expl3 1981 (11jul10)

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

5 files changed, 1142 insertions, 8 deletions

diff --git a/Master/texmf-dist/tex/latex/expl3/expl3.sty b/Master/texmf-dist/tex/latex/expl3/expl3.sty
index c943d158a23..5bd262fbb19 100644
--- a/Master/texmf-dist/tex/latex/expl3/expl3.sty
+++ b/Master/texmf-dist/tex/latex/expl3/expl3.sty
@@ -49,7 +49,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: expl3.dtx 1905 2010-05-19 07:45:31Z joseph $
+\GetIdInfo$Id: expl3.dtx 1955 2010-06-15 06:04:59Z joseph $
        {L3 Experimental code bundle wrapper}%
 \ProvidesExplPackage
   {\filename}{\filedate}{\fileversion}{\filedescription}
@@ -87,7 +87,8 @@
   l3precom,
   l3calc,
   l3xref,
-  l3file
+  l3file,
+  l3fp,
 }
 \bool_if:nT { \@l@expl@check@declarations@bool } {
   \msg_kernel_new:nnnn { check } { non-declared-variable }
diff --git a/Master/texmf-dist/tex/latex/expl3/l3expan.sty b/Master/texmf-dist/tex/latex/expl3/l3expan.sty
index cbe31dd98b5..8a356ca0295 100644
--- a/Master/texmf-dist/tex/latex/expl3/l3expan.sty
+++ b/Master/texmf-dist/tex/latex/expl3/l3expan.sty
@@ -48,7 +48,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3expan.dtx 1873 2010-03-24 08:32:54Z joseph $
+\GetIdInfo$Id: l3expan.dtx 1948 2010-06-10 18:53:09Z joseph $
        {L3 Experimental Argument Expansion module}
 \ProvidesExplPackage
   {\filename}{\filedate}{\fileversion}{\filedescription}
@@ -292,15 +292,19 @@
 }
 \cs_new_nopar:Npn \exp_last_unbraced:Nf { \::f_unbraced \::: }
 \cs_new_nopar:Npn \exp_last_unbraced:NV { \::V_unbraced \::: }
+\cs_new_nopar:Npn \exp_last_unbraced:No { \::o_unbraced \::: }
 \cs_new_nopar:Npn \exp_last_unbraced:Nv { \::v_unbraced \::: }
 \cs_new_nopar:Npn \exp_last_unbraced:NcV {
   \::c \::V_unbraced \:::
 }
+\cs_new_nopar:Npn \exp_last_unbraced:NNV {
+  \::N \::V_unbraced \:::
+}
 \cs_new:Npn \exp_last_unbraced:NNo #1#2#3 {
   \exp_after:wN #1 \exp_after:wN #2 #3
 }
-\cs_new_nopar:Npn \exp_last_unbraced:NNV {
-  \::N \::V_unbraced \:::
+\cs_new_nopar:Npn \exp_last_unbraced:NNNV {
+  \::N \::N \::V_unbraced \:::
 }
 \cs_new:Npn \exp_last_unbraced:NNNo #1#2#3#4 {
   \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN #3 #4
diff --git a/Master/texmf-dist/tex/latex/expl3/l3fp.sty b/Master/texmf-dist/tex/latex/expl3/l3fp.sty
new file mode 100644
index 00000000000..f2677b2c481
--- /dev/null
+++ b/Master/texmf-dist/tex/latex/expl3/l3fp.sty
@@ -0,0 +1,1092 @@
+%%
+%% This is file `l3fp.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% l3fp.dtx  (with options: `package')
+%% 
+%% 
+%% EXPERIMENTAL CODE
+%% 
+%% Do not distribute this file without also distributing the
+%% source files specified above.
+%% 
+%% Do not distribute a modified version of this file.
+%% 
+%% 
+%% File: l3fp.dtx Copyright (C) 2010 LaTeX3 project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the ``expl3 bundle'' (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp.dtx 1979 2010-07-08 19:51:19Z joseph $
+  {L3 Experimental floating-point operations}
+\ProvidesExplPackage
+  {\filename}{\filedate}{\fileversion}{\filedescription}
+\package_check_loaded_expl:
+\int_new:N \l_fp_input_a_integer_int
+\int_new:N \l_fp_input_a_decimal_int
+\int_new:N \l_fp_input_b_integer_int
+\int_new:N \l_fp_input_b_decimal_int
+\int_new:N \l_fp_input_a_sign_int
+\int_new:N \l_fp_input_b_sign_int
+\int_new:N \l_fp_split_sign_int
+\int_new:N \l_fp_mul_a_i_int
+\int_new:N \l_fp_mul_a_ii_int
+\int_new:N \l_fp_mul_a_iii_int
+\int_new:N \l_fp_mul_a_iv_int
+\int_new:N \l_fp_mul_a_v_int
+\int_new:N \l_fp_mul_a_vi_int
+\int_new:N \l_fp_mul_b_i_int
+\int_new:N \l_fp_mul_b_ii_int
+\int_new:N \l_fp_mul_b_iii_int
+\int_new:N \l_fp_mul_b_iv_int
+\int_new:N \l_fp_mul_b_v_int
+\int_new:N \l_fp_mul_b_vi_int
+\int_new:N \l_fp_mul_output_int
+\tl_new:N  \l_fp_mul_output_tl
+\int_new:N \l_fp_div_count_int
+\int_new:N \l_fp_div_offset_int
+\int_new:N \l_fp_output_sign_int
+\int_new:N \l_fp_output_integer_int
+\int_new:N \l_fp_output_decimal_int
+\bool_new:N \l_fp_round_carry_bool
+\tl_new:N \l_fp_round_decimal_tl
+\int_new:N \l_fp_round_discard_int
+\int_new:N \l_fp_round_position_int
+\int_new:N \l_fp_tmp_int
+\tl_new:N \l_fp_tmp_tl
+\tl_new:N  \c_zero_fp
+\tl_set:Nn \c_zero_fp { + 0.000000000 }
+\tl_new:N  \c_undefined_fp
+\tl_set:Nn \c_undefined_fp { X 0.000000000 }
+\tl_new:N  \c_infinity_fp
+\tl_set:Nn \c_infinity_fp { +2147483647.2147483647 }
+\tl_new:N  \c_minus_infinity_fp
+\tl_set:Nn \c_minus_infinity_fp { -2147483647.2147483647 }
+\int_new:N  \c_one_hundred_million
+\int_set:Nn \c_one_hundred_million  { 100000000 }
+\int_new:N  \c_one_thousand_million
+\int_set:Nn \c_one_thousand_million { 1000000000 }
+\prg_new_conditional:Npnn \fp_if_infinite:N #1 { p , T , F , TF } {
+  \tex_ifx:D #1 \c_infinity_fp
