number is then stored as a decimal:
+% there are always nine digits in the decimal part. This ensures that
+% two numbers which are equal to one another will always be stored in 
+% the same way. For the same reason, zero is stored as "+0.000000000".
+%    
+%\subsection{General variables}
+%    
+%\begin{macro}{\l_fp_input_a_integer_int}
+%\begin{macro}{\l_fp_input_a_decimal_int}
+%\begin{macro}{\l_fp_input_b_integer_int}
+%\begin{macro}{\l_fp_input_b_decimal_int}
+% Storage for the input, divided into integer and decimal parts.
+%    \begin{macrocode}
+\int_new:N \l_fp_input_a_integer_int
+\int_new:N \l_fp_input_a_decimal_int
+\int_new:N \l_fp_input_b_integer_int
+\int_new:N \l_fp_input_b_decimal_int
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\l_fp_input_a_sign_int}
+%\begin{macro}{\l_fp_input_b_sign_int}
+% The sign of each item in the input is stored as an \texttt{int} as
+% this allows some faster manipulation than would otherwise be possible.
+%    \begin{macrocode}
+\int_new:N \l_fp_input_a_sign_int
+\int_new:N \l_fp_input_b_sign_int
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\l_fp_split_sign_int}
+% Used to speed up the sign-finding system.
+%    \begin{macrocode}
+\int_new:N \l_fp_split_sign_int
+%    \end{macrocode}
+%\end{macro}
+%
+%\begin{macro}{\l_fp_mul_a_i_int}
+%\begin{macro}{\l_fp_mul_a_ii_int}
+%\begin{macro}{\l_fp_mul_a_iii_int}
+%\begin{macro}{\l_fp_mul_a_iv_int}
+%\begin{macro}{\l_fp_mul_a_v_int}
+%\begin{macro}{\l_fp_mul_a_vi_int}
+%\begin{macro}{\l_fp_mul_b_i_int}
+%\begin{macro}{\l_fp_mul_b_ii_int}
+%\begin{macro}{\l_fp_mul_b_iii_int}
+%\begin{macro}{\l_fp_mul_b_iv_int}
+%\begin{macro}{\l_fp_mul_b_v_int}
+%\begin{macro}{\l_fp_mul_b_vi_int}
+% For multiplication, each number is split into six parts (three for the
+% decimal, three for the integer). So that they are a bt easier to keep
+% a track of these are simply numbered: i--iii are the integer and iv-vi
+% the decimal part.
+%    \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{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}{\l_fp_mul_output_int}
+%\begin{macro}{\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{macro}
+%\end{macro}
+%
+%\begin{macro}{\l_fp_div_count_int}
+%\begin{macro}{\l_fp_div_offset_int}
+% Values used during division: an offset for small denominators and
+% a count for the actual division.
+%    \begin{macrocode}
+\int_new:N \l_fp_div_count_int
+\int_new:N \l_fp_div_offset_int
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\l_fp_output_sign_int}
+%\begin{macro}{\l_fp_output_integer_int}
+%\begin{macro}{\l_fp_output_decimal_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
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\l_fp_round_carry_bool}
+%\begin{macro}{\l_fp_round_decimal_tl}
+%\begin{macro}{\l_fp_round_discard_int}
+%\begin{macro}{\l_fp_round_position_int}
+% The rounding system needs space to track carrying forward and also
+% to hold onto dicarded material (which may be relevant when rounding
+% to an even last digit). The current position in the decimal part also
+% needs to be tracked. For speed reasons, the decimal part of the number 
+% is build back up in a token list when rounding, as this avoids
+% worrying about place value.
+%    \begin{macrocode}
+\bool_new:N \l_fp_round_carry_bool
+\tl_new:N \l_fp_round_decimal_tl
+\int_new:N \l_fp_round_discard_int
+\int_new:N \l_fp_round_position_int
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\l_fp_tmp_int}
+% A scratch \texttt{int}: used only where the value is not carried
+% forward.
+%    \begin{macrocode}
+\int_new:N \l_fp_tmp_int
+%    \end{macrocode}
+%\end{macro}
+%
+%\begin{macro}{\l_fp_tmp_tl}
+% The usual scratch token list.
+%    \begin{macrocode}
+\tl_new:N \l_fp_tmp_tl
+%    \end{macrocode}
+%\end{macro}
+%
+%\subsection{Constants}
+%
+%\begin{macro}{\c_zero_fp}
+% The constanct zero value.
+%    \begin{macrocode}
+\tl_new:N  \c_zero_fp
+\tl_set:Nn \c_zero_fp { + 0.000000000 }
+%    \end{macrocode}
+%\end{macro}
+%
+%\begin{macro}{\c_undefined_fp}
+%\begin{macro}{\c_infinity_fp}
+%\begin{macro}{\c_minus_infinity_fp}
+% Special marker values for various mathematically-valid results which
+% are not fixed-point numbers.
+%    \begin{macrocode}
+\tl_new:N  \c_undefined_fp
+\tl_set:Nn \c_undefined_fp { X 0.000000000 }
+\tl_new:N  \c_infinity_fp
+\tl_set:Nn \c_infinity_fp { +2147483647.2147483647 }
+\tl_new:N  \c_minus_infinity_fp
+\tl_set:Nn \c_minus_infinity_fp { -2147483647.2147483647 }
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\c_one_hundred_million}
+%\begin{macro}{\c_one_thousand_million}
+% There is some speed to gain by moving numbers into fixed positions.
+%    \begin{macrocode}
+\int_new:N  \c_one_hundred_million
+\int_set:Nn \c_one_hundred_million  { 100000000 }
+\int_new:N  \c_one_thousand_million
+\int_set:Nn \c_one_thousand_million { 1000000000 }
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%
+%\subsection{Tests for special values}
+%
+%\begin{macro}{\fp_if_infinite_p:N}
+%\begin{macro}[TF]{\fp_if_infinite:N}
+%\begin{macro}{\fp_if_plus_infinity_p:N}
+%\begin{macro}[TF]{\fp_if_plus_infinity:N}
+%\begin{macro}{\fp_if_minus_infinity_p:N}
+%\begin{macro}[TF]{\fp_if_minus_infinity:N}
+% Testing for infinite values is complicated by the sign of infinity.
+% There are therefore three tests, one which will match \( +\infty \)
+% or \( -\infty \) and one test each for the two individual cases.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \fp_if_infinite:N #1 { p , T , F , TF } {
+  \tex_ifx:D #1 \c_infinity_fp
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifx:D #1 \c_minus_infinity_fp
+      \prg_return_true:
+    \tex_else:D
+      \prg_return_false:
+    \tex_fi:D
+  \tex_fi:D
+}
+\prg_new_conditional:Npnn \fp_if_plus_infinity:N #1 { p , T , F , TF } {
+  \tex_ifx:D #1 \c_infinity_fp
+    \prg_return_true:
+  \tex_else:D
+    \prg_return_false:
+  \tex_fi:D
+}
+\prg_new_conditional:Npnn \fp_if_minus_infinity:N #1 { p , T , F , TF } 
+  {
+  \tex_ifx:D #1 \c_minus_infinity_fp
+    \prg_return_true:
+  \tex_else:D
+    \prg_return_false:
+  \tex_fi:D
+}
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_if_undefined_p:N}
+%\begin{macro}[TF]{\fp_if_undefined:N}
+% Testing for an undefined value is easy.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF } {
+  \tex_ifx:D #1 \c_undefined_fp
+    \prg_return_true:
+  \tex_else:D
+    \prg_return_false:
+  \tex_fi:D
+}
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_if_zero_p:N}
+%\begin{macro}[TF]{\fp_if_zero:N}
+% Testing for a zero fixed-point is also easy.
+%    \begin{macrocode}
+\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF } {
+  \tex_ifx:D #1 \c_zero_fp
+    \prg_return_true:
+  \tex_else:D
+    \prg_return_false:
+  \tex_fi:D
+}
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%
+%\subsection{Operations for \texttt{fp} variables}
+%
+%\begin{macro}{\fp_new:N}
+%\begin{macro}{\fp_new:c}
+% Fixed-points always have a value, and of course this has to be
+% initialised globally.
+%    \begin{macrocode}
+\cs_new_protected_nopar: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}
+%\end{macro}
+%
+%\begin{macro}{\fp_zero:N}
+%\begin{macro}{\fp_zero:c}
+%\begin{macro}{\fp_gzero:N}
+%\begin{macro}{\fp_gzero:c}
+% Zeroing fixed-points is pretty obvious.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_zero:N #1 {
+  \tl_set_eq:NN #1 \c_zero_fp
+}
+\cs_new_protected_nopar: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}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_set:Nn}
+%\begin{macro}{\fp_set:cn}
+%\begin{macro}{\fp_gset:Nn}
+%\begin{macro}{\fp_gset:cn} 
+%\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_nopar:Npn \fp_set_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_split:Nn a {#3}
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+          -
+        \tex_else:D
+          +  
+        \tex_fi:D  
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \exp_after:wN \use_none:n 
+          \int_use:N \l_fp_input_a_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN 
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_generate_variant:Nn \fp_set:Nn  { c }
+\cs_generate_variant:Nn \fp_gset:Nn { c }
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_set_from_dim:Nn}
+%\begin{macro}{\fp_set_from_dim:cn}
+%\begin{macro}{\fp_gset_from_dim:Nn}
+%\begin{macro}{\fp_gset_from_dim:cn} 
+%\begin{macro}[aux]{\fp_set_from_dim_aux:NNn} 
+%\begin{macro}[aux]{\fp_set_from_dim_aux:w} 
+%\begin{macro}{\l_fp_tmp_dim}
+% 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.
+%    \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_nopar:Npn \fp_set_from_dim_aux:NNn #1#2#3 {
+  \group_begin:
+    \l_fp_tmp_dim \etex_dimexpr:D #3 \scan_stop: 
+    \fp_split:Nn a 
+      { 
+        \exp_after:wN \fp_set_from_dim_aux:w 
+          \dim_use:N \l_fp_tmp_dim  
+      }
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+          -
+        \tex_else:D
+          +  
+        \tex_fi:D  
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \exp_after:wN \use_none:n 
+          \int_use:N \l_fp_input_a_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN 
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_set_protected_nopar:Npx \fp_set_from_dim_aux:w {
+  \cs_set_nopar: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_tmp_dim
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_set_eq:NN}
+%\begin{macro}{\fp_set_eq:cN}
+%\begin{macro}{\fp_set_eq:Nc}
+%\begin{macro}{\fp_set_eq:cc}
+%\begin{macro}{\fp_gset_eq:NN}
+%\begin{macro}{\fp_gset_eq:cN}
+%\begin{macro}{\fp_gset_eq:Nc}
+%\begin{macro}{\fp_gset_eq:cc}
+% 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}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_show:N}
+%\begin{macro}{\fp_show:c}
+% 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}
+%\end{macro}
+%
+%\begin{macro}{\fp_use:N}
+%\begin{macro}{\fp_use:c}
+% These are token lists, so this is easy.
