l3kernel 3160 (31aug12)

git-svn-id: svn://tug.org/texlive/trunk@27559 c570f23f-e606-0410-a88d-b1316a301751

49 files changed, 2495 insertions, 1669 deletions

diff --git a/Master/texmf-dist/doc/latex/l3kernel/expl3.pdf b/Master/texmf-dist/doc/latex/l3kernel/expl3.pdf
index 23fe9cdd425..9fce016693f 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/expl3.pdf
+++ b/Master/texmf-dist/doc/latex/l3kernel/expl3.pdf
diff --git a/Master/texmf-dist/doc/latex/l3kernel/interface3.pdf b/Master/texmf-dist/doc/latex/l3kernel/interface3.pdf
index e58e5afaaaa..078b6ba6ec5 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/interface3.pdf
+++ b/Master/texmf-dist/doc/latex/l3kernel/interface3.pdf
diff --git a/Master/texmf-dist/doc/latex/l3kernel/l3docstrip.pdf b/Master/texmf-dist/doc/latex/l3kernel/l3docstrip.pdf
index 5868f4cf1a4..7fc4478083e 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/l3docstrip.pdf
+++ b/Master/texmf-dist/doc/latex/l3kernel/l3docstrip.pdf
diff --git a/Master/texmf-dist/doc/latex/l3kernel/l3styleguide.pdf b/Master/texmf-dist/doc/latex/l3kernel/l3styleguide.pdf
index 7f0725051bb..eb85cd4ae51 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/l3styleguide.pdf
+++ b/Master/texmf-dist/doc/latex/l3kernel/l3styleguide.pdf
diff --git a/Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.pdf b/Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.pdf
index 68d31904d2e..faff73c2004 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.pdf
+++ b/Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.pdf
diff --git a/Master/texmf-dist/doc/latex/l3kernel/source3.pdf b/Master/texmf-dist/doc/latex/l3kernel/source3.pdf
index 4a44d224368..ec3908fb73a 100644
--- a/Master/texmf-dist/doc/latex/l3kernel/source3.pdf
+++ b/Master/texmf-dist/doc/latex/l3kernel/source3.pdf
diff --git a/Master/texmf-dist/source/latex/l3kernel/expl3.dtx b/Master/texmf-dist/source/latex/l3kernel/expl3.dtx
index 5003992c6e0..24dd30934c9 100644
--- a/Master/texmf-dist/source/latex/l3kernel/expl3.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/expl3.dtx
@@ -49,8 +49,8 @@
 %<*driver|package>
 \def\ExplFileName{expl3}
 \def\ExplFileDescription{L3 Experimental code bundle wrapper}
-\def\ExplFileDate{2012/08/14}
-\def\ExplFileVersion{4091}
+\def\ExplFileDate{2012/08/29}
+\def\ExplFileVersion{4160}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3alloc.dtx b/Master/texmf-dist/source/latex/l3kernel/l3alloc.dtx
index ec718e88d18..ed3580db09f 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3alloc.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3alloc.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3alloc.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3alloc.dtx 4145 2012-08-27 20:30:30Z bruno $
   {L3 Register allocation}
 %</driver|package>
 %<*driver>
@@ -217,8 +217,8 @@
           \seq_put_right:Nn \g__dim_allocation_seq  {#1}
           \seq_put_right:Nn \g__int_allocation_seq  {#1}
           \seq_put_right:Nn \g__skip_allocation_seq {#1}
-          \exp_args:Nf \@@_reserve_insert:n
-            { \etex_numexpr:D #1 + 1 \scan_stop: }
+          \exp_args:No \@@_reserve_insert:n
+            { \tex_the:D \etex_numexpr:D #1 + 1 \scan_stop: }
         }
     }
   \@@_reserve_insert:n { 221 }
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3basics.dtx b/Master/texmf-dist/source/latex/l3kernel/l3basics.dtx
index ede47fd6312..ac429fd8883 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3basics.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3basics.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3basics.dtx 4069 2012-08-08 23:12:57Z bruno $
+\GetIdInfo$Id: l3basics.dtx 4144 2012-08-27 19:37:16Z bruno $
   {L3 Basic definitions}
 %</driver|package>
 %<*driver>
@@ -1447,10 +1447,13 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[EXP]{\exp_args:Nc}
+% \begin{macro}[EXP]{\exp_args:Nc, \exp_args:cc}
 %   Discussed in \pkg{l3expan}, but needed much earlier.
 %    \begin{macrocode}
-\tex_long:D \tex_def:D \exp_args:Nc #1#2 { \exp_after:wN #1 \cs:w #2 \cs_end: }
+\tex_long:D \tex_def:D \exp_args:Nc #1#2
+  { \exp_after:wN #1 \cs:w #2 \cs_end: }
+\tex_long:D \tex_def:D \exp_args:cc #1#2
+  { \cs:w #1 \exp_after:wN \cs_end: \cs:w #2 \cs_end: }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1937,7 +1940,7 @@
       \exp_after:wN \use_ii:nn
     \fi:
       {
-        \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 _p: #5 } #6
+        \exp_args:cc { cs_ #2 #3 :Npn } { #4 _p: #5 } #6
           { #7 \c_zero \c_true_bool \c_false_bool }
       }
       {
@@ -1947,17 +1950,17 @@
   }
 \cs_set_protected:Npn \__prg_generate_T_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 T } #6
+    \exp_args:cc { cs_ #2 #3 :Npn } { #4 : #5 T } #6
       { #7 \c_zero \use:n \use_none:n }
   }
 \cs_set_protected:Npn \__prg_generate_F_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 F } #6
+    \exp_args:cc { cs_ #2 #3 :Npn } { #4 : #5 F } #6
       { #7 \c_zero { } }
   }
 \cs_set_protected:Npn \__prg_generate_TF_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 TF } #6
+    \exp_args:cc { cs_ #2 #3 :Npn } { #4 : #5 TF } #6
       { #7 \c_zero }
   }
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3clist.dtx b/Master/texmf-dist/source/latex/l3kernel/l3clist.dtx
index c7493dc6846..948976f4110 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3clist.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3clist.dtx
@@ -37,7 +37,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3clist.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3clist.dtx 4102 2012-08-15 16:08:27Z bruno $
   {L3 Comma separated lists}
 %</driver|package>
 %<*driver>
@@ -847,7 +847,7 @@
 \cs_new_protected_nopar:Npn \clist_put_right:Nn
   { \@@_put_right:NNNn \clist_concat:NNN \clist_set:Nn }
 \cs_new_protected_nopar:Npn \clist_gput_right:Nn
-  { \@@_put_right:NNNn \clist_gconcat:NNN \clist_gset:Nn }
+  { \@@_put_right:NNNn \clist_gconcat:NNN \clist_set:Nn }
 \cs_new_protected:Npn \@@_put_right:NNNn #1#2#3#4
   {
     #2 \l_@@_internal_clist {#4}
@@ -1357,25 +1357,20 @@
 %
 % \begin{macro}{\clist_show:N, \clist_show:c}
 % \begin{macro}{\clist_show:n}
-%   Apply the general \cs{__msg_show_variable:Nnn}. In the case
+%   Apply the general \cs{__msg_show_variable:Nnx}. In the case
 %   of an \texttt{n}-type comma-list, first store it
-%   in a scratch variable, then show that variable,
-%   omitting its name from the $4$-th argument.
+%   in a scratch variable, then show that variable:
+%   The message takes care of omitting its name.
 %    \begin{macrocode}
 \cs_new_protected:Npn \clist_show:N #1
   {
-    \__msg_show_variable:Nnn
-      #1
-      { clist }
+    \__msg_show_variable:Nnx #1 { clist }
       { \clist_map_function:NN #1 \__msg_show_item:n }
   }
 \cs_new_protected:Npn \clist_show:n #1
   {
     \clist_set:Nn \l_@@_internal_clist {#1}
-    \__msg_show_variable:Nnn
-      \l_@@_internal_clist
-      { clist }
-      { \clist_map_function:NN \l_@@_internal_clist \__msg_show_item:n }
+    \clist_show:N \l_@@_internal_clist
   }
 \cs_generate_variant:Nn \clist_show:N { c }
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx b/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
index cc205d5da4a..1c7f4836804 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3coffins.dtx 4011 2012-07-20 21:02:59Z joseph $
+\GetIdInfo$Id: l3coffins.dtx 4092 2012-08-14 14:04:41Z bruno $
   {L3 Coffin code layer}
 %</driver|package>
 %<*driver>
@@ -1676,7 +1676,7 @@
   {
     \@@_if_exist:NT #1
       {
-        \__msg_show_variable:Nnn #1 { coffins }
+        \__msg_show_variable:Nnx #1 { coffins }
           {
             \prop_map_function:cN
               { l_@@_poles_ \__int_value:w #1 _prop }
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3color.dtx b/Master/texmf-dist/source/latex/l3kernel/l3color.dtx
index 3b1476f3714..caf5f258333 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3color.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3color.dtx
@@ -36,8 +36,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3color.dtx 3991 2012-07-16 19:00:35Z joseph $
-  {L3 Experimental colour support}
+\GetIdInfo$Id: l3color.dtx 4156 2012-08-29 11:10:09Z joseph $
+  {L3 Experimental color support}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -68,14 +68,14 @@
 %
 % \begin{documentation}
 %
-% This module provides support for colour in \LaTeX3{}. At present, the
+% This module provides support for color in \LaTeX3{}. At present, the
 % material here is mainly intended to support a small number of low-level
 % requirements in other \pkg{l3kernel} modules.
 %
 % \section{Colour in boxes}
 %
-% Controlling the colour of text in boxes requires a small number of control
-% functions, so that the boxed material uses the colour at the point where
+% Controlling the color of text in boxes requires a small number of control
+% functions, so that the boxed material uses the color at the point where
 % it is set, rather than where it is used.
 %
 % \begin{function}[added = 2011-09-03]{\color_group_begin:, \color_group_end:}
@@ -84,14 +84,14 @@
 %       \ldots
 %     \cs{color_group_end:}
 %   \end{syntax}
-%   Creates a colour group: one used to \enquote{trap} colour settings.
+%   Creates a color group: one used to \enquote{trap} color settings.
 % \end{function}
 %
 % \begin{function}[added = 2011-09-03]{\color_ensure_current:}
 %   \begin{syntax}
 %     \cs{color_ensure_current:}
 %   \end{syntax}
-%   Ensures that material inside a box will use the foreground colour
+%   Ensures that material inside a box will use the foreground color
 %   at the point where the box is set, rather than that in force when the
 %   box is used. This function should usually be used within a
 %   \cs{color_group_begin:} \ldots \cs{color_group_end:} group.
@@ -116,7 +116,7 @@
 %    \end{macrocode}
 %
 % \begin{macro}{\color_group_begin:, \color_group_end:}
-%   Grouping for colour is almost the same as using the basic \cs{group_begin:}
+%   Grouping for color is almost the same as using the basic \cs{group_begin:}
 %   and \cs{group_end:} functions.  However, in vertical mode the end-of-group
 %   needs a \tn{par}, which in horizontal mode does nothing.
 %    \begin{macrocode}
@@ -130,8 +130,8 @@
 % \end{macro}
 %
 % \begin{macro}{\color_ensure_current:}
-%   A driver-independent wrapper for setting the foreground colour to the
-%   current colour \enquote{now}.
+%   A driver-independent wrapper for setting the foreground color to the
+%   current color \enquote{now}.
 %    \begin{macrocode}
 %<*initex>
 \cs_new_protected_nopar:Npn \color_ensure_current:
@@ -140,7 +140,7 @@
 %    \end{macrocode}
 %   In package mode, the driver code may not be loaded. To keep down
 %   dependencies, if there is no driver code available and no \cs{set@color}
-%   then colour is not in use and this function can be a no-op.
+%   then color is not in use and this function can be a no-op.
 %    \begin{macrocode}
 %<*package>
 \cs_new_protected_nopar:Npn \color_ensure_current: { }
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3doc.dtx b/Master/texmf-dist/source/latex/l3kernel/l3doc.dtx
index 8e0c1fd39e8..bea9cf251ce 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3doc.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3doc.dtx
@@ -78,7 +78,7 @@ Do not distribute a modified version of this file.
 %</driver|class>
 %
 %<*driver|class>
-\GetIdInfo$Id: l3doc.dtx 4070 2012-08-09 11:04:46Z joseph $
+\GetIdInfo$Id: l3doc.dtx 4130 2012-08-20 21:30:22Z joseph $
           {L3 Experimental documentation class}
 %</driver|class>
 %
@@ -481,7 +481,7 @@ Do not distribute a modified version of this file.
 \tl_new:N \l_@@_macro_tl
 \int_new:N \l_@@_macro_int
 \int_new:N \g_@@_nested_macro_int
-\int_new:N \g_@@_codeline_int
+%\int_new:N \c@CodelineNo
 \prop_new:N \g_@@_missing_tests_prop
 \clist_new:N \g_docinput_clist
 \tl_new:N \l_@@_at_replaced_macro_tl
@@ -1525,7 +1525,7 @@ Do not distribute a modified version of this file.
       \tl_to_str:N \l_@@_at_replaced_macro_tl
     }]
    }
-  \int_gincr:N \g_@@_codeline_int
+  \int_gincr:N \c@CodelineNo
 
   \bool_if:NF \l_@@_macro_aux_bool
    {
@@ -1549,7 +1549,7 @@ Do not distribute a modified version of this file.
     \exp_args:Nx \DoNotIndex{ \tl_to_str:N \l_@@_at_replaced_macro_tl }
    }
 
-  \int_gdecr:N \g_@@_codeline_int
+  \int_gdecr:N \c@CodelineNo
   \ignorespaces
  }
 %    \end{macrocode}
@@ -2158,7 +2158,7 @@ Do not distribute a modified version of this file.
   \immediate\write\@indexfile
    {
     \string\indexentry{#1}
-    { \filesep \int_use:N \g_@@_codeline_int }
+    { \filesep \int_use:N \c@CodelineNo }
    }
  }
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3drivers.dtx b/Master/texmf-dist/source/latex/l3kernel/l3drivers.dtx
index b088943d88c..6d6f17a4910 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3drivers.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3drivers.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3drivers.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3drivers.dtx 4156 2012-08-29 11:10:09Z joseph $
   {L3 Experimental drivers}
 %</driver|package>
 %<*driver>
@@ -69,7 +69,7 @@
 % \begin{documentation}
 %
 % \TeX{} relies on drivers in order to carry out a number of tasks, such
-% as using colour, including graphics and setting up hyper-links. The nature
+% as using color, including graphics and setting up hyper-links. The nature
 % of the code required depends on the exact driver in use. Currently,
 % \LaTeX3 is aware of the following drivers:
 % \begin{itemize}
@@ -140,11 +140,11 @@
 %   \begin{syntax}
 %     \cs{__driver_color_ensure_current:}
 %   \end{syntax}
-%   Ensures that the colour used to typeset material is that which was
+%   Ensures that the color used to typeset material is that which was
 %   set when the material was placed in a box. This function is therefore
-%   required inside any \enquote{colour safe} box to ensure that the box may
-%   be inserted in a location where the foreground colour has been altered,
-%   while preserving the colour used in the box.
+%   required inside any \enquote{color safe} box to ensure that the box may
+%   be inserted in a location where the foreground color has been altered,
+%   while preserving the color used in the box.
 % \end{function}
 %
 % \end{documentation}
@@ -484,7 +484,7 @@
 % \subsection{Colour support}
 %
 % \begin{variable}{\l_@@_current_color_tl}
-%   The current colour is needed by all of the engines, but the way this
+%   The current color is needed by all of the engines, but the way this
 %   is stored varies.
 %    \begin{macrocode}
 \tl_new:N \l_@@_current_color_tl
@@ -502,7 +502,7 @@
 %
 % \begin{variable}{\l_@@_color_stack_int}
 %   \pdfTeX{} (version~1.40.0 or later) and \LuaTeX{} have multiple stacks
-%   available, and the colour stack therefore needs a number.
+%   available, and the color stack therefore needs a number.
 %    \begin{macrocode}
 %<*pdfmode>
 \int_new:N \l_@@_color_stack_int
@@ -512,8 +512,8 @@
 %
 % \begin{macro}{\@@_color_ensure_current:}
 % \begin{macro}[aux]{\@@_color_reset:}
-%   Setting the current colour depends on the nature of the colour stack
-%   available. In all cases there is a need to reset the colour after
+%   Setting the current color depends on the nature of the color stack
+%   available. In all cases there is a need to reset the color after
 %   the current group.
 %    \begin{macrocode}
 %<*dvips|xdvipdfmx>
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3expan.dtx b/Master/texmf-dist/source/latex/l3kernel/l3expan.dtx
index 5c853a3a321..d912433ee8d 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3expan.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3expan.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3expan.dtx 4073 2012-08-10 01:33:13Z bruno $
+\GetIdInfo$Id: l3expan.dtx 4149 2012-08-28 10:50:40Z bruno $
   {L3 Argument expansion}
 %</driver|package>
 %<*driver>
@@ -116,7 +116,7 @@
 %
 % \section{Methods for defining variants}
 %
-% \begin{function}[updated = 2012-06-21]{\cs_generate_variant:Nn}
+% \begin{function}[updated = 2012-08-28]{\cs_generate_variant:Nn}
 %   \begin{syntax}
 %     \cs{cs_generate_variant:Nn} \meta{parent control sequence} \Arg{variant argument specifiers}
 %   \end{syntax}
@@ -598,7 +598,7 @@
 %   with other functions using temporary variables.
 % \end{variable}
 %
-% \begin{function}{\::n, \::N, \::c, \::o, \::f, \::x, \::v, \::V, \:::}
+% \begin{function}{\::n, \::N, \::p, \::c, \::o, \::f, \::x, \::v, \::V, \:::}
 %   \begin{syntax}
 %     |\cs_set_nopar:Npn \exp_args:Ncof { \::c \::o \::f \::: }|
 %   \end{syntax}
@@ -644,11 +644,7 @@
 % argument handling is defined.  These general expansion functions are
 % expandable unless |x| is used.  (Any version of |x| is going to have
 % to use one of the \LaTeX3 names for \cs{cs_set_nopar:Npx} at some
-% point, and so is never going to be expandable.\footnote{Some
-%   primitives have certain characteristics that means that their
-%   arguments undergo an expansion similar to an \texttt{x} type
-%   expansion but the primitive is in fact still expandable. We make it
-%   very clear when such a function is expandable.})
+% point, and so is never going to be expandable.)
 %
 % The definition of expansion functions with this technique happens
 % in section~\ref{sec:gendef}.
@@ -671,6 +667,8 @@
 % \cs{:::} serves as an end marker for the list of manipulations, |#2|
 % is the carried over result of the previous expansion steps and |#3| is
 % the argument about to be processed.
+% One exception to this rule is \cs{::p}, which has to grab an argument
+% delimited by a left brace.
 %
 % \begin{macro}[aux, EXP]{\@@_arg_next:nnn}
 % \begin{macro}[aux, EXP]{\@@_arg_next:Nnn}
@@ -713,9 +711,18 @@
 %    \end{macrocode}
 % \end{macro}
 %
+% \begin{macro}[int, EXP]{\::p}
+%   This function is used to skip an argument that is delimited by a
+%   left brace and doesn't need to be expanded.  It should not be
+%   wrapped in braces in the result.
+%    \begin{macrocode}
+\cs_new:Npn \::p #1 \::: #2#3# { #1 \::: {#2#3} }
+%    \end{macrocode}
+% \end{macro}
+%
 % \begin{macro}[int, EXP]{\::c}
 %   This function is used to skip an argument that is turned into
-%   as control sequence without expansion.
+%   a control sequence without expansion.
 %    \begin{macrocode}
 \cs_new:Npn \::c #1 \::: #2#3
   { \exp_after:wN \@@_arg_next:Nnn \cs:w #3 \cs_end: {#1} {#2} }
@@ -890,17 +897,14 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[EXP]{\exp_args:Nc}
-% In \pkg{l3basics}
-%\end{macro}
+% \begin{macro}[EXP]{\exp_args:Nc, \exp_args:cc}
+%   In \pkg{l3basics}.
+% \end{macro}
 %
-% \begin{macro}[EXP]
-%   {\exp_args:cc, \exp_args:NNc, \exp_args:Ncc, \exp_args:Nccc}
-%    Here are the functions that turn their argument into csnames but
-%    are  expandable.
+% \begin{macro}[EXP]{\exp_args:NNc, \exp_args:Ncc, \exp_args:Nccc}
+%   Here are the functions that turn their argument into csnames but are
+%   expandable.
 %    \begin{macrocode}
-\cs_new:Npn \exp_args:cc #1#2
-  { \cs:w #1 \exp_after:wN \cs_end: \cs:w #2 \cs_end: }
 \cs_new:Npn \exp_args:NNc #1#2#3
   { \exp_after:wN #1 \exp_after:wN #2 \cs:w # 3\cs_end: }
 \cs_new:Npn \exp_args:Ncc #1#2#3
@@ -1283,43 +1287,60 @@
     \exp_after:wN #1
     \exp_after:wN \@@_generate_variant:nnNN
     \exp_after:wN #1
-    \etex_detokenize:D {#2} , ? , \q_recursion_stop
+    \etex_detokenize:D {#2} , \scan_stop: , \q_recursion_stop
   }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}[aux]{\@@_generate_variant:N}
-% \begin{macro}[aux]{\@@_generate_variant:w}
-%   The idea here is to pick up protected parent functions, using the
-%   nature of the meaning string that they generate.  If |\protected|
-%   appears in the meaning, the first \cs{q_mark} is taken as an
-%   argument, and |#3| is \cs{cs_new_protected_nopar:Npx}, otherwise it
+% \begin{macro}[aux]{\@@_generate_variant:ww, \@@_generate_variant:wwNw}
+%   The goal here is to pick up protected parent functions.  There are
+%   four cases: the parent function can be a primitive or a macro, and
+%   can be expandable or not.  For non-expandable primitives, all
+%   variants should be protected; skipping the \cs{else:} branch is safe
+%   because all primitive \TeX{} conditionals are expandable.
+%
+%   The other case where variants should be protected is when the parent
+%   function is a protected macro: then |protected| appears in the
+%   meaning before the fist occurrence of |macro|.  The |ww| auxiliary
+%   removes everything in the meaning string after the first |ma|.  We
+%   use |ma| rather than the full |macro| because the meaning of the
+%   \tn{firstmark} primitive (and four others) can contain an arbitrary
+%   string after a leading |firstmark:|.  Then, look for |pr| in the
+%   part we extracted: no need to look for anything longer: the only
+%   strings we can have are an empty string, \verb*|\long |,
+%   \verb*|\protected |, \verb*|\protected\long |, |\first|, |\top|,
+%   |\bot|, |\splittop|, or |\splitbot|, with |\| replaced by the
+%   appropriate escape character.  If |pr| appears in the part before
+%   |ma|, the first \cs{q_mark} is taken as an argument of the |wwNw|
+%   auxiliary, and |#3| is \cs{cs_new_protected_nopar:Npx}, otherwise it
 %   is \cs{cs_new_nopar:Npx}.
 %    \begin{macrocode}
 \group_begin:
-  \tex_lccode:D `\Z = `\d \scan_stop:
-  \tex_lccode:D `\? =`\\ \scan_stop:
+  \tex_catcode:D `\M = 12 \scan_stop:
+  \tex_catcode:D `\A = 12 \scan_stop:
   \tex_catcode:D `\P = 12 \scan_stop:
   \tex_catcode:D `\R = 12 \scan_stop:
-  \tex_catcode:D `\O = 12 \scan_stop:
-  \tex_catcode:D `\T = 12 \scan_stop:
-  \tex_catcode:D `\E = 12 \scan_stop:
-  \tex_catcode:D `\C = 12 \scan_stop:
-  \tex_catcode:D `\Z = 12 \scan_stop:
 \tex_lowercase:D
   {
     \group_end:
     \cs_new_protected:Npn \@@_generate_variant:N #1
       {
-        \exp_after:wN \@@_generate_variant:w
-          \token_to_meaning:N #1
-          \q_mark \cs_new_protected_nopar:Npx
-          ? PROTECTEZ
-          \q_mark \cs_new_nopar:Npx
-          \q_stop
+        \exp_after:wN \if_meaning:w \exp_not:N #1 #1
+          \cs_set_eq:NN \@@_tmp:w \cs_new_protected_nopar:Npx
+        \else:
+          \exp_after:wN \@@_generate_variant:ww
+            \token_to_meaning:N #1 MA \q_mark
+            \q_mark \cs_new_protected_nopar:Npx
+            PR
+            \q_mark \cs_new_nopar:Npx
+            \q_stop
+        \fi:
       }
-    \cs_new_protected:Npn \@@_generate_variant:w
-        #1 ? PROTECTEZ #2 \q_mark #3 #4 \q_stop
+    \cs_new_protected:Npn \@@_generate_variant:ww #1 MA #2 \q_mark
+      { \@@_generate_variant:wwNw #1 }
+    \cs_new_protected:Npn \@@_generate_variant:wwNw
+        #1 PR #2 \q_mark #3 #4 \q_stop
       {
         \cs_set_eq:NN \@@_tmp:w #3
       }
@@ -1335,12 +1356,20 @@
 %     \item Boolean.
 %     \item Base function.
 %   \end{arguments}
-%   We discard the boolean and then set off a loop through the desired
-%   variant forms. The original function is retained as |#4| for
+%   If the boolean is \cs{c_false_bool}, the base function has no colon
+%   and we abort with an error; otherwise, set off a loop through the
+%   desired variant forms. The original function is retained as |#4| for
 %   efficiency.
 %    \begin{macrocode}
 \cs_new_protected:Npn \@@_generate_variant:nnNN #1#2#3#4
-  { \@@_generate_variant:Nnnw #4 {#1}{#2} }
+  {
+    \if_meaning:w \c_false_bool #3
+      \__msg_kernel_error:nnx { kernel } { missing-colon }
+        { \token_to_str:c {#1} }
+      \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
+    \fi:
+    \@@_generate_variant:Nnnw #4 {#1}{#2}
+  }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1351,108 +1380,232 @@
 %     \item Base signature.
 %     \item Beginning of variant signature.
 %   \end{arguments}
-%   First check whether to terminate the loop over variant forms.  Then
-%   build the variant function name once, to avoid repeating this
-%   relatively expensive operation. Then recurse, calling
-%   \cs{@@_generate_variant:Nnnw} with the three same arguments (and a
-%   new item from the comma list of variant forms).
-%
-%   For each variant form, construct a new function name using the
+%   First check whether to terminate the loop over variant forms.  Then,
+%   for each variant form, construct a new function name using the
 %   original base name, the variant signature consisting of $l$ letters
 %   and the last $k-l$ letters of the base signature (of length $k$).
 %   For example, for a base function \cs{prop_put:Nnn} which needs a
-%   |cV| variant form, we want the new signature to be |cVn|.  This
-%   could be done by placing the variant form letters, then
-%   \cs{use_none:nn} followed by the signature (the choice of
-%   \cs{use_none:nn} would depend on the variant form).  However, this
-%   would crash badly if the base signature is mistakenly shorter than
-%   the variant form (this includes cases where the base function had no
-%   colon).  Instead, we do a loop which at each step removes a
-%   character from the base signature and leaves one from the variant
-%   form behind it in a \cs{cs:w} \ldots{} \cs{cs_end:} construction.
-%   This \texttt{c}-type expansion is not done using \cs{exp_args:NNc}
-%   because some error-reporting mechanism must escape out of this
-%   construction.
+%   |cV| variant form, we want the new signature to be |cVn|.
+%
+%   There are further subtleties:
+%   \begin{itemize}
+%     \item In \cs{cs_generate_variant:Nn} |\foo:nnTF| |{xxTF}|, it
+%       would be better to define |\foo:xxTF| using |\exp_args:Nxx|,
+%       rather than a hypothetical |\exp_args:NxxTF|.  Thus, we wish to
+%       trim a common trailing part from the base signature and the
+%       variant signature.
+%     \item In \cs{cs_generate_variant:Nn} |\foo:on| |{ox}|, the
+%       function |\foo:ox| should be defined using |\exp_args:Nnx|, not
+%       |\exp_args:Nox|, to avoid double |o| expansion.
+%     \item Lastly, \cs{cs_generate_variant:Nn} |\foo:on| |{xn}| should
+%       trigger an error, because we do not have a means to replace
+%       |o|-expansion by |x|-expansion.
+%     \end{itemize}
+%     All this boils down to a few rules.  Only |n| and |N|-type
+%     arguments can be replaced by \cs{cs_generate_variant:Nn}.  Other
+%     argument types are allowed to be passed unchanged from the base
+%     form to the variant: in the process they are changed to |n|
+%     (except for two cases: |N| and |p|-type arguments).  A common
+%     trailing part is ignored.
+%
+%     We compare the base and variant signatures one character at a time
+%     within |x|-expansion.  The result is given to
+%     \cs{@@_generate_variant:wwNN} in the form \meta{processed variant
+%       signature} \cs{q_mark} \meta{errors} \cs{q_stop} \meta{base
+%       function} \meta{new function}.  If all went well, \meta{errors}
+%     is empty; otherwise, it is a kernel error message, followed by
+%     some clean-up code (\cs{use_none:nnnn}).
+%
+%     Note the space after |#3| and after the following brace group.
+%     Those are ignored by \TeX{} when fetching the last argument for
+%     \cs{@@_generate_variant_loop:nNwN}, but can be used as a delimiter
+%     for \cs{@@_generate_variant_loop_end:nwwwNNnn}.
 %    \begin{macrocode}
 \cs_new_protected:Npn \@@_generate_variant:Nnnw #1#2#3#4 ,
   {
-    \if:w ? #4
+    \if_meaning:w \scan_stop: #4
       \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
     \fi:
-    \exp_after:wN \@@_generate_variant:NNn
-    \exp_after:wN #1
-      \cs:w
-        #2 :
-        \@@_generate_variant_loop:NwN
-          ? #3
-          \q_mark #4 \@@_generate_variant_loop_end:w
-          \q_mark \@@_generate_variant_loop_error:wnNNnn
-        \q_stop
-      \cs_end:
-      {#4}
+    \use:x
+      {
+        \exp_not:N \@@_generate_variant:wwNN
+        \@@_generate_variant_loop:nNwN { }
+          #4
+          \@@_generate_variant_loop_end:nwwwNNnn
+          \q_mark
+          #3 ~
+          { ~ { } \fi: \@@_generate_variant_loop_long:wNNnn } ~
+          { }
+          \q_stop
+        \exp_not:N #1 {#2} {#4}
+      }
     \@@_generate_variant:Nnnw #1 {#2} {#3}
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux, rEXP]{\@@_generate_variant_loop:NwN}
 % \begin{macro}[aux, EXP]
 %   {
-%     \@@_generate_variant_loop_end:w,
-%     \@@_generate_variant_loop_error:wnNNnn
+%     \@@_generate_variant_loop:nNwN,
+%     \@@_generate_variant_loop_same:w,
+%     \@@_generate_variant_loop_end:nwwwNNnn,
+%     \@@_generate_variant_loop_long:wNNnn,
+%     \@@_generate_variant_loop_invalid:NNwNNnn,
 %   }
-%   Normally, the loop takes one character of the base signature and one
-%   from the variant form (after \cs{q_mark}), and leaves the latter one
-%   in the input stream.  This stops when |#3| is the \texttt{loop_end}
-%   auxiliary, which, once left in the input stream, cleans up the rest
-%   of the csname construction.  In case the base signature was in fact
-%   shorter, one reaches the point where |#1| is the \cs{q_mark} which
-%   is supposed to separate the base signature from the variant form.
-%   Then |#2| is delimited by the next \cs{q_mark}, and the
-%   \texttt{loop_error} auxiliary is taken as |#3|.  This function
-%   fetches appropriate arguments for an error message, and places it
-%   outside the csname construction.
-%
-%   Note in the definition of \cs{@@_generate_variant:Nnnw} the base
-%   signature is preceeded by a question mark.  This shifts the base
-%   signature and variant form to compensate for the presence of the
-%   \texttt{loop_end} auxiliary at the end of the variant form.
+%   \begin{arguments}
+%     \item Last few (consecutive) letters common between the base
+%       and variant (in fact, \cs{@@_generate_variant_same:N}
+%       \meta{letter} for each letter).
+%     \item Next variant letter.
+%     \item Remainder of variant form.
+%     \item Next base letter.
+%   \end{arguments}
+%   The first argument is populated by
+%   \cs{@@_generate_variant_loop_same:w} when a variant letter and a
+%   base letter match.  It is flushed into the input stream whenever the
+%   two letters are different: if the loop ends before, the argument is
+%   dropped, which means that trailing common letters are ignored.
+%
+%   The case where the two letters are different is only allowed with a
+%   base letter of |N| or |n|.  Otherwise, call
+%   \cs{@@_generate_variant_loop_invalid:NNwNNnn} to remove the end of
+%   the loop, get arguments at the end of the loop, and place an
+%   appropriate error message as a second argument of
+%   \cs{@@_generate_variant:wwNN}.  If the letters are distinct and
+%   the base letter is indeed |n| or |N|, leave in the input stream
+%   whatever argument was collected, and the next variant letter |#2|,
+%   then loop by calling \cs{@@_generate_variant_loop:nNwN}.
+%
+%   The loop can stop in three ways.
+%   \begin{itemize}
+%     \item If the end of the variant form is encountered first, |#2| is
+%       \cs{@@_generate_variant_loop_end:nwwwNNnn} (expanded by the
+%       conditional \cs{if:w}), which inserts some tokens to end the
+%       conditional; grabs the \meta{base name} as |#7|, the
+%       \meta{variant signature} |#8|, the \meta{next base letter} |#1|
+%       and the part |#3| of the base signature that wasn't read yet;
+%       and combines those into the \meta{new function} to be defined.
+%     \item If the end of the base form is encountered first, |#4| is
+%       |~{}\fi:| which ends the conditional (with an empty expansion),
+%       followed by \cs{@@_generate_variant_loop_long:wNNnn}, which
+%       places an error as the second argument of
+%       \cs{@@_generate_variant:wwNN}.
+%     \item The loop can be interrupted early if the requested expansion
+%       is unavailable, namely when the variant and base letters differ
+%       and the base is neither |n| nor |N|.  Again, an error is placed
+%       as the second argument of \cs{@@_generate_variant:wwNN}.
+%   \end{itemize}
+%   Note that if the variant form has the same length as the base form,
+%   |#2| is as described in the first point, and |#4| as described in
+%   the second point above.  The \cs{@@_generate_variant_loop_end:nwwwNNnn}
+%   breaking function takes the empty brace group in |#4| as its first
+%   argument: this empty brace group produces the correct signature for
+%   the full variant.
 %    \begin{macrocode}
-\cs_new:Npn \@@_generate_variant_loop:NwN #1 #2 \q_mark #3
-  { #3 \@@_generate_variant_loop:NwN #2 \q_mark }
-\cs_new:Npn \@@_generate_variant_loop_end:w #1#2 \q_mark #3 \q_stop {#2}
-\cs_new:Npn \@@_generate_variant_loop_error:wnNNnn
-    #1 \q_stop \cs_end: #2 #3#4#5#6
+\cs_new:Npn \@@_generate_variant_loop:nNwN #1#2#3 \q_mark #4
+  {
+    \if:w #2 #4
+      \exp_after:wN \@@_generate_variant_loop_same:w
+    \else:
+      \if:w N #4 \else:
+        \if:w n #4 \else:
+          \@@_generate_variant_loop_invalid:NNwNNnn #4#2
+        \fi:
+      \fi:
+    \fi:
+    #1
+    \prg_do_nothing:
+    #2
+    \@@_generate_variant_loop:nNwN { } #3 \q_mark
+  }
+\cs_new:Npn \@@_generate_variant_loop_same:w
+    #1 \prg_do_nothing: #2#3#4
+  {
+    #3 { #1 \@@_generate_variant_same:N #2 }
+  }
+\cs_new:Npn \@@_generate_variant_loop_end:nwwwNNnn
+    #1#2 \q_mark #3 ~ #4 \q_stop #5#6#7#8
   {
-    \cs_end: {#2}
-    \__msg_kernel_error:nnxx { kernel } { variant-too-long }
-      { \tl_to_str:n {#2} } { \token_to_str:N #4 }
-    #3 #4 {#5} {#6}
+    \scan_stop: \scan_stop: \fi:
+    \exp_not:N \q_mark
+    \exp_not:N \q_stop
+    \exp_not:N #6
+    \exp_not:c { #7 : #8 #1 #3 }
+  }
+\cs_new:Npn \@@_generate_variant_loop_long:wNNnn #1 \q_stop #2#3#4#5
+  {
+    \exp_not:n
+      {
+        \q_mark
+        \__msg_kernel_error:nnxx { kernel } { variant-too-long }
+          {#5} { \token_to_str:N #3 }
+        \use_none:nnnn
+        \q_stop
+        #3
+        #3
+      }
+  }
+\cs_new:Npn \@@_generate_variant_loop_invalid:NNwNNnn
+    #1#2 \fi: \fi: \fi: #3 \q_stop #4#5#6#7
+  {
+    \fi: \fi: \fi:
+    \exp_not:n
+      {
+        \q_mark
+        \__msg_kernel_error:nnxxxx { kernel } { invalid-variant }
+          {#7} { \token_to_str:N #5 } {#1} {#2}
+        \use_none:nnnn
+        \q_stop
+        #5
+        #5
+      }
   }
 %    \end{macrocode}
 % \end{macro}
+%
+% \begin{macro}[aux, rEXP]{\@@_generate_variant_same:N}
+%   When the base and variant letters are identical, don't do any
+%   expansion.  For most argument types, we can use the |n|-type
+%   no-expansion, but the |N| and |p| types require a slightly different
+%   behaviour with respect to braces.
+%    \begin{macrocode}
+\cs_new:Npn \@@_generate_variant_same:N #1
+  {
+    \if:w N #1
+      N
+    \else:
+      \if:w p #1
+        p
+      \else:
+        n
+      \fi:
+    \fi:
+  }
+%    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux]{\@@_generate_variant:NNn}
+% \begin{macro}[aux]{\@@_generate_variant:wwNN}
 %   If the variant form has already been defined, log its existence.
 %   Otherwise, make sure that the |\exp_args:N #3| form is defined, and
 %   if it contains |x|, change \cs{@@_tmp:w} locally to
 %   \cs{cs_new_protected_nopar:Npx}.  Then define the variant by
 %   combining the |\exp_args:N #3| variant and the base function.
 %    \begin{macrocode}
-\cs_new_protected:Npn \@@_generate_variant:NNn #1 #2 #3
+\cs_new_protected:Npn \@@_generate_variant:wwNN
+    #1 \q_mark #2 \q_stop #3#4
   {
-    \cs_if_free:NTF #2
+    #2
+    \cs_if_free:NTF #4
       {
         \group_begin:
-          \@@_generate_internal_variant:n {#3}
-          \@@_tmp:w #2 { \exp_not:c { exp_args:N #3 } \exp_not:N #1 }
+          \@@_generate_internal_variant:n {#1}
+          \@@_tmp:w #4 { \exp_not:c { exp_args:N #1 } \exp_not:N #3 }
         \group_end:
       }
       {
         \iow_log:x
           {
-            Variant~\token_to_str:N #2~%
+            Variant~\token_to_str:N #4~%
             already~defined;~ not~ changing~ it~on~line~%
             \tex_the:D \tex_inputlineno:D
           }
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3file.dtx b/Master/texmf-dist/source/latex/l3kernel/l3file.dtx
index 3816602c541..5011c868715 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3file.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3file.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3file.dtx 4059 2012-08-08 13:12:06Z bruno $
+\GetIdInfo$Id: l3file.dtx 4101 2012-08-15 16:05:33Z bruno $
   {L3 File and I/O operations}
 %</driver|package>
 %<*driver>
@@ -565,6 +565,14 @@
 %    \end{macrocode}
 % \end{variable}
 %
+% \begin{variable}{\l_@@_internal_tl}
+%   Used as a short-term scratch variable.  It may be possible to reuse
+%   \cs{l_@@_internal_name_tl} there.
+%    \begin{macrocode}
+\tl_new:N \l_@@_internal_tl
+%    \end{macrocode}
+% \end{variable}
+%
 % \begin{variable}{\l_@@_internal_name_tl}
 %   Used to return the fully-qualified name of a file.
 %    \begin{macrocode}
@@ -726,10 +734,11 @@
       { \@addtofilelist {#1} }
       { \seq_gput_right:Nn \g_@@_record_seq {#1} }
 %</package>
-    \seq_gpush:Nn \g_@@_stack_seq \g_file_current_name_tl
+    \seq_gpush:No \g_@@_stack_seq \g_file_current_name_tl
     \tl_gset:Nn \g_file_current_name_tl {#1}
     \tex_input:D #1 \c_space_tl
-    \seq_gpop:NN \g_@@_stack_seq \g_file_current_name_tl
+    \seq_gpop:NN \g_@@_stack_seq \l_@@_internal_tl
+    \tl_gset_eq:NN \g_file_current_name_tl \l_@@_internal_tl
   }
 \cs_generate_variant:Nn \@@_input_aux:n { o }
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-assign.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-assign.dtx
index 92307fbacf7..142a3c5afac 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-assign.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-assign.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3fp-assign.dtx 4082 2012-08-12 12:14:17Z bruno $
+\GetIdInfo$Id: l3fp-assign.dtx 4129 2012-08-20 20:38:28Z mittelba $
   {L3 Floating-point assignments}
 \documentclass[full]{l3doc}
 \begin{document}
@@ -187,7 +187,14 @@
 %   form, starting with |>|, and displays the rest.
 %    \begin{macrocode}
 \cs_new_protected:Npn \fp_show:N #1
-  { \__msg_show_variable:x { > \fp_to_tl:N #1 } }
+  {
+    \fp_if_exist:NTF #1
+      { \__msg_show_variable:x { > \fp_to_tl:N #1 } }
+      {
+        \__msg_kernel_error:nnx { kernel } { variable-not-defined }
+          { \token_to_str:N #1 }
+      }
+  }
 \cs_new_protected:Npn \fp_show:n #1
   { \__msg_show_variable:x { > \fp_to_tl:n {#1} } }
 \cs_generate_variant:Nn \fp_show:N { c }
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-aux.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-aux.dtx
index 2a26c63ada5..74bacd5d9d8 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-aux.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-aux.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3fp-aux.dtx 4089 2012-08-14 04:52:20Z bruno $
+\GetIdInfo$Id: l3fp-aux.dtx 4151 2012-08-28 11:51:52Z bruno $
   {L3 Floating-point support functions}
 \documentclass[full]{l3doc}
 \begin{document}
@@ -210,7 +210,7 @@
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\c_@@_max_exponent_int}
+% \begin{variable}[int]{\c_@@_max_exponent_int}
 %   Normal floating point numbers have an exponent at most
 %   \texttt{max_exponent} in absolute value.  Larger numbers are rounded
 %   to $\pm\infty$.  Smaller numbers are subnormal (not implemented yet),
@@ -325,7 +325,7 @@
 %   \cs{exp_after:wN}) or \texttt{f}-expansion, and leaves the floating
 %   point number unchanged.
 %
-%   We first distinguish normal floating points, which have a mantissa,
+%   We first distinguish normal floating points, which have a significand,
 %   from the much simpler special floating points.
 %    \begin{macrocode}
 \cs_new:Npn \@@_exp_after_o:w \s_@@ \@@_chk:w #1
@@ -464,8 +464,8 @@
 % provide different sets of packing functions and shifts, depending on
 % ranges of input.
 %
-% \begin{macro}[int, EXP]{\@@_pack:NNNNNw}
-% \begin{variable}
+% \begin{macro}[int, EXP]{\@@_pack:NNNNNw, \@@_pack:NNNNNwn}
+% \begin{variable}[int]
 %   {
 %     \c_@@_trailing_shift_int ,
 %     \c_@@_middle_shift_int   ,
@@ -473,18 +473,21 @@
 %   }
 %   This set of shifts allows for computations involving results in the
 %   range $[-4\cdot 10^{8}, 5\cdot 10^{8}-1]$.  Shifted values all have
-%   exactly $9$ digits.
+%   exactly $9$ digits.  The \cs{@@_pack:NNNNNwn} function brings a
+%   braced \meta{continuation} up through the levels of expansion.
 %    \begin{macrocode}
 \int_const:Nn \c_@@_leading_shift_int  { - 5 0000 }
 \int_const:Nn \c_@@_middle_shift_int   { 5 0000 *  9999 }
 \int_const:Nn \c_@@_trailing_shift_int { 5 0000 * 10000 }
 \cs_new:Npn \@@_pack:NNNNNw #1 #2#3#4#5 #6; { + #1#2#3#4#5 ; {#6} }
+\cs_new:Npn \@@_pack:NNNNNwn #1 #2#3#4#5 #6; #7
+  { + #1#2#3#4#5 ; {#7} {#6} }
 %    \end{macrocode}
 % \end{variable}
 % \end{macro}
 %
-% \begin{macro}[int, EXP]{\@@_pack_big:NNNNNNw}
-% \begin{variable}
+% \begin{macro}[int, EXP]{\@@_pack_big:NNNNNNw, \@@_pack_big:NNNNNNwn}
+% \begin{variable}[int]
 %   {
 %     \c_@@_big_trailing_shift_int ,
 %     \c_@@_big_middle_shift_int   ,
@@ -502,12 +505,14 @@
 \int_const:Nn \c_@@_big_trailing_shift_int { 15 2374 * 10000 }
 \cs_new:Npn \@@_pack_big:NNNNNNw #1#2 #3#4#5#6 #7;
   { + #1#2#3#4#5#6 ; {#7} }
+\cs_new:Npn \@@_pack_big:NNNNNNwn #1#2 #3#4#5#6 #7; #8
+  { + #1#2#3#4#5#6 ; {#8} {#7} }
 %    \end{macrocode}
 % \end{variable}
 % \end{macro}
 %
 % \begin{macro}[int, EXP]{\@@_pack_Bigg:NNNNNNw}
-% \begin{variable}
+% \begin{variable}[int]
 %   {
 %     \c_@@_Bigg_trailing_shift_int ,
 %     \c_@@_Bigg_middle_shift_int   ,
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx
index 591ccf5615e..22c72c7b482 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3fp-basics.dtx 4089 2012-08-14 04:52:20Z bruno $
+\GetIdInfo$Id: l3fp-basics.dtx 4151 2012-08-28 11:51:52Z bruno $
   {L3 Floating-point arithmetic}
 \documentclass[full]{l3doc}
 \begin{document}
@@ -97,7 +97,7 @@
 %     \@@_basics_pack_high:NNNNNw,
 %     \@@_basics_pack_high_carry:w
 %   }
-%   Addition and multiplication of mantissas are done in two steps:
+%   Addition and multiplication of significands are done in two steps:
 %   first compute a (more or less) exact result, then round and pack
 %   digits in the final (braced) form.  These functions take care of the
 %   packing, with special attention given to the case where rounding has
@@ -166,8 +166,8 @@
 %     detect an invalid operation in the case of $\infty - \infty$;
 %   \item for normal floating point numbers, compare the signs;
 %   \item to add two floating point numbers of the same sign or of
-%     opposite signs, shift the mantissa of the smaller one to match the
-%     bigger one, perform the addition or subtraction of mantissas,
+%     opposite signs, shift the significand of the smaller one to match the
+%     bigger one, perform the addition or subtraction of significands,
 %     check for a carry, round, and pack using the
 %     |\__fp_basics_pack_...| functions.
 % \end{itemize}
@@ -332,7 +332,7 @@
 %   the result, and the \meta{final sign} are then given to
 %   \cs{@@_sanitize:Nw} which checks for overflow.  The exponent is
 %   computed as the largest exponent |#2| or |#5|, incremented if there
-%   is a carry.  To add the mantissas, we decimate the smaller number by
+%   is a carry.  To add the significands, we decimate the smaller number by
 %   the difference between the exponents.  This is done by
 %   \cs{@@_add_big_i:wNww} or \cs{@@_add_big_ii:wNww}.  We need to bring
 %   the final sign with us in the midst of the calculation to round
@@ -361,13 +361,13 @@
 %     \cs{@@_add_big_i_o:wNww} \meta{shift} |;| \meta{final sign}
 %       \meta{body_1} |;| \meta{body_2} |;|
 %   \end{quote}
-%   Shift the mantissa of the small number, then add with
-%   \cs{@@_add_mantissa_o:NnnwnnnnN}.
+%   Shift the significand of the small number, then add with
+%   \cs{@@_add_significand_o:NnnwnnnnN}.
