rm expl3, now l3kernel

git-svn-id: svn://tug.org/texlive/trunk@23285 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 0 insertions, 3434 deletions

diff --git a/Master/texmf-dist/tex/latex/expl3/l3fp.sty b/Master/texmf-dist/tex/latex/expl3/l3fp.sty
deleted file mode 100644
index 9c042acad1b..00000000000
--- a/Master/texmf-dist/tex/latex/expl3/l3fp.sty
+++ /dev/null
@@ -1,3434 +0,0 @@
-%%
-%% 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) 2010-2011 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 2201 2011-03-19 17:16:13Z joseph $
-  {L3 Experimental floating-point operations}
-\ProvidesExplPackage
-  {\filename}{\filedate}{\fileversion}{\filedescription}
-\package_check_loaded_expl:
-\int_const:Nn \c_forty_four { 44 }
-\int_const:Nn \c_one_hundred { 100 }
-\int_const:Nn \c_one_thousand { 1000 }
-\int_const:Nn \c_one_million { 1 000 000 }
-\int_const:Nn \c_one_hundred_million { 100 000 000 }
-\int_const:Nn \c_five_hundred_million { 500 000 000 }
-\int_const:Nn \c_one_thousand_million { 1 000 000 000 }
-\int_new:N  \c_fp_pi_by_four_decimal_int
-\int_set:Nn \c_fp_pi_by_four_decimal_int { 785 398 158 }
-\int_new:N  \c_fp_pi_by_four_extended_int
-\int_set:Nn \c_fp_pi_by_four_extended_int { 897 448 310 }
-\int_new:N  \c_fp_pi_decimal_int
-\int_set:Nn \c_fp_pi_decimal_int { 141 592 653 }
-\int_new:N  \c_fp_pi_extended_int
-\int_set:Nn \c_fp_pi_extended_int { 589 793 238 }
-\int_new:N  \c_fp_two_pi_decimal_int
-\int_set:Nn \c_fp_two_pi_decimal_int { 283 185 307 }
-\int_new:N  \c_fp_two_pi_extended_int
-\int_set:Nn \c_fp_two_pi_extended_int { 179 586 477 }
-\tl_new:N \c_e_fp
-\tl_set:Nn \c_e_fp { + 2.718281828 e 0 }
-\tl_new:N \c_one_fp
-\tl_set:Nn \c_one_fp { + 1.000000000 e 0 }
-\tl_new:N \c_pi_fp
-\tl_set:Nn \c_pi_fp { + 3.141592654 e 0 }
-\tl_new:N \c_undefined_fp
-\tl_set:Nn \c_undefined_fp { X 0.000000000 e 0 }
-\tl_new:N \c_zero_fp
-\tl_set:Nn \c_zero_fp { + 0.000000000 e 0 }
-\tl_new:N \l_fp_arg_tl
-\int_new:N \l_fp_count_int
-\int_new:N \l_fp_div_offset_int
-\int_new:N \l_fp_exp_integer_int
-\int_new:N \l_fp_exp_decimal_int
-\int_new:N \l_fp_exp_extended_int
-\int_new:N \l_fp_exp_exponent_int
-\int_new:N \l_fp_input_a_sign_int
-\int_new:N \l_fp_input_a_integer_int
-\int_new:N \l_fp_input_a_decimal_int
-\int_new:N \l_fp_input_a_exponent_int
-\int_new:N \l_fp_input_b_sign_int
-\int_new:N \l_fp_input_b_integer_int
-\int_new:N \l_fp_input_b_decimal_int
-\int_new:N \l_fp_input_b_exponent_int
-\int_new:N \l_fp_input_a_extended_int
-\int_new:N \l_fp_input_b_extended_int
-\int_new:N \l_fp_mul_a_i_int
-\int_new:N \l_fp_mul_a_ii_int
-\int_new:N \l_fp_mul_a_iii_int
-\int_new:N \l_fp_mul_a_iv_int
-\int_new:N \l_fp_mul_a_v_int
-\int_new:N \l_fp_mul_a_vi_int
-\int_new:N \l_fp_mul_b_i_int
-\int_new:N \l_fp_mul_b_ii_int
-\int_new:N \l_fp_mul_b_iii_int
-\int_new:N \l_fp_mul_b_iv_int
-\int_new:N \l_fp_mul_b_v_int
-\int_new:N \l_fp_mul_b_vi_int
-\int_new:N \l_fp_mul_output_int
-\tl_new:N  \l_fp_mul_output_tl
-\int_new:N \l_fp_output_sign_int
-\int_new:N \l_fp_output_integer_int
-\int_new:N \l_fp_output_decimal_int
-\int_new:N \l_fp_output_exponent_int
-\int_new:N \l_fp_output_extended_int
-\bool_new:N \l_fp_round_carry_bool
-\tl_new:N \l_fp_round_decimal_tl
-\int_new:N \l_fp_round_position_int
-\int_new:N \l_fp_round_target_int
-\tl_new:N \l_fp_sign_tl
-\int_new:N \l_fp_split_sign_int
-\int_new:N \l_fp_tmp_int
-\tl_new:N \l_fp_tmp_tl
-\int_new:N \l_fp_trig_octant_int
-\int_new:N \l_fp_trig_sign_int
-\int_new:N \l_fp_trig_decimal_int
-\int_new:N \l_fp_trig_extended_int
-\cs_new_protected_nopar:Npn \fp_read:N #1 {
-  \tex_expandafter:D \fp_read_aux:w #1 \q_stop
-}
-\cs_new_protected_nopar:Npn \fp_read_aux:w #1#2 . #3 e #4 \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:
-  \l_fp_input_a_exponent_int #4 \scan_stop:
-}
-\cs_new_protected_nopar:Npn \fp_split:Nn #1#2 {
-  \tl_set:Nx \l_fp_tmp_tl {#2}
-  \tl_set_rescan:Nno \l_fp_tmp_tl { \char_make_ignore:n { 32 } }
-    { \l_fp_tmp_tl }
-  \l_fp_split_sign_int \c_one
-  \fp_split_sign:
-  \use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int
-  \tex_expandafter:D \fp_split_exponent:w \l_fp_tmp_tl e e \q_stop #1
-}
-\cs_new_protected_nopar:Npn \fp_split_sign: {
-  \tex_ifnum:D \pdf_strcmp:D
-    { \tex_expandafter:D \tl_head:w \l_fp_tmp_tl ? \q_stop } { - }
-      = \c_zero
-    \tl_set:Nx \l_fp_tmp_tl
-      {
-        \tex_expandafter:D
-          \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop
-      }
-    \l_fp_split_sign_int -\l_fp_split_sign_int
-    \tex_expandafter:D \fp_split_sign:
-  \tex_else:D
-    \tex_ifnum:D \pdf_strcmp:D
-      { \tex_expandafter:D \tl_head:w \l_fp_tmp_tl ? \q_stop } { + }
-        = \c_zero
-      \tl_set:Nx \l_fp_tmp_tl
-        {
-          \tex_expandafter:D
-            \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop
-        }
-      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \fp_split_sign:
-     \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn
-  \fp_split_exponent:w #1 e #2 e #3 \q_stop #4 {
-  \use:c { l_fp_input_ #4 _exponent_int }
-    \etex_numexpr:D 0 #2 \scan_stop:
-  \tex_afterassignment:D \fp_split_aux_i:w
-  \use:c { l_fp_input_ #4 _integer_int }
-    \etex_numexpr:D 0 #1 . . \q_stop #4
-}
-\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:
-  \tex_expandafter:D \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
-  \tex_ifnum:D
-    \use:c { l_fp_input_ #4 _integer_int } < \c_one_thousand_million
-  \tex_else:D
-    \tex_expandafter:D \fp_overflow_msg:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_standardise:NNNN #1#2#3#4 {
-  \tex_ifnum:D
-    \etex_numexpr:D #2 + #3 = \c_zero
-    #1 \c_one
-    #4 \c_zero
-    \tex_expandafter:D \use_none:nnnn
-  \tex_else:D
-    \tex_expandafter:D \fp_standardise_aux:NNNN
-  \tex_fi:D
-  #1#2#3#4
-}
-\cs_new_protected_nopar:Npn \fp_standardise_aux:NNNN #1#2#3#4 {
-  \cs_set_protected_nopar:Npn \fp_standardise_aux:
-    {
-      \tex_ifnum:D #2 = \c_zero
-        \tex_advance:D #3 \c_one_thousand_million
-        \tex_expandafter:D \fp_standardise_aux:w
-          \int_use:N #3 \q_stop
-         \tex_expandafter:D \fp_standardise_aux:
-       \tex_fi:D
-    }
-  \cs_set_protected_nopar:Npn
-    \fp_standardise_aux:w ##1##2##3##4##5##6##7##8##9 \q_stop
-    {
-      #2 ##2 \scan_stop:
-      #3 ##3##4##5##6##7##8##9 0 \scan_stop:
-      \tex_advance:D #4 \c_minus_one
-    }
-  \fp_standardise_aux:
-  \cs_set_protected_nopar:Npn \fp_standardise_aux:
-    {
-      \tex_ifnum:D #2 > \c_nine
-        \tex_advance:D #2 \c_one_thousand_million
-        \tex_expandafter:D \use_i:nn \tex_expandafter:D
-          \fp_standardise_aux:w \int_use:N #2
-         \tex_expandafter:D \fp_standardise_aux:
-       \tex_fi:D
-    }
-  \cs_set_protected_nopar:Npn
-    \fp_standardise_aux:w ##1##2##3##4##5##6##7##8##9
-    {
-      #2 ##1##2##3##4##5##6##7##8 \scan_stop:
-      \tex_advance:D #3 \c_one_thousand_million
-      \tex_divide:D #3 \c_ten
-      \tl_set:Nx \l_fp_tmp_tl
-        {
-          ##9
-          \tex_expandafter:D \use_none:n \int_use:N #3
-        }
-      #3 \l_fp_tmp_tl \scan_stop:
-      \tex_advance:D #4 \c_one
-    }
-  \fp_standardise_aux:
-  \tex_ifnum:D #4 < \c_one_hundred
-    \tex_ifnum:D #4 > -\c_one_hundred
-    \tex_else:D
-      #1 \c_one
-      #2 \c_zero
-      #3 \c_zero
-      #4 \c_zero
-    \tex_fi:D
-  \tex_else:D
-    \tex_expandafter:D \fp_overflow_msg:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_standardise_aux: { }
-\cs_new_protected_nopar:Npn \fp_standardise_aux:w { }
-\cs_new_protected_nopar:Npn \fp_level_input_exponents: {
-  \tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
-    \tex_expandafter:D \fp_level_input_exponents_a:
-  \tex_else:D
-    \tex_expandafter:D \fp_level_input_exponents_b:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_level_input_exponents_a: {
-  \tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
-    \tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million
-    \tex_expandafter:D \use_i:nn \tex_expandafter:D
-      \fp_level_input_exponents_a:NNNNNNNNN
-        \int_use:N \l_fp_input_b_integer_int
-    \tex_expandafter:D \fp_level_input_exponents_a:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn
-  \fp_level_input_exponents_a:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  \l_fp_input_b_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
-  \tex_advance:D \l_fp_input_b_decimal_int \c_one_thousand_million
-  \tex_divide:D \l_fp_input_b_decimal_int \c_ten
-  \tl_set:Nx \l_fp_tmp_tl
-    {
-      #9
-      \tex_expandafter:D \use_none:n
-        \int_use:N \l_fp_input_b_decimal_int
-    }
-  \l_fp_input_b_decimal_int \l_fp_tmp_tl \scan_stop:
-  \tex_advance:D \l_fp_input_b_exponent_int \c_one
-}
-\cs_new_protected_nopar:Npn \fp_level_input_exponents_b: {
-  \tex_ifnum:D \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int
-    \tex_advance:D \l_fp_input_a_integer_int \c_one_thousand_million
-    \tex_expandafter:D \use_i:nn \tex_expandafter:D
-      \fp_level_input_exponents_b:NNNNNNNNN
-        \int_use:N \l_fp_input_a_integer_int
-    \tex_expandafter:D \fp_level_input_exponents_b:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn
-  \fp_level_input_exponents_b:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  \l_fp_input_a_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
-  \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-  \tex_divide:D \l_fp_input_a_decimal_int \c_ten
-  \tl_set:Nx \l_fp_tmp_tl
-    {
-      #9
-      \tex_expandafter:D \use_none:n
-        \int_use:N \l_fp_input_a_decimal_int
-    }
-  \l_fp_input_a_decimal_int \l_fp_tmp_tl \scan_stop:
-  \tex_advance:D \l_fp_input_a_exponent_int \c_one
-}
-\cs_new_protected_nopar:Npn \fp_tmp:w #1#2 { }
-\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_const:Nn #1#2 {
-  \cs_if_free:NTF #1
-    {
-      \fp_new:N #1
-      \fp_gset:Nn #1 {#2}
-    }
-    {
-      \msg_kernel_error:nx { variable-already-defined }
-        { \token_to_str:N #1 }
-    }
-}
-\cs_generate_variant:Nn \fp_const:Nn { 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}
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int
-      \l_fp_input_a_decimal_int
-      \l_fp_input_a_exponent_int
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \cs_set_protected_nopar:Npx \fp_tmp:w
-      {
-        \group_end:
-        #1 \exp_not:N #2
-          {
-            \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
-            .