+%    \begin{macrocode}
+\cs_new_eq:NN \fp_use:N \tl_use:N
+\cs_new_eq:NN \fp_use:c \tl_use:c
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%
+%\subsection{Internal utilities}
+%
+%\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_nopar:Npn \fp_read:N #1 {
+  \exp_after:wN \fp_read_aux:w #1 \q_stop
+}
+\cs_new_protected_nopar:Npn \fp_read_aux:w #1#2 . #3 \q_stop {
+  \tex_if:D #1 -
+    \l_fp_input_a_sign_int \c_minus_one
+  \tex_else:D
+    \l_fp_input_a_sign_int \c_one
+  \tex_fi:D
+  \l_fp_input_a_integer_int #2 \scan_stop:
+  \l_fp_input_a_decimal_int #3 \scan_stop:
+}
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_split:Nn}
+%\begin{macro}[aux]{\fp_split_sign:}
+%\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. 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_nopar:Npn \fp_split:Nn #1#2 {
+  \tl_set:Nx \l_fp_tmp_tl {#2}
+  \l_fp_split_sign_int \c_one
+  \fp_split_sign:  
+  \use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int
+  \tex_afterassignment:D \fp_split_aux_i:w 
+  \use:c { l_fp_input_ #1 _integer_int } 
+    \etex_numexpr:D 0 \l_fp_tmp_tl . . \q_stop #1
+}
+\cs_new_protected_nopar:Npn \fp_split_sign: {
+  \tex_ifnum:D \pdf_strcmp:D 
+    { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_nil } { - } 
+      = \c_zero
+    \tl_set:Nx \l_fp_tmp_tl
+      { 
+        \exp_after:wN 
+          \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_nil 
+      }
+    \l_fp_split_sign_int -\l_fp_split_sign_int 
+    \exp_after:wN \fp_split_sign:
+  \tex_else:D 
+    \tex_ifnum:D \pdf_strcmp:D 
+      { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_nil } { + } 
+        = \c_zero
+      \tl_set:Nx \l_fp_tmp_tl
+        { 
+          \exp_after:wN 
+            \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_nil 
+        }
+      \exp_after:wN \exp_after:wN \exp_after:wN
+        \fp_split_sign:  
+     \tex_fi:D   
+  \tex_fi:D  
+}
+\cs_new_protected_nopar:Npn \fp_split_aux_i:w #1 . #2 . #3 \q_stop {
+  \fp_split_aux_ii:w #2 000000000 \q_stop
+}
+\cs_new_protected_nopar: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_nopar:Npn \fp_split_aux_iii:w #1#2 \q_stop {
+  \l_fp_tmp_int 1 #1 \scan_stop:
+  \exp_after:wN \fp_split_decimal:w 
+    \int_use:N \l_fp_tmp_int 000000000 \q_stop
+}
+\cs_new_protected_nopar: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_nopar:Npn \fp_split_decimal_aux:w #1#2#3 \q_stop #4 {
+  \use:c { l_fp_input_ #4 _decimal_int } #1#2 \scan_stop:
+  \tex_ifnum:D
+    \etex_numexpr:D 
+      \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  
+   \tex_fi:D    
+}
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\subsection{Unary functions}
+%
+%\begin{macro}{\fp_abs:N}
+%\begin{macro}{\fp_abs:c}
+%\begin{macro}{\fp_gabs:N}
+%\begin{macro}{\fp_gabs:c}
+%\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:NN \tl_set:Nn 
+}
+\cs_new_protected_nopar:Npn \fp_gabs:N {
+  \fp_abs:NN \tl_gset:Nn 
+}
+\cs_generate_variant:Nn \fp_abs:N  { c }
+\cs_generate_variant:Nn \fp_gabs:N { c }
+\cs_new_protected_nopar:Npn \fp_abs: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_tmp_tl
+      {
+        +
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \exp_after:wN \use_none:n 
+          \int_use:N \l_fp_input_a_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_neg:N}
+%\begin{macro}{\fp_neg:c}
+%\begin{macro}{\fp_gneg:N}
+%\begin{macro}{\fp_gneg:c}
+%\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_nopar: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_tmp_tl
+      {
+        \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+          +
+        \tex_else:D
+          -
+        \tex_fi:D  
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \exp_after:wN \use_none:n 
+          \int_use:N \l_fp_input_a_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\subsection{Basic arithmetic}
+%  
+%\begin{macro}{\fp_add:Nn}
+%\begin{macro}{\fp_add:cn}
+%\begin{macro}{\fp_gadd:Nn}
+%\begin{macro}{\fp_gadd:cn}
+%\begin{macro}[aux]{\fp_add_aux:NNn}
+%\begin{macro}[aux]{\fp_add_core:}
+% 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_nopar:Npn \fp_add_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \fp_split:Nn b {#3}
+    \fp_add_core:
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_new_protected_nopar:Npn \fp_add_core: {
+  \tex_ifnum:D 
+    \etex_numexpr:D
+      \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
+    \scan_stop:
+      > \c_zero
+    \exp_after:wN \fp_add_sum:  
+  \tex_else:D
+    \exp_after:wN \fp_add_difference:     
+  \tex_fi:D    
+  \tl_set:Nx \l_fp_tmp_tl
+    {
+      \tex_ifnum:D \l_fp_output_sign_int < \c_zero
+        -
+      \tex_else:D
+        +
+      \tex_fi:D  
+      \int_use:N \l_fp_output_integer_int
+      .
+      \exp_after:wN \use_none:n 
+        \int_use:N \l_fp_output_decimal_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
+    \etex_numexpr:D
+      \l_fp_input_a_integer_int + \l_fp_input_b_integer_int
+    \scan_stop:
+  \l_fp_output_decimal_int
+    \etex_numexpr:D
+      \l_fp_input_a_decimal_int + \l_fp_input_b_decimal_int
+    \scan_stop:
+  \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
+    \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+  \tex_else:D
+    \tex_advance:D \l_fp_output_integer_int \c_one
+  \tex_fi:D  
+}
+%    \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 caculation to
+% see which way around everything has worked out, so that the final
+% sign is correct. The differnce might also give a zero resul 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
+    \etex_numexpr:D
+      \l_fp_input_a_integer_int - \l_fp_input_b_integer_int
+    \scan_stop:
+  \l_fp_output_decimal_int
+    \etex_numexpr:D
+      \l_fp_input_a_decimal_int - \l_fp_input_b_decimal_int
+    \scan_stop:
+  \tex_ifnum:D \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
+  \tex_fi:D
+  \tex_ifnum:D \l_fp_output_integer_int < \c_zero
+    \l_fp_output_sign_int \l_fp_input_b_sign_int 
+    \tex_ifnum:D \l_fp_output_decimal_int = \c_zero
+      \l_fp_output_integer_int -\l_fp_output_integer_int
+    \tex_else:D
+      \l_fp_output_decimal_int 
+        \etex_numexpr:D
+          \c_one_thousand_million - \l_fp_output_decimal_int 
+        \scan_stop:
+      \l_fp_output_integer_int
+         \etex_numexpr:D
+           - \l_fp_output_integer_int - \c_one
+         \scan_stop:
+    \tex_fi:D
+  \tex_else:D
+    \l_fp_output_sign_int \l_fp_input_a_sign_int  
+  \tex_fi:D 
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \l_fp_output_integer_int + \l_fp_output_decimal_int 
+    \scan_stop:  
+      = \c_zero
+    \l_fp_output_sign_int \c_one  
+  \tex_fi:D  
+  \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million  
+}
+%    \end{macrocode}
+%\end{macro}
+%\end{macro} 
+%\end{macro}
+%\end{macro} 
+%\end{macro} 
+%\end{macro}
+%
+%\begin{macro}{\fp_sub:Nn}
+%\begin{macro}{\fp_sub:cn}
+%\begin{macro}{\fp_gsub:Nn}
+%\begin{macro}{\fp_gsub:cn}
+%\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_nopar:Npn \fp_sub_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \fp_split:Nn b {#3}
+    \tex_multiply:D \l_fp_input_b_sign_int \c_minus_one
+    \fp_add_core:
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+%    \end{macrocode}
+%\end{macro} 
+%\end{macro} 
+%\end{macro}
+%\end{macro} 
+%\end{macro} 
+%
+%\begin{macro}{\fp_mul:Nn}
+%\begin{macro}{\fp_mul:cn}
+%\begin{macro}{\fp_gmul:Nn}
+%\begin{macro}{\fp_gmul:cn}
+%\begin{macro}[aux]{\fp_mul_aux:NNn}
+%\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:w}
+% 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_nopar:Npn \fp_mul_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \fp_split:Nn b {#3}
+    \fp_mul_split:NNNN \l_fp_input_a_integer_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_a_decimal_int
+      \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
+    \fp_mul_split:NNNN \l_fp_input_b_integer_int
+      \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
+    \fp_mul_split:NNNN \l_fp_input_b_decimal_int
+      \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_iv_int \l_fp_mul_b_vi_int
+    \fp_mul_product:NN \l_fp_mul_a_v_int  \l_fp_mul_b_v_int
+    \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_iv_int
+    \tex_divide:D \l_fp_mul_output_int \c_thousand
+    \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_vi_int
+    \fp_mul_product:NN \l_fp_mul_a_iv_int  \l_fp_mul_b_v_int
+    \fp_mul_product:NN \l_fp_mul_a_v_int   \l_fp_mul_b_iv_int
+    \fp_mul_product:NN \l_fp_mul_a_vi_int  \l_fp_mul_b_iii_int
+    \fp_mul_end_level:
+    \fp_mul_product:NN \l_fp_mul_a_ii_int  \l_fp_mul_b_vi_int
+    \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_v_int
+    \fp_mul_product:NN \l_fp_mul_a_iv_int  \l_fp_mul_b_iv_int
+    \fp_mul_product:NN \l_fp_mul_a_v_int   \l_fp_mul_b_iii_int
+    \fp_mul_product:NN \l_fp_mul_a_vi_int  \l_fp_mul_b_ii_int
+    \fp_mul_end_level:
+    \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
+    \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_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:
+    \l_fp_output_integer_int 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:
+    \tex_ifnum:D \l_fp_mul_output_tl = \c_zero
+    \tex_else:D
+      \exp_after:wN \fp_msg_overflow:
+    \tex_fi:D
+    \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D 
+          \etex_numexpr:D 
+            \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
+          \scan_stop:
+            < \c_zero
+          \tex_ifnum:D
+            \etex_numexpr:D 
+              \l_fp_output_integer_int + \l_fp_output_decimal_int
+            \scan_stop:
+              = \c_one_thousand_million
+            +    
+          \tex_else:D    
+            -
+          \tex_fi:D
+        \tex_else:D
+          +
+        \tex_fi:D
+        \int_use:N \l_fp_output_integer_int
+        .
+        \exp_after:wN \use_none:n 
+          \int_use:N \l_fp_output_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+%    \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_nopar:Npn \fp_mul_split:NNNN #1#2#3#4 {
+  \tex_advance:D #1 \c_one_thousand_million
+  \cs_set_protected_nopar: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  
+}
+\cs_new_protected_nopar:Npn \fp_mul_product:NN #1#2 {
+  \l_fp_mul_output_int
+    \etex_numexpr:D \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 \fp_mul_end_level:w 
+    \int_use:N \l_fp_mul_output_int \q_stop
+}
+\cs_new_protected_nopar:Npn \fp_mul_end_level:w 
+  #1#2#3#4#5#6#7#8#9 \q_stop {
+  \tl_set:Nx \l_fp_mul_output_tl { #8#9 \l_fp_mul_output_tl }
+  \l_fp_mul_output_int #5#6#7 \scan_stop:
+}
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro} 
+%\end{macro}
+%\end{macro} 
+%\end{macro} 
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\begin{macro}{\fp_div:Nn}
+%\begin{macro}{\fp_div:cn}
+%\begin{macro}{\fp_gdiv:Nn}
+%\begin{macro}{\fp_gdiv:cn}
+%\begin{macro}[aux]{\fp_div_aux:NNn}
+%\begin{macro}[aux]{\fp_div_aux:}
+%\begin{macro}[aux]{\fp_div_offset_create:}
+%\begin{macro}[aux]{\fp_div_offset_create_aux:w}
+%\begin{macro}[aux]{\fp_div_loop:}
+%\begin{macro}[aux]{\fp_div_loop_aux_i:w}
+%\begin{macro}[aux]{\fp_div_loop_aux_ii:w}
+%\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_nopar:Npn \fp_div_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \fp_split:Nn b {#3}
+    \tex_ifnum:D
+      \etex_numexpr:D 
+        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+      \scan_stop:
+        = \c_zero
+      \tl_set_eq:NN \l_fp_tmp_tl \c_undefined_fp
+    \tex_else:D  
+      \tex_ifnum:D
+        \etex_numexpr:D 
+          \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+        \scan_stop:
+          = \c_zero
+          \tl_set_eq:NN \l_fp_tmp_tl \c_zero_fp
+      \tex_else:D  
+        \exp_after:wN \exp_after:wN \exp_after:wN 
+          \fp_div_aux:  
+      \tex_fi:D   
+    \tex_fi:D 
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+%    \end{macrocode}
+% The main division algorithm has to avoid overflows for awkward
+% cases (division of large numbers by small ones). That requires that
+% the denominator has an integer part if the numerator does: an offset
+% is only created if it is needed.  The idea then is find how many
+% times the denominator can be removed from the numerator. This
+% is stored in the result, the denominator is divided by ten and 
+% the process is repeated with the remainder of the numerator. Cycling
+% through this sequence eventually removes all of the digits of the
+% denominator, if the numerator does not reach zero first.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_div_aux: {
+  \l_fp_div_offset_int \c_one
+  \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero
+    \exp_after:wN \fp_div_offset_create: 
+  \tex_fi:D
+  \l_fp_output_integer_int \c_zero
+  \l_fp_output_decimal_int \c_one_thousand_million
+  \cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
+  \fp_div_loop:
+  \tl_set:Nx \l_fp_tmp_tl
+    {
+      \tex_ifnum:D 
+        \etex_numexpr:D 
+          \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
+        \scan_stop:
+          < \c_zero
+        \tex_ifnum:D
+          \etex_numexpr:D 
+            \l_fp_output_integer_int + \l_fp_output_decimal_int
+          \scan_stop:
+            = \c_one_thousand_million
+          +    
+        \tex_else:D    
+          -
+        \tex_fi:D
+      \tex_else:D
+        +
+      \tex_fi:D
+      \int_use:N \l_fp_output_integer_int
+      .