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifx:D #1 \c_minus_infinity_fp
+      \prg_return_true:
+    \tex_else:D
+      \prg_return_false:
+    \tex_fi:D
+  \tex_fi:D
+}
+\prg_new_conditional:Npnn \fp_if_plus_infinity:N #1 { p , T , F , TF } {
+  \tex_ifx:D #1 \c_infinity_fp
+    \prg_return_true:
+  \tex_else:D
+    \prg_return_false:
+  \tex_fi:D
+}
+\prg_new_conditional:Npnn \fp_if_minus_infinity:N #1 { p , T , F , TF }
+  {
+  \tex_ifx:D #1 \c_minus_infinity_fp
+    \prg_return_true:
+  \tex_else:D
+    \prg_return_false:
+  \tex_fi:D
+}
+\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF } {
+  \tex_ifx:D #1 \c_undefined_fp
+    \prg_return_true:
+  \tex_else:D
+    \prg_return_false:
+  \tex_fi:D
+}
+\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF } {
+  \tex_ifx:D #1 \c_zero_fp
+    \prg_return_true:
+  \tex_else:D
+    \prg_return_false:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_new:N #1 {
+  \tl_new:N #1
+  \tl_gset_eq:NN #1 \c_zero_fp
+}
+\cs_generate_variant:Nn \fp_new:N { c }
+\cs_new_protected_nopar:Npn \fp_zero:N #1 {
+  \tl_set_eq:NN #1 \c_zero_fp
+}
+\cs_new_protected_nopar:Npn \fp_gzero:N #1 {
+  \tl_gset_eq:NN #1 \c_zero_fp
+}
+\cs_generate_variant:Nn \fp_zero:N { c }
+\cs_generate_variant:Nn \fp_gzero:N { c }
+\cs_new_protected_nopar:Npn \fp_set:Nn {
+  \fp_set_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gset:Nn {
+  \fp_set_aux:NNn \tl_gset:Nn
+}
+\cs_new_protected_nopar:Npn \fp_set_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_split:Nn a {#3}
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+          -
+        \tex_else:D
+          +
+        \tex_fi:D
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \exp_after:wN \use_none:n
+          \int_use:N \l_fp_input_a_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_generate_variant:Nn \fp_set:Nn  { c }
+\cs_generate_variant:Nn \fp_gset:Nn { c }
+\cs_new_protected_nopar:Npn \fp_set_from_dim:Nn {
+  \fp_set_from_dim_aux:NNn \tl_set:Nx
+}
+\cs_new_protected_nopar:Npn \fp_gset_from_dim:Nn {
+  \fp_set_from_dim_aux:NNn \tl_gset:Nx
+}
+\cs_new_protected_nopar:Npn \fp_set_from_dim_aux:NNn #1#2#3 {
+  \group_begin:
+    \l_fp_tmp_dim \etex_dimexpr:D #3 \scan_stop:
+    \fp_split:Nn a
+      {
+        \exp_after:wN \fp_set_from_dim_aux:w
+          \dim_use:N \l_fp_tmp_dim
+      }
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+          -
+        \tex_else:D
+          +
+        \tex_fi:D
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \exp_after:wN \use_none:n
+          \int_use:N \l_fp_input_a_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_set_protected_nopar:Npx \fp_set_from_dim_aux:w {
+  \cs_set_nopar:Npn \exp_not:N \fp_set_from_dim_aux:w
+    ##1 \tl_to_str:n { pt } {##1}
+}
+\fp_set_from_dim_aux:w
+\cs_generate_variant:Nn \fp_set_from_dim:Nn  { c }
+\cs_generate_variant:Nn \fp_gset_from_dim:Nn { c }
+\dim_new:N \l_fp_tmp_dim
+\cs_new_eq:NN \fp_set_eq:NN  \tl_set_eq:NN
+\cs_new_eq:NN \fp_set_eq:cN  \tl_set_eq:cN
+\cs_new_eq:NN \fp_set_eq:Nc  \tl_set_eq:Nc
+\cs_new_eq:NN \fp_set_eq:cc  \tl_set_eq:cc
+\cs_new_eq:NN \fp_gset_eq:NN \tl_gset_eq:NN
+\cs_new_eq:NN \fp_gset_eq:cN \tl_gset_eq:cN
+\cs_new_eq:NN \fp_gset_eq:Nc \tl_gset_eq:Nc
+\cs_new_eq:NN \fp_gset_eq:cc \tl_gset_eq:cc
+\cs_new_eq:NN \fp_show:N \tl_show:N
+\cs_new_eq:NN \fp_show:c \tl_show:c
+\cs_new_eq:NN \fp_use:N \tl_use:N
+\cs_new_eq:NN \fp_use:c \tl_use:c
+\cs_new_protected_nopar:Npn \fp_read:N #1 {
+  \exp_after:wN \fp_read_aux:w #1 \q_stop
+}
+\cs_new_protected_nopar:Npn \fp_read_aux:w #1#2 . #3 \q_stop {
+  \tex_if:D #1 -
+    \l_fp_input_a_sign_int \c_minus_one
+  \tex_else:D
+    \l_fp_input_a_sign_int \c_one
+  \tex_fi:D
+  \l_fp_input_a_integer_int #2 \scan_stop:
+  \l_fp_input_a_decimal_int #3 \scan_stop:
+}
+\cs_new_protected_nopar:Npn \fp_split:Nn #1#2 {
+  \tl_set:Nx \l_fp_tmp_tl {#2}
+  \l_fp_split_sign_int \c_one
+  \fp_split_sign:
+  \use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int
+  \tex_afterassignment:D \fp_split_aux_i:w
+  \use:c { l_fp_input_ #1 _integer_int }
+    \etex_numexpr:D 0 \l_fp_tmp_tl . . \q_stop #1
+}
+\cs_new_protected_nopar:Npn \fp_split_sign: {
+  \tex_ifnum:D \pdf_strcmp:D
+    { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_nil } { - }
+      = \c_zero
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \exp_after:wN
+          \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_nil
+      }
+    \l_fp_split_sign_int -\l_fp_split_sign_int
+    \exp_after:wN \fp_split_sign:
+  \tex_else:D
+    \tex_ifnum:D \pdf_strcmp:D
+      { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_nil } { + }
+        = \c_zero
+      \tl_set:Nx \l_fp_tmp_tl
+        {
+          \exp_after:wN
+            \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_nil