-            \tex_expandafter:D \use_none:n
-              \int_use:N \l_fp_input_a_decimal_int
-            e
-            \int_use:N \l_fp_input_a_exponent_int
-          }
-      }
-  \fp_tmp:w
-}
-\cs_generate_variant:Nn \fp_set:Nn  { c }
-\cs_generate_variant:Nn \fp_gset:Nn { c }
-\cs_new_protected_nopar:Npn \fp_set_from_dim:Nn {
-  \fp_set_from_dim_aux:NNn \tl_set:Nx
-}
-\cs_new_protected_nopar:Npn \fp_gset_from_dim:Nn {
-  \fp_set_from_dim_aux:NNn \tl_gset:Nx
-}
-\cs_new_protected_nopar:Npn \fp_set_from_dim_aux:NNn #1#2#3 {
-  \group_begin:
-    \l_fp_tmp_skip \etex_glueexpr:D #3 \scan_stop:
-    \l_fp_tmp_dim \l_fp_tmp_skip
-    \fp_split:Nn a
-      {
-        \tex_expandafter:D \fp_set_from_dim_aux:w
-          \dim_use:N \l_fp_tmp_dim
-      }
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int
-      \l_fp_input_a_decimal_int
-      \l_fp_input_a_exponent_int
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \cs_set_protected_nopar:Npx \fp_tmp:w
-      {
-        \group_end:
-        #1 \exp_not:N #2
-          {
-            \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
-            .
-            \tex_expandafter:D \use_none:n
-              \int_use:N \l_fp_input_a_decimal_int
-            e
-            \int_use:N \l_fp_input_a_exponent_int
-          }
-      }
-  \fp_tmp:w
-}
-\cs_set_protected_nopar:Npx \fp_set_from_dim_aux:w {
-  \cs_set_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
-\skip_new:N \l_fp_tmp_skip
-\cs_new_eq:NN \fp_set_eq:NN  \tl_set_eq:NN
-\cs_new_eq:NN \fp_set_eq:cN  \tl_set_eq:cN
-\cs_new_eq:NN \fp_set_eq:Nc  \tl_set_eq:Nc
-\cs_new_eq:NN \fp_set_eq:cc  \tl_set_eq:cc
-\cs_new_eq:NN \fp_gset_eq:NN \tl_gset_eq:NN
-\cs_new_eq:NN \fp_gset_eq:cN \tl_gset_eq:cN
-\cs_new_eq:NN \fp_gset_eq:Nc \tl_gset_eq:Nc
-\cs_new_eq:NN \fp_gset_eq:cc \tl_gset_eq:cc
-\cs_new_eq:NN \fp_show:N \tl_show:N
-\cs_new_eq:NN \fp_show:c \tl_show:c
-\cs_new_nopar:Npn \fp_use:N #1 {
-  \tex_expandafter:D \fp_use_aux:w #1 \q_stop
-}
-\cs_generate_variant:Nn \fp_use:N { c }
-\cs_new_nopar:Npn \fp_use_aux:w #1#2 e #3 \q_stop {
-  \tex_if:D #1 -
-    -
-  \tex_fi:D
-  \tex_ifnum:D #3 > \c_zero
-    \tex_expandafter:D \fp_use_large:w
-  \tex_else:D
-    \tex_ifnum:D #3 < \c_zero
-      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \fp_use_small:w
-    \tex_else:D
-      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \fp_use_none:w
-    \tex_fi:D
-  \tex_fi:D
-  #2 e #3 \q_stop
-}
-\cs_new_nopar:Npn \fp_use_none:w #1 e #2 \q_stop {#1}
-\cs_new_nopar:Npn \fp_use_small:w #1 . #2 e #3 \q_stop {
-  0 .
-  \prg_replicate:nn { -#3 - 1 } { 0 }
-  #1#2
-}
-\cs_new_nopar:Npn \fp_use_large:w #1 . #2 e #3 \q_stop {
-  \tex_ifnum:D #3 < \c_ten
-    \tex_expandafter:D \fp_use_large_aux_i:w
-  \tex_else:D
-    \tex_expandafter:D \fp_use_large_aux_ii:w
-  \tex_fi:D
-  #1#2 e #3 \q_stop
-}
-\cs_new_nopar:Npn \fp_use_large_aux_i:w #1#2 e #3 \q_stop {
-  #1
-  \use:c { fp_use_large_aux_ #3 :w } #2 \q_stop
-}
-\cs_new_nopar:cpn { fp_use_large_aux_1:w } #1#2 \q_stop { #1 . #2 }
-\cs_new_nopar:cpn { fp_use_large_aux_2:w } #1#2#3 \q_stop {
-  #1#2 . #3
-}
-\cs_new_nopar:cpn { fp_use_large_aux_3:w } #1#2#3#4 \q_stop {
-  #1#2#3 . #4
-}
-\cs_new_nopar:cpn { fp_use_large_aux_4:w } #1#2#3#4#5 \q_stop {
-  #1#2#3#4 . #5
-}
-\cs_new_nopar:cpn { fp_use_large_aux_5:w } #1#2#3#4#5#6 \q_stop {
-  #1#2#3#4#5 . #6
-}
-\cs_new_nopar:cpn { fp_use_large_aux_6:w } #1#2#3#4#5#6#7 \q_stop {
-  #1#2#3#4#5#6 . #7
-}
-\cs_new_nopar:cpn { fp_use_large_aux_7:w } #1#2#3#4#5#6#7#8 \q_stop {
-  #1#2#3#4#6#7 . #8
-}
-\cs_new_nopar:cpn { fp_use_large_aux_8:w } #1#2#3#4#5#6#7#8#9 \q_stop {
-  #1#2#3#4#5#6#7#8 . #9
-}
-\cs_new_nopar:cpn { fp_use_large_aux_9:w } #1 \q_stop { #1 . }
-\cs_new_nopar:Npn \fp_use_large_aux_ii:w #1 e #2 \q_stop {
-  #1
-  \prg_replicate:nn { #2 - 9 } { 0 }
-  .
-}
-\cs_new_nopar:Npn \fp_to_dim:N #1 { \fp_use:N #1 pt }
-\cs_generate_variant:Nn \fp_to_dim:N { c }
-\cs_new_nopar:Npn \fp_to_int:N #1 {
-  \tex_expandafter:D \fp_to_int_aux:w #1 \q_stop
-}
-\cs_generate_variant:Nn \fp_to_int:N { c }
-\cs_new_nopar:Npn \fp_to_int_aux:w #1#2 e #3 \q_stop {
-  \tex_if:D #1 -
-    -
-  \tex_fi:D
-  \tex_ifnum:D #3 < \c_zero
-    \tex_expandafter:D \fp_to_int_small:w
-  \tex_else:D
-    \tex_expandafter:D \fp_to_int_large:w
-  \tex_fi:D
-  #2 e #3 \q_stop
-}
-\cs_new_nopar:Npn \fp_to_int_small:w #1 . #2 e #3 \q_stop {
-  \tex_ifnum:D #3 > \c_one
-  \tex_else:D
-    \tex_ifnum:D #1 < \c_five
-      0
-    \tex_else:D
-      1
-    \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_nopar:Npn \fp_to_int_large:w #1 . #2 e #3 \q_stop {
-  \tex_ifnum:D #3 < \c_ten
-    \tex_expandafter:D \fp_to_int_large_aux_i:w
-  \tex_else:D
-    \tex_expandafter:D \fp_to_int_large_aux_ii:w
-  \tex_fi:D
-  #1#2 e #3 \q_stop
-}
-\cs_new_nopar:Npn \fp_to_int_large_aux_i:w #1#2 e #3 \q_stop {
-  \use:c { fp_to_int_large_aux_ #3 :w } #2 \q_stop {#1}
-}
-\cs_new_nopar:cpn { fp_to_int_large_aux_1:w } #1#2 \q_stop {
-  \fp_to_int_large_aux:nnn { #2 0 } {#1}
-}
-\cs_new_nopar:cpn { fp_to_int_large_aux_2:w } #1#2#3 \q_stop {
-  \fp_to_int_large_aux:nnn { #3 00 } {#1#2}
-}
-\cs_new_nopar:cpn { fp_to_int_large_aux_3:w } #1#2#3#4 \q_stop {
-  \fp_to_int_large_aux:nnn { #4 000 } {#1#2#3}
-}
-\cs_new_nopar:cpn { fp_to_int_large_aux_4:w } #1#2#3#4#5 \q_stop {
-  \fp_to_int_large_aux:nnn { #5 0000 } {#1#2#3#4}
-}
-\cs_new_nopar:cpn { fp_to_int_large_aux_5:w } #1#2#3#4#5#6 \q_stop {
-  \fp_to_int_large_aux:nnn { #6 00000 } {#1#2#3#4#5}
-}
-\cs_new_nopar:cpn { fp_to_int_large_aux_6:w } #1#2#3#4#5#6#7 \q_stop {
-  \fp_to_int_large_aux:nnn { #7 000000 } {#1#2#3#4#5#6}
-}
-\cs_new_nopar:cpn
-  { fp_to_int_large_aux_7:w } #1#2#3#4#5#6#7#8 \q_stop {
-  \fp_to_int_large_aux:nnn { #8 0000000 } {#1#2#3#4#5#6#7}
-}
-\cs_new_nopar:cpn
-  { fp_to_int_large_aux_8:w } #1#2#3#4#5#6#7#8#9 \q_stop {
-  \fp_to_int_large_aux:nnn { #9 00000000 } {#1#2#3#4#5#6#7#8}
-}
-\cs_new_nopar:cpn { fp_to_int_large_aux_9:w } #1 \q_stop {#1}
-\cs_new_nopar:Npn \fp_to_int_large_aux:nnn #1#2#3 {
-  \tex_ifnum:D #1 < \c_five_hundred_million
-    #3#2
-  \tex_else:D
-    \tex_number:D \etex_numexpr:D #3#2 + 1 \scan_stop:
-  \tex_fi:D
-}
-\cs_new_nopar:Npn \fp_to_int_large_aux_ii:w #1 e #2 \q_stop {
-  #1
-  \prg_replicate:nn { #2 - 9 } { 0 }
-}
-\cs_new_nopar:Npn \fp_to_tl:N #1 {
-  \tex_expandafter:D \fp_to_tl_aux:w #1 \q_stop
-}
-\cs_generate_variant:Nn \fp_to_tl:N { c }
-\cs_new_nopar:Npn \fp_to_tl_aux:w #1#2 e #3 \q_stop {
-  \tex_if:D #1 -
-    -
-  \tex_fi:D
-  \tex_ifnum:D #3 < \c_zero
-    \tex_expandafter:D \fp_to_tl_small:w
-  \tex_else:D
-    \tex_expandafter:D \fp_to_tl_large:w
-  \tex_fi:D
-  #2 e #3 \q_stop
-}
-\cs_new_nopar:Npn \fp_to_tl_large:w #1 e #2 \q_stop {
-  \tex_ifnum:D #2 < \c_ten
-    \tex_expandafter:D \fp_to_tl_large_aux_i:w
-  \tex_else:D
-    \tex_expandafter:D \fp_to_tl_large_aux_ii:w
-  \tex_fi:D
-  #1 e #2 \q_stop
-}
-\cs_new_nopar:Npn \fp_to_tl_large_aux_i:w #1 e #2 \q_stop {
-  \use:c { fp_to_tl_large_ #2 :w } #1 \q_stop
-}
-\cs_new_nopar:Npn \fp_to_tl_large_aux_ii:w #1 . #2 e #3 \q_stop {
-  #1
-  \fp_to_tl_large_zeros:NNNNNNNNN #2
-  e #3
-}
-\cs_new_nopar:cpn { fp_to_tl_large_0:w } #1 . #2 \q_stop {
-  #1
-  \fp_to_tl_large_zeros:NNNNNNNNN #2
-}
-\cs_new_nopar:cpn { fp_to_tl_large_1:w } #1 . #2#3 \q_stop {
-  #1#2
-  \fp_to_tl_large_zeros:NNNNNNNNN #3 0
-}
-\cs_new_nopar:cpn { fp_to_tl_large_2:w } #1 . #2#3#4 \q_stop {
-  #1#2#3
-  \fp_to_tl_large_zeros:NNNNNNNNN #4 00
-}
-\cs_new_nopar:cpn { fp_to_tl_large_3:w } #1 . #2#3#4#5 \q_stop {
-  #1#2#3#4
-  \fp_to_tl_large_zeros:NNNNNNNNN #5 000
-}
-\cs_new_nopar:cpn { fp_to_tl_large_4:w } #1 . #2#3#4#5#6 \q_stop {
-  #1#2#3#4#5
-  \fp_to_tl_large_zeros:NNNNNNNNN #6 0000
-}
-\cs_new_nopar:cpn { fp_to_tl_large_5:w } #1 . #2#3#4#5#6#7 \q_stop {
-  #1#2#3#4#5#6
-  \fp_to_tl_large_zeros:NNNNNNNNN #7 00000
-}
-\cs_new_nopar:cpn { fp_to_tl_large_6:w } #1 . #2#3#4#5#6#7#8 \q_stop {
-  #1#2#3#4#5#6#7
-  \fp_to_tl_large_zeros:NNNNNNNNN #8 000000
-}
-\cs_new_nopar:cpn { fp_to_tl_large_7:w } #1 . #2#3#4#5#6#7#8#9 \q_stop {
-  #1#2#3#4#5#6#7#8
-  \fp_to_tl_large_zeros:NNNNNNNNN #9 0000000
-}
-\cs_new_nopar:cpn { fp_to_tl_large_8:w } #1 . {
-  #1
-  \use:c { fp_to_tl_large_8_aux:w }
-}
-\cs_new_nopar:cpn
-  { fp_to_tl_large_8_aux:w } #1#2#3#4#5#6#7#8#9 \q_stop {
-  #1#2#3#4#5#6#7#8
-  \fp_to_tl_large_zeros:NNNNNNNNN #9 00000000
-}
-\cs_new_nopar:cpn { fp_to_tl_large_9:w } #1 . #2 \q_stop {#1#2}
-\cs_new_nopar:Npn \fp_to_tl_small:w #1 e #2 \q_stop {
-  \tex_ifnum:D #2 = \c_minus_one
-    \tex_expandafter:D \fp_to_tl_small_one:w
-  \tex_else:D
-    \tex_ifnum:D #2 = -\c_two
-      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \fp_to_tl_small_two:w
-    \tex_else:D
-      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \fp_to_tl_small_aux:w
-    \tex_fi:D
-  \tex_fi:D
-  #1 e #2 \q_stop
-}
-\cs_new_nopar:Npn \fp_to_tl_small_one:w #1 . #2 e #3 \q_stop {
-  \tex_ifnum:D \fp_use_ix:NNNNNNNNN #2 > \c_four
-    \tex_ifnum:D
-      \etex_numexpr:D #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
-        < \c_one_thousand_million
-      0.