+      \exp_after:wN \use_none:n 
+        \int_use:N \l_fp_output_decimal_int
+    }
+}
+%    \end{macrocode}
+% The offset is created such that it will automatically be accounted
+% for in the rest of the process. Rather than doing any integer division
+% a delimited function is used to transfer the digit from the
+% integer to the decimal parts.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_div_offset_create: {
+  \tex_ifnum:D \l_fp_input_b_integer_int = \c_zero
+    \tex_advance:D \l_fp_input_b_decimal_int \c_one_thousand_million
+    \exp_after:wN \fp_div_offset_create_aux:w
+      \int_use:N \l_fp_input_b_decimal_int \q_stop
+    \exp_after:wN \fp_div_offset_create:  
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_div_offset_create_aux:w 
+  #1#2#3#4#5#6#7#8#9 \q_stop {
+  \l_fp_input_b_integer_int #2 \scan_stop:
+  \l_fp_input_b_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
+  \tex_multiply:D \l_fp_div_offset_int \c_ten
+}
+%    \end{macrocode}
+% The main division loop must start with both numerator and
+% denominator above zero, so the test is at the tail of the loop.
+% Once again, division by ten for the denominator is avoided, with
+% a delimited function doing the job. The test at the end of the
+% function means that the loop terminates as soon as one part of the
+% input reaches zero: this saves dead loops if the division is 
+% exact.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_div_loop: {
+  \l_fp_div_count_int \c_zero
+  \fp_div_divide: 
+  \tex_divide:D \l_fp_input_b_decimal_int \c_ten
+  \tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million
+  \exp_after:wN \fp_div_loop_aux_i:w 
+    \int_use:N \l_fp_input_b_integer_int
+  \fp_div_store:
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+      > \c_zero
+    \tex_ifnum:D 
+      \etex_numexpr:D
+        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+        > \c_zero
+      \exp_after:wN \exp_after:wN \exp_after:wN  
+        \fp_div_loop:
+    \tex_fi:D    
+  \tex_fi:D      
+}
+%    \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: {
+  \tex_ifnum:D \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
+    \exp_after:wN \fp_div_divide_aux:
+  \tex_else:D 
+    \tex_ifnum:D \l_fp_input_a_integer_int < \l_fp_input_b_integer_int 
+    \tex_else:D
+      \tex_ifnum:D 
+        \l_fp_input_a_decimal_int < \l_fp_input_b_decimal_int
+      \tex_else:D
+        \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:
+      \tex_fi:D  
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_div_loop_aux_i:w #1#2#3#4#5#6#7#8#9 {
+  \fp_div_loop_aux_ii:w #2#3#4#5#6#7#8#9
+}
+\cs_new_protected_nopar:Npn \fp_div_loop_aux_ii:w #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:
+  \l_fp_input_b_decimal_int
+    \etex_numexpr:D
+      \l_fp_input_b_decimal_int + \c_one_hundred_million * #9
+    \scan_stop:
+}
+\cs_new_protected_nopar:Npn \fp_div_divide_aux: {
+  \tex_advance:D \l_fp_div_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
+  \tex_ifnum:D \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
+  \tex_fi:D
+  \fp_div_divide:
+}
+%    \end{macrocode}
+% The final stage of each loop is to store the result. This is done
+% separately for the integer and decimal parts. The offset is used to
+% get the digits in the correct place, and so also indicates when the
+% switch from the integer to the decimal.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_div_store: { }
+\cs_new_protected_nopar:Npn \fp_div_store_integer: {
+  \l_fp_output_integer_int
+    \etex_numexpr:D
+      \l_fp_output_integer_int + 
+      \l_fp_div_count_int * \l_fp_div_offset_int
+    \scan_stop:
+  \tex_ifnum:D \l_fp_div_offset_int > \c_one
+    \tex_divide:D \l_fp_div_offset_int \c_ten
+  \tex_else:D   
+    \cs_set_eq:NN \fp_div_store: \fp_div_store_decimal:
+    \l_fp_div_offset_int \c_one_hundred_million
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_div_store_decimal: {
+  \l_fp_output_decimal_int
+    \etex_numexpr:D
+      \l_fp_output_decimal_int + 
+      \l_fp_div_count_int * \l_fp_div_offset_int
+    \scan_stop:
+  \tex_divide:D \l_fp_div_offset_int \c_ten
+}
+%    \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} 
+%
+%\subsection{Fixed-point conditionals}
+%
+%\begin{macro}[TF]{\fp_compare:nNn}
+%\begin{macro}[TF]{\fp_compare:NNN}
+%\begin{macro}[aux]{\fp_compare_aux:N}
+%\begin{macro}[aux]{\fp_compare_=:}
+%\begin{macro}[aux]{\fp_compare_<:}
+%\begin{macro}[aux]{\fp_compare_>:}
+%\begin{macro}[aux]{\fp_compare_absolute_a>b:}
+%\begin{macro}[aux]{\fp_compare_absolute_a<b:}
+% 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_split:Nn b {#3}
+    \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
+    \fp_read:N #1
+    \fp_compare_aux:N #2
+}
+\cs_new_protected_nopar: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_=: } {
+  \tex_ifnum:D \l_fp_input_a_sign_int = \l_fp_input_b_sign_int
+    \tex_ifnum:D \l_fp_input_a_integer_int = \l_fp_input_b_integer_int
+      \tex_ifnum:D \l_fp_input_a_decimal_int = \l_fp_input_b_decimal_int
+        \group_end:
+        \prg_return_true:
+      \tex_else:D
+        \group_end:
+        \prg_return_false:
+      \tex_fi:D
+    \tex_else:D
+      \group_end:
+      \prg_return_false:
+    \tex_fi:D
+  \tex_else:D
+    \group_end:
+    \prg_return_false:
+  \tex_fi:D  
+}
+%    \end{macrocode}
+% For comparitors life is a lot moe complex, as there are three cases for
+% the integer part (equality as well as greater and less than). The
+% code here is quite repetitive to keep speed up, and simply does 
+% exhaustive checks.
+%    \begin{macrocode}
+\cs_new_protected_nopar:cpn { fp_compare_>: } {
+  \tex_ifnum:D \l_fp_input_a_sign_int > \l_fp_input_b_sign_int
+    \group_end:
+    \prg_return_true:
+  \tex_else:D  
+    \tex_ifnum:D \l_fp_input_a_sign_int < \l_fp_input_b_sign_int
+      \group_end:
+      \prg_return_false:
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+        \use:c { fp_compare_absolute_a > b: }
+      \tex_else:D
+        \use:c { fp_compare_absolute_a < b: }
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D  
+}
+\cs_new_protected_nopar:cpn { fp_compare_<: } {
+  \tex_ifnum:D \l_fp_input_b_sign_int > \l_fp_input_a_sign_int
+    \group_end:
+    \prg_return_true:
+  \tex_else:D  
+    \tex_ifnum:D \l_fp_input_b_sign_int < \l_fp_input_a_sign_int
+      \group_end:
+      \prg_return_false:
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero
+        \use:c { fp_compare_absolute_a < b: }
+      \tex_else:D
+        \use:c { fp_compare_absolute_a > b: }
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D   
+}
+\cs_new_protected_nopar:cpn { fp_compare_absolute_a > b: } {
+  \tex_ifnum:D \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
+    \group_end:
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
+      \group_end:
+      \prg_return_false:
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_a_decimal_int > \l_fp_input_b_decimal_int
+        \group_end:
+        \prg_return_true:
+      \tex_else:D
+        \group_end:
+        \prg_return_false:
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:cpn { fp_compare_absolute_a < b: } {
+  \tex_ifnum:D \l_fp_input_b_integer_int > \l_fp_input_a_integer_int
+    \group_end:
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_b_integer_int < \l_fp_input_a_integer_int
+      \group_end:
+      \prg_return_false:
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_b_decimal_int > \l_fp_input_a_decimal_int
+        \group_end:
+        \prg_return_true:
+      \tex_else:D
+        \group_end:
+        \prg_return_false:
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+}
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%
+%\subsection{Formatting fixed point numbers}
+%
+% When transferring fixed points to higher level code it is desirable
+% to allow flexible formatting.