 %    \begin{macrocode}
 \cs_new:Npn \@@_add_big_i_o:wNww #1; #2 #3; #4;
   {
     \@@_decimate:nNnnnn {#1}
-      \@@_add_mantissa_o:NnnwnnnnN
+      \@@_add_significand_o:NnnwnnnnN
       #4
     #3
     #2
@@ -375,7 +375,7 @@
 \cs_new:Npn \@@_add_big_ii_o:wNww #1; #2 #3; #4;
   {
     \@@_decimate:nNnnnn {#1}
-      \@@_add_mantissa_o:NnnwnnnnN
+      \@@_add_significand_o:NnnwnnnnN
       #3
     #4
     #2
@@ -384,11 +384,11 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[aux, rEXP]{\@@_add_mantissa_o:NnnwnnnnN}
+% \begin{macro}[aux, rEXP]{\@@_add_significand_o:NnnwnnnnN}
 % \begin{macro}[aux, rEXP]
-%   {\@@_add_mantissa_pack:NNNNNNN, \@@_add_mantissa_test_o:N}
+%   {\@@_add_significand_pack:NNNNNNN, \@@_add_significand_test_o:N}
 %   \begin{quote}
-%     \cs{@@_add_mantissa_o:NnnwnnnnN}
+%     \cs{@@_add_significand_o:NnnwnnnnN}
 %       \meta{rounding digit}
 %       \Arg{Y'_1} \Arg{Y'_2} \meta{extra-digits} |;|
 %       \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4}
@@ -403,35 +403,35 @@
 %   give an exact power of $10$, for which it is easy to correct
 %   the result at the end.
 %    \begin{macrocode}
-\cs_new:Npn \@@_add_mantissa_o:NnnwnnnnN #1 #2#3 #4; #5#6#7#8
+\cs_new:Npn \@@_add_significand_o:NnnwnnnnN #1 #2#3 #4; #5#6#7#8
   {
-    \exp_after:wN \@@_add_mantissa_test_o:N
+    \exp_after:wN \@@_add_significand_test_o:N
     \int_use:N \__int_eval:w 1#5#6 + #2
-      \exp_after:wN \@@_add_mantissa_pack:NNNNNNN
+      \exp_after:wN \@@_add_significand_pack:NNNNNNN
       \int_use:N \__int_eval:w 1#7#8 + #3 ; #1
   }
-\cs_new:Npn \@@_add_mantissa_pack:NNNNNNN #1 #2#3#4#5#6#7
+\cs_new:Npn \@@_add_significand_pack:NNNNNNN #1 #2#3#4#5#6#7
   {
     \if_meaning:w 2 #1
       + \c_one
     \fi:
     ; #2 #3 #4 #5 #6 #7 ;
   }
-\cs_new:Npn \@@_add_mantissa_test_o:N #1
+\cs_new:Npn \@@_add_significand_test_o:N #1
   {
     \if_meaning:w 2 #1
-      \exp_after:wN \@@_add_mantissa_carry_o:wwwNN
+      \exp_after:wN \@@_add_significand_carry_o:wwwNN
     \else:
-      \exp_after:wN \@@_add_mantissa_no_carry_o:wwwNN
+      \exp_after:wN \@@_add_significand_no_carry_o:wwwNN
     \fi:
   }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[aux, rEXP]{\@@_add_mantissa_no_carry_o:wwwNN}
+% \begin{macro}[aux, rEXP]{\@@_add_significand_no_carry_o:wwwNN}
 %   \begin{quote}
-%     \cs{@@_add_mantissa_no_carry_o:wwwNN}
+%     \cs{@@_add_significand_no_carry_o:wwwNN}
 %       \meta{8d} |;| \meta{6d} |;| \meta{2d} |;|
 %       \meta{rounding digit} \meta{sign}
 %   \end{quote}
@@ -439,7 +439,7 @@
 %   packing function \cs{@@_basics_pack_high:NNNNNw} takes care of the
 %   case where rounding brings a carry.
 %    \begin{macrocode}
-\cs_new:Npn \@@_add_mantissa_no_carry_o:wwwNN
+\cs_new:Npn \@@_add_significand_no_carry_o:wwwNN
     #1; #2; #3#4 ; #5#6
   {
     \exp_after:wN \@@_basics_pack_high:NNNNNw
@@ -452,16 +452,16 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux, rEXP]{\@@_add_mantissa_carry_o:wwwNN}
+% \begin{macro}[aux, rEXP]{\@@_add_significand_carry_o:wwwNN}
 %   \begin{quote}
-%     \cs{@@_add_mantissa_carry_o:wwwNN}
+%     \cs{@@_add_significand_carry_o:wwwNN}
 %       \meta{8d} |;| \meta{6d} |;| \meta{2d} |;|
 %       \meta{rounding digit} \meta{sign}
 %   \end{quote}
 %   The case where there is a carry is very similar.  Rounding can even
 %   raise the first digit from $1$ to $2$, but we don't care.
 %    \begin{macrocode}
-\cs_new:Npn \@@_add_mantissa_carry_o:wwwNN
+\cs_new:Npn \@@_add_significand_carry_o:wwwNN
     #1; #2; #3#4; #5#6
   {
     + \c_one
@@ -490,7 +490,7 @@
 %   \end{quote}
 %   Rounding properly in some modes requires to know what the sign of
 %   the result will be.  Thus, we start by comparing the exponents and
-%   mantissas.  If the numbers coincide, return zero.  If the second
+%   significands.  If the numbers coincide, return zero.  If the second
 %   number is larger, swap the numbers and call
 %   \cs{@@_sub_npos_i_o:Nnwnw} with the opposite of \meta{sign_1}.
 %    \begin{macrocode}
@@ -524,7 +524,7 @@
 %   and may be decreased if the two numbers are very close.  If the two
 %   numbers have the same exponent, call the \texttt{near} auxiliary.
 %   Otherwise, decimate $y$, then call the \texttt{far} auxiliary to
-%   evaluate the difference between the two mantissas.  Note that we
+%   evaluate the difference between the two significands.  Note that we
 %   decimate by $1$ less than one could expect.
 %    \begin{macrocode}
 \cs_new:Npn \@@_sub_npos_i_o:Nnwnw #1 #2#3; #4#5;
@@ -650,7 +650,7 @@
 %   and semi-colon delimiters to allow the \texttt{not_far} auxiliary to
 %   grab each piece individually, the \texttt{very_far} auxiliary to use
 %   \cs{@@_pack_eight:wNNNNNNNN}, and the \texttt{quite_far} to ignore
-%   the mantissas easily (using the |;| delimiter).
+%   the significands easily (using the |;| delimiter).
 %    \begin{macrocode}
 \cs_new:Npn \@@_sub_back_far_o:NnnwnnnnN #1 #2#3 #4; #5#6#7#8
   {
@@ -738,7 +738,7 @@
 % \begin{macro}[aux, EXP]{\@@_sub_back_very_far_ii_o:nnNwwNN}
 %   The case where $x-y$ and $x$ have the same exponent is a bit more
 %   tricky, mostly because it cannot reuse the same auxiliaries.  Shift
-%   the $y$~mantissa by adding a leading~$0$.  Then the logic is similar
+%   the $y$~significand by adding a leading~$0$.  Then the logic is similar
 %   to the \texttt{not_far} functions above.  Rounding is a bit more
 %   complicated: we have two \meta{rounding} digits |#3| and |#6| (from
 %   the decimation, and from the new shift) to take into account, and
@@ -869,9 +869,9 @@
 %   After the computation, \cs{@@_sanitize:Nw} checks for overflow or
 %   underflow.  As we did for addition, \cs{__int_eval:w} computes the
 %   exponent, catching any shift coming from the computation in the
-%   mantissa.  The \meta{final sign} is needed to do the rounding
-%   properly in the mantissa computation.  We setup the post-expansion
-%   here, triggered by \cs{@@_mul_mantissa_o:nnnnNnnnn}.
+%   significand.  The \meta{final sign} is needed to do the rounding
+%   properly in the significand computation.  We setup the post-expansion
+%   here, triggered by \cs{@@_mul_significand_o:nnnnNnnnn}.
 %    \begin{macrocode}
 \cs_new:Npn \@@_mul_npos_o:Nww
     #1 \s_@@ \@@_chk:w #2 #3 #4 #5 ; \s_@@ \@@_chk:w #6 #7 #8 #9 ;
@@ -880,21 +880,21 @@
     \exp_after:wN #1
     \int_use:N \__int_eval:w
       #4 + #8
-      \@@_mul_mantissa_o:nnnnNnnnn #5 #1 #9
+      \@@_mul_significand_o:nnnnNnnnn #5 #1 #9
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux, rEXP]{\@@_mul_mantissa_o:nnnnNnnnn}
+% \begin{macro}[aux, rEXP]{\@@_mul_significand_o:nnnnNnnnn}
 % \begin{macro}[aux, EXP]
-%   {\@@_mul_mantissa_drop:NNNNNw, \@@_mul_mantissa_keep:NNNNNw}
+%   {\@@_mul_significand_drop:NNNNNw, \@@_mul_significand_keep:NNNNNw}
 %   \begin{quote}
-%     \cs{@@_mul_mantissa_o:nnnnNnnnn}
+%     \cs{@@_mul_significand_o:nnnnNnnnn}
 %       \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \meta{sign}
 %       \Arg{Y_1} \Arg{Y_2} \Arg{Y_3} \Arg{Y_4}
 %   \end{quote}
 %   Note the three semicolons at the end of the definition.  One is for
-%   the last \cs{@@_mul_mantissa_drop:NNNNNw}; one is for
+%   the last \cs{@@_mul_significand_drop:NNNNNw}; one is for
 %   \cs{@@_round_digit:Nw} later on; and one, preceeded by
 %   \cs{exp_after:wN}, which is correctly expanded (within an
 %   \cs{__int_eval:w}), is used by \cs{@@_basics_pack_low:NNNNNw}.
@@ -909,36 +909,36 @@
 %   known, and we can do the rounding within yet another set of
 %   \cs{__int_eval:w}.
 %    \begin{macrocode}
-\cs_new:Npn \@@_mul_mantissa_o:nnnnNnnnn #1#2#3#4 #5 #6#7#8#9
+\cs_new:Npn \@@_mul_significand_o:nnnnNnnnn #1#2#3#4 #5 #6#7#8#9
   {
-    \exp_after:wN \@@_mul_mantissa_test_f:NNN
+    \exp_after:wN \@@_mul_significand_test_f:NNN
     \exp_after:wN #5
     \int_use:N \__int_eval:w 99990000 + #1*#6 +
-      \exp_after:wN \@@_mul_mantissa_keep:NNNNNw
+      \exp_after:wN \@@_mul_significand_keep:NNNNNw
       \int_use:N \__int_eval:w 99990000 + #1*#7 + #2*#6 +
-        \exp_after:wN \@@_mul_mantissa_keep:NNNNNw
+        \exp_after:wN \@@_mul_significand_keep:NNNNNw
         \int_use:N \__int_eval:w 99990000 + #1*#8 + #2*#7 + #3*#6 +
-          \exp_after:wN \@@_mul_mantissa_drop:NNNNNw
+          \exp_after:wN \@@_mul_significand_drop:NNNNNw
           \int_use:N \__int_eval:w  99990000 + #1*#9 + #2*#8 + #3*#7 + #4*#6 +
-            \exp_after:wN \@@_mul_mantissa_drop:NNNNNw
+            \exp_after:wN \@@_mul_significand_drop:NNNNNw
             \int_use:N \__int_eval:w  99990000 + #2*#9 + #3*#8 + #4*#7 +
-              \exp_after:wN \@@_mul_mantissa_drop:NNNNNw
+              \exp_after:wN \@@_mul_significand_drop:NNNNNw
               \int_use:N \__int_eval:w  99990000 + #3*#9 + #4*#8 +
-                \exp_after:wN \@@_mul_mantissa_drop:NNNNNw
+                \exp_after:wN \@@_mul_significand_drop:NNNNNw
                 \int_use:N \__int_eval:w 100000000 + #4*#9 ;
     ; \exp_after:wN ;
   }
-\cs_new:Npn \@@_mul_mantissa_drop:NNNNNw #1#2#3#4#5 #6;
+\cs_new:Npn \@@_mul_significand_drop:NNNNNw #1#2#3#4#5 #6;
   { #1#2#3#4#5 ; + #6 }
-\cs_new:Npn \@@_mul_mantissa_keep:NNNNNw #1#2#3#4#5 #6;
+\cs_new:Npn \@@_mul_significand_keep:NNNNNw #1#2#3#4#5 #6;
   { #1#2#3#4#5 ; #6 ; }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[aux, rEXP]{\@@_mul_mantissa_test_f:NNN}
+% \begin{macro}[aux, rEXP]{\@@_mul_significand_test_f:NNN}
 %   \begin{quote}
-%     \cs{@@_mul_mantissa_test_f:NNN} \meta{sign} |1|
+%     \cs{@@_mul_significand_test_f:NNN} \meta{sign} |1|
 %       \meta{digits 1--8} |;| \meta{digits 9--12} |;| \meta{digits 13--16} |;|
 %       |+| \meta{digits 17--20} |+| \meta{digits 21--24}
 %       |+| \meta{digits 25--28} |+| \meta{digits 29--32} |;|
@@ -950,19 +950,19 @@
 %   is zero, we care about digits $17$ and $18$, and whether further
 %   digits are zero.
 %    \begin{macrocode}
-\cs_new:Npn \@@_mul_mantissa_test_f:NNN #1 #2 #3
+\cs_new:Npn \@@_mul_significand_test_f:NNN #1 #2 #3
   {
     \if_meaning:w 0 #3
-      \exp_after:wN \@@_mul_mantissa_small_f:NNwwwN
+      \exp_after:wN \@@_mul_significand_small_f:NNwwwN
     \else:
-      \exp_after:wN \@@_mul_mantissa_large_f:NwwNNNN
+      \exp_after:wN \@@_mul_significand_large_f:NwwNNNN
     \fi:
     #1 #3
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux, EXP]{\@@_mul_mantissa_large_f:NwwNNNN}
+% \begin{macro}[aux, EXP]{\@@_mul_significand_large_f:NwwNNNN}
 %   In this branch, \meta{digit 1} is non-zero. The result is thus
 %   \meta{digits 1--16}, plus some rounding which depends on the digits
 %   $16$, $17$, and whether all subsequent digits are zero or not.
@@ -970,7 +970,7 @@
 %   integer expression), and replaces it by a \meta{rounding digit},
 %   suitable for \cs{@@_round:NNN}.
 %    \begin{macrocode}
-\cs_new:Npn \@@_mul_mantissa_large_f:NwwNNNN #1 #2; #3; #4#5#6#7; +
+\cs_new:Npn \@@_mul_significand_large_f:NwwNNNN #1 #2; #3; #4#5#6#7; +
   {
     \exp_after:wN \@@_basics_pack_high:NNNNNw
     \int_use:N \__int_eval:w 1#2
@@ -984,7 +984,7 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux, rEXP]{\@@_mul_mantissa_small_f:NNwwwN}
+% \begin{macro}[aux, rEXP]{\@@_mul_significand_small_f:NNwwwN}
 %   In this branch, \meta{digit 1} is zero. Our result will thus be
 %   \meta{digits 2--17}, plus some rounding which depends on the digits
 %   $17$, $18$, and whether all subsequent digits are zero or not.
@@ -992,7 +992,7 @@
 %   \texttt{small_pack} auxiliary, by the next digit, to form a $9$
 %   digit number.
 %    \begin{macrocode}
-\cs_new:Npn \@@_mul_mantissa_small_f:NNwwwN #1 #2#3; #4#5; #6; + #7
+\cs_new:Npn \@@_mul_significand_small_f:NNwwwN #1 #2#3; #4#5; #6; + #7
   {
     - \c_one
     \exp_after:wN \@@_basics_pack_high:NNNNNw
@@ -1056,7 +1056,7 @@
 %   \cs{@@_sanitize:Nw} checks for overflow or underflow; we provide it
 %   with the \meta{final sign}, and an integer expression in which we
 %   compute the exponent.  We set up the arguments of
-%   \cs{@@_div_mantissa_i_o:wnnw}, namely an integer \meta{y} obtained
+%   \cs{@@_div_significand_i_o:wnnw}, namely an integer \meta{y} obtained
 %   by adding $1$ to the first $5$ digits of $Z$ (explanation given soon
 %   below), then the four \Arg{A_{i}}, then the four \Arg{Z_{i}}, a
 %   semi-colon, and the \meta{final sign}, used for rounding at the end.
@@ -1068,7 +1068,7 @@
     \exp_after:wN #1
     \int_use:N \__int_eval:w
       #3 - #6
-      \exp_after:wN \@@_div_mantissa_i_o:wnnw
+      \exp_after:wN \@@_div_significand_i_o:wnnw
         \int_use:N \__int_eval:w #7 \use_i:nnnn #8 + \c_one ;
         #4
         {#7}{#8}#9 ;
@@ -1246,46 +1246,46 @@
 % In each case, we know how to round to an integer, depending on the
 % parity of $P$, and the rounding mode.
 %
-% \subsubsection{Implementing the mantissa division}
+% \subsubsection{Implementing the significand division}
 %
-% \begin{macro}[aux, rEXP]{\@@_div_mantissa_i_o:wnnw}
+% \begin{macro}[aux, rEXP]{\@@_div_significand_i_o:wnnw}
 %   \begin{quote}
-%     \cs{@@_div_mantissa_i_o:wnnw} \meta{y} |;|
+%     \cs{@@_div_significand_i_o:wnnw} \meta{y} |;|
 %       \Arg{A_1} \Arg{A_2} \Arg{A_3} \Arg{A_4}
 %       \Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} |;| \meta{sign}
 %   \end{quote}
 %   Compute $10^{6} + Q_{A}$ (a $7$~digit number thanks to the shift),
 %   unbrace \meta{A_1} and \meta{A_2}, and prepare the
 %   \meta{continuation} arguments for $4$ consecutive calls to
-%   \cs{@@_div_mantissa_calc:wwnnnnnnn}.  Each of these calls will need
+%   \cs{@@_div_significand_calc:wwnnnnnnn}.  Each of these calls will need
 %   \meta{y} (|#1|), and it turns out that we need post-expansion there,
 %   hence the \cs{__int_value:w}.  Here, |#4| is six brace groups, which
 %   give the six first |n|-type arguments of the \texttt{calc} function.
 %    \begin{macrocode}
-\cs_new:Npn \@@_div_mantissa_i_o:wnnw #1 ; #2#3 #4 ;
+\cs_new:Npn \@@_div_significand_i_o:wnnw #1 ; #2#3 #4 ;
   {
-    \exp_after:wN \@@_div_mantissa_test_o:w
+    \exp_after:wN \@@_div_significand_test_o:w
     \int_use:N \__int_eval:w
-      \exp_after:wN \@@_div_mantissa_calc:wwnnnnnnn
+      \exp_after:wN \@@_div_significand_calc:wwnnnnnnn
       \int_use:N \__int_eval:w 999999 + #2 #3 0 / #1 ;
         #2 #3 ;
         #4
-        { \exp_after:wN \@@_div_mantissa_ii:wwn \__int_value:w #1 }
-        { \exp_after:wN \@@_div_mantissa_ii:wwn \__int_value:w #1 }
-        { \exp_after:wN \@@_div_mantissa_ii:wwn \__int_value:w #1 }
-        { \exp_after:wN \@@_div_mantissa_iii:wwnnnnn \__int_value:w #1 }
+        { \exp_after:wN \@@_div_significand_ii:wwn \__int_value:w #1 }
+        { \exp_after:wN \@@_div_significand_ii:wwn \__int_value:w #1 }
+        { \exp_after:wN \@@_div_significand_ii:wwn \__int_value:w #1 }
+        { \exp_after:wN \@@_div_significand_iii:wwnnnnn \__int_value:w #1 }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[int, rEXP]{\@@_div_mantissa_calc:wwnnnnnnn}
+% \begin{macro}[int, rEXP]{\@@_div_significand_calc:wwnnnnnnn}
 % \begin{macro}[aux, rEXP]
 %   {
-%     \@@_div_mantissa_calc_i:wwnnnnnnn,
-%     \@@_div_mantissa_calc_ii:wwnnnnnnn,
+%     \@@_div_significand_calc_i:wwnnnnnnn,
+%     \@@_div_significand_calc_ii:wwnnnnnnn,
 %   }
 %   \begin{quote}
-%     \cs{@@_div_mantissa_calc:wwnnnnnnn} \meta{$10^{6}+{}$Q_{A}} |;|
+%     \cs{@@_div_significand_calc:wwnnnnnnn} \meta{$10^{6}+{}$Q_{A}} |;|
 %       \meta{A_1} \meta{A_2} |;| \Arg{A_3} \Arg{A_4}
 %       \Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4}
 %       \Arg{continuation}
@@ -1337,15 +1337,15 @@
 %   which produces totals in the range $[10^{9}, 2.1\cdot 10^{9}]$.  We
 %   are flirting with \TeX{}'s limits once more.
 %    \begin{macrocode}
-\cs_new:Npn \@@_div_mantissa_calc:wwnnnnnnn 1#1
+\cs_new:Npn \@@_div_significand_calc:wwnnnnnnn 1#1
   {
     \if_meaning:w 1 #1
-      \exp_after:wN \@@_div_mantissa_calc_i:wwnnnnnnn
+      \exp_after:wN \@@_div_significand_calc_i:wwnnnnnnn
     \else:
-      \exp_after:wN \@@_div_mantissa_calc_ii:wwnnnnnnn
+      \exp_after:wN \@@_div_significand_calc_ii:wwnnnnnnn
     \fi:
   }
-\cs_new:Npn \@@_div_mantissa_calc_i:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
+\cs_new:Npn \@@_div_significand_calc_i:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
   {
     1 1 #1
     #9 \exp_after:wN ;
@@ -1362,7 +1362,7 @@
             - #1 * #8 ;
     {#5}{#6}{#7}{#8}
   }
-\cs_new:Npn \@@_div_mantissa_calc_ii:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
+\cs_new:Npn \@@_div_significand_calc_ii:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
   {
     1 0 #1
     #9 \exp_after:wN ;
@@ -1383,9 +1383,9 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[aux, EXP]{\@@_div_mantissa_ii:wwn}
+% \begin{macro}[aux, EXP]{\@@_div_significand_ii:wwn}
 %   \begin{quote}
-%     \cs{@@_div_mantissa_ii:wwn} \meta{y} |;|
+%     \cs{@@_div_significand_ii:wwn} \meta{y} |;|
 %       \meta{B_1} |;| \Arg{B_2} \Arg{B_3} \Arg{B_4}
 %       \Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4}
 %       \meta{continuations} \meta{sign}
@@ -1399,19 +1399,19 @@
 %   auxiliary is also used to compute $Q_{C}$ and $Q_{D}$ with the
 %   inputs $C$ and $D$ instead of $B$.
 %    \begin{macrocode}
-\cs_new:Npn \@@_div_mantissa_ii:wwn #1; #2;#3
+\cs_new:Npn \@@_div_significand_ii:wwn #1; #2;#3
   {
-    \exp_after:wN \@@_div_mantissa_pack:NNN
+    \exp_after:wN \@@_div_significand_pack:NNN
     \int_use:N \__int_eval:w
-      \exp_after:wN \@@_div_mantissa_calc:wwnnnnnnn
+      \exp_after:wN \@@_div_significand_calc:wwnnnnnnn
       \int_use:N \__int_eval:w 999999 + #2 #3 0 / #1 ; #2 #3 ;
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux, rEXP]{\@@_div_mantissa_iii:wwnnnnn}
+% \begin{macro}[aux, rEXP]{\@@_div_significand_iii:wwnnnnn}
 %   \begin{quote}
-%     \cs{@@_div_mantissa_iii:wwnnnnn} \meta{y} |;|
+%     \cs{@@_div_significand_iii:wwnnnnn} \meta{y} |;|
 %       \meta{E_1} |;| \Arg{E_2} \Arg{E_3} \Arg{E_4}
 %       \Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \meta{sign}
 %   \end{quote}
@@ -1420,10 +1420,10 @@
 %   add (roughly) $5\cdot P$, which amounts to adding $P/2 \simeq E/Z$
 %   to $Q_{D}$, the appropriate correction from a hypothetical $Q_{E}$.
 %    \begin{macrocode}
-\cs_new:Npn \@@_div_mantissa_iii:wwnnnnn #1; #2;#3#4#5 #6#7
+\cs_new:Npn \@@_div_significand_iii:wwnnnnn #1; #2;#3#4#5 #6#7
   {
     0
-    \exp_after:wN \@@_div_mantissa_iv:wwnnnnnnn
+    \exp_after:wN \@@_div_significand_iv:wwnnnnnnn
     \int_use:N \__int_eval:w (\c_two * #2 #3) / #6 #7 ; % <- P
       #2 ; {#3} {#4} {#5}
       {#6} {#7}
@@ -1433,12 +1433,12 @@
 %
 % \begin{macro}[aux, rEXP]
 %   {
-%     \@@_div_mantissa_iv:wwnnnnnnn,
-%     \@@_div_mantissa_v:NNw,
-%     \@@_div_mantissa_vi:Nw
+%     \@@_div_significand_iv:wwnnnnnnn,
+%     \@@_div_significand_v:NNw,
+%     \@@_div_significand_vi:Nw
 %   }
 %   \begin{quote}
-%     \cs{@@_div_mantissa_iv:wwnnnnnnn} \meta{P} |;|
+%     \cs{@@_div_significand_iv:wwnnnnnnn} \meta{P} |;|
 %       \meta{E_1} |;| \Arg{E_2} \Arg{E_3} \Arg{E_4}
 %       \Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \meta{sign}
 %   \end{quote}
@@ -1476,21 +1476,21 @@
 %   expressions explicitly).  $T$ is negative if the first character is
 %   |-|, it is positive if the first character is neither |0| nor |-|.
 %   It is also positive if the first character is |0| and second
-%   argument of \cs{@@_div_mantissa_vi:Nw}, a sum of several terms, is
+%   argument of \cs{@@_div_significand_vi:Nw}, a sum of several terms, is
 %   also zero.  Otherwise, there was an exact agreement: $T = 0$.
 %    \begin{macrocode}
-\cs_new:Npn \@@_div_mantissa_iv:wwnnnnnnn #1; #2;#3#4#5 #6#7#8#9
+\cs_new:Npn \@@_div_significand_iv:wwnnnnnnn #1; #2;#3#4#5 #6#7#8#9
   {
     + \c_five * #1
-    \exp_after:wN \@@_div_mantissa_vi:Nw
+    \exp_after:wN \@@_div_significand_vi:Nw
     \int_use:N \__int_eval:w -20 + 2*#2#3 - #1*#6#7 +
-      \exp_after:wN \@@_div_mantissa_v:NN
+      \exp_after:wN \@@_div_significand_v:NN
       \int_use:N \__int_eval:w 199980 + 2*#4 - #1*#8 +
-        \exp_after:wN \@@_div_mantissa_v:NN
+        \exp_after:wN \@@_div_significand_v:NN
         \int_use:N \__int_eval:w 200000 + 2*#5 - #1*#9 ;
   }
-\cs_new:Npn \@@_div_mantissa_v:NN #1#2 { #1#2 \__int_eval_end: + }
-\cs_new:Npn \@@_div_mantissa_vi:Nw #1#2;
+\cs_new:Npn \@@_div_significand_v:NN #1#2 { #1#2 \__int_eval_end: + }
+\cs_new:Npn \@@_div_significand_vi:Nw #1#2;
   {
     \if_meaning:w 0 #1
       \if_int_compare:w \__int_eval:w #2 > \c_zero + \c_one \fi:
@@ -1502,15 +1502,15 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux, EXP]{\@@_div_mantissa_pack:NNN}
+% \begin{macro}[aux, EXP]{\@@_div_significand_pack:NNN}
 %   At this stage, we are in the following situation: \TeX{} is in the
 %   process of expanding several integer expressions, thus functions at
 %   the bottom expand before those above.
 %   \begin{quote}
-%     \cs{@@_div_mantissa_test_o:w} $10^{6} + Q_{A}$
-%     \cs{@@_div_mantissa_pack:NNN} $10^{6} + Q_{B}$
-%     \cs{@@_div_mantissa_pack:NNN} $10^{6} + Q_{C}$
-%     \cs{@@_div_mantissa_pack:NNN}
+%     \cs{@@_div_significand_test_o:w} $10^{6} + Q_{A}$
+%     \cs{@@_div_significand_pack:NNN} $10^{6} + Q_{B}$
+%     \cs{@@_div_significand_pack:NNN} $10^{6} + Q_{C}$
+%     \cs{@@_div_significand_pack:NNN}
 %     $10^{7} + 10\cdot Q_{D} + 5 \cdot P + \varepsilon$ |;| \meta{sign}
 %   \end{quote}
 %   Here, $\varepsilon = \operatorname{sign}(T)$ is $0$ in case $2E=PZ$,
@@ -1520,13 +1520,13 @@
 %   nothing special: it removes the $10^{6}$ and carries two digits (for
 %   the $10^{5}$'s and the $10^{4}$'s).
 %    \begin{macrocode}
-\cs_new:Npn \@@_div_mantissa_pack:NNN 1 #1 #2 { + #1 #2 ; }
+\cs_new:Npn \@@_div_significand_pack:NNN 1 #1 #2 { + #1 #2 ; }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux, rEXP]{\@@_div_mantissa_test_o:w}
+% \begin{macro}[aux, rEXP]{\@@_div_significand_test_o:w}
 %   \begin{quote}
-%     \cs{@@_div_mantissa_test_o:w} |1| |0| \meta{5d} |;|
+%     \cs{@@_div_significand_test_o:w} |1| |0| \meta{5d} |;|
 %     ~~\meta{4d} |;| \meta{4d} |;| \meta{5d} |;| \meta{sign}
 %   \end{quote}
 %   The reason we know that the first two digits are |1| and |0| is that
@@ -1538,28 +1538,28 @@
 %   It is now time to round. This depends on how many digits the final
 %   result will have.
 %    \begin{macrocode}
-\cs_new:Npn \@@_div_mantissa_test_o:w 10 #1
+\cs_new:Npn \@@_div_significand_test_o:w 10 #1
   {
     \if_meaning:w 0 #1
-      \exp_after:wN \@@_div_mantissa_small_o:wwwNNNNwN
+      \exp_after:wN \@@_div_significand_small_o:wwwNNNNwN
     \else:
-      \exp_after:wN \@@_div_mantissa_large_o:wwwNNNNwN
+      \exp_after:wN \@@_div_significand_large_o:wwwNNNNwN
     \fi:
     #1
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux, EXP]{\@@_div_mantissa_small_o:wwwNNNNwN}
+% \begin{macro}[aux, EXP]{\@@_div_significand_small_o:wwwNNNNwN}
 %   \begin{quote}
-%     \cs{@@_div_mantissa_small_o:wwwNNNNwN} |0| \meta{4d} |;|
+%     \cs{@@_div_significand_small_o:wwwNNNNwN} |0| \meta{4d} |;|
 %     ~~\meta{4d} |;| \meta{4d} |;| \meta{5d} |;| \meta{final sign}
 %   \end{quote}
 %   Standard use of \cs{@@_basics_pack_low:NNNNNw} and
 %   \cs{@@_basics_pack_high:NNNNNw}.  We finally get to use the
 %   \meta{final sign} which has been sitting there for a while.
 %    \begin{macrocode}
-\cs_new:Npn \@@_div_mantissa_small_o:wwwNNNNwN
+\cs_new:Npn \@@_div_significand_small_o:wwwNNNNwN
     0 #1; #2; #3; #4#5#6#7#8; #9
   {
     \exp_after:wN \@@_basics_pack_high:NNNNNw
@@ -1572,9 +1572,9 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux, rEXP]{\@@_div_mantissa_large_o:wwwNNNNwN}
+% \begin{macro}[aux, rEXP]{\@@_div_significand_large_o:wwwNNNNwN}
 %   \begin{quote}
-%     \cs{@@_div_mantissa_large_o:wwwNNNNwN} \meta{5d} |;|
+%     \cs{@@_div_significand_large_o:wwwNNNNwN} \meta{5d} |;|
 %     ~~\meta{4d} |;| \meta{4d} |;| \meta{5d} |;| \meta{sign}
 %   \end{quote}
 %   We know that the final result cannot reach $10$, hence |1#1#2|,
@@ -1582,7 +1582,7 @@
 %   $2\cdot 10^{9}$.  For rounding, we build the \meta{rounding digit}
 %   from the last two of our $18$ digits.
 %    \begin{macrocode}
-\cs_new:Npn \@@_div_mantissa_large_o:wwwNNNNwN
+\cs_new:Npn \@@_div_significand_large_o:wwwNNNNwN
     #1; #2; #3; #4#5#6#7#8; #9
   {
     + \c_one
@@ -1603,15 +1603,17 @@
 %
 % \begin{macro}[int, EXP]{\@@_neg_o:w}
 %   This function flips the sign of the \meta{floating point} and
-%   expands after it in the input stream, just like \cs{@@_+_o:ww} etc.
+%   expands after it in the input stream, just like \cs{@@_+_o:ww}
+%   \emph{etc.}  We add a hook used by \pkg{l3fp-expo}: anything before
+%   \cs{s_@@} is ignored.
 %    \begin{macrocode}
-\cs_new:Npn \@@_neg_o:w \s_@@ \@@_chk:w #1 #2
+\cs_new:Npn \@@_neg_o:w #1 \s_@@ \@@_chk:w #2 #3
   {
     \exp_after:wN \@@_exp_after_o:w
     \exp_after:wN \s_@@
     \exp_after:wN \@@_chk:w
-    \exp_after:wN #1
-    \int_use:N \__int_eval:w \c_two - #2 \__int_eval_end:
+    \exp_after:wN #2
+    \int_use:N \__int_eval:w \c_two - #3 \__int_eval_end:
   }
 %    \end{macrocode}
 % \end{macro}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-convert.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-convert.dtx
index 8f0c2848ea4..0135da6304b 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-convert.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-convert.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3fp-convert.dtx 4090 2012-08-14 07:57:01Z joseph $
+\GetIdInfo$Id: l3fp-convert.dtx 4129 2012-08-20 20:38:28Z mittelba $
   {L3 Floating-point conversion}
 \documentclass[full]{l3doc}
 \begin{document}
@@ -469,6 +469,31 @@
 %    \end{macrocode}
 % \end{macro}
 %
+% \subsection{Convert an array of floating points to a comma list}
+%
+% \begin{macro}[int, EXP]{\@@_array_to_clist:n}
+% \begin{macro}[aux, EXP]{\@@_array_to_clist_i:wwww, \@@_array_to_clist_ii:ww}
+%   Converts an array of floating point numbers to a comma-list.
+%    \begin{macrocode}
+\cs_new:Npn \@@_array_to_clist:n #1
+  {
+    \@@_array_to_clist_i:wwww ;
+      #1
+      \@@_array_to_clist_ii:ww \s_@@ ; @
+      ; , ~ , ~ @ \s_stop
+  }
+\cs_new:Npn \@@_array_to_clist_i:wwww #1; #2 \s_@@ #3; #4 @
+  {
+    #2
+    \exp_after:wN \@@_array_to_clist_i:wwww
+    \tex_romannumeral:D -`0 \@@_to_tl:w \s_@@ #3 ; ;
+    #4 , ~ #1 @
+  }
+\cs_new:Npn \@@_array_to_clist_ii:ww #1 ; , ~ , ~ #2 @ #3 \s_stop {#2}
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
 %    \begin{macrocode}
 %</initex|package>
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx
index fee1b90ed58..f228794e7a4 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3fp-expo.dtx 4089 2012-08-14 04:52:20Z bruno $
+\GetIdInfo$Id: l3fp-expo.dtx 4151 2012-08-28 11:51:52Z bruno $
   {L3 Floating-point exponential-related functions}
 \documentclass[full]{l3doc}
 \begin{document}
@@ -324,7 +324,7 @@
 %    \begin{macrocode}
 \cs_new:Npn \@@_ln_x_iv:wnnnnnnnn #1; #2#3#4#5 #6#7#8#9
   {
-    \exp_after:wN \@@_div_mantissa_pack:NNN
+    \exp_after:wN \@@_div_significand_pack:NNN
     \int_use:N \__int_eval:w
     \@@_ln_div_i:w #1 ;
       #6 #7 ; {#8} {#9}
@@ -337,20 +337,20 @@
   }
 \cs_new:Npn \@@_ln_div_i:w #1;
   {
-    \exp_after:wN \@@_div_mantissa_calc:wwnnnnnnn
+    \exp_after:wN \@@_div_significand_calc:wwnnnnnnn
     \int_use:N \__int_eval:w 999999 + 2 0000 0000 / #1 ; % Q1
   }
 \cs_new:Npn \@@_ln_div_ii:wwn #1; #2;#3 % y; B1;B2 <- for k=1
   {
-    \exp_after:wN \@@_div_mantissa_pack:NNN
+    \exp_after:wN \@@_div_significand_pack:NNN
     \int_use:N \__int_eval:w
-      \exp_after:wN \@@_div_mantissa_calc:wwnnnnnnn
+      \exp_after:wN \@@_div_significand_calc:wwnnnnnnn
       \int_use:N \__int_eval:w 999999 + #2 #3 / #1 ; % Q2
       #2 #3 ;
   }
 \cs_new:Npn \@@_ln_div_vi:wwn #1; #2;#3#4#5 #6#7#8#9 %y;F1;F2F3F4x1x2x3x4
   {
-    \exp_after:wN \@@_div_mantissa_pack:NNN
+    \exp_after:wN \@@_div_significand_pack:NNN
     \int_use:N \__int_eval:w 1000000 + #2 #3 / #1 ; % Q6
   }
 %    \end{macrocode}
@@ -360,18 +360,18 @@
 %     result, small enough in all cases.}
 %   \begin{quote}
 %     \cs{@@_ln_div_after:Nw} \meta{fixed tl}
-%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{1}$
-%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{2}$
-%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{3}$
-%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{4}$
-%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{5}$
-%     \cs{@@_div_mantissa_pack:NNN} $10^6 + Q_{6}$ |;|
+%     \cs{@@_div_significand_pack:NNN} $10^6 + Q_{1}$
+%     \cs{@@_div_significand_pack:NNN} $10^6 + Q_{2}$
+%     \cs{@@_div_significand_pack:NNN} $10^6 + Q_{3}$
+%     \cs{@@_div_significand_pack:NNN} $10^6 + Q_{4}$
+%     \cs{@@_div_significand_pack:NNN} $10^6 + Q_{5}$
+%     \cs{@@_div_significand_pack:NNN} $10^6 + Q_{6}$ |;|
 %     \meta{exponent} |;| \meta{continuation}
 %   \end{quote}
 %   where \meta{fixed tl} holds the logarithm of a number
 %   in $[1,10]$, and \meta{exponent} is
 %   the exponent. Also, the expansion is done backwards. Then
-%   \cs{@@_div_mantissa_pack:NNN} puts things in the
+%   \cs{@@_div_significand_pack:NNN} puts things in the
 %   correct order to add the $Q_{i}$ together and put semicolons
 %   between each piece. Once those have been expanded, we get
 %   \begin{quote}
@@ -491,7 +491,7 @@
       \@@_ln_Taylor_break:w
     \fi:
     \exp_after:wN \@@_fixed_div_int:wwN \c_@@_one_fixed_tl ; #1;
-    \@@_fixed_add:wwN #2;
+    \@@_fixed_add:wwn #2;
     \@@_fixed_mul:wwn #3;
     {
       \exp_after:wN \@@_ln_Taylor_loop:www
@@ -499,7 +499,7 @@
     }
     #3;
   }
-\cs_new:Npn \@@_ln_Taylor_break:w \fi: #1 \@@_fixed_add:wwN #2#3; #4 ;;
+\cs_new:Npn \@@_ln_Taylor_break:w \fi: #1 \@@_fixed_add:wwn #2#3; #4 ;;
   {
     \fi:
     \exp_after:wN \@@_fixed_mul:wwn
@@ -527,9 +527,9 @@
 \cs_new:Npn \@@_ln_c:NwNw #1 #2; #3
   {
     \if_meaning:w + #1
-      \exp_after:wN \exp_after:wN \exp_after:wN \@@_fixed_sub:wwN
+      \exp_after:wN \exp_after:wN \exp_after:wN \@@_fixed_sub:wwn
     \else:
-      \exp_after:wN \exp_after:wN \exp_after:wN \@@_fixed_add:wwN
+      \exp_after:wN \exp_after:wN \exp_after:wN \@@_fixed_add:wwn
     \fi:
     #3 ; #2 ;
   }
@@ -564,11 +564,11 @@
       \if_int_compare:w #2 > \c_zero
         \exp_after:wN \@@_ln_exponent_small:NNww
         \exp_after:wN 0
-        \exp_after:wN \@@_fixed_sub:wwN \__int_value:w
+        \exp_after:wN \@@_fixed_sub:wwn \__int_value:w
       \else:
         \exp_after:wN \@@_ln_exponent_small:NNww
         \exp_after:wN 2
-        \exp_after:wN \@@_fixed_add:wwN \__int_value:w -
+        \exp_after:wN \@@_fixed_add:wwn \__int_value:w -
       \fi:
     \fi:
     #2; #1;
@@ -580,7 +580,7 @@
 \cs_new:Npn \@@_ln_exponent_one:ww 1; #1;
   {
     \c_zero
-    \exp_after:wN \@@_fixed_sub:wwN \c_@@_ln_x_fixed_tl ; #1;
+    \exp_after:wN \@@_fixed_sub:wwn \c_@@_ln_x_fixed_tl ; #1;
     \@@_fixed_to_float:wN 0
   }
 %    \end{macrocode}
@@ -673,7 +673,7 @@
           }
           #5
           {#4}
-          #2 0
+          #1 #2 0
           \tex_romannumeral:D
         \fi:
       \fi:
@@ -693,8 +693,9 @@
 %   delimited by a semicolon, form a fixed point number, so we pack it
 %   in blocks of $4$ digits.
 %    \begin{macrocode}
-\cs_new:Npn \@@_exp_Taylor:Nnnwn #1#2#3 #4; #5
+\cs_new:Npn \@@_exp_Taylor:Nnnwn #1#2#3 #4; #5 #6
   {
+    #6
     \@@_pack_twice_four:wNNNNNNNN
     \@@_pack_twice_four:wNNNNNNNN
     \@@_pack_twice_four:wNNNNNNNN
@@ -749,7 +750,7 @@
 %   stream (we are currently within an \cs{__int_eval:w}), and keeping
 %   track of a fixed point number, |#1| for the numbered auxiliaries.
 %   Our usage of \cs{if_case:w} is somewhat dirty for optimization:
-%   \TeX{} jumps to the appropriate case, but we then lose the
+%   \TeX{} jumps to the appropriate case, but we then close the
 %   \cs{if_case:w} \enquote{by hand}, using \cs{or:} and \cs{fi:} as
 %   delimiters.
 %    \begin{macrocode}
@@ -860,9 +861,9 @@
     #1;
     \@@_exp_large_after:wwn
   }
-\cs_new:Npn \@@_exp_large_after:wwn #1; #2;
+\cs_new:Npn \@@_exp_large_after:wwn #1; #2; #3
   {
-    \@@_exp_Taylor:Nnnwn ? { } { } 0 #2; {}
+    \@@_exp_Taylor:Nnnwn ? { } { } 0 #2; {} #3
     \@@_fixed_mul:wwn #1;
   }
 %    \end{macrocode}
@@ -942,10 +943,12 @@
 % \begin{macro}[aux, EXP]{\@@_pow_zero_or_inf:ww}
 %   Raising $-0$ or $-\infty$ to \texttt{nan} yields \texttt{nan}.  For
 %   other powers, the result is $+0$ if $0$ is raised to a positive
-%   power or $\infty$ to a negative power, and $+\infty$ otherwise.  We
-%   can thus know the result by comparing the type of $a$ with the sign
-%   of $b$, since those conveniently take the same possible values, $0$
-%   and~$2$.
+%   power or $\infty$ to a negative power, and $+\infty$ otherwise.
+%   Thus, if the type of $a$ and the sign of $b$ coincide, the result
+%   is~$0$, since those conveniently take the same possible values, $0$
+%   and~$2$.  Otherwise, either $a=\pm 0$ with $b<0$ and we have a
+%   division by zero, or $a=\pm\infty$ and $b>0$ and the result is also
+%   $+\infty$, but without any exception.
 %    \begin{macrocode}
 \cs_new:Npn \@@_pow_zero_or_inf:ww \s_@@ \@@_chk:w #1#2; \s_@@ \@@_chk:w #3#4
   {
@@ -954,6 +957,13 @@
     \fi:
     \if_meaning:w #1 #4
       \@@_case_return_o:Nw \c_zero_fp
+    \fi:
+    \if_meaning:w 0 #1
+      \@@_case_use:nw
+        {
+          \@@_division_by_zero_o:NNww \c_inf_fp ^
+            \s_@@ \@@_chk:w #1 #2 ;
+        }
     \else:
       \@@_case_return_o:Nw \c_inf_fp
     \fi:
@@ -986,7 +996,7 @@
       \fi:
       \@@_case_return_o:Nww \c_one_fp
     \fi:
-    \if_case:w #4 ~
+    \if_case:w #4 \exp_stop_f:
     \or:
       \exp_after:wN \@@_pow_npos:Nww
       \exp_after:wN #5
@@ -1028,11 +1038,12 @@
     \exp_after:wN 0
     \__int_value:w
       \if:w #1 \if_int_compare:w #3 > \c_zero 0 \else: 2 \fi:
-        \exp_after:wN \@@_pow_npos_aux:Nnww
+        \exp_after:wN \@@_pow_npos_aux:NNnww
+        \exp_after:wN +
         \exp_after:wN \@@_fixed_to_float:wN
       \else:
-        -
-        \exp_after:wN \@@_pow_npos_aux:Nnww
+        \exp_after:wN \@@_pow_npos_aux:NNnww
+        \exp_after:wN -
         \exp_after:wN \@@_fixed_inv_to_float:wN
       \fi:
       {#3}
@@ -1041,46 +1052,52 @@
 % \end{macro}
 %
 %^^A begin[todo]
-% \begin{macro}[aux, EXP]{\@@_pow_npos_aux:Nnww}
+% \begin{macro}[aux, EXP]{\@@_pow_npos_aux:NNnww}
 %   The first argument is the conversion function from fixed point to
 %   float.  Then comes an exponent and the $4$ brace groups of $x$,
 %   followed by $b$.  Compute $-\ln(x)$.
 %    \begin{macrocode}
-\cs_new:Npn \@@_pow_npos_aux:Nnww #1#2#3#4; \s_@@ \@@_chk:w 1#5#6#7;
+\cs_new:Npn \@@_pow_npos_aux:NNnww #1#2#3#4#5; \s_@@ \@@_chk:w 1#6#7#8;
   {
+    #1
     \__int_eval:w
-      \@@_ln_significand:NNNNnnnN #3#4
-      \@@_pow_exponent:wnN {#2}
-      \@@_fixed_mul:wwn #7 {0000}{0000} ;
-      \@@_pow_B:wwN #6;
-      #1 0 % fixed_to_float:wN
+      \@@_ln_significand:NNNNnnnN #4#5
+      \@@_pow_exponent:wnN {#3}
+      \@@_fixed_mul:wwn #8 {0000}{0000} ;
+      \@@_pow_B:wwN #7;
+      #1 #2 0 % fixed_to_float:wN
   }
 \cs_new:Npn \@@_pow_exponent:wnN #1; #2
   {
     \if_int_compare:w #2 > \c_zero
-      \exp_after:wN \@@_pow_exponent:Nwnnnnnn % n\ln(10) - (-\ln(x))
+      \exp_after:wN \@@_pow_exponent:Nwnnnnnwn % n\ln(10) - (-\ln(x))
       \exp_after:wN +
     \else:
-      \exp_after:wN \@@_pow_exponent:Nwnnnnnn % -( |n|\ln(10) + (-\ln(x)) )
+      \exp_after:wN \@@_pow_exponent:Nwnnnnnwn % -( |n|\ln(10) + (-\ln(x)) )
       \exp_after:wN -
     \fi:
     #2; #1;
   }
-\cs_new:Npn \@@_pow_exponent:Nwnnnnnn #1#2; #3#4#5#6#7#8;
-  { %^^A todo: use that in ln. %^^A todo: log(1.00...) too inaccurate?