-      \tex_expandafter:D \fp_to_tl_small_zeros:NNNNNNNNN
-        \tex_number:D
-          \etex_numexpr:D
-            #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
-          \scan_stop:
-    \tex_else:D
-      1
-    \tex_fi:D
-  \tex_else:D
-    0. #1
-    \fp_to_tl_small_zeros:NNNNNNNNN #2
-  \tex_fi:D
-}
-\cs_new_nopar:Npn \fp_to_tl_small_two:w #1 . #2 e #3 \q_stop {
-  \tex_ifnum:D \fp_use_iix_ix:NNNNNNNNN #2 > \c_forty_four
-    \tex_ifnum:D
-      \etex_numexpr:D #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
-        < \c_one_thousand_million
-      0.0
-      \tex_expandafter:D \fp_to_tl_small_zeros:NNNNNNNNN
-        \tex_number:D
-          \etex_numexpr:D
-            #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
-          \scan_stop:
-    \tex_else:D
-      0.1
-    \tex_fi:D
-  \tex_else:D
-    0.0
-    #1
-    \fp_to_tl_small_zeros:NNNNNNNNN #2
-  \tex_fi:D
-}
-\cs_new_nopar:Npn \fp_to_tl_small_aux:w #1 . #2 e #3 \q_stop {
-  #1
-  \fp_to_tl_large_zeros:NNNNNNNNN #2
-  e #3
-}
-\cs_new_nopar:Npn \fp_to_tl_large_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  \tex_ifnum:D #9 = \c_zero
-    \tex_ifnum:D #8 = \c_zero
-      \tex_ifnum:D #7 = \c_zero
-        \tex_ifnum:D #6 = \c_zero
-          \tex_ifnum:D #5 = \c_zero
-            \tex_ifnum:D #4 = \c_zero
-              \tex_ifnum:D #3 = \c_zero
-                \tex_ifnum:D #2 = \c_zero
-                  \tex_ifnum:D #1 = \c_zero
-                  \tex_else:D
-                    . #1
-                  \tex_fi:D
-                \tex_else:D
-                  . #1#2
-                \tex_fi:D
-              \tex_else:D
-                . #1#2#3
-              \tex_fi:D
-            \tex_else:D
-              . #1#2#3#4
-            \tex_fi:D
-          \tex_else:D
-            . #1#2#3#4#5
-          \tex_fi:D
-        \tex_else:D
-          . #1#2#3#4#5#6
-        \tex_fi:D
-      \tex_else:D
-        . #1#2#3#4#5#6#7
-      \tex_fi:D
-    \tex_else:D
-       . #1#2#3#4#5#6#7#8
-    \tex_fi:D
-  \tex_else:D
-    . #1#2#3#4#5#6#7#8#9
-  \tex_fi:D
-}
-\cs_new_nopar:Npn \fp_to_tl_small_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  \tex_ifnum:D #9 = \c_zero
-    \tex_ifnum:D #8 = \c_zero
-      \tex_ifnum:D #7 = \c_zero
-        \tex_ifnum:D #6 = \c_zero
-          \tex_ifnum:D #5 = \c_zero
-            \tex_ifnum:D #4 = \c_zero
-              \tex_ifnum:D #3 = \c_zero
-                \tex_ifnum:D #2 = \c_zero
-                  \tex_ifnum:D #1 = \c_zero
-                  \tex_else:D
-                    #1
-                  \tex_fi:D
-                \tex_else:D
-                  #1#2
-                \tex_fi:D
-              \tex_else:D
-                #1#2#3
-              \tex_fi:D
-            \tex_else:D
-              #1#2#3#4
-            \tex_fi:D
-          \tex_else:D
-            #1#2#3#4#5
-          \tex_fi:D
-        \tex_else:D
-          #1#2#3#4#5#6
-        \tex_fi:D
-      \tex_else:D
-        #1#2#3#4#5#6#7
-      \tex_fi:D
-    \tex_else:D
-       #1#2#3#4#5#6#7#8
-    \tex_fi:D
-  \tex_else:D
-    #1#2#3#4#5#6#7#8#9
-  \tex_fi:D
-}
-\cs_new_nopar:Npn \fp_use_iix_ix:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {#8#9}
-\cs_new_nopar:Npn \fp_use_ix:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {#9}
-\cs_new_nopar:Npn \fp_use_i_to_vii:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  #1#2#3#4#5#6#7
-}
-\cs_new_nopar:Npn \fp_use_i_to_iix:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  #1#2#3#4#5#6#7#8
-}
-\cs_new_protected_nopar:Npn \fp_round_figures:Nn {
-  \fp_round_figures_aux:NNn \tl_set:Nn
-}
-\cs_generate_variant:Nn \fp_round_figures:Nn { c }
-\cs_new_protected_nopar:Npn \fp_ground_figures:Nn {
-  \fp_round_figures_aux:NNn \tl_gset:Nn
-}
-\cs_generate_variant:Nn \fp_ground_figures:Nn { c }
-\cs_new_protected_nopar:Npn \fp_round_figures_aux:NNn #1#2#3 {
-  \group_begin:
-    \fp_read:N #2
-    \int_set:Nn \l_fp_round_target_int { #3 - 1 }
-    \tex_ifnum:D \l_fp_round_target_int < \c_ten
-      \tex_expandafter:D \fp_round:
-    \tex_fi:D
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \cs_set_protected_nopar:Npx \fp_tmp:w
-      {
-        \group_end:
-        #1 \exp_not:N #2
-          {
-            \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
-            .
-            \tex_expandafter:D \use_none:n
-              \int_use:N \l_fp_input_a_decimal_int
-            e
-            \int_use:N \l_fp_input_a_exponent_int
-          }
-      }
-  \fp_tmp:w
-}
-\cs_new_protected_nopar:Npn \fp_round_places:Nn {
-  \fp_round_places_aux:NNn \tl_set:Nn
-}
-\cs_generate_variant:Nn \fp_round_places:Nn { c }
-\cs_new_protected_nopar:Npn \fp_ground_places:Nn {
-  \fp_round_places_aux:NNn \tl_gset:Nn
-}
-\cs_generate_variant:Nn \fp_ground_places:Nn { c }
-\cs_new_protected_nopar:Npn \fp_round_places_aux:NNn #1#2#3 {
-  \group_begin:
-    \fp_read:N #2
-    \int_set:Nn \l_fp_round_target_int
-      { #3 + \l_fp_input_a_exponent_int }
-    \tex_ifnum:D \l_fp_round_target_int < \c_ten
-      \tex_expandafter:D \fp_round:
-    \tex_fi:D
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \cs_set_protected_nopar:Npx \fp_tmp:w
-      {
-        \group_end:
-        #1 \exp_not:N #2
-          {
-            \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
-            .
-            \tex_expandafter:D \use_none:n
-              \int_use:N \l_fp_input_a_decimal_int
-            e
-            \int_use:N \l_fp_input_a_exponent_int
-          }
-      }
-  \fp_tmp:w
-}
-\cs_new_protected_nopar:Npn \fp_round: {
-  \bool_set_false:N \l_fp_round_carry_bool
-  \l_fp_round_position_int \c_eight
-  \tl_clear:N \l_fp_round_decimal_tl
-  \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-  \tex_expandafter:D \use_i:nn \tex_expandafter:D
-    \fp_round_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int
-}
-\cs_new_protected_nopar:Npn \fp_round_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  \fp_round_loop:N #9#8#7#6#5#4#3#2#1
-  \bool_if:NT \l_fp_round_carry_bool
-    { \tex_advance:D \l_fp_input_a_integer_int \c_one }
-  \l_fp_input_a_decimal_int \l_fp_round_decimal_tl \scan_stop:
-  \tex_ifnum:D \l_fp_input_a_integer_int < \c_ten
-  \tex_else:D
-    \l_fp_input_a_integer_int \c_one
-    \tex_divide:D \l_fp_input_a_decimal_int \c_ten
-    \tex_advance:D \l_fp_input_a_exponent_int \c_one
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_round_loop:N #1 {
-  \tex_ifnum:D \l_fp_round_position_int < \l_fp_round_target_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_target_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
-    \tex_expandafter:D \fp_round_loop:N
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_abs:N {
-  \fp_abs_aux:NN \tl_set:Nn
-}
-\cs_new_protected_nopar:Npn \fp_gabs:N {
-  \fp_abs_aux:NN \tl_gset:Nn
-}
-\cs_generate_variant:Nn \fp_abs:N  { c }
-\cs_generate_variant:Nn \fp_gabs:N { c }
-\cs_new_protected_nopar:Npn \fp_abs_aux:NN #1#2 {
-  \group_begin:
-    \fp_read:N #2
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \cs_set_protected_nopar:Npx \fp_tmp:w
-      {
-        \group_end:
-        #1 \exp_not:N #2
-          {
-            +
-            \int_use:N \l_fp_input_a_integer_int
-            .
-            \tex_expandafter:D \use_none:n
-              \int_use:N \l_fp_input_a_decimal_int
-            e
-            \int_use:N \l_fp_input_a_exponent_int
-          }
-      }
-  \fp_tmp:w
-}
-\cs_new_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
-        .