+% 
+%\begin{macro}{\l_fp_round_precision_int}
+%\begin{macro}{\l_fp_remove_zeros_bool}
+%\begin{macro}{\l_fp_round_mode_tl}
+%    \begin{macrocode}
+\keys_define:nn { fp } {
+  precision             .int_set:N  = \l_fp_round_precision_int ,
+  remove-trailing-zeros .bool_set:N = \l_fp_remove_zeros_bool   ,
+  round-mode            .choice:                                ,
+  round-mode
+    / half-even         .tl_set:N   = \l_fp_round_mode_tl       ,
+  round-mode
+    / half-from-zero    .tl_set:N   = \l_fp_round_mode_tl       ,
+  round-mode
+    / none              .tl_set:N   = \l_fp_round_mode_tl       ,
+  round-mode
+    / truncate          .tl_set:N   = \l_fp_round_mode_tl       ,
+}
+\keys_set:nn { fp } {
+  precision             = 9    ,
+  remove-trailing-zeros = true ,
+  round-mode            = none ,
+}
+%    \end{macrocode}
+%\end{macro}
+%\end{macro}
+%\end{macro}
+%    
+%\begin{macro}{\fp_to_tl:NN}
+%\begin{macro}{\fp_to_tl:Nc}
+%\begin{macro}{\fp_to_tl:cN}
+%\begin{macro}{\fp_to_tl:cc}
+%\begin{macro}{\fp_gto_tl:NN}
+%\begin{macro}{\fp_gto_tl:Nc}
+%\begin{macro}{\fp_gto_tl:cN}
+%\begin{macro}{\fp_gto_tl:cc}
+%\begin{macro}[aux]{\fp_to_tl_aux:NNN}
+%\begin{macro}[aux]{\fp_remove_zeros:NNNNNNNNN}
+%\begin{macro}[aux]{\fp_remove_zeros_aux:w}
+%\begin{macro}[aux]{\fp_round_half-from-zero:}
+%\begin{macro}[aux]{\fp_round_from_zero:}
+%\begin{macro}[aux]{\fp_round_from_zero_aux:NNNNNNNNN}
+%\begin{macro}[aux]{\fp_round_from_zero_decimal:N}
+%\begin{macro}[aux]{\fp_round_from_zero_integer:}
+%\begin{macro}[aux]{\fp_round_half-even:}
+%\begin{macro}[aux]{\fp_round_even:}
+%\begin{macro}[aux]{\fp_round_even_aux:NNNNNNNNN}
+%\begin{macro}[aux]{\fp_round_even_decimal:N}
+%\begin{macro}[aux]{\fp_round_even_integer:}
+%\begin{macro}[aux]{\fp_round_none:}
+%\begin{macro}[aux]{\fp_round_truncate:}
+% The usual lead off with a series of wrapper functions.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_to_tl:NN {
+  \fp_to_tl_aux:NNN \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gto_tl:NN {
+  \fp_to_tl_aux:NNN \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_to_tl:NN  { Nc }
+\cs_generate_variant:Nn \fp_to_tl:NN  { c }
+\cs_generate_variant:Nn \fp_to_tl:NN  { cc }
+\cs_generate_variant:Nn \fp_gto_tl:NN { Nc }
+\cs_generate_variant:Nn \fp_gto_tl:NN { c }
+\cs_generate_variant:Nn \fp_gto_tl:NN { cc }
+%    \end{macrocode}
+% The main body of the conversion follows the pattern of reading the
+% \texttt{fp} then processing it. Rounding takes place first, so
+% that zero stripping is easier. This may involve loosing the decimal
+% part entirely.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_to_tl_aux:NNN #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \use:c { fp_round_ \l_fp_round_mode_tl :}
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D  \l_fp_input_a_sign_int < \c_zero
+          -
+        \tex_fi:D
+        \int_use:N \l_fp_input_a_integer_int
+        \intexpr_compare:nNnT { \l_fp_round_precision_int } > { \c_zero }
+          {
+            .
+            \bool_if:NTF \l_fp_remove_zeros_bool
+              { 
+                \exp_after:wN \use_i:nn 
+                  \exp_after:wN \fp_remove_zeros:NNNNNNNNN
+              }
+              { \exp_after:wN \use_none:n }
+            \int_use:N \l_fp_input_a_decimal_int
+          }
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #3 \exp_after:wN { \l_fp_tmp_tl }
+}
+%    \end{macrocode}
+% For removing zeros, the code above ensures there will be exactly
+% \( 9 \) tokens to deal with. The idea here is to go through them one
+% at a time and see if the remained is equal to zero. The input can
+% then be discarded if the precision in the output is correct. Speed
+% is not quite so vital here so everything is coded in \LaTeX3 rather
+% than primitives. This approach avoids needing to reverse the input.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \fp_remove_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+  \fp_remove_zeros_aux:w #1#2#3#4#5#6#7#8#9 \q_stop 1
+}
+\cs_new_nopar:Npn \fp_remove_zeros_aux:w #1#2 \q_stop #3 {
+  #1
+  \intexpr_compare:nNnTF { 0 #2 } = { \c_zero }
+    {
+      \intexpr_compare:nNnF { \l_fp_round_precision_int } < { #3 + 1 }
+        {
+          \intexpr_compare:nNnT {#3} < { 9 }
+            { \fp_remove_zeros_aux:w #2 \q_stop { #3 + 1 } }
+        }
+    }
+    {
+      \intexpr_compare:nNnT {#3} < { 9 }
+        { \fp_remove_zeros_aux:w #2 \q_stop { #3 + 1 } }
+    }
+}
+%    \end{macrocode}
+% Rounding away from zero is relatively easy, as it only depends on
+% the digit immediately before the rounded position. The code here
+% therefore does a fast reversal of the direct of the input, then 
+% checks the position before considering the size of the digit itself.
+% The position here refers to the digit that will be rounded, which is
+% therefore out by one from the digit being considered during the loop.
+%    \begin{macrocode}
+\cs_new_protected_nopar:cpn { fp_round_half-from-zero: } {
+  \tex_ifnum:D \l_fp_round_precision_int < \c_nine
+    \exp_after:wN \fp_round_from_zero:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_round_from_zero: {
+  \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_from_zero_aux:NNNNNNNNN
+    \int_use:N \l_fp_input_a_decimal_int
+}
+\cs_new_protected_nopar:Npn \fp_round_from_zero_aux:NNNNNNNNN
+  #1#2#3#4#5#6#7#8#9 {
+  \fp_round_from_zero_decimal:N #9#8#7#6#5#4#3#2#1
+  \fp_round_from_zero_integer:
+}
+\cs_new_protected_nopar:Npn \fp_round_from_zero_decimal:N #1 {
+  \tex_ifnum:D \l_fp_round_position_int < \l_fp_round_precision_int
+    \bool_if:NTF \l_fp_round_carry_bool
+      { \l_fp_tmp_int \etex_numexpr:D #1 + \c_one \scan_stop: }
+      { \l_fp_tmp_int \etex_numexpr:D #1 \scan_stop: }
+    \tex_ifnum:D \l_fp_tmp_int = \c_ten
+      \l_fp_tmp_int \c_zero
+    \tex_else:D 
+      \bool_set_false:N \l_fp_round_carry_bool  
+    \tex_fi:D  
+    \tl_set:Nx \l_fp_round_decimal_tl
+      { \int_use:N \l_fp_tmp_int \l_fp_round_decimal_tl }    
+  \tex_else:D
+    \tl_set:Nx \l_fp_round_decimal_tl { 0 \l_fp_round_decimal_tl }
+    \tex_ifnum:D \l_fp_round_position_int = \l_fp_round_precision_int
+      \tex_ifnum:D #1 > \c_four
+        \bool_set_true:N \l_fp_round_carry_bool 
+      \tex_fi:D
+    \tex_fi:D  
+  \tex_fi:D  
+  \tex_advance:D \l_fp_round_position_int \c_minus_one
+  \tex_ifnum:D \l_fp_round_position_int > \c_minus_one
+    \exp_after:wN \fp_round_from_zero_decimal:N
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_round_from_zero_integer: {
+  \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:
+}
+%    \end{macrocode}
+% The general outline is similar when rounding where ties go to the
+% nearest even number. However, life is more complicated as there is a 
+% need to track the discarded digits, and to see whether the digit to
+% round is odd or even. This is done by tracking the discarded digits.
+% When reaching the digit to check for rounding, the discards are used
+% to indicate if there is an exact half to take into account. When the
+% rounding takes place without an exact half, things are the same as
+% for the \enquote{away from zero} approach. When rounding an exact
+% half, there is an odd/even test before applying any modification.
+%    \begin{macrocode}
+\cs_new_protected_nopar:cpn { fp_round_half-even: } {
+  \tex_ifnum:D \l_fp_round_precision_int < \c_nine
+    \exp_after:wN \fp_round_even:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_round_even: {
+  \bool_set_false:N \l_fp_round_carry_bool
+  \l_fp_round_position_int \c_eight
+  \tl_clear:N \l_fp_round_decimal_tl
+  \int_zero:N \l_fp_round_discard_int
+  \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+  \exp_after:wN \use_i:nn \exp_after:wN
+    \fp_round_even_aux:NNNNNNNNN
+    \int_use:N \l_fp_input_a_decimal_int
+}
+\cs_new_protected_nopar:Npn \fp_round_even_aux:NNNNNNNNN
+  #1#2#3#4#5#6#7#8#9 {
+  \fp_round_even_decimal:N #9#8#7#6#5#4#3#2#1
+  \fp_round_even_integer:
+}
+\cs_new_protected_nopar:Npn \fp_round_even_decimal:N #1 {
+  \tex_ifnum:D \l_fp_round_position_int < \l_fp_round_precision_int
+    \bool_if:NTF \l_fp_round_carry_bool
+      { 
+        \tex_ifnum:D \l_fp_round_discard_int = \c_zero
+          \l_fp_round_discard_int \c_one
+          \tex_ifodd:D #1 \scan_stop:
+            \l_fp_tmp_int \etex_numexpr:D #1 + \c_one \scan_stop: 
+          \tex_else:D
+            \l_fp_tmp_int \etex_numexpr:D #1 \scan_stop: 
+          \tex_fi:D
+        \tex_else:D
+          \l_fp_tmp_int \etex_numexpr:D #1 + \c_one \scan_stop: 
+        \tex_fi:D
+      }
+      { \l_fp_tmp_int \etex_numexpr:D #1 \scan_stop: }
+    \tex_ifnum:D \l_fp_tmp_int = \c_ten
+      \l_fp_tmp_int \c_zero
+    \tex_else:D 
+      \bool_set_false:N \l_fp_round_carry_bool  
+    \tex_fi:D  
+    \tl_set:Nx \l_fp_round_decimal_tl
+      { \int_use:N \l_fp_tmp_int \l_fp_round_decimal_tl }    
+  \tex_else:D
+    \tl_set:Nx \l_fp_round_decimal_tl { 0 \l_fp_round_decimal_tl }
+    \tex_ifnum:D \l_fp_round_position_int = \l_fp_round_precision_int
+      \tex_ifnum:D #1 > \c_four
+        \bool_set_true:N \l_fp_round_carry_bool
+        \tex_ifnum:D #1 = \c_five
+        \tex_else:D
+          \l_fp_round_discard_int \c_one
+        \tex_fi:D
+      \tex_fi:D
+    \tex_else:D
+      \tex_advance:D \l_fp_round_discard_int #1 \scan_stop:  
+    \tex_fi:D  
+  \tex_fi:D  
+  \tex_advance:D \l_fp_round_position_int \c_minus_one
+  \tex_ifnum:D \l_fp_round_position_int > \c_minus_one
+    \exp_after:wN \fp_round_even_decimal:N
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_round_even_integer: {
+  \bool_if:NT \l_fp_round_carry_bool
+    { 
+      \tex_ifnum:D \l_fp_round_discard_int = \c_zero
+        \tex_ifodd:D \l_fp_input_a_integer_int
+          \tex_advance:D \l_fp_input_a_integer_int \c_one 
+        \tex_fi:D
+      \tex_else:D
+        \tex_advance:D \l_fp_input_a_integer_int \c_one 
+      \tex_fi:D
+    }
+  \l_fp_input_a_decimal_int \l_fp_round_decimal_tl \scan_stop:
+}
+%    \end{macrocode}
+% The only task that is needed when not rounding is to ensure that
+% the zero-stripping function will remove things reliably. This is
+% done by setting the precision to one digit: no rounding will always
+% leave at least one decimal digit, even if it is zero.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_round_none: { 
+  \l_fp_round_precision_int \c_one
+}
+%    \end{macrocode}
+% Truncating input is done by using the \cs{tex_divide:D} primitive
+% as this turns out to be the most convenient method to do this.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_round_truncate: {
+  \intexpr_compare:nNnF { \l_fp_round_precision_int } > { 8 }
+    {
+      \intexpr_compare:nNnTF { \l_fp_round_precision_int } < { 1 }
+        { \l_fp_input_a_decimal_int \c_zero \scan_stop: }
+        {
+          \int_set:Nn \l_fp_tmp_int
+            {
+              \prg_replicate:nn { 9 - \l_fp_round_precision_int }
+                { 10 * }
+              1
+            } 
+          \tex_divide:D \l_fp_input_a_decimal_int \l_fp_tmp_int
+          \tex_multiply:D \l_fp_input_a_decimal_int \l_fp_tmp_int
+        }
+    }
+}
+%    \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}
+%
+%\subsection{Messages}
+%
+%\begin{macro}{\fp_msg_overflow:}
+% To avoid expansion issues above, the messages are all set up as
+% functions.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \fp_msg_overflow: {
+  \msg_kernel_error:nn { fpu } { overflow }
+}
+%    \end{macrocode}
+%\end{macro}
+%
+%    \begin{macrocode}
+\msg_kernel_new:nnnn { fpu } { overflow }
+  { Arithmetic~overflow. }
+  {
+    The~calculation~requested~exceeds~the~capacity \\
+    of~the~fixed-point~unit.