+        }
+      \exp_after:wN \exp_after:wN \exp_after:wN
+        \fp_split_sign:
+     \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_split_aux_i:w #1 . #2 . #3 \q_stop {
+  \fp_split_aux_ii:w #2 000000000 \q_stop
+}
+\cs_new_protected_nopar:Npn \fp_split_aux_ii:w #1#2#3#4#5#6#7#8#9 {
+  \fp_split_aux_iii:w {#1#2#3#4#5#6#7#8#9}
+}
+\cs_new_protected_nopar:Npn \fp_split_aux_iii:w #1#2 \q_stop {
+  \l_fp_tmp_int 1 #1 \scan_stop:
+  \exp_after:wN \fp_split_decimal:w
+    \int_use:N \l_fp_tmp_int 000000000 \q_stop
+}
+\cs_new_protected_nopar:Npn \fp_split_decimal:w #1#2#3#4#5#6#7#8#9 {
+  \fp_split_decimal_aux:w {#2#3#4#5#6#7#8#9}
+}
+\cs_new_protected_nopar:Npn \fp_split_decimal_aux:w #1#2#3 \q_stop #4 {
+  \use:c { l_fp_input_ #4 _decimal_int } #1#2 \scan_stop:
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \use:c { l_fp_input_ #4 _integer_int } +
+      \use:c { l_fp_input_ #4 _decimal_int }
+    \scan_stop:
+      = \c_zero
+    \use:c { l_fp_input_ #4 _sign_int } \c_one
+   \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_abs:N {
+  \fp_abs:NN \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gabs:N {
+  \fp_abs:NN \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_abs:N  { c }
+\cs_generate_variant:Nn \fp_gabs:N { c }
+\cs_new_protected_nopar:Npn \fp_abs:NN #1#2 {
+  \group_begin:
+    \fp_read:N #2
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        +
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \exp_after:wN \use_none:n
+          \int_use:N \l_fp_input_a_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_new_protected_nopar:Npn \fp_neg:N {
+  \fp_neg_aux:NN \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gneg:N {
+  \fp_neg_aux:NN \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_neg:N  { c }
+\cs_generate_variant:Nn \fp_gneg:N { c }
+\cs_new_protected_nopar:Npn \fp_neg_aux:NN #1#2 {
+  \group_begin:
+    \fp_read:N #2
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+          +
+        \tex_else:D
+          -
+        \tex_fi:D
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \exp_after:wN \use_none:n
+          \int_use:N \l_fp_input_a_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_new_protected_nopar:Npn \fp_add:Nn {
+  \fp_add_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gadd:Nn {
+  \fp_add_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_add:Nn   { c }
+\cs_generate_variant:Nn \fp_gadd:Nn  { c }
+\cs_new_protected_nopar:Npn \fp_add_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \fp_split:Nn b {#3}
+    \fp_add_core:
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_new_protected_nopar:Npn \fp_add_core: {
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
+    \scan_stop:
+      > \c_zero
+    \exp_after:wN \fp_add_sum:
+  \tex_else:D
+    \exp_after:wN \fp_add_difference:
+  \tex_fi:D
+  \tl_set:Nx \l_fp_tmp_tl
+    {
+      \tex_ifnum:D \l_fp_output_sign_int < \c_zero
+        -
+      \tex_else:D
+        +
+      \tex_fi:D
+      \int_use:N \l_fp_output_integer_int
+      .
+      \exp_after:wN \use_none:n
+        \int_use:N \l_fp_output_decimal_int
+    }
+}
+\cs_new_protected_nopar:Npn \fp_add_sum: {
+  \l_fp_output_sign_int \l_fp_input_a_sign_int
+  \l_fp_output_integer_int
+    \etex_numexpr:D
+      \l_fp_input_a_integer_int + \l_fp_input_b_integer_int
+    \scan_stop:
+  \l_fp_output_decimal_int
+    \etex_numexpr:D
+      \l_fp_input_a_decimal_int + \l_fp_input_b_decimal_int
+    \scan_stop:
+  \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
+    \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+  \tex_else:D
+    \tex_advance:D \l_fp_output_integer_int \c_one
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_add_difference: {
+  \l_fp_output_integer_int
+    \etex_numexpr:D
+      \l_fp_input_a_integer_int - \l_fp_input_b_integer_int
+    \scan_stop:
+  \l_fp_output_decimal_int
+    \etex_numexpr:D
+      \l_fp_input_a_decimal_int - \l_fp_input_b_decimal_int
+    \scan_stop:
+  \tex_ifnum:D \l_fp_output_decimal_int < \c_zero
+    \tex_advance:D \l_fp_output_integer_int \c_minus_one
+    \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+  \tex_fi:D
+  \tex_ifnum:D \l_fp_output_integer_int < \c_zero
+    \l_fp_output_sign_int \l_fp_input_b_sign_int
+    \tex_ifnum:D \l_fp_output_decimal_int = \c_zero
+      \l_fp_output_integer_int -\l_fp_output_integer_int
+    \tex_else:D
+      \l_fp_output_decimal_int
+        \etex_numexpr:D
+          \c_one_thousand_million - \l_fp_output_decimal_int
+        \scan_stop:
+      \l_fp_output_integer_int
+         \etex_numexpr:D
+           - \l_fp_output_integer_int - \c_one
+         \scan_stop:
+    \tex_fi:D
+  \tex_else:D
+    \l_fp_output_sign_int \l_fp_input_a_sign_int
+  \tex_fi:D