-    \exp_after:wN \@@_fixed_mul_after:wwn
-    \int_use:N \__int_eval:w -5 0000
-      \exp_after:wN \@@_fixed_mul_pack:NNNNNw
-      \int_use:N \__int_eval:w 4 9995 0000 #1#2*23025 - #1 #3
-        \exp_after:wN \@@_fixed_mul_pack:NNNNNw
-        \int_use:N \__int_eval:w 4 9995 0000 #1 #2*8509 - #1 #4
-          \exp_after:wN \@@_fixed_mul_pack:NNNNNw
-          \int_use:N \__int_eval:w 4 9995 0000 #1 #2*2994 - #1 #5
-            \exp_after:wN \@@_fixed_mul_pack:NNNNNw
-            \int_use:N \__int_eval:w 4 9995 0000 #1 #2*0456 - #1 #6
-              \exp_after:wN \@@_fixed_mul_pack:NNNNNw
-              \int_use:N \__int_eval:w 5 0000 0000 #1 #2*8401 - #1 #7
-                #1 ( #2*7991 - #8 ) / 1 0000 ; ;
+\cs_new:Npn \@@_pow_exponent:Nwnnnnnwn #1#2; #3#4#5#6#7#8; #9
+  { %^^A todo: use that in ln.
+    \exp_after:wN \@@_fixed_mul_after:wn
+    \int_use:N \__int_eval:w \c_@@_leading_shift_int
+      \exp_after:wN \@@_pack:NNNNNwn
+      \int_use:N \__int_eval:w \c_@@_middle_shift_int
+        #1#2*23025 - #1 #3
+        \exp_after:wN \@@_pack:NNNNNwn
+        \int_use:N \__int_eval:w \c_@@_middle_shift_int
+          #1 #2*8509 - #1 #4
+          \exp_after:wN \@@_pack:NNNNNwn
+          \int_use:N \__int_eval:w \c_@@_middle_shift_int
+            #1 #2*2994 - #1 #5
+            \exp_after:wN \@@_pack:NNNNNwn
+            \int_use:N \__int_eval:w \c_@@_middle_shift_int
+              #1 #2*0456 - #1 #6
+              \exp_after:wN \@@_pack:NNNNNwn
+              \int_use:N \__int_eval:w \c_@@_trailing_shift_int
+                #1 #2*8401 - #1 #7
+                #1 ( #2*7991 - #8 ) / 1 0000 ; {#9} ;
   }
 \cs_new:Npn \@@_pow_B:wwN #1#2#3#4#5#6; #7;
   {
@@ -1097,7 +1114,7 @@
     \int_use:N \__int_eval:w 10 0000 + #1 \__int_eval_end:
     #2#3#4#5#6 0000 0000 0000 0000 0000 0000 ; %^^A todo: how many 0?
   }
-\cs_new:Npn \@@_pow_C_overflow:w #1; #2;
+\cs_new:Npn \@@_pow_C_overflow:w #1; #2; #3
   {
     + \c_two * \c_@@_max_exponent_int
     \exp_after:wN \@@_fixed_continue:wn \c_@@_one_fixed_tl ;
@@ -1129,11 +1146,11 @@
 % \end{macro}
 %^^A end[todo]
 %
-% \begin{macro}[aux, EXP]{\@@_pow_neg:www, \@@_pow_neg_neg:w}
+% \begin{macro}[aux, EXP]{\@@_pow_neg:www}
 %   This function is followed by three floating point numbers: $|a|^b$,
 %   $a\in[-\infty,-0]$, and $b$.  If $b$ is an even integer (case $-1$),
 %   $a^b=|a|^b$.  If $b$ is an odd integer (case $0$), $a^b=-|a|^b$,
-%   obtained by a call to \cs{@@_pow_neg_neg:w}.  Otherwise, the sign is
+%   obtained by a call to \cs{@@_neg_o:w}.  Otherwise, the sign is
 %   undefined.  This is invalid, unless $|a|^b$ turns out to be $+0$ or
 %   \texttt{nan}, in which case we return that as $a^b$.  In particular,
 %   since the underflow detection occurs before \cs{@@_pow_neg:www} is
@@ -1143,7 +1160,7 @@
 \cs_new:Npn \@@_pow_neg:www \s_@@ \@@_chk:w #1#2; #3; #4;
   {
     \if_case:w \@@_pow_neg_case:w #4 ;
-      \exp_after:wN \@@_pow_neg_neg:w
+      \exp_after:wN \@@_neg_o:w
     \or:
       \if_int_compare:w \__int_eval:w #1 / \c_two = \c_one
         \@@_invalid_operation_o:Nww ^ #3; #4;
@@ -1155,14 +1172,6 @@
     \@@_exp_after_o:w
     \s_@@ \@@_chk:w #1#2;
   }
-\cs_new:Npn \@@_pow_neg_neg:w \@@_exp_after_o:w \s_@@ \@@_chk:w #1#2
-  {
-    \exp_after:wN \@@_exp_after_o:w
-    \exp_after:wN \s_@@
-    \exp_after:wN \@@_chk:w
-    \exp_after:wN #1
-    \int_use:N \__int_eval:w \c_two - #2 \__int_eval_end:
-  }
 %    \end{macrocode}
 % \end{macro}
 %
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-extended.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-extended.dtx
index febda1e81b1..b3952ea8aa5 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-extended.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-extended.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3fp-extended.dtx 2474 2011-06-17 12:54:02Z bruno $
+\GetIdInfo$Id: l3fp-extended.dtx 4151 2012-08-28 11:51:52Z bruno $
   {L3 Floating-point extended precision fixed-points}
 \documentclass[full]{l3doc}
 \begin{document}
@@ -77,6 +77,8 @@
 %<@@=fp>
 %    \end{macrocode}
 %
+% \subsection{Description of extended fixed points}
+%
 % In this module, we work on (almost) fixed-point numbers with
 % extended ($24$ digits) precision.  This is used in the computation of
 % Taylor series for the logarithm, exponential, and trigonometric
@@ -89,23 +91,28 @@
 % \begin{quote}
 %   \Arg{a_1} \Arg{a_2} \Arg{a_3} \Arg{a_4} \Arg{a_5} \Arg{a_6} |;|
 % \end{quote}
-% where each \meta{a_i} is exactly $4$ digits, except
-% \meta{a_1}, which may be any positive \TeX{} integer.  The fixed point
+% where each \meta{a_i} is exactly $4$ digits (ranging from |0000| to
+% |9999|), except \meta{a_1}, which may be any \enquote{not-too-large}
+% non-negative integer, with or without trailing zeros.  Here,
+% \enquote{not-too-large} depends on the specific function (see the
+% corresponding comments for details).  Checking for overflow is the
+% responsibility of the code calling those functions.  The fixed point
 % number $a$ corresponding to the representation above is $a =
 % \sum_{i=1}^{6} \meta{a_i} \cdot 10^{-4i}$.
 %
 % Most functions we define here have the form
 % \begin{syntax}
-%   \cs{@@_fixed_\meta{calculation}:wwN} \meta{operand_1} |;| \meta{operand_2} |;| \meta{continuation}
+%   \cs{@@_fixed_\meta{calculation}:wwn} \meta{operand_1} |;| \meta{operand_2} |;| \Arg{continuation}
 % \end{syntax}
 % They perform the \meta{calculation} on the two \meta{operands}, then
 % feed the result ($6$ brace groups followed by a semicolon) to the
 % \meta{continuation}, responsible for the next step of the calculation.
+% Some functions only accept an \texttt{N}-type \meta{continuation}.
 % This allows constructions such as
 % \begin{quote}
-%   \cs{@@_fixed_add:wwN} \meta{X_1} |;| \meta{X_2} |;| \\
+%   \cs{@@_fixed_add:wwn} \meta{X_1} |;| \meta{X_2} |;| \\
 %   \cs{@@_fixed_mul:wwn} \meta{X_3} |;| \\
-%   \cs{@@_fixed_add:wwN} \meta{X_4} |;| \\
+%   \cs{@@_fixed_add:wwn} \meta{X_4} |;| \\
 % \end{quote}
 % to compute $(X_1+X_2)\cdot X_3 + X_4$.  This turns out to be very
 % appropriate for computing continued fractions and Taylor series.
@@ -116,7 +123,10 @@
 % after starting an integer expression for the overall exponent of the
 % result.
 %
-% \begin{variable}{\c_@@_one_fixed_tl}
+% \subsection{Helpers for extended fixed points}
+%
+% \begin{variable}[int]{\c_@@_one_fixed_tl}
+%   The extended fixed-point number~$1$, used in \pkg{l3fp-expo}.
 %    \begin{macrocode}
 \tl_const:Nn \c_@@_one_fixed_tl
   { {10000} {0000} {0000} {0000} {0000} {0000} }
@@ -124,38 +134,92 @@
 % \end{variable}
 %
 % \begin{macro}[int, EXP]{\@@_fixed_continue:wn}
-%   This function does nothing.
+%   This function does nothing.  Of course, there is no bound on
+%   $a_1$ (except \TeX{}'s own $2^{31}-1$).
 %    \begin{macrocode}
 \cs_new:Npn \@@_fixed_continue:wn #1; #2 { #2 #1; }
 %    \end{macrocode}
 % \end{macro}
 %
+% \begin{macro}[int, EXP]{\@@_fixed_add_one:wN}
+%   \begin{syntax}
+%     \cs{@@_fixed_add_one:wN} \meta{a} |;| \meta{continuation}
+%   \end{syntax}
+%   This function adds $1$ to the fixed point \meta{a}, by changing
+%   $a_1$ to $10000+a_1$, then calls the \meta{continuation}.  This
+%   requires $a_1 \leq 2^{31} - 10001$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_fixed_add_one:wN #1#2; #3
+  {
+    \exp_after:wN #3 \exp_after:wN
+      { \int_use:N \__int_eval:w \c_ten_thousand + #1 } #2 ;
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_fixed_mul_after:wn}
+%   The fixed point operations which involve multiplication end by
+%   calling this auxiliary.  It braces the last block of digits, and
+%   places the \meta{continuation} |#2| in front.  The
+%   \meta{continuation} was brought up through the expansions by
+%   the packing functions.
+%    \begin{macrocode}
+\cs_new:Npn \@@_fixed_mul_after:wn #1; #2 { #2 {#1} }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Dividing a fixed point number by a small integer}
+%
 % \begin{macro}[int, EXP]{\@@_fixed_div_int:wwN}
 % \begin{macro}[aux, EXP]
 %   {
 %     \@@_fixed_div_int_i:wnN, \@@_fixed_div_int_ii:wnn,
-%     \@@_fixed_div_int_end:wnn, \@@_fixed_div_int_pack:Nw,
+%     \@@_fixed_div_int_iii:wnn, \@@_fixed_div_int_pack:Nw,
 %     \@@_fixed_div_int_after:Nw
 %   }
 %   \begin{syntax}
-%     \cs{@@_fixed_div_int:wwN} \meta{a} |;| \meta{n} |;| \meta{function}
+%     \cs{@@_fixed_div_int:wwN} \meta{a} |;| \meta{n} |;| \meta{continuation}
 %   \end{syntax}
 %   Divides the fixed point number \meta{a} by the (small) integer
-%   $0<\meta{n}<10^4$ and feeds the result to the \meta{function}.  The
-%   \texttt{wnN} auxiliary receives $a_{i}$, $n$, and a continuation
-%   function as arguments, and computes a (rather tight) lower bound
-%   $Q_{i}$ for the quotient.  The \texttt{wnn} auxiliary receives
-%   $Q_{i}$, $n$, and $a_{i}$.  It adds $Q_{i}$ to a surrounding integer
-%   expression, and starts a new one.  It also computes $a_{i}-n\cdot
-%   Q_{i}$, putting the result in front of $a_{i+1}$ to serve as the
-%   first argument for a new call to the \texttt{wnN} auxiliary. At the
-%   end, the path we took to the lowest levels rewinds: the
-%   \texttt{pack} auxiliary receives $5$ digits, braces the last $4$,
-%   and carries the leading digit to the level above.  The offsets used
-%   to ensure a given number of digits are as follows: we first subtract
-%   $1$ from the top-level, then add $9999$ at every subsequent level,
-%   and add $2$ to the last level.  This last number is not $1$, because
-%   it compensates for the |- \c_one| in the \texttt{wnN} auxiliary.
+%   $0<\meta{n}<10^4$ and feeds the result to the \meta{continuation}.
+%   There is no bound on $a_1$.
+%
+%   The arguments of the \texttt{i} auxiliary are 1: one of the $a_{i}$,
+%   2: $n$, 3: the \texttt{ii} or the \texttt{iii} auxiliary.  It
+%   computes a (somewhat tight) lower bound $Q_{i}$ for the ratio
+%   $a_{i}/n$.
+%
+%   The \texttt{ii} auxiliary receives $Q_{i}$, $n$, and $a_{i}$ as
+%   arguments.  It adds $Q_{i}$ to a surrounding integer expression, and
+%   starts a new one with the initial value $9999$, which ensures that
+%   the result of this expression will have $5$ digits.  The auxiliary
+%   also computes $a_{i}-n\cdot Q_{i}$, placing the result in front of
+%   the $4$ digits of $a_{i+1}$.  The resulting $a'_{i+1} = 10^{4}
+%   (a_{i} - n \cdot Q_{i}) + a_{i+1}$ serves as the first argument for
+%   a new call to the \texttt{i} auxiliary.
+%
+%   When the \texttt{iii} auxiliary is called, the situation looks like
+%   this:
+%   \begin{quote}
+%     \cs{@@_fixed_div_int_after:Nw} \meta{continuation} \\
+%     $-1 + Q_{1}$ \\
+%     \cs{@@_fixed_div_int_pack:Nw} $9999 + Q_{2}$ \\
+%     \cs{@@_fixed_div_int_pack:Nw} $9999 + Q_{3}$ \\
+%     \cs{@@_fixed_div_int_pack:Nw} $9999 + Q_{4}$ \\
+%     \cs{@@_fixed_div_int_pack:Nw} $9999 + Q_{5}$ \\
+%     \cs{@@_fixed_div_int_pack:Nw} $9999$ \\
+%     \cs{@@_fixed_div_int_iii:wnn} $Q_{6}$ |;| \Arg{n} \Arg{a_{6}}
+%   \end{quote}
+%   where expansion is happening from the last line up.  The
+%   \texttt{iii} auxiliary adds $Q_{6} + 2 \simeq a_{6}/n + 1$ to the
+%   last $9999$, giving the integer closest to $10000 + a_{6}/n$.
+%
+%   Each \texttt{pack} auxiliary receives $5$ digits followed by a
+%   semicolon.  The first digit is added as a carry to the integer
+%   expression above, and the $4$ other digits are braced.  Each call to
+%   the \texttt{pack} auxiliary thus produces one brace group.  The last
+%   brace group is produced by the \texttt{after} auxiliary, which
+%   places the \meta{continuation} as appropriate.
 %    \begin{macrocode}
 \cs_new:Npn \@@_fixed_div_int:wwN #1#2#3#4#5#6 ; #7 ; #8
   {
@@ -168,7 +232,7 @@
       #3; {#7} \@@_fixed_div_int_ii:wnn
       #4; {#7} \@@_fixed_div_int_ii:wnn
       #5; {#7} \@@_fixed_div_int_ii:wnn
-      #6; {#7} \@@_fixed_div_int_end:wnn ;
+      #6; {#7} \@@_fixed_div_int_iii:wnn ;
   }
 \cs_new:Npn \@@_fixed_div_int_i:wnN #1; #2 #3
   {
@@ -185,185 +249,287 @@
       \exp_after:wN \@@_fixed_div_int_i:wnN
       \int_use:N \__int_eval:w #3 - #1*#2 \__int_eval_end:
   }
-\cs_new:Npn \@@_fixed_div_int_end:wnn #1; #2 #3 { + #1 + \c_two ; }
+\cs_new:Npn \@@_fixed_div_int_iii:wnn #1; #2 #3 { + #1 + \c_two ; }
 \cs_new:Npn \@@_fixed_div_int_pack:Nw #1 #2; { + #1; {#2} }
 \cs_new:Npn \@@_fixed_div_int_after:Nw #1 #2; { #1 {#2} }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int, EXP]{\@@_fixed_add_one:wN}
-%   \begin{syntax}
-%     \cs{@@_fixed_add_one:wN} \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \Arg{X_5} \Arg{X_6} |;| \meta{function}
-%   \end{syntax}
-%    \begin{macrocode}
-\cs_new:Npn \@@_fixed_add_one:wN #1#2; #3
-  {
-    \exp_after:wN #3 \exp_after:wN
-      { \int_use:N \__int_eval:w 10000 + #1 } #2 ;
-  }
-%    \end{macrocode}
-% \end{macro}
+% \subsection{Adding and subtracting fixed points}
 %
-% \begin{macro}[int, EXP]
-%   {\@@_fixed_add:wwN, \@@_fixed_sub:wwN, \@@_fixed_sub_back:wwN}
-%^^A todo: remove sub_back.
+% \begin{macro}[int, EXP]{\@@_fixed_add:wwn, \@@_fixed_sub:wwn}
 % \begin{macro}[aux, EXP]
 %   {
-%     \@@_fixed_add_i:NNnnnnwnn,
-%     \@@_fixed_add_ii:NnnNnnnnw,
-%     \@@_fixed_add_pack:NNNNNwN,
-%     \@@_fixed_add_after:NNNNNwN
+%     \@@_fixed_add_i:Nnnnnwnn,
+%     \@@_fixed_add_ii:nnNnnnwn,
+%     \@@_fixed_add_pack:NNNNNwn,
+%     \@@_fixed_add_after:NNNNNwn
 %   }
 %   \begin{syntax}
-%     \cs{@@_fixed_add:wwN} \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \Arg{X_5} \Arg{X_6} |;| \Arg{Y_1} \Arg{Y_2} \Arg{Y_3} \Arg{Y_4} \Arg{Y_5} \Arg{Y_6} |;| \meta{function}
+%     \cs{@@_fixed_add:wwn} \meta{a} |;| \meta{b} |;| \Arg{continuation}
 %   \end{syntax}
-%   Computes $X+Y$ (resp.\ $X-Y$ and $Y-X$) and feeds the result to
-%   \meta{function}.  The three functions only differ by some signs and
-%   use a common auxiliary.  It would be nice to grab the $12$ brace
-%   groups in one go, only $9$ arguments are allowed.  Start by grabbing
-%   the two signs, $X_{1}, \ldots, X_{4}$, the rest of $X$, and $Y_{1}$
-%   and $Y_{2}$.  The second auxiliary receives the sign of $X$, the
-%   rest of $X$, the sign of $Y$, the rest of $Y$, and the
-%   \meta{function}.  After going down through the various level, we go
-%   back up, packing digits and bringing the \meta{function} (|#9|, then
-%   |#7|) from the end of the argument list to its start.
+%   Computes $a+b$ (resp.\ $a-b$) and feeds the result to the
+%   \meta{continuation}.  This function requires $0\leq
+%   a_{1},b_{1}<50000$, and requires the result to be positive (this
+%   happens automatically for addition).  The two functions only differ
+%   a sign, hence use a common auxiliary.  It would be nice to grab the
+%   $12$ brace groups in one go; only $9$ parameters are allowed.  Start
+%   by grabbing the two signs, $a_{1}, \ldots, a_{4}$, the rest of $a$,
+%   and $b_{1}$ and $b_{2}$.  The second auxiliary receives the rest of
+%   $a$, the sign multiplying $b$, the rest of $b$, and the
+%   \meta{continuation} as arguments.  After going down through the
+%   various level, we go back up, packing digits and bringing the
+%   \meta{continuation} (|#8|, then |#7|) from the end of the argument
+%   list to its start.
 %    \begin{macrocode}
-\cs_new_nopar:Npn \@@_fixed_add:wwN { \@@_fixed_add_i:NNnnnnwnn + + }
-\cs_new_nopar:Npn \@@_fixed_sub:wwN { \@@_fixed_add_i:NNnnnnwnn + - }
-\cs_new_nopar:Npn \@@_fixed_sub_back:wwN { \@@_fixed_add_i:NNnnnnwnn - + }
-\cs_new:Npn \@@_fixed_add_i:NNnnnnwnn #1#2 #3#4#5#6 #7; #8#9
-  {
-    \exp_after:wN \@@_fixed_add_after:NNNNNwN
-    \int_use:N \__int_eval:w 1 9999 9998 #1 #3#4 #2 #8#9
-      \exp_after:wN \@@_fixed_add_pack:NNNNNwN
-      \int_use:N \__int_eval:w 1 9999 9998 #1 #5#6
-        \@@_fixed_add_ii:NnnNnnnnw #1 #7 #2
-  }
-\cs_new:Npn \@@_fixed_add_ii:NnnNnnnnw #1 #2#3 #4 #5#6 #7#8 ; #9
+\cs_new_nopar:Npn \@@_fixed_add:wwn { \@@_fixed_add_i:Nnnnnwnn + }
+\cs_new_nopar:Npn \@@_fixed_sub:wwn { \@@_fixed_add_i:Nnnnnwnn - }
+\cs_new:Npn \@@_fixed_add_i:Nnnnnwnn #1 #2#3#4#5 #6; #7#8
   {
-    #4 #5#6
-    \exp_after:wN \@@_fixed_add_pack:NNNNNwN
-    \int_use:N \__int_eval:w 2 0000 0000 #4 #7#8 #1 #2#3 ; #9 ;
+    \exp_after:wN \@@_fixed_add_after:NNNNNwn
+    \int_use:N \__int_eval:w 9 9999 9998 + #2#3 #1 #7#8
+      \exp_after:wN \@@_fixed_add_pack:NNNNNwn
+      \int_use:N \__int_eval:w 1 9999 9998 + #4#5
+        \@@_fixed_add_ii:nnNnnnwn #6 #1
   }
-\cs_new:Npn \@@_fixed_add_pack:NNNNNwN #1 #2#3#4#5 #6; #7
-  { + #1 ; #7 {#2#3#4#5} {#6} }
-\cs_new:Npn \@@_fixed_add_after:NNNNNwN #1 #2#3#4#5 #6; #7
+\cs_new:Npn \@@_fixed_add_ii:nnNnnnwn #1#2 #3 #4#5 #6#7 ; #8
   {
-    \exp_after:wN #7
-    \exp_after:wN { \int_use:N \__int_eval:w - 2 0000 + #1#2#3#4#5 }
-    {#6}
+    #3 #4#5
+    \exp_after:wN \@@_fixed_add_pack:NNNNNwn
+    \int_use:N \__int_eval:w 2 0000 0000 #3 #6#7 + #1#2 ; {#8} ;
   }
+\cs_new:Npn \@@_fixed_add_pack:NNNNNwn #1 #2#3#4#5 #6; #7
+  { + #1 ; {#7} {#2#3#4#5} {#6} }
+\cs_new:Npn \@@_fixed_add_after:NNNNNwn 1 #1 #2#3#4#5 #6; #7
+  { #7 {#1#2#3#4#5} {#6} }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
+% \subsection{Multiplying fixed points}
+%
 % \begin{macro}[int, EXP]{\@@_fixed_mul:wwn}
-% \begin{macro}[aux, EXP]
-%   {
-%     \@@_fixed_mul_i:nnnnnnnn   ,
-%     \@@_fixed_mul_pack:NNNNNw    ,
-%     \@@_fixed_mul_after:wwn
-%   }
+% \begin{macro}[aux, EXP]{\@@_fixed_mul_i:nnnnnnnwn}
 %   \begin{syntax}
-%     \cs{@@_fixed_mul:wwn} \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \Arg{X_5} \Arg{X_6} |;| \Arg{Y_1} \Arg{Y_2} \Arg{Y_3} \Arg{Y_4} \Arg{Y_5} \Arg{Y_6} |;| \Arg{tokens}
+%     \cs{@@_fixed_mul:wwn} \meta{a} |;| \meta{b} |;| \Arg{continuation}
 %   \end{syntax}
-%   Computes $X\times Y$ and feeds the result to \meta{function}. It
-%   would be nice to grab the $12$ brace groups in one go, but that's
-%   not possible.  On the other hand, we don't need to obtain an exact
-%   rounding, contrarily to the case in \cs{@@_*_o:ww}, so things are
-%   not quite as bad as they may seem.  The parenthesis computing the
-%   seventh group of digits (computed because we need to know its
-%   potentially large carry) is closed by
-%   \cs{@@_fixed_mul_i:nnnnnnnn}, once we access the last two brace
-%   groups, which were not read before. Also, in
-%   \cs{@@_fixed_mul_after:wwn}, |#3| is the continuation
-%   tokens.\footnote{Bruno: insist on the difference compared to
-%     \cs{@@_fixed_add:wwN}.}
+%   Computes $a\times b$ and feeds the result to \meta{continuation}.
+%   This function requires $0\leq a_{1}, b_{1} < 10000$.  Once more, we
+%   need to play around the limit of $9$ arguments for \TeX{} macros.
+%   Note that we don't need to obtain an exact rounding, contrarily to
+%   the |*| operator, so things could be harder.  We wish to perform
+%   carries in
+%   \begin{align*}
+%     a \times b =
+%     & a_{1} \cdot b_{1} \cdot 10^{-8} \\
+%     & + (a_{1} \cdot b_{2} + a_{2} \cdot b_{1}) \cdot 10^{-12} \\
+%     & + (a_{1} \cdot b_{3} + a_{2} \cdot b_{2}
+%           + a_{3} \cdot b_{1}) \cdot 10^{-16} \\
+%     & + (a_{1} \cdot b_{4} + a_{2} \cdot b_{3}
+%           + a_{3} \cdot b_{2} + a_{4} \cdot b_{1}) \cdot 10^{-20} \\
+%     & + \left(a_{2} \cdot b_{4} + a_{3} \cdot b_{3} + a_{4} \cdot b_{2}
+%           + \frac{a_{3} \cdot b_{4} + a_{4} \cdot b_{3}
+%             + a_{1} \cdot b_{6} + a_{2} \cdot b_{5}
+%             + a_{5} \cdot b_{2} + a_{6} \cdot b_{1}}{10^{4}}
+%           + a_{1} \cdot b_{5} + a_{5} \cdot b_{1}\right) \cdot 10^{-24}
+%     + O(10^{-24}),
+%   \end{align*}
+%   where the $O(10^{-24})$ stands for terms which are at most $5\cdot
+%   10^{-24}$; ignoring those leads to an error of at most
+%   $5$~\texttt{ulp}.  Note how the first $15$~terms only depend on
+%   $a_{1},\ldots{},a_{4}$ and $b_{1},\ldots,b_{4}$, while the last
+%   $6$~terms only depend on $a_{1},a_{2},a_{5},a_{6}$, and the
+%   corresponding parts of~$b$.  Hence, the first function grabs
+%   $a_{1},\ldots,a_{4}$, the rest of $a$, and $b_{1},\ldots,b_{4}$, and
+%   writes the $15$ first terms of the expression, including a left
+%   parenthesis for the fraction.  The \texttt{i} auxiliary receives
+%   $a_{5}$, $a_{6}$, $b_{1}$, $b_{2}$, $a_{1}$, $a_{2}$, $b_{5}$,
+%   $b_{6}$ and finally the \meta{continuation} as arguments.  It writes
+%   the end of the expression, including the right parenthesis and the
+%   denominator of the fraction.  The packing auxiliaries bring the
+%   \meta{continuation} up through the expansion chain, as |#7|, and it
+%   is finally placed in front of the $6$ brace groups by
+%   \cs{@@_fixed_mul_after:wn}.
 %    \begin{macrocode}
 \cs_new:Npn \@@_fixed_mul:wwn #1#2#3#4 #5; #6#7#8#9
   {
-    \exp_after:wN \@@_fixed_mul_after:wwn
+    \exp_after:wN \@@_fixed_mul_after:wn
     \int_use:N \__int_eval:w \c_@@_leading_shift_int
-      \exp_after:wN \@@_pack:NNNNNw
+      \exp_after:wN \@@_pack:NNNNNwn
       \int_use:N \__int_eval:w \c_@@_middle_shift_int
         + #1*#6
-        \exp_after:wN \@@_pack:NNNNNw
+        \exp_after:wN \@@_pack:NNNNNwn
         \int_use:N \__int_eval:w \c_@@_middle_shift_int
           + #1*#7 + #2*#6
-          \exp_after:wN \@@_pack:NNNNNw
+          \exp_after:wN \@@_pack:NNNNNwn
           \int_use:N \__int_eval:w \c_@@_middle_shift_int
             + #1*#8 + #2*#7 + #3*#6
-            \exp_after:wN \@@_pack:NNNNNw
+            \exp_after:wN \@@_pack:NNNNNwn
             \int_use:N \__int_eval:w \c_@@_middle_shift_int
               + #1*#9 + #2*#8 + #3*#7 + #4*#6
-              \exp_after:wN \@@_pack:NNNNNw
+              \exp_after:wN \@@_pack:NNNNNwn
               \int_use:N \__int_eval:w \c_@@_trailing_shift_int
                 + #2*#9 + #3*#8 + #4*#7
                 + ( #3*#9 + #4*#8
-                  + \@@_fixed_mul_i:nnnnnnnn #5 {#6}{#7}  {#1}{#2}
+                  + \@@_fixed_mul_i:nnnnnnnwn #5 {#6}{#7}  {#1}{#2}
+  }
+\cs_new:Npn \@@_fixed_mul_i:nnnnnnnwn #1#2 #3#4 #5#6 #7#8 ; #9
+  {
+    #1*#4 + #2*#3 + #5*#8 + #6*#7 ) / \c_ten_thousand
+    + #1*#3 + #5*#7 ;
+    {#9} ;
   }
-\cs_new:Npn \@@_fixed_mul_i:nnnnnnnn #1#2 #3#4 #5#6 #7#8
-  { #1*#4 + #2*#3 + #5*#8 + #6*#7 )/10000 + #1*#3 + #5*#7 ; }
-\cs_new:Npn \@@_fixed_mul_pack:NNNNNw
-    #1 #2#3#4#5 #6; { + #1#2#3#4#5 ; {#6} }
-\cs_new:Npn \@@_fixed_mul_after:wwn #1; #2; #3 { #3 {#1} #2 ; }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int, EXP]{\@@_fixed_mul_add:wwwn, \@@_fixed_mul_sub_back:wwwn}
+% \subsection{Combining product and sum of fixed points}
+%
+% \begin{macro}[int, EXP]
+%   {
+%     \@@_fixed_mul_add:wwwn,
+%     \@@_fixed_mul_sub_back:wwwn,
+%     \@@_fixed_mul_one_minus_mul:wwn,
+%   }
 %   \begin{syntax}
-%     \cs{@@_fixed_mul_add:wwn} \Arg{X_1} \Arg{X_2} \Arg{X_3} \Arg{X_4} \Arg{X_5} \Arg{X_6} |;| \Arg{Y_1} \Arg{Y_2} \Arg{Y_3} \Arg{Y_4} \Arg{Y_5} \Arg{Y_6} |;| \Arg{Z_1} \Arg{Z_2} \Arg{Z_3} \Arg{Z_4} \Arg{Z_5} \Arg{Z_6} |;| \Arg{tokens}
+%     \cs{@@_fixed_mul_add:wwwn} \meta{a} |;| \meta{b} |;| \meta{c} |;| \Arg{continuation}
+%     \cs{@@_fixed_mul_sub_back:wwwn} \meta{a} |;| \meta{b} |;| \meta{c} |;| \Arg{continuation}
+%     \cs{@@_fixed_one_minus_mul:wwn} \meta{a} |;| \meta{b} |;| \Arg{continuation}
 %   \end{syntax}
-%   These functions compute $X\times Y + Z$ or $Z-X\times Y$ and feed
-%   the result to the \meta{tokens}.  This is tough because we have $18$
-%   brace groups in front of us.
+%   Compute $a\times b + c$, $c - a\times b$, and $1 - a\times b$ and
+%   feed the result to the \meta{continuation}.  Those functions require
+%   $0\leq a_{1}, b_{1}, c_{1} \leq 10000$.  Since those functions are
+%   at the heart of the computation of Taylor expansions, we
+%   over-optimize them a bit, and in particular we do not factor out the
+%   common parts of the three functions.
+%
+%   For definiteness, consider the task of computing $a\times b + c$.
+%   We will perform carries in
+%   \begin{align*}
+%     a \times b + c =
+%     & (a_{1} \cdot b_{1} + c_{1} c_{2})\cdot 10^{-8} \\
+%     & + (a_{1} \cdot b_{2} + a_{2} \cdot b_{1}) \cdot 10^{-12} \\
+%     & + (a_{1} \cdot b_{3} + a_{2} \cdot b_{2} + a_{3} \cdot b_{1}
+%           + c_{3} c_{4}) \cdot 10^{-16} \\
+%     & + (a_{1} \cdot b_{4} + a_{2} \cdot b_{3} + a_{3} \cdot b_{2}
+%           + a_{4} \cdot b_{1}) \cdot 10^{-20} \\
+%     & + \Big(a_{2} \cdot b_{4} + a_{3} \cdot b_{3} + a_{4} \cdot b_{2}
+%           + \frac{a_{3} \cdot b_{4} + a_{4} \cdot b_{3}
+%             + a_{1} \cdot b_{6} + a_{2} \cdot b_{5}
+%             + a_{5} \cdot b_{2} + a_{6} \cdot b_{1}}{10^{4}}
+%           + a_{1} \cdot b_{5} + a_{5} \cdot b_{1}
+%           + c_{5} c_{6} \Big) \cdot 10^{-24}
+%     + O(10^{-24}),
+%   \end{align*}
+%   where $c_{1} c_{2}$, $c_{3} c_{4}$, $c_{5} c_{6}$ denote the
+%   $8$-digit number obtained by juxtaposing the two blocks of digits of
+%   $c$, and $\cdot$ denotes multiplication.  The task is obviously
+%   tough because we have $18$ brace groups in front of us.
+%
+%   Each of the three function starts the first two levels (the first,
+%   corresponding to $10^{-4}$, is empty), with $c_{1} c_{2}$ in the
+%   first level, calls the \texttt{i} auxiliary with arguments described
+%   later, and adds a trailing ${} + c_{5}c_{6}$ |;|
+%   \Arg{continuation}~|;|.  The ${} + c_{5}c_{6}$ piece, which is
+%   omitted for \cs{@@_fixed_one_minus_mul:wwn}, will be taken in the
+%   integer expression for the $10^{-24}$ level.  The
+%   \meta{continuation} is placed correctly to be taken upstream by
+%   packing auxiliaries.
 %    \begin{macrocode}
-\cs_new:Npn \@@_fixed_one_minus_mul:wwn #1; #2#3#4#5;
+\cs_new:Npn \@@_fixed_mul_add:wwwn #1; #2; #3#4#5#6#7#8; #9
   {
-    \exp_after:wN \@@_fixed_mul_after:wwn
-    \int_use:N \__int_eval:w \c_@@_big_leading_shift_int + \c_ten_thousand
-      \exp_after:wN \@@_pack_big:NNNNNNw
-      \int_use:N \__int_eval:w \c_@@_big_middle_shift_int
-        \@@_fixed_mul_add_i:Nnwnnwnnn
-          - 00; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; - 00 ;
+    \exp_after:wN \@@_fixed_mul_after:wn
+    \int_use:N \__int_eval:w \c_@@_big_leading_shift_int
+      \exp_after:wN \@@_pack_big:NNNNNNwn
+      \int_use:N \__int_eval:w \c_@@_big_middle_shift_int + #3 #4
+        \@@_fixed_mul_add_i:Nwnnnwnnn +
+          + #5 #6 ; #2 ; #1 ; #2 ; +
+          + #7 #8 ; {#9} ;
   }
-\cs_new:Npn \@@_fixed_mul_add:wwwn #1; #2#3#4#5; #6#7#8#9
+\cs_new:Npn \@@_fixed_mul_sub_back:wwwn #1; #2; #3#4#5#6#7#8; #9
   {
-    \exp_after:wN \@@_fixed_mul_after:wwn
-    \int_use:N \__int_eval:w \c_@@_big_leading_shift_int + #6
-      \exp_after:wN \@@_pack_big:NNNNNNw
-      \int_use:N \__int_eval:w \c_@@_big_middle_shift_int + #7
-        \@@_fixed_mul_add_i:Nnwnnwnnn
-          + {#8}{#9}; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; +
+    \exp_after:wN \@@_fixed_mul_after:wn
+    \int_use:N \__int_eval:w \c_@@_big_leading_shift_int
+      \exp_after:wN \@@_pack_big:NNNNNNwn
+      \int_use:N \__int_eval:w \c_@@_big_middle_shift_int + #3 #4
+        \@@_fixed_mul_add_i:Nwnnnwnnn -
+          + #5 #6 ; #2 ; #1 ; #2 ; -
+          + #7 #8 ; {#9} ;
   }
-\cs_new:Npn \@@_fixed_mul_sub_back:wwwn #1; #2#3#4#5; #6#7#8#9
+\cs_new:Npn \@@_fixed_one_minus_mul:wwn #1; #2; #3
   {
-    \exp_after:wN \@@_fixed_mul_after:wwn
-    \int_use:N \__int_eval:w \c_@@_big_leading_shift_int + #6
-      \exp_after:wN \@@_pack_big:NNNNNNw
-      \int_use:N \__int_eval:w \c_@@_big_middle_shift_int + #7
-        \@@_fixed_mul_add_i:Nnwnnwnnn
-          - {#8}{#9}; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; -
+    \exp_after:wN \@@_fixed_mul_after:wn
+    \int_use:N \__int_eval:w \c_@@_big_leading_shift_int
+      \exp_after:wN \@@_pack_big:NNNNNNwn
+      \int_use:N \__int_eval:w \c_@@_big_middle_shift_int + 1 0000 0000
+        \@@_fixed_mul_add_i:Nwnnnwnnn -
+          ; #2 ; #1 ; #2 ; -
+          ; {#3} ;
   }
-\cs_new:Npn \@@_fixed_mul_add_i:Nnwnnwnnn #1 #2#3; #4#5#6; #7#8#9
-  { % sg z3z4; y1y2y3; x1x2x3  x4x5x6; y1y2y3y4y5y6; sg z5z6;
-        #1 #7*#4
-        \exp_after:wN \@@_pack_big:NNNNNNw
-        \int_use:N \__int_eval:w \c_@@_big_middle_shift_int + #2
-          #1 #7*#5 #1 #8*#4
-          \exp_after:wN \@@_pack_big:NNNNNNw
-          \int_use:N \__int_eval:w \c_@@_big_middle_shift_int + #3
-            #1 #7*#6 #1 #8*#5 #1 #9*#4
-            \exp_after:wN \@@_pack_big:NNNNNNw
-            \int_use:N \__int_eval:w \c_@@_big_middle_shift_int
-              #1 \@@_fixed_mul_add_ii:nnnnwnnnn {#7}{#8}{#9}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_fixed_mul_add_i:Nwnnnwnnn}
+%   \begin{syntax}
+%     \cs{@@_fixed_mul_add_i:Nwnnnwnnn} \meta{op} |+| \meta{c_3} \meta{c_4} |;|
+%     ~~\meta{b} |;| \meta{a} |;| \meta{b} |;| \meta{op}
+%     ~~|+| \meta{c_5} \meta{c_6} |;|
+%   \end{syntax}
+%   Here, \meta{op} is either |+| or |-|.  Arguments |#3|, |#4|, |#5|
+%   are \meta{b_1}, \meta{b_2}, \meta{b_3}; arguments |#7|, |#8|, |#9|
+%   are \meta{a_1}, \meta{a_2}, \meta{a_3}.  We can build three levels:
+%   $a_{1} \cdot b_{1}$ for $10^{-8}$, $(a_{1} \cdot b_{2} + a_{2} \cdot
+%   b_{1})$ for $10^{-12}$, and $(a_{1} \cdot b_{3} + a_{2} \cdot b_{2}
+%   + a_{3} \cdot b_{1} + c_{3} c_{4})$ for $10^{-16}$.  The $a$--$b$
+%   products huse the sign |#1|.  Note that |#2| is empty for
+%   \cs{@@_fixed_one_minus_mul:wwn}.  We call the \texttt{ii} auxiliary
+%   for levels $10^{-20}$ and $10^{-24}$, keeping the pieces of \meta{a}
+%   we've read, but not \meta{b}, since there is another copy later in
+%   the input stream.
+%    \begin{macrocode}
+\cs_new:Npn \@@_fixed_mul_add_i:Nwnnnwnnn #1 #2; #3#4#5#6; #7#8#9
+  {
+    #1 #7*#3
+    \exp_after:wN \@@_pack_big:NNNNNNwn
+    \int_use:N \__int_eval:w \c_@@_big_middle_shift_int
+      #1 #7*#4 #1 #8*#3
+      \exp_after:wN \@@_pack_big:NNNNNNwn
+      \int_use:N \__int_eval:w \c_@@_big_middle_shift_int
+        #1 #7*#5 #1 #8*#4 #1 #9*#3 #2
+        \exp_after:wN \@@_pack_big:NNNNNNwn
+        \int_use:N \__int_eval:w \c_@@_big_middle_shift_int
+          #1 \@@_fixed_mul_add_ii:nnnnwnnnn {#7}{#8}{#9}
   }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_fixed_mul_add_ii:nnnnwnnnn}
+%   \begin{syntax}
+%     \cs{@@_fixed_mul_add_ii:nnnnwnnnn} \meta{a} |;| \meta{b} |;| \meta{op}
+%     ~~|+| \meta{c_5} \meta{c_6} |;|
+%   \end{syntax}
+%   Level $10^{-20}$ is $(a_{1} \cdot b_{4} + a_{2} \cdot b_{3} + a_{3}
+%   \cdot b_{2} + a_{4} \cdot b_{1})$, multiplied by the sign, which was
+%   inserted by the \texttt{i} auxiliary.  Then we prepare level
+%   $10^{-24}$.  We don't have access to all parts of \meta{a} and
+%   \meta{b} needed to make all products.  Instead, we prepare the
+%   partial expressions
+%   \begin{align*}
+%     & b_{1} + a_{4} \cdot b_{2} + a_{3} \cdot b_{3} + a_{2} \cdot b_{4} + a_{1} \\
+%     & b_{2} + a_{4} \cdot b_{3} + a_{3} \cdot b_{4} + a_{2} .
+%   \end{align*}
+%   Obviously, those expressions make no mathematical sense: we will
+%   complete them with $a_{5} \cdot {}$ and ${} \cdot b_{5}$, and with
+%   $a_{6} \cdot b_{1} + a_{5} \cdot {}$ and ${} \cdot b_{5} + a_{1}
+%   \cdot b_{6}$, and of course with the trailing ${} + c_{5} c_{6}$.
+%   To do all this, we keep $a_{1}$, $a_{5}$, $a_{6}$, and the
+%   corresponding pieces of \meta{b}.
+%    \begin{macrocode}
 \cs_new:Npn \@@_fixed_mul_add_ii:nnnnwnnnn #1#2#3#4#5; #6#7#8#9
-  { % x1x2x3x4 x5x6; y1y2y3y4  y5y6; sg z5z6;
+  {
     ( #1*#9 + #2*#8 + #3*#7 + #4*#6 )
-    \exp_after:wN \@@_pack_big:NNNNNNw
+    \exp_after:wN \@@_pack_big:NNNNNNwn
     \int_use:N \__int_eval:w \c_@@_big_trailing_shift_int
       \@@_fixed_mul_add_iii:nnnnwnnwN
         { #6 + #4*#7 + #3*#8 + #2*#9 + #1 }
@@ -371,25 +537,37 @@
         {#1} #5;
         {#6}
   }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[aux, EXP]{\@@_fixed_mul_add_iii:nnnnwnnwN}
+%   \begin{syntax}
+%     \cs{@@_fixed_mul_add_iii:nnnnwnnwN} \Arg{partial_1} \Arg{partial_2}
+%     ~~\Arg{a_1} \Arg{a_5} \Arg{a_6} |;| \Arg{b_1} \Arg{b_5} \Arg{b_6} |;|
+%     ~~\meta{op} |+| \meta{c_5} \meta{c_6} |;|
+%   \end{syntax}
+%   Complete the \meta{partial_1} and \meta{partial_2} expressions as
+%   explained for the \texttt{ii} auxiliary.  The second one is divided
+%   by $10000$: this is the carry from level $10^{-28}$.  The trailing
+%   ${} + c_{5} c_{6}$ is taken into the expression for level
+%   $10^{-24}$.  Note that the total of level $10^{-24}$ is in the
+%   interval $[-5\cdot 10^{8}, 6\cdot 10^{8}$ (give or take a couple of
+%   $10000$), hence adding it to the shift gives a $10$-digit number, as
+%   expected by the packing auxiliaries.  See \pkg{l3fp-aux} for the
+%   definition of the shifts and packing auxiliaries.
+%    \begin{macrocode}
 \cs_new:Npn \@@_fixed_mul_add_iii:nnnnwnnwN #1#2 #3#4#5; #6#7#8; #9
-  { % {y1+x4*y2+x3*y3+x2*y4+x1} {y2+x4*y3+x3*y4+x2}
-    % x1x5x6; y1y5y6; sg z5z6;
-    % =>
-    % sg (x5*y1+x4*y2+x3*y3+x2*y4+x1*y5)
-    % sg (x6*y1+x5*y2+x4*y3+x3*y4+x2*y5+x1*y6)/10000
-    % + z5z6;
+  {
     #9 (#4* #1 *#7)
     #9 (#5*#6+#4* #2 *#7+#3*#8) / \c_ten_thousand
-    + \@@_use_s:nn
   }
 %    \end{macrocode}
 % \end{macro}
 %
-%    \begin{macrocode}
-\cs_new:Npn \@@_fixed_to_float:Nw #1#2; { \@@_fixed_to_float:wN #2; #1 }
-%    \end{macrocode}
+% \subsection{Converting from fixed point to floating point}
 %
-% \begin{macro}[int, rEXP]{\@@_fixed_to_float:wN}
+% \begin{macro}[int, rEXP]
+%   {\@@_fixed_to_float:wN, \@@_fixed_to_float:Nw}
 %   \begin{syntax}
 %     \ldots{} \cs{__int_eval:w} \meta{exponent} \cs{@@_fixed_to_float:wN} \Arg{a_1} \Arg{a_2} \Arg{a_3} \Arg{a_4} \Arg{a_5} \Arg{a_6} |;| \meta{sign}
 %   \end{syntax}
@@ -405,6 +583,7 @@
 %
 %^^A todo: round properly when rounding to infinity: I need to know the sign.
 %    \begin{macrocode}
+\cs_new:Npn \@@_fixed_to_float:Nw #1#2; { \@@_fixed_to_float:wN #2; #1 }
 \cs_new:Npn \@@_fixed_to_float:wN #1#2#3#4#5#6; #7
   {
     + \c_four % for the 8-digit-at-the-start thing.
@@ -471,7 +650,7 @@
 %    \begin{macrocode}
 \cs_new:Npn \@@_fixed_inv_to_float:wN #1#2; #3
   {
-    - \__int_eval:w
+    + \__int_eval:w % ^^A todo: remove the +?
         \if_int_compare:w #1 < \c_one_thousand
           \@@_fixed_dtf_zeros:wNnnnnnn
         \fi:
@@ -654,7 +833,7 @@
   { #1 ; {#2#3#4#5} {#6} }
 \cs_new:Npn \@@_fixed_dtf_epsilon_ii:NNNNNww #1#2#3#4#5#6; #7;
   {
-    \@@_fixed_mul:wwn %^^A todo: optimize to use \@@_mul_mantissa.
+    \@@_fixed_mul:wwn %^^A todo: optimize to use \@@_mul_significand.
       {0000} {#2#3#4#5} {#6} #7 ;
       {0000} {#2#3#4#5} {#6} #7 ;
     \@@_fixed_add_one:wN
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-logic.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-logic.dtx
index 9813509686d..20f94e2abe4 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-logic.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-logic.dtx
@@ -205,7 +205,7 @@
 % \end{macro}
 %
 % \begin{macro}[int, EXP]{\@@_compare_npos:nwnw}
-% \begin{macro}[aux, EXP]{\@@_compare_mantissa:nnnnnnnn}
+% \begin{macro}[aux, EXP]{\@@_compare_significand:nnnnnnnn}
 %   \begin{quote}
 %     \cs{@@_compare_npos:nwnw}
 %       \Arg{expo_1} \meta{body_1} |;|
@@ -215,7 +215,7 @@
 %   this expands to $0$ if the two numbers are equal, $-1$ if the first
 %   is smaller, and $1$ if the first is bigger.  First compare the
 %   exponents: the larger one denotes the larger number.  If they are
-%   equal, we must compare mantissas.  If both the first $8$ digits and
+%   equal, we must compare significands.  If both the first $8$ digits and
 %   the next $8$ digits coincide, the numbers are equal.  If only the
 %   first $8$ digits coincide, the next $8$ decide.  Otherwise, the
 %   first $8$ digits are compared.