+  }
+%    \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/expl3/l3intexpr.dtx b/Master/texmf-dist/source/latex/expl3/l3intexpr.dtx
index 4c43e63e6db..71801f8780d 100644
--- a/Master/texmf-dist/source/latex/expl3/l3intexpr.dtx
+++ b/Master/texmf-dist/source/latex/expl3/l3intexpr.dtx
@@ -36,7 +36,7 @@
 \RequirePackage{l3names}
 %</driver|package>
 %\fi
-\GetIdInfo$Id: l3intexpr.dtx 1086 2009-03-20 19:29:35Z morten $
+\GetIdInfo$Id: l3intexpr.dtx 1957 2010-06-15 06:33:43Z mittelba $
        {L3 Integer Expressions}
 %\iffalse
 %<*driver>
@@ -463,11 +463,32 @@
 % \begin{macro}[TF]{\intexpr_compare:nNn}
 % More efficient but less natural in typing.
 %    \begin{macrocode}
-\prg_set_conditional:Npnn \intexpr_compare:nNn #1#2#3{p,TF,T,F}{
+\prg_set_conditional:Npnn \intexpr_compare:nNn #1#2#3{p}{
   \if_intexpr_compare:w \intexpr_eval:w #1 #2 \intexpr_eval:w #3
   \intexpr_eval_end:
   \prg_return_true: \else: \prg_return_false: \fi:
 }
+\cs_set_nopar:Npn \intexpr_compare:nNnT #1#2#3 {
+  \tex_ifnum:D \etex_numexpr:D #1 #2 \etex_numexpr:D #3 \scan_stop:
+    \tex_expandafter:D \use:n
+  \tex_else:D
+    \tex_expandafter:D \use_none:n
+  \tex_fi:D
+}
+\cs_set_nopar:Npn \intexpr_compare:nNnF #1#2#3 {
+  \tex_ifnum:D \etex_numexpr:D #1 #2 \etex_numexpr:D #3 \scan_stop:
+    \tex_expandafter:D \use_none:n
+  \tex_else:D
+    \tex_expandafter:D \use:n
+  \tex_fi:D
+}
+\cs_set_nopar:Npn \intexpr_compare:nNnTF #1#2#3 {
+  \tex_ifnum:D \etex_numexpr:D #1 #2 \etex_numexpr:D #3 \scan_stop:
+    \tex_expandafter:D \use_i:nn
+  \tex_else:D
+    \tex_expandafter:D \use_ii:nn
+  \tex_fi:D
+}
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
diff --git a/Master/texmf-dist/source/latex/expl3/l3names.dtx b/Master/texmf-dist/source/latex/expl3/l3names.dtx
index 651be378791..99b224d62c5 100644
--- a/Master/texmf-dist/source/latex/expl3/l3names.dtx
+++ b/Master/texmf-dist/source/latex/expl3/l3names.dtx
@@ -128,7 +128,7 @@
 \RequirePackage{l3names}
 %</driver>
 %\fi
-\GetIdInfo$Id: l3names.dtx 1853 2010-03-21 09:11:08Z joseph $
+\GetIdInfo$Id: l3names.dtx 1981 2010-07-11 07:28:30Z will $
      {L3 Experimental Naming Scheme for TeX Primitives}
 %
 %
@@ -324,6 +324,10 @@
   \endlinechar  =\the \endlinechar \relax
   \catcode  95=\the \catcode 95 \relax
   \catcode  58=\the \catcode 58 \relax
+  \catcode 124=\the \catcode 124 \relax
+  \catcode  38=\the \catcode 38 \relax
+  \catcode  94=\the \catcode 94 \relax
+  \catcode  34=\the \catcode 34 \relax
   \noexpand\fi
 }
 \catcode126=10\relax  % tilde is a space char.
@@ -332,6 +336,10 @@
 \endlinechar=32\relax % endline is space
 \catcode95=11\relax   % underscore letter
 \catcode58=11\relax   % colon letter
+\catcode124=12\relax  % vert bar, other
+\catcode38=4\relax    % ampersand, alignment token
+\catcode34=12\relax   % doublequote, other
+\catcode94=7\relax    % caret, math superscript
 %    \end{macrocode}
 %
 % \subsection{Setting up primitive names}
@@ -981,6 +989,10 @@
       \tex_endlinechar:D  =\tex_the:D \tex_endlinechar:D \tex_relax:D
       \tex_catcode:D  95=\tex_the:D \tex_catcode:D 95 \tex_relax:D
       \tex_catcode:D  58=\tex_the:D \tex_catcode:D 58 \tex_relax:D
+      \tex_catcode:D 124=\tex_the:D \tex_catcode:D 124 \tex_relax:D
+      \tex_catcode:D  38=\tex_the:D \tex_catcode:D 38 \tex_relax:D
+      \tex_catcode:D  94=\tex_the:D \tex_catcode:D 94 \tex_relax:D
+      \tex_catcode:D  34=\tex_the:D \tex_catcode:D 34 \tex_relax:D
       \tex_noexpand:D \tex_fi:D
     }
     \tex_def:D \ExplSyntaxStatus { 1 }
@@ -990,6 +1002,10 @@
     \tex_endlinechar:D =32 \tex_relax:D % endline is space
     \tex_catcode:D   95=11 \tex_relax:D % underscore letter
     \tex_catcode:D   58=11 \tex_relax:D % colon letter
+    \tex_catcode:D  124=11 \tex_relax:D % vertical bar, other
+    \tex_catcode:D   38=4  \tex_relax:D % ampersand, alignment token
+    \tex_catcode:D   94=7  \tex_relax:D % caret, math superscript
+    \tex_catcode:D   34=12 \tex_relax:D % doublequote, other
   \tex_fi:D
 }
 %    \end{macrocode}
@@ -1138,7 +1154,7 @@
 % as the packages in this distribution do like this:
 % \begin{verbatim}
 % \RequirePackage{l3names}
-% \GetIdInfo$Id: l3names.dtx 1853 2010-03-21 09:11:08Z joseph $
+% \GetIdInfo$Id: l3names.dtx 1981 2010-07-11 07:28:30Z will $
 %          {L3 Experimental Box module}
 % \ProvidesExplPackage
 %   {\filename}{\filedate}{\fileversion}{\filedescription}
diff --git a/Master/texmf-dist/tex/latex/expl3/expl3.sty b/Master/texmf-dist/tex/latex/expl3/expl3.sty
index c943d158a23..5bd262fbb19 100644
--- a/Master/texmf-dist/tex/latex/expl3/expl3.sty
+++ b/Master/texmf-dist/tex/latex/expl3/expl3.sty
@@ -49,7 +49,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: expl3.dtx 1905 2010-05-19 07:45:31Z joseph $
+\GetIdInfo$Id: expl3.dtx 1955 2010-06-15 06:04:59Z joseph $
        {L3 Experimental code bundle wrapper}%
 \ProvidesExplPackage
   {\filename}{\filedate}{\fileversion}{\filedescription}
@@ -87,7 +87,8 @@
   l3precom,
   l3calc,
   l3xref,
-  l3file
+  l3file,
+  l3fp,
 }
 \bool_if:nT { \@l@expl@check@declarations@bool } {
   \msg_kernel_new:nnnn { check } { non-declared-variable }
diff --git a/Master/texmf-dist/tex/latex/expl3/l3expan.sty b/Master/texmf-dist/tex/latex/expl3/l3expan.sty
index cbe31dd98b5..8a356ca0295 100644
--- a/Master/texmf-dist/tex/latex/expl3/l3expan.sty
+++ b/Master/texmf-dist/tex/latex/expl3/l3expan.sty
@@ -48,7 +48,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3expan.dtx 1873 2010-03-24 08:32:54Z joseph $
+\GetIdInfo$Id: l3expan.dtx 1948 2010-06-10 18:53:09Z joseph $
        {L3 Experimental Argument Expansion module}
 \ProvidesExplPackage
   {\filename}{\filedate}{\fileversion}{\filedescription}
@@ -292,15 +292,19 @@
 }
 \cs_new_nopar:Npn \exp_last_unbraced:Nf { \::f_unbraced \::: }
 \cs_new_nopar:Npn \exp_last_unbraced:NV { \::V_unbraced \::: }
+\cs_new_nopar:Npn \exp_last_unbraced:No { \::o_unbraced \::: }
 \cs_new_nopar:Npn \exp_last_unbraced:Nv { \::v_unbraced \::: }
 \cs_new_nopar:Npn \exp_last_unbraced:NcV {
   \::c \::V_unbraced \:::
 }
+\cs_new_nopar:Npn \exp_last_unbraced:NNV {
+  \::N \::V_unbraced \:::
+}
 \cs_new:Npn \exp_last_unbraced:NNo #1#2#3 {
   \exp_after:wN #1 \exp_after:wN #2 #3
 }
-\cs_new_nopar:Npn \exp_last_unbraced:NNV {
-  \::N \::V_unbraced \:::
+\cs_new_nopar:Npn \exp_last_unbraced:NNNV {
+  \::N \::N \::V_unbraced \:::
 }
 \cs_new:Npn \exp_last_unbraced:NNNo #1#2#3#4 {
   \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN #3 #4
diff --git a/Master/texmf-dist/tex/latex/expl3/l3fp.sty b/Master/texmf-dist/tex/latex/expl3/l3fp.sty
new file mode 100644
index 00000000000..f2677b2c481
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/expl3/l3fp.sty
@@ -0,0 +1,1092 @@
+%%
+%% This is file `l3fp.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% l3fp.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: l3fp.dtx Copyright (C) 2010 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 ``expl3 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: l3fp.dtx 1979 2010-07-08 19:51:19Z joseph $
+  {L3 Experimental floating-point operations}
+\ProvidesExplPackage
+  {\filename}{\filedate}{\fileversion}{\filedescription}
+\package_check_loaded_expl:
+\int_new:N \l_fp_input_a_integer_int
+\int_new:N \l_fp_input_a_decimal_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_a_sign_int
+\int_new:N \l_fp_input_b_sign_int
+\int_new:N \l_fp_split_sign_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_div_count_int
+\int_new:N \l_fp_div_offset_int
+\int_new:N \l_fp_output_sign_int
+\int_new:N \l_fp_output_integer_int
+\int_new:N \l_fp_output_decimal_int
+\bool_new:N \l_fp_round_carry_bool
+\tl_new:N \l_fp_round_decimal_tl
+\int_new:N \l_fp_round_discard_int
+\int_new:N \l_fp_round_position_int
+\int_new:N \l_fp_tmp_int
+\tl_new:N \l_fp_tmp_tl
+\tl_new:N  \c_zero_fp
+\tl_set:Nn \c_zero_fp { + 0.000000000 }
+\tl_new:N  \c_undefined_fp
+\tl_set:Nn \c_undefined_fp { X 0.000000000 }
+\tl_new:N  \c_infinity_fp
+\tl_set:Nn \c_infinity_fp { +2147483647.2147483647 }
+\tl_new:N  \c_minus_infinity_fp
+\tl_set:Nn \c_minus_infinity_fp { -2147483647.2147483647 }
+\int_new:N  \c_one_hundred_million
+\int_set:Nn \c_one_hundred_million  { 100000000 }
+\int_new:N  \c_one_thousand_million
+\int_set:Nn \c_one_thousand_million { 1000000000 }
+\prg_new_conditional:Npnn \fp_if_infinite:N #1 { p , T , F , TF } {
+  \tex_ifx:D #1 \c_infinity_fp
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifx:D #1 \c_minus_infinity_fp
+      \prg_return_true:
+    \tex_else:D
+      \prg_return_false:
+    \tex_fi:D
+  \tex_fi:D
+}
+\prg_new_conditional:Npnn \fp_if_plus_infinity:N #1 { p , T , F , TF } {
+  \tex_ifx:D #1 \c_infinity_fp
+    \prg_return_true:
+  \tex_else:D
+    \prg_return_false:
+  \tex_fi:D
+}
+\prg_new_conditional:Npnn \fp_if_minus_infinity:N #1 { p , T , F , TF }
+  {
+  \tex_ifx:D #1 \c_minus_infinity_fp
+    \prg_return_true:
+  \tex_else:D
+    \prg_return_false:
+  \tex_fi:D
+}
+\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF } {
+  \tex_ifx:D #1 \c_undefined_fp
+    \prg_return_true:
+  \tex_else:D
+    \prg_return_false:
+  \tex_fi:D
+}
+\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF } {
+  \tex_ifx:D #1 \c_zero_fp
+    \prg_return_true:
+  \tex_else:D
+    \prg_return_false:
+  \tex_fi:D
+}
+\cs_new_protected_nopar: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 }
+\cs_new_protected_nopar:Npn \fp_zero:N #1 {
+  \tl_set_eq:NN #1 \c_zero_fp
+}