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \l_fp_output_integer_int + \l_fp_output_decimal_int
+    \scan_stop:
+      = \c_zero
+    \l_fp_output_sign_int \c_one
+  \tex_fi:D
+  \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+}
+\cs_new_protected_nopar:Npn \fp_sub:Nn {
+  \fp_sub_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gsub:Nn {
+  \fp_sub_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_sub:Nn   { c }
+\cs_generate_variant:Nn \fp_gsub:Nn  { c }
+\cs_new_protected_nopar:Npn \fp_sub_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \fp_split:Nn b {#3}
+    \tex_multiply:D \l_fp_input_b_sign_int \c_minus_one
+    \fp_add_core:
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_new_protected_nopar:Npn \fp_mul:Nn {
+  \fp_mul_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gmul:Nn {
+  \fp_mul_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_mul:Nn  { c }
+\cs_generate_variant:Nn \fp_gmul:Nn { c }
+\cs_new_protected_nopar:Npn \fp_mul_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \fp_split:Nn b {#3}
+    \fp_mul_split:NNNN \l_fp_input_a_integer_int
+      \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
+    \fp_mul_split:NNNN \l_fp_input_a_decimal_int
+      \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
+    \fp_mul_split:NNNN \l_fp_input_b_integer_int
+      \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
+    \fp_mul_split:NNNN \l_fp_input_b_decimal_int
+      \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int
+    \l_fp_mul_output_int \c_zero
+    \tl_clear:N \l_fp_mul_output_tl
+    \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_vi_int
+    \fp_mul_product:NN \l_fp_mul_a_v_int  \l_fp_mul_b_v_int
+    \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_iv_int
+    \tex_divide:D \l_fp_mul_output_int \c_thousand
+    \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_vi_int
+    \fp_mul_product:NN \l_fp_mul_a_iv_int  \l_fp_mul_b_v_int
+    \fp_mul_product:NN \l_fp_mul_a_v_int   \l_fp_mul_b_iv_int
+    \fp_mul_product:NN \l_fp_mul_a_vi_int  \l_fp_mul_b_iii_int
+    \fp_mul_end_level:
+    \fp_mul_product:NN \l_fp_mul_a_ii_int  \l_fp_mul_b_vi_int
+    \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_v_int
+    \fp_mul_product:NN \l_fp_mul_a_iv_int  \l_fp_mul_b_iv_int
+    \fp_mul_product:NN \l_fp_mul_a_v_int   \l_fp_mul_b_iii_int
+    \fp_mul_product:NN \l_fp_mul_a_vi_int  \l_fp_mul_b_ii_int
+    \fp_mul_end_level:
+    \fp_mul_product:NN \l_fp_mul_a_i_int   \l_fp_mul_b_vi_int
+    \fp_mul_product:NN \l_fp_mul_a_ii_int  \l_fp_mul_b_v_int
+    \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iv_int
+    \fp_mul_product:NN \l_fp_mul_a_iv_int  \l_fp_mul_b_iii_int
+    \fp_mul_product:NN \l_fp_mul_a_v_int   \l_fp_mul_b_ii_int
+    \fp_mul_product:NN \l_fp_mul_a_vi_int  \l_fp_mul_b_i_int
+    \fp_mul_end_level:
+    \l_fp_output_decimal_int 0 \l_fp_mul_output_tl \scan_stop:
+    \tl_clear:N \l_fp_mul_output_tl
+    \fp_mul_product:NN \l_fp_mul_a_i_int   \l_fp_mul_b_v_int
+    \fp_mul_product:NN \l_fp_mul_a_ii_int  \l_fp_mul_b_iv_int
+    \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iii_int
+    \fp_mul_product:NN \l_fp_mul_a_iv_int  \l_fp_mul_b_ii_int
+    \fp_mul_product:NN \l_fp_mul_a_v_int   \l_fp_mul_b_i_int
+    \fp_mul_end_level:
+    \fp_mul_product:NN \l_fp_mul_a_i_int   \l_fp_mul_b_iv_int
+    \fp_mul_product:NN \l_fp_mul_a_ii_int  \l_fp_mul_b_iii_int
+    \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_ii_int
+    \fp_mul_product:NN \l_fp_mul_a_iv_int  \l_fp_mul_b_i_int
+    \fp_mul_end_level:
+    \fp_mul_product:NN \l_fp_mul_a_i_int   \l_fp_mul_b_iii_int
+    \fp_mul_product:NN \l_fp_mul_a_ii_int  \l_fp_mul_b_ii_int
+    \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_i_int
+    \fp_mul_end_level:
+    \l_fp_output_integer_int 0 \l_fp_mul_output_tl \scan_stop:
+    \tl_clear:N \l_fp_mul_output_tl
+    \fp_mul_product:NN \l_fp_mul_a_i_int   \l_fp_mul_b_ii_int
+    \fp_mul_product:NN \l_fp_mul_a_ii_int  \l_fp_mul_b_i_int
+    \fp_mul_end_level:
+    \fp_mul_product:NN \l_fp_mul_a_i_int   \l_fp_mul_b_i_int
+    \fp_mul_end_level:
+    \tex_ifnum:D \l_fp_mul_output_tl = \c_zero
+    \tex_else:D
+      \exp_after:wN \fp_msg_overflow:
+    \tex_fi:D
+    \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D
+          \etex_numexpr:D
+            \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
+          \scan_stop:
+            < \c_zero
+          \tex_ifnum:D
+            \etex_numexpr:D
+              \l_fp_output_integer_int + \l_fp_output_decimal_int
+            \scan_stop:
+              = \c_one_thousand_million
+            +
+          \tex_else:D
+            -
+          \tex_fi:D
+        \tex_else:D
+          +
+        \tex_fi:D
+        \int_use:N \l_fp_output_integer_int
+        .