-        \tex_expandafter:D \use_none:n
-          \int_use:N \l_fp_input_a_decimal_int
-        e
-        \int_use:N \l_fp_input_a_exponent_int
-      }
-  \tex_expandafter:D \group_end: \tex_expandafter:D
-  #1 \tex_expandafter:D #2 \tex_expandafter:D { \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_standardise:NNNN
-      \l_fp_input_b_sign_int
-      \l_fp_input_b_integer_int
-      \l_fp_input_b_decimal_int
-      \l_fp_input_b_exponent_int
-    \fp_add_core:
-  \fp_tmp:w #1#2
-}
-\cs_new_protected_nopar:Npn \fp_add_core: {
-  \fp_level_input_exponents:
-  \tex_ifnum:D
-    \etex_numexpr:D
-      \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
-    \scan_stop:
-      > \c_zero
-    \tex_expandafter:D \fp_add_sum:
-  \tex_else:D
-    \tex_expandafter:D \fp_add_difference:
-  \tex_fi:D
-  \l_fp_output_exponent_int \l_fp_input_a_exponent_int
-  \fp_standardise:NNNN
-    \l_fp_output_sign_int
-    \l_fp_output_integer_int
-    \l_fp_output_decimal_int
-    \l_fp_output_exponent_int
-  \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-    {
-      \group_end:
-      ##1 ##2
-        {
-          \tex_ifnum:D \l_fp_output_sign_int < \c_zero
-            -
-          \tex_else:D
-            +
-          \tex_fi:D
-          \int_use:N \l_fp_output_integer_int
-          .
-          \tex_expandafter:D \use_none:n
-            \tex_number:D \etex_numexpr:D
-               \l_fp_output_decimal_int + \c_one_thousand_million
-          e
-          \int_use:N \l_fp_output_exponent_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_else:D
-    \tex_advance:D \l_fp_output_integer_int \c_one
-    \tex_advance:D \l_fp_output_decimal_int -\c_one_thousand_million
-  \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
-}
-\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}
-    \fp_standardise:NNNN
-      \l_fp_input_b_sign_int
-      \l_fp_input_b_integer_int
-      \l_fp_input_b_decimal_int
-      \l_fp_input_b_exponent_int
-    \tex_multiply:D \l_fp_input_b_sign_int \c_minus_one
-    \fp_add_core:
-  \fp_tmp:w #1#2
-}
-\cs_new_protected_nopar:Npn \fp_mul:Nn {
-  \fp_mul_aux:NNn \tl_set:Nn
-}
-\cs_new_protected_nopar:Npn \fp_gmul:Nn {
-  \fp_mul_aux:NNn \tl_gset:Nn
-}
-\cs_generate_variant:Nn \fp_mul:Nn  { c }
-\cs_generate_variant:Nn \fp_gmul:Nn { c }
-\cs_new_protected_nopar:Npn \fp_mul_aux:NNn #1#2#3 {
-  \group_begin:
-    \fp_read:N #2
-    \fp_split:Nn b {#3}
-    \fp_standardise:NNNN
-      \l_fp_input_b_sign_int
-      \l_fp_input_b_integer_int
-      \l_fp_input_b_decimal_int
-      \l_fp_input_b_exponent_int
-    \fp_mul_internal:
-    \l_fp_output_exponent_int
-      \etex_numexpr:D
-        \l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int
-      \scan_stop:
-    \fp_standardise:NNNN
-      \l_fp_output_sign_int
-      \l_fp_output_integer_int
-      \l_fp_output_decimal_int
-      \l_fp_output_exponent_int
-    \cs_set_protected_nopar:Npx \fp_tmp:w
-      {
-        \group_end:
-        #1 \exp_not:N #2
-          {
-            \tex_ifnum:D
-              \etex_numexpr:D
-                \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
-                < \c_zero
-              \tex_ifnum:D
-                \etex_numexpr:D
-                  \l_fp_output_integer_int + \l_fp_output_decimal_int
-                  = \c_zero
-                +
-              \tex_else:D
-                -
-              \tex_fi:D
-            \tex_else:D
-              +
-           \tex_fi:D
-            \int_use:N \l_fp_output_integer_int
-            .
-            \tex_expandafter:D \use_none:n
-              \tex_number:D \etex_numexpr:D
-                 \l_fp_output_decimal_int + \c_one_thousand_million
-            e
-            \int_use:N \l_fp_output_exponent_int
-          }
-      }
-  \fp_tmp:w
-}
-\cs_new_protected_nopar:Npn \fp_mul_internal: {
-  \fp_mul_split:NNNN \l_fp_input_a_decimal_int
-    \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
-  \fp_mul_split:NNNN \l_fp_input_b_decimal_int
-    \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
-  \l_fp_mul_output_int \c_zero
-  \tl_clear:N \l_fp_mul_output_tl
-  \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_iii_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_mul_b_i_int
-  \tex_divide:D \l_fp_mul_output_int \c_one_thousand
-  \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_iii_int
-  \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_i_int
-  \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_input_b_integer_int
-  \fp_mul_end_level:
-  \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_i_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_input_b_integer_int
-  \fp_mul_end_level:
-  \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_i_int
-  \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_input_b_integer_int
-  \fp_mul_end_level:
-  \l_fp_output_decimal_int 0 \l_fp_mul_output_tl \scan_stop:
-  \tl_clear:N \l_fp_mul_output_tl
-  \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_input_b_integer_int
-  \fp_mul_end_level:
-  \l_fp_output_integer_int 0 \l_fp_mul_output_tl \scan_stop:
-}
-\cs_new_protected_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:
-    }
-  \tex_expandafter:D \fp_mul_split_aux:w \int_use:N #1 \q_stop
-  \tex_advance:D #1 -\c_one_thousand_million
-}
-\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
-  \tex_expandafter:D \use_i:nn \tex_expandafter:D
-    \fp_mul_end_level:NNNNNNNNN \int_use:N \l_fp_mul_output_int
-}
-\cs_new_protected_nopar:Npn \fp_mul_end_level:NNNNNNNNN
-  #1#2#3#4#5#6#7#8#9 {
-  \tl_set:Nx \l_fp_mul_output_tl { #7#8#9 \l_fp_mul_output_tl }
-  \l_fp_mul_output_int #1#2#3#4#5#6 \scan_stop:
-}
-\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}
-    \fp_standardise:NNNN
-      \l_fp_input_b_sign_int
-      \l_fp_input_b_integer_int
-      \l_fp_input_b_decimal_int
-      \l_fp_input_b_exponent_int
-    \tex_ifnum:D
-      \etex_numexpr:D
-        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
-        = \c_zero
-      \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-        {
-          \group_end:
-          #1 \exp_not:N #2 { \c_undefined_fp }
-        }
-    \tex_else:D
-      \tex_ifnum:D
-        \etex_numexpr:D
-          \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-          = \c_zero
-        \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-          {
-            \group_end:
-            #1 \exp_not:N #2 { \c_zero_fp }
-          }
-      \tex_else:D
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \fp_div_internal:
-      \tex_fi:D
-    \tex_fi:D
-  \fp_tmp:w #1#2
-}
-\cs_new_protected_nopar:Npn \fp_div_internal: {
-  \l_fp_output_integer_int \c_zero
-  \l_fp_output_decimal_int \c_zero
-  \cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
-  \l_fp_div_offset_int \c_one_hundred_million
-  \fp_div_loop:
-  \l_fp_output_exponent_int
-    \etex_numexpr:D
-      \l_fp_input_a_exponent_int - \l_fp_input_b_exponent_int
-    \scan_stop:
-  \fp_standardise:NNNN
-    \l_fp_output_sign_int
-    \l_fp_output_integer_int
-    \l_fp_output_decimal_int
-    \l_fp_output_exponent_int
-  \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-    {
-      \group_end:
-      ##1 ##2
-        {
-          \tex_ifnum:D
-            \etex_numexpr:D
-              \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
-              < \c_zero
-            \tex_ifnum:D
-              \etex_numexpr:D
-                \l_fp_output_integer_int + \l_fp_output_decimal_int
-                = \c_zero
-              +
-            \tex_else:D
-              -
-            \tex_fi:D
-          \tex_else:D
-            +
-          \tex_fi:D
-          \int_use:N \l_fp_output_integer_int
-          .
-          \tex_expandafter:D \use_none:n
-            \tex_number:D \etex_numexpr:D
-               \l_fp_output_decimal_int + \c_one_thousand_million
-             \scan_stop:
-          e
-          \int_use:N \l_fp_output_exponent_int
-        }
-    }
-}
-\cs_new_protected_nopar:Npn \fp_div_loop: {
-  \l_fp_count_int \c_zero
-  \fp_div_divide:
-  \fp_div_store:
-  \tex_multiply:D \l_fp_input_a_integer_int \c_ten
-  \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-  \tex_expandafter:D \fp_div_loop_step:w
-    \int_use:N \l_fp_input_a_decimal_int \q_stop
-  \tex_ifnum:D
-    \etex_numexpr:D
-      \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-      > \c_zero
-      \tex_ifnum:D \l_fp_div_offset_int > \c_zero
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \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
-    \tex_expandafter:D \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
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \fp_div_divide_aux:
-      \tex_fi:D
-    \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_div_divide_aux: {
-  \tex_advance:D \l_fp_count_int \c_one
-  \tex_advance:D \l_fp_input_a_integer_int -\l_fp_input_b_integer_int
-  \tex_advance:D \l_fp_input_a_decimal_int -\l_fp_input_b_decimal_int
-  \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 \l_fp_count_int
-  \cs_set_eq:NN \fp_div_store: \fp_div_store_decimal:
-}
-\cs_new_protected_nopar:Npn \fp_div_store_decimal: {
-  \l_fp_output_decimal_int
-    \etex_numexpr:D
-      \l_fp_output_decimal_int +
-      \l_fp_count_int * \l_fp_div_offset_int
-    \scan_stop:
-  \tex_divide:D \l_fp_div_offset_int \c_ten
-}
-\cs_new_protected_nopar:Npn
-  \fp_div_loop_step:w #1#2#3#4#5#6#7#8#9 \q_stop {
-  \l_fp_input_a_integer_int
-    \etex_numexpr:D
-      #2 + \l_fp_input_a_integer_int
-    \scan_stop:
-  \l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
-}
-\cs_new_protected_nopar:Npn \fp_add:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  #7 \etex_numexpr:D #1 + #4 \scan_stop:
-  #8 \etex_numexpr:D #2 + #5 \scan_stop:
-  #9 \etex_numexpr:D #3 + #6 \scan_stop:
-  \tex_ifnum:D #9 < \c_one_thousand_million
-  \tex_else:D
-    \tex_advance:D #8 \c_one
-    \tex_advance:D #9 -\c_one_thousand_million
-  \tex_fi:D
-  \tex_ifnum:D #8 < \c_one_thousand_million
-  \tex_else:D
-    \tex_advance:D #7 \c_one
-    \tex_advance:D #8 -\c_one_thousand_million
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_sub:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  #7 \etex_numexpr:D #1 - #4 \scan_stop:
-  #8 \etex_numexpr:D #2 - #5 \scan_stop:
-  #9 \etex_numexpr:D #3 - #6 \scan_stop:
-  \tex_ifnum:D #9 < \c_zero
-    \tex_advance:D #8 \c_minus_one
-    \tex_advance:D #9 \c_one_thousand_million
-  \tex_fi:D
-  \tex_ifnum:D #8 < \c_zero
-    \tex_advance:D #7 \c_minus_one
-    \tex_advance:D #8 \c_one_thousand_million
-  \tex_fi:D
-  \tex_ifnum:D #7 < \c_zero
-    \tex_ifnum:D \etex_numexpr:D #8 + #9 = \c_zero
-      #7 -#7
-    \tex_else:D
-      \tex_advance:D #7 \c_one
-      #8 \etex_numexpr:D \c_one_thousand_million - #8 \scan_stop:
-      #9 \etex_numexpr:D \c_one_thousand_million - #9 \scan_stop:
-    \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_mul:NNNNNN #1#2#3#4#5#6 {
-  \fp_mul_split:NNNN #1
-    \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
-  \fp_mul_split:NNNN #2
-    \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
-  \fp_mul_split:NNNN #3
-    \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
-  \fp_mul_split:NNNN #4
-    \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int
-  \l_fp_mul_output_int \c_zero
-  \tl_clear:N \l_fp_mul_output_tl
-  \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_vi_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_v_int
-  \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_mul_b_iv_int
-  \fp_mul_product:NN \l_fp_mul_a_iv_int        \l_fp_mul_b_iii_int
-  \fp_mul_product:NN \l_fp_mul_a_v_int         \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_vi_int        \l_fp_mul_b_i_int
-  \tex_divide:D \l_fp_mul_output_int \c_one_thousand
-  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_v_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iv_int
-  \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_iii_int
-  \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_v_int        \l_fp_mul_b_i_int
-  \fp_mul_end_level:
-  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iv_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iii_int
-  \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_i_int