+\cs_new_protected_nopar: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_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_nopar:Npn \fp_set_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_split:Nn a {#3}
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+          -
+        \tex_else:D
+          +
+        \tex_fi:D
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \exp_after:wN \use_none:n
+          \int_use:N \l_fp_input_a_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\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_nopar:Npn \fp_set_from_dim_aux:NNn #1#2#3 {
+  \group_begin:
+    \l_fp_tmp_dim \etex_dimexpr:D #3 \scan_stop:
+    \fp_split:Nn a
+      {
+        \exp_after:wN \fp_set_from_dim_aux:w
+          \dim_use:N \l_fp_tmp_dim
+      }
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+          -
+        \tex_else:D
+          +
+        \tex_fi:D
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \exp_after:wN \use_none:n
+          \int_use:N \l_fp_input_a_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_set_protected_nopar:Npx \fp_set_from_dim_aux:w {
+  \cs_set_nopar: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_tmp_dim
+\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_eq:NN \fp_use:N \tl_use:N
+\cs_new_eq:NN \fp_use:c \tl_use:c
+\cs_new_protected_nopar:Npn \fp_read:N #1 {
+  \exp_after:wN \fp_read_aux:w #1 \q_stop
+}
+\cs_new_protected_nopar:Npn \fp_read_aux:w #1#2 . #3 \q_stop {
+  \tex_if:D #1 -
+    \l_fp_input_a_sign_int \c_minus_one
+  \tex_else:D
+    \l_fp_input_a_sign_int \c_one
+  \tex_fi:D
+  \l_fp_input_a_integer_int #2 \scan_stop:
+  \l_fp_input_a_decimal_int #3 \scan_stop:
+}
+\cs_new_protected_nopar:Npn \fp_split:Nn #1#2 {
+  \tl_set:Nx \l_fp_tmp_tl {#2}
+  \l_fp_split_sign_int \c_one
+  \fp_split_sign:
+  \use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int
+  \tex_afterassignment:D \fp_split_aux_i:w
+  \use:c { l_fp_input_ #1 _integer_int }
+    \etex_numexpr:D 0 \l_fp_tmp_tl . . \q_stop #1
+}
+\cs_new_protected_nopar:Npn \fp_split_sign: {
+  \tex_ifnum:D \pdf_strcmp:D
+    { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_nil } { - }
+      = \c_zero
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \exp_after:wN
+          \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_nil
+      }
+    \l_fp_split_sign_int -\l_fp_split_sign_int
+    \exp_after:wN \fp_split_sign:
+  \tex_else:D
+    \tex_ifnum:D \pdf_strcmp:D
+      { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_nil } { + }
+        = \c_zero
+      \tl_set:Nx \l_fp_tmp_tl
+        {
+          \exp_after:wN
+            \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_nil
+        }
+      \exp_after:wN \exp_after:wN \exp_after:wN
+        \fp_split_sign:
+     \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_split_aux_i:w #1 . #2 . #3 \q_stop {
+  \fp_split_aux_ii:w #2 000000000 \q_stop
+}
+\cs_new_protected_nopar: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_nopar:Npn \fp_split_aux_iii:w #1#2 \q_stop {
+  \l_fp_tmp_int 1 #1 \scan_stop:
+  \exp_after:wN \fp_split_decimal:w
+    \int_use:N \l_fp_tmp_int 000000000 \q_stop
+}
+\cs_new_protected_nopar: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_nopar:Npn \fp_split_decimal_aux:w #1#2#3 \q_stop #4 {
+  \use:c { l_fp_input_ #4 _decimal_int } #1#2 \scan_stop:
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \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
+   \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_abs:N {
+  \fp_abs:NN \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gabs:N {
+  \fp_abs:NN \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_abs:N  { c }
+\cs_generate_variant:Nn \fp_gabs:N { c }
+\cs_new_protected_nopar:Npn \fp_abs: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_tmp_tl
+      {
+        +
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \exp_after:wN \use_none:n
+          \int_use:N \l_fp_input_a_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\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_nopar: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_tmp_tl
+      {
+        \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+          +
+        \tex_else:D
+          -
+        \tex_fi:D
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \exp_after:wN \use_none:n
+          \int_use:N \l_fp_input_a_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_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_nopar:Npn \fp_add_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \fp_split:Nn b {#3}
+    \fp_add_core:
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_new_protected_nopar:Npn \fp_add_core: {
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
+    \scan_stop:
+      > \c_zero
+    \exp_after:wN \fp_add_sum:
+  \tex_else:D
+    \exp_after:wN \fp_add_difference:
+  \tex_fi:D
+  \tl_set:Nx \l_fp_tmp_tl
+    {
+      \tex_ifnum:D \l_fp_output_sign_int < \c_zero
+        -
+      \tex_else:D
+        +
+      \tex_fi:D
+      \int_use:N \l_fp_output_integer_int
+      .
+      \exp_after:wN \use_none:n
+        \int_use:N \l_fp_output_decimal_int
+    }
+}
+\cs_new_protected_nopar:Npn \fp_add_sum: {
+  \l_fp_output_sign_int \l_fp_input_a_sign_int
+  \l_fp_output_integer_int
+    \etex_numexpr:D
+      \l_fp_input_a_integer_int + \l_fp_input_b_integer_int
+    \scan_stop:
+  \l_fp_output_decimal_int
+    \etex_numexpr:D
+      \l_fp_input_a_decimal_int + \l_fp_input_b_decimal_int
+    \scan_stop:
+  \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
+    \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+  \tex_else:D
+    \tex_advance:D \l_fp_output_integer_int \c_one
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_add_difference: {
+  \l_fp_output_integer_int
+    \etex_numexpr:D
+      \l_fp_input_a_integer_int - \l_fp_input_b_integer_int
+    \scan_stop:
+  \l_fp_output_decimal_int
+    \etex_numexpr:D
+      \l_fp_input_a_decimal_int - \l_fp_input_b_decimal_int
+    \scan_stop:
+  \tex_ifnum:D \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
+  \tex_fi:D
+  \tex_ifnum:D \l_fp_output_integer_int < \c_zero
+    \l_fp_output_sign_int \l_fp_input_b_sign_int
+    \tex_ifnum:D \l_fp_output_decimal_int = \c_zero
+      \l_fp_output_integer_int -\l_fp_output_integer_int
+    \tex_else:D
+      \l_fp_output_decimal_int
+        \etex_numexpr:D
+          \c_one_thousand_million - \l_fp_output_decimal_int
+        \scan_stop:
+      \l_fp_output_integer_int
+         \etex_numexpr:D
+           - \l_fp_output_integer_int - \c_one
+         \scan_stop:
+    \tex_fi:D
+  \tex_else:D
+    \l_fp_output_sign_int \l_fp_input_a_sign_int
+  \tex_fi:D
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \l_fp_output_integer_int + \l_fp_output_decimal_int
+    \scan_stop:
+      = \c_zero
+    \l_fp_output_sign_int \c_one
+  \tex_fi:D
+  \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+}
+\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_nopar:Npn \fp_sub_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \fp_split:Nn b {#3}
+    \tex_multiply:D \l_fp_input_b_sign_int \c_minus_one
+    \fp_add_core:
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\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_nopar:Npn \fp_mul_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \fp_split:Nn b {#3}
+    \fp_mul_split:NNNN \l_fp_input_a_integer_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_a_decimal_int
+      \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
+    \fp_mul_split:NNNN \l_fp_input_b_integer_int
+      \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
+    \fp_mul_split:NNNN \l_fp_input_b_decimal_int
+      \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_iv_int \l_fp_mul_b_vi_int
+    \fp_mul_product:NN \l_fp_mul_a_v_int  \l_fp_mul_b_v_int
+    \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_iv_int
+    \tex_divide:D \l_fp_mul_output_int \c_thousand
+    \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_vi_int
+    \fp_mul_product:NN \l_fp_mul_a_iv_int  \l_fp_mul_b_v_int
+    \fp_mul_product:NN \l_fp_mul_a_v_int   \l_fp_mul_b_iv_int
+    \fp_mul_product:NN \l_fp_mul_a_vi_int  \l_fp_mul_b_iii_int
+    \fp_mul_end_level:
+    \fp_mul_product:NN \l_fp_mul_a_ii_int  \l_fp_mul_b_vi_int
+    \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_v_int
+    \fp_mul_product:NN \l_fp_mul_a_iv_int  \l_fp_mul_b_iv_int
+    \fp_mul_product:NN \l_fp_mul_a_v_int   \l_fp_mul_b_iii_int
+    \fp_mul_product:NN \l_fp_mul_a_vi_int  \l_fp_mul_b_ii_int
+    \fp_mul_end_level:
+    \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
+    \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_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:
+    \l_fp_output_integer_int 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:
+    \tex_ifnum:D \l_fp_mul_output_tl = \c_zero
+    \tex_else:D
+      \exp_after:wN \fp_msg_overflow:
+    \tex_fi:D
+    \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D
+          \etex_numexpr:D
+            \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
+          \scan_stop:
+            < \c_zero
+          \tex_ifnum:D
+            \etex_numexpr:D
+              \l_fp_output_integer_int + \l_fp_output_decimal_int
+            \scan_stop:
+              = \c_one_thousand_million
+            +
+          \tex_else:D
+            -
+          \tex_fi:D
+        \tex_else:D
+          +
+        \tex_fi:D
+        \int_use:N \l_fp_output_integer_int
+        .