+        \exp_after:wN \use_none:n
+          \int_use:N \l_fp_output_decimal_int
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_new_protected_nopar:Npn \fp_mul_split:NNNN #1#2#3#4 {
+  \tex_advance:D #1 \c_one_thousand_million
+  \cs_set_protected_nopar:Npn \fp_mul_split_aux:w
+    ##1##2##3##4##5##6##7##8##9 \q_stop {
+      #2 ##2##3##4 \scan_stop:
+      #3 ##5##6##7 \scan_stop:
+      #4 ##8##9    \scan_stop:
+    }
+  \exp_after:wN \fp_mul_split_aux:w \int_use:N #1 \q_stop
+}
+\cs_new_protected_nopar:Npn \fp_mul_product:NN #1#2 {
+  \l_fp_mul_output_int
+    \etex_numexpr:D \l_fp_mul_output_int + #1 * #2 \scan_stop:
+}
+\cs_new_protected_nopar:Npn \fp_mul_end_level: {
+  \tex_advance:D \l_fp_mul_output_int \c_one_thousand_million
+  \exp_after:wN \fp_mul_end_level:w
+    \int_use:N \l_fp_mul_output_int \q_stop
+}
+\cs_new_protected_nopar:Npn \fp_mul_end_level:w
+  #1#2#3#4#5#6#7#8#9 \q_stop {
+  \tl_set:Nx \l_fp_mul_output_tl { #8#9 \l_fp_mul_output_tl }
+  \l_fp_mul_output_int #5#6#7 \scan_stop:
+}
+\cs_new_protected_nopar:Npn \fp_div:Nn {
+  \fp_div_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gdiv:Nn {
+  \fp_div_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_div:Nn  { c }
+\cs_generate_variant:Nn \fp_gdiv:Nn { c }
+
+\cs_new_protected_nopar:Npn \fp_div_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \fp_split:Nn b {#3}
+    \tex_ifnum:D
+      \etex_numexpr:D
+        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+      \scan_stop:
+        = \c_zero
+      \tl_set_eq:NN \l_fp_tmp_tl \c_undefined_fp
+    \tex_else:D
+      \tex_ifnum:D
+        \etex_numexpr:D
+          \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+        \scan_stop:
+          = \c_zero
+          \tl_set_eq:NN \l_fp_tmp_tl \c_zero_fp
+      \tex_else:D
+        \exp_after:wN \exp_after:wN \exp_after:wN
+          \fp_div_aux:
+      \tex_fi:D
+    \tex_fi:D
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_new_protected_nopar:Npn \fp_div_aux: {
+  \l_fp_div_offset_int \c_one
+  \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero
+    \exp_after:wN \fp_div_offset_create:
+  \tex_fi:D
+  \l_fp_output_integer_int \c_zero
+  \l_fp_output_decimal_int \c_one_thousand_million
+  \cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
+  \fp_div_loop:
+  \tl_set:Nx \l_fp_tmp_tl
+    {
+      \tex_ifnum:D
+        \etex_numexpr:D
+          \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
+        \scan_stop:
+          < \c_zero
+        \tex_ifnum:D
+          \etex_numexpr:D
+            \l_fp_output_integer_int + \l_fp_output_decimal_int
+          \scan_stop:
+            = \c_one_thousand_million
+          +
+        \tex_else:D
+          -
+        \tex_fi:D
+      \tex_else:D
+        +
+      \tex_fi:D
+      \int_use:N \l_fp_output_integer_int
+      .
+      \exp_after:wN \use_none:n
+        \int_use:N \l_fp_output_decimal_int
+    }
+}
+\cs_new_protected_nopar:Npn \fp_div_offset_create: {
+  \tex_ifnum:D \l_fp_input_b_integer_int = \c_zero
+    \tex_advance:D \l_fp_input_b_decimal_int \c_one_thousand_million
+    \exp_after:wN \fp_div_offset_create_aux:w
+      \int_use:N \l_fp_input_b_decimal_int \q_stop
+    \exp_after:wN \fp_div_offset_create:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_div_offset_create_aux:w
+  #1#2#3#4#5#6#7#8#9 \q_stop {
+  \l_fp_input_b_integer_int #2 \scan_stop:
+  \l_fp_input_b_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
+  \tex_multiply:D \l_fp_div_offset_int \c_ten
+}
+\cs_new_protected_nopar:Npn \fp_div_loop: {
+  \l_fp_div_count_int \c_zero
+  \fp_div_divide:
+  \tex_divide:D \l_fp_input_b_decimal_int \c_ten
+  \tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million
+  \exp_after:wN \fp_div_loop_aux_i:w
+    \int_use:N \l_fp_input_b_integer_int
+  \fp_div_store:
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+      > \c_zero
+    \tex_ifnum:D
+      \etex_numexpr:D
+        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+        > \c_zero
+      \exp_after:wN \exp_after:wN \exp_after:wN
+        \fp_div_loop:
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_div_divide: {
+  \tex_ifnum:D \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
+    \exp_after:wN \fp_div_divide_aux:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
+    \tex_else:D
+      \tex_ifnum:D
+        \l_fp_input_a_decimal_int < \l_fp_input_b_decimal_int
+      \tex_else:D
+        \exp_after:wN \exp_after:wN \exp_after:wN
+          \exp_after:wN \exp_after:wN \exp_after:wN
+          \exp_after:wN \fp_div_divide_aux:
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_div_loop_aux_i:w #1#2#3#4#5#6#7#8#9 {
+  \fp_div_loop_aux_ii:w #2#3#4#5#6#7#8#9
+}
+\cs_new_protected_nopar:Npn \fp_div_loop_aux_ii:w #1#2#3#4#5#6#7#8#9 {
+  \l_fp_input_b_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
+  \l_fp_input_b_decimal_int
+    \etex_numexpr:D
+      \l_fp_input_b_decimal_int + \c_one_hundred_million * #9
+    \scan_stop:
+}
+\cs_new_protected_nopar:Npn \fp_div_divide_aux: {
+  \tex_advance:D \l_fp_div_count_int \c_one
+  \tex_advance:D \l_fp_input_a_integer_int -\l_fp_input_b_integer_int
+  \tex_advance:D \l_fp_input_a_decimal_int -\l_fp_input_b_decimal_int
+  \tex_ifnum:D \l_fp_input_a_decimal_int < \c_zero
+    \tex_advance:D \l_fp_input_a_integer_int \c_minus_one
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+  \tex_fi:D
+  \fp_div_divide:
+}
+\cs_new_protected_nopar:Npn \fp_div_store: { }
+\cs_new_protected_nopar:Npn \fp_div_store_integer: {
+  \l_fp_output_integer_int
+    \etex_numexpr:D
+      \l_fp_output_integer_int +
+      \l_fp_div_count_int * \l_fp_div_offset_int
+    \scan_stop:
+  \tex_ifnum:D \l_fp_div_offset_int > \c_one
+    \tex_divide:D \l_fp_div_offset_int \c_ten
+  \tex_else:D
+    \cs_set_eq:NN \fp_div_store: \fp_div_store_decimal:
+    \l_fp_div_offset_int \c_one_hundred_million
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_div_store_decimal: {
+  \l_fp_output_decimal_int
+    \etex_numexpr:D
+      \l_fp_output_decimal_int +
+      \l_fp_div_count_int * \l_fp_div_offset_int
+    \scan_stop:
+  \tex_divide:D \l_fp_div_offset_int \c_ten
+}
+\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3
+  { T , F , TF } {
+  \group_begin:
+    \fp_split:Nn a {#1}
+    \fp_split:Nn b {#3}
+    \fp_compare_aux:N #2
+}
+\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3
+  { T , F , TF } {
+  \group_begin:
+    \fp_read:N #3
+    \l_fp_input_b_sign_int \l_fp_input_a_sign_int
+    \l_fp_input_b_integer_int \l_fp_input_a_integer_int
+    \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
+    \fp_read:N #1
+    \fp_compare_aux:N #2
+}
+\cs_new_protected_nopar:Npn \fp_compare_aux:N #1 {
+  \cs_if_exist:cTF { fp_compare_#1: }
+    { \use:c { fp_compare_#1: } }
+    {
+      \group_end:
+      \prg_return_false:
+    }
+}
+\cs_new_protected_nopar:cpn { fp_compare_=: } {
+  \tex_ifnum:D \l_fp_input_a_sign_int = \l_fp_input_b_sign_int
+    \tex_ifnum:D \l_fp_input_a_integer_int = \l_fp_input_b_integer_int
+      \tex_ifnum:D \l_fp_input_a_decimal_int = \l_fp_input_b_decimal_int
+        \group_end:
+        \prg_return_true:
+      \tex_else:D
+        \group_end:
+        \prg_return_false:
+      \tex_fi:D
+    \tex_else:D
+      \group_end:
+      \prg_return_false:
+    \tex_fi:D
+  \tex_else:D
+    \group_end:
+    \prg_return_false:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:cpn { fp_compare_>: } {
+  \tex_ifnum:D \l_fp_input_a_sign_int > \l_fp_input_b_sign_int
+    \group_end:
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_a_sign_int < \l_fp_input_b_sign_int
+      \group_end:
+      \prg_return_false:
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+        \use:c { fp_compare_absolute_a > b: }
+      \tex_else:D
+        \use:c { fp_compare_absolute_a < b: }
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:cpn { fp_compare_<: } {
+  \tex_ifnum:D \l_fp_input_b_sign_int > \l_fp_input_a_sign_int
+    \group_end:
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_b_sign_int < \l_fp_input_a_sign_int
+      \group_end:
+      \prg_return_false:
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero
+        \use:c { fp_compare_absolute_a < b: }
+      \tex_else:D
+        \use:c { fp_compare_absolute_a > b: }
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:cpn { fp_compare_absolute_a > b: } {
+  \tex_ifnum:D \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
+    \group_end:
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
+      \group_end:
+      \prg_return_false:
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_a_decimal_int > \l_fp_input_b_decimal_int
+        \group_end:
+        \prg_return_true:
+      \tex_else:D
+        \group_end:
+        \prg_return_false:
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:cpn { fp_compare_absolute_a < b: } {
+  \tex_ifnum:D \l_fp_input_b_integer_int > \l_fp_input_a_integer_int
+    \group_end:
+    \prg_return_true:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_b_integer_int < \l_fp_input_a_integer_int
+      \group_end:
+      \prg_return_false:
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_b_decimal_int > \l_fp_input_a_decimal_int
+        \group_end:
+        \prg_return_true:
+      \tex_else:D
+        \group_end:
+        \prg_return_false:
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+}
+\keys_define:nn { fp } {
+  precision             .int_set:N  = \l_fp_round_precision_int ,
+  remove-trailing-zeros .bool_set:N = \l_fp_remove_zeros_bool   ,
+  round-mode            .choice:                                ,
+  round-mode
+    / half-even         .tl_set:N   = \l_fp_round_mode_tl       ,
+  round-mode
+    / half-from-zero    .tl_set:N   = \l_fp_round_mode_tl       ,
+  round-mode
+    / none              .tl_set:N   = \l_fp_round_mode_tl       ,
+  round-mode
+    / truncate          .tl_set:N   = \l_fp_round_mode_tl       ,
+}
+\keys_set:nn { fp } {
+  precision             = 9    ,
+  remove-trailing-zeros = true ,
+  round-mode            = none ,
+}
+\cs_new_protected_nopar:Npn \fp_to_tl:NN {
+  \fp_to_tl_aux:NNN \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gto_tl:NN {
+  \fp_to_tl_aux:NNN \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_to_tl:NN  { Nc }
+\cs_generate_variant:Nn \fp_to_tl:NN  { c }
+\cs_generate_variant:Nn \fp_to_tl:NN  { cc }
+\cs_generate_variant:Nn \fp_gto_tl:NN { Nc }
+\cs_generate_variant:Nn \fp_gto_tl:NN { c }
+\cs_generate_variant:Nn \fp_gto_tl:NN { cc }
+\cs_new_protected_nopar:Npn \fp_to_tl_aux:NNN #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \use:c { fp_round_ \l_fp_round_mode_tl :}
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_ifnum:D  \l_fp_input_a_sign_int < \c_zero
+          -
+        \tex_fi:D
+        \int_use:N \l_fp_input_a_integer_int
+        \intexpr_compare:nNnT { \l_fp_round_precision_int } > { \c_zero }
+          {
+            .
+            \bool_if:NTF \l_fp_remove_zeros_bool
+              {
+                \exp_after:wN \use_i:nn
+                  \exp_after:wN \fp_remove_zeros:NNNNNNNNN
+              }
+              { \exp_after:wN \use_none:n }
+            \int_use:N \l_fp_input_a_decimal_int
+          }
+      }
+  \exp_after:wN \group_end: \exp_after:wN
+  #1 \exp_after:wN #3 \exp_after:wN { \l_fp_tmp_tl }
+}
+\cs_new_nopar:Npn \fp_remove_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+  \fp_remove_zeros_aux:w #1#2#3#4#5#6#7#8#9 \q_stop 1
+}
+\cs_new_nopar:Npn \fp_remove_zeros_aux:w #1#2 \q_stop #3 {
+  #1
+  \intexpr_compare:nNnTF { 0 #2 } = { \c_zero }
+    {
+      \intexpr_compare:nNnF { \l_fp_round_precision_int } < { #3 + 1 }