-  \fp_mul_end_level:
-  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iii_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_i_int
-  \fp_mul_end_level:
-  #6 0 \l_fp_mul_output_tl \scan_stop:
-  \tl_clear:N \l_fp_mul_output_tl
-  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_i_int
-  \fp_mul_end_level:
-  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_i_int
-  \fp_mul_end_level:
-  \fp_mul_end_level:
-  #5 0 \l_fp_mul_output_tl \scan_stop:
-}
-\cs_new_protected_nopar:Npn \fp_mul:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  \fp_mul_split:NNNN #2
-    \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
-  \fp_mul_split:NNNN #3
-    \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
-  \fp_mul_split:NNNN #5
-    \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
-  \fp_mul_split:NNNN #6
-    \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int
-  \l_fp_mul_output_int \c_zero
-  \tl_clear:N \l_fp_mul_output_tl
-  \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_vi_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_v_int
-  \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_mul_b_iv_int
-  \fp_mul_product:NN \l_fp_mul_a_iv_int        \l_fp_mul_b_iii_int
-  \fp_mul_product:NN \l_fp_mul_a_v_int         \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_vi_int        \l_fp_mul_b_i_int
-  \tex_divide:D \l_fp_mul_output_int \c_one_thousand
-  \fp_mul_product:NN #1                       \l_fp_mul_b_vi_int
-  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_v_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iv_int
-  \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_iii_int
-  \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_v_int        \l_fp_mul_b_i_int
-  \fp_mul_product:NN \l_fp_mul_a_vi_int       #4
-  \fp_mul_end_level:
-  \fp_mul_product:NN #1                       \l_fp_mul_b_v_int
-  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iv_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iii_int
-  \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_i_int
-  \fp_mul_product:NN \l_fp_mul_a_v_int        #4
-  \fp_mul_end_level:
-  \fp_mul_product:NN #1                       \l_fp_mul_b_iv_int
-  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iii_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_i_int
-  \fp_mul_product:NN \l_fp_mul_a_iv_int       #4
-  \fp_mul_end_level:
-  #9 0 \l_fp_mul_output_tl \scan_stop:
-  \tl_clear:N \l_fp_mul_output_tl
-  \fp_mul_product:NN #1                       \l_fp_mul_b_iii_int
-  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_i_int
-  \fp_mul_product:NN \l_fp_mul_a_iii_int      #4
-  \fp_mul_end_level:
-  \fp_mul_product:NN #1                       \l_fp_mul_b_ii_int
-  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_i_int
-  \fp_mul_product:NN \l_fp_mul_a_ii_int       #4
-  \fp_mul_end_level:
-  \fp_mul_product:NN #1                       \l_fp_mul_b_i_int
-  \fp_mul_product:NN \l_fp_mul_a_i_int        #4
-  \fp_mul_end_level:
-  #8 0 \l_fp_mul_output_tl \scan_stop:
-  \tl_clear:N \l_fp_mul_output_tl
-  \fp_mul_product:NN #1 #4
-  \fp_mul_end_level:
-  #7 0 \l_fp_mul_output_tl \scan_stop:
-}
-\cs_new_protected_nopar:Npn \fp_div_integer:NNNNN #1#2#3#4#5 {
-  \l_fp_tmp_int #1
-  \tex_divide:D \l_fp_tmp_int #3
-  \l_fp_tmp_int \etex_numexpr:D #1 - \l_fp_tmp_int * #3 \scan_stop:
-  #4 #1
-  \tex_divide:D #4 #3
-  #5 #2
-  \tex_divide:D #5 #3
-  \tex_multiply:D \l_fp_tmp_int \c_one_thousand
-  \tex_divide:D \l_fp_tmp_int #3
-  #5 \etex_numexpr:D #5 + \l_fp_tmp_int * \c_one_million \scan_stop:
-  \tex_ifnum:D #5 > \c_one_thousand_million
-    \tex_advance:D #4 \c_one
-    \tex_advancd:D #5 -\c_one_thousand_million
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_extended_normalise: {
-  \fp_extended_normalise_aux_i:
-  \fp_extended_normalise_aux_ii:
-}
-\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_i: {
-  \tex_ifnum:D \l_fp_input_a_exponent_int > \c_zero
-    \tex_multiply:D \l_fp_input_a_integer_int \c_ten
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \tex_expandafter:D \fp_extended_normalise_aux_i:w
-      \int_use:N \l_fp_input_a_decimal_int \q_stop
-     \tex_expandafter:D \fp_extended_normalise_aux_i:
-   \tex_fi:D
-}
-\cs_new_protected_nopar:Npn
-  \fp_extended_normalise_aux_i:w #1#2#3#4#5#6#7#8#9 \q_stop {
-  \l_fp_input_a_integer_int
-    \etex_numexpr:D \l_fp_input_a_integer_int + #2 \scan_stop:
-  \l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
-  \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
-  \tex_expandafter:D \fp_extended_normalise_aux_ii:w
-      \int_use:N \l_fp_input_a_extended_int \q_stop
-}
-\cs_new_protected_nopar:Npn
-  \fp_extended_normalise_aux_ii:w #1#2#3#4#5#6#7#8#9 \q_stop {
-  \l_fp_input_a_decimal_int
-    \etex_numexpr:D \l_fp_input_a_decimal_int + #2 \scan_stop:
-  \l_fp_input_a_extended_int #3#4#5#6#7#8#9 0 \scan_stop:
-  \tex_advance:D \l_fp_input_a_exponent_int \c_minus_one
-}
-\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_ii: {
-  \tex_ifnum:D \l_fp_input_a_exponent_int < \c_zero
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \tex_expandafter:D \use_i:nn \tex_expandafter:D
-      \fp_extended_normalise_ii_aux:NNNNNNNNN
-      \int_use:N \l_fp_input_a_decimal_int
-     \tex_expandafter:D \fp_extended_normalise_aux_ii:
-   \tex_fi:D
-}
-\cs_new_protected_nopar:Npn
-  \fp_extended_normalise_ii_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  \tex_ifnum:D \l_fp_input_a_integer_int = \c_zero
-    \l_fp_input_a_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
-  \tex_else:D
-    \tl_set:Nx \l_fp_tmp_tl
-      {
-        \int_use:N \l_fp_input_a_integer_int
-        #1#2#3#4#5#6#7#8
-      }
-    \l_fp_input_a_integer_int \c_zero
-    \l_fp_input_a_decimal_int \l_fp_tmp_tl \scan_stop:
-  \tex_fi:D
-  \tex_divide:D \l_fp_input_a_extended_int \c_ten
-  \tl_set:Nx \l_fp_tmp_tl
-    {
-      #9
-      \int_use:N \l_fp_input_a_extended_int
-    }
-  \l_fp_input_a_extended_int \l_fp_tmp_tl \scan_stop:
-  \tex_advance:D \l_fp_input_a_exponent_int \c_one
-}
-\cs_new_protected_nopar:Npn \fp_extended_normalise_output: {
-  \tex_ifnum:D \l_fp_output_integer_int > \c_nine
-    \tex_advance:D \l_fp_output_integer_int \c_one_thousand_million
-    \tex_expandafter:D \use_i:nn \tex_expandafter:D
-      \fp_extended_normalise_output_aux_i:NNNNNNNNN
-      \int_use:N \l_fp_output_integer_int
-    \tex_expandafter:D \fp_extended_normalise_output:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn
-  \fp_extended_normalise_output_aux_i:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  \l_fp_output_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
-  \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
-  \tl_set:Nx \l_fp_tmp_tl
-    {
-      #9
-      \tex_expandafter:D \use_none:n
-      \int_use:N \l_fp_output_decimal_int
-    }
-  \tex_expandafter:D \fp_extended_normalise_output_aux_ii:NNNNNNNNN
-    \l_fp_tmp_tl
-}
-\cs_new_protected_nopar:Npn
-  \fp_extended_normalise_output_aux_ii:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  \l_fp_output_decimal_int #1#2#3#4#5#6#7#8#9 \scan_stop:
-  \fp_extended_normalise_output_aux:N
-}
-\cs_new_protected_nopar:Npn \fp_extended_normalise_output_aux:N #1 {
-  \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million
-  \tex_divide:D \l_fp_output_extended_int \c_ten
-  \tl_set:Nx \l_fp_tmp_tl
-    {
-      #1
-      \tex_expandafter:D \use_none:n
-        \int_use:N \l_fp_output_extended_int
-    }
-  \l_fp_output_extended_int \l_fp_tmp_tl \scan_stop:
-  \tex_advance:D \l_fp_output_exponent_int \c_one
-}
-\cs_new_protected_nopar:Npn \fp_trig_normalise: {
-  \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
-    \l_fp_input_a_extended_int \c_zero
-    \fp_extended_normalise:
-    \fp_trig_normalise_aux:
-    \tex_ifnum:D \l_fp_input_a_integer_int < \c_zero
-      \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
-    \tex_fi:D
-     \tex_expandafter:D \fp_trig_octant:
-  \tex_else:D
-    \l_fp_input_a_sign_int    \c_one
-    \l_fp_output_integer_int  \c_zero
-    \l_fp_output_decimal_int  \c_zero
-    \l_fp_output_exponent_int \c_zero
-    \tex_expandafter:D \fp_trig_overflow_msg:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_trig_normalise_aux: {
-  \tex_ifnum:D \l_fp_input_a_integer_int > \c_three
-    \fp_trig_sub:NNN
-      \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
-    \tex_expandafter:D \fp_trig_normalise_aux:
-  \tex_else:D
-    \tex_ifnum:D \l_fp_input_a_integer_int > \c_two
-      \tex_ifnum:D \l_fp_input_a_decimal_int > \c_fp_pi_decimal_int
-        \fp_trig_sub:NNN
-          \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \fp_trig_normalise_aux:
-        \tex_fi:D
-    \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_trig_sub:NNN #1#2#3 {
-  \l_fp_input_a_integer_int
-    \etex_numexpr:D \l_fp_input_a_integer_int - #1 \scan_stop:
-  \l_fp_input_a_decimal_int
-    \etex_numexpr:D \l_fp_input_a_decimal_int - #2 \scan_stop:
-  \l_fp_input_a_extended_int
-    \etex_numexpr:D \l_fp_input_a_extended_int - #3 \scan_stop:
-  \tex_ifnum:D \l_fp_input_a_extended_int < \c_zero
-    \tex_advance:D \l_fp_input_a_decimal_int \c_minus_one
-    \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
-  \tex_fi:D
-  \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
-  \tex_ifnum:D \l_fp_input_a_integer_int < \c_zero
-    \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
-    \tex_ifnum:D
-      \etex_numexpr:D
-        \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
-      = \c_zero
-      \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
-    \tex_else:D
-      \l_fp_input_a_integer_int
-         \etex_numexpr:D
-           - \l_fp_input_a_integer_int - \c_one
-         \scan_stop:
-      \l_fp_input_a_decimal_int
-        \etex_numexpr:D
-          \c_one_thousand_million - \l_fp_input_a_decimal_int
-        \scan_stop:
-      \l_fp_input_a_extended_int
-        \etex_numexpr:D
-          \c_one_thousand_million - \l_fp_input_a_extended_int
-        \scan_stop:
-    \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_trig_octant: {
-  \l_fp_trig_octant_int \c_one
-  \fp_trig_octant_aux:
-  \tex_ifnum:D \l_fp_input_a_decimal_int < \c_ten
-    \l_fp_input_a_decimal_int  \c_zero
-    \l_fp_input_a_extended_int \c_zero
-  \tex_fi:D
-  \tex_ifodd:D \l_fp_trig_octant_int
-  \tex_else:D
-    \fp_sub:NNNNNNNNN
-      \c_zero \c_fp_pi_by_four_decimal_int \c_fp_pi_by_four_extended_int
-      \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-        \l_fp_input_a_extended_int
-      \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-        \l_fp_input_a_extended_int
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_trig_octant_aux: {
-  \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero
-    \fp_sub:NNNNNNNNN
-      \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-        \l_fp_input_a_extended_int
-      \c_zero \c_fp_pi_by_four_decimal_int \c_fp_pi_by_four_extended_int
-      \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-        \l_fp_input_a_extended_int
-    \tex_advance:D \l_fp_trig_octant_int \c_one
-    \tex_expandafter:D \fp_trig_octant_aux:
-  \tex_else:D
-    \tex_ifnum:D
-      \l_fp_input_a_decimal_int > \c_fp_pi_by_four_decimal_int
-      \fp_sub:NNNNNNNNN
-        \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-          \l_fp_input_a_extended_int
-        \c_zero \c_fp_pi_by_four_decimal_int
-          \c_fp_pi_by_four_extended_int
-        \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-          \l_fp_input_a_extended_int
-      \tex_advance:D \l_fp_trig_octant_int \c_one
-      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \fp_trig_octant_aux:
-    \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_sin:Nn {
-  \fp_sin_aux:NNn \tl_set:Nn
-}
-\cs_new_protected_nopar:Npn \fp_gsin:Nn {
-  \fp_sin_aux:NNn \tl_gset:Nn
-}
-\cs_generate_variant:Nn \fp_sin:Nn   { c }
-\cs_generate_variant:Nn \fp_gsin:Nn  { c }
-\cs_new_protected_nopar:Npn \fp_sin_aux:NNn #1#2#3 {
-  \group_begin:
-    \fp_split:Nn a {#3}
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int
-      \l_fp_input_a_decimal_int
-      \l_fp_input_a_exponent_int
-    \tl_set:Nx \l_fp_arg_tl
-      {
-        \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
-        .