@@ -223,12 +223,12 @@
 \cs_new:Npn \@@_compare_npos:nwnw #1#2; #3#4;
   {
     \if_int_compare:w #1 = #3 \exp_stop_f:
-      \@@_compare_mantissa:nnnnnnnn #2 #4
+      \@@_compare_significand:nnnnnnnn #2 #4
     \else:
       \if_int_compare:w #1 < #3 - \fi: 1
     \fi:
   }
-\cs_new:Npn \@@_compare_mantissa:nnnnnnnn #1#2#3#4#5#6#7#8
+\cs_new:Npn \@@_compare_significand:nnnnnnnn #1#2#3#4#5#6#7#8
   {
     \if_int_compare:w #1#2 = #5#6 \exp_stop_f:
       \if_int_compare:w #3#4 = #7#8 \exp_stop_f:
@@ -244,6 +244,86 @@
 % \end{macro}
 % \end{macro}
 %
+% \subsection{Floating point expression loops}
+%
+% \begin{macro}[rEXP]
+%   {
+%     \fp_do_until:nn, \fp_do_while:nn,
+%     \fp_until_do:nn, \fp_while_do:nn
+%   }
+%   These are quite easy given the above functions. The |do_until| and
+%   |do_while| versions execute the body, then test.  The |until_do| and
+%   |while_do| do it the other way round.
+%    \begin{macrocode}
+\cs_new:Npn \fp_do_until:nn #1#2
+  {
+    #2
+    \fp_compare:nF {#1}
+      { \fp_do_until:nn {#1} {#2} }
+  }
+\cs_new:Npn \fp_do_while:nn #1#2
+  {
+    #2
+    \fp_compare:nT {#1}
+      { \fp_do_while:nn {#1} {#2} }
+  }
+\cs_new:Npn \fp_until_do:nn #1#2
+  {
+    \fp_compare:nF {#1}
+      {
+        #2
+        \fp_until_do:nn {#1} {#2}
+      }
+  }
+\cs_new:Npn \fp_while_do:nn #1#2
+  {
+    \fp_compare:nT {#1}
+      {
+        #2
+        \fp_while_do:nn {#1} {#2}
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[rEXP]
+%   {
+%     \fp_do_until:nNnn, \fp_do_while:nNnn,
+%     \fp_until_do:nNnn, \fp_while_do:nNnn
+%   }
+%   As above but not using the |nNn| syntax.
+%    \begin{macrocode}
+\cs_new:Npn \fp_do_until:nNnn #1#2#3#4
+  {
+    #4
+    \fp_compare:nNnF {#1} #2 {#3}
+      { \fp_do_until:nNnn {#1} #2 {#3} {#4} }
+  }
+\cs_new:Npn \fp_do_while:nNnn #1#2#3#4
+  {
+    #4
+    \fp_compare:nNnT {#1} #2 {#3}
+      { \fp_do_while:nNnn {#1} #2 {#3} {#4} }
+  }
+\cs_new:Npn \fp_until_do:nNnn #1#2#3#4
+  {
+    \fp_compare:nNnF {#1} #2 {#3}
+      {
+        #4
+        \fp_until_do:nNnn {#1} #2 {#3} {#4}
+      }
+  }
+\cs_new:Npn \fp_while_do:nNnn #1#2#3#4
+  {
+    \fp_compare:nNnT {#1} #2 {#3}
+      {
+        #4
+        \fp_while_do:nNnn {#1} #2 {#3} {#4}
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
 % \subsection{Extrema}
 %
 % \begin{macro}[int, EXP]{\@@_max_o:w, \@@_min_o:w}
@@ -403,7 +483,7 @@
       \@@_ternary_break_point:n { \exp_after:wN \@@_ternary_i:NwwN }
       \exp_after:wN #1
       \tex_romannumeral:D -`0
-      \@@_parse_exp_after_array:wf #3 \s_@@_stop
+      \@@_exp_after_array_f:w #3 \s_@@_stop
       \exp_after:wN @
       \tex_romannumeral:D
         \@@_parse_until:Nw \c_two
@@ -414,7 +494,7 @@
       \exp_after:wN \@@_parse_until_test:NwN
       \exp_after:wN #1
       \tex_romannumeral:D -`0
-      \@@_parse_exp_after_array:wf #3 \s_@@_stop
+      \@@_exp_after_array_f:w #3 \s_@@_stop
       \exp_after:wN #4
       \exp_after:wN #1
     \fi:
@@ -437,7 +517,7 @@
     \exp_after:wN \@@_parse_until_test:NwN
     \exp_after:wN #1
     \tex_romannumeral:D -`0
-    \@@_parse_exp_after_array:wf #2 \s_@@_stop
+    \@@_exp_after_array_f:w #2 \s_@@_stop
     #4 #1
   }
 \cs_new:Npn \@@_ternary_ii:NwwN #1#2@#3@#4
@@ -445,7 +525,7 @@
     \exp_after:wN \@@_parse_until_test:NwN
     \exp_after:wN #1
     \tex_romannumeral:D -`0
-    \@@_parse_exp_after_array:wf #3 \s_@@_stop
+    \@@_exp_after_array_f:w #3 \s_@@_stop
     #4 #1
   }
 %    \end{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-parse.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-parse.dtx
index f74c2cf0a92..bb9c792adff 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-parse.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-parse.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3fp-parse.dtx 4081 2012-08-12 11:06:18Z bruno $
+\GetIdInfo$Id: l3fp-parse.dtx 4159 2012-08-29 13:21:59Z bruno $
   {L3 Floating-point expression parsing}
 \documentclass[full]{l3doc}
 \begin{document}
@@ -119,7 +119,6 @@
 % \item[-1] Start and end of the expression.
 % \end{itemize}
 %
-% ^^A todo: change 'mantissa' => 'significand' everywhere.
 % ^^A todo: ask SO when sNaN can arise.
 %
 % \section{Evaluating an expression}
@@ -754,7 +753,7 @@
 %
 %^^A end[todo]
 %
-% \begin{macro}[rEXP, aux]{\@@_parse_expand:w}
+% \begin{macro}[aux, rEXP]{\@@_parse_expand:w}
 %   \begin{syntax}
 %     \cs{tex_romannumeral:D} \cs{@@_parse_expand:w} \meta{tokens}
 %   \end{syntax}
@@ -767,7 +766,7 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[EXP, aux]{\@@_parse_return_semicolon:w}
+% \begin{macro}[aux, EXP]{\@@_parse_return_semicolon:w}
 %   This very odd function swaps its position with the following
 %   \cs{fi:} and removes \cs{@@_parse_expand:w} normally responsible for
 %   expansion.  That turns out to be useful.
@@ -779,13 +778,13 @@
 %
 % \subsection{Fp object type}
 %
-% \begin{macro}[EXP, int]{\@@_type_from_scan:N}
+% \begin{macro}[aux, EXP]{\@@_type_from_scan:N, \@@_type_from_scan:w}
 %   \begin{syntax}
 %     \cs{@@_type_from_scan:N} \meta{token}
 %   \end{syntax}
 %   Grabs the pieces of the stringified \meta{token} which lies after
 %   the first |s__fp|.  If the \meta{token} does not contain that
-%   string, the result is empty.
+%   string, the result is |_?|.
 %    \begin{macrocode}
 \group_begin:
 \char_set_catcode_other:N \S
@@ -798,7 +797,7 @@
     \cs_new:Npn \@@_type_from_scan:N #1
       {
         \exp_after:wN \@@_type_from_scan:w
-        \token_to_str:N #1 \q_mark S--FP \q_mark \q_stop
+        \token_to_str:N #1 \q_mark S--FP-? \q_mark \q_stop
       }
     \cs_new:Npn \@@_type_from_scan:w #1 S--FP #2 \q_mark #3 \q_stop {#2}
   }
@@ -955,47 +954,50 @@
 % \end{macro}
 %
 % \begin{macro}[aux, EXP]
-%   {\@@_parse_operand_relax:NN, \@@_parse_operand_relax_aux:wwnw} The
-%   argument is a token equal to \cs{tex_relax:D}.  This can be
-%   \cs{s_@@}, \cs{s_@@_mark}, or a badly initialized register.  We make
-%   sure that the last argument of \cs{@@_parse_infix:NN} is
+%   {
+%     \@@_parse_operand_relax:NN,
+%     \@@_exp_after_mark_f:nw,
+%     \@@_exp_after_?_f:nw
+%   }
+%   The second argument is a control sequence equal to \cs{tex_relax:D}.
+%   There are three cases, dispatched using \cs{@@_type_from_scan:N}.
+%   \begin{itemize}
+%     \item \cs{s_@@} starts a floating point number, and we call
+%       \cs{@@_exp_after_f:nw}.
+%     \item \cs{s_@@_mark} is a premature end, we call
+%       \cs{@@_exp_after_mark_f:nw}, which triggers the appropriate
+%       error.
+%     \item For a control sequence not containing |\s__fp|, we call
+%       \cs{@@_exp_after_?_f:nw}, causing a |bad-variable| error.
+%   \end{itemize}
+%   This scheme is extensible: additional types can be added by starting
+%   the variables with a scan mark of the form |\s__fp_|\meta{type} and
+%   defining |\__fp_exp_after_|\meta{type}|_f:nw|.  In all cases, we
+%   make sure that the last argument of \cs{@@_parse_infix:NN} is
 %   correctly expanded.
 %    \begin{macrocode}
 \cs_new:Npn \@@_parse_operand_relax:NN #1#2
   {
-      \@@_parse_operand_relax_aux:wwnw
-        #2 \s_@@_mark
-          {
-            \@@_exp_after_o:nw
-              {
-                \tex_romannumeral:D -`0
-                \exp_after:wN \@@_parse_infix:NN
-                \exp_after:wN #1 \tex_romannumeral:D \@@_parse_expand:w
-              }
-            \s_@@
-          }
-        \s_@@ #2
-          {
-            \__msg_kernel_expandable_error:nn { kernel } { fp-early-end }
-            \exp_after:wN \c_nan_fp
-            \tex_romannumeral:D -`0
-              \@@_parse_infix:NN #1
-              \s_@@_mark
-          }
-        \s_@@_mark
-          {
-            \__msg_kernel_expandable_error:nnn
-              { kernel } { bad-variable } {#2}
-            \exp_after:wN \c_nan_fp
-            \tex_romannumeral:D -`0
-              \exp_after:wN \@@_parse_infix:NN
-              \exp_after:wN #1
-              \tex_romannumeral:D \@@_parse_expand:w
-          }
-        \s_@@_mark \s_@@_stop
-  }
-\cs_new:Npn \@@_parse_operand_relax_aux:wwnw
-    #1 \s_@@ #2 \s_@@_mark #3 #4 \s_@@_mark \s_@@_stop { #3 }
+    \cs:w @@_exp_after \@@_type_from_scan:N #2 _f:nw \cs_end:
+      {
+        \exp_after:wN \@@_parse_infix:NN
+        \exp_after:wN #1 \tex_romannumeral:D \@@_parse_expand:w
+      }
+    #2
+  }
+\cs_new:Npn \@@_exp_after_mark_f:nw #1
+  {
+    \__msg_kernel_expandable_error:nn { kernel } { fp-early-end }
+    \exp_after:wN \c_nan_fp
+    \tex_romannumeral:D -`0 #1
+  }
+\cs_new:cpn { @@_exp_after_?_f:nw } #1#2
+  {
+    \__msg_kernel_expandable_error:nnn
+      { kernel } { bad-variable } {#2}
+    \exp_after:wN \c_nan_fp
+    \tex_romannumeral:D -`0 #1
+  }
 %    \end{macrocode}
 % \end{macro}
 %
@@ -1356,9 +1358,9 @@
 %   shift as its first argument, which we add to the exponent found in
 %   the |e...| syntax.  If the trailing digits cause a carry, the
 %   integer expression for the leading digits is incremented (|+ \c_one|
-%   in the code below).  If the leading digits propagte this carry all
+%   in the code below).  If the leading digits propagate this carry all
 %   the way up, the function \cs{@@_parse_pack_carry:w} increments the
-%   exponent, and changes the mantissa from |0000...| to |1000...|: this
+%   exponent, and changes the significand from |0000...| to |1000...|: this
 %   is simple because such a carry can only occur to give rise to a
 %   power of $10$.
 %    \begin{macrocode}
@@ -1998,8 +2000,9 @@
       \cs:w
         @@
         \@@_type_from_scan:N #2
+        _ #4
         \@@_type_from_scan:N #5
-        _ #4 _o:ww
+        _o:ww
       \cs_end:
       #2#3 #5#6
     \tex_romannumeral:D -`0 #7 #1
@@ -2092,15 +2095,18 @@
 %     \@@_parse_word_abs:N   ,
 %     \@@_parse_word_cos:N   ,
 %     \@@_parse_word_cot:N   ,
+%     \@@_parse_word_csc:N   ,
 %     \@@_parse_word_exp:N   ,
 %     \@@_parse_word_ln:N    ,
+%     \@@_parse_word_sec:N   ,
 %     \@@_parse_word_sin:N   ,
 %     \@@_parse_word_tan:N   ,
 %   }
 %   Unary functions, which are applied to all of their arguments when
 %   receiving an array.
 %    \begin{macrocode}
-\tl_map_inline:nn { {abs} {cos} {cot} {exp} {ln} {sin} {tan} }
+\tl_map_inline:nn
+  { {abs} {cos} {cot} {csc} {exp} {ln} {sec} {sin} {tan} }
   {
     \cs_new:cpn { @@_parse_word_#1:N } ##1
       {
@@ -2234,7 +2240,7 @@
     {
       \token_if_eq_meaning:NNTF #3 \@@_parse_infix_):N
         {
-          \@@_parse_exp_after_array:wf #2 \s_@@_stop
+          \@@_exp_after_array_f:w #2 \s_@@_stop
           \exp_after:wN \@@_parse_infix:NN
           \exp_after:wN #1
           \tex_romannumeral:D \@@_parse_expand:w
@@ -2248,16 +2254,15 @@
 %    \end{macrocode}
 % \end{macro}
 %
-%^^A todo: rename to exp_after_array_f:w
-% \begin{macro}[int, EXP]{\@@_parse_exp_after_array:wf}
+% \begin{macro}[int, EXP]{\@@_exp_after_array_f:w}
 %    \begin{macrocode}
-\cs_new:Npn \@@_parse_exp_after_array:wf #1
+\cs_new:Npn \@@_exp_after_array_f:w #1
   {
-    \cs:w @@ \@@_type_from_scan:N #1 _exp_after_f:nw \cs_end:
-      { \@@_parse_exp_after_array:wf }
+    \cs:w @@_exp_after \@@_type_from_scan:N #1 _f:nw \cs_end:
+      { \@@_exp_after_array_f:w }
     #1
   }
-\cs_new:Npn \@@_stop_exp_after_f:nw #1#2 { }
+\cs_new:Npn \@@_exp_after_stop_f:nw #1#2 { }
 %    \end{macrocode}
 % \end{macro}
 %
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-round.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-round.dtx
index b14d3e1058f..b485a0616c3 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-round.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-round.dtx
@@ -89,7 +89,7 @@
 % \subsection{Rounding tools}
 %
 % Floating point operations often yield a result that cannot be exactly
-% represented in a mantissa with $16$ digits.  In that case, we need to
+% represented in a significand with $16$ digits.  In that case, we need to
 % round the exact result to a representable number.  The \textsc{ieee}
 % standard defines four rounding modes:
 % \begin{itemize}
@@ -329,7 +329,10 @@
 \cs_new:Npn \@@_round:Nww #1#2 ; #3 ;
   {
     \@@_small_int:wTF #3; { \@@_round:Nwn #1#2; }
-      { \@@_array_invalid_operation_o:nw { round } #2; #3; @ }
+      {
+        \@@_invalid_operation_tl_o:nf
+          { round } { \@@_array_to_clist:n { #2; #3; } }
+      }
   }
 \cs_new:Npn \@@_round:Nwn #1 \s_@@ \@@_chk:w #2#3#4; #5
   {
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-traps.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-traps.dtx
index f3e3955c1b1..107b94ac0ca 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-traps.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-traps.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3fp-traps.dtx 2479 2011-06-19 21:57:25Z bruno $
+\GetIdInfo$Id: l3fp-traps.dtx 4129 2012-08-20 20:38:28Z mittelba $
   {L3 Floating-point exception trapping}
 \documentclass[full]{l3doc}
 \begin{document}
@@ -118,7 +118,7 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{variable}
+% \begin{variable}[aux]
 %   {
 %     \l_@@_invalid_operation_flag_token ,
 %     \l_@@_division_by_zero_flag_token  ,
@@ -152,7 +152,7 @@
 % \begin{itemize}
 % \item \cs{@@_invalid_operation:nnw},
 % \item \cs{@@_invalid_operation_o:Nww},
-% \item \cs{@@_array_invalid_operation_o:nw},
+% \item \cs{@@_invalid_operation_tl_o:nf},
 % \item \cs{@@_division_by_zero_o:Nnw},
 % \item \cs{@@_division_by_zero_o:NNww},
 % \item \cs{@@_overflow:w},
@@ -163,7 +163,10 @@
 % \meta{way of trapping} is one of \texttt{error}, \texttt{flag}, or
 % \texttt{none}.
 %
-% \begin{macro}{\fp_trap:nn} %^^A todo: user command => document
+% We also provide \cs{@@_invalid_operation_o:nw}, defined in terms of
+% \cs{@@_invalid_operation:nnw}.
+%
+% \begin{macro}{\fp_trap:nn}
 %    \begin{macrocode}
 \cs_new_protected:Npn \fp_trap:nn #1#2
   {
@@ -207,7 +210,7 @@
       { \cs_set:Npn \@@_invalid_operation:nnw ##1##2##3; }
       {
         #1
-        \@@_error:nffn { invalid } {##2} { \@@_to_tl:w ##3; } { }
+        \@@_error:nnfn { invalid } {##2} { \@@_to_tl:w ##3; } { }
         \fp_flag_on:n { invalid_operation }
         ##1
       }
@@ -221,11 +224,10 @@
         \exp_after:wN \c_nan_fp
       }
     \exp_args:Nno \use:n
-      { \cs_set:Npn \@@_array_invalid_operation_o:nw ##1##2@ }
+      { \cs_set:Npn \@@_invalid_operation_tl_o:nf ##1##2 }
       {
         #1
-        \@@_error:nffn { invalid }
-          {##1} { \@@_array_to_clist:w ##2 @ } { }
+        \@@_error:nnfn { invalid } {##1} {##2} { }
         \fp_flag_on:n { invalid_operation }
         \exp_after:wN \c_nan_fp
       }
@@ -258,7 +260,7 @@
       { \cs_set:Npn \@@_division_by_zero_o:Nnw ##1##2##3; }
       {
         #1
-        \@@_error:nffn { zero-div } {##2} { \@@_to_tl:w ##3; } { }
+        \@@_error:nnfn { zero-div } {##2} { \@@_to_tl:w ##3; } { }
         \fp_flag_on:n { division_by_zero }
         \exp_after:wN ##1
       }
@@ -343,7 +345,7 @@
 % \begin{macro}[int, EXP]
 %   {
 %     \@@_invalid_operation:nnw, \@@_invalid_operation_o:Nww,
-%     \@@_array_invalid_operation_o:nw,
+%     \@@_invalid_operation_tl_o:nf,
 %     \@@_division_by_zero_o:Nnw, \@@_division_by_zero_o:NNww,
 %     \@@_overflow:w , \@@_underflow:w
 %   }
@@ -354,7 +356,7 @@
 %    \begin{macrocode}
 \cs_new:Npn \@@_invalid_operation:nnw #1#2#3; { }
 \cs_new:Npn \@@_invalid_operation_o:Nww #1#2; #3; { }
-\cs_new:Npn \@@_array_invalid_operation_o:nw #1 #2 @ { }
+\cs_new:Npn \@@_invalid_operation_tl_o:nf #1 #2 { }
 \cs_new:Npn \@@_division_by_zero_o:Nnw #1#2#3; { }
 \cs_new:Npn \@@_division_by_zero_o:NNww #1#2#3; #4; { }
 \cs_new:Npn \@@_overflow:w { }
@@ -379,39 +381,15 @@
 % \subsection{Errors}
 %
 %^^A begin[todo]
-% \begin{macro}[int, EXP]{\@@_error:nnnn, \@@_error:nffn}
+% \begin{macro}[int, EXP]{\@@_error:nnnn, \@@_error:nnfn, \@@_error:nffn}
 %    \begin{macrocode}
 \cs_new:Npn \@@_error:nnnn #1
   { \__msg_kernel_expandable_error:nnnnn { kernel } { fp - #1 } }
-\cs_generate_variant:Nn \@@_error:nnnn { nff }
+\cs_generate_variant:Nn \@@_error:nnnn { nnf, nff }
 %    \end{macrocode}
 % \end{macro}
 % ^^A end[todo]
 %
-% ^^A todo: move \@@_array_to_clist:w elsewhere.
-% \begin{macro}[int, EXP]{\@@_array_to_clist:w}
-% \begin{macro}[aux, EXP]{\@@_array_to_clist_i:wwww, \@@_array_to_clist_ii:ww}
-%   Converts an array of floating point numbers to a comma-list.  Does
-%   not work for empty arrays.
-%    \begin{macrocode}
-\cs_new:Npn \@@_array_to_clist:w #1 @
-  {
-    \@@_array_to_clist_i:wwww ;
-      #1
-      \@@_array_to_clist_ii:ww \s_@@ ; @
-  }
-\cs_new:Npn \@@_array_to_clist_i:wwww #1; #2 \s_@@ #3; #4 @
-  {
-    #2
-    \exp_after:wN \@@_array_to_clist_i:wwww
-    \tex_romannumeral:D -`0 \@@_to_tl:w \s_@@ #3 ; ;
-    #4 , ~ #1 @
-  }
-\cs_new:Npn \@@_array_to_clist_ii:ww #1 ; , ~ , ~ #2 @ {#2}
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
 % \subsection{Messages}
 %
 % Some messages.
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx
index d6682a661c3..1f5874ca602 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3fp-trig.dtx 3514 2012-03-08 06:14:48Z bruno $
+\GetIdInfo$Id: l3fp-trig.dtx 4151 2012-08-28 11:51:52Z bruno $
   {L3 Floating-point trigonometric functions}
 \documentclass[full]{l3doc}
 \begin{document}
@@ -79,39 +79,25 @@
 %
 %^^A todo: check EXP/rEXP everywhere.
 %
-% \subsection{Inverting a floating point number}
-%
-% \begin{macro}[int, EXP]{\@@_one_over:w}
-%   Expects a floating point of the form \cs{s_@@} \ldots{} |;| and
-%   computes its multiplicative inverse.  This is used to compute the
-%   cotangent function very near $0$.
-%    \begin{macrocode}
-\cs_new_nopar:Npx \@@_one_over:w
-  {
-    \exp_not:N \exp_after:wN
-    \exp_not:c { @@_/_o:ww }
-    \exp_not:N \c_one_fp
-  }
-%    \end{macrocode}
-% \end{macro}
-%
 % \subsection{Direct trigonometric functions}
 %
 % The approach for all trigonometric functions (sine, cosine, tangent,
-% and cotangent) is the same.
+% cotangent, cosecant, and secant) is the same.
 % \begin{itemize}
-% \item Filter out special cases ($\pm 0$, $\pm\inf$ and \nan{}).
-% \item Keep the sign for later, and work with the absolute value $|x|$
-%   of the argument.
-% \item For numbers less than $1$, shift the mantissa to convert them to
-%   fixed point numbers.  Very small numbers take a slightly different
-%   route.
-% \item For numbers $\geq 1$, subtract a multiple of $\pi/2$ to bring
-%   them to the range to $[0, \pi/2]$.
-% \item Reduce further to $[0, \pi/4]$ using $\sin x = \cos (\pi/2-x)$.
-% \item Use the appropriate power series depending on the octant
-%   $\lfloor\frac{|x|}{\pi/4}\rfloor \mod 8$, the sign, and the function
-%   to compute.
+%   \item Filter out special cases ($\pm 0$, $\pm\inf$ and \nan{}).
+%   \item Keep the sign for later, and work with the absolute value
+%     $|x|$ of the argument.
+%   \item For numbers less than $1$, shift the significand to convert them
+%     to fixed point numbers.  Very small numbers take a slightly
+%     different route.
+%   \item For numbers $\geq 1$, subtract a multiple of $\pi/2$ to bring
+%     them to the range to $[0, \pi/2]$.  (This is called argument
+%     reduction.)
+%   \item Reduce further to $[0, \pi/4]$ using $\sin x = \cos
+%     (\pi/2-x)$.
+%   \item Use the appropriate power series depending on the octant
+%     $\lfloor\frac{|x|}{\pi/4}\rfloor \mod 8$, the sign, and the
+%     function to compute.
 % \end{itemize}
 %
 % \subsubsection{Sign and special numbers}
@@ -119,23 +105,25 @@
 % \begin{macro}[int, EXP]{\@@_sin_o:w}
 %   The sine of $\pm 0$ or \nan{} is the same floating point number.
 %   The sine of $\pm\infty$ raises an invalid operation exception.
-%   Otherwise, check the exponent, preparing to use
-%   \cs{@@_sin_series:NNwww} for the calculation, with a sign |#2|, and
-%   an initial octant of $0$.  The question mark is an argument which is
-%   not used in this case.
+%   Otherwise, \cs{@@_trig_exponent:NNNNNwn} checks the exponent: if the
+%   number is tiny, use \cs{@@_trig_epsilon_o:w} which returns
+%   $\sin\epsilon = \epsilon$.  For larger inputs, use the series
+%   \cs{@@_sin_series:NNwww} after argument reduction.  In this second
+%   case, we will use a sign~|#2|, an initial octant of~$0$, and convert
+%   the result of the series to a floating point directly, since
+%   $\sin(x) = \#2 \sin\lvert x\rvert$.
 %    \begin{macrocode}
 \cs_new:Npn \@@_sin_o:w \s_@@ \@@_chk:w #1#2
   {
     \if_case:w #1 \exp_stop_f:
            \@@_case_return_same_o:w
     \or:
-      \exp_after:wN \@@_trig_exponent:NNNNwn
-      \exp_after:wN \@@_sin_series:NNwww
-      \exp_after:wN ?
-      \exp_after:wN #2
-      \exp_after:wN \c_zero
-    \or:
-      \@@_case_use:nw { \@@_invalid_operation_o:nw { sin } }
+      \@@_case_use:nw
+        {
+          \@@_trig_exponent:NNNNNwn \@@_trig_epsilon_o:w
+            \@@_sin_series:NNwww \@@_fixed_to_float:wN #2 \c_zero
+        }
+    \or:   \@@_case_use:nw { \@@_invalid_operation_o:nw { sin } }
     \else: \@@_case_return_same_o:w
     \fi:
     \s_@@ \@@_chk:w #1#2
@@ -146,27 +134,81 @@
 % \begin{macro}[int, EXP]{\@@_cos_o:w}
 %   The cosine of $\pm 0$ is $1$.  The cosine of $\pm\infty$ raises an
 %   invalid operation exception.  The cosine of \nan{} is itself.
-%   Otherwise, check the exponent, preparing to use
-%   \cs{@@_sin_series:NNwww} for the calculation, with a positive sign
-%   ($0$), and an initial octant of $2$, because $\cos x = \sin ( \pi/2
-%   + |x|)$.  The question mark is an argument which is not used in this
-%   case.
+%   Otherwise, \cs{@@_trig_exponent:NNNNNwn} checks the exponent: if the
+%   number is tiny, use \cs{@@_trig_epsilon_one_o:w} which returns
+%   $\cos\epsilon = 1$.  For larger inputs, use the same series as for
+%   sine, but using a positive sign~|0| and with an initial octant
+%   of~$2$, because $\cos(x) = + \sin(\pi/2 + \lvert x\rvert)$.
 %    \begin{macrocode}
 \cs_new:Npn \@@_cos_o:w \s_@@ \@@_chk:w #1#2
   {
     \if_case:w #1 \exp_stop_f:
            \@@_case_return_o:Nw \c_one_fp
     \or:
-      \@@_case_use:nw %^^A todo: is that faster than the exp_after route?
+      \@@_case_use:nw
+        {
+          \@@_trig_exponent:NNNNNwn \@@_trig_epsilon_one_o:w
+            \@@_sin_series:NNwww \@@_fixed_to_float:wN 0 \c_two
+        }
+    \or:   \@@_case_use:nw { \@@_invalid_operation_o:nw { cos } }
+    \else: \@@_case_return_same_o:w
+    \fi:
+    \s_@@ \@@_chk:w #1#2
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_csc_o:w}
+%   The cosecant of $\pm 0$ is $\pm \infty$ with the same sign, with a
+%   division by zero exception (see \cs{@@_cot_zero_o:Nnw} defined
+%   below).  The cosecant of $\pm\infty$ raises an invalid operation
+%   exception.  The cosecant of \nan{} is itself.  Otherwise,
+%   \cs{@@_trig_exponent:NNNNNwn} checks the exponent: if the number is
+%   tiny, use \cs{@@_trig_epsilon_inv_o:w} which returns $\csc\epsilon =
+%   1/\epsilon$.  For larger inputs, use the same series as for sine,
+%   using the sign~|#2|, a starting octant of~$0$, and inverting during
+%   the conversion from the fixed point sine to the floating point
+%   result, because $\csc(x) = \#2 \big( \sin\lvert x\rvert\big)^{-1}$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_csc_o:w \s_@@ \@@_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+           \@@_cot_zero_o:Nnw #2 { csc }
+    \or:
+      \@@_case_use:nw
         {
-          \@@_trig_exponent:NNNNwn
-          \@@_sin_series:NNwww
-          ?
-          0
-          \c_two
+          \@@_trig_exponent:NNNNNwn \@@_trig_epsilon_inv_o:w
+            \@@_sin_series:NNwww \@@_fixed_inv_to_float:wN #2 \c_zero
         }
+    \or:   \@@_case_use:nw { \@@_invalid_operation_o:nw { csc } }
+    \else: \@@_case_return_same_o:w
+    \fi:
+    \s_@@ \@@_chk:w #1#2
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[int, EXP]{\@@_sec_o:w}
+%   The secant of $\pm 0$ is $1$.  The secant of $\pm \infty$ raises an
+%   invalid operation exception.  The secant of \nan{} is itself.
+%   Otherwise, \cs{@@_trig_exponent:NNNNNwn} checks the exponent: if the
+%   number is tiny, use \cs{@@_trig_epsilon_one_o:w} which returns
+%   $\sec\epsilon = 1$.  For larger inputs, use the same series as for
+%   sine, using a positive sign~$0$, a starting octant of~$2$, and
+%   inverting upon conversion, because $\sec(x) = + 1 / \sin(\pi/2 +
+%   \lvert x\rvert)$.
+%    \begin{macrocode}
+\cs_new:Npn \@@_sec_o:w \s_@@ \@@_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+           \@@_case_return_o:Nw \c_one_fp
     \or:
-      \@@_case_use:nw { \@@_invalid_operation_o:nw { cos } }
+      \@@_case_use:nw
+        {
+          \@@_trig_exponent:NNNNNwn \@@_trig_epsilon_one_o:w
+            \@@_sin_series:NNwww \@@_fixed_inv_to_float:wN 0 \c_two
+        }
+    \or:   \@@_case_use:nw { \@@_invalid_operation_o:nw { sec } }
     \else: \@@_case_return_same_o:w
     \fi:
     \s_@@ \@@_chk:w #1#2
@@ -177,24 +219,25 @@
 % \begin{macro}[int, EXP]{\@@_tan_o:w}
 %   The tangent of $\pm 0$ or \nan{} is the same floating point number.
 %   The tangent of $\pm\infty$ raises an invalid operation exception.
-%   Otherwise, check the exponent, preparing to use
-%   \cs{@@_tan_series:NNwww} for the calculation, with a positive sign
-%   ($0$), and an initial octant of $1$, chosen to be distinct from the
-%   octants for sine and cosine.  See \cs{@@_cot_o:w} for an
-%   explanation of the $0$ argument.
+%   Otherwise, \cs{@@_trig_exponent:NNNNNwn} checks the exponent: if the
+%   number is tiny, use \cs{@@_trig_epsilon_o:w} which returns
+%   $\tan\epsilon = \epsilon$.  For larger inputs, use
+%   \cs{@@_tan_series_o:NNwww} for the calculation after argument
+%   reduction, with a sign~|#2| and an initial octant of~$1$ (this shift
+%   is somewhat arbitrary).  See \cs{@@_cot_o:w} for an explanation of
+%   the $0$~argument.
 %    \begin{macrocode}
 \cs_new:Npn \@@_tan_o:w \s_@@ \@@_chk:w #1#2
   {
     \if_case:w #1 \exp_stop_f:
            \@@_case_return_same_o:w
     \or:
-      \exp_after:wN \@@_trig_exponent:NNNNwn
-      \exp_after:wN \@@_tan_series:NNwww
-      \exp_after:wN 0
-      \exp_after:wN #2
-      \exp_after:wN \c_one
-    \or:
-      \@@_case_use:nw { \@@_invalid_operation_o:nw { tan } }
+      \@@_case_use:nw
+        {
+          \@@_trig_exponent:NNNNNwn \@@_trig_epsilon_o:w
+            \@@_tan_series_o:NNwww 0 #2 \c_one
+        }
+    \or:   \@@_case_use:nw { \@@_invalid_operation_o:nw { tan } }
     \else: \@@_case_return_same_o:w
     \fi:
     \s_@@ \@@_chk:w #1#2
@@ -203,110 +246,123 @@
 % \end{macro}
 %
 % \begin{macro}[int, EXP]{\@@_cot_o:w}
-%   The cotangent of $\pm 0$ is $\pm \infty$ with the same sign,
-%   produced by \cs{@@_one_over:w}.  The cotangent of $\pm\infty$ raises
-%   an invalid operation exception.  The cotangent of \nan{} is itself.
-%   We use $\cot x = - \tan (\pi/2 + x)$, and the initial octant for the
-%   tangent was chosen to be $1$, so the octant here starts at $3$.  The
-%   change in sign is obtained by feeding \cs{@@_tan_series:NNwww} two
-%   signs rather than just the sign of the argument: the first of those
-%   indicates whether we compute tangent or cotangent.  Those signs are
-%   eventually combined.
+% \begin{macro}[aux, EXP]{\@@_cot_zero_o:Nnw}
+%   The cotangent of $\pm 0$ is $\pm \infty$ with the same sign, with a
+%   division by zero exception (see \cs{@@_cot_zero_o:Nnw}.  The
+%   cotangent of $\pm\infty$ raises an invalid operation exception.  The
+%   cotangent of \nan{} is itself.  We use $\cot x = - \tan (\pi/2 +
+%   x)$, and the initial octant for the tangent was chosen to be $1$, so
+%   the octant here starts at $3$.  The change in sign is obtained by
+%   feeding \cs{@@_tan_series_o:NNwww} two signs rather than just the sign
+%   of the argument: the first of those indicates whether we compute
+%   tangent or cotangent.  Those signs are eventually combined.
 %    \begin{macrocode}
 \cs_new:Npn \@@_cot_o:w \s_@@ \@@_chk:w #1#2
   {
     \if_case:w #1 \exp_stop_f:
-           \exp_after:wN \@@_one_over:w
-    \or:
-      \exp_after:wN \@@_trig_exponent:NNNNwn
-      \exp_after:wN \@@_tan_series:NNwww
-      \exp_after:wN 2
-      \exp_after:wN #2
-      \exp_after:wN \c_three
+           \@@_cot_zero_o:Nnw #2 { cot }
     \or:
-      \@@_case_use:nw { \@@_invalid_operation_o:nw { cot } }
+      \@@_case_use:nw
+        {
+          \@@_trig_exponent:NNNNNwn \@@_trig_epsilon_inv_o:w
+            \@@_tan_series_o:NNwww 2 #2 \c_three
+        }
+    \or:   \@@_case_use:nw { \@@_invalid_operation_o:nw { cot } }
     \else: \@@_case_return_same_o:w
     \fi:
     \s_@@ \@@_chk:w #1#2
   }
+\cs_new:Npn \@@_cot_zero_o:Nnw #1 #2 #3 \fi:
+  {
+    \fi:
+    \if_meaning:w 0 #1
+      \exp_after:wN \@@_division_by_zero_o:Nnw \exp_after:wN \c_inf_fp
+    \else:
+      \exp_after:wN \@@_division_by_zero_o:Nnw \exp_after:wN \c_minus_inf_fp
+    \fi:
+    {#2}
+  }
 %    \end{macrocode}
 % \end{macro}
+% \end{macro}
 %
 % \subsubsection{Small and tiny arguments}
 %
-% \begin{macro}[aux, EXP]{\@@_trig_exponent:NNNNwn}
-%   The first four arguments control what trigonometric function we
+% \begin{macro}[aux, EXP]{\@@_trig_exponent:NNNNNwn}
+%   The first five arguments control what trigonometric function we
 %   compute, then follows a normal floating point number.  If the
-%   floating point is smaller than $10^{-8}$, then call the appropriate
-%   \texttt{_epsilon} auxiliary.  Otherwise, call the function |#1|,
-%   with arguments |#2|, |#3|, the octant, computed in an integer
-%   expression starting with |#4|, and a fixed point number obtained
-%   from the floating point number by argument reduction.  Numbers less
-%   than $1$ are converted using \cs{@@_trig_small:w} which simply
-%   shifts the mantissa, while large numbers need argument reduction.
+%   floating point is smaller than $10^{-8}$, then call the
+%   \texttt{_epsilon} auxiliary~|#1|.  Otherwise, call the function
+%   |#2|, with arguments |#3|; |#4|; the octant, computed in an integer
+%   expression starting with |#5| and stopped by a period; and a fixed
+%   point number obtained from the floating point number by argument
+%   reduction.  Argument reduction leaves a shift into the integer
+%   expression for the octant.  Numbers less than~$1$ are converted
+%   using \cs{@@_trig_small:w} which simply shifts the significand, while
+%   large numbers need argument reduction.
 %    \begin{macrocode}
-\cs_new:Npn \@@_trig_exponent:NNNNwn #1#2#3#4 \s_@@ \@@_chk:w 1#5#6
+\cs_new:Npn \@@_trig_exponent:NNNNNwn #1#2#3#4#5 \s_@@ \@@_chk:w 1#6#7
   {
-    \if_int_compare:w #6 > - \c_eight
-      \exp_after:wN #1
+    \if_int_compare:w #7 > - \c_eight
       \exp_after:wN #2
       \exp_after:wN #3
-      \int_use:N \__int_eval:w #4
-        \if_int_compare:w #6 > \c_zero
-          \exp_after:wN \@@_trig_large:w \__int_value:w
+      \exp_after:wN #4
+      \int_use:N \__int_eval:w #5
+        \if_int_compare:w #7 > \c_zero
+          \exp_after:wN \@@_trig_large:ww \__int_value:w
         \else:
-          \exp_after:wN \@@_trig_small:w \__int_value:w
+          \exp_after:wN \@@_trig_small:ww \__int_value:w
         \fi:
     \else:
-      \if_case:w #4
-             \@@_sin_epsilon:w
-      \or:   \@@_sin_epsilon:w
-      \or:   \@@_cos_epsilon:w
-      \else: \@@_cot_epsilon:w
-      \fi:
-      #5
+      \exp_after:wN #1
+      \exp_after:wN #6
     \fi:
-    #6 ;
+    #7 ;
   }
 %    \end{macrocode}
 % \end{macro}
 %
 % \begin{macro}[aux, EXP]
-%   {\@@_sin_epsilon:w, \@@_cos_epsilon:w, \@@_cot_epsilon:w}
+%   {\@@_trig_epsilon_o:w, \@@_trig_epsilon_one_o:w, \@@_trig_epsilon_inv_o:w}
 %   Sine and tangent of tiny numbers give the number itself: the
 %   relative error is less than $5 \cdot 10^{-17}$, which is
-%   appropriate.  Cosine simply gives $1$.  Cotangent computes the
-%   inverse.  This is actually slightly wrong because further terms in
-%   the power series could affect the rounding for cotangent.
+%   appropriate.  Cosine and secant simply give~$1$.  Cotangent and
+%   cosecant compute $1/\epsilon$.  This is actually slightly wrong
+%   because further terms in the power series could affect the rounding
+%   for cotangent.
 %    \begin{macrocode}
-\cs_new:Npn \@@_sin_epsilon:w #1 \fi: #2 \fi: #3 ;
-  { \fi: \fi: \@@_exp_after_o:w \s_@@ \@@_chk:w 1 #2 {#3} }
-\cs_new:Npn \@@_cos_epsilon:w #1 \fi: #2 \fi: #3 ; #4 ;
-  { \fi: \fi: \exp_after:wN \c_one_fp }
-\cs_new:Npn \@@_cot_epsilon:w \fi: #1 \fi: #2 ;
-  { \fi: \fi: \@@_one_over:w \s_@@ \@@_chk:w 1 #1 {#2} }
+\cs_new:Npn \@@_trig_epsilon_o:w #1 #2 ;
+  { \@@_exp_after_o:w \s_@@ \@@_chk:w 1 #1 {#2} }
+\cs_new:Npn \@@_trig_epsilon_one_o:w #1 ; #2 ;
+  { \exp_after:wN \c_one_fp }
+\group_begin:
+  \char_set_catcode_letter:N /
+  \cs_new:Npn \@@_trig_epsilon_inv_o:w #1 #2 ;
+    {
+      \exp_after:wN \@@_/_o:ww
+        \c_one_fp
+        \s_@@ \@@_chk:w 1 #1 {#2}
+    }
+\group_end:
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux, EXP]{\@@_trig_small:w, \@@_trig_small_aux:wwNN}
+% \begin{macro}[aux, EXP]{\@@_trig_small:ww}
 %   Floating point numbers less than $1$ are converted to fixed point
-%   numbers by shifting the mantissa.  Since we have already filtered
-%   out numbers less than $10^{-8}$, no digit is lost in converting to
-%   a fixed point number.
+%   numbers by prepending a number of zeroes to the significand.  Since we
+%   have already filtered out numbers less than $10^{-8}$, we add at
+%   most $7$ zeroes, hence no digit is lost in converting to a fixed
+%   point number.
 %    \begin{macrocode}
-\cs_new:Npn \@@_trig_small:w #1;
+\cs_new:Npn \@@_trig_small:ww #1; #2#3#4#5;
   {
-    \exp_after:wN \exp_after:wN \exp_after:wN \@@_trig_small_aux:wwNN
-    \prg_replicate:nn { - #1 } { 0 } ;
-  }
-\cs_new:Npn \@@_trig_small_aux:wwNN #1; #2#3#4#5;
-  {
-    \@@_pack_twice_four:wNNNNNNNN
-    \@@_pack_twice_four:wNNNNNNNN
-    \@@_pack_twice_four:wNNNNNNNN
-    .
-    ;
-    #1#2#3#4#5 0000 0000;
+    \exp_after:wN \@@_pack_twice_four:wNNNNNNNN
+    \exp_after:wN \@@_pack_twice_four:wNNNNNNNN
+    \exp_after:wN \@@_pack_twice_four:wNNNNNNNN
+    \exp_after:wN .
+    \exp_after:wN ;
+    \tex_romannumeral:D -`0
+      \prg_replicate:nn { - #1 } { 0 } #2#3#4#5 0000 0000 ;
   }
 %    \end{macrocode}
 % \end{macro}
@@ -318,10 +374,10 @@
 %
 % \begin{macro}[aux, rEXP]
 %   {
-%     \@@_trig_large:w, \@@_trig_large_i:www,
-%     \@@_trig_large_ii:wnnnnnn, \@@_trig_large_break:w
+%     \@@_trig_large:ww, \@@_trig_large_i:www,
+%     \@@_trig_large_ii_o:wnnnn, \@@_trig_large_break:w
 %   }
-%   We shift the mantissa by one digit at a time, subtracting a multiple
+%   We shift the significand by one digit at a time, subtracting a multiple
 %   of $2\pi$ at each step.  We use a value of $2\pi$ rounded up,
 %   consistent with the choice of \cs{c_pi_fp}.  This is not quite
 %   correct from an accuracy perspective, but has the nice property that
@@ -333,98 +389,82 @@
 %   non-negative integer).  The subtraction has a form similar to our
 %   usual multiplications (see \pkg{l3fp-basics} or
 %   \pkg{l3fp-extended}).  Once the exponent reaches $0$, we are done
-%   subtracting $2\pi$, and we call \cs{@@_trig_octant_loop:nw} to do
+%   subtracting $2\pi$, and we call \cs{@@_trig_octant_loop:nnnnnw} to do
 %   the reduction by $\pi/2$.
 %    \begin{macrocode}
-\cs_new:Npn \@@_trig_large:w #1; #2#3;
+\cs_new:Npn \@@_trig_large:ww #1; #2#3;
   { \@@_trig_large_i:www #2; #3 ;  #1; }
 \cs_new:Npn \@@_trig_large_i:www #1; #2; #3;
   {
     \if_meaning:w 0 #3 \@@_trig_large_break:w \fi:
-    \exp_after:wN \@@_trig_large_ii:wnnnnnn
+    \exp_after:wN \@@_trig_large_ii_o:wnnnn
     \int_use:N \__int_eval:w ( #1 - 3141 ) / 6283 ;
-    {#1} #2;
+    {#1} #2
+    \exp_after:wN ;
     \int_use:N \__int_eval:w \c_minus_one + #3;
   }
-\cs_new:Npn \@@_trig_large_ii:wnnnnnn #1; #2#3#4#5;
+\cs_new:Npn \@@_trig_large_ii_o:wnnnn #1; #2#3#4#5
   {
     \exp_after:wN \@@_trig_large_i:www
-    \int_use:N \__int_eval:w -5 0000 + #20 - #1*62831
-      \exp_after:wN \@@_fixed_mul_pack:NNNNNw
-      \int_use:N \__int_eval:w 4 9995 0000 + #30 - #1*8530
-        \exp_after:wN \@@_fixed_mul_pack:NNNNNw
-        \int_use:N \__int_eval:w 4 9995 0000 + #40 - #1*7179
-          \exp_after:wN \@@_fixed_mul_pack:NNNNNw
-          \int_use:N \__int_eval:w 5 0000 0000 + #50 - #1*5880
-    \exp_after:wN ;
+    \int_use:N \__int_eval:w \c_@@_leading_shift_int + #20 - #1*62831
+      \exp_after:wN \@@_pack:NNNNNw
+      \int_use:N \__int_eval:w \c_@@_middle_shift_int + #30 - #1*8530
+        \exp_after:wN \@@_pack:NNNNNw
+        \int_use:N \__int_eval:w \c_@@_middle_shift_int + #40 - #1*7179
+          \exp_after:wN \@@_pack:NNNNNw
+          \int_use:N \__int_eval:w \c_@@_trailing_shift_int + #50 - #1*5880
     \exp_after:wN ;
   }
 \cs_new:Npn \@@_trig_large_break:w \fi: #1; #2;
-  { \fi: \@@_trig_octant_loop:nw #2 {0000} {0000} ; }
+  { \fi: \@@_trig_octant_loop:nnnnnw #2 {0000} {0000} ; }
 %    \end{macrocode}
 % \end{macro}
 %
-%^^A todo: optimize: we don't need 6x4 digits here, only 4x4.
-%
 % \begin{macro}[aux, rEXP]
-%   {
-%     \@@_trig_octant_loop:nw, \@@_trig_octant_break:w,
-%     \@@_trig_octant_neg:w
-%   }
+%   {\@@_trig_octant_loop:nnnnnw, \@@_trig_octant_break:w}
 %   We receive a fixed point number as argument.  As long as it is
-%   greater than $1.5707$ (a slight underestimate of $\pi/2$), subtract
-%   $\pi/2$, and leave |+ \c_two| in the integer expression for the
-%   octant.  Once it becomes smaller, if it is greater than $0.7854$
-%   (overestimate of $\pi/4$), then compute $\pi/2 - x$ and increment
-%   the octant.  If it is negative, correct this by changing the sign
-%   and decrementing the octant (by adding $7$).  The result is in all
-%   cases in the range $[0, 0.7854]$, appropriate for a series
-%   expansion.
+%   greater than half of \cs{c_pi_fp}, namely $1.5707963267948970$,
+%   subtract that fixed-point approximation of $\pi/2$, and leave |+|
+%   |\c_two| in the integer expression for the octant.  Once the argument
+%   becomes smaller, break the initial loop.  If the number is greater
+%   than $0.7854$ (overestimate of $\pi/4$), then compute $\pi/2 - x$
+%   and increment the octant.  The result is in all cases in the range
+%   $[0, 0.7854]$, appropriate for the series expansions.