+        \exp_after:wN \use_none:n
+          \int_use:N \l_fp_output_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_new_protected_nopar:Npn \fp_mul_split:NNNN #1#2#3#4 {
+  \tex_advance:D #1 \c_one_thousand_million
+  \cs_set_protected_nopar: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
+}
+\cs_new_protected_nopar:Npn \fp_mul_product:NN #1#2 {
+  \l_fp_mul_output_int
+    \etex_numexpr:D \l_fp_mul_output_int + #1 * #2 \scan_stop:
+}
+\cs_new_protected_nopar:Npn \fp_mul_end_level: {
+  \tex_advance:D \l_fp_mul_output_int \c_one_thousand_million
+  \exp_after:wN \fp_mul_end_level:w
+    \int_use:N \l_fp_mul_output_int \q_stop
+}
+\cs_new_protected_nopar:Npn \fp_mul_end_level:w
+  #1#2#3#4#5#6#7#8#9 \q_stop {
+  \tl_set:Nx \l_fp_mul_output_tl { #8#9 \l_fp_mul_output_tl }
+  \l_fp_mul_output_int #5#6#7 \scan_stop:
+}
+\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_nopar:Npn \fp_div_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \fp_split:Nn b {#3}
+    \tex_ifnum:D
+      \etex_numexpr:D
+        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+      \scan_stop:
+        = \c_zero
+      \tl_set_eq:NN \l_fp_tmp_tl \c_undefined_fp
+    \tex_else:D
+      \tex_ifnum:D
+        \etex_numexpr:D
+          \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+        \scan_stop:
+          = \c_zero
+          \tl_set_eq:NN \l_fp_tmp_tl \c_zero_fp
+      \tex_else:D
+        \exp_after:wN \exp_after:wN \exp_after:wN
+          \fp_div_aux:
+      \tex_fi:D
+    \tex_fi:D
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_new_protected_nopar:Npn \fp_div_aux: {
+  \l_fp_div_offset_int \c_one
+  \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero
+    \exp_after:wN \fp_div_offset_create:
+  \tex_fi:D
+  \l_fp_output_integer_int \c_zero
+  \l_fp_output_decimal_int \c_one_thousand_million
+  \cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
+  \fp_div_loop:
+  \tl_set:Nx \l_fp_tmp_tl
+    {
+      \tex_ifnum:D
+        \etex_numexpr:D
+          \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
+        \scan_stop:
+          < \c_zero
+        \tex_ifnum:D
+          \etex_numexpr:D
+            \l_fp_output_integer_int + \l_fp_output_decimal_int
+          \scan_stop:
+            = \c_one_thousand_million
+          +
+        \tex_else:D
+          -
+        \tex_fi:D
+      \tex_else:D
+        +
+      \tex_fi:D
+      \int_use:N \l_fp_output_integer_int
+      .
+      \exp_after:wN \use_none:n
+        \int_use:N \l_fp_output_decimal_int
+    }
+}
+\cs_new_protected_nopar:Npn \fp_div_offset_create: {
+  \tex_ifnum:D \l_fp_input_b_integer_int = \c_zero
+    \tex_advance:D \l_fp_input_b_decimal_int \c_one_thousand_million
+    \exp_after:wN \fp_div_offset_create_aux:w
+      \int_use:N \l_fp_input_b_decimal_int \q_stop
+    \exp_after:wN \fp_div_offset_create:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_div_offset_create_aux:w
+  #1#2#3#4#5#6#7#8#9 \q_stop {
+  \l_fp_input_b_integer_int #2 \scan_stop:
+  \l_fp_input_b_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
+  \tex_multiply:D \l_fp_div_offset_int \c_ten
+}
+\cs_new_protected_nopar:Npn \fp_div_loop: {
+  \l_fp_div_count_int \c_zero
+  \fp_div_divide:
+  \tex_divide:D \l_fp_input_b_decimal_int \c_ten
+  \tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million
+  \exp_after:wN \fp_div_loop_aux_i:w
+    \int_use:N \l_fp_input_b_integer_int
+  \fp_div_store:
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+      > \c_zero
+    \tex_ifnum:D
+      \etex_numexpr:D
+        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+        > \c_zero
+      \exp_after:wN \exp_after:wN \exp_after:wN
+        \fp_div_loop:
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_div_divide: {
+  \tex_ifnum:D \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
+    \exp_after:wN \fp_div_divide_aux:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
+    \tex_else:D
+      \tex_ifnum:D
+        \l_fp_input_a_decimal_int < \l_fp_input_b_decimal_int
+      \tex_else:D
+        \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:
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_div_loop_aux_i:w #1#2#3#4#5#6#7#8#9 {
+  \fp_div_loop_aux_ii:w #2#3#4#5#6#7#8#9
+}
+\cs_new_protected_nopar:Npn \fp_div_loop_aux_ii:w #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:
+  \l_fp_input_b_decimal_int
+    \etex_numexpr:D
+      \l_fp_input_b_decimal_int + \c_one_hundred_million * #9
+    \scan_stop:
+}
+\cs_new_protected_nopar:Npn \fp_div_divide_aux: {
+  \tex_advance:D \l_fp_div_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
+  \tex_ifnum:D \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
+  \tex_fi:D
+  \fp_div_divide:
+}
+\cs_new_protected_nopar:Npn \fp_div_store: { }
+\cs_new_protected_nopar:Npn \fp_div_store_integer: {
+  \l_fp_output_integer_int
+    \etex_numexpr:D
+      \l_fp_output_integer_int +
+      \l_fp_div_count_int * \l_fp_div_offset_int
+    \scan_stop:
+  \tex_ifnum:D \l_fp_div_offset_int > \c_one
+    \tex_divide:D \l_fp_div_offset_int \c_ten
+  \tex_else:D
+    \cs_set_eq:NN \fp_div_store: \fp_div_store_decimal:
+    \l_fp_div_offset_int \c_one_hundred_million
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_div_store_decimal: {
+  \l_fp_output_decimal_int
+    \etex_numexpr:D
+      \l_fp_output_decimal_int +
+      \l_fp_div_count_int * \l_fp_div_offset_int
+    \scan_stop:
+  \tex_divide:D \l_fp_div_offset_int \c_ten
+}
+\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3
+  { T , F , TF } {
+  \group_begin:
+    \fp_split:Nn a {#1}
+    \fp_split:Nn b {#3}
+    \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
+    \fp_read:N #1
+    \fp_compare_aux:N #2
+}
+\cs_new_protected_nopar:Npn \fp_compare_aux:N #1 {
+  \cs_if_exist:cTF { fp_compare_#1: }
+    { \use:c { fp_compare_#1: } }
+    {
+      \group_end:
+      \prg_return_false:
+    }
+}
+\cs_new_protected_nopar:cpn { fp_compare_=: } {
+  \tex_ifnum:D \l_fp_input_a_sign_int = \l_fp_input_b_sign_int
+    \tex_ifnum:D \l_fp_input_a_integer_int = \l_fp_input_b_integer_int
+      \tex_ifnum:D \l_fp_input_a_decimal_int = \l_fp_input_b_decimal_int
+        \group_end:
+        \prg_return_true:
+      \tex_else:D
+        \group_end:
+        \prg_return_false:
+      \tex_fi:D
+    \tex_else:D
+      \group_end:
+      \prg_return_false:
+    \tex_fi:D
+  \tex_else:D
+    \group_end:
+    \prg_return_false:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:cpn { fp_compare_>: } {
+  \tex_ifnum:D \l_fp_input_a_sign_int > \l_fp_input_b_sign_int
+    \group_end:
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_a_sign_int < \l_fp_input_b_sign_int
+      \group_end:
+      \prg_return_false:
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+        \use:c { fp_compare_absolute_a > b: }
+      \tex_else:D
+        \use:c { fp_compare_absolute_a < b: }
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:cpn { fp_compare_<: } {
+  \tex_ifnum:D \l_fp_input_b_sign_int > \l_fp_input_a_sign_int
+    \group_end:
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_b_sign_int < \l_fp_input_a_sign_int
+      \group_end:
+      \prg_return_false:
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero
+        \use:c { fp_compare_absolute_a < b: }
+      \tex_else:D
+        \use:c { fp_compare_absolute_a > b: }
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:cpn { fp_compare_absolute_a > b: } {
+  \tex_ifnum:D \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
+    \group_end:
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
+      \group_end:
+      \prg_return_false:
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_a_decimal_int > \l_fp_input_b_decimal_int
+        \group_end:
+        \prg_return_true:
+      \tex_else:D
+        \group_end:
+        \prg_return_false:
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:cpn { fp_compare_absolute_a < b: } {
+  \tex_ifnum:D \l_fp_input_b_integer_int > \l_fp_input_a_integer_int
+    \group_end:
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_b_integer_int < \l_fp_input_a_integer_int
+      \group_end:
+      \prg_return_false:
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_b_decimal_int > \l_fp_input_a_decimal_int
+        \group_end:
+        \prg_return_true:
+      \tex_else:D
+        \group_end:
+        \prg_return_false:
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+}
+\keys_define:nn { fp } {
+  precision             .int_set:N  = \l_fp_round_precision_int ,
+  remove-trailing-zeros .bool_set:N = \l_fp_remove_zeros_bool   ,
+  round-mode            .choice:                                ,
+  round-mode
+    / half-even         .tl_set:N   = \l_fp_round_mode_tl       ,
+  round-mode
+    / half-from-zero    .tl_set:N   = \l_fp_round_mode_tl       ,
+  round-mode
+    / none              .tl_set:N   = \l_fp_round_mode_tl       ,
+  round-mode
+    / truncate          .tl_set:N   = \l_fp_round_mode_tl       ,
+}
+\keys_set:nn { fp } {
+  precision             = 9    ,
+  remove-trailing-zeros = true ,
+  round-mode            = none ,
+}
+\cs_new_protected_nopar:Npn \fp_to_tl:NN {
+  \fp_to_tl_aux:NNN \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gto_tl:NN {
+  \fp_to_tl_aux:NNN \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_to_tl:NN  { Nc }
+\cs_generate_variant:Nn \fp_to_tl:NN  { c }
+\cs_generate_variant:Nn \fp_to_tl:NN  { cc }
+\cs_generate_variant:Nn \fp_gto_tl:NN { Nc }
+\cs_generate_variant:Nn \fp_gto_tl:NN { c }
+\cs_generate_variant:Nn \fp_gto_tl:NN { cc }
+\cs_new_protected_nopar:Npn \fp_to_tl_aux:NNN #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \use:c { fp_round_ \l_fp_round_mode_tl :}
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D  \l_fp_input_a_sign_int < \c_zero
+          -
+        \tex_fi:D
+        \int_use:N \l_fp_input_a_integer_int
+        \intexpr_compare:nNnT { \l_fp_round_precision_int } > { \c_zero }
+          {
+            .
