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authorKarl Berry <karl@freefriends.org>2012-08-31 17:58:55 +0000
committerKarl Berry <karl@freefriends.org>2012-08-31 17:58:55 +0000
commit3301423440393adfdbbcfa0d8471e4b4c63df1e6 (patch)
tree6aa86f66a252f654a2bd2f28ee7b680fdac1b0a3 /Master/texmf-dist
parenta511edd7e6a05e250f2b2d8062a470734e3af33d (diff)
l3kernel 3160 (31aug12)
git-svn-id: svn://tug.org/texlive/trunk@27559 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist')
-rw-r--r--Master/texmf-dist/doc/latex/l3kernel/expl3.pdfbin662103 -> 665195 bytes
-rw-r--r--Master/texmf-dist/doc/latex/l3kernel/interface3.pdfbin1245009 -> 1279407 bytes
-rw-r--r--Master/texmf-dist/doc/latex/l3kernel/l3docstrip.pdfbin446894 -> 449468 bytes
-rw-r--r--Master/texmf-dist/doc/latex/l3kernel/l3styleguide.pdfbin270448 -> 270448 bytes
-rw-r--r--Master/texmf-dist/doc/latex/l3kernel/l3syntax-changes.pdfbin220216 -> 220216 bytes
-rw-r--r--Master/texmf-dist/doc/latex/l3kernel/source3.pdfbin3674966 -> 3863848 bytes
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/expl3.dtx4
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3alloc.dtx6
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3basics.dtx17
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3clist.dtx19
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx4
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3color.dtx22
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3doc.dtx10
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3drivers.dtx20
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3expan.dtx367
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3file.dtx15
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-assign.dtx11
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-aux.dtx23
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-basics.dtx240
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-convert.dtx27
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-expo.dtx147
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-extended.dtx503
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-logic.dtx96
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-parse.dtx115
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-round.dtx7
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-traps.dtx52
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp-trig.dtx526
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3fp.dtx422
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3int.dtx106
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3msg.dtx31
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3prg.dtx96
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3prop.dtx8
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3seq.dtx8
-rw-r--r--Master/texmf-dist/source/latex/l3kernel/l3skip.dtx88
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/expl3.sty4
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3basics.sty15
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3clist.sty13
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty4
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3color.sty4
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3doc.cls9
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3expan.sty162
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3file.sty8
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3fp.sty909
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3int.sty12
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3msg.sty14
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3prg.sty6
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3prop.sty6
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3seq.sty6
-rw-r--r--Master/texmf-dist/tex/latex/l3kernel/l3skip.sty2
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
Binary files differ
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
Binary files differ
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
Binary files differ
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
Binary files differ
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
Binary files differ
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
Binary files differ
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}