 %    \begin{macrocode}
-\cs_new:Npn \@@_trig_octant_loop:nw #1#2;
+\cs_new:Npn \@@_trig_octant_loop:nnnnnw #1#2#3#4#5#6;
   {
-    \if_int_compare:w #1 < 15707 \exp_stop_f:
+    \if_int_compare:w #1#2 < 157079633 \exp_stop_f:
+      \if_int_compare:w #1#2 = 157079632 \exp_stop_f:
+        \if_int_compare:w #3#4 > 67948969 \exp_stop_f:
+          \use_i_ii:nnn
+        \fi:
+      \fi:
       \@@_trig_octant_break:w
     \fi:
     + \c_two
-    \@@_fixed_sub_back:wwN
+    \@@_fixed_sub:wwn
+      {#1} {#2} {#3} {#4} {0000} {0000} ;
       {15707} {9632} {6794} {8970} {0000} {0000} ;
-      {#1} #2;
-    \@@_trig_octant_loop:nw
+    \@@_trig_octant_loop:nnnnnw
   }
-\cs_new:Npn \@@_trig_octant_break:w #1 \fi: + #2#3 #4; #5#6; #7;
+\cs_new:Npn \@@_trig_octant_break:w #1 \fi: + #2#3 #4#5; #6; #7;
   {
     \fi:
-    \if_int_compare:w #5 < 7854 \exp_stop_f:
-      \if_int_compare:w #5 < \c_zero
-        \exp_after:wN \@@_trig_octant_neg:w
-      \fi:
+    \if_int_compare:w #4 < 7854 \exp_stop_f:
       \exp_after:wN \@@_use_i_until_s:nw
       \exp_after:wN .
     \fi:
     + \c_one
-    \@@_fixed_sub:wwN
-    {15707} {9632} {6794} {8970} {0000} {0000} ;
-    {#5} #6 ; . ;
-  }
-\cs_new:Npn \@@_trig_octant_neg:w #1\fi: #2; #3#4#5#6#7#8; #9
-  {
-    \fi:
-    + \c_seven
-    \exp_after:wN \@@_fixed_add_after:NNNNNwN
-    \int_use:N \__int_eval:w 1 9999 9998 - #30000 - #4
-      \exp_after:wN \@@_fixed_add_pack:NNNNNwN
-      \int_use:N \__int_eval:w 1 9999 9998 - #5#6
-        \exp_after:wN \@@_fixed_add_pack:NNNNNwN
-        \int_use:N \__int_eval:w 2 0000 0000 - #7#8 ; {#9} ;
+    \@@_fixed_sub:wwn #6 ; {#4} #5 ; . ;
   }
 %    \end{macrocode}
 % \end{macro}
 %
 % \subsection{Computing the power series}
 %
-% \begin{macro}[aux, EXP]{\@@_sin_series:NNwww, \@@_sin_series_aux:Nnww}
-%   Here we receive an unused |?|, a \meta{sign} ($0$ or $2$), a
+% \begin{macro}[aux, EXP]{\@@_sin_series:NNwww, \@@_sin_series_aux:NNnww}
+%   Here we receive a conversion function \cs{@@_fixed_to_float:wN} or
+%   \cs{@@_fixed_inv_to_float:wN}, a \meta{sign} ($0$ or $2$), a
 %   (non-negative) \meta{octant} delimited by a dot, a \meta{fixed
 %     point} number, and junk delimited by a semicolon.  The auxiliary
 %   receives:
@@ -448,14 +488,15 @@
 %   \frac{1}{5!} - x^2 \bigg( \cdots \bigg) \bigg) \bigg) \bigg)
 %   \]
 %   is used.  Finally, the fixed point number is converted to a floating
-%   point number with the given sign, and we check for overflow or
-%   underflow. %^^A todo: can over/underflow really happen??
+%   point number with the given sign, and \cs{@@_sanitize:Nw} checks for
+%   overflow and underflow.
 %    \begin{macrocode}
 \cs_new:Npn \@@_sin_series:NNwww #1#2#3 . #4; #5;
   {
     \@@_fixed_mul:wwn #4; #4;
     {
-      \exp_after:wN \@@_sin_series_aux:Nnww
+      \exp_after:wN \@@_sin_series_aux:NNnww
+      \exp_after:wN #1
       \__int_value:w
         \if_int_odd:w \__int_eval:w ( #3 + \c_two ) / \c_four \__int_eval_end:
           #2
@@ -466,66 +507,81 @@
     }
     #4 ;
   }
-\cs_new:Npn \@@_sin_series_aux:Nnww #1#2 #3; #4;
+\cs_new:Npn \@@_sin_series_aux:NNnww #1#2#3 #4; #5;
   {
-    \if_int_odd:w \__int_eval:w #2 / \c_two \__int_eval_end:
+    \if_int_odd:w \__int_eval:w #3 / \c_two \__int_eval_end:
       \exp_after:wN \use_i:nn
     \else:
       \exp_after:wN \use_ii:nn
     \fi:
-    {
-      \@@_fixed_continue:wn {0000}{0000}{0000}{0001}{5619}{2070}; % 1/18!
-      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0000}{0477}{9477}{3324};
-      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0011}{4707}{4559}{7730};
-      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0000}{2087}{6756}{9878}{6810};
-      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0027}{5573}{1922}{3985}{8907};
-      \@@_fixed_mul_sub_back:wwwn #3; {0000}{2480}{1587}{3015}{8730}{1587};
-      \@@_fixed_mul_sub_back:wwwn #3; {0013}{8888}{8888}{8888}{8888}{8889};
-      \@@_fixed_mul_sub_back:wwwn #3; {0416}{6666}{6666}{6666}{6666}{6667};
-      \@@_fixed_mul_sub_back:wwwn #3; {5000}{0000}{0000}{0000}{0000}{0000};
-      \@@_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
+    { % 1/18!
+      \@@_fixed_mul_sub_back:wwwn     {0000}{0000}{0000}{0001}{5619}{2070};
+                                  #4; {0000}{0000}{0000}{0477}{9477}{3324};
+      \@@_fixed_mul_sub_back:wwwn #4; {0000}{0000}{0011}{4707}{4559}{7730};
+      \@@_fixed_mul_sub_back:wwwn #4; {0000}{0000}{2087}{6756}{9878}{6810};
+      \@@_fixed_mul_sub_back:wwwn #4; {0000}{0027}{5573}{1922}{3985}{8907};
+      \@@_fixed_mul_sub_back:wwwn #4; {0000}{2480}{1587}{3015}{8730}{1587};
+      \@@_fixed_mul_sub_back:wwwn #4; {0013}{8888}{8888}{8888}{8888}{8889};
+      \@@_fixed_mul_sub_back:wwwn #4; {0416}{6666}{6666}{6666}{6666}{6667};
+      \@@_fixed_mul_sub_back:wwwn #4; {5000}{0000}{0000}{0000}{0000}{0000};
+      \@@_fixed_mul_sub_back:wwwn #4;{10000}{0000}{0000}{0000}{0000}{0000};
     }
-    {
-      \@@_fixed_continue:wn {0000}{0000}{0000}{0028}{1145}{7254}; % 1/17!
-      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0000}{7647}{1637}{3182};
-      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0160}{5904}{3836}{8216};
-      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0002}{5052}{1083}{8544}{1719};
-      \@@_fixed_mul_sub_back:wwwn #3; {0000}{0275}{5731}{9223}{9858}{9065};
-      \@@_fixed_mul_sub_back:wwwn #3; {0001}{9841}{2698}{4126}{9841}{2698};
-      \@@_fixed_mul_sub_back:wwwn #3; {0083}{3333}{3333}{3333}{3333}{3333};
-      \@@_fixed_mul_sub_back:wwwn #3; {1666}{6666}{6666}{6666}{6666}{6667};
-      \@@_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
-      \@@_fixed_mul:wwn #4;
+    { % 1/17!
+      \@@_fixed_mul_sub_back:wwwn     {0000}{0000}{0000}{0028}{1145}{7254};
+                                  #4; {0000}{0000}{0000}{7647}{1637}{3182};
+      \@@_fixed_mul_sub_back:wwwn #4; {0000}{0000}{0160}{5904}{3836}{8216};
+      \@@_fixed_mul_sub_back:wwwn #4; {0000}{0002}{5052}{1083}{8544}{1719};
+      \@@_fixed_mul_sub_back:wwwn #4; {0000}{0275}{5731}{9223}{9858}{9065};
+      \@@_fixed_mul_sub_back:wwwn #4; {0001}{9841}{2698}{4126}{9841}{2698};
+      \@@_fixed_mul_sub_back:wwwn #4; {0083}{3333}{3333}{3333}{3333}{3333};
+      \@@_fixed_mul_sub_back:wwwn #4; {1666}{6666}{6666}{6666}{6666}{6667};
+      \@@_fixed_mul_sub_back:wwwn #4;{10000}{0000}{0000}{0000}{0000}{0000};
+      \@@_fixed_mul:wwn #5;
     }
     {
       \exp_after:wN \@@_sanitize:Nw
-      \exp_after:wN #1
-      \int_use:N \__int_eval:w \@@_fixed_to_float:wN
+      \exp_after:wN #2
+      \int_use:N \__int_eval:w #1
     }
-    #1
+    #2
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}[aux, EXP]{\@@_tan_series:NNwww, \@@_tan_series_aux:Nnww}
-%   Similar to \cs{@@_sin_series:NNwww}, but with slightly different
-%   rules to find the sign.  The result is expressed as a ratio of
-%   polynomials, of the form
+% \begin{macro}[aux, EXP]{\@@_tan_series_o:NNwww, \@@_tan_series_aux_o:Nnww}
+%   Contrarily to \cs{@@_sin_series:NNwww} which received the conversion
+%   auxiliary as |#1|, here |#1| is $0$ for tangent, and $2$ for
+%   cotangent.  Consider first the case of the tangent.  The octant |#3|
+%   starts at $1$, which means that it is $1$ or $2$ for $\lvert
+%   x\rvert\in[0,\pi/2]$, it is $3$ or $4$ for $\lvert
+%   x\rvert\in[\pi/2,\pi]$, and so on: the intervals on which
+%   $\tan\lvert x\rvert\geq 0$ coincide with those for which $\lfloor
+%   (|#3| + 1) / 2\rfloor$ is odd.  We also have to take into account
+%   the original sign of $x$ to get the sign of the final result; it is
+%   straightforward to check that the first \cs{__int_value:w} expansion
+%   produces $0$ for a positive final result, and $2$ otherwise.  A
+%   similar story holds for $\cot(x)$.
+%
+%   The auxiliary receives the sign, the octant, the square of the
+%   (reduced) input, and the (reduced) input as arguments.  It then
+%   computes the numerator and denominator of
 %   \[
 %   \tan(x) \simeq
 %   \frac{x (1 - x^2 (a_1 - x^2 (a_2 - x^2 (a_3 - x^2 (a_4 - x^2 a_5)))))}
 %     {1 - x^2 (b_1 - x^2 (b_2 - x^2 (b_3 - x^2 (b_4 - x^2 b_5))))} .
 %   \]
-%   The ratio of the two fixed point numbers is converted to a floating
-%   point number directly to avoid rounding issues.  The two fixed
-%   points may be exchanged before computing the ratio, depending on the
-%   quadrant.
+%   The ratio itself is computed by \cs{@@_fixed_div_to_float:ww}, which
+%   converts it directly to a floating point number to avoid rounding
+%   issues.  For octants~|#2| (really, quadrants) next to a pole of the
+%   functions, the fixed point numerator and denominator are exchanged
+%   before computing the ratio.  Note that this \cs{if_int_odd:w} test
+%   relies on the fact that the octant is at least~$1$.
 %    \begin{macrocode}
-\cs_new:Npn \@@_tan_series:NNwww #1#2#3. #4; #5;
+\cs_new:Npn \@@_tan_series_o:NNwww #1#2#3. #4; #5;
   {
     \@@_fixed_mul:wwn #4; #4;
     {
-      \exp_after:wN \@@_tan_series_aux:Nnww
+      \exp_after:wN \@@_tan_series_aux_o:Nnww
       \__int_value:w
         \if_int_odd:w \__int_eval:w #3 / \c_two \__int_eval_end:
           \exp_after:wN \reverse_if:N
@@ -535,18 +591,18 @@
     }
     #4 ;
   }
-\cs_new:Npn \@@_tan_series_aux:Nnww #1 #2 #3; #4;
+\cs_new:Npn \@@_tan_series_aux_o:Nnww #1 #2 #3; #4;
   {
-    \@@_fixed_continue:wn {0000}{0000}{1527}{3493}{0856}{7059};
-    \@@_fixed_mul_sub_back:wwwn #3; {0000}{0159}{6080}{0274}{5257}{6472};
+    \@@_fixed_mul_sub_back:wwwn     {0000}{0000}{1527}{3493}{0856}{7059};
+                                #3; {0000}{0159}{6080}{0274}{5257}{6472};
     \@@_fixed_mul_sub_back:wwwn #3; {0002}{4571}{2320}{0157}{2558}{8481};
     \@@_fixed_mul_sub_back:wwwn #3; {0115}{5830}{7533}{5397}{3168}{2147};
     \@@_fixed_mul_sub_back:wwwn #3; {1929}{8245}{6140}{3508}{7719}{2982};
     \@@_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
     \@@_fixed_mul:wwn #4;
       {
-        \@@_fixed_continue:wn {0000}{0007}{0258}{0681}{9408}{4706};
-        \@@_fixed_mul_sub_back:wwwn #3; {0000}{2343}{7175}{1399}{6151}{7670};
+        \@@_fixed_mul_sub_back:wwwn     {0000}{0007}{0258}{0681}{9408}{4706};
+                                    #3; {0000}{2343}{7175}{1399}{6151}{7670};
         \@@_fixed_mul_sub_back:wwwn #3; {0019}{2638}{4588}{9232}{8861}{3691};
         \@@_fixed_mul_sub_back:wwwn #3; {0536}{6357}{0691}{4344}{6852}{4252};
         \@@_fixed_mul_sub_back:wwwn #3; {5263}{1578}{9473}{6842}{1052}{6315};
@@ -574,4 +630,4 @@
 %
 % \PrintChanges
 %
-% \PrintIndex 
+% \PrintIndex
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3fp.dtx b/Master/texmf-dist/source/latex/l3kernel/l3fp.dtx
index 059ca848304..5cf7c0ccf91 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3fp.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3fp.dtx
@@ -36,19 +36,22 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3fp.dtx 4089 2012-08-14 04:52:20Z bruno $
+\GetIdInfo$Id: l3fp.dtx 4151 2012-08-28 11:51:52Z bruno $
   {L3 Floating points}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
 \usepackage{amsmath}
-\providecommand\nan{\texttt{NaN}}
 \begin{document}
   \DocInput{\jobname.dtx}
 \end{document}
 %</driver>
 % \fi
 %
+% ^^A need to provide this inside the file:
+%
+% \providecommand\nan{\texttt{NaN}}
+%
 %
 % \title{^^A
 %   The \textsf{l3fp} package: floating points^^A
@@ -71,7 +74,7 @@
 %
 % \begin{documentation}
 %
-% A decimal floating point number is one which is stored as a mantissa and a
+% A decimal floating point number is one which is stored as a significand and a
 % separate exponent.  The module implements expandably a wide set of
 % arithmetic, trigonometric, and other operations on decimal floating point
 % numbers, to be used within floating point expressions.  Floating point
@@ -87,8 +90,8 @@
 %     $x\mathop{\&\&}y$, disjunction $x\mathop{\vert\vert}y$, ternary
 %     operator $x\mathop{?}y\mathop{:}z$.
 %   \item Exponentials: $\exp x$, $\ln x$, $x^y$.
-%   \item Trigonometry: $\sin x$, $\cos x$, $\tan x$, $\cot x$.
-%     \emph{Not yet:} $\sec x$, $\csc x$.
+%   \item Trigonometry: $\sin x$, $\cos x$, $\tan x$, $\cot x$, $\sec
+%     x$, $\csc x$.
 %   \item [\emph{(not yet)}] Inverse trigonometric functions:
 %     $\operatorname{asin} x$, $\operatorname{acos} x$,
 %     $\operatorname{atan} x$, $\operatorname{acot} x$,
@@ -181,7 +184,7 @@
 %
 % \section{Setting floating point variables}
 %
-% \begin{function}[updated = 2012-05-08]
+% \begin{function}[updated = 2012-05-08, tested = m3fp002]
 %   {\fp_set:Nn, \fp_set:cn, \fp_gset:Nn, \fp_gset:cn}
 %   \begin{syntax}
 %     \cs{fp_set:Nn} \meta{fp~var} \Arg{floating point expression}
@@ -190,7 +193,7 @@
 %   \meta{floating point expression}.
 % \end{function}
 %
-% \begin{function}[updated = 2012-05-08]
+% \begin{function}[updated = 2012-05-08, tested = m3fp002]
 %   {
 %     \fp_set_eq:NN , \fp_set_eq:cN , \fp_set_eq:Nc , \fp_set_eq:cc ,
 %     \fp_gset_eq:NN, \fp_gset_eq:cN, \fp_gset_eq:Nc, \fp_gset_eq:cc
@@ -202,7 +205,7 @@
 %   value of \meta{fp~var_2}.
 % \end{function}
 %
-% \begin{function}[updated = 2012-05-08]
+% \begin{function}[updated = 2012-05-08, tested = m3fp002]
 %   {\fp_add:Nn, \fp_add:cn, \fp_gadd:Nn, \fp_gadd:cn}
 %   \begin{syntax}
 %     \cs{fp_add:Nn} \meta{fp~var} \Arg{floating point expression}
@@ -211,7 +214,7 @@
 %   the \meta{fp~var}.
 % \end{function}
 %
-% \begin{function}[updated = 2012-05-08]
+% \begin{function}[updated = 2012-05-08, tested = m3fp002]
 %   {\fp_sub:Nn, \fp_sub:cn, \fp_gsub:Nn, \fp_gsub:cn}
 %   \begin{syntax}
 %     \cs{fp_sub:Nn} \meta{fp~var} \Arg{floating point expression}
@@ -222,7 +225,8 @@
 %
 % \section{Using floating point numbers}
 %
-% \begin{function}[EXP, added = 2012-05-08, updated = 2012-07-08]{\fp_eval:n}
+% \begin{function}[EXP, added = 2012-05-08, updated = 2012-07-08,
+%   tested = m3fp-convert003]{\fp_eval:n}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \Arg{floating point expression}
 %   \end{syntax}
@@ -231,11 +235,12 @@
 %   exponent.  Leading or trailing zeros may be inserted to compensate
 %   for the exponent.  Non-significant trailing zeros are trimmed, and
 %   integers are expressed without a decimal separator.  The values
-%   $\pm\infty$ and \texttt{nan} trigger an \enquote{invalid operation}
+%   $\pm\infty$ and \nan{} trigger an \enquote{invalid operation}
 %   exception.  This function is identical to \cs{fp_to_decimal:n}.
 % \end{function}
 %
-% \begin{function}[EXP, added = 2012-05-08, updated = 2012-07-08]
+% \begin{function}[EXP, added = 2012-05-08, updated = 2012-07-08,
+%   tested = m3fp-convert003]
 %   {\fp_to_decimal:N, \fp_to_decimal:c, \fp_to_decimal:n}
 %   \begin{syntax}
 %     \cs{fp_to_decimal:N} \meta{fp~var}
@@ -246,11 +251,11 @@
 %   exponent.  Leading or trailing zeros may be inserted to compensate
 %   for the exponent.  Non-significant trailing zeros are trimmed, and
 %   integers are expressed without a decimal separator.  The values
-%   $\pm\infty$ and \texttt{nan} trigger an \enquote{invalid operation}
+%   $\pm\infty$ and \nan{} trigger an \enquote{invalid operation}
 %   exception.
 % \end{function}
 %
-% \begin{function}[EXP, updated = 2012-07-08]
+% \begin{function}[EXP, updated = 2012-07-08, tested = m3fp-convert003]
 %   {\fp_to_dim:N, \fp_to_dim:c, \fp_to_dim:n}
 %   \begin{syntax}
 %     \cs{fp_to_dim:N} \meta{fp~var}
@@ -262,11 +267,11 @@
 %   an additional trailing \texttt{pt}.  In particular, the result may
 %   be outside the range $[- 2^{14} + 2^{-17}, 2^{14} - 2^{-17}]$ of
 %   valid \TeX{} dimensions, leading to overflow errors if used as a
-%   dimension.  The values $\pm\infty$ and \texttt{nan} trigger an
+%   dimension.  The values $\pm\infty$ and \nan{} trigger an
 %   \enquote{invalid operation} exception.
 % \end{function}
 %
-% \begin{function}[EXP, updated = 2012-07-08]
+% \begin{function}[EXP, updated = 2012-07-08, tested = m3fp-convert003]
 %   {\fp_to_int:N, \fp_to_int:c, \fp_to_int:n}
 %   \begin{syntax}
 %     \cs{fp_to_int:N} \meta{fp~var}
@@ -276,11 +281,12 @@
 %   result to the closest integer, with ties rounded to an even integer.
 %   The result may be outside the range $[- 2^{31} + 1, 2^{31} - 1]$ of
 %   valid \TeX{} integers, triggering \TeX{} errors if used in an
-%   integer expression.  The values $\pm\infty$ and \texttt{nan} trigger
+%   integer expression.  The values $\pm\infty$ and \nan{} trigger
 %   an \enquote{invalid operation} exception.
 % \end{function}
 %
-% \begin{function}[EXP, added = 2012-05-08, updated = 2012-07-08]
+% \begin{function}[EXP, added = 2012-05-08, updated = 2012-07-08,
+%   tested = m3fp-convert003]
 %   {\fp_to_scientific:N, \fp_to_scientific:c, \fp_to_scientific:n}
 %   \begin{syntax}
 %     \cs{fp_to_scientific:N} \meta{fp~var}
@@ -292,11 +298,11 @@
 %     \meta{optional \texttt{-}}\meta{digit}\texttt{.}\meta{15 digits}\texttt{e}\meta{optional sign}\meta{exponent}
 %   \end{quote}
 %   The leading \meta{digit} is non-zero except in the case of $\pm 0$.
-%   The values $\pm\infty$ and \texttt{nan} trigger an \enquote{invalid
+%   The values $\pm\infty$ and \nan{} trigger an \enquote{invalid
 %     operation} exception.
 % \end{function}
 %
-% \begin{function}[EXP, updated = 2012-07-08]
+% \begin{function}[EXP, updated = 2012-07-08, tested = m3fp-convert003]
 %   {\fp_to_tl:N, \fp_to_tl:c, \fp_to_tl:n}
 %   \begin{syntax}
 %     \cs{fp_to_tl:N} \meta{fp~var}
@@ -310,12 +316,13 @@
 %   are expressed in a decimal notation without exponent, with trailing
 %   zeros trimmed, and no decimal separator for integer values (see
 %   \cs{fp_to_decimal:n}.  Negative numbers start with |-|.  The
-%   special values $\pm 0$, $\pm \inf$ and \texttt{nan} are rendered as
+%   special values $\pm 0$, $\pm \inf$ and \nan{} are rendered as
 %   |0|, |-0|, \texttt{inf}, \texttt{-inf}, and \texttt{nan}
 %   respectively.
 % \end{function}
 %
-% \begin{function}[EXP, updated = 2012-07-08]{\fp_use:N, \fp_use:c}
+% \begin{function}[EXP, updated = 2012-07-08, tested = m3fp-convert003]
+%   {\fp_use:N, \fp_use:c}
 %   \begin{syntax}
 %     \cs{fp_use:N} \meta{fp~var}
 %   \end{syntax}
@@ -324,13 +331,13 @@
 %   Leading or trailing zeros may be inserted to compensate for the
 %   exponent.  Non-significant trailing zeros are trimmed.  Integers are
 %   expressed without a decimal separator.  The values $\pm\infty$ and
-%   \texttt{nan} trigger an \enquote{invalid operation} exception.  This
+%   \nan{} trigger an \enquote{invalid operation} exception.  This
 %   function is identical to \cs{fp_to_decimal:N}.
 % \end{function}
 %
 % \section{Floating point conditionals}
 %
-% \begin{function}[EXP, pTF, updated = 2012-05-08]
+% \begin{function}[EXP, pTF, updated = 2012-05-08, tested = m3fp002]
 %   {\fp_if_exist:N, \fp_if_exist:c}
 %   \begin{syntax}
 %     \cs{fp_if_exist_p:N} \meta{fp~var}
@@ -340,8 +347,8 @@
 %   check that the \meta{fp~var} really is a floating point variable.
 % \end{function}
 %
-% \begin{function}[EXP, pTF, updated = 2012-05-08]
-%   {\fp_compare:nNn, \fp_compare:n}
+% \begin{function}[EXP, pTF, updated = 2012-05-08,
+%   tested = m3fp-logic001]{\fp_compare:nNn, \fp_compare:n}
 %   \begin{syntax}
 %     \cs{fp_compare_p:nNn} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2}
 %     \cs{fp_compare:nNnTF} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2} \Arg{true code} \Arg{false code}
@@ -352,7 +359,7 @@
 %   \texttt{true} if the \meta{relation} is obeyed.  Two floating point
 %   numbers $x$ and $y$ may obey four mutually exclusive relations:
 %   $x<y$, $x=y$, $x>y$, or $x$ and $y$ are not ordered.  The latter
-%   case occurs exactly when one of the operands is \texttt{nan}, and
+%   case occurs exactly when one of the operands is \nan{}, and
 %   this relations is denoted by the symbol |?|.  The \texttt{nNn}
 %   functions support the \meta{relations} |<|, |=|, |>|, and |?|.  The
 %   \texttt{n} functions support as a \meta{relation} any combination of
@@ -360,9 +367,9 @@
 %   \meta{relation}), with the restriction that the \meta{relation} may
 %   not start with |?|.  Common choices of \meta{relation} include |>=|
 %   (greater or equal), |!=| (not equal), |!?| (comparable).  Note that
-%   a \texttt{nan} is distinct from any value, even another
-%   \texttt{nan}, hence $x=x$ is not true for a \texttt{nan}. Thus to
-%   test if a value is \texttt{nan}, use
+%   a \nan{} is distinct from any value, even another
+%   \nan{}, hence $x=x$ is not true for a \nan{}. Thus to
+%   test if a value is \nan{}, use
 %   \begin{verbatim}
 %     \fp_compare:nNnTF { <value> } != { <value> }
 %       { } % <value> is nan
@@ -370,6 +377,112 @@
 %   \end{verbatim}
 % \end{function}
 %
+% \section{Floating point expression loops}
+%
+% \begin{function}[rEXP, added = 2012-08-16, tested = m3fp-logic003]
+%   {\fp_do_until:nNnn}
+%   \begin{syntax}
+%      \cs{fp_do_until:nNnn} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2} \Arg{code}
+%   \end{syntax}
+%   Places the \meta{code} in the input stream for \TeX{} to process,
+%   and then evaluates the relationship between the two \meta{floating
+%     point expressions} as described for \cs{fp_compare:nNnTF}.  If the
+%   test is \texttt{false} then the \meta{code} will be inserted into
+%   the input stream again and a loop will occur until the
+%   \meta{relation} is \texttt{true}.
+% \end{function}
+%
+% \begin{function}[rEXP, added = 2012-08-16, tested = m3fp-logic003]
+%   {\fp_do_while:nNnn}
+%   \begin{syntax}
+%      \cs{fp_do_while:nNnn} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2} \Arg{code}
+%   \end{syntax}
+%   Places the \meta{code} in the input stream for \TeX{} to process,
+%   and then evaluates the relationship between the two \meta{floating
+%     point expressions} as described for \cs{fp_compare:nNnTF}.  If the
+%   test is \texttt{true} then the \meta{code} will be inserted into the
+%   input stream again and a loop will occur until the \meta{relation}
+%   is \texttt{false}.
+% \end{function}
+%
+% \begin{function}[rEXP, added = 2012-08-16, tested = m3fp-logic003]
+%   {\fp_until_do:nNnn}
+%   \begin{syntax}
+%      \cs{fp_until_do:nNnn} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2} \Arg{code}
+%   \end{syntax}
+%   Evaluates the relationship between the two \meta{floating point
+%     expressions} as described for \cs{fp_compare:nNnTF}, and then
+%   places the \meta{code} in the input stream if the \meta{relation} is
+%   \texttt{false}.  After the \meta{code} has been processed by \TeX{}
+%   the test will be repeated, and a loop will occur until the test is
+%   \texttt{true}.
+% \end{function}
+%
+% \begin{function}[rEXP, added = 2012-08-16, tested = m3fp-logic003]
+%   {\fp_while_do:nNnn}
+%   \begin{syntax}
+%      \cs{fp_while_do:nNnn} \Arg{fpexpr_1} \meta{relation} \Arg{fpexpr_2} \Arg{code}
+%   \end{syntax}
+%   Evaluates the relationship between the two \meta{floating point
+%     expressions} as described for \cs{fp_compare:nNnTF}, and then
+%   places the \meta{code} in the input stream if the \meta{relation} is
+%   \texttt{true}.  After the \meta{code} has been processed by \TeX{}
+%   the test will be repeated, and a loop will occur until the test is
+%   \texttt{false}.
+% \end{function}
+%
+% \begin{function}[rEXP, added = 2012-08-16, tested = m3fp-logic003]
+%   {\fp_do_until:nn}
+%   \begin{syntax}
+%      \cs{fp_do_until:nn} \{ \meta{fpexpr_1} \meta{relation} \meta{fpexpr_2} \} \Arg{code}
+%   \end{syntax}
+%   Places the \meta{code} in the input stream for \TeX{} to process,
+%   and then evaluates the relationship between the two \meta{floating
+%     point expressions} as described for \cs{fp_compare:nTF}.  If the
+%   test is \texttt{false} then the \meta{code} will be inserted into
+%   the input stream again and a loop will occur until the
+%   \meta{relation} is \texttt{true}.
+% \end{function}
+%
+% \begin{function}[rEXP, added = 2012-08-16, tested = m3fp-logic003]
+%   {\fp_do_while:nn}
+%   \begin{syntax}
+%      \cs{fp_do_while:nn} \{ \meta{fpexpr_1} \meta{relation} \meta{fpexpr_2} \} \Arg{code}
+%   \end{syntax}
+%   Places the \meta{code} in the input stream for \TeX{} to process,
+%   and then evaluates the relationship between the two \meta{floating
+%     point expressions} as described for \cs{fp_compare:nTF}.  If the
+%   test is \texttt{true} then the \meta{code} will be inserted into the
+%   input stream again and a loop will occur until the \meta{relation}
+%   is \texttt{false}.
+% \end{function}
+%
+% \begin{function}[rEXP, added = 2012-08-16, tested = m3fp-logic003]
+%   {\fp_until_do:nn}
+%   \begin{syntax}
+%      \cs{fp_until_do:nn} \{ \meta{fpexpr_1} \meta{relation} \meta{fpexpr_2} \} \Arg{code}
+%   \end{syntax}
+%   Evaluates the relationship between the two \meta{floating point
+%     expressions} as described for \cs{fp_compare:nTF}, and then places
+%   the \meta{code} in the input stream if the \meta{relation} is
+%   \texttt{false}.  After the \meta{code} has been processed by \TeX{}
+%   the test will be repeated, and a loop will occur until the test is
+%   \texttt{true}.
+% \end{function}
+%
+% \begin{function}[rEXP, added = 2012-08-16, tested = m3fp-logic003]
+%   {\fp_while_do:nn}
+%   \begin{syntax}
+%      \cs{fp_while_do:nn} \{ \meta{fpexpr_1} \meta{relation} \meta{fpexpr_2} \} \Arg{code}
+%   \end{syntax}
+%   Evaluates the relationship between the two \meta{floating point
+%     expressions} as described for \cs{fp_compare:nTF}, and then places
+%   the \meta{code} in the input stream if the \meta{relation} is
+%   \texttt{true}.  After the \meta{code} has been processed by \TeX{}
+%   the test will be repeated, and a loop will occur until the test is
+%   \texttt{false}.
+% \end{function}
+%
 % \section{Some useful constants, and scratch variables}
 %
 % \begin{variable}[added = 2012-05-08]{\c_zero_fp, \c_minus_zero_fp}
@@ -450,8 +563,8 @@
 % (using \cs{fp_trap:nn}) to either produce an error and turn the flag
 % on, or only turn the flag on, or do nothing at all.
 %
-% \begin{function}[EXP, pTF, added = 2012-08-08,
-%   tested = m3fp-traps001]{\fp_if_flag_on:n}
+% \begin{function}[EXP, pTF, added = 2012-08-08, tested = m3fp-traps001]
+%   {\fp_if_flag_on:n}
 %   \begin{syntax}
 %     \cs{fp_if_flag_on_p:n} \Arg{exception}
 %     \cs{fp_if_flag_on:nTF} \Arg{exception} \Arg{true code} \Arg{false code}
@@ -461,8 +574,8 @@
 %   \emph{This function is experimental, and may be altered or removed.}
 % \end{function}
 %
-% \begin{function}[added = 2012-08-08,
-%   tested = m3fp-traps001]{\fp_flag_off:n}
+% \begin{function}[added = 2012-08-08, tested = m3fp-traps001]
+%   {\fp_flag_off:n}
 %   \begin{syntax}
 %     \cs{fp_flag_off:n} \Arg{exception}
 %   \end{syntax}
@@ -471,8 +584,8 @@
 %   \emph{This function is experimental, and may be altered or removed.}
 % \end{function}
 %
-% \begin{function}[EXP, added = 2012-08-08,
-%   tested = m3fp-traps001]{\fp_flag_on:n}
+% \begin{function}[EXP, added = 2012-08-08, tested = m3fp-traps001]
+%   {\fp_flag_on:n}
 %   \begin{syntax}
 %     \cs{fp_flag_on:n} \Arg{exception}
 %   \end{syntax}
@@ -506,8 +619,8 @@
 %
 % \section{Viewing floating points}
 %
-% \begin{function}[added = 2012-05-08, updated = 2012-05-27]
-%   {\fp_show:N, \fp_show:c, \fp_show:n}
+% \begin{function}[added = 2012-05-08, updated = 2012-08-14,
+%   tested = m3fp002]{\fp_show:N, \fp_show:c, \fp_show:n}
 %   \begin{syntax}
 %     \cs{fp_show:N} \meta{fp~var}
 %     \cs{fp_show:n} \Arg{floating point expression}
@@ -520,9 +633,6 @@
 %
 % \subsection{Input of floating point numbers} \label{sec:fp-floats}
 %
-% ^^A todo: redoc subsection, write a grammar
-% ^^A todo: clarify what has changed compared to the previous l3fp
-%
 % We support four types of floating point numbers:
 % \begin{itemize}
 %   \item $\pm 0.d_1d_2\ldots{}d_{16} \cdot 10^{n}$, a normal floating
@@ -530,7 +640,7 @@
 %     \leq \ExplSyntaxOn \int_use:N \c__fp_max_exponent_int$;
 %   \item $\pm 0$, zero, with a given sign;
 %   \item $\pm \infty$, infinity, with a given sign;
-%   \item \texttt{nan}, is \enquote{not a number}, and can be either quiet
+%   \item \nan{}, is \enquote{not a number}, and can be either quiet
 %     or signalling (\emph{not yet}: this distinction is currently
 %     unsupported);
 %   \item [\emph{(not yet)}] subnormal numbers $\pm 0.d_1d_2\ldots{}d_{16}
@@ -543,7 +653,7 @@
 % On input, a normal floating point number consists of:
 % \begin{itemize}
 %   \item \meta{sign}: a possibly empty string of |+| and |-| characters;
-%   \item \meta{mantissa}: a non-empty string of digits together with zero
+%   \item \meta{significand}: a non-empty string of digits together with zero
 %     or one dot;
 %   \item \meta{exponent} optionally: the character |e|, followed by a
 %     possibly empty string of |+|~and~|-| tokens, and a non-empty string
@@ -551,41 +661,42 @@
 % \end{itemize}
 % The sign of the resulting number is |+| if \meta{sign} contains an
 % even number of |-|, and |-| otherwise, hence, an empty \meta{sign}
-% denotes a non-negative input.  The stored mantissa is obtained from
-% \meta{mantissa} by omitting the decimal separator and leading zeros,
+% denotes a non-negative input.  The stored significand is obtained from
+% \meta{significand} by omitting the decimal separator and leading zeros,
 % and rounding to $16$ significant digits, filling with trailing zeros
 % if necessary.  In particular, the value stored is exact if the input
-% \meta{mantissa} has at most $16$ digits.  The stored \meta{exponent}
+% \meta{significand} has at most $16$ digits.  The stored \meta{exponent}
 % is obtained by combining the input \meta{exponent} ($0$ if absent)
-% with a shift depending on the position of the mantissa and the number
+% with a shift depending on the position of the significand and the number
 % of leading zeros.
 %
-% A special case arises if the resulting \meta{exponent} is either
-% too large or too small to be represented. This results either in an
-% overflow (the number is then replaced by $\pm\infty$), or an
-% underflow (resulting in $\pm 0$).
+% A special case arises if the resulting \meta{exponent} is either too
+% large or too small for the floating point number to be
+% represented.  This results either in an overflow (the number is then
+% replaced by $\pm\infty$), or an underflow (resulting in $\pm 0$).
 %
-% The result is thus $\pm 0$ if and only if \meta{mantissa} contains no
+% The result is thus $\pm 0$ if and only if \meta{significand} contains no
 % non-zero digit (\emph{i.e.}, consists only in~|0| characters, and an
-% optional |.| character), or there is an underflow.  Note that a single
-% dot is currently a valid floating point number, equal to~$+0$, but
-% that is not guaranteed to remain the case.
+% optional |.| character), or if there is an underflow.  Note that a
+% single dot is currently a valid floating point number, equal to~$+0$,
+% but that is not guaranteed to remain true.
 %
 % Special numbers are input as follows:
 % \begin{itemize}
 %   \item \texttt{inf} represents $+\infty$, and can be preceded by any
-%     \meta{sign}.
-%   \item \texttt{nan} represents a (quiet) non-number. It can be preceded
-%     by any sign, but that will be ignored.
-%   \item Any unrecognisable string will yield a signalling \texttt{nan}.
+%     \meta{sign}, yielding $\pm\infty$ as appropriate.
+%   \item \texttt{nan} represents a (quiet) non-number.  It can be
+%     preceded by any sign, but that will be ignored.
+%   \item Any unrecognizable string triggers an error, and produces a
+%     \nan{}.
 % \end{itemize}
 %
-% Note that~|e-1| is not a representation of $10^{-1}$, because it
-% could be mistaken with the difference of \enquote{\texttt{e}} and
-% $1$. This is consistent with several other programming languages.
-% However, in order to avoid confusions, |e-1| is not considered to
-% be this difference either. To input the base of natural logarithms,
-% use \texttt{exp(1)} or \cs{c_e_fp}.
+% Note that~|e-1| is not a representation of $10^{-1}$, because it could
+% be mistaken with the difference of \enquote{\texttt{e}} and $1$.  This
+% is consistent with several other programming languages.  However, in
+% order to avoid confusions, |e-1| is not considered to be this
+% difference either.  To input the base of natural logarithms, use
+% \texttt{exp(1)} or \cs{c_e_fp}.
 %
 % \subsection{Precedence of operators}
 % \label{sec:fp-precedence}
@@ -602,7 +713,7 @@
 %   \item Binary |+| and |-|.
 %   \item Comparisons |>=|, |!=|, |<?|, \emph{etc}.
 %   \item Logical \texttt{and}, denoted by |&&|.
-%   \item Logical \texttt{or}, denoted by \verb*+||+.
+%   \item Logical \texttt{or}, denoted by \verb+||+.
 %   \item Ternary operator |?:| (right associative).
 % \end{itemize}
 % The precedence of operations can be overridden using parentheses.
@@ -617,14 +728,11 @@
 % \subsection{Operations} \label{sec:fp-operations}
 %
 % We now present the various operations allowed in floating point
-% expressions.  When used as a truth value, a floating point expression
-% is \texttt{false} if it is $\pm 0$, and \texttt{true} otherwise.
+% expressions, from the lowest precedence to the highest.  When used as
+% a truth value, a floating point expression is \texttt{false} if it is
+% $\pm 0$, and \texttt{true} otherwise, including when it is \nan{}.
 %
-% The exceptions listed below are mostly not implemented yet.
-% ^^A todo: implement all exceptions already listed.
-% ^^A todo: add exceptions to '?:', '!<=>?', etc.
-%
-% \begin{function}{?:}
+% \begin{function}[tested = m3fp-logic002]{?:}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ \meta{operand_1} |?| \meta{operand_2} |:| \meta{operand_3} \}
 %   \end{syntax}
@@ -649,7 +757,7 @@
 % \end{function}
 %
 % \begingroup \catcode`\|=12
-% \begin{function}{TWO BARS} ^^A todo:fix
+% \begin{function}[tested = m3fp-logic002]{TWO BARS}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ \meta{operand_1} \texttt{||} \meta{operand_2} \}
 %   \end{syntax}
@@ -660,7 +768,7 @@
 % \endgroup
 %
 % \begingroup \catcode`\&=12
-% \begin{function}{&&}
+% \begin{function}[tested = m3fp-logic002]{&&}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ \meta{operand_1} \texttt{&&} \meta{operand_2} \}
 %   \end{syntax}
@@ -670,7 +778,7 @@
 % \end{function}
 % \endgroup
 %
-% \begin{function}{\<, =, >, ?}
+% \begin{function}[tested = m3fp-logic001]{\<, =, >, ?}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ \meta{operand_1} \meta{comparison} \meta{operand_2} \}
 %   \end{syntax}
@@ -680,18 +788,17 @@
 %   \meta{operand_1} and \meta{operand_2} is true, and $+0$ otherwise.
 % \end{function}
 %
-% \begin{function}{+, -}
+% \begin{function}[tested = m3fp-basics001]{+, -}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ \meta{operand_1} |+| \meta{operand_2} \}
 %     \cs{fp_eval:n} \{ \meta{operand_1} |-| \meta{operand_2} \}
 %   \end{syntax}
 %   Computes the sum or the difference of its two \meta{operands}.  The
 %   \enquote{invalid operation} exception occurs for $\infty-\infty$.
-%   \enquote{Inexact}, \enquote{underflow} and \enquote{overflow} occur
-%   when appropriate.
+%   \enquote{Underflow} and \enquote{overflow} occur when appropriate.
 % \end{function}
 %
-% \begin{function}{*, /}
+% \begin{function}[tested = {m3fp-basics002, m3fp-basics003}]{*, /}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ \meta{operand_1} |*| \meta{operand_2} \}
 %     \cs{fp_eval:n} \{ \meta{operand_1} |/| \meta{operand_2} \}
@@ -699,12 +806,11 @@
 %   Computes the product or the ratio of its two \meta{operands}.  The
 %   \enquote{invalid operation} exception occurs for $\infty/\infty$,
 %   $0/0$, or $0*\infty$.  \enquote{Division by zero} occurs when
-%   dividing a finite non-zero number by $\pm 0$.  The
-%   \enquote{inexact}, \enquote{underflow} and \enquote{overflow}
-%   exceptions occur when appropriate.
+%   dividing a finite non-zero number by $\pm 0$.  \enquote{Underflow}
+%   and \enquote{overflow} occur when appropriate.
 % \end{function}
 %
-% \begin{function}{+, -, !}
+% \begin{function}[tested = m3fp-basics004]{+, -, !}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ |+| \meta{operand} \}
 %     \cs{fp_eval:n} \{ |-| \meta{operand} \}
@@ -713,116 +819,124 @@
 %   The unary |+| does nothing, the unary |-| changes the sign of the
 %   \meta{operand}, and |!| \meta{operand} evaluates to $1$ if
 %   \meta{operand} is false and $0$ otherwise (this is the \texttt{not}
-%   boolean function).
+%   boolean function).  Those operations never raise exceptions.
 % \end{function}
 %
 % \begingroup\catcode`\^=12
-% \begin{function}{**, ^}
+% \begin{function}[tested = m3fp-expo001]{**, ^}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ \meta{operand_1} |**| \meta{operand_2} \}
 %     \cs{fp_eval:n} \{ \meta{operand_1} |^| \meta{operand_2} \}
 %   \end{syntax}
-%   Raises \meta{operand_1} to the power \meta{operand_2}.  This operation
-%   is right associative, hence \texttt{2 ** 2 ** 3} equals
-%   $2^{2^{3}} = 256$.  The \enquote{invalid operation} exception
-%   occurs if \meta{operand_1} is negative or $-0$, and \meta{operand_2} is
-%   not an integer, and the result is non-zero.  \enquote{Division by
-%     zero} occurs \emph{not yet}.  The \enquote{inexact},
-%   \enquote{underflow} and \enquote{overflow} exceptions occur when
-%   appropriate.
+%   Raises \meta{operand_1} to the power \meta{operand_2}.  This
+%   operation is right associative, hence \texttt{2 ** 2 ** 3} equals
+%   $2^{2^{3}} = 256$.  The \enquote{invalid operation} exception occurs
+%   if \meta{operand_1} is negative or $-0$, and \meta{operand_2} is not
+%   an integer, unless the result is zero (in that case, the sign is
+%   chosen arbitrarily to be $+0$).  \enquote{Division by zero} occurs
+%   when raising $\pm 0$ to a strictly negative power.
+%   \enquote{Underflow} and \enquote{overflow} occur when appropriate.
 % \end{function}
 % \endgroup
 %
-% \begin{function}{abs}
+% \begin{function}[tested = m3fp-basics004]{abs}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ |abs(| \meta{fpexpr} |)| \}
 %   \end{syntax}
 %   Computes the absolute value of the \meta{fpexpr}.  This function
 %   does not raise any exception beyond those raised when computing its
-%   operand \meta{fpexpr}.
+%   operand \meta{fpexpr}.  See also \cs{fp_abs:n}.
 % \end{function}
 %
-% \begin{function}{exp}
+% \begin{function}[tested = m3fp-expo001]{exp}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ |exp(| \meta{fpexpr} |)| \}
 %   \end{syntax}
-%   Computes the exponential of the \meta{fpexpr}.  The
-%   \enquote{underflow} and \enquote{overflow}
-%   exceptions occur when appropriate.
+%   Computes the exponential of the \meta{fpexpr}.  \enquote{Underflow}
+%   and \enquote{overflow} occur when appropriate.
 % \end{function}
 %
-% \begin{function}{ln}
+% \begin{function}[tested = m3fp-expo001]{ln}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ |ln(| \meta{fpexpr} |)| \}
 %   \end{syntax}
 %   Computes the natural logarithm of the \meta{fpexpr}.  Negative
 %   numbers have no (real) logarithm, hence the \enquote{invalid
 %     operation} is raised in that case, including for $\ln(-0)$.
-%   \enquote{Division by zero} occurs when evaluating $\ln(+0)$.  The
-%   \enquote{underflow} and \enquote{overflow}
-%   exceptions occur when appropriate.
+%   \enquote{Division by zero} occurs when evaluating $\ln(+0) =
+%   -\infty$.  \enquote{Underflow} and \enquote{overflow} occur when
+%   appropriate.
 % \end{function}
 %
-% \begin{function}{max, min}
+% \begin{function}[tested = m3fp-logic002]{max, min}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ |max(| \meta{fpexpr_1} |,| \meta{fpexpr_2} |,| \ldots{} |)| \}
 %     \cs{fp_eval:n} \{ |min(| \meta{fpexpr_1} |,| \meta{fpexpr_2} |,| \ldots{} |)| \}
 %   \end{syntax}
 %   Evalutes each \meta{fpexpr} and computes the largest (smallest) of
 %   those.  If any of the \meta{fpexpr} is a \nan{}, the result is
-%   \nan{}.
+%   \nan{}.  Those operations do not raise exceptions.
 % \end{function}
 %
-% \begin{function}{round, round0, round+, round-}
+% \begin{function}[tested = {m3fp-round001, m3fp-round002}]
+%   {round, round0, round+, round-}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ |round| \meta{option} |(| \meta{fpexpr} |)| \}
 %     \cs{fp_eval:n} \{ |round| \meta{option} |(| \meta{fpexpr_1} , \meta{fpexpr_2} |)| \}
 %   \end{syntax}
-%   Rounds \meta{fpexpr_1} to \meta{fpexpr_2} places (this must be an
-%   integer).  When \meta{fpexpr_2} is missing, it is assumed to be $0$,
-%   \emph{i.e.}, \meta{fpexpr_1} is rounded to an integer.  The
-%   \meta{option} controls the rounding direction:
+%   Rounds \meta{fpexpr_1} to \meta{fpexpr_2} places.  When
+%   \meta{fpexpr_2} is omitted, it is assumed to be $0$, \emph{i.e.},
+%   \meta{fpexpr_1} is rounded to an integer.  The \meta{option}
+%   controls the rounding direction:
 %   \begin{itemize}
-%     \item by default, the function rounds to the closest allowed number
+%     \item by default, the operation rounds to the closest allowed number
 %       (rounding ties to even);
-%     \item with |0|, the function rounds towards $0$, \emph{i.e.}, truncates;
-%     \item with |+|, the function rounds towards $+\infty$;
-%     \item with |-|, the function rounds towards $-\infty$.
+%     \item with |0|, the operation rounds towards $0$, \emph{i.e.}, truncates;
+%     \item with |+|, the operation rounds towards $+\infty$;
+%     \item with |-|, the operation rounds towards $-\infty$.