-        \tex_expandafter:D \use_none:n
-          \tex_number:D \etex_numexpr:D
-            \l_fp_input_a_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_input_a_exponent_int
-      }
-    \tex_ifnum:D \l_fp_input_a_exponent_int < -\c_five
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-      {
-        \group_end:
-        #1 \exp_not:N #2 { \l_fp_arg_tl }
-      }
-    \tex_else:D
-      \etex_ifcsname:D
-        c_fp_sin ( \l_fp_arg_tl ) _fp
-      \tex_endcsname:D
-      \tex_else:D
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \fp_sin_aux_i:
-      \tex_fi:D
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            { \use:c { c_fp_sin ( \l_fp_arg_tl ) _fp } }
-        }
-    \tex_fi:D
-  \fp_tmp:w
-}
-\cs_new_protected_nopar:Npn \fp_sin_aux_i: {
-  \fp_trig_normalise:
-  \fp_sin_aux_ii:
-  \tex_ifnum:D \l_fp_output_integer_int = \c_one
-    \l_fp_output_exponent_int \c_zero
-  \tex_else:D
-    \l_fp_output_integer_int \l_fp_output_decimal_int
-    \l_fp_output_decimal_int \l_fp_output_extended_int
-    \l_fp_output_exponent_int -\c_nine
-  \tex_fi:D
-  \fp_standardise:NNNN
-    \l_fp_input_a_sign_int
-    \l_fp_output_integer_int
-    \l_fp_output_decimal_int
-    \l_fp_output_exponent_int
-  \tl_new:c { c_fp_sin ( \l_fp_arg_tl ) _fp }
-  \tl_gset:cx { c_fp_sin ( \l_fp_arg_tl ) _fp }
-    {
-      \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
-        +
-      \tex_else:D
-        -
-      \tex_fi:D
-      \int_use:N \l_fp_output_integer_int
-      .
-      \tex_expandafter:D \use_none:n
-        \tex_number:D \etex_numexpr:D
-           \l_fp_output_decimal_int + \c_one_thousand_million
-         \scan_stop:
-      e
-      \int_use:N \l_fp_output_exponent_int
-    }
-}
-\cs_new_protected_nopar:Npn \fp_sin_aux_ii: {
-  \tex_ifcase:D \l_fp_trig_octant_int
-  \tex_or:D
-    \tex_expandafter:D \fp_trig_calc_sin:
-  \tex_or:D
-    \tex_expandafter:D \fp_trig_calc_cos:
-  \tex_or:D
-    \tex_expandafter:D \fp_trig_calc_cos:
-  \tex_or:D
-    \tex_expandafter:D \fp_trig_calc_sin:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_cos:Nn {
-  \fp_cos_aux:NNn \tl_set:Nn
-}
-\cs_new_protected_nopar:Npn \fp_gcos:Nn {
-  \fp_cos_aux:NNn \tl_gset:Nn
-}
-\cs_generate_variant:Nn \fp_cos:Nn   { c }
-\cs_generate_variant:Nn \fp_gcos:Nn  { c }
-\cs_new_protected_nopar:Npn \fp_cos_aux:NNn #1#2#3 {
-  \group_begin:
-    \fp_split:Nn a {#3}
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int
-      \l_fp_input_a_decimal_int
-      \l_fp_input_a_exponent_int
-    \tl_set:Nx \l_fp_arg_tl
-      {
-        \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
-        .
-      \tex_expandafter:D \use_none:n
-        \tex_number:D \etex_numexpr:D
-           \l_fp_input_a_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_input_a_exponent_int
-      }
-    \etex_ifcsname:D c_fp_cos ( \l_fp_arg_tl ) _fp \tex_endcsname:D
-    \tex_else:D
-      \tex_expandafter:D \fp_cos_aux_i:
-    \tex_fi:D
-    \cs_set_protected_nopar:Npx \fp_tmp:w
-      {
-        \group_end:
-        #1 \exp_not:N #2
-          { \use:c { c_fp_cos ( \l_fp_arg_tl ) _fp } }
-      }
-  \fp_tmp:w
-}
-\cs_new_protected_nopar:Npn \fp_cos_aux_i: {
-  \fp_trig_normalise:
-  \fp_cos_aux_ii:
-  \tex_ifnum:D \l_fp_output_integer_int = \c_one
-    \l_fp_output_exponent_int \c_zero
-  \tex_else:D
-    \l_fp_output_integer_int \l_fp_output_decimal_int
-    \l_fp_output_decimal_int \l_fp_output_extended_int
-    \l_fp_output_exponent_int -\c_nine
-  \tex_fi:D
-  \fp_standardise:NNNN
-    \l_fp_input_a_sign_int
-    \l_fp_output_integer_int
-    \l_fp_output_decimal_int
-    \l_fp_output_exponent_int
-  \tl_new:c { c_fp_cos ( \l_fp_arg_tl ) _fp }
-  \tl_gset:cx { c_fp_cos ( \l_fp_arg_tl ) _fp }
-    {
-      \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
-        +
-      \tex_else:D
-        -
-      \tex_fi:D
-      \int_use:N \l_fp_output_integer_int
-      .
-      \tex_expandafter:D \use_none:n
-        \tex_number:D \etex_numexpr:D
-           \l_fp_output_decimal_int + \c_one_thousand_million
-         \scan_stop:
-      e
-      \int_use:N \l_fp_output_exponent_int
-    }
-}
-\cs_new_protected_nopar:Npn \fp_cos_aux_ii: {
-  \tex_ifcase:D \l_fp_trig_octant_int
-  \tex_or:D
-    \tex_expandafter:D \fp_trig_calc_cos:
-  \tex_or:D
-    \tex_expandafter:D \fp_trig_calc_sin:
-  \tex_or:D
-    \tex_expandafter:D \fp_trig_calc_sin:
-  \tex_or:D
-    \tex_expandafter:D \fp_trig_calc_cos:
-  \tex_fi:D
-  \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
-    \tex_ifnum:D \l_fp_trig_octant_int > \c_two
-      \l_fp_input_a_sign_int \c_minus_one
-    \tex_fi:D
-  \tex_else:D
-    \tex_ifnum:D \l_fp_trig_octant_int > \c_two
-    \tex_else:D
-      \l_fp_input_a_sign_int \c_one
-    \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_trig_calc_cos: {
-  \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
-    \l_fp_output_integer_int \c_one
-    \l_fp_output_decimal_int \c_zero
-  \tex_else:D
-    \l_fp_trig_sign_int \c_minus_one
-    \fp_mul:NNNNNN
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \fp_div_integer:NNNNN
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-      \c_two
-      \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \l_fp_count_int \c_three
-    \tex_ifnum:D \l_fp_trig_extended_int = \c_zero
-      \tex_ifnum:D \l_fp_trig_decimal_int = \c_zero
-        \l_fp_output_integer_int \c_one
-        \l_fp_output_decimal_int \c_zero
-        \l_fp_output_extended_int \c_zero
-      \tex_else:D
-        \l_fp_output_integer_int \c_zero
-        \l_fp_output_decimal_int \c_one_thousand_million
-        \l_fp_output_extended_int \c_zero
-      \tex_fi:D
-    \tex_else:D
-      \l_fp_output_integer_int \c_zero
-      \l_fp_output_decimal_int 999999999 \scan_stop:
-      \l_fp_output_extended_int \c_one_thousand_million
-    \tex_fi:D
-    \tex_advance:D \l_fp_output_extended_int -\l_fp_trig_extended_int
-    \tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int
-    \tex_expandafter:D \fp_trig_calc_Taylor:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_trig_calc_sin: {
-  \l_fp_output_integer_int \c_zero
-  \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
-    \l_fp_output_decimal_int \c_zero
-  \tex_else:D
-    \l_fp_output_decimal_int \l_fp_input_a_decimal_int
-    \l_fp_output_extended_int \l_fp_input_a_extended_int
-    \l_fp_trig_sign_int \c_one
-    \l_fp_trig_decimal_int \l_fp_input_a_decimal_int
-    \l_fp_trig_extended_int \l_fp_input_a_extended_int
-    \l_fp_count_int \c_two
-    \tex_expandafter:D \fp_trig_calc_Taylor:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_trig_calc_Taylor: {
-  \l_fp_trig_sign_int -\l_fp_trig_sign_int
-  \fp_mul:NNNNNN
-    \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-    \l_fp_trig_decimal_int \l_fp_trig_extended_int
-  \fp_mul:NNNNNN
-    \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-    \l_fp_trig_decimal_int \l_fp_trig_extended_int
-  \fp_div_integer:NNNNN
-    \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \l_fp_count_int
-    \l_fp_trig_decimal_int \l_fp_trig_extended_int
-  \tex_advance:D \l_fp_count_int \c_one
-  \fp_div_integer:NNNNN
-    \l_fp_trig_decimal_int \l_fp_trig_extended_int
-    \l_fp_count_int
-    \l_fp_trig_decimal_int \l_fp_trig_extended_int
-  \tex_advance:D \l_fp_count_int \c_one
-  \tex_ifnum:D \l_fp_trig_decimal_int > \c_zero
-    \tex_ifnum:D \l_fp_trig_sign_int > \c_zero
-      \tex_advance:D \l_fp_output_decimal_int \l_fp_trig_decimal_int
-      \tex_advance:D \l_fp_output_extended_int
-        \l_fp_trig_extended_int
-      \tex_ifnum:D \l_fp_output_extended_int < \c_one_thousand_million
-      \tex_else:D
-        \tex_advance:D \l_fp_output_decimal_int \c_one
-        \tex_advance:D \l_fp_output_extended_int
-          -\c_one_thousand_million
-      \tex_fi:D
-      \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
-      \tex_else:D
-        \tex_advance:D \l_fp_output_integer_int \c_one
-        \tex_advance:D \l_fp_output_decimal_int
-          -\c_one_thousand_million
-      \tex_fi:D
-    \tex_else:D
-      \tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int
-      \tex_advance:D \l_fp_output_extended_int
-        -\l_fp_input_a_extended_int
-      \tex_ifnum:D \l_fp_output_extended_int < \c_zero
-        \tex_advance:D \l_fp_output_decimal_int \c_minus_one
-        \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million
-      \tex_fi:D
-      \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_fi:D
-    \tex_expandafter:D \fp_trig_calc_Taylor:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_tan:Nn {
-  \fp_tan_aux:NNn \tl_set:Nn
-}
-\cs_new_protected_nopar:Npn \fp_gtan:Nn {
-  \fp_tan_aux:NNn \tl_gset:Nn
-}
-\cs_generate_variant:Nn \fp_tan:Nn   { c }
-\cs_generate_variant:Nn \fp_gtan:Nn  { c }
-\cs_new_protected_nopar:Npn \fp_tan_aux:NNn #1#2#3 {
-  \group_begin:
-    \fp_split:Nn a {#3}
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int
-      \l_fp_input_a_decimal_int
-      \l_fp_input_a_exponent_int
-    \tl_set:Nx \l_fp_arg_tl
-      {
-        \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
-        .