+        {
+          \intexpr_compare:nNnT {#3} < { 9 }
+            { \fp_remove_zeros_aux:w #2 \q_stop { #3 + 1 } }
+        }
+    }
+    {
+      \intexpr_compare:nNnT {#3} < { 9 }
+        { \fp_remove_zeros_aux:w #2 \q_stop { #3 + 1 } }
+    }
+}
+\cs_new_protected_nopar:cpn { fp_round_half-from-zero: } {
+  \tex_ifnum:D \l_fp_round_precision_int < \c_nine
+    \exp_after:wN \fp_round_from_zero:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_round_from_zero: {
+  \bool_set_false:N \l_fp_round_carry_bool
+  \l_fp_round_position_int \c_eight
+  \tl_clear:N \l_fp_round_decimal_tl
+  \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+  \exp_after:wN \use_i:nn \exp_after:wN
+    \fp_round_from_zero_aux:NNNNNNNNN
+    \int_use:N \l_fp_input_a_decimal_int
+}
+\cs_new_protected_nopar:Npn \fp_round_from_zero_aux:NNNNNNNNN
+  #1#2#3#4#5#6#7#8#9 {
+  \fp_round_from_zero_decimal:N #9#8#7#6#5#4#3#2#1
+  \fp_round_from_zero_integer:
+}
+\cs_new_protected_nopar:Npn \fp_round_from_zero_decimal:N #1 {
+  \tex_ifnum:D \l_fp_round_position_int < \l_fp_round_precision_int
+    \bool_if:NTF \l_fp_round_carry_bool
+      { \l_fp_tmp_int \etex_numexpr:D #1 + \c_one \scan_stop: }
+      { \l_fp_tmp_int \etex_numexpr:D #1 \scan_stop: }
+    \tex_ifnum:D \l_fp_tmp_int = \c_ten
+      \l_fp_tmp_int \c_zero
+    \tex_else:D
+      \bool_set_false:N \l_fp_round_carry_bool
+    \tex_fi:D
+    \tl_set:Nx \l_fp_round_decimal_tl
+      { \int_use:N \l_fp_tmp_int \l_fp_round_decimal_tl }
+  \tex_else:D
+    \tl_set:Nx \l_fp_round_decimal_tl { 0 \l_fp_round_decimal_tl }
+    \tex_ifnum:D \l_fp_round_position_int = \l_fp_round_precision_int
+      \tex_ifnum:D #1 > \c_four
+        \bool_set_true:N \l_fp_round_carry_bool
+      \tex_fi:D
+    \tex_fi:D
+  \tex_fi:D
+  \tex_advance:D \l_fp_round_position_int \c_minus_one
+  \tex_ifnum:D \l_fp_round_position_int > \c_minus_one
+    \exp_after:wN \fp_round_from_zero_decimal:N
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_round_from_zero_integer: {
+  \bool_if:NT \l_fp_round_carry_bool
+    { \tex_advance:D \l_fp_input_a_integer_int \c_one }
+  \l_fp_input_a_decimal_int \l_fp_round_decimal_tl \scan_stop:
+}
+\cs_new_protected_nopar:cpn { fp_round_half-even: } {
+  \tex_ifnum:D \l_fp_round_precision_int < \c_nine
+    \exp_after:wN \fp_round_even:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_round_even: {
+  \bool_set_false:N \l_fp_round_carry_bool
+  \l_fp_round_position_int \c_eight
+  \tl_clear:N \l_fp_round_decimal_tl
+  \int_zero:N \l_fp_round_discard_int
+  \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+  \exp_after:wN \use_i:nn \exp_after:wN
+    \fp_round_even_aux:NNNNNNNNN
+    \int_use:N \l_fp_input_a_decimal_int
+}
+\cs_new_protected_nopar:Npn \fp_round_even_aux:NNNNNNNNN
+  #1#2#3#4#5#6#7#8#9 {
+  \fp_round_even_decimal:N #9#8#7#6#5#4#3#2#1
+  \fp_round_even_integer:
+}
+\cs_new_protected_nopar:Npn \fp_round_even_decimal:N #1 {
+  \tex_ifnum:D \l_fp_round_position_int < \l_fp_round_precision_int
+    \bool_if:NTF \l_fp_round_carry_bool
+      {
+        \tex_ifnum:D \l_fp_round_discard_int = \c_zero
+          \l_fp_round_discard_int \c_one
+          \tex_ifodd:D #1 \scan_stop:
+            \l_fp_tmp_int \etex_numexpr:D #1 + \c_one \scan_stop:
+          \tex_else:D
+            \l_fp_tmp_int \etex_numexpr:D #1 \scan_stop:
+          \tex_fi:D
+        \tex_else:D
+          \l_fp_tmp_int \etex_numexpr:D #1 + \c_one \scan_stop:
+        \tex_fi:D
+      }
+      { \l_fp_tmp_int \etex_numexpr:D #1 \scan_stop: }
+    \tex_ifnum:D \l_fp_tmp_int = \c_ten
+      \l_fp_tmp_int \c_zero
+    \tex_else:D
+      \bool_set_false:N \l_fp_round_carry_bool
+    \tex_fi:D
+    \tl_set:Nx \l_fp_round_decimal_tl
+      { \int_use:N \l_fp_tmp_int \l_fp_round_decimal_tl }
+  \tex_else:D
+    \tl_set:Nx \l_fp_round_decimal_tl { 0 \l_fp_round_decimal_tl }
+    \tex_ifnum:D \l_fp_round_position_int = \l_fp_round_precision_int
+      \tex_ifnum:D #1 > \c_four
+        \bool_set_true:N \l_fp_round_carry_bool
+        \tex_ifnum:D #1 = \c_five
+        \tex_else:D
+          \l_fp_round_discard_int \c_one
+        \tex_fi:D
+      \tex_fi:D
+    \tex_else:D
+      \tex_advance:D \l_fp_round_discard_int #1 \scan_stop:
+    \tex_fi:D
+  \tex_fi:D
+  \tex_advance:D \l_fp_round_position_int \c_minus_one
+  \tex_ifnum:D \l_fp_round_position_int > \c_minus_one
+    \exp_after:wN \fp_round_even_decimal:N
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_round_even_integer: {
+  \bool_if:NT \l_fp_round_carry_bool
+    {
+      \tex_ifnum:D \l_fp_round_discard_int = \c_zero
+        \tex_ifodd:D \l_fp_input_a_integer_int
+          \tex_advance:D \l_fp_input_a_integer_int \c_one
+        \tex_fi:D
+      \tex_else:D
+        \tex_advance:D \l_fp_input_a_integer_int \c_one
+      \tex_fi:D
+    }
+  \l_fp_input_a_decimal_int \l_fp_round_decimal_tl \scan_stop:
+}
+\cs_new_protected_nopar:Npn \fp_round_none: {
+  \l_fp_round_precision_int \c_one
+}
+\cs_new_protected_nopar:Npn \fp_round_truncate: {
+  \intexpr_compare:nNnF { \l_fp_round_precision_int } > { 8 }
+    {
+      \intexpr_compare:nNnTF { \l_fp_round_precision_int } < { 1 }
+        { \l_fp_input_a_decimal_int \c_zero \scan_stop: }
+        {
+          \int_set:Nn \l_fp_tmp_int
+            {
+              \prg_replicate:nn { 9 - \l_fp_round_precision_int }
+                { 10 * }
+              1
+            }
+          \tex_divide:D \l_fp_input_a_decimal_int \l_fp_tmp_int
+          \tex_multiply:D \l_fp_input_a_decimal_int \l_fp_tmp_int
+        }
+    }
+}
+\cs_new_protected_nopar:Npn \fp_msg_overflow: {
+  \msg_kernel_error:nn { fpu } { overflow }
+}
+\msg_kernel_new:nnnn { fpu } { overflow }
+  { Arithmetic~overflow. }
+  {
+    The~calculation~requested~exceeds~the~capacity \\
+    of~the~fixed-point~unit.