+            \bool_if:NTF \l_fp_remove_zeros_bool
+              {
+                \exp_after:wN \use_i:nn
+                  \exp_after:wN \fp_remove_zeros:NNNNNNNNN
+              }
+              { \exp_after:wN \use_none:n }
+            \int_use:N \l_fp_input_a_decimal_int
+          }
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #3 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_new_nopar:Npn \fp_remove_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+  \fp_remove_zeros_aux:w #1#2#3#4#5#6#7#8#9 \q_stop 1
+}
+\cs_new_nopar:Npn \fp_remove_zeros_aux:w #1#2 \q_stop #3 {
+  #1
+  \intexpr_compare:nNnTF { 0 #2 } = { \c_zero }
+    {
+      \intexpr_compare:nNnF { \l_fp_round_precision_int } < { #3 + 1 }
+        {
+          \intexpr_compare:nNnT {#3} < { 9 }
+            { \fp_remove_zeros_aux:w #2 \q_stop { #3 + 1 } }
+        }
+    }
+    {
+      \intexpr_compare:nNnT {#3} < { 9 }
+        { \fp_remove_zeros_aux:w #2 \q_stop { #3 + 1 } }
+    }
+}
+\cs_new_protected_nopar:cpn { fp_round_half-from-zero: } {
+  \tex_ifnum:D \l_fp_round_precision_int < \c_nine
+    \exp_after:wN \fp_round_from_zero:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_round_from_zero: {
+  \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_from_zero_aux:NNNNNNNNN
+    \int_use:N \l_fp_input_a_decimal_int
+}
+\cs_new_protected_nopar:Npn \fp_round_from_zero_aux:NNNNNNNNN
+  #1#2#3#4#5#6#7#8#9 {
+  \fp_round_from_zero_decimal:N #9#8#7#6#5#4#3#2#1
+  \fp_round_from_zero_integer:
+}
+\cs_new_protected_nopar:Npn \fp_round_from_zero_decimal:N #1 {
+  \tex_ifnum:D \l_fp_round_position_int < \l_fp_round_precision_int
+    \bool_if:NTF \l_fp_round_carry_bool
+      { \l_fp_tmp_int \etex_numexpr:D #1 + \c_one \scan_stop: }
+      { \l_fp_tmp_int \etex_numexpr:D #1 \scan_stop: }
+    \tex_ifnum:D \l_fp_tmp_int = \c_ten
+      \l_fp_tmp_int \c_zero
+    \tex_else:D
+      \bool_set_false:N \l_fp_round_carry_bool
+    \tex_fi:D
+    \tl_set:Nx \l_fp_round_decimal_tl
+      { \int_use:N \l_fp_tmp_int \l_fp_round_decimal_tl }
+  \tex_else:D
+    \tl_set:Nx \l_fp_round_decimal_tl { 0 \l_fp_round_decimal_tl }
+    \tex_ifnum:D \l_fp_round_position_int = \l_fp_round_precision_int
+      \tex_ifnum:D #1 > \c_four
+        \bool_set_true:N \l_fp_round_carry_bool
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+  \tex_advance:D \l_fp_round_position_int \c_minus_one
+  \tex_ifnum:D \l_fp_round_position_int > \c_minus_one
+    \exp_after:wN \fp_round_from_zero_decimal:N
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_round_from_zero_integer: {
+  \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:
+}
+\cs_new_protected_nopar:cpn { fp_round_half-even: } {
+  \tex_ifnum:D \l_fp_round_precision_int < \c_nine
+    \exp_after:wN \fp_round_even:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_round_even: {
+  \bool_set_false:N \l_fp_round_carry_bool
+  \l_fp_round_position_int \c_eight
+  \tl_clear:N \l_fp_round_decimal_tl
+  \int_zero:N \l_fp_round_discard_int
+  \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+  \exp_after:wN \use_i:nn \exp_after:wN
+    \fp_round_even_aux:NNNNNNNNN
+    \int_use:N \l_fp_input_a_decimal_int
+}
+\cs_new_protected_nopar:Npn \fp_round_even_aux:NNNNNNNNN
+  #1#2#3#4#5#6#7#8#9 {
+  \fp_round_even_decimal:N #9#8#7#6#5#4#3#2#1
+  \fp_round_even_integer:
+}
+\cs_new_protected_nopar:Npn \fp_round_even_decimal:N #1 {
+  \tex_ifnum:D \l_fp_round_position_int < \l_fp_round_precision_int
+    \bool_if:NTF \l_fp_round_carry_bool
+      {
+        \tex_ifnum:D \l_fp_round_discard_int = \c_zero
+          \l_fp_round_discard_int \c_one
+          \tex_ifodd:D #1 \scan_stop:
+            \l_fp_tmp_int \etex_numexpr:D #1 + \c_one \scan_stop:
+          \tex_else:D
+            \l_fp_tmp_int \etex_numexpr:D #1 \scan_stop:
+          \tex_fi:D
+        \tex_else:D
+          \l_fp_tmp_int \etex_numexpr:D #1 + \c_one \scan_stop:
+        \tex_fi:D
+      }
+      { \l_fp_tmp_int \etex_numexpr:D #1 \scan_stop: }
+    \tex_ifnum:D \l_fp_tmp_int = \c_ten
+      \l_fp_tmp_int \c_zero
+    \tex_else:D
+      \bool_set_false:N \l_fp_round_carry_bool
+    \tex_fi:D
+    \tl_set:Nx \l_fp_round_decimal_tl
+      { \int_use:N \l_fp_tmp_int \l_fp_round_decimal_tl }
+  \tex_else:D
+    \tl_set:Nx \l_fp_round_decimal_tl { 0 \l_fp_round_decimal_tl }
+    \tex_ifnum:D \l_fp_round_position_int = \l_fp_round_precision_int
+      \tex_ifnum:D #1 > \c_four
+        \bool_set_true:N \l_fp_round_carry_bool
+        \tex_ifnum:D #1 = \c_five
+        \tex_else:D
+          \l_fp_round_discard_int \c_one
+        \tex_fi:D
+      \tex_fi:D
+    \tex_else:D
+      \tex_advance:D \l_fp_round_discard_int #1 \scan_stop:
+    \tex_fi:D
+  \tex_fi:D
+  \tex_advance:D \l_fp_round_position_int \c_minus_one
+  \tex_ifnum:D \l_fp_round_position_int > \c_minus_one
+    \exp_after:wN \fp_round_even_decimal:N
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_round_even_integer: {
+  \bool_if:NT \l_fp_round_carry_bool
+    {
+      \tex_ifnum:D \l_fp_round_discard_int = \c_zero
+        \tex_ifodd:D \l_fp_input_a_integer_int
+          \tex_advance:D \l_fp_input_a_integer_int \c_one
+        \tex_fi:D
+      \tex_else:D
+        \tex_advance:D \l_fp_input_a_integer_int \c_one
+      \tex_fi:D
+    }
+  \l_fp_input_a_decimal_int \l_fp_round_decimal_tl \scan_stop:
+}
+\cs_new_protected_nopar:Npn \fp_round_none: {
+  \l_fp_round_precision_int \c_one
+}
+\cs_new_protected_nopar:Npn \fp_round_truncate: {
+  \intexpr_compare:nNnF { \l_fp_round_precision_int } > { 8 }
+    {
+      \intexpr_compare:nNnTF { \l_fp_round_precision_int } < { 1 }
+        { \l_fp_input_a_decimal_int \c_zero \scan_stop: }
+        {
+          \int_set:Nn \l_fp_tmp_int
+            {
+              \prg_replicate:nn { 9 - \l_fp_round_precision_int }
+                { 10 * }
+              1
+            }
+          \tex_divide:D \l_fp_input_a_decimal_int \l_fp_tmp_int
+          \tex_multiply:D \l_fp_input_a_decimal_int \l_fp_tmp_int
+        }
+    }
+}
+\cs_new_protected_nopar:Npn \fp_msg_overflow: {
+  \msg_kernel_error:nn { fpu } { overflow }
+}
+\msg_kernel_new:nnnn { fpu } { overflow }
+  { Arithmetic~overflow. }
+  {
+    The~calculation~requested~exceeds~the~capacity \\
+    of~the~fixed-point~unit.
+  }
+%% 
+%%
+%% End of file `l3fp.sty'.
diff --git a/Master/texmf-dist/tex/latex/expl3/l3intexpr.sty b/Master/texmf-dist/tex/latex/expl3/l3intexpr.sty
index ab4271cc46e..268881a29df 100644
--- a/Master/texmf-dist/tex/latex/expl3/l3intexpr.sty
+++ b/Master/texmf-dist/tex/latex/expl3/l3intexpr.sty
@@ -48,7 +48,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3intexpr.dtx 1086 2009-03-20 19:29:35Z morten $
+\GetIdInfo$Id: l3intexpr.dtx 1957 2010-06-15 06:33:43Z mittelba $
        {L3 Integer Expressions}
 \ProvidesExplPackage
   {\filename}{\filedate}{\fileversion}{\filedescription}
@@ -106,11 +106,32 @@
   \if_intexpr_compare:w #1<\intexpr_eval:w #2 \intexpr_eval_end:
   \prg_return_false: \else: \prg_return_true: \fi:
 }
-\prg_set_conditional:Npnn \intexpr_compare:nNn #1#2#3{p,TF,T,F}{
+\prg_set_conditional:Npnn \intexpr_compare:nNn #1#2#3{p}{
   \if_intexpr_compare:w \intexpr_eval:w #1 #2 \intexpr_eval:w #3
   \intexpr_eval_end:
   \prg_return_true: \else: \prg_return_false: \fi:
 }
+\cs_set_nopar:Npn \intexpr_compare:nNnT #1#2#3 {
+  \tex_ifnum:D \etex_numexpr:D #1 #2 \etex_numexpr:D #3 \scan_stop:
+    \tex_expandafter:D \use:n
+  \tex_else:D
+    \tex_expandafter:D \use_none:n
+  \tex_fi:D
+}
+\cs_set_nopar:Npn \intexpr_compare:nNnF #1#2#3 {
+  \tex_ifnum:D \etex_numexpr:D #1 #2 \etex_numexpr:D #3 \scan_stop:
+    \tex_expandafter:D \use_none:n
+  \tex_else:D
+    \tex_expandafter:D \use:n
+  \tex_fi:D
+}
+\cs_set_nopar:Npn \intexpr_compare:nNnTF #1#2#3 {
+  \tex_ifnum:D \etex_numexpr:D #1 #2 \etex_numexpr:D #3 \scan_stop:
+    \tex_expandafter:D \use_i:nn
+  \tex_else:D
+    \tex_expandafter:D \use_ii:nn
+  \tex_fi:D
+}
 \cs_set:Npn \intexpr_abs:n #1{
   \intexpr_value:w
   \if_intexpr_compare:w \intexpr_eval:w #1<\c_zero
diff --git a/Master/texmf-dist/tex/latex/expl3/l3names.sty b/Master/texmf-dist/tex/latex/expl3/l3names.sty
index 0c475563656..da660a756e5 100644
--- a/Master/texmf-dist/tex/latex/expl3/l3names.sty
+++ b/Master/texmf-dist/tex/latex/expl3/l3names.sty
@@ -87,7 +87,7 @@
   \gdef\filedescription{#1}%
   \ProvidesPackage{[unknown package]}[0000/00/00 v0.0 #1]
 }
-\GetIdInfo$Id: l3names.dtx 1853 2010-03-21 09:11:08Z joseph $
+\GetIdInfo$Id: l3names.dtx 1981 2010-07-11 07:28:30Z will $
      {L3 Experimental Naming Scheme for TeX Primitives}
 \endgroup
 \begingroup
@@ -116,6 +116,10 @@
   \endlinechar  =\the \endlinechar \relax
   \catcode  95=\the \catcode 95 \relax
   \catcode  58=\the \catcode 58 \relax
+  \catcode 124=\the \catcode 124 \relax
+  \catcode  38=\the \catcode 38 \relax
+  \catcode  94=\the \catcode 94 \relax
+  \catcode  34=\the \catcode 34 \relax
   \noexpand\fi
 }
 \catcode126=10\relax  % tilde is a space char.
@@ -124,6 +128,10 @@
 \endlinechar=32\relax % endline is space
 \catcode95=11\relax   % underscore letter
 \catcode58=11\relax   % colon letter
+\catcode124=12\relax  % vert bar, other
+\catcode38=4\relax    % ampersand, alignment token
+\catcode34=12\relax   % doublequote, other
+\catcode94=7\relax    % caret, math superscript
 \let \tex_let:D \let
 \DeclareOption{removeoldnames}{
   \long\def\name_undefine:N#1{
@@ -649,6 +657,10 @@
       \tex_endlinechar:D  =\tex_the:D \tex_endlinechar:D \tex_relax:D
       \tex_catcode:D  95=\tex_the:D \tex_catcode:D 95 \tex_relax:D
       \tex_catcode:D  58=\tex_the:D \tex_catcode:D 58 \tex_relax:D
+      \tex_catcode:D 124=\tex_the:D \tex_catcode:D 124 \tex_relax:D
+      \tex_catcode:D  38=\tex_the:D \tex_catcode:D 38 \tex_relax:D
+      \tex_catcode:D  94=\tex_the:D \tex_catcode:D 94 \tex_relax:D
+      \tex_catcode:D  34=\tex_the:D \tex_catcode:D 34 \tex_relax:D
       \tex_noexpand:D \tex_fi:D
     }
     \tex_def:D \ExplSyntaxStatus { 1 }
@@ -658,6 +670,10 @@
     \tex_endlinechar:D =32 \tex_relax:D % endline is space
     \tex_catcode:D   95=11 \tex_relax:D % underscore letter
     \tex_catcode:D   58=11 \tex_relax:D % colon letter
+    \tex_catcode:D  124=11 \tex_relax:D % vertical bar, other
+    \tex_catcode:D   38=4  \tex_relax:D % ampersand, alignment token
+    \tex_catcode:D   94=7  \tex_relax:D % caret, math superscript
+    \tex_catcode:D   34=12 \tex_relax:D % doublequote, other
   \tex_fi:D
 }
 \tex_def:D \ExplSyntaxStatus { 1 }