-        \tex_expandafter:D \use_none:n
-          \tex_number:D \etex_numexpr:D
-            \l_fp_input_a_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_input_a_exponent_int
-      }
-    \tex_ifnum:D \l_fp_input_a_exponent_int < -\c_five
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-      {
-        \group_end:
-        #1 \exp_not:N #2 { \l_fp_arg_tl }
-      }
-    \tex_else:D
-      \etex_ifcsname:D
-        c_fp_tan ( \l_fp_arg_tl ) _fp
-      \tex_endcsname:D
-      \tex_else:D
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \fp_tan_aux_i:
-      \tex_fi:D
-      \cs_set_protected_nopar:Npx \fp_tmp:w
-        {
-          \group_end:
-          #1 \exp_not:N #2
-            { \use:c { c_fp_tan ( \l_fp_arg_tl ) _fp } }
-        }
-    \tex_fi:D
-  \fp_tmp:w
-}
-\cs_new_protected_nopar:Npn \fp_tan_aux_i: {
-  \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
-    \tex_expandafter:D \fp_tan_aux_ii:
-  \tex_else:D
-    \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
-      \c_zero_fp
-    \tex_expandafter:D \fp_trig_overflow_msg:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_tan_aux_ii: {
-  \fp_trig_normalise:
-  \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
-    \tex_ifnum:D \l_fp_trig_octant_int > \c_two
-      \l_fp_output_sign_int \c_minus_one
-    \tex_else:D
-      \l_fp_output_sign_int \c_one
-    \tex_fi:D
-  \tex_else:D
-    \tex_ifnum:D \l_fp_trig_octant_int > \c_two
-      \l_fp_output_sign_int \c_one
-    \tex_else:D
-      \l_fp_output_sign_int \c_minus_one
-    \tex_fi:D
-  \tex_fi:D
-  \fp_cos_aux_ii:
-  \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
-    \tex_ifnum:D \l_fp_input_a_integer_int = \c_zero
-      \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
-        \c_undefined_fp
-    \tex_else:D
-      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \fp_tan_aux_iii:
-    \tex_fi:D
-  \tex_else:D
-    \tex_expandafter:D \fp_tan_aux_iii:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_tan_aux_iii: {
-  \l_fp_input_b_integer_int \l_fp_output_decimal_int
-  \l_fp_input_b_decimal_int \l_fp_output_extended_int
-  \l_fp_input_b_exponent_int -\c_nine
-  \fp_standardise:NNNN
-    \l_fp_input_b_sign_int
-    \l_fp_input_b_integer_int
-    \l_fp_input_b_decimal_int
-    \l_fp_input_b_exponent_int
-  \fp_sin_aux_ii:
-  \l_fp_input_a_integer_int \l_fp_output_decimal_int
-  \l_fp_input_a_decimal_int \l_fp_output_extended_int
-  \l_fp_input_a_exponent_int -\c_nine
-  \fp_standardise:NNNN
-    \l_fp_input_a_sign_int
-    \l_fp_input_a_integer_int
-    \l_fp_input_a_decimal_int
-    \l_fp_input_a_exponent_int
-  \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
-    \tex_ifnum:D \l_fp_input_a_integer_int = \c_zero
-      \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
-        \c_zero_fp
-    \tex_else:D
-      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \fp_tan_aux_iv:
-    \tex_fi:D
-  \tex_else:D
-    \tex_expandafter:D \fp_tan_aux_iv:
-  \tex_fi:D
-}
- \cs_new_protected_nopar:Npn \fp_tan_aux_iv: {
-  \l_fp_output_integer_int \c_zero
-  \l_fp_output_decimal_int \c_zero
-  \cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
-  \l_fp_div_offset_int \c_one_hundred_million
-  \fp_div_loop:
-  \l_fp_output_exponent_int
-    \etex_numexpr:D
-      \l_fp_input_a_exponent_int - \l_fp_input_b_exponent_int
-    \scan_stop:
-  \fp_standardise:NNNN
-    \l_fp_output_sign_int
-    \l_fp_output_integer_int
-    \l_fp_output_decimal_int
-    \l_fp_output_exponent_int
-  \tl_new:c { c_fp_tan ( \l_fp_arg_tl ) _fp }
-  \tl_gset:cx { c_fp_tan ( \l_fp_arg_tl ) _fp }
-    {
-      \tex_ifnum:D \l_fp_output_sign_int > \c_zero
-        +
-      \tex_else:D
-        -
-      \tex_fi:D
-      \int_use:N \l_fp_output_integer_int
-      .
-      \tex_expandafter:D \use_none:n
-        \tex_number:D \etex_numexpr:D
-           \l_fp_output_decimal_int + \c_one_thousand_million
-         \scan_stop:
-      e
-      \int_use:N \l_fp_output_exponent_int
-    }
-}
-\tl_new:c { c_fp_exp_1_tl }
-\tl_set:cn { c_fp_exp_1_tl }
-  { { 2 } { 718281828 } { 459045235 } { 0 } }
-\tl_new:c { c_fp_exp_2_tl }
-\tl_set:cn { c_fp_exp_2_tl }
-  { { 7 } { 389056098 } { 930650227 } { 0 } }
-\tl_new:c { c_fp_exp_3_tl }
-\tl_set:cn { c_fp_exp_3_tl }
-  { { 2 } { 008553692 } { 318766774 } { 1 } }
-\tl_new:c { c_fp_exp_4_tl }
-\tl_set:cn { c_fp_exp_4_tl }
-  { { 5 } { 459815003 } { 314423908 } { 1 } }
-\tl_new:c { c_fp_exp_5_tl }
-\tl_set:cn { c_fp_exp_5_tl }
-  { { 1 } { 484131591 } { 025766034 } { 2 } }
-\tl_new:c { c_fp_exp_6_tl }
-\tl_set:cn { c_fp_exp_6_tl }
-  { { 4 } { 034287934 } { 927351226 } { 2 } }
-\tl_new:c { c_fp_exp_7_tl }
-\tl_set:cn { c_fp_exp_7_tl }
-  { { 1 } { 096633158 } { 428458599 } { 3 } }
-\tl_new:c { c_fp_exp_8_tl }
-\tl_set:cn { c_fp_exp_8_tl }
-  { { 2 } { 980957987 } { 041728275 } { 3 } }
-\tl_new:c { c_fp_exp_9_tl }
-\tl_set:cn { c_fp_exp_9_tl }
-  { { 8 } { 103083927 } { 575384008 } { 3 } }
-\tl_new:c { c_fp_exp_10_tl }
-\tl_set:cn { c_fp_exp_10_tl }
-  { { 2 } { 202646579 } { 480671652 } { 4 } }
-\tl_new:c { c_fp_exp_20_tl }
-\tl_set:cn { c_fp_exp_20_tl }
-  { { 4 } { 851651954 } { 097902280 } { 8 } }
-\tl_new:c { c_fp_exp_30_tl }
-\tl_set:cn { c_fp_exp_30_tl }
-  { { 1 } { 068647458 } { 152446215 } { 13 } }
-\tl_new:c { c_fp_exp_40_tl }
-\tl_set:cn { c_fp_exp_40_tl }
-  { { 2 } { 353852668 } { 370199854 } { 17 } }
-\tl_new:c { c_fp_exp_50_tl }
-\tl_set:cn { c_fp_exp_50_tl }
-  { { 5 } { 184705528 } { 587072464 } { 21 } }
-\tl_new:c { c_fp_exp_60_tl }
-\tl_set:cn { c_fp_exp_60_tl }
-  { { 1 } { 142007389 } { 815684284 } { 26 } }
-\tl_new:c { c_fp_exp_70_tl }
-\tl_set:cn { c_fp_exp_70_tl }
-  { { 2 } { 515438670 } { 919167006 } { 30 } }
-\tl_new:c { c_fp_exp_80_tl }
-\tl_set:cn { c_fp_exp_80_tl }
-  { { 5 } { 540622384 } { 393510053 } { 34 } }
-\tl_new:c { c_fp_exp_90_tl }
-\tl_set:cn { c_fp_exp_90_tl }
-  { { 1 } { 220403294 } { 317840802 } { 39 } }
-\tl_new:c { c_fp_exp_100_tl }
-\tl_set:cn { c_fp_exp_100_tl }
-  { { 2 } { 688117141 } { 816135448 } { 43 } }
-\tl_new:c { c_fp_exp_200_tl }
-\tl_set:cn { c_fp_exp_200_tl }
-  { { 7 } { 225973768 } { 125749258 } { 86 } }
-\tl_new:c { c_fp_exp_-1_tl }
-\tl_set:cn { c_fp_exp_-1_tl }
-  { { 3 } { 678794411 } { 71442322 } { -1 } }
-\tl_new:c { c_fp_exp_-2_tl }
-\tl_set:cn { c_fp_exp_-2_tl }
-  { { 1 } { 353352832 } { 366132692 } { -1 } }
-\tl_new:c { c_fp_exp_-3_tl }
-\tl_set:cn { c_fp_exp_-3_tl }
-  { { 4 } { 978706836 } { 786394298 } { -2 } }
-\tl_new:c { c_fp_exp_-4_tl }
-\tl_set:cn { c_fp_exp_-4_tl }
-  { { 1 } { 831563888 } { 873418029 } { -2 } }
-\tl_new:c { c_fp_exp_-5_tl }
-\tl_set:cn { c_fp_exp_-5_tl }
-  { { 6 } { 737946999 } { 085467097 } { -3 } }
-\tl_new:c { c_fp_exp_-6_tl }
-\tl_set:cn { c_fp_exp_-6_tl }
-  { { 2 } { 478752176 } { 666358423 } { -3 } }
-\tl_new:c { c_fp_exp_-7_tl }
-\tl_set:cn { c_fp_exp_-7_tl }
-  { { 9 } { 118819655 } { 545162080 } { -4 } }
-\tl_new:c { c_fp_exp_-8_tl }
-\tl_set:cn { c_fp_exp_-8_tl }
-  { { 3 } { 354626279 } { 025118388 } { -4 } }
-\tl_new:c { c_fp_exp_-9_tl }
-\tl_set:cn { c_fp_exp_-9_tl }
-  { { 1 } { 234098040 } { 866795495 } { -4 } }
-\tl_new:c { c_fp_exp_-10_tl }
-\tl_set:cn { c_fp_exp_-10_tl }
-  { { 4 } { 539992976 } { 248451536 } { -5 } }
-\tl_new:c { c_fp_exp_-20_tl }
-\tl_set:cn { c_fp_exp_-20_tl }
-  { { 2 } { 061153622 } { 438557828 } { -9 } }
-\tl_new:c { c_fp_exp_-30_tl }
-\tl_set:cn { c_fp_exp_-30_tl }
-  { { 9 } { 357622968 } { 840174605 } { -14 } }
-\tl_new:c { c_fp_exp_-40_tl }
-\tl_set:cn { c_fp_exp_-40_tl }
-  { { 4 } { 248354255 } { 291588995 } { -18 } }
-\tl_new:c { c_fp_exp_-50_tl }
-\tl_set:cn { c_fp_exp_-50_tl }
-  { { 1 } { 928749847 } { 963917783 } { -22 } }
-\tl_new:c { c_fp_exp_-60_tl }
-\tl_set:cn { c_fp_exp_-60_tl }
-  { { 8 } { 756510762 } { 696520338 } { -27 } }
-\tl_new:c { c_fp_exp_-70_tl }
-\tl_set:cn { c_fp_exp_-70_tl }
-  { { 3 } { 975449735 } { 908646808 } { -31 } }
-\tl_new:c { c_fp_exp_-80_tl }
-\tl_set:cn { c_fp_exp_-80_tl }
-  { { 1 } { 804851387 } { 845415172 } { -35 } }
-\tl_new:c { c_fp_exp_-90_tl }
-\tl_set:cn { c_fp_exp_-90_tl }
-  { { 8 } { 194012623 } { 990515430 } { -40 } }
-\tl_new:c { c_fp_exp_-100_tl }
-\tl_set:cn { c_fp_exp_-100_tl }
-  { { 3 } { 720075976 } { 020835963 } { -44 } }
-\tl_new:c { c_fp_exp_-200_tl }
-\tl_set:cn { c_fp_exp_-200_tl }
-  { { 1 } { 383896526 } { 736737530 } { -87 } }
-\cs_new_protected_nopar:Npn \fp_exp:Nn {
-  \fp_exp_aux:NNn \tl_set:Nn
-}
-\cs_new_protected_nopar:Npn \fp_gexp:Nn {
-  \fp_exp_aux:NNn \tl_gset:Nn
-}
-\cs_generate_variant:Nn \fp_exp:Nn  { c }
-\cs_generate_variant:Nn \fp_gexp:Nn { c }
-\cs_new_protected_nopar:Npn \fp_exp_aux:NNn #1#2#3 {
-  \group_begin:
-    \fp_split:Nn a {#3}
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int
-      \l_fp_input_a_decimal_int
-      \l_fp_input_a_exponent_int
-    \l_fp_input_a_extended_int \c_zero
-    \tl_set:Nx \l_fp_arg_tl
-      {
-        \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
-        .