+  }
+%% 
+%%
+%% End of file `l3fp.sty'.
diff --git a/Master/texmf-dist/tex/latex/expl3/l3intexpr.sty b/Master/texmf-dist/tex/latex/expl3/l3intexpr.sty
index ab4271cc46e..268881a29df 100644
--- a/Master/texmf-dist/tex/latex/expl3/l3intexpr.sty
+++ b/Master/texmf-dist/tex/latex/expl3/l3intexpr.sty
@@ -48,7 +48,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3intexpr.dtx 1086 2009-03-20 19:29:35Z morten $
+\GetIdInfo$Id: l3intexpr.dtx 1957 2010-06-15 06:33:43Z mittelba $
        {L3 Integer Expressions}
 \ProvidesExplPackage
   {\filename}{\filedate}{\fileversion}{\filedescription}
@@ -106,11 +106,32 @@
   \if_intexpr_compare:w #1<\intexpr_eval:w #2 \intexpr_eval_end:
   \prg_return_false: \else: \prg_return_true: \fi:
 }
-\prg_set_conditional:Npnn \intexpr_compare:nNn #1#2#3{p,TF,T,F}{
+\prg_set_conditional:Npnn \intexpr_compare:nNn #1#2#3{p}{
   \if_intexpr_compare:w \intexpr_eval:w #1 #2 \intexpr_eval:w #3
   \intexpr_eval_end:
   \prg_return_true: \else: \prg_return_false: \fi:
 }
+\cs_set_nopar:Npn \intexpr_compare:nNnT #1#2#3 {
+  \tex_ifnum:D \etex_numexpr:D #1 #2 \etex_numexpr:D #3 \scan_stop:
+    \tex_expandafter:D \use:n
+  \tex_else:D
+    \tex_expandafter:D \use_none:n
+  \tex_fi:D
+}
+\cs_set_nopar:Npn \intexpr_compare:nNnF #1#2#3 {
+  \tex_ifnum:D \etex_numexpr:D #1 #2 \etex_numexpr:D #3 \scan_stop:
+    \tex_expandafter:D \use_none:n
+  \tex_else:D
+    \tex_expandafter:D \use:n
+  \tex_fi:D
+}
+\cs_set_nopar:Npn \intexpr_compare:nNnTF #1#2#3 {
+  \tex_ifnum:D \etex_numexpr:D #1 #2 \etex_numexpr:D #3 \scan_stop:
+    \tex_expandafter:D \use_i:nn
+  \tex_else:D
+    \tex_expandafter:D \use_ii:nn
+  \tex_fi:D
+}
 \cs_set:Npn \intexpr_abs:n #1{
   \intexpr_value:w
   \if_intexpr_compare:w \intexpr_eval:w #1<\c_zero
diff --git a/Master/texmf-dist/tex/latex/expl3/l3names.sty b/Master/texmf-dist/tex/latex/expl3/l3names.sty
index 0c475563656..da660a756e5 100644
--- a/Master/texmf-dist/tex/latex/expl3/l3names.sty
+++ b/Master/texmf-dist/tex/latex/expl3/l3names.sty
@@ -87,7 +87,7 @@
   \gdef\filedescription{#1}%
   \ProvidesPackage{[unknown package]}[0000/00/00 v0.0 #1]
 }
-\GetIdInfo$Id: l3names.dtx 1853 2010-03-21 09:11:08Z joseph $
+\GetIdInfo$Id: l3names.dtx 1981 2010-07-11 07:28:30Z will $
      {L3 Experimental Naming Scheme for TeX Primitives}
 \endgroup
 \begingroup
@@ -116,6 +116,10 @@
   \endlinechar  =\the \endlinechar \relax
   \catcode  95=\the \catcode 95 \relax
   \catcode  58=\the \catcode 58 \relax
+  \catcode 124=\the \catcode 124 \relax
+  \catcode  38=\the \catcode 38 \relax
+  \catcode  94=\the \catcode 94 \relax
+  \catcode  34=\the \catcode 34 \relax
   \noexpand\fi
 }
 \catcode126=10\relax  % tilde is a space char.
@@ -124,6 +128,10 @@
 \endlinechar=32\relax % endline is space
 \catcode95=11\relax   % underscore letter
 \catcode58=11\relax   % colon letter
+\catcode124=12\relax  % vert bar, other
+\catcode38=4\relax    % ampersand, alignment token
+\catcode34=12\relax   % doublequote, other
+\catcode94=7\relax    % caret, math superscript
 \let \tex_let:D \let
 \DeclareOption{removeoldnames}{
   \long\def\name_undefine:N#1{
@@ -649,6 +657,10 @@
       \tex_endlinechar:D  =\tex_the:D \tex_endlinechar:D \tex_relax:D
       \tex_catcode:D  95=\tex_the:D \tex_catcode:D 95 \tex_relax:D
       \tex_catcode:D  58=\tex_the:D \tex_catcode:D 58 \tex_relax:D
+      \tex_catcode:D 124=\tex_the:D \tex_catcode:D 124 \tex_relax:D
+      \tex_catcode:D  38=\tex_the:D \tex_catcode:D 38 \tex_relax:D
+      \tex_catcode:D  94=\tex_the:D \tex_catcode:D 94 \tex_relax:D
+      \tex_catcode:D  34=\tex_the:D \tex_catcode:D 34 \tex_relax:D
       \tex_noexpand:D \tex_fi:D
     }
     \tex_def:D \ExplSyntaxStatus { 1 }
@@ -658,6 +670,10 @@
     \tex_endlinechar:D =32 \tex_relax:D % endline is space
     \tex_catcode:D   95=11 \tex_relax:D % underscore letter
     \tex_catcode:D   58=11 \tex_relax:D % colon letter
+    \tex_catcode:D  124=11 \tex_relax:D % vertical bar, other
+    \tex_catcode:D   38=4  \tex_relax:D % ampersand, alignment token
+    \tex_catcode:D   94=7  \tex_relax:D % caret, math superscript
+    \tex_catcode:D   34=12 \tex_relax:D % doublequote, other
   \tex_fi:D
 }
 \tex_def:D \ExplSyntaxStatus { 1 }