 %   \end{itemize}
+%   If \meta{fpexpr_2} does not yield an integer less than $10^{8}$ in
+%   absolute value, then an \enquote{invalid operation} exception is
+%   raised.  \enquote{Overflow} may occur if the result is infinite
+%   (this cannot happen unless $\meta{fpexpr_2}\string<-9984$).
 % \end{function}
 %
-% \begin{function}{sin, cos, tan, cot}
+% \begin{function}[tested = m3fp-trig001]{sin, cos, tan, cot, csc, sec}
 %   \begin{syntax}
 %     \cs{fp_eval:n} \{ |sin(| \meta{fpexpr} |)| \}
 %     \cs{fp_eval:n} \{ |cos(| \meta{fpexpr} |)| \}
 %     \cs{fp_eval:n} \{ |tan(| \meta{fpexpr} |)| \}
 %     \cs{fp_eval:n} \{ |cot(| \meta{fpexpr} |)| \}
+%     \cs{fp_eval:n} \{ |csc(| \meta{fpexpr} |)| \}
+%     \cs{fp_eval:n} \{ |sec(| \meta{fpexpr} |)| \}
 %   \end{syntax}
-%   Computes the sine, cosine, tangent or cotangent of the
-%   \meta{fpexpr}.  The trigonometric functions are undefined for an
-%   argument of $\pm\infty$, leading to the \enquote{invalid operation}
-%   exception.  Additionally, evaluating tangent or cotangent at one of
-%   their poles leads to a \enquote{division by zero} exception.  Other
-%   exceptions occur when appropriate.
+%   Computes the sine, cosine, tangent, cotangent, cosecant, or secant
+%   of the \meta{fpexpr}.  The trigonometric functions are undefined for
+%   an argument of $\pm\infty$, leading to the \enquote{invalid
+%     operation} exception.  Additionally, evaluating tangent,
+%   cotangent, cosecant, or secant at one of their poles leads to a
+%   \enquote{division by zero} exception.  \enquote{Underflow} and
+%   \enquote{overflow} occur when appropriate.
 % \end{function}
 %
-% \begin{variable}{inf, nan}
+% \begin{variable}[tested = m3fp-parse001]{inf, nan}
 %   The special values $+\infty$, $-\infty$, and \nan{} are represented
 %   as \texttt{inf}, \texttt{-inf} and \texttt{nan} (see \cs{c_inf_fp},
 %   \cs{c_minus_inf_fp} and \cs{c_nan_fp}).
 % \end{variable}
 %
-% \begin{variable}{pi}
+% \begin{variable}[tested = m3fp-parse001]{pi}
 %   The value of $\pi$ (see \cs{c_pi_fp}).
 % \end{variable}
 %
-% \begin{variable}{deg}
+% \begin{variable}[tested = m3fp-parse001]{deg}
 %   The value of $1^{\circ}$ in radians (see \cs{c_one_degree_fp}).
 % \end{variable}
 %
-% \begin{variable}{em, ex, in, pt, pc, cm, mm, dd, cc, nd, nc, bp, sp}
+% \begin{variable}[tested = m3fp-parse001]
+%   {em, ex, in, pt, pc, cm, mm, dd, cc, nd, nc, bp, sp}
 %   \newcommand{\unit}[1]{\text{\texttt{#1}}}
-%   Those units of measurement are equal to their values in \texttt{pt},
+%   Those units of measurement are equal to their values in \unit{pt},
 %   namely
 %   \begin{align*}
 %     1 \unit{in} & = 72.27 \unit{pt} \\
@@ -837,16 +951,17 @@
 %     1 \unit{bp} & = \frac{1}{72} \unit{in} = 1.00375 \unit{pt} \\
 %     1 \unit{sp} & = 2^{-16} \unit{pt} = 1.52587890625e-5 \unit{pt}.
 %   \end{align*}
-%   The values of the (font-dependent) units \texttt{em} and \texttt{ex}
-%   are gathered from \TeX{} when the surrounding floating point
-%   expression is evaluated.
+%   The values of the (font-dependent) units \unit{em} and \unit{ex} are
+%   gathered from \TeX{} when the surrounding floating point expression
+%   is evaluated.
 % \end{variable}
 %
-% \begin{variable}{true, false}
+% \begin{variable}[tested = m3fp-parse001]{true, false}
 %   Other names for $1$ and $+0$.
 % \end{variable}
 %
-% \begin{function}[EXP, added = 2012-05-08]{\dim_to_fp:n}
+% \begin{function}[EXP, added = 2012-05-08, tested = m3fp-convert002]
+%   {\dim_to_fp:n}
 %   \begin{syntax}
 %     \cs{dim_to_fp:n} \Arg{dimexpr}
 %   \end{syntax}
@@ -857,29 +972,18 @@
 %   where a low precision is acceptable.
 % \end{function}
 %
-% \begin{function}[EXP, added = 2012-05-14, updated = 2012-07-08]{\fp_abs:n}
+% \begin{function}[EXP, added = 2012-05-14, updated = 2012-07-08,
+%   tested = m3fp-convert003]{\fp_abs:n}
 %   \begin{syntax}
 %     \cs{fp_abs:n} \Arg{floating point expression}
 %   \end{syntax}
 %   Evaluates the \meta{floating point expression} as described for
-%   \cs{fp_eval:n} and leaves the absolute value of the result in
-%   the input stream.
+%   \cs{fp_eval:n} and leaves the absolute value of the result in the
+%   input stream.  This function does not raise any exception beyond
+%   those raised when evaluating its argument.  Within floating point
+%   expressios, |abs()| can be used.
 % \end{function}
 %
-% ^^A todo
-% ^^A \section{Rounding}
-% ^^A
-% ^^A This explains how to go from a floating point number to a
-% ^^A rounded value for various applications. Perhaps worth coding
-% ^^A functionalities up to what siunitx can do on this matter.
-%
-% ^^A todo
-% ^^A \section{Floating points}
-% ^^A
-% ^^A Here, there may be a discussion of what floating point numbers
-% ^^A are, and a list of relevant resources (\emph{e.g.}, some of
-% ^^A Kahan's articles), and previous \TeX{} packages.
-%
 % \section{Disclaimer and roadmap}
 %
 % The package may break down if:
@@ -907,7 +1011,8 @@
 %     \texttt{any}, and \texttt{xor}?
 %   \item Add \texttt{csc} and \texttt{sec}.
 %   \item Add $\log(x,b)$ for logarithm of $x$ in base $b$.
-%   \item \texttt{hypot} (Euclidean length) and $\atan(x,y) = \atan(x/y)$,
+%   \item \texttt{hypot} (Euclidean length) and 
+%     $\operatorname{atan}(x,y) = \operatorname{atan}(x/y)$,
 %     also called \texttt{atan2} in other math packages.
 %     Cartesian-to-polar transform.  Other inverse trigonometric functions
 %     \texttt{acos}, \texttt{asin}, \texttt{atan} (one and two arguments).
@@ -918,8 +1023,8 @@
 %   \item Random numbers (pgfmath provides |rnd|, |rand|, |random|), with
 %     seed reset at every \cs{fp_set:Nn}.
 %   \item Factorial (not with |!|), gamma function.
-%   \item Improve coefficients of \texttt{sin}, \texttt{cos} and
-%     \texttt{tan}.
+%   \item Improve coefficients of the \texttt{sin} and \texttt{tan}
+%     series.
 %   \item Treat upper and lower case letters identically in
 %     identifiers, and ignore underscores.
 %   \item Parse $-3<-2<-1$ as it should, not $(-3<-2)<-1$.
@@ -933,6 +1038,10 @@
 %
 % Bugs. (Exclamation points mark important bugs.)
 % \begin{itemize}
+% \item[!] Some functions are not monotonic when they should.  For
+%   instance, $\sin(1-10^{-16})$ is wrongly greater than $\sin(1)$.
+%   \item Add exceptions to |?:|, |!<=>?|, |&&|, \verb"||", and |!|.
+%   \item |round| should accept any integer as its second argument.
 %   \item Logarithms of numbers very close to $1$ are inaccurate.
 %   \item \texttt{tan} and \texttt{cot} give very slightly wrong results
 %     for arguments near $10^{-8}$.
@@ -952,6 +1061,10 @@
 %
 % Possible optimizations/improvements.
 % \begin{itemize}
+%   \item Optimize argument reduction for trigonometric functions: we
+%     don't need $6\times 4$ digits here, only $4\times 4$.
+%   \item In subsection~\ref{sec:fp-floats}, write a grammar.
+%   \item Fix the |TWO BARS| business with the index.
 %   \item It would be nice if the \texttt{parse} auxiliaries for each
 %     operation were set up in the corresponding module, rather than
 %     centralizing in \pkg{l3fp-parse}.
@@ -974,6 +1087,11 @@
 %     and \cs{@@_basics_pack_weird_high:NNNNNNNNw} better.  Move the
 %     other \texttt{basics_pack} auxiliaries to \pkg{l3fp-aux} under a
 %     better name.
+%   \item Find out if underflow can really occur for trigonometric
+%     functions, and redoc as appropriate.
+%   \item Add bibliography.  Some of Kahan's articles, some previous
+%     \TeX{} fp packages, the international standards,\ldots{}
+%   \item Also take into account the \enquote{inexact} exception?
 % \end{itemize}
 %
 % \end{documentation}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3int.dtx b/Master/texmf-dist/source/latex/l3kernel/l3int.dtx
index d0f7ab46de7..7a176c93588 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3int.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3int.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3int.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3int.dtx 4121 2012-08-17 01:36:30Z bruno $
   {L3 Integers}
 %</driver|package>
 %<*driver>
@@ -258,7 +258,7 @@
 %   \begin{syntax}
 %     \cs{int_sub:Nn} \meta{integer} \Arg{integer expression}
 %   \end{syntax}
-%   Subtracts the result of the \meta{integer expression} to the
+%   Subtracts the result of the \meta{integer expression} from the
 %   current content of the \meta{integer}.
 % \end{function}
 %
@@ -365,36 +365,9 @@
 %
 % \section{Integer expression loops}
 %
-% \begin{function}[rEXP]{\int_do_while:nNnn}
-%   \begin{syntax}
-%      \cs{int_do_while:nNnn}
-%      ~~\Arg{intexpr_1} \meta{relation} \Arg{intexpr_2} \Arg{code}
-%   \end{syntax}
-%   Evaluates the relationship between the two \meta{integer expressions}
-%   as described for \cs{int_compare:nNnTF}, and then places the
-%   \meta{code} in the input stream if the \meta{relation} is
-%   \texttt{true}. After the \meta{code} has been processed by \TeX{} the
-%   test will be repeated, and a loop will occur until the test is
-%   \texttt{false}.
-% \end{function}
-%
 % \begin{function}[rEXP]{\int_do_until:nNnn}
 %   \begin{syntax}
-%      \cs{int_do_until:nNnn}
-%      ~~\Arg{intexpr_1} \meta{relation} \Arg{intexpr_2} \Arg{code}
-%   \end{syntax}
-%   Evaluates the relationship between the two \meta{integer expressions}
-%   as described for \cs{int_compare:nNnTF}, and then places the
-%   \meta{code} in the input stream if the \meta{relation} is
-%   \texttt{false}. After the \meta{code} has been processed by \TeX{} the
-%   test will be repeated, and a loop will occur until the test is
-%   \texttt{true}.
-% \end{function}
-%
-% \begin{function}[rEXP]{\int_until_do:nNnn}
-%   \begin{syntax}
-%      \cs{int_until_do:nNnn}
-%      ~~\Arg{intexpr_1} \meta{relation} \Arg{intexpr_2} \Arg{code}
+%      \cs{int_do_until:nNnn} \Arg{intexpr_1} \meta{relation} \Arg{intexpr_2} \Arg{code}
 %   \end{syntax}
 %   Places the \meta{code} in the input stream for \TeX{} to process, and
 %   then evaluates the relationship between the two
@@ -404,10 +377,9 @@
 %   \meta{relation} is \texttt{true}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\int_while_do:nNnn}
+% \begin{function}[rEXP]{\int_do_while:nNnn}
 %   \begin{syntax}
-%      \cs{int_while_do:nNnn} \
-%      ~~\Arg{intexpr_1} \meta{relation} \Arg{intexpr_2} \Arg{code}
+%      \cs{int_do_while:nNnn} \Arg{intexpr_1} \meta{relation} \Arg{intexpr_2} \Arg{code}
 %   \end{syntax}
 %   Places the \meta{code} in the input stream for \TeX{} to process, and
 %   then evaluates the relationship between the two
@@ -417,38 +389,35 @@
 %   \meta{relation} is \texttt{false}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\int_do_while:nn}
+% \begin{function}[rEXP]{\int_until_do:nNnn}
 %   \begin{syntax}
-%      \cs{int_do_while:nn}
-%      ~~\{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \Arg{code}
+%      \cs{int_until_do:nNnn} \Arg{intexpr_1} \meta{relation} \Arg{intexpr_2} \Arg{code}
 %   \end{syntax}
 %   Evaluates the relationship between the two \meta{integer expressions}
-%   as described for \cs{int_compare:nTF}, and then places the
+%   as described for \cs{int_compare:nNnTF}, and then places the
 %   \meta{code} in the input stream if the \meta{relation} is
-%   \texttt{true}. After the \meta{code} has been processed by \TeX{} the
+%   \texttt{false}. After the \meta{code} has been processed by \TeX{} the
 %   test will be repeated, and a loop will occur until the test is
-%   \texttt{false}.
+%   \texttt{true}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\int_do_until:nn}
+% \begin{function}[rEXP]{\int_while_do:nNnn}
 %   \begin{syntax}
-%      \cs{int_do_until:nn}
-%      ~~\{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \Arg{code}
+%      \cs{int_while_do:nNnn} \Arg{intexpr_1} \meta{relation} \Arg{intexpr_2} \Arg{code}
 %   \end{syntax}
 %   Evaluates the relationship between the two \meta{integer expressions}
-%   as described for \cs{int_compare:nTF}, and then places the
+%   as described for \cs{int_compare:nNnTF}, and then places the
 %   \meta{code} in the input stream if the \meta{relation} is
-%   \texttt{false}. After the \meta{code} has been processed by \TeX{} the
+%   \texttt{true}. After the \meta{code} has been processed by \TeX{} the
 %   test will be repeated, and a loop will occur until the test is
-%   \texttt{true}.
+%   \texttt{false}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\int_until_do:nn}
+% \begin{function}[rEXP]{\int_do_until:nn}
 %   \begin{syntax}
-%      \cs{int_until_do:nn}
-%      ~~\{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \Arg{code}
+%      \cs{int_do_until:nn} \{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \Arg{code}
 %   \end{syntax}
-%   Places the \meta{code} in the input stream for \TeX\ to process, and
+%   Places the \meta{code} in the input stream for \TeX{} to process, and
 %   then evaluates the relationship between the two
 %   \meta{integer expressions} as described for \cs{int_compare:nTF}.
 %   If the test is \texttt{false} then the \meta{code} will be inserted
@@ -456,10 +425,9 @@
 %   \meta{relation} is \texttt{true}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\int_while_do:nn}
+% \begin{function}[rEXP]{\int_do_while:nn}
 %   \begin{syntax}
-%      \cs{int_while_do:nn} \
-%      ~~\{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \Arg{code}
+%      \cs{int_do_while:nn} \{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \Arg{code}
 %   \end{syntax}
 %   Places the \meta{code} in the input stream for \TeX{} to process, and
 %   then evaluates the relationship between the two
@@ -469,6 +437,30 @@
 %   \meta{relation} is \texttt{false}.
 % \end{function}
 %
+% \begin{function}[rEXP]{\int_until_do:nn}
+%   \begin{syntax}
+%      \cs{int_until_do:nn} \{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \Arg{code}
+%   \end{syntax}
+%   Evaluates the relationship between the two \meta{integer expressions}
+%   as described for \cs{int_compare:nTF}, and then places the
+%   \meta{code} in the input stream if the \meta{relation} is
+%   \texttt{false}. After the \meta{code} has been processed by \TeX{} the
+%   test will be repeated, and a loop will occur until the test is
+%   \texttt{true}.
+% \end{function}
+%
+% \begin{function}[rEXP]{\int_while_do:nn}
+%   \begin{syntax}
+%      \cs{int_while_do:nn} \{ \meta{intexpr_1} \meta{relation} \meta{intexpr_2} \} \Arg{code}
+%   \end{syntax}
+%   Evaluates the relationship between the two \meta{integer expressions}
+%   as described for \cs{int_compare:nTF}, and then places the
+%   \meta{code} in the input stream if the \meta{relation} is
+%   \texttt{true}. After the \meta{code} has been processed by \TeX{} the
+%   test will be repeated, and a loop will occur until the test is
+%   \texttt{false}.
+% \end{function}
+%
 % \section{Integer step functions}
 %
 % \begin{function}[added = 2012-06-04, updated = 2012-06-29, rEXP]
@@ -1508,11 +1500,11 @@
   }
 \cs_new:Npn \int_until_do:nNnn #1#2#3#4
   {
-  \int_compare:nNnF {#1} #2 {#3}
-    {
-      #4
-      \int_until_do:nNnn {#1} #2 {#3} {#4}
-    }
+    \int_compare:nNnF {#1} #2 {#3}
+      {
+        #4
+        \int_until_do:nNnn {#1} #2 {#3} {#4}
+      }
   }
 \cs_new:Npn \int_do_while:nNnn #1#2#3#4
   {
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3msg.dtx b/Master/texmf-dist/source/latex/l3kernel/l3msg.dtx
index 5d690ced2cf..a1e30326917 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3msg.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3msg.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3msg.dtx 4077 2012-08-10 23:30:52Z bruno $
+\GetIdInfo$Id: l3msg.dtx 4147 2012-08-28 10:27:33Z bruno $
   {L3 Messages}
 %</driver|package>
 %<*driver>
@@ -722,8 +722,9 @@
 %   formatting. Used in messages which print complex variable contents
 %   completely.
 % \end{function}
-% 
-% \begin{function}{\__msg_show_variable:Nnn, \__msg_show_variable:Nnx}
+%
+% \begin{function}[updated = 2012-08-14]
+%   {\__msg_show_variable:Nnn, \__msg_show_variable:Nnx}
 %   \begin{syntax}
 %     \cs{__msg_show_variable:Nnn} \meta{variable} \Arg{type} \Arg{formatted content}
 %   \end{syntax}
@@ -731,8 +732,10 @@
 %   in the terminal. The \meta{formatted content} will typically be generated
 %   by \texttt{x}-type expansion using the \cs{__msg_show_variable:Nnx} variant:
 %   the nature of the formatting is dependent on the calling module.
+%   The \meta{formatted content} must be a string, either empty or
+%   containing |>|; everything until the first |>| will be removed.
 % \end{function}
-% 
+%
 % \begin{function}{\__msg_show_variable:n, \__msg_show_variable:x}
 %   \begin{syntax}
 %     \cs{__msg_show_variable:n} \Arg{formatted string}
@@ -742,7 +745,7 @@
 %   and the part of \meta{formatted string} before the first |>| is
 %   removed. Failure to do so causes low-level \TeX{} errors.
 % \end{function}
-% 
+%
 % \begin{function}
 %   {\__msg_show_item:n, \__msg_show_item:nn, \__msg_show_item_unbraced:nn}
 %   \begin{syntax}
@@ -752,7 +755,7 @@
 %   Auxiliary functions used within the argument of
 %   \cs{__msg_show_variable:Nnx} to format variable items correctly for
 %   display. The \cs{__msg_show_item:n} version is used for simple lists,
-%   the \cs{__msg_show_item:nn} and \cs{__msg_show_item_ubraced:nn} versions
+%   the \cs{__msg_show_item:nn} and \cs{__msg_show_item_unbraced:nn} versions
 %   for key--value like data structures.
 % \end{function}
 %
@@ -1815,7 +1818,7 @@
     \c_msg_coding_error_text_tl
     Code-level~functions~must~contain~':'~to~separate~the~
     argument~specification~from~the~function~name.~This~is~
-    needed~when~defining~conditionals~or~when~building~a~
+    needed~when~defining~conditionals~or~variants,~or~when~building~a~
     parameter~text~from~the~number~of~arguments~of~the~function.
   }
 \@@_kernel_new:nnnn { kernel } { protected-predicate }
@@ -1854,6 +1857,14 @@
     with~a~signature~starting~with~'#1',~but~that~is~longer~than~
     the~signature~(part~after~the~colon)~of~'#2'.
   }
+\@@_kernel_new:nnnn { kernel } { invalid-variant }
+  { Variant~form~'#1'~invalid~for~base~form~'#2'. }
+  {
+    \c_msg_coding_error_text_tl
+    LaTeX~has~been~asked~to~create~a~variant~of~the~function~'#2'~
+    with~a~signature~starting~with~'#1',~but~cannot~change~an~argument~
+    from~type~'#3'~to~type~'#4'.
+  }
 %    \end{macrocode}
 %
 % Some errors only appear in expandable settings,
@@ -2027,10 +2038,10 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}[int]{\@@_show_variable:Nnn, \@@_show_variable:Nnn}
+% \begin{macro}[int]{\@@_show_variable:Nnn, \@@_show_variable:Nnx}
 % \begin{macro}[int]{\@@_show_variable:n, \@@_show_variable:x}
 % \begin{macro}[aux,EXP]{\@@_show_variable:w}
-%   The arguments of \cs{@@_show_variable:Nnn} are
+%   The arguments of \cs{@@_show_variable:Nnx} are
 %   \begin{itemize}
 %     \item The \meta{variable} to be shown.
 %     \item The \texttt{TF} emptiness conditional for that type of variables.
@@ -2050,7 +2061,7 @@
     \cs_if_exist:NTF #1
       {
         \@@_term:nnn { LaTeX / kernel } { show- #2 } {#1}
-        \@@_show_variable:x {#3}
+        \@@_show_variable:x { \tl_to_str:n {#3} }
       }
       {
         \@@_kernel_error:nnx { kernel } { variable-not-defined }
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3prg.dtx b/Master/texmf-dist/source/latex/l3kernel/l3prg.dtx
index 0db3e319bb2..0c81f7f9951 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3prg.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3prg.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3prg.dtx 4061 2012-08-08 15:19:07Z bruno $
+\GetIdInfo$Id: l3prg.dtx 4114 2012-08-16 01:57:02Z bruno $
   {L3 Control structures}
 %</driver|package>
 %<*driver>
@@ -282,8 +282,8 @@
 %
 % \begin{function}[EXP,pTF]{\bool_if:N, \bool_if:c}
 %   \begin{syntax}
-%     \cs{bool_if_p:N} \Arg{boolean}
-%     \cs{bool_if:NTF} \Arg{boolean} \Arg{true code} \Arg{false code}
+%     \cs{bool_if_p:N} \meta{boolean}
+%     \cs{bool_if:NTF} \meta{boolean} \Arg{true code} \Arg{false code}
 %   \end{syntax}
 %   Tests the current truth of \meta{boolean}, and continues expansion
 %   based on this result.
@@ -406,11 +406,33 @@
 %
 % \section{Logical loops}
 %
-%  Loops using either boolean expressions or stored boolean values.
+% Loops using either boolean expressions or stored boolean values.
+%
+% \begin{function}[rEXP]{\bool_do_until:Nn, \bool_do_until:cn}
+%   \begin{syntax}
+%     \cs{bool_do_until:Nn} \meta{boolean} \Arg{code}
+%   \end{syntax}
+%   Places the \meta{code} in the input stream for \TeX{} to process,
+%   and then checks the logical value of the \meta{boolean}.  If it is
+%   \texttt{false} then the \meta{code} will be inserted into the input
+%   stream again and the process will loop until the \meta{boolean} is
+%   \texttt{true}.
+% \end{function}
+%
+% \begin{function}[rEXP]{\bool_do_while:Nn, \bool_do_while:cn}
+%   \begin{syntax}
+%     \cs{bool_do_while:Nn} \meta{boolean} \Arg{code}
+%   \end{syntax}
+%   Places the \meta{code} in the input stream for \TeX{} to process,
+%   and then checks the logical value of the \meta{boolean}.  If it is
+%   \texttt{true} then the \meta{code} will be inserted into the input
+%   stream again and the process will loop until the \meta{boolean} is
+%   \texttt{false}.
+% \end{function}
 %
 % \begin{function}[rEXP]{\bool_until_do:Nn, \bool_until_do:cn}
 %   \begin{syntax}
-%     \cs{bool_until_do:Nn} \Arg{boolean} \Arg{code}
+%     \cs{bool_until_do:Nn} \meta{boolean} \Arg{code}
 %   \end{syntax}
 %   This function firsts checks the logical value of the \meta{boolean}.
 %   If it is \texttt{false} the \meta{code} is placed in the input stream
@@ -421,7 +443,7 @@
 %
 % \begin{function}[rEXP]{\bool_while_do:Nn, \bool_while_do:cn}
 %   \begin{syntax}
-%     \cs{bool_while_do:Nn} \Arg{boolean} \Arg{code}
+%     \cs{bool_while_do:Nn} \meta{boolean} \Arg{code}
 %   \end{syntax}
 %   This function firsts checks the logical value of the \meta{boolean}.
 %   If it is \texttt{true} the \meta{code} is placed in the input stream
@@ -430,6 +452,30 @@
 %   until the \meta{boolean} is \texttt{false}.
 % \end{function}
 %
+% \begin{function}[rEXP, updated = 2012-07-08]{\bool_do_until:nn}
+%   \begin{syntax}
+%     \cs{bool_do_until:nn} \Arg{boolean expression} \Arg{code}
+%   \end{syntax}
+%   Places the \meta{code} in the input stream for \TeX{} to process,
+%   and then checks the logical value of the \meta{boolean expression}
+%   as described for \cs{bool_if:nTF}.  If it is \texttt{false} then the
+%   \meta{code} will be inserted into the input stream again and the
+%   process will loop until the \meta{boolean expression} evaluates to
+%   \texttt{true}.
+% \end{function}
+%
+% \begin{function}[rEXP, updated = 2012-07-08]{\bool_do_while:nn}
+%   \begin{syntax}
+%     \cs{bool_do_while:nn} \Arg{boolean expression} \Arg{code}
+%   \end{syntax}
+%   Places the \meta{code} in the input stream for \TeX{} to process,
+%   and then checks the logical value of the \meta{boolean expression}
+%   as described for \cs{bool_if:nTF}.  If it is \texttt{true} then the
+%   \meta{code} will be inserted into the input stream again and the
+%   process will loop until the \meta{boolean expression} evaluates to
+%   \texttt{false}.
+% \end{function}
+%
 % \begin{function}[rEXP, updated = 2012-07-08]{\bool_until_do:nn}
 %   \begin{syntax}
 %     \cs{bool_until_do:nn} \Arg{boolean expression} \Arg{code}
@@ -789,7 +835,7 @@
 %
 % \begin{macro}{\bool_show:N, \bool_show:c, \bool_show:n}
 %   Show the truth value of the boolean, as \texttt{true} or
-%   \texttt{false}. We use \cs{__msg_show_variable:x} to get a better output;
+%   \texttt{false}. We use \cs{__msg_show_variable:n} to get a better output;
 %   this function requires its argument to start with |>|.
 %    \begin{macrocode}
 \cs_new_protected:Npn \bool_show:N #1
@@ -804,8 +850,8 @@
 \cs_new_protected:Npn \bool_show:n #1
   {
     \bool_if:nTF {#1}
-      { \__msg_show_variable:x { > true } }
-      { \__msg_show_variable:x { > false } }
+      { \__msg_show_variable:n { > true } }
+      { \__msg_show_variable:n { > false } }
   }
 \cs_generate_variant:Nn \bool_show:N { c }
 %    \end{macrocode}
@@ -1182,7 +1228,7 @@
 %    \begin{macrocode}
 \cs_new:Npn \bool_not_p:n #1 { \bool_if_p:n { ! ( #1 ) } }
 %    \end{macrocode}
-%  \end{macro}
+% \end{macro}
 %
 % \begin{macro}{\bool_xor_p:nn}
 % \UnitTested
@@ -1242,7 +1288,7 @@
 %     \bool_while_do:nn, \bool_do_while:nn ,
 %     \bool_until_do:nn, \bool_do_until:nn
 %   }
-%  \UnitTested
+%   \UnitTested
 %   Loop functions with the test either before or after the first body
 %   expansion.
 %    \begin{macrocode}
@@ -1479,11 +1525,21 @@
 %
 % \begin{macro}[int]{\scan_align_safe_stop:}
 %   When \TeX{} is in the beginning of an align cell (right after the
-%   \tn{cr}) it is in a somewhat strange mode as it is looking ahead to
-%   find an \tn{omit} or \tn{noalign} and hasn't looked at the
-%   preamble yet. Thus an \tn{ifmmode} test will always fail unless
-%   we insert \cs{scan_stop:} to stop \TeX{}'s scanning ahead. On the other
-%   hand we don't want to insert a \cs{scan_stop:} every time as that will
+%   \tn{cr} or |&|) it is in a somewhat strange mode as it is looking
+%   ahead to find an \tn{omit} or \tn{noalign} and hasn't looked at the
+%   preamble yet.  Thus an \tn{ifmmode} test at the start of an array
+%   cell (where math mode is introduced by the preamble, not in the cell
+%   itself) will always fail unless we stop \TeX{} from scanning ahead.
+%   With \eTeX{}'s first version, this required inserting
+%   \cs{scan_stop:}, but not in all cases (see below).  This is no
+%   longer needed with a newer \eTeX{}, since protected macros are not
+%   expanded anymore at the beginning of an alignment cell.  We can thus
+%   use an empty protected macro to stop \TeX{}.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \scan_align_safe_stop: { }
+%    \end{macrocode}
+%   Let us now explain the earlier version.  We don't want to insert
+%   a \cs{scan_stop:} every time as that will
 %   destroy kerning between letters\footnote{Unless we enforce an extra
 %   pass with an appropriate value of \tn{pretolerance}.}
 %   Unfortunately there is no way to detect if we're in the beginning of
@@ -1508,12 +1564,8 @@
 %           }
 %      }
 %    \end{verbatim}
-%  However, this is not truly expandable, as there are places where the
-%  \cs{scan_stop:} ends up in the result. A simpler alternative, which
-%  can be used selectively, is therefore defined.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \scan_align_safe_stop: { }
-%    \end{macrocode}
+%   However, this is not truly expandable, as there are places where the
+%   \cs{scan_stop:} ends up in the result.
 % \end{macro}
 %
 %    \begin{macrocode}
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3prop.dtx b/Master/texmf-dist/source/latex/l3kernel/l3prop.dtx
index d27c6c48382..cda5912494a 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3prop.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3prop.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3prop.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3prop.dtx 4092 2012-08-14 14:04:41Z bruno $
   {L3 Property lists}
 %</driver|package>
 %<*driver>
@@ -1026,15 +1026,13 @@
 % \subsection{Viewing property lists}
 %
 % \begin{macro}[tested = m3show001]{\prop_show:N, \prop_show:c}
-%   Apply the general \cs{__msg_show_variable:Nnn}. Contrarily
+%   Apply the general \cs{__msg_show_variable:Nnx}. Contrarily
 %   to sequences and comma lists, we use \cs{__msg_show_item:nn}
 %   to format both the key and the value for each pair.
 %    \begin{macrocode}
 \cs_new_protected:Npn \prop_show:N #1
   {
-    \__msg_show_variable:Nnn
-      #1
-      { prop }
+    \__msg_show_variable:Nnx #1 { prop }
       { \prop_map_function:NN #1 \__msg_show_item:nn }
   }
 \cs_generate_variant:Nn \prop_show:N { c }
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3seq.dtx b/Master/texmf-dist/source/latex/l3kernel/l3seq.dtx
index 38491dd1223..596d6b832cd 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3seq.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3seq.dtx
@@ -35,7 +35,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3seq.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3seq.dtx 4092 2012-08-14 14:04:41Z bruno $
   {L3 Sequences and stacks}
 %</driver|package>
 %<*driver>
@@ -1551,13 +1551,11 @@
 %
 % \begin{macro}{\seq_show:N, \seq_show:c}
 % \UnitTested
-% Apply the general \cs{__msg_show_variable:Nnn}.
+% Apply the general \cs{__msg_show_variable:Nnx}.
 %    \begin{macrocode}
 \cs_new_protected:Npn \seq_show:N #1
   {
-    \__msg_show_variable:Nnn
-      #1
-      { seq }
+    \__msg_show_variable:Nnx #1 { seq }
       { \seq_map_function:NN #1 \__msg_show_item:n }
   }
 \cs_generate_variant:Nn \seq_show:N { c }
diff --git a/Master/texmf-dist/source/latex/l3kernel/l3skip.dtx b/Master/texmf-dist/source/latex/l3kernel/l3skip.dtx
index 26797004a54..911fe7571f0 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3skip.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3skip.dtx
@@ -36,7 +36,7 @@
 %
 %<*driver|package>
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3skip.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3skip.dtx 4121 2012-08-17 01:36:30Z bruno $
   {L3 Dimensions and skips}
 %</driver|package>
 %<*driver>
@@ -181,7 +181,7 @@
 %   \begin{syntax}
 %     \cs{dim_sub:Nn} \meta{dimension} \Arg{dimension expression}
 %   \end{syntax}
-%   Subtracts the result of the \meta{dimension expression} to the
+%   Subtracts the result of the \meta{dimension expression} from the
 %   current content of the \meta{dimension}.
 % \end{function}
 %
@@ -292,34 +292,10 @@
 %
 % \section{Dimension expression loops}
 %
-% \begin{function}[rEXP]{\dim_do_while:nNnn}
-%   \begin{syntax}
-%      \cs{dim_do_while:nNnn} \Arg{dimexpr_1} \meta{relation} \Arg{dimexpr_2} \Arg{code}
-%   \end{syntax}
-%   Evaluates the relationship between the two \meta{dimension expressions}
-%   as described for \cs{dim_compare:nNnTF}, and then places the
-%   \meta{code} in the input stream if the \meta{relation} is
-%   \texttt{true}. After the \meta{code} has been processed by \TeX{} the
-%   test will be repeated, and a loop will occur until the test is
-%   \texttt{false}.
-% \end{function}
-%
 % \begin{function}[rEXP]{\dim_do_until:nNnn}
 %   \begin{syntax}
 %      \cs{dim_do_until:nNnn} \Arg{dimexpr_1} \meta{relation} \Arg{dimexpr_2} \Arg{code}
 %   \end{syntax}
-%   Evaluates the relationship between the two \meta{dimension expressions}
-%   as described for \cs{dim_compare:nNnTF}, and then places the
-%   \meta{code} in the input stream if the \meta{relation} is
-%   \texttt{false}. After the \meta{code} has been processed by \TeX{} the
-%   test will be repeated, and a loop will occur until the test is
-%   \texttt{true}.
-% \end{function}
-%
-% \begin{function}[rEXP]{\dim_until_do:nNnn}
-%   \begin{syntax}
-%      \cs{dim_until_do:nNnn} \Arg{dimexpr_1} \meta{relation} \Arg{dimexpr_2} \Arg{code}
-%   \end{syntax}
 %   Places the \meta{code} in the input stream for \TeX{} to process, and
 %   then evaluates the relationship between the two
 %   \meta{dimension expressions} as described for \cs{dim_compare:nNnTF}.
@@ -328,9 +304,9 @@
 %   \meta{relation} is \texttt{true}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\dim_while_do:nNnn}
+% \begin{function}[rEXP]{\dim_do_while:nNnn}
 %   \begin{syntax}
-%      \cs{dim_while_do:nNnn} \Arg{dimexpr_1} \meta{relation} \Arg{dimexpr_2} \Arg{code}
+%      \cs{dim_do_while:nNnn} \Arg{dimexpr_1} \meta{relation} \Arg{dimexpr_2} \Arg{code}
 %   \end{syntax}
 %   Places the \meta{code} in the input stream for \TeX{} to process, and
 %   then evaluates the relationship between the two
@@ -340,33 +316,33 @@
 %   \meta{relation} is \texttt{false}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\dim_do_while:nn}
+% \begin{function}[rEXP]{\dim_until_do:nNnn}
 %   \begin{syntax}
-%      \cs{dim_do_while:nn} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \Arg{code}
+%      \cs{dim_until_do:nNnn} \Arg{dimexpr_1} \meta{relation} \Arg{dimexpr_2} \Arg{code}
 %   \end{syntax}
 %   Evaluates the relationship between the two \meta{dimension expressions}
-%   as described for \cs{dim_compare:nTF}, and then places the
+%   as described for \cs{dim_compare:nNnTF}, and then places the
 %   \meta{code} in the input stream if the \meta{relation} is
-%   \texttt{true}. After the \meta{code} has been processed by \TeX{} the
+%   \texttt{false}. After the \meta{code} has been processed by \TeX{} the
 %   test will be repeated, and a loop will occur until the test is
-%   \texttt{false}.
+%   \texttt{true}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\dim_do_until:nn}
+% \begin{function}[rEXP]{\dim_while_do:nNnn}
 %   \begin{syntax}
-%      \cs{dim_do_until:nn} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \Arg{code}
+%      \cs{dim_while_do:nNnn} \Arg{dimexpr_1} \meta{relation} \Arg{dimexpr_2} \Arg{code}
 %   \end{syntax}
 %   Evaluates the relationship between the two \meta{dimension expressions}
-%   as described for \cs{dim_compare:nTF}, and then places the
+%   as described for \cs{dim_compare:nNnTF}, and then places the
 %   \meta{code} in the input stream if the \meta{relation} is
-%   \texttt{false}. After the \meta{code} has been processed by \TeX{} the
+%   \texttt{true}. After the \meta{code} has been processed by \TeX{} the
 %   test will be repeated, and a loop will occur until the test is
-%   \texttt{true}.
+%   \texttt{false}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\dim_until_do:nn}
+% \begin{function}[rEXP]{\dim_do_until:nn}
 %   \begin{syntax}
-%      \cs{dim_until_do:nn} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \Arg{code}
+%      \cs{dim_do_until:nn} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \Arg{code}
 %   \end{syntax}
 %   Places the \meta{code} in the input stream for \TeX{} to process, and
 %   then evaluates the relationship between the two
@@ -376,9 +352,9 @@
 %   \meta{relation} is \texttt{true}.
 % \end{function}
 %
-% \begin{function}[rEXP]{\dim_while_do:nn}
+% \begin{function}[rEXP]{\dim_do_while:nn}
 %   \begin{syntax}
-%      \cs{dim_while_do:nn} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \Arg{code}
+%      \cs{dim_do_while:nn} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \Arg{code}
 %   \end{syntax}
 %   Places the \meta{code} in the input stream for \TeX{} to process, and
 %   then evaluates the relationship between the two
@@ -388,6 +364,30 @@
 %   \meta{relation} is \texttt{false}.
 % \end{function}
 %
+% \begin{function}[rEXP]{\dim_until_do:nn}
+%   \begin{syntax}
+%      \cs{dim_until_do:nn} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \Arg{code}
+%   \end{syntax}
+%   Evaluates the relationship between the two \meta{dimension expressions}
+%   as described for \cs{dim_compare:nTF}, and then places the
+%   \meta{code} in the input stream if the \meta{relation} is
+%   \texttt{false}. After the \meta{code} has been processed by \TeX{} the
+%   test will be repeated, and a loop will occur until the test is
+%   \texttt{true}.
+% \end{function}
+%
+% \begin{function}[rEXP]{\dim_while_do:nn}
+%   \begin{syntax}
+%      \cs{dim_while_do:nn} \{ \meta{dimexpr_1} \meta{relation} \meta{dimexpr_2} \} \Arg{code}
+%   \end{syntax}
+%   Evaluates the relationship between the two \meta{dimension expressions}
+%   as described for \cs{dim_compare:nTF}, and then places the
+%   \meta{code} in the input stream if the \meta{relation} is
+%   \texttt{true}. After the \meta{code} has been processed by \TeX{} the
+%   test will be repeated, and a loop will occur until the test is
+%   \texttt{false}.
+% \end{function}
+%
 % \section{Using \texttt{dim} expressions and variables}
 %
 % \begin{function}[updated = 2011-10-22, EXP]{\dim_eval:n}
@@ -548,7 +548,7 @@
 %   \begin{syntax}
 %     \cs{skip_sub:Nn} \meta{skip} \Arg{skip expression}
 %   \end{syntax}
-%   Subtracts the result of the \meta{skip expression} to the
+%   Subtracts the result of the \meta{skip expression} from the
 %   current content of the \meta{skip}.
 % \end{function}
 %
@@ -769,7 +769,7 @@
 %   \begin{syntax}
 %     \cs{muskip_sub:Nn} \meta{muskip} \Arg{muskip expression}
 %   \end{syntax}
-%   Subtracts the result of the \meta{muskip expression} to the
+%   Subtracts the result of the \meta{muskip expression} from the
 %   current content of the \meta{skip}.
 % \end{function}
 %
diff --git a/Master/texmf-dist/tex/latex/l3kernel/expl3.sty b/Master/texmf-dist/tex/latex/l3kernel/expl3.sty
index 6adfc5fed60..edf7566552f 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/expl3.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/expl3.sty
@@ -60,8 +60,8 @@
   }
 \def\ExplFileName{expl3}
 \def\ExplFileDescription{L3 Experimental code bundle wrapper}
-\def\ExplFileDate{2012/08/14}
-\def\ExplFileVersion{4091}
+\def\ExplFileDate{2012/08/29}
+\def\ExplFileVersion{4160}
 \RequirePackage{etex}
 \reserveinserts{32}
 \ProvidesExplPackage
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3basics.sty b/Master/texmf-dist/tex/latex/l3kernel/l3basics.sty
index c7c5bcb0eb8..d9dfc41083c 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3basics.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3basics.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3basics.dtx 4069 2012-08-08 23:12:57Z bruno $
+\GetIdInfo$Id: l3basics.dtx 4144 2012-08-27 19:37:16Z bruno $
   {L3 Basic definitions}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -82,7 +82,10 @@
 \tex_let:D \if_int_compare:w   \tex_ifnum:D
 \tex_let:D \__int_to_roman:w     \tex_romannumeral:D
 \tex_let:D \group_insert_after:N \tex_aftergroup:D
-\tex_long:D \tex_def:D \exp_args:Nc #1#2 { \exp_after:wN #1 \cs:w #2 \cs_end: }
+\tex_long:D \tex_def:D \exp_args:Nc #1#2
+  { \exp_after:wN #1 \cs:w #2 \cs_end: }
+\tex_long:D \tex_def:D \exp_args:cc #1#2
+  { \cs:w #1 \exp_after:wN \cs_end: \cs:w #2 \cs_end: }
 \tex_def:D \token_to_str:c { \exp_args:Nc \token_to_str:N }
 \tex_long:D \tex_def:D \cs_meaning:c #1
   {
@@ -254,7 +257,7 @@
       \exp_after:wN \use_ii:nn
     \fi:
       {
-        \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 _p: #5 } #6
+        \exp_args:cc { cs_ #2 #3 :Npn } { #4 _p: #5 } #6
           { #7 \c_zero \c_true_bool \c_false_bool }
       }
       {
@@ -264,17 +267,17 @@
   }
 \cs_set_protected:Npn \__prg_generate_T_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 T } #6
+    \exp_args:cc { cs_ #2 #3 :Npn } { #4 : #5 T } #6
       { #7 \c_zero \use:n \use_none:n }
   }
 \cs_set_protected:Npn \__prg_generate_F_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 F } #6
+    \exp_args:cc { cs_ #2 #3 :Npn } { #4 : #5 F } #6
       { #7 \c_zero { } }
   }
 \cs_set_protected:Npn \__prg_generate_TF_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 TF } #6
+    \exp_args:cc { cs_ #2 #3 :Npn } { #4 : #5 TF } #6
       { #7 \c_zero }
   }
 \cs_set_protected_nopar:Npn \prg_set_eq_conditional:NNn
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3clist.sty b/Master/texmf-dist/tex/latex/l3kernel/l3clist.sty
index 35d5381e677..18cee384adc 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3clist.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3clist.sty
@@ -48,7 +48,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3clist.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3clist.dtx 4102 2012-08-15 16:08:27Z bruno $
   {L3 Comma separated lists}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -146,7 +146,7 @@
 \cs_new_protected_nopar:Npn \clist_put_right:Nn
   { \__clist_put_right:NNNn \clist_concat:NNN \clist_set:Nn }
 \cs_new_protected_nopar:Npn \clist_gput_right:Nn
-  { \__clist_put_right:NNNn \clist_gconcat:NNN \clist_gset:Nn }
+  { \__clist_put_right:NNNn \clist_gconcat:NNN \clist_set:Nn }
 \cs_new_protected:Npn \__clist_put_right:NNNn #1#2#3#4
   {
     #2 \l__clist_internal_clist {#4}
@@ -419,18 +419,13 @@
   }
 \cs_new_protected:Npn \clist_show:N #1
   {
-    \__msg_show_variable:Nnn
-      #1
-      { clist }
+    \__msg_show_variable:Nnx #1 { clist }
       { \clist_map_function:NN #1 \__msg_show_item:n }
   }
 \cs_new_protected:Npn \clist_show:n #1
   {
     \clist_set:Nn \l__clist_internal_clist {#1}
-    \__msg_show_variable:Nnn
-      \l__clist_internal_clist
-      { clist }
-      { \clist_map_function:NN \l__clist_internal_clist \__msg_show_item:n }
+    \clist_show:N \l__clist_internal_clist
   }
 \cs_generate_variant:Nn \clist_show:N { c }
 \clist_new:N \l_tmpa_clist
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty b/Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty
index a126e8fd5c4..1b8d88d4761 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty
@@ -47,7 +47,7 @@
 %% -----------------------------------------------------------------------
 %%
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3coffins.dtx 4011 2012-07-20 21:02:59Z joseph $
+\GetIdInfo$Id: l3coffins.dtx 4092 2012-08-14 14:04:41Z bruno $
   {L3 Coffin code layer}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -807,7 +807,7 @@
   {
     \__coffin_if_exist:NT #1
       {
-        \__msg_show_variable:Nnn #1 { coffins }
+        \__msg_show_variable:Nnx #1 { coffins }
           {
             \prop_map_function:cN
               { l__coffin_poles_ \__int_value:w #1 _prop }
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3color.sty b/Master/texmf-dist/tex/latex/l3kernel/l3color.sty
index 1584c055979..12b019250a5 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3color.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3color.sty
@@ -47,8 +47,8 @@
 %% -----------------------------------------------------------------------
 %%
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3color.dtx 3991 2012-07-16 19:00:35Z joseph $
-  {L3 Experimental colour support}
+\GetIdInfo$Id: l3color.dtx 4156 2012-08-29 11:10:09Z joseph $
+  {L3 Experimental color support}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
 \__expl_package_check:
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3doc.cls b/Master/texmf-dist/tex/latex/l3kernel/l3doc.cls
index 111db55e442..641a13ec78c 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3doc.cls
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3doc.cls
@@ -52,7 +52,7 @@
 \let     \fileversionOld        \ExplFileVersion
 \let \filedescriptionOld        \ExplFileDescription
 \RequirePackage{expl3,xparse,calc}
-\GetIdInfo$Id: l3doc.dtx 4070 2012-08-09 11:04:46Z joseph $
+\GetIdInfo$Id: l3doc.dtx 4130 2012-08-20 21:30:22Z joseph $
           {L3 Experimental documentation class}
 \ProvidesExplClass
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -71,7 +71,6 @@
 \tl_new:N \l__codedoc_macro_tl
 \int_new:N \l__codedoc_macro_int
 \int_new:N \g__codedoc_nested_macro_int
-\int_new:N \g__codedoc_codeline_int
 \prop_new:N \g__codedoc_missing_tests_prop
 \clist_new:N \g_docinput_clist
 \tl_new:N \l__codedoc_at_replaced_macro_tl
@@ -798,7 +797,7 @@
       \tl_to_str:N \l__codedoc_at_replaced_macro_tl
     }]
    }
-  \int_gincr:N \g__codedoc_codeline_int
+  \int_gincr:N \c@CodelineNo
 
   \bool_if:NF \l__codedoc_macro_aux_bool
    {
@@ -822,7 +821,7 @@
     \exp_args:Nx \DoNotIndex{ \tl_to_str:N \l__codedoc_at_replaced_macro_tl }
    }
 
-  \int_gdecr:N \g__codedoc_codeline_int
+  \int_gdecr:N \c@CodelineNo
   \ignorespaces
  }
 \tl_clear:N \l__codedoc_macro_tl
@@ -1250,7 +1249,7 @@
   \immediate\write\@indexfile
    {
     \string\indexentry{#1}
-    { \filesep \int_use:N \g__codedoc_codeline_int }
+    { \filesep \int_use:N \c@CodelineNo }
    }
  }
 \cs_set_eq:NN \filesep \@empty
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3expan.sty b/Master/texmf-dist/tex/latex/l3kernel/l3expan.sty
index f7a458e9a88..6dceea954ad 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3expan.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3expan.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3expan.dtx 4073 2012-08-10 01:33:13Z bruno $
+\GetIdInfo$Id: l3expan.dtx 4149 2012-08-28 10:50:40Z bruno $
   {L3 Argument expansion}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -56,6 +56,7 @@
 \cs_new:Npn \::: #1 {#1}
 \cs_new:Npn \::n #1 \::: #2#3 { #1 \::: { #2 {#3} } }
 \cs_new:Npn \::N #1 \::: #2#3 { #1 \::: {#2#3} }
+\cs_new:Npn \::p #1 \::: #2#3# { #1 \::: {#2#3} }
 \cs_new:Npn \::c #1 \::: #2#3
   { \exp_after:wN \__exp_arg_next:Nnn \cs:w #3 \cs_end: {#1} {#2} }
 \cs_new:Npn \::o #1 \::: #2#3
@@ -109,8 +110,6 @@
   { \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN {#3} }
 \cs_new:Npn \exp_args:NNNo #1#2#3#4
   { \exp_after:wN #1 \exp_after:wN#2 \exp_after:wN #3 \exp_after:wN {#4} }
-\cs_new:Npn \exp_args:cc #1#2
-  { \cs:w #1 \exp_after:wN \cs_end: \cs:w #2 \cs_end: }
 \cs_new:Npn \exp_args:NNc #1#2#3
   { \exp_after:wN #1 \exp_after:wN #2 \cs:w # 3\cs_end: }
 \cs_new:Npn \exp_args:Ncc #1#2#3
@@ -313,80 +312,151 @@
     \exp_after:wN #1
     \exp_after:wN \__cs_generate_variant:nnNN
     \exp_after:wN #1
-    \etex_detokenize:D {#2} , ? , \q_recursion_stop
+    \etex_detokenize:D {#2} , \scan_stop: , \q_recursion_stop
   }
 \group_begin:
-  \tex_lccode:D `\Z = `\d \scan_stop:
-  \tex_lccode:D `\? =`\\ \scan_stop:
+  \tex_catcode:D `\M = 12 \scan_stop:
+  \tex_catcode:D `\A = 12 \scan_stop:
   \tex_catcode:D `\P = 12 \scan_stop:
   \tex_catcode:D `\R = 12 \scan_stop:
-  \tex_catcode:D `\O = 12 \scan_stop:
-  \tex_catcode:D `\T = 12 \scan_stop:
-  \tex_catcode:D `\E = 12 \scan_stop:
-  \tex_catcode:D `\C = 12 \scan_stop:
-  \tex_catcode:D `\Z = 12 \scan_stop:
 \tex_lowercase:D
   {
     \group_end:
     \cs_new_protected:Npn \__cs_generate_variant:N #1
       {
-        \exp_after:wN \__cs_generate_variant:w
-          \token_to_meaning:N #1
-          \q_mark \cs_new_protected_nopar:Npx
-          ? PROTECTEZ
-          \q_mark \cs_new_nopar:Npx
-          \q_stop
+        \exp_after:wN \if_meaning:w \exp_not:N #1 #1
+          \cs_set_eq:NN \__cs_tmp:w \cs_new_protected_nopar:Npx
+        \else:
+          \exp_after:wN \__cs_generate_variant:ww
+            \token_to_meaning:N #1 MA \q_mark
+            \q_mark \cs_new_protected_nopar:Npx
+            PR
+            \q_mark \cs_new_nopar:Npx
+            \q_stop
+        \fi:
       }
-    \cs_new_protected:Npn \__cs_generate_variant:w
-        #1 ? PROTECTEZ #2 \q_mark #3 #4 \q_stop
+    \cs_new_protected:Npn \__cs_generate_variant:ww #1 MA #2 \q_mark
+      { \__cs_generate_variant:wwNw #1 }
+    \cs_new_protected:Npn \__cs_generate_variant:wwNw
+        #1 PR #2 \q_mark #3 #4 \q_stop
       {
         \cs_set_eq:NN \__cs_tmp:w #3
       }
   }
 \cs_new_protected:Npn \__cs_generate_variant:nnNN #1#2#3#4
-  { \__cs_generate_variant:Nnnw #4 {#1}{#2} }
+  {
+    \if_meaning:w \c_false_bool #3
+      \__msg_kernel_error:nnx { kernel } { missing-colon }
+        { \token_to_str:c {#1} }
+      \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
+    \fi:
+    \__cs_generate_variant:Nnnw #4 {#1}{#2}
+  }
 \cs_new_protected:Npn \__cs_generate_variant:Nnnw #1#2#3#4 ,
   {
-    \if:w ? #4
+    \if_meaning:w \scan_stop: #4
       \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
     \fi:
-    \exp_after:wN \__cs_generate_variant:NNn
-    \exp_after:wN #1
-      \cs:w
-        #2 :
-        \__cs_generate_variant_loop:NwN
-          ? #3
-          \q_mark #4 \__cs_generate_variant_loop_end:w
-          \q_mark \__cs_generate_variant_loop_error:wnNNnn
-        \q_stop
-      \cs_end:
-      {#4}
+    \use:x
+      {
+        \exp_not:N \__cs_generate_variant:wwNN
+        \__cs_generate_variant_loop:nNwN { }
+          #4
+          \__cs_generate_variant_loop_end:nwwwNNnn
+          \q_mark
+          #3 ~
+          { ~ { } \fi: \__cs_generate_variant_loop_long:wNNnn } ~
+          { }
+          \q_stop
+        \exp_not:N #1 {#2} {#4}
+      }
     \__cs_generate_variant:Nnnw #1 {#2} {#3}
   }
-\cs_new:Npn \__cs_generate_variant_loop:NwN #1 #2 \q_mark #3
-  { #3 \__cs_generate_variant_loop:NwN #2 \q_mark }
-\cs_new:Npn \__cs_generate_variant_loop_end:w #1#2 \q_mark #3 \q_stop {#2}
-\cs_new:Npn \__cs_generate_variant_loop_error:wnNNnn
-    #1 \q_stop \cs_end: #2 #3#4#5#6
+\cs_new:Npn \__cs_generate_variant_loop:nNwN #1#2#3 \q_mark #4
+  {
+    \if:w #2 #4
+      \exp_after:wN \__cs_generate_variant_loop_same:w
+    \else:
+      \if:w N #4 \else:
+        \if:w n #4 \else:
+          \__cs_generate_variant_loop_invalid:NNwNNnn #4#2
+        \fi:
+      \fi:
+    \fi:
+    #1
+    \prg_do_nothing:
+    #2
+    \__cs_generate_variant_loop:nNwN { } #3 \q_mark
+  }
+\cs_new:Npn \__cs_generate_variant_loop_same:w
+    #1 \prg_do_nothing: #2#3#4
+  {
+    #3 { #1 \__cs_generate_variant_same:N #2 }
+  }
+\cs_new:Npn \__cs_generate_variant_loop_end:nwwwNNnn
+    #1#2 \q_mark #3 ~ #4 \q_stop #5#6#7#8
   {
-    \cs_end: {#2}
-    \__msg_kernel_error:nnxx { kernel } { variant-too-long }
-      { \tl_to_str:n {#2} } { \token_to_str:N #4 }
-    #3 #4 {#5} {#6}
+    \scan_stop: \scan_stop: \fi:
+    \exp_not:N \q_mark
+    \exp_not:N \q_stop
+    \exp_not:N #6
+    \exp_not:c { #7 : #8 #1 #3 }
+  }
+\cs_new:Npn \__cs_generate_variant_loop_long:wNNnn #1 \q_stop #2#3#4#5
+  {
+    \exp_not:n
+      {
+        \q_mark
+        \__msg_kernel_error:nnxx { kernel } { variant-too-long }
+          {#5} { \token_to_str:N #3 }
+        \use_none:nnnn
+        \q_stop
+        #3
+        #3
+      }
+  }
+\cs_new:Npn \__cs_generate_variant_loop_invalid:NNwNNnn
+    #1#2 \fi: \fi: \fi: #3 \q_stop #4#5#6#7
+  {
+    \fi: \fi: \fi:
+    \exp_not:n
+      {
+        \q_mark
+        \__msg_kernel_error:nnxxxx { kernel } { invalid-variant }
+          {#7} { \token_to_str:N #5 } {#1} {#2}
+        \use_none:nnnn
+        \q_stop
+        #5
+        #5
+      }
+  }
+\cs_new:Npn \__cs_generate_variant_same:N #1
+  {
+    \if:w N #1
+      N
+    \else:
+      \if:w p #1
+        p
+      \else:
+        n
+      \fi:
+    \fi:
   }
-\cs_new_protected:Npn \__cs_generate_variant:NNn #1 #2 #3
+\cs_new_protected:Npn \__cs_generate_variant:wwNN
+    #1 \q_mark #2 \q_stop #3#4
   {
-    \cs_if_free:NTF #2
+    #2
+    \cs_if_free:NTF #4
       {
         \group_begin:
-          \__cs_generate_internal_variant:n {#3}
-          \__cs_tmp:w #2 { \exp_not:c { exp_args:N #3 } \exp_not:N #1 }
+          \__cs_generate_internal_variant:n {#1}
+          \__cs_tmp:w #4 { \exp_not:c { exp_args:N #1 } \exp_not:N #3 }
         \group_end:
       }
       {
         \iow_log:x
           {
-            Variant~\token_to_str:N #2~%
+            Variant~\token_to_str:N #4~%
             already~defined;~ not~ changing~ it~on~line~%
             \tex_the:D \tex_inputlineno:D
           }
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3file.sty b/Master/texmf-dist/tex/latex/l3kernel/l3file.sty
index c222c3a6358..44e02bdff7c 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3file.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3file.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3file.dtx 4059 2012-08-08 13:12:06Z bruno $
+\GetIdInfo$Id: l3file.dtx 4101 2012-08-15 16:05:33Z bruno $
   {L3 File and I/O operations}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -55,6 +55,7 @@
 \tl_gset_eq:NN \g_file_current_name_tl \@currname
 \seq_new:N \g__file_stack_seq
 \seq_new:N \g__file_record_seq
+\tl_new:N \l__file_internal_tl
 \tl_new:N \l__file_internal_name_tl
 \seq_new:N \l__file_search_path_seq
 \seq_new:N \l__file_saved_search_path_seq
@@ -141,10 +142,11 @@
     \clist_if_exist:NTF \@filelist
       { \@addtofilelist {#1} }
       { \seq_gput_right:Nn \g__file_record_seq {#1} }
-    \seq_gpush:Nn \g__file_stack_seq \g_file_current_name_tl
+    \seq_gpush:No \g__file_stack_seq \g_file_current_name_tl
     \tl_gset:Nn \g_file_current_name_tl {#1}
     \tex_input:D #1 \c_space_tl
-    \seq_gpop:NN \g__file_stack_seq \g_file_current_name_tl
+    \seq_gpop:NN \g__file_stack_seq \l__file_internal_tl
+    \tl_gset_eq:NN \g_file_current_name_tl \l__file_internal_tl
   }
 \cs_generate_variant:Nn \__file_input_aux:n { o }
 \cs_new_protected:Npn \file_path_include:n #1
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty b/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty
index 3918bd5a161..cd23b05bfc1 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty
@@ -59,7 +59,7 @@
 %% -----------------------------------------------------------------------
 %%
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3fp.dtx 4089 2012-08-14 04:52:20Z bruno $
+\GetIdInfo$Id: l3fp.dtx 4151 2012-08-28 11:51:52Z bruno $
   {L3 Floating points}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -218,11 +218,15 @@
 \int_const:Nn \c__fp_middle_shift_int   { 5 0000 *  9999 }
 \int_const:Nn \c__fp_trailing_shift_int { 5 0000 * 10000 }
 \cs_new:Npn \__fp_pack:NNNNNw #1 #2#3#4#5 #6; { + #1#2#3#4#5 ; {#6} }
+\cs_new:Npn \__fp_pack:NNNNNwn #1 #2#3#4#5 #6; #7
+  { + #1#2#3#4#5 ; {#7} {#6} }
 \int_const:Nn \c__fp_big_leading_shift_int  { - 15 2374 }
 \int_const:Nn \c__fp_big_middle_shift_int   { 15 2374 *  9999 }
 \int_const:Nn \c__fp_big_trailing_shift_int { 15 2374 * 10000 }
 \cs_new:Npn \__fp_pack_big:NNNNNNw #1#2 #3#4#5#6 #7;
   { + #1#2#3#4#5#6 ; {#7} }
+\cs_new:Npn \__fp_pack_big:NNNNNNwn #1#2 #3#4#5#6 #7; #8
+  { + #1#2#3#4#5#6 ; {#8} {#7} }
 \int_const:Nn \c__fp_Bigg_leading_shift_int  { - 20 0000 }
 \int_const:Nn \c__fp_Bigg_middle_shift_int   { 20 0000 *  9999 }
 \int_const:Nn \c__fp_Bigg_trailing_shift_int { 20 0000 * 10000 }
@@ -417,7 +421,7 @@
       { \cs_set:Npn \__fp_invalid_operation:nnw ##1##2##3; }
       {
         #1
-        \__fp_error:nffn { invalid } {##2} { \__fp_to_tl:w ##3; } { }
+        \__fp_error:nnfn { invalid } {##2} { \__fp_to_tl:w ##3; } { }
         \fp_flag_on:n { invalid_operation }
         ##1
       }
@@ -431,11 +435,10 @@
         \exp_after:wN \c_nan_fp
       }
     \exp_args:Nno \use:n
-      { \cs_set:Npn \__fp_array_invalid_operation_o:nw ##1##2@ }
+      { \cs_set:Npn \__fp_invalid_operation_tl_o:nf ##1##2 }
       {
         #1
-        \__fp_error:nffn { invalid }
-          {##1} { \__fp_array_to_clist:w ##2 @ } { }
+        \__fp_error:nnfn { invalid } {##1} {##2} { }
         \fp_flag_on:n { invalid_operation }
         \exp_after:wN \c_nan_fp
       }
@@ -452,7 +455,7 @@
       { \cs_set:Npn \__fp_division_by_zero_o:Nnw ##1##2##3; }
       {
         #1
-        \__fp_error:nffn { zero-div } {##2} { \__fp_to_tl:w ##3; } { }
+        \__fp_error:nnfn { zero-div } {##2} { \__fp_to_tl:w ##3; } { }
         \fp_flag_on:n { division_by_zero }
         \exp_after:wN ##1
       }
@@ -499,7 +502,7 @@
   }
 \cs_new:Npn \__fp_invalid_operation:nnw #1#2#3; { }
 \cs_new:Npn \__fp_invalid_operation_o:Nww #1#2; #3; { }
-\cs_new:Npn \__fp_array_invalid_operation_o:nw #1 #2 @ { }
+\cs_new:Npn \__fp_invalid_operation_tl_o:nf #1 #2 { }
 \cs_new:Npn \__fp_division_by_zero_o:Nnw #1#2#3; { }
 \cs_new:Npn \__fp_division_by_zero_o:NNww #1#2#3; #4; { }
 \cs_new:Npn \__fp_overflow:w { }
@@ -512,21 +515,7 @@
   { \__fp_invalid_operation:nnw { \exp_after:wN \c_nan_fp } }
 \cs_new:Npn \__fp_error:nnnn #1
   { \__msg_kernel_expandable_error:nnnnn { kernel } { fp - #1 } }
-\cs_generate_variant:Nn \__fp_error:nnnn { nff }
-\cs_new:Npn \__fp_array_to_clist:w #1 @
-  {
-    \__fp_array_to_clist_i:wwww ;
-      #1
-      \__fp_array_to_clist_ii:ww \s__fp ; @
-  }
-\cs_new:Npn \__fp_array_to_clist_i:wwww #1; #2 \s__fp #3; #4 @
-  {
-    #2
-    \exp_after:wN \__fp_array_to_clist_i:wwww
-    \tex_romannumeral:D -`0 \__fp_to_tl:w \s__fp #3 ; ;
-    #4 , ~ #1 @
-  }
-\cs_new:Npn \__fp_array_to_clist_ii:ww #1 ; , ~ , ~ #2 @ {#2}
+\cs_generate_variant:Nn \__fp_error:nnnn { nnf, nff }
 \__msg_kernel_new:nnnn { kernel } { unknown-fpu-exception }
   { The~FPU~exception~'#1'~is~not~known:~that~trap~will~never~be~triggered. }
   {
@@ -687,7 +676,10 @@
 \cs_new:Npn \__fp_round:Nww #1#2 ; #3 ;
   {
     \__fp_small_int:wTF #3; { \__fp_round:Nwn #1#2; }
-      { \__fp_array_invalid_operation_o:nw { round } #2; #3; @ }
+      {
+        \__fp_invalid_operation_tl_o:nf
+          { round } { \__fp_array_to_clist:n { #2; #3; } }
+      }
   }
 \cs_new:Npn \__fp_round:Nwn #1 \s__fp \__fp_chk:w #2#3#4; #5
   {
@@ -808,7 +800,7 @@
     \cs_new:Npn \__fp_type_from_scan:N #1
       {
         \exp_after:wN \__fp_type_from_scan:w
-        \token_to_str:N #1 \q_mark S--FP \q_mark \q_stop
+        \token_to_str:N #1 \q_mark S--FP-? \q_mark \q_stop
       }
     \cs_new:Npn \__fp_type_from_scan:w #1 S--FP #2 \q_mark #3 \q_stop {#2}
   }
@@ -877,39 +869,26 @@
   }
 \cs_new:Npn \__fp_parse_operand_relax:NN #1#2
   {
-      \__fp_parse_operand_relax_aux:wwnw
-        #2 \s__fp_mark
-          {
-            \__fp_exp_after_o:nw
-              {
-                \tex_romannumeral:D -`0
-                \exp_after:wN \__fp_parse_infix:NN
-                \exp_after:wN #1 \tex_romannumeral:D \__fp_parse_expand:w
-              }
-            \s__fp
-          }
-        \s__fp #2
-          {
-            \__msg_kernel_expandable_error:nn { kernel } { fp-early-end }
-            \exp_after:wN \c_nan_fp
-            \tex_romannumeral:D -`0
-              \__fp_parse_infix:NN #1
-              \s__fp_mark
-          }
-        \s__fp_mark
-          {
-            \__msg_kernel_expandable_error:nnn
-              { kernel } { bad-variable } {#2}
-            \exp_after:wN \c_nan_fp
-            \tex_romannumeral:D -`0
-              \exp_after:wN \__fp_parse_infix:NN
-              \exp_after:wN #1
-              \tex_romannumeral:D \__fp_parse_expand:w
-          }
-        \s__fp_mark \s__fp_stop
+    \cs:w __fp_exp_after \__fp_type_from_scan:N #2 _f:nw \cs_end:
+      {
+        \exp_after:wN \__fp_parse_infix:NN
+        \exp_after:wN #1 \tex_romannumeral:D \__fp_parse_expand:w
+      }
+    #2
+  }
+\cs_new:Npn \__fp_exp_after_mark_f:nw #1
+  {
+    \__msg_kernel_expandable_error:nn { kernel } { fp-early-end }
+    \exp_after:wN \c_nan_fp
+    \tex_romannumeral:D -`0 #1
+  }
+\cs_new:cpn { __fp_exp_after_?_f:nw } #1#2
+  {
+    \__msg_kernel_expandable_error:nnn
+      { kernel } { bad-variable } {#2}
+    \exp_after:wN \c_nan_fp
+    \tex_romannumeral:D -`0 #1
   }
-\cs_new:Npn \__fp_parse_operand_relax_aux:wwnw
-    #1 \s__fp #2 \s__fp_mark #3 #4 \s__fp_mark \s__fp_stop { #3 }
 \cs_new:Npn \__fp_parse_operand_other:NN #1 #2
   {
     \if_int_compare:w
@@ -1447,8 +1426,9 @@
       \cs:w
         __fp
         \__fp_type_from_scan:N #2
+        _ #4
         \__fp_type_from_scan:N #5
-        _ #4 _o:ww
+        _o:ww
       \cs_end:
       #2#3 #5#6
     \tex_romannumeral:D -`0 #7 #1
@@ -1504,7 +1484,8 @@
         \tex_romannumeral:D -`0 \__fp_parse_infix:NN
       }
   }
-\tl_map_inline:nn { {abs} {cos} {cot} {exp} {ln} {sin} {tan} }
+\tl_map_inline:nn
+  { {abs} {cos} {cot} {csc} {exp} {ln} {sec} {sin} {tan} }
   {
     \cs_new:cpn { __fp_parse_word_#1:N } ##1
       {
@@ -1600,7 +1581,7 @@
     {
       \token_if_eq_meaning:NNTF #3 \__fp_parse_infix_):N
         {
-          \__fp_parse_exp_after_array:wf #2 \s__fp_stop
+          \__fp_exp_after_array_f:w #2 \s__fp_stop
           \exp_after:wN \__fp_parse_infix:NN
           \exp_after:wN #1
           \tex_romannumeral:D \__fp_parse_expand:w
@@ -1611,13 +1592,13 @@
         }
     }
 \group_end:
-\cs_new:Npn \__fp_parse_exp_after_array:wf #1
+\cs_new:Npn \__fp_exp_after_array_f:w #1
   {
-    \cs:w __fp \__fp_type_from_scan:N #1 _exp_after_f:nw \cs_end:
-      { \__fp_parse_exp_after_array:wf }
+    \cs:w __fp_exp_after \__fp_type_from_scan:N #1 _f:nw \cs_end:
+      { \__fp_exp_after_array_f:w }
     #1
   }
-\cs_new:Npn \__fp_stop_exp_after_f:nw #1#2 { }
+\cs_new:Npn \__fp_exp_after_stop_f:nw #1#2 { }
 \cs_new:cpn {__fp_parse_prefix_.:Nw} #1
   {
     \exp_after:wN \__fp_parse_infix_after_operand:NwN
@@ -1990,12 +1971,12 @@
 \cs_new:Npn \__fp_compare_npos:nwnw #1#2; #3#4;
   {
     \if_int_compare:w #1 = #3 \exp_stop_f:
-      \__fp_compare_mantissa:nnnnnnnn #2 #4
+      \__fp_compare_significand:nnnnnnnn #2 #4
     \else:
       \if_int_compare:w #1 < #3 - \fi: 1
     \fi:
   }
-\cs_new:Npn \__fp_compare_mantissa:nnnnnnnn #1#2#3#4#5#6#7#8
+\cs_new:Npn \__fp_compare_significand:nnnnnnnn #1#2#3#4#5#6#7#8
   {
     \if_int_compare:w #1#2 = #5#6 \exp_stop_f:
       \if_int_compare:w #3#4 = #7#8 \exp_stop_f:
@@ -2007,6 +1988,62 @@
       \if_int_compare:w #1#2 < #5#6 - \fi: 1
     \fi:
   }
+\cs_new:Npn \fp_do_until:nn #1#2
+  {
+    #2
+    \fp_compare:nF {#1}
+      { \fp_do_until:nn {#1} {#2} }
+  }
+\cs_new:Npn \fp_do_while:nn #1#2
+  {
+    #2
+    \fp_compare:nT {#1}
+      { \fp_do_while:nn {#1} {#2} }
+  }
+\cs_new:Npn \fp_until_do:nn #1#2
+  {
+    \fp_compare:nF {#1}
+      {
+        #2
+        \fp_until_do:nn {#1} {#2}
+      }
+  }
+\cs_new:Npn \fp_while_do:nn #1#2
+  {
+    \fp_compare:nT {#1}
+      {
+        #2
+        \fp_while_do:nn {#1} {#2}
+      }
+  }
+\cs_new:Npn \fp_do_until:nNnn #1#2#3#4
+  {
+    #4
+    \fp_compare:nNnF {#1} #2 {#3}
+      { \fp_do_until:nNnn {#1} #2 {#3} {#4} }
+  }
+\cs_new:Npn \fp_do_while:nNnn #1#2#3#4
+  {
+    #4
+    \fp_compare:nNnT {#1} #2 {#3}
+      { \fp_do_while:nNnn {#1} #2 {#3} {#4} }
+  }
+\cs_new:Npn \fp_until_do:nNnn #1#2#3#4
+  {
+    \fp_compare:nNnF {#1} #2 {#3}
+      {
+        #4
+        \fp_until_do:nNnn {#1} #2 {#3} {#4}
+      }
+  }
+\cs_new:Npn \fp_while_do:nNnn #1#2#3#4
+  {
+    \fp_compare:nNnT {#1} #2 {#3}
+      {
+        #4
+        \fp_while_do:nNnn {#1} #2 {#3} {#4}
+      }
+  }
 \cs_new:Npn \__fp_max_o:w #1 @
   {
     \exp_after:wN \__fp_minmax_loop:Nww
@@ -2083,7 +2120,7 @@
       \__fp_ternary_break_point:n { \exp_after:wN \__fp_ternary_i:NwwN }
       \exp_after:wN #1
       \tex_romannumeral:D -`0
-      \__fp_parse_exp_after_array:wf #3 \s__fp_stop
+      \__fp_exp_after_array_f:w #3 \s__fp_stop
       \exp_after:wN @
       \tex_romannumeral:D
         \__fp_parse_until:Nw \c_two
@@ -2094,7 +2131,7 @@
       \exp_after:wN \__fp_parse_until_test:NwN
       \exp_after:wN #1
       \tex_romannumeral:D -`0
-      \__fp_parse_exp_after_array:wf #3 \s__fp_stop
+      \__fp_exp_after_array_f:w #3 \s__fp_stop
       \exp_after:wN #4
       \exp_after:wN #1
     \fi:
@@ -2117,7 +2154,7 @@
     \exp_after:wN \__fp_parse_until_test:NwN
     \exp_after:wN #1
     \tex_romannumeral:D -`0
-    \__fp_parse_exp_after_array:wf #2 \s__fp_stop
+    \__fp_exp_after_array_f:w #2 \s__fp_stop
     #4 #1
   }
 \cs_new:Npn \__fp_ternary_ii:NwwN #1#2@#3@#4
@@ -2125,7 +2162,7 @@
     \exp_after:wN \__fp_parse_until_test:NwN
     \exp_after:wN #1
     \tex_romannumeral:D -`0
-    \__fp_parse_exp_after_array:wf #3 \s__fp_stop
+    \__fp_exp_after_array_f:w #3 \s__fp_stop
     #4 #1
   }
 %% File: l3fp-basics.dtx Copyright (C) 2011-2012 The LaTeX3 Project
@@ -2273,7 +2310,7 @@
 \cs_new:Npn \__fp_add_big_i_o:wNww #1; #2 #3; #4;
   {
     \__fp_decimate:nNnnnn {#1}
-      \__fp_add_mantissa_o:NnnwnnnnN
+      \__fp_add_significand_o:NnnwnnnnN
       #4
     #3
     #2
@@ -2281,34 +2318,34 @@
 \cs_new:Npn \__fp_add_big_ii_o:wNww #1; #2 #3; #4;
   {
     \__fp_decimate:nNnnnn {#1}
-      \__fp_add_mantissa_o:NnnwnnnnN
+      \__fp_add_significand_o:NnnwnnnnN
       #3
     #4
     #2
   }
-\cs_new:Npn \__fp_add_mantissa_o:NnnwnnnnN #1 #2#3 #4; #5#6#7#8
+\cs_new:Npn \__fp_add_significand_o:NnnwnnnnN #1 #2#3 #4; #5#6#7#8
   {
-    \exp_after:wN \__fp_add_mantissa_test_o:N
+    \exp_after:wN \__fp_add_significand_test_o:N
     \int_use:N \__int_eval:w 1#5#6 + #2
-      \exp_after:wN \__fp_add_mantissa_pack:NNNNNNN
+      \exp_after:wN \__fp_add_significand_pack:NNNNNNN
       \int_use:N \__int_eval:w 1#7#8 + #3 ; #1
   }
-\cs_new:Npn \__fp_add_mantissa_pack:NNNNNNN #1 #2#3#4#5#6#7
+\cs_new:Npn \__fp_add_significand_pack:NNNNNNN #1 #2#3#4#5#6#7
   {
     \if_meaning:w 2 #1
       + \c_one
     \fi:
     ; #2 #3 #4 #5 #6 #7 ;
   }
-\cs_new:Npn \__fp_add_mantissa_test_o:N #1
+\cs_new:Npn \__fp_add_significand_test_o:N #1
   {
     \if_meaning:w 2 #1
-      \exp_after:wN \__fp_add_mantissa_carry_o:wwwNN
+      \exp_after:wN \__fp_add_significand_carry_o:wwwNN
     \else:
-      \exp_after:wN \__fp_add_mantissa_no_carry_o:wwwNN
+      \exp_after:wN \__fp_add_significand_no_carry_o:wwwNN
     \fi:
   }
-\cs_new:Npn \__fp_add_mantissa_no_carry_o:wwwNN
+\cs_new:Npn \__fp_add_significand_no_carry_o:wwwNN
     #1; #2; #3#4 ; #5#6
   {
     \exp_after:wN \__fp_basics_pack_high:NNNNNw
@@ -2318,7 +2355,7 @@
         + \__fp_round:NNN #6 #4 #5
         \exp_after:wN ;
   }
-\cs_new:Npn \__fp_add_mantissa_carry_o:wwwNN
+\cs_new:Npn \__fp_add_significand_carry_o:wwwNN
     #1; #2; #3#4; #5#6
   {
     + \c_one
@@ -2527,41 +2564,41 @@
     \exp_after:wN #1
     \int_use:N \__int_eval:w
       #4 + #8
-      \__fp_mul_mantissa_o:nnnnNnnnn #5 #1 #9
+      \__fp_mul_significand_o:nnnnNnnnn #5 #1 #9
   }
-\cs_new:Npn \__fp_mul_mantissa_o:nnnnNnnnn #1#2#3#4 #5 #6#7#8#9
+\cs_new:Npn \__fp_mul_significand_o:nnnnNnnnn #1#2#3#4 #5 #6#7#8#9
   {
-    \exp_after:wN \__fp_mul_mantissa_test_f:NNN
+    \exp_after:wN \__fp_mul_significand_test_f:NNN
     \exp_after:wN #5
     \int_use:N \__int_eval:w 99990000 + #1*#6 +
-      \exp_after:wN \__fp_mul_mantissa_keep:NNNNNw
+      \exp_after:wN \__fp_mul_significand_keep:NNNNNw
       \int_use:N \__int_eval:w 99990000 + #1*#7 + #2*#6 +
-        \exp_after:wN \__fp_mul_mantissa_keep:NNNNNw
+        \exp_after:wN \__fp_mul_significand_keep:NNNNNw
         \int_use:N \__int_eval:w 99990000 + #1*#8 + #2*#7 + #3*#6 +
-          \exp_after:wN \__fp_mul_mantissa_drop:NNNNNw
+          \exp_after:wN \__fp_mul_significand_drop:NNNNNw
           \int_use:N \__int_eval:w  99990000 + #1*#9 + #2*#8 + #3*#7 + #4*#6 +
-            \exp_after:wN \__fp_mul_mantissa_drop:NNNNNw
+            \exp_after:wN \__fp_mul_significand_drop:NNNNNw
             \int_use:N \__int_eval:w  99990000 + #2*#9 + #3*#8 + #4*#7 +
-              \exp_after:wN \__fp_mul_mantissa_drop:NNNNNw
+              \exp_after:wN \__fp_mul_significand_drop:NNNNNw
               \int_use:N \__int_eval:w  99990000 + #3*#9 + #4*#8 +
-                \exp_after:wN \__fp_mul_mantissa_drop:NNNNNw
+                \exp_after:wN \__fp_mul_significand_drop:NNNNNw
                 \int_use:N \__int_eval:w 100000000 + #4*#9 ;
     ; \exp_after:wN ;
   }
-\cs_new:Npn \__fp_mul_mantissa_drop:NNNNNw #1#2#3#4#5 #6;
+\cs_new:Npn \__fp_mul_significand_drop:NNNNNw #1#2#3#4#5 #6;
   { #1#2#3#4#5 ; + #6 }
-\cs_new:Npn \__fp_mul_mantissa_keep:NNNNNw #1#2#3#4#5 #6;
+\cs_new:Npn \__fp_mul_significand_keep:NNNNNw #1#2#3#4#5 #6;
   { #1#2#3#4#5 ; #6 ; }
-\cs_new:Npn \__fp_mul_mantissa_test_f:NNN #1 #2 #3
+\cs_new:Npn \__fp_mul_significand_test_f:NNN #1 #2 #3
   {
     \if_meaning:w 0 #3
-      \exp_after:wN \__fp_mul_mantissa_small_f:NNwwwN
+      \exp_after:wN \__fp_mul_significand_small_f:NNwwwN
     \else:
-      \exp_after:wN \__fp_mul_mantissa_large_f:NwwNNNN
+      \exp_after:wN \__fp_mul_significand_large_f:NwwNNNN
     \fi:
     #1 #3
   }
-\cs_new:Npn \__fp_mul_mantissa_large_f:NwwNNNN #1 #2; #3; #4#5#6#7; +
+\cs_new:Npn \__fp_mul_significand_large_f:NwwNNNN #1 #2; #3; #4#5#6#7; +
   {
     \exp_after:wN \__fp_basics_pack_high:NNNNNw
     \int_use:N \__int_eval:w 1#2
@@ -2572,7 +2609,7 @@
           \exp_after:wN #7
           \__int_value:w \__fp_round_digit:Nw
   }
-\cs_new:Npn \__fp_mul_mantissa_small_f:NNwwwN #1 #2#3; #4#5; #6; + #7
+\cs_new:Npn \__fp_mul_significand_small_f:NNwwwN #1 #2#3; #4#5; #6; + #7
   {
     - \c_one
     \exp_after:wN \__fp_basics_pack_high:NNNNNw
@@ -2606,34 +2643,34 @@
     \exp_after:wN #1
     \int_use:N \__int_eval:w
       #3 - #6
-      \exp_after:wN \__fp_div_mantissa_i_o:wnnw
+      \exp_after:wN \__fp_div_significand_i_o:wnnw
         \int_use:N \__int_eval:w #7 \use_i:nnnn #8 + \c_one ;
         #4
         {#7}{#8}#9 ;
         #1
   }
-\cs_new:Npn \__fp_div_mantissa_i_o:wnnw #1 ; #2#3 #4 ;
+\cs_new:Npn \__fp_div_significand_i_o:wnnw #1 ; #2#3 #4 ;
   {
-    \exp_after:wN \__fp_div_mantissa_test_o:w
+    \exp_after:wN \__fp_div_significand_test_o:w
     \int_use:N \__int_eval:w
-      \exp_after:wN \__fp_div_mantissa_calc:wwnnnnnnn
+      \exp_after:wN \__fp_div_significand_calc:wwnnnnnnn
       \int_use:N \__int_eval:w 999999 + #2 #3 0 / #1 ;
         #2 #3 ;
         #4
-        { \exp_after:wN \__fp_div_mantissa_ii:wwn \__int_value:w #1 }
-        { \exp_after:wN \__fp_div_mantissa_ii:wwn \__int_value:w #1 }
-        { \exp_after:wN \__fp_div_mantissa_ii:wwn \__int_value:w #1 }
-        { \exp_after:wN \__fp_div_mantissa_iii:wwnnnnn \__int_value:w #1 }
+        { \exp_after:wN \__fp_div_significand_ii:wwn \__int_value:w #1 }
+        { \exp_after:wN \__fp_div_significand_ii:wwn \__int_value:w #1 }
+        { \exp_after:wN \__fp_div_significand_ii:wwn \__int_value:w #1 }
+        { \exp_after:wN \__fp_div_significand_iii:wwnnnnn \__int_value:w #1 }
   }
-\cs_new:Npn \__fp_div_mantissa_calc:wwnnnnnnn 1#1
+\cs_new:Npn \__fp_div_significand_calc:wwnnnnnnn 1#1
   {
     \if_meaning:w 1 #1
-      \exp_after:wN \__fp_div_mantissa_calc_i:wwnnnnnnn
+      \exp_after:wN \__fp_div_significand_calc_i:wwnnnnnnn
     \else:
-      \exp_after:wN \__fp_div_mantissa_calc_ii:wwnnnnnnn
+      \exp_after:wN \__fp_div_significand_calc_ii:wwnnnnnnn
     \fi:
   }
-\cs_new:Npn \__fp_div_mantissa_calc_i:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
+\cs_new:Npn \__fp_div_significand_calc_i:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
   {
     1 1 #1
     #9 \exp_after:wN ;
@@ -2650,7 +2687,7 @@
             - #1 * #8 ;
     {#5}{#6}{#7}{#8}
   }
-\cs_new:Npn \__fp_div_mantissa_calc_ii:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
+\cs_new:Npn \__fp_div_significand_calc_ii:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
   {
     1 0 #1
     #9 \exp_after:wN ;
@@ -2667,33 +2704,33 @@
             - #1 * #8 ;
     {#5}{#6}{#7}{#8}
   }
-\cs_new:Npn \__fp_div_mantissa_ii:wwn #1; #2;#3
+\cs_new:Npn \__fp_div_significand_ii:wwn #1; #2;#3
   {
-    \exp_after:wN \__fp_div_mantissa_pack:NNN
+    \exp_after:wN \__fp_div_significand_pack:NNN
     \int_use:N \__int_eval:w
-      \exp_after:wN \__fp_div_mantissa_calc:wwnnnnnnn
+      \exp_after:wN \__fp_div_significand_calc:wwnnnnnnn
       \int_use:N \__int_eval:w 999999 + #2 #3 0 / #1 ; #2 #3 ;
   }
-\cs_new:Npn \__fp_div_mantissa_iii:wwnnnnn #1; #2;#3#4#5 #6#7
+\cs_new:Npn \__fp_div_significand_iii:wwnnnnn #1; #2;#3#4#5 #6#7
   {
     0
-    \exp_after:wN \__fp_div_mantissa_iv:wwnnnnnnn
+    \exp_after:wN \__fp_div_significand_iv:wwnnnnnnn
     \int_use:N \__int_eval:w (\c_two * #2 #3) / #6 #7 ; % <- P
       #2 ; {#3} {#4} {#5}
       {#6} {#7}
   }
-\cs_new:Npn \__fp_div_mantissa_iv:wwnnnnnnn #1; #2;#3#4#5 #6#7#8#9
+\cs_new:Npn \__fp_div_significand_iv:wwnnnnnnn #1; #2;#3#4#5 #6#7#8#9
   {
     + \c_five * #1
-    \exp_after:wN \__fp_div_mantissa_vi:Nw
+    \exp_after:wN \__fp_div_significand_vi:Nw
     \int_use:N \__int_eval:w -20 + 2*#2#3 - #1*#6#7 +
-      \exp_after:wN \__fp_div_mantissa_v:NN
+      \exp_after:wN \__fp_div_significand_v:NN
       \int_use:N \__int_eval:w 199980 + 2*#4 - #1*#8 +
-        \exp_after:wN \__fp_div_mantissa_v:NN
+        \exp_after:wN \__fp_div_significand_v:NN
         \int_use:N \__int_eval:w 200000 + 2*#5 - #1*#9 ;
   }
-\cs_new:Npn \__fp_div_mantissa_v:NN #1#2 { #1#2 \__int_eval_end: + }
-\cs_new:Npn \__fp_div_mantissa_vi:Nw #1#2;
+\cs_new:Npn \__fp_div_significand_v:NN #1#2 { #1#2 \__int_eval_end: + }
+\cs_new:Npn \__fp_div_significand_vi:Nw #1#2;
   {
     \if_meaning:w 0 #1
       \if_int_compare:w \__int_eval:w #2 > \c_zero + \c_one \fi:
@@ -2702,17 +2739,17 @@
     \fi:
     ;
   }
-\cs_new:Npn \__fp_div_mantissa_pack:NNN 1 #1 #2 { + #1 #2 ; }
-\cs_new:Npn \__fp_div_mantissa_test_o:w 10 #1
+\cs_new:Npn \__fp_div_significand_pack:NNN 1 #1 #2 { + #1 #2 ; }
+\cs_new:Npn \__fp_div_significand_test_o:w 10 #1
   {
     \if_meaning:w 0 #1
-      \exp_after:wN \__fp_div_mantissa_small_o:wwwNNNNwN
+      \exp_after:wN \__fp_div_significand_small_o:wwwNNNNwN
     \else:
-      \exp_after:wN \__fp_div_mantissa_large_o:wwwNNNNwN
+      \exp_after:wN \__fp_div_significand_large_o:wwwNNNNwN
     \fi:
     #1
   }
-\cs_new:Npn \__fp_div_mantissa_small_o:wwwNNNNwN
+\cs_new:Npn \__fp_div_significand_small_o:wwwNNNNwN
     0 #1; #2; #3; #4#5#6#7#8; #9
   {
     \exp_after:wN \__fp_basics_pack_high:NNNNNw
@@ -2722,7 +2759,7 @@
         + \__fp_round:NNN #9 #7 #8
         \exp_after:wN ;
   }
-\cs_new:Npn \__fp_div_mantissa_large_o:wwwNNNNwN
+\cs_new:Npn \__fp_div_significand_large_o:wwwNNNNwN
     #1; #2; #3; #4#5#6#7#8; #9
   {
     + \c_one
@@ -2736,13 +2773,13 @@
         \__int_value:w \__fp_round_digit:Nw #7 #8 ;
       \exp_after:wN ;
   }
-\cs_new:Npn \__fp_neg_o:w \s__fp \__fp_chk:w #1 #2
+\cs_new:Npn \__fp_neg_o:w #1 \s__fp \__fp_chk:w #2 #3
   {
     \exp_after:wN \__fp_exp_after_o:w
     \exp_after:wN \s__fp
     \exp_after:wN \__fp_chk:w
-    \exp_after:wN #1
-    \int_use:N \__int_eval:w \c_two - #2 \__int_eval_end:
+    \exp_after:wN #2
+    \int_use:N \__int_eval:w \c_two - #3 \__int_eval_end:
   }
 \cs_new:Npn \__fp_abs_o:w \s__fp \__fp_chk:w #1 #2
   {
@@ -2788,6 +2825,12 @@
 \tl_const:Nn \c__fp_one_fixed_tl
   { {10000} {0000} {0000} {0000} {0000} {0000} }
 \cs_new:Npn \__fp_fixed_continue:wn #1; #2 { #2 #1; }
+\cs_new:Npn \__fp_fixed_add_one:wN #1#2; #3
+  {
+    \exp_after:wN #3 \exp_after:wN
+      { \int_use:N \__int_eval:w \c_ten_thousand + #1 } #2 ;
+  }
+\cs_new:Npn \__fp_fixed_mul_after:wn #1; #2 { #2 {#1} }
 \cs_new:Npn \__fp_fixed_div_int:wwN #1#2#3#4#5#6 ; #7 ; #8
   {
     \exp_after:wN \__fp_fixed_div_int_after:Nw
@@ -2799,7 +2842,7 @@
       #3; {#7} \__fp_fixed_div_int_ii:wnn
       #4; {#7} \__fp_fixed_div_int_ii:wnn
       #5; {#7} \__fp_fixed_div_int_ii:wnn
-      #6; {#7} \__fp_fixed_div_int_end:wnn ;
+      #6; {#7} \__fp_fixed_div_int_iii:wnn ;
   }
 \cs_new:Npn \__fp_fixed_div_int_i:wnN #1; #2 #3
   {
@@ -2816,110 +2859,104 @@
       \exp_after:wN \__fp_fixed_div_int_i:wnN
       \int_use:N \__int_eval:w #3 - #1*#2 \__int_eval_end:
   }
-\cs_new:Npn \__fp_fixed_div_int_end:wnn #1; #2 #3 { + #1 + \c_two ; }
+\cs_new:Npn \__fp_fixed_div_int_iii:wnn #1; #2 #3 { + #1 + \c_two ; }
 \cs_new:Npn \__fp_fixed_div_int_pack:Nw #1 #2; { + #1; {#2} }
 \cs_new:Npn \__fp_fixed_div_int_after:Nw #1 #2; { #1 {#2} }
-\cs_new:Npn \__fp_fixed_add_one:wN #1#2; #3
-  {
-    \exp_after:wN #3 \exp_after:wN
-      { \int_use:N \__int_eval:w 10000 + #1 } #2 ;
-  }
-\cs_new_nopar:Npn \__fp_fixed_add:wwN { \__fp_fixed_add_i:NNnnnnwnn + + }
-\cs_new_nopar:Npn \__fp_fixed_sub:wwN { \__fp_fixed_add_i:NNnnnnwnn + - }
-\cs_new_nopar:Npn \__fp_fixed_sub_back:wwN { \__fp_fixed_add_i:NNnnnnwnn - + }
-\cs_new:Npn \__fp_fixed_add_i:NNnnnnwnn #1#2 #3#4#5#6 #7; #8#9
-  {
-    \exp_after:wN \__fp_fixed_add_after:NNNNNwN
-    \int_use:N \__int_eval:w 1 9999 9998 #1 #3#4 #2 #8#9
-      \exp_after:wN \__fp_fixed_add_pack:NNNNNwN
-      \int_use:N \__int_eval:w 1 9999 9998 #1 #5#6
-        \__fp_fixed_add_ii:NnnNnnnnw #1 #7 #2
-  }
-\cs_new:Npn \__fp_fixed_add_ii:NnnNnnnnw #1 #2#3 #4 #5#6 #7#8 ; #9
-  {
-    #4 #5#6
-    \exp_after:wN \__fp_fixed_add_pack:NNNNNwN
-    \int_use:N \__int_eval:w 2 0000 0000 #4 #7#8 #1 #2#3 ; #9 ;
-  }
-\cs_new:Npn \__fp_fixed_add_pack:NNNNNwN #1 #2#3#4#5 #6; #7
-  { + #1 ; #7 {#2#3#4#5} {#6} }
-\cs_new:Npn \__fp_fixed_add_after:NNNNNwN #1 #2#3#4#5 #6; #7
-  {
-    \exp_after:wN #7
-    \exp_after:wN { \int_use:N \__int_eval:w - 2 0000 + #1#2#3#4#5 }
-    {#6}
-  }
+\cs_new_nopar:Npn \__fp_fixed_add:wwn { \__fp_fixed_add_i:Nnnnnwnn + }
+\cs_new_nopar:Npn \__fp_fixed_sub:wwn { \__fp_fixed_add_i:Nnnnnwnn - }
+\cs_new:Npn \__fp_fixed_add_i:Nnnnnwnn #1 #2#3#4#5 #6; #7#8
+  {
+    \exp_after:wN \__fp_fixed_add_after:NNNNNwn
+    \int_use:N \__int_eval:w 9 9999 9998 + #2#3 #1 #7#8
+      \exp_after:wN \__fp_fixed_add_pack:NNNNNwn
+      \int_use:N \__int_eval:w 1 9999 9998 + #4#5
+        \__fp_fixed_add_ii:nnNnnnwn #6 #1
+  }
+\cs_new:Npn \__fp_fixed_add_ii:nnNnnnwn #1#2 #3 #4#5 #6#7 ; #8
+  {
+    #3 #4#5
+    \exp_after:wN \__fp_fixed_add_pack:NNNNNwn
+    \int_use:N \__int_eval:w 2 0000 0000 #3 #6#7 + #1#2 ; {#8} ;
+  }
+\cs_new:Npn \__fp_fixed_add_pack:NNNNNwn #1 #2#3#4#5 #6; #7
+  { + #1 ; {#7} {#2#3#4#5} {#6} }
+\cs_new:Npn \__fp_fixed_add_after:NNNNNwn 1 #1 #2#3#4#5 #6; #7
+  { #7 {#1#2#3#4#5} {#6} }
 \cs_new:Npn \__fp_fixed_mul:wwn #1#2#3#4 #5; #6#7#8#9
   {
-    \exp_after:wN \__fp_fixed_mul_after:wwn
+    \exp_after:wN \__fp_fixed_mul_after:wn
     \int_use:N \__int_eval:w \c__fp_leading_shift_int
-      \exp_after:wN \__fp_pack:NNNNNw
+      \exp_after:wN \__fp_pack:NNNNNwn
       \int_use:N \__int_eval:w \c__fp_middle_shift_int
         + #1*#6
-        \exp_after:wN \__fp_pack:NNNNNw
+        \exp_after:wN \__fp_pack:NNNNNwn
         \int_use:N \__int_eval:w \c__fp_middle_shift_int
           + #1*#7 + #2*#6
-          \exp_after:wN \__fp_pack:NNNNNw
+          \exp_after:wN \__fp_pack:NNNNNwn
           \int_use:N \__int_eval:w \c__fp_middle_shift_int
             + #1*#8 + #2*#7 + #3*#6
-            \exp_after:wN \__fp_pack:NNNNNw
+            \exp_after:wN \__fp_pack:NNNNNwn
             \int_use:N \__int_eval:w \c__fp_middle_shift_int
               + #1*#9 + #2*#8 + #3*#7 + #4*#6
-              \exp_after:wN \__fp_pack:NNNNNw
+              \exp_after:wN \__fp_pack:NNNNNwn
               \int_use:N \__int_eval:w \c__fp_trailing_shift_int
                 + #2*#9 + #3*#8 + #4*#7
                 + ( #3*#9 + #4*#8
-                  + \__fp_fixed_mul_i:nnnnnnnn #5 {#6}{#7}  {#1}{#2}
-  }
-\cs_new:Npn \__fp_fixed_mul_i:nnnnnnnn #1#2 #3#4 #5#6 #7#8
-  { #1*#4 + #2*#3 + #5*#8 + #6*#7 )/10000 + #1*#3 + #5*#7 ; }
-\cs_new:Npn \__fp_fixed_mul_pack:NNNNNw
-    #1 #2#3#4#5 #6; { + #1#2#3#4#5 ; {#6} }
-\cs_new:Npn \__fp_fixed_mul_after:wwn #1; #2; #3 { #3 {#1} #2 ; }
-\cs_new:Npn \__fp_fixed_one_minus_mul:wwn #1; #2#3#4#5;
-  {
-    \exp_after:wN \__fp_fixed_mul_after:wwn
-    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int + \c_ten_thousand
-      \exp_after:wN \__fp_pack_big:NNNNNNw
+                  + \__fp_fixed_mul_i:nnnnnnnwn #5 {#6}{#7}  {#1}{#2}
+  }
+\cs_new:Npn \__fp_fixed_mul_i:nnnnnnnwn #1#2 #3#4 #5#6 #7#8 ; #9
+  {
+    #1*#4 + #2*#3 + #5*#8 + #6*#7 ) / \c_ten_thousand
+    + #1*#3 + #5*#7 ;
+    {#9} ;
+  }
+\cs_new:Npn \__fp_fixed_mul_add:wwwn #1; #2; #3#4#5#6#7#8; #9
+  {
+    \exp_after:wN \__fp_fixed_mul_after:wn
+    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int
+      \exp_after:wN \__fp_pack_big:NNNNNNwn
+      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #3 #4
+        \__fp_fixed_mul_add_i:Nwnnnwnnn +
+          + #5 #6 ; #2 ; #1 ; #2 ; +
+          + #7 #8 ; {#9} ;
+  }
+\cs_new:Npn \__fp_fixed_mul_sub_back:wwwn #1; #2; #3#4#5#6#7#8; #9
+  {
+    \exp_after:wN \__fp_fixed_mul_after:wn
+    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int
+      \exp_after:wN \__fp_pack_big:NNNNNNwn
+      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #3 #4
+        \__fp_fixed_mul_add_i:Nwnnnwnnn -
+          + #5 #6 ; #2 ; #1 ; #2 ; -
+          + #7 #8 ; {#9} ;
+  }
+\cs_new:Npn \__fp_fixed_one_minus_mul:wwn #1; #2; #3
+  {
+    \exp_after:wN \__fp_fixed_mul_after:wn
+    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int
+      \exp_after:wN \__fp_pack_big:NNNNNNwn
+      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + 1 0000 0000
+        \__fp_fixed_mul_add_i:Nwnnnwnnn -
+          ; #2 ; #1 ; #2 ; -
+          ; {#3} ;
+  }
+\cs_new:Npn \__fp_fixed_mul_add_i:Nwnnnwnnn #1 #2; #3#4#5#6; #7#8#9
+  {
+    #1 #7*#3
+    \exp_after:wN \__fp_pack_big:NNNNNNwn
+    \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
+      #1 #7*#4 #1 #8*#3
+      \exp_after:wN \__fp_pack_big:NNNNNNwn
       \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
-        \__fp_fixed_mul_add_i:Nnwnnwnnn
-          - 00; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; - 00 ;
-  }
-\cs_new:Npn \__fp_fixed_mul_add:wwwn #1; #2#3#4#5; #6#7#8#9
-  {
-    \exp_after:wN \__fp_fixed_mul_after:wwn
-    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int + #6
-      \exp_after:wN \__fp_pack_big:NNNNNNw
-      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #7
-        \__fp_fixed_mul_add_i:Nnwnnwnnn
-          + {#8}{#9}; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; +
-  }
-\cs_new:Npn \__fp_fixed_mul_sub_back:wwwn #1; #2#3#4#5; #6#7#8#9
-  {
-    \exp_after:wN \__fp_fixed_mul_after:wwn
-    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int + #6
-      \exp_after:wN \__fp_pack_big:NNNNNNw
-      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #7
-        \__fp_fixed_mul_add_i:Nnwnnwnnn
-          - {#8}{#9}; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; -
-  }
-\cs_new:Npn \__fp_fixed_mul_add_i:Nnwnnwnnn #1 #2#3; #4#5#6; #7#8#9
-  { % sg z3z4; y1y2y3; x1x2x3  x4x5x6; y1y2y3y4y5y6; sg z5z6;
-        #1 #7*#4
-        \exp_after:wN \__fp_pack_big:NNNNNNw
-        \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #2
-          #1 #7*#5 #1 #8*#4
-          \exp_after:wN \__fp_pack_big:NNNNNNw
-          \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #3
-            #1 #7*#6 #1 #8*#5 #1 #9*#4
-            \exp_after:wN \__fp_pack_big:NNNNNNw
-            \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
-              #1 \__fp_fixed_mul_add_ii:nnnnwnnnn {#7}{#8}{#9}
+        #1 #7*#5 #1 #8*#4 #1 #9*#3 #2
+        \exp_after:wN \__fp_pack_big:NNNNNNwn
+        \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
+          #1 \__fp_fixed_mul_add_ii:nnnnwnnnn {#7}{#8}{#9}
   }
 \cs_new:Npn \__fp_fixed_mul_add_ii:nnnnwnnnn #1#2#3#4#5; #6#7#8#9
-  { % x1x2x3x4 x5x6; y1y2y3y4  y5y6; sg z5z6;
+  {
     ( #1*#9 + #2*#8 + #3*#7 + #4*#6 )
-    \exp_after:wN \__fp_pack_big:NNNNNNw
+    \exp_after:wN \__fp_pack_big:NNNNNNwn
     \int_use:N \__int_eval:w \c__fp_big_trailing_shift_int
       \__fp_fixed_mul_add_iii:nnnnwnnwN
         { #6 + #4*#7 + #3*#8 + #2*#9 + #1 }
@@ -2928,15 +2965,9 @@
         {#6}
   }
 \cs_new:Npn \__fp_fixed_mul_add_iii:nnnnwnnwN #1#2 #3#4#5; #6#7#8; #9
-  { % {y1+x4*y2+x3*y3+x2*y4+x1} {y2+x4*y3+x3*y4+x2}
-    % x1x5x6; y1y5y6; sg z5z6;
-    % =>
-    % sg (x5*y1+x4*y2+x3*y3+x2*y4+x1*y5)
-    % sg (x6*y1+x5*y2+x4*y3+x3*y4+x2*y5+x1*y6)/10000
-    % + z5z6;
+  {
     #9 (#4* #1 *#7)
     #9 (#5*#6+#4* #2 *#7+#3*#8) / \c_ten_thousand
-    + \__fp_use_s:nn
   }
 \cs_new:Npn \__fp_fixed_to_float:Nw #1#2; { \__fp_fixed_to_float:wN #2; #1 }
 \cs_new:Npn \__fp_fixed_to_float:wN #1#2#3#4#5#6; #7
@@ -2996,7 +3027,7 @@
   }
 \cs_new:Npn \__fp_fixed_inv_to_float:wN #1#2; #3
   {
-    - \__int_eval:w
+    + \__int_eval:w % ^^A todo: remove the +?
         \if_int_compare:w #1 < \c_one_thousand
           \__fp_fixed_dtf_zeros:wNnnnnnn
         \fi:
@@ -3092,7 +3123,7 @@
   { #1 ; {#2#3#4#5} {#6} }
 \cs_new:Npn \__fp_fixed_dtf_epsilon_ii:NNNNNww #1#2#3#4#5#6; #7;
   {
-    \__fp_fixed_mul:wwn %^^A todo: optimize to use \__fp_mul_mantissa.
+    \__fp_fixed_mul:wwn %^^A todo: optimize to use \__fp_mul_significand.
       {0000} {#2#3#4#5} {#6} #7 ;
       {0000} {#2#3#4#5} {#6} #7 ;
     \__fp_fixed_add_one:wN
@@ -3209,7 +3240,7 @@
   }
 \cs_new:Npn \__fp_ln_x_iv:wnnnnnnnn #1; #2#3#4#5 #6#7#8#9
   {
-    \exp_after:wN \__fp_div_mantissa_pack:NNN
+    \exp_after:wN \__fp_div_significand_pack:NNN
     \int_use:N \__int_eval:w
     \__fp_ln_div_i:w #1 ;
       #6 #7 ; {#8} {#9}
@@ -3222,20 +3253,20 @@
   }
 \cs_new:Npn \__fp_ln_div_i:w #1;
   {
-    \exp_after:wN \__fp_div_mantissa_calc:wwnnnnnnn
+    \exp_after:wN \__fp_div_significand_calc:wwnnnnnnn
     \int_use:N \__int_eval:w 999999 + 2 0000 0000 / #1 ; % Q1
   }
 \cs_new:Npn \__fp_ln_div_ii:wwn #1; #2;#3 % y; B1;B2 <- for k=1
   {
-    \exp_after:wN \__fp_div_mantissa_pack:NNN
+    \exp_after:wN \__fp_div_significand_pack:NNN
     \int_use:N \__int_eval:w
-      \exp_after:wN \__fp_div_mantissa_calc:wwnnnnnnn
+      \exp_after:wN \__fp_div_significand_calc:wwnnnnnnn
       \int_use:N \__int_eval:w 999999 + #2 #3 / #1 ; % Q2
       #2 #3 ;
   }
 \cs_new:Npn \__fp_ln_div_vi:wwn #1; #2;#3#4#5 #6#7#8#9 %y;F1;F2F3F4x1x2x3x4
   {
-    \exp_after:wN \__fp_div_mantissa_pack:NNN
+    \exp_after:wN \__fp_div_significand_pack:NNN
     \int_use:N \__int_eval:w 1000000 + #2 #3 / #1 ; % Q6
   }
 \cs_new:Npn \__fp_ln_div_after:Nw #1#2;
@@ -3303,7 +3334,7 @@
       \__fp_ln_Taylor_break:w
     \fi:
     \exp_after:wN \__fp_fixed_div_int:wwN \c__fp_one_fixed_tl ; #1;
-    \__fp_fixed_add:wwN #2;
+    \__fp_fixed_add:wwn #2;
     \__fp_fixed_mul:wwn #3;
     {
       \exp_after:wN \__fp_ln_Taylor_loop:www
@@ -3311,7 +3342,7 @@
     }
     #3;
   }
-\cs_new:Npn \__fp_ln_Taylor_break:w \fi: #1 \__fp_fixed_add:wwN #2#3; #4 ;;
+\cs_new:Npn \__fp_ln_Taylor_break:w \fi: #1 \__fp_fixed_add:wwn #2#3; #4 ;;
   {
     \fi:
     \exp_after:wN \__fp_fixed_mul:wwn
@@ -3320,9 +3351,9 @@
 \cs_new:Npn \__fp_ln_c:NwNw #1 #2; #3
   {
     \if_meaning:w + #1
-      \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_sub:wwN
+      \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_sub:wwn
     \else:
-      \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_add:wwN
+      \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_add:wwn
     \fi:
     #3 ; #2 ;
   }
@@ -3336,11 +3367,11 @@
       \if_int_compare:w #2 > \c_zero
         \exp_after:wN \__fp_ln_exponent_small:NNww
         \exp_after:wN 0
-        \exp_after:wN \__fp_fixed_sub:wwN \__int_value:w
+        \exp_after:wN \__fp_fixed_sub:wwn \__int_value:w
       \else:
         \exp_after:wN \__fp_ln_exponent_small:NNww
         \exp_after:wN 2
-        \exp_after:wN \__fp_fixed_add:wwN \__int_value:w -
+        \exp_after:wN \__fp_fixed_add:wwn \__int_value:w -
       \fi:
     \fi:
     #2; #1;
@@ -3348,7 +3379,7 @@
 \cs_new:Npn \__fp_ln_exponent_one:ww 1; #1;
   {
     \c_zero
-    \exp_after:wN \__fp_fixed_sub:wwN \c__fp_ln_x_fixed_tl ; #1;
+    \exp_after:wN \__fp_fixed_sub:wwn \c__fp_ln_x_fixed_tl ; #1;
     \__fp_fixed_to_float:wN 0
   }
 \cs_new:Npn \__fp_ln_exponent_small:NNww #1#2#3; #4#5#6#7#8#9;
@@ -3421,7 +3452,7 @@
           }
           #5
           {#4}
-          #2 0
+          #1 #2 0
           \tex_romannumeral:D
         \fi:
       \fi:
@@ -3429,8 +3460,9 @@
   }
 \cs_new:Npn \__fp_exp_overflow:
   { + \c_two * \c__fp_max_exponent_int ; {1000} {0000} {0000} {0000} ; }
-\cs_new:Npn \__fp_exp_Taylor:Nnnwn #1#2#3 #4; #5
+\cs_new:Npn \__fp_exp_Taylor:Nnnwn #1#2#3 #4; #5 #6
   {
+    #6
     \__fp_pack_twice_four:wNNNNNNNN
     \__fp_pack_twice_four:wNNNNNNNN
     \__fp_pack_twice_four:wNNNNNNNN
@@ -3562,9 +3594,9 @@
     #1;
     \__fp_exp_large_after:wwn
   }
-\cs_new:Npn \__fp_exp_large_after:wwn #1; #2;
+\cs_new:Npn \__fp_exp_large_after:wwn #1; #2; #3
   {
-    \__fp_exp_Taylor:Nnnwn ? { } { } 0 #2; {}
+    \__fp_exp_Taylor:Nnnwn ? { } { } 0 #2; {} #3
     \__fp_fixed_mul:wwn #1;
   }
 \cs_new:cpn { __fp_ \iow_char:N \^ _o:ww }
@@ -3599,6 +3631,13 @@
     \fi:
     \if_meaning:w #1 #4
       \__fp_case_return_o:Nw \c_zero_fp
+    \fi:
+    \if_meaning:w 0 #1
+      \__fp_case_use:nw
+        {
+          \__fp_division_by_zero_o:NNww \c_inf_fp ^
+            \s__fp \__fp_chk:w #1 #2 ;
+        }
     \else:
       \__fp_case_return_o:Nw \c_inf_fp
     \fi:
@@ -3613,7 +3652,7 @@
       \fi:
       \__fp_case_return_o:Nww \c_one_fp
     \fi:
-    \if_case:w #4 ~
+    \if_case:w #4 \exp_stop_f:
     \or:
       \exp_after:wN \__fp_pow_npos:Nww
       \exp_after:wN #5
@@ -3638,50 +3677,57 @@
     \exp_after:wN 0
     \__int_value:w
       \if:w #1 \if_int_compare:w #3 > \c_zero 0 \else: 2 \fi:
-        \exp_after:wN \__fp_pow_npos_aux:Nnww
+        \exp_after:wN \__fp_pow_npos_aux:NNnww
+        \exp_after:wN +
         \exp_after:wN \__fp_fixed_to_float:wN
       \else:
-        -
-        \exp_after:wN \__fp_pow_npos_aux:Nnww
+        \exp_after:wN \__fp_pow_npos_aux:NNnww
+        \exp_after:wN -
         \exp_after:wN \__fp_fixed_inv_to_float:wN
       \fi:
       {#3}
   }
-\cs_new:Npn \__fp_pow_npos_aux:Nnww #1#2#3#4; \s__fp \__fp_chk:w 1#5#6#7;
+\cs_new:Npn \__fp_pow_npos_aux:NNnww #1#2#3#4#5; \s__fp \__fp_chk:w 1#6#7#8;
   {
+    #1
     \__int_eval:w
-      \__fp_ln_significand:NNNNnnnN #3#4
-      \__fp_pow_exponent:wnN {#2}
-      \__fp_fixed_mul:wwn #7 {0000}{0000} ;
-      \__fp_pow_B:wwN #6;
-      #1 0 % fixed_to_float:wN
+      \__fp_ln_significand:NNNNnnnN #4#5
+      \__fp_pow_exponent:wnN {#3}
+      \__fp_fixed_mul:wwn #8 {0000}{0000} ;
+      \__fp_pow_B:wwN #7;
+      #1 #2 0 % fixed_to_float:wN
   }
 \cs_new:Npn \__fp_pow_exponent:wnN #1; #2
   {
     \if_int_compare:w #2 > \c_zero
-      \exp_after:wN \__fp_pow_exponent:Nwnnnnnn % n\ln(10) - (-\ln(x))
+      \exp_after:wN \__fp_pow_exponent:Nwnnnnnwn % n\ln(10) - (-\ln(x))
       \exp_after:wN +
     \else:
-      \exp_after:wN \__fp_pow_exponent:Nwnnnnnn % -( |n|\ln(10) + (-\ln(x)) )
+      \exp_after:wN \__fp_pow_exponent:Nwnnnnnwn % -( |n|\ln(10) + (-\ln(x)) )
       \exp_after:wN -
     \fi:
     #2; #1;
   }
-\cs_new:Npn \__fp_pow_exponent:Nwnnnnnn #1#2; #3#4#5#6#7#8;
-  { %^^A todo: use that in ln. %^^A todo: log(1.00...) too inaccurate?
-    \exp_after:wN \__fp_fixed_mul_after:wwn
-    \int_use:N \__int_eval:w -5 0000
-      \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-      \int_use:N \__int_eval:w 4 9995 0000 #1#2*23025 - #1 #3
-        \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-        \int_use:N \__int_eval:w 4 9995 0000 #1 #2*8509 - #1 #4
-          \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-          \int_use:N \__int_eval:w 4 9995 0000 #1 #2*2994 - #1 #5
-            \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-            \int_use:N \__int_eval:w 4 9995 0000 #1 #2*0456 - #1 #6
-              \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-              \int_use:N \__int_eval:w 5 0000 0000 #1 #2*8401 - #1 #7
-                #1 ( #2*7991 - #8 ) / 1 0000 ; ;
+\cs_new:Npn \__fp_pow_exponent:Nwnnnnnwn #1#2; #3#4#5#6#7#8; #9
+  { %^^A todo: use that in ln.
+    \exp_after:wN \__fp_fixed_mul_after:wn
+    \int_use:N \__int_eval:w \c__fp_leading_shift_int
+      \exp_after:wN \__fp_pack:NNNNNwn
+      \int_use:N \__int_eval:w \c__fp_middle_shift_int
+        #1#2*23025 - #1 #3
+        \exp_after:wN \__fp_pack:NNNNNwn
+        \int_use:N \__int_eval:w \c__fp_middle_shift_int
+          #1 #2*8509 - #1 #4
+          \exp_after:wN \__fp_pack:NNNNNwn
+          \int_use:N \__int_eval:w \c__fp_middle_shift_int
+            #1 #2*2994 - #1 #5
+            \exp_after:wN \__fp_pack:NNNNNwn
+            \int_use:N \__int_eval:w \c__fp_middle_shift_int
+              #1 #2*0456 - #1 #6
+              \exp_after:wN \__fp_pack:NNNNNwn
+              \int_use:N \__int_eval:w \c__fp_trailing_shift_int
+                #1 #2*8401 - #1 #7
+                #1 ( #2*7991 - #8 ) / 1 0000 ; {#9} ;
   }
 \cs_new:Npn \__fp_pow_B:wwN #1#2#3#4#5#6; #7;
   {
@@ -3698,7 +3744,7 @@
     \int_use:N \__int_eval:w 10 0000 + #1 \__int_eval_end:
     #2#3#4#5#6 0000 0000 0000 0000 0000 0000 ; %^^A todo: how many 0?
   }
-\cs_new:Npn \__fp_pow_C_overflow:w #1; #2;
+\cs_new:Npn \__fp_pow_C_overflow:w #1; #2; #3
   {
     + \c_two * \c__fp_max_exponent_int
     \exp_after:wN \__fp_fixed_continue:wn \c__fp_one_fixed_tl ;
@@ -3729,7 +3775,7 @@
 \cs_new:Npn \__fp_pow_neg:www \s__fp \__fp_chk:w #1#2; #3; #4;
   {
     \if_case:w \__fp_pow_neg_case:w #4 ;
-      \exp_after:wN \__fp_pow_neg_neg:w
+      \exp_after:wN \__fp_neg_o:w
     \or:
       \if_int_compare:w \__int_eval:w #1 / \c_two = \c_one
         \__fp_invalid_operation_o:Nww ^ #3; #4;
@@ -3741,14 +3787,6 @@
     \__fp_exp_after_o:w
     \s__fp \__fp_chk:w #1#2;
   }
-\cs_new:Npn \__fp_pow_neg_neg:w \__fp_exp_after_o:w \s__fp \__fp_chk:w #1#2
-  {
-    \exp_after:wN \__fp_exp_after_o:w
-    \exp_after:wN \s__fp
-    \exp_after:wN \__fp_chk:w
-    \exp_after:wN #1
-    \int_use:N \__int_eval:w \c_two - #2 \__int_eval_end:
-  }
 \cs_new:Npn \__fp_pow_neg_case:w \s__fp \__fp_chk:w #1#2#3;
   {
     \if_case:w #1 \exp_stop_f:
@@ -3826,24 +3864,17 @@
 %%
 %% -----------------------------------------------------------------------
 %%
-\cs_new_nopar:Npx \__fp_one_over:w
-  {
-    \exp_not:N \exp_after:wN
-    \exp_not:c { __fp_/_o:ww }
-    \exp_not:N \c_one_fp
-  }
 \cs_new:Npn \__fp_sin_o:w \s__fp \__fp_chk:w #1#2
   {
     \if_case:w #1 \exp_stop_f:
            \__fp_case_return_same_o:w
     \or:
-      \exp_after:wN \__fp_trig_exponent:NNNNwn
-      \exp_after:wN \__fp_sin_series:NNwww
-      \exp_after:wN ?
-      \exp_after:wN #2
-      \exp_after:wN \c_zero
-    \or:
-      \__fp_case_use:nw { \__fp_invalid_operation_o:nw { sin } }
+      \__fp_case_use:nw
+        {
+          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_o:w
+            \__fp_sin_series:NNwww \__fp_fixed_to_float:wN #2 \c_zero
+        }
+    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { sin } }
     \else: \__fp_case_return_same_o:w
     \fi:
     \s__fp \__fp_chk:w #1#2
@@ -3853,16 +3884,42 @@
     \if_case:w #1 \exp_stop_f:
            \__fp_case_return_o:Nw \c_one_fp
     \or:
-      \__fp_case_use:nw %^^A todo: is that faster than the exp_after route?
+      \__fp_case_use:nw
         {
-          \__fp_trig_exponent:NNNNwn
-          \__fp_sin_series:NNwww
-          ?
-          0
-          \c_two
+          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_one_o:w
+            \__fp_sin_series:NNwww \__fp_fixed_to_float:wN 0 \c_two
         }
+    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { cos } }
+    \else: \__fp_case_return_same_o:w
+    \fi:
+    \s__fp \__fp_chk:w #1#2
+  }
+\cs_new:Npn \__fp_csc_o:w \s__fp \__fp_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+           \__fp_cot_zero_o:Nnw #2 { csc }
+    \or:
+      \__fp_case_use:nw
+        {
+          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_inv_o:w
+            \__fp_sin_series:NNwww \__fp_fixed_inv_to_float:wN #2 \c_zero
+        }
+    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { csc } }
+    \else: \__fp_case_return_same_o:w
+    \fi:
+    \s__fp \__fp_chk:w #1#2
+  }
+\cs_new:Npn \__fp_sec_o:w \s__fp \__fp_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+           \__fp_case_return_o:Nw \c_one_fp
     \or:
-      \__fp_case_use:nw { \__fp_invalid_operation_o:nw { cos } }
+      \__fp_case_use:nw
+        {
+          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_one_o:w
+            \__fp_sin_series:NNwww \__fp_fixed_inv_to_float:wN 0 \c_two
+        }
+    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { sec } }
     \else: \__fp_case_return_same_o:w
     \fi:
     \s__fp \__fp_chk:w #1#2
@@ -3872,13 +3929,12 @@
     \if_case:w #1 \exp_stop_f:
            \__fp_case_return_same_o:w
     \or:
-      \exp_after:wN \__fp_trig_exponent:NNNNwn
-      \exp_after:wN \__fp_tan_series:NNwww
-      \exp_after:wN 0
-      \exp_after:wN #2
-      \exp_after:wN \c_one
-    \or:
-      \__fp_case_use:nw { \__fp_invalid_operation_o:nw { tan } }
+      \__fp_case_use:nw
+        {
+          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_o:w
+            \__fp_tan_series_o:NNwww 0 #2 \c_one
+        }
+    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { tan } }
     \else: \__fp_case_return_same_o:w
     \fi:
     \s__fp \__fp_chk:w #1#2
@@ -3886,129 +3942,126 @@
 \cs_new:Npn \__fp_cot_o:w \s__fp \__fp_chk:w #1#2
   {
     \if_case:w #1 \exp_stop_f:
-           \exp_after:wN \__fp_one_over:w
-    \or:
-      \exp_after:wN \__fp_trig_exponent:NNNNwn
-      \exp_after:wN \__fp_tan_series:NNwww
-      \exp_after:wN 2
-      \exp_after:wN #2
-      \exp_after:wN \c_three
+           \__fp_cot_zero_o:Nnw #2 { cot }
     \or:
-      \__fp_case_use:nw { \__fp_invalid_operation_o:nw { cot } }
+      \__fp_case_use:nw
+        {
+          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_inv_o:w
+            \__fp_tan_series_o:NNwww 2 #2 \c_three
+        }
+    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { cot } }
     \else: \__fp_case_return_same_o:w
     \fi:
     \s__fp \__fp_chk:w #1#2
   }
-\cs_new:Npn \__fp_trig_exponent:NNNNwn #1#2#3#4 \s__fp \__fp_chk:w 1#5#6
+\cs_new:Npn \__fp_cot_zero_o:Nnw #1 #2 #3 \fi:
   {
-    \if_int_compare:w #6 > - \c_eight
-      \exp_after:wN #1
+    \fi:
+    \if_meaning:w 0 #1
+      \exp_after:wN \__fp_division_by_zero_o:Nnw \exp_after:wN \c_inf_fp
+    \else:
+      \exp_after:wN \__fp_division_by_zero_o:Nnw \exp_after:wN \c_minus_inf_fp
+    \fi:
+    {#2}
+  }
+\cs_new:Npn \__fp_trig_exponent:NNNNNwn #1#2#3#4#5 \s__fp \__fp_chk:w 1#6#7
+  {
+    \if_int_compare:w #7 > - \c_eight
       \exp_after:wN #2
       \exp_after:wN #3
-      \int_use:N \__int_eval:w #4
-        \if_int_compare:w #6 > \c_zero
-          \exp_after:wN \__fp_trig_large:w \__int_value:w
+      \exp_after:wN #4
+      \int_use:N \__int_eval:w #5
+        \if_int_compare:w #7 > \c_zero
+          \exp_after:wN \__fp_trig_large:ww \__int_value:w
         \else:
-          \exp_after:wN \__fp_trig_small:w \__int_value:w
+          \exp_after:wN \__fp_trig_small:ww \__int_value:w
         \fi:
     \else:
-      \if_case:w #4
-             \__fp_sin_epsilon:w
-      \or:   \__fp_sin_epsilon:w
-      \or:   \__fp_cos_epsilon:w
-      \else: \__fp_cot_epsilon:w
-      \fi:
-      #5
+      \exp_after:wN #1
+      \exp_after:wN #6
     \fi:
-    #6 ;
-  }
-\cs_new:Npn \__fp_sin_epsilon:w #1 \fi: #2 \fi: #3 ;
-  { \fi: \fi: \__fp_exp_after_o:w \s__fp \__fp_chk:w 1 #2 {#3} }
-\cs_new:Npn \__fp_cos_epsilon:w #1 \fi: #2 \fi: #3 ; #4 ;
-  { \fi: \fi: \exp_after:wN \c_one_fp }
-\cs_new:Npn \__fp_cot_epsilon:w \fi: #1 \fi: #2 ;
-  { \fi: \fi: \__fp_one_over:w \s__fp \__fp_chk:w 1 #1 {#2} }
-\cs_new:Npn \__fp_trig_small:w #1;
-  {
-    \exp_after:wN \exp_after:wN \exp_after:wN \__fp_trig_small_aux:wwNN
-    \prg_replicate:nn { - #1 } { 0 } ;
+    #7 ;
   }
-\cs_new:Npn \__fp_trig_small_aux:wwNN #1; #2#3#4#5;
+\cs_new:Npn \__fp_trig_epsilon_o:w #1 #2 ;
+  { \__fp_exp_after_o:w \s__fp \__fp_chk:w 1 #1 {#2} }
+\cs_new:Npn \__fp_trig_epsilon_one_o:w #1 ; #2 ;
+  { \exp_after:wN \c_one_fp }
+\group_begin:
+  \char_set_catcode_letter:N /
+  \cs_new:Npn \__fp_trig_epsilon_inv_o:w #1 #2 ;
+    {
+      \exp_after:wN \__fp_/_o:ww
+        \c_one_fp
+        \s__fp \__fp_chk:w 1 #1 {#2}
+    }
+\group_end:
+\cs_new:Npn \__fp_trig_small:ww #1; #2#3#4#5;
   {
-    \__fp_pack_twice_four:wNNNNNNNN
-    \__fp_pack_twice_four:wNNNNNNNN
-    \__fp_pack_twice_four:wNNNNNNNN
-    .
-    ;
-    #1#2#3#4#5 0000 0000;
+    \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
+    \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
+    \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
+    \exp_after:wN .
+    \exp_after:wN ;
+    \tex_romannumeral:D -`0
+      \prg_replicate:nn { - #1 } { 0 } #2#3#4#5 0000 0000 ;
   }
-\cs_new:Npn \__fp_trig_large:w #1; #2#3;
+\cs_new:Npn \__fp_trig_large:ww #1; #2#3;
   { \__fp_trig_large_i:www #2; #3 ;  #1; }
 \cs_new:Npn \__fp_trig_large_i:www #1; #2; #3;
   {
     \if_meaning:w 0 #3 \__fp_trig_large_break:w \fi:
-    \exp_after:wN \__fp_trig_large_ii:wnnnnnn
+    \exp_after:wN \__fp_trig_large_ii_o:wnnnn
     \int_use:N \__int_eval:w ( #1 - 3141 ) / 6283 ;
-    {#1} #2;
+    {#1} #2
+    \exp_after:wN ;
     \int_use:N \__int_eval:w \c_minus_one + #3;
   }
-\cs_new:Npn \__fp_trig_large_ii:wnnnnnn #1; #2#3#4#5;
+\cs_new:Npn \__fp_trig_large_ii_o:wnnnn #1; #2#3#4#5
   {
     \exp_after:wN \__fp_trig_large_i:www
-    \int_use:N \__int_eval:w -5 0000 + #20 - #1*62831
-      \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-      \int_use:N \__int_eval:w 4 9995 0000 + #30 - #1*8530
-        \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-        \int_use:N \__int_eval:w 4 9995 0000 + #40 - #1*7179
-          \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-          \int_use:N \__int_eval:w 5 0000 0000 + #50 - #1*5880
-    \exp_after:wN ;
+    \int_use:N \__int_eval:w \c__fp_leading_shift_int + #20 - #1*62831
+      \exp_after:wN \__fp_pack:NNNNNw
+      \int_use:N \__int_eval:w \c__fp_middle_shift_int + #30 - #1*8530
+        \exp_after:wN \__fp_pack:NNNNNw
+        \int_use:N \__int_eval:w \c__fp_middle_shift_int + #40 - #1*7179
+          \exp_after:wN \__fp_pack:NNNNNw
+          \int_use:N \__int_eval:w \c__fp_trailing_shift_int + #50 - #1*5880
     \exp_after:wN ;
   }
 \cs_new:Npn \__fp_trig_large_break:w \fi: #1; #2;
-  { \fi: \__fp_trig_octant_loop:nw #2 {0000} {0000} ; }
-\cs_new:Npn \__fp_trig_octant_loop:nw #1#2;
+  { \fi: \__fp_trig_octant_loop:nnnnnw #2 {0000} {0000} ; }
+\cs_new:Npn \__fp_trig_octant_loop:nnnnnw #1#2#3#4#5#6;
   {
-    \if_int_compare:w #1 < 15707 \exp_stop_f:
+    \if_int_compare:w #1#2 < 157079633 \exp_stop_f:
+      \if_int_compare:w #1#2 = 157079632 \exp_stop_f:
+        \if_int_compare:w #3#4 > 67948969 \exp_stop_f:
+          \use_i_ii:nnn
+        \fi:
+      \fi:
       \__fp_trig_octant_break:w
     \fi:
     + \c_two
-    \__fp_fixed_sub_back:wwN
+    \__fp_fixed_sub:wwn
+      {#1} {#2} {#3} {#4} {0000} {0000} ;
       {15707} {9632} {6794} {8970} {0000} {0000} ;
-      {#1} #2;
-    \__fp_trig_octant_loop:nw
+    \__fp_trig_octant_loop:nnnnnw
   }
-\cs_new:Npn \__fp_trig_octant_break:w #1 \fi: + #2#3 #4; #5#6; #7;
+\cs_new:Npn \__fp_trig_octant_break:w #1 \fi: + #2#3 #4#5; #6; #7;
   {
     \fi:
-    \if_int_compare:w #5 < 7854 \exp_stop_f:
-      \if_int_compare:w #5 < \c_zero
-        \exp_after:wN \__fp_trig_octant_neg:w
-      \fi:
+    \if_int_compare:w #4 < 7854 \exp_stop_f:
       \exp_after:wN \__fp_use_i_until_s:nw
       \exp_after:wN .
     \fi:
     + \c_one
-    \__fp_fixed_sub:wwN
-    {15707} {9632} {6794} {8970} {0000} {0000} ;
-    {#5} #6 ; . ;
-  }
-\cs_new:Npn \__fp_trig_octant_neg:w #1\fi: #2; #3#4#5#6#7#8; #9
-  {
-    \fi:
-    + \c_seven
-    \exp_after:wN \__fp_fixed_add_after:NNNNNwN
-    \int_use:N \__int_eval:w 1 9999 9998 - #30000 - #4
-      \exp_after:wN \__fp_fixed_add_pack:NNNNNwN
-      \int_use:N \__int_eval:w 1 9999 9998 - #5#6
-        \exp_after:wN \__fp_fixed_add_pack:NNNNNwN
-        \int_use:N \__int_eval:w 2 0000 0000 - #7#8 ; {#9} ;
+    \__fp_fixed_sub:wwn #6 ; {#4} #5 ; . ;
   }
 \cs_new:Npn \__fp_sin_series:NNwww #1#2#3 . #4; #5;
   {
     \__fp_fixed_mul:wwn #4; #4;
     {
-      \exp_after:wN \__fp_sin_series_aux:Nnww
+      \exp_after:wN \__fp_sin_series_aux:NNnww
+      \exp_after:wN #1
       \__int_value:w
         \if_int_odd:w \__int_eval:w ( #3 + \c_two ) / \c_four \__int_eval_end:
           #2
@@ -4019,49 +4072,49 @@
     }
     #4 ;
   }
-\cs_new:Npn \__fp_sin_series_aux:Nnww #1#2 #3; #4;
+\cs_new:Npn \__fp_sin_series_aux:NNnww #1#2#3 #4; #5;
   {
-    \if_int_odd:w \__int_eval:w #2 / \c_two \__int_eval_end:
+    \if_int_odd:w \__int_eval:w #3 / \c_two \__int_eval_end:
       \exp_after:wN \use_i:nn
     \else:
       \exp_after:wN \use_ii:nn
     \fi:
-    {
-      \__fp_fixed_continue:wn {0000}{0000}{0000}{0001}{5619}{2070}; % 1/18!
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0000}{0477}{9477}{3324};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0011}{4707}{4559}{7730};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{2087}{6756}{9878}{6810};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0027}{5573}{1922}{3985}{8907};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{2480}{1587}{3015}{8730}{1587};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0013}{8888}{8888}{8888}{8888}{8889};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0416}{6666}{6666}{6666}{6666}{6667};
-      \__fp_fixed_mul_sub_back:wwwn #3; {5000}{0000}{0000}{0000}{0000}{0000};
-      \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
+    { % 1/18!
+      \__fp_fixed_mul_sub_back:wwwn     {0000}{0000}{0000}{0001}{5619}{2070};
+                                  #4; {0000}{0000}{0000}{0477}{9477}{3324};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0000}{0011}{4707}{4559}{7730};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0000}{2087}{6756}{9878}{6810};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0027}{5573}{1922}{3985}{8907};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{2480}{1587}{3015}{8730}{1587};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0013}{8888}{8888}{8888}{8888}{8889};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0416}{6666}{6666}{6666}{6666}{6667};
+      \__fp_fixed_mul_sub_back:wwwn #4; {5000}{0000}{0000}{0000}{0000}{0000};
+      \__fp_fixed_mul_sub_back:wwwn #4;{10000}{0000}{0000}{0000}{0000}{0000};
     }
-    {
-      \__fp_fixed_continue:wn {0000}{0000}{0000}{0028}{1145}{7254}; % 1/17!
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0000}{7647}{1637}{3182};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0160}{5904}{3836}{8216};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0002}{5052}{1083}{8544}{1719};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0275}{5731}{9223}{9858}{9065};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0001}{9841}{2698}{4126}{9841}{2698};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0083}{3333}{3333}{3333}{3333}{3333};
-      \__fp_fixed_mul_sub_back:wwwn #3; {1666}{6666}{6666}{6666}{6666}{6667};
-      \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
-      \__fp_fixed_mul:wwn #4;
+    { % 1/17!
+      \__fp_fixed_mul_sub_back:wwwn     {0000}{0000}{0000}{0028}{1145}{7254};
+                                  #4; {0000}{0000}{0000}{7647}{1637}{3182};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0000}{0160}{5904}{3836}{8216};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0002}{5052}{1083}{8544}{1719};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0275}{5731}{9223}{9858}{9065};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0001}{9841}{2698}{4126}{9841}{2698};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0083}{3333}{3333}{3333}{3333}{3333};
+      \__fp_fixed_mul_sub_back:wwwn #4; {1666}{6666}{6666}{6666}{6666}{6667};
+      \__fp_fixed_mul_sub_back:wwwn #4;{10000}{0000}{0000}{0000}{0000}{0000};
+      \__fp_fixed_mul:wwn #5;
     }
     {
       \exp_after:wN \__fp_sanitize:Nw
-      \exp_after:wN #1
-      \int_use:N \__int_eval:w \__fp_fixed_to_float:wN
+      \exp_after:wN #2
+      \int_use:N \__int_eval:w #1
     }
-    #1
+    #2
   }
-\cs_new:Npn \__fp_tan_series:NNwww #1#2#3. #4; #5;
+\cs_new:Npn \__fp_tan_series_o:NNwww #1#2#3. #4; #5;
   {
     \__fp_fixed_mul:wwn #4; #4;
     {
-      \exp_after:wN \__fp_tan_series_aux:Nnww
+      \exp_after:wN \__fp_tan_series_aux_o:Nnww
       \__int_value:w
         \if_int_odd:w \__int_eval:w #3 / \c_two \__int_eval_end:
           \exp_after:wN \reverse_if:N
@@ -4071,18 +4124,18 @@
     }
     #4 ;
   }
-\cs_new:Npn \__fp_tan_series_aux:Nnww #1 #2 #3; #4;
+\cs_new:Npn \__fp_tan_series_aux_o:Nnww #1 #2 #3; #4;
   {
-    \__fp_fixed_continue:wn {0000}{0000}{1527}{3493}{0856}{7059};
-    \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0159}{6080}{0274}{5257}{6472};
+    \__fp_fixed_mul_sub_back:wwwn     {0000}{0000}{1527}{3493}{0856}{7059};
+                                #3; {0000}{0159}{6080}{0274}{5257}{6472};
     \__fp_fixed_mul_sub_back:wwwn #3; {0002}{4571}{2320}{0157}{2558}{8481};
     \__fp_fixed_mul_sub_back:wwwn #3; {0115}{5830}{7533}{5397}{3168}{2147};
     \__fp_fixed_mul_sub_back:wwwn #3; {1929}{8245}{6140}{3508}{7719}{2982};
     \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
     \__fp_fixed_mul:wwn #4;
       {
-        \__fp_fixed_continue:wn {0000}{0007}{0258}{0681}{9408}{4706};
-        \__fp_fixed_mul_sub_back:wwwn #3; {0000}{2343}{7175}{1399}{6151}{7670};
+        \__fp_fixed_mul_sub_back:wwwn     {0000}{0007}{0258}{0681}{9408}{4706};
+                                    #3; {0000}{2343}{7175}{1399}{6151}{7670};
         \__fp_fixed_mul_sub_back:wwwn #3; {0019}{2638}{4588}{9232}{8861}{3691};
         \__fp_fixed_mul_sub_back:wwwn #3; {0536}{6357}{0691}{4344}{6852}{4252};
         \__fp_fixed_mul_sub_back:wwwn #3; {5263}{1578}{9473}{6842}{1052}{6315};
@@ -4350,6 +4403,21 @@
 \cs_new_eq:NN \fp_eval:n \fp_to_decimal:n
 \cs_new:Npn \fp_abs:n #1
   { \fp_to_decimal:n { abs \__fp_parse:n {#1} } }
+\cs_new:Npn \__fp_array_to_clist:n #1
+  {
+    \__fp_array_to_clist_i:wwww ;
+      #1
+      \__fp_array_to_clist_ii:ww \s__fp ; @
+      ; , ~ , ~ @ \s_stop
+  }
+\cs_new:Npn \__fp_array_to_clist_i:wwww #1; #2 \s__fp #3; #4 @
+  {
+    #2
+    \exp_after:wN \__fp_array_to_clist_i:wwww
+    \tex_romannumeral:D -`0 \__fp_to_tl:w \s__fp #3 ; ;
+    #4 , ~ #1 @
+  }
+\cs_new:Npn \__fp_array_to_clist_ii:ww #1 ; , ~ , ~ #2 @ #3 \s_stop {#2}
 %%
 %% File: l3fp-assign.dtx Copyright (C) 2011-2012 The LaTeX3 project
 %%
@@ -4421,7 +4489,14 @@
 \cs_generate_variant:Nn \fp_sub:Nn  { c }
 \cs_generate_variant:Nn \fp_gsub:Nn { c }
 \cs_new_protected:Npn \fp_show:N #1
-  { \__msg_show_variable:x { > \fp_to_tl:N #1 } }
+  {
+    \fp_if_exist:NTF #1
+      { \__msg_show_variable:x { > \fp_to_tl:N #1 } }
+      {
+        \__msg_kernel_error:nnx { kernel } { variable-not-defined }
+          { \token_to_str:N #1 }
+      }
+  }
 \cs_new_protected:Npn \fp_show:n #1
   { \__msg_show_variable:x { > \fp_to_tl:n {#1} } }
 \cs_generate_variant:Nn \fp_show:N { c }
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3int.sty b/Master/texmf-dist/tex/latex/l3kernel/l3int.sty
index 531f0a0e7c9..25667fc8c75 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3int.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3int.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3int.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3int.dtx 4121 2012-08-17 01:36:30Z bruno $
   {L3 Integers}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -329,11 +329,11 @@
   }
 \cs_new:Npn \int_until_do:nNnn #1#2#3#4
   {
-  \int_compare:nNnF {#1} #2 {#3}
-    {
-      #4
-      \int_until_do:nNnn {#1} #2 {#3} {#4}
-    }
+    \int_compare:nNnF {#1} #2 {#3}
+      {
+        #4
+        \int_until_do:nNnn {#1} #2 {#3} {#4}
+      }
   }
 \cs_new:Npn \int_do_while:nNnn #1#2#3#4
   {
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3msg.sty b/Master/texmf-dist/tex/latex/l3kernel/l3msg.sty
index 3845880de85..0d717006172 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3msg.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3msg.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3msg.dtx 4077 2012-08-10 23:30:52Z bruno $
+\GetIdInfo$Id: l3msg.dtx 4147 2012-08-28 10:27:33Z bruno $
   {L3 Messages}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -591,7 +591,7 @@
     \c_msg_coding_error_text_tl
     Code-level~functions~must~contain~':'~to~separate~the~
     argument~specification~from~the~function~name.~This~is~
-    needed~when~defining~conditionals~or~when~building~a~
+    needed~when~defining~conditionals~or~variants,~or~when~building~a~
     parameter~text~from~the~number~of~arguments~of~the~function.
   }
 \__msg_kernel_new:nnnn { kernel } { protected-predicate }
@@ -630,6 +630,14 @@
     with~a~signature~starting~with~'#1',~but~that~is~longer~than~
     the~signature~(part~after~the~colon)~of~'#2'.
   }
+\__msg_kernel_new:nnnn { kernel } { invalid-variant }
+  { Variant~form~'#1'~invalid~for~base~form~'#2'. }
+  {
+    \c_msg_coding_error_text_tl
+    LaTeX~has~been~asked~to~create~a~variant~of~the~function~'#2'~
+    with~a~signature~starting~with~'#1',~but~cannot~change~an~argument~
+    from~type~'#3'~to~type~'#4'.
+  }
 \__msg_kernel_new:nnn { kernel } { bad-variable }
   { Erroneous~variable~#1 used! }
 \__msg_kernel_new:nnn { kernel } { misused-sequence }
@@ -736,7 +744,7 @@
     \cs_if_exist:NTF #1
       {
         \__msg_term:nnn { LaTeX / kernel } { show- #2 } {#1}
-        \__msg_show_variable:x {#3}
+        \__msg_show_variable:x { \tl_to_str:n {#3} }
       }
       {
         \__msg_kernel_error:nnx { kernel } { variable-not-defined }
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3prg.sty b/Master/texmf-dist/tex/latex/l3kernel/l3prg.sty
index 22fa6688784..93ef25ee4b6 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3prg.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3prg.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3prg.dtx 4061 2012-08-08 15:19:07Z bruno $
+\GetIdInfo$Id: l3prg.dtx 4114 2012-08-16 01:57:02Z bruno $
   {L3 Control structures}
 %%
 \ProvidesExplPackage
@@ -106,8 +106,8 @@
 \cs_new_protected:Npn \bool_show:n #1
   {
     \bool_if:nTF {#1}
-      { \__msg_show_variable:x { > true } }
-      { \__msg_show_variable:x { > false } }
+      { \__msg_show_variable:n { > true } }
+      { \__msg_show_variable:n { > false } }
   }
 \cs_generate_variant:Nn \bool_show:N { c }
 \bool_new:N \l_tmpa_bool
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3prop.sty b/Master/texmf-dist/tex/latex/l3kernel/l3prop.sty
index e65ebc5e2bc..1e692963872 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3prop.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3prop.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3prop.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3prop.dtx 4092 2012-08-14 14:04:41Z bruno $
   {L3 Property lists}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -295,9 +295,7 @@
   { \__prg_map_break:Nn \prop_map_break: }
 \cs_new_protected:Npn \prop_show:N #1
   {
-    \__msg_show_variable:Nnn
-      #1
-      { prop }
+    \__msg_show_variable:Nnx #1 { prop }
       { \prop_map_function:NN #1 \__msg_show_item:nn }
   }
 \cs_generate_variant:Nn \prop_show:N { c }
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3seq.sty b/Master/texmf-dist/tex/latex/l3kernel/l3seq.sty
index 5b4fe8c3790..58e3b205359 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3seq.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3seq.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3seq.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3seq.dtx 4092 2012-08-14 14:04:41Z bruno $
   {L3 Sequences and stacks}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -433,9 +433,7 @@
 \prg_new_eq_conditional:NNn \seq_gpop:cN \seq_gpop_left:cN { T , F , TF }
 \cs_new_protected:Npn \seq_show:N #1
   {
-    \__msg_show_variable:Nnn
-      #1
-      { seq }
+    \__msg_show_variable:Nnx #1 { seq }
       { \seq_map_function:NN #1 \__msg_show_item:n }
   }
 \cs_generate_variant:Nn \seq_show:N { c }
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3skip.sty b/Master/texmf-dist/tex/latex/l3kernel/l3skip.sty
index 8888a5b9056..adbdbc68d8c 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3skip.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3skip.sty
@@ -47,7 +47,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3skip.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3skip.dtx 4121 2012-08-17 01:36:30Z bruno $
   {L3 Dimensions and skips}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}