-        \tex_expandafter:D \use_none:n
-          \tex_number:D \etex_numexpr:D
-             \l_fp_input_a_decimal_int + \c_one_thousand_million
-        e
-        \int_use:N \l_fp_input_a_exponent_int
-      }
-    \etex_ifcsname:D c_fp_exp ( \l_fp_arg_tl ) _fp \tex_endcsname:D
-    \tex_else:D
-      \tex_expandafter:D \fp_exp_internal:
-    \tex_fi:D
-    \cs_set_protected_nopar:Npx \fp_tmp:w
-      {
-        \group_end:
-        #1 \exp_not:N #2
-          {
-            \etex_ifcsname:D c_fp_exp ( \l_fp_arg_tl ) _fp
-              \tex_endcsname:D
-              \use:c { c_fp_exp ( \l_fp_arg_tl ) _fp }
-            \tex_else:D
-              \c_zero_fp
-            \tex_fi:D
-          }
-      }
-  \fp_tmp:w
-}
-\cs_new_protected_nopar:Npn \fp_exp_internal: {
-  \tex_ifnum:D \l_fp_input_a_exponent_int < \c_three
-    \fp_extended_normalise:
-    \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
-      \tex_ifnum:D \l_fp_input_a_integer_int < 230 \scan_stop:
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \fp_exp_aux:
-      \tex_else:D
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \fp_exp_overflow_msg:
-        \tex_fi:D
-    \tex_else:D
-      \tex_ifnum:D \l_fp_input_a_integer_int < 230 \scan_stop:
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D  \fp_exp_aux:
-      \tex_else:D
-        \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
-          { \c_zero_fp }
-      \tex_fi:D
-    \tex_fi:D
-  \tex_else:D
-    \tex_expandafter:D \fp_exp_overflow_msg:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_exp_aux: {
-  \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero
-    \tex_expandafter:D \fp_exp_integer:
-  \tex_else:D
-    \l_fp_output_integer_int  \c_one
-    \l_fp_output_decimal_int  \c_zero
-    \l_fp_output_extended_int \c_zero
-    \l_fp_output_exponent_int \c_zero
-    \tex_expandafter:D \fp_exp_decimal:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_exp_integer: {
-  \tex_ifnum:D \l_fp_input_a_integer_int < \c_one_hundred
-    \l_fp_exp_integer_int  \c_one
-    \l_fp_exp_decimal_int  \c_zero
-    \l_fp_exp_extended_int \c_zero
-    \l_fp_exp_exponent_int \c_zero
-    \tex_expandafter:D \fp_exp_integer_tens:
-  \tex_else:D
-    \tl_set:Nx \l_fp_tmp_tl
-      {
-        \tex_expandafter:D \use_i:nnn
-          \int_use:N \l_fp_input_a_integer_int
-      }
-    \l_fp_input_a_integer_int
-      \etex_numexpr:D
-        \l_fp_input_a_integer_int - \l_fp_tmp_tl 00
-      \scan_stop:
-    \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
-      \tex_ifnum:D \l_fp_output_integer_int > 200 \scan_stop:
-        \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
-          { \c_zero_fp }
-      \tex_else:D
-        \fp_exp_integer_const:n { - \l_fp_tmp_tl 00 }
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \fp_exp_integer_tens:
-      \tex_fi:D
-    \tex_else:D
-      \fp_exp_integer_const:n { \l_fp_tmp_tl 00 }
-      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \tex_expandafter:D \fp_exp_integer_tens:
-    \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_exp_integer_tens: {
-  \l_fp_output_integer_int  \l_fp_exp_integer_int
-  \l_fp_output_decimal_int  \l_fp_exp_decimal_int
-  \l_fp_output_extended_int \l_fp_exp_extended_int
-  \l_fp_output_exponent_int \l_fp_exp_exponent_int
-  \tex_ifnum:D \l_fp_input_a_integer_int > \c_nine
-    \tl_set:Nx \l_fp_tmp_tl
-      {
-        \tex_expandafter:D \use_i:nn
-          \int_use:N \l_fp_input_a_integer_int
-      }
-    \l_fp_input_a_integer_int
-      \etex_numexpr:D
-        \l_fp_input_a_integer_int - \l_fp_tmp_tl 0
-      \scan_stop:
-    \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
-      \fp_exp_integer_const:n { \l_fp_tmp_tl 0 }
-    \tex_else:D
-      \fp_exp_integer_const:n { - \l_fp_tmp_tl 0 }
-    \tex_fi:D
-    \fp_mul:NNNNNNNNN
-      \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-    \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
-    \fp_extended_normalise_output:
-  \tex_fi:D
-  \fp_exp_integer_units:
-}
-\cs_new_protected_nopar:Npn \fp_exp_integer_units: {
-  \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero
-    \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
-      \fp_exp_integer_const:n { \int_use:N \l_fp_input_a_integer_int }
-    \tex_else:D
-      \fp_exp_integer_const:n
-        { - \int_use:N \l_fp_input_a_integer_int }
-    \tex_fi:D
-    \fp_mul:NNNNNNNNN
-      \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-    \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
-    \fp_extended_normalise_output:
-  \tex_fi:D
-  \fp_exp_decimal:
-}
-\cs_new_protected_nopar:Npn \fp_exp_integer_const:n #1 {
-  \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-    \fp_exp_integer_const:nnnn
-    \tex_csname:D c_fp_exp_ #1 _tl \tex_endcsname:D
-}
-\cs_new_protected_nopar:Npn \fp_exp_integer_const:nnnn #1#2#3#4 {
-  \l_fp_exp_integer_int  #1 \scan_stop:
-  \l_fp_exp_decimal_int  #2 \scan_stop:
-  \l_fp_exp_extended_int #3 \scan_stop:
-  \l_fp_exp_exponent_int #4 \scan_stop:
-}
-\cs_new_protected_nopar:Npn \fp_exp_decimal: {
-  \tex_ifnum:D \l_fp_input_a_decimal_int > \c_zero
-    \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
-      \l_fp_exp_integer_int  \c_one
-      \l_fp_exp_decimal_int  \l_fp_input_a_decimal_int
-      \l_fp_exp_extended_int \l_fp_input_a_extended_int
-    \tex_else:D
-      \l_fp_exp_integer_int \c_zero
-      \tex_ifnum:D \l_fp_exp_extended_int = \c_zero
-        \l_fp_exp_decimal_int
-          \etex_numexpr:D
-            \c_one_thousand_million - \l_fp_input_a_decimal_int
-          \scan_stop:
-        \l_fp_exp_extended_int \c_zero
-      \tex_else:D
-        \l_fp_exp_decimal_int
-          \etex_numexpr:D
-            999999999 - \l_fp_input_a_decimal_int
-          \scan_stop:
-        \l_fp_exp_extended_int
-          \etex_numexpr:D
-            \c_one_thousand_million - \l_fp_input_a_extended_int
-          \scan_stop:
-      \tex_fi:D
-    \tex_fi:D
-    \l_fp_input_b_sign_int     \l_fp_input_a_sign_int
-    \l_fp_input_b_decimal_int  \l_fp_input_a_decimal_int
-    \l_fp_input_b_extended_int \l_fp_input_a_extended_int
-    \l_fp_count_int \c_one
-    \fp_exp_Taylor:
-    \fp_mul:NNNNNNNNN
-      \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-  \tex_fi:D
-  \tex_ifnum:D \l_fp_output_extended_int < \c_five_hundred_million
-  \tex_else:D
-    \tex_advance:D \l_fp_output_decimal_int \c_one
-    \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
-    \tex_else:D
-      \l_fp_output_decimal_int \c_zero
-      \tex_advance:D \l_fp_output_integer_int \c_one
-    \tex_fi:D
-  \tex_fi:D
-  \fp_standardise:NNNN
-    \l_fp_output_sign_int
-    \l_fp_output_integer_int
-    \l_fp_output_decimal_int
-    \l_fp_output_exponent_int
-  \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
-    {
-      +
-      \int_use:N \l_fp_output_integer_int
-      .
-      \tex_expandafter:D \use_none:n
-        \tex_number:D \etex_numexpr:D
-           \l_fp_output_decimal_int + \c_one_thousand_million
-         \scan_stop:
-      e
-      \int_use:N \l_fp_output_exponent_int
-    }
-}
-\cs_new_protected_nopar:Npn \fp_exp_Taylor: {
-  \tex_advance:D \l_fp_count_int \c_one
-  \tex_multiply:D \l_fp_input_b_sign_int \l_fp_input_a_sign_int
-  \fp_mul:NNNNNN
-    \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-    \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-    \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-  \fp_div_integer:NNNNN
-    \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-    \l_fp_count_int
-    \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-  \tex_ifnum:D
-    \etex_numexpr:D
-      \l_fp_input_b_decimal_int + \l_fp_input_b_extended_int
-      > \c_zero
-    \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero
-      \tex_advance:D \l_fp_exp_decimal_int \l_fp_input_b_decimal_int
-      \tex_advance:D \l_fp_exp_extended_int
-        \l_fp_input_b_extended_int
-      \tex_ifnum:D \l_fp_exp_extended_int < \c_one_thousand_million
-      \tex_else:D
-        \tex_advance:D \l_fp_exp_decimal_int \c_one
-        \tex_advance:D \l_fp_exp_extended_int
-          -\c_one_thousand_million
-      \tex_fi:D
-      \tex_ifnum:D \l_fp_exp_decimal_int < \c_one_thousand_million
-      \tex_else:D
-        \tex_advance:D \l_fp_exp_integer_int \c_one
-        \tex_advance:D \l_fp_exp_decimal_int
-          -\c_one_thousand_million
-      \tex_fi:D
-    \tex_else:D
-      \tex_advance:D \l_fp_exp_decimal_int -\l_fp_input_b_decimal_int
-      \tex_advance:D \l_fp_exp_extended_int
-        -\l_fp_input_a_extended_int
-      \tex_ifnum:D \l_fp_exp_extended_int < \c_zero
-        \tex_advance:D \l_fp_exp_decimal_int \c_minus_one
-        \tex_advance:D \l_fp_exp_extended_int \c_one_thousand_million
-      \tex_fi:D
-      \tex_ifnum:D \l_fp_exp_decimal_int < \c_zero
-        \tex_advance:D \l_fp_exp_integer_int \c_minus_one
-        \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
-      \tex_fi:D
-    \tex_fi:D
-    \tex_expandafter:D \fp_exp_Taylor:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_exp_const:Nx #1#2 {
-  \tl_new:N #1
-  \tl_gset:Nx #1 {#2}
-}
-\cs_generate_variant:Nn \fp_exp_const:Nx { c }
-\tl_new:c { c_fp_ln_10_1_tl }
-\tl_set:cn { c_fp_ln_10_1_tl }
-  { { 2 } { 302585092 } { 994045684 } { 0 } }
-\tl_new:c { c_fp_ln_10_2_tl }
-\tl_set:cn { c_fp_ln_10_2_tl }
-  { { 4 } { 605170185 } { 988091368 } { 0 } }
-\tl_new:c { c_fp_ln_10_3_tl }
-\tl_set:cn { c_fp_ln_10_3_tl }
-  { { 6 } { 907755278 } { 982137052 } { 0 } }
-\tl_new:c { c_fp_ln_10_4_tl }
-\tl_set:cn { c_fp_ln_10_4_tl }
-  { { 9 } { 210340371 } { 976182736 } { 0 } }
-\tl_new:c { c_fp_ln_10_5_tl }
-\tl_set:cn { c_fp_ln_10_5_tl }
-  { { 1 } { 151292546 } { 497022842 } { 1 } }
-\tl_new:c { c_fp_ln_10_6_tl }
-\tl_set:cn { c_fp_ln_10_6_tl }
-  { { 1 } { 381551055 } { 796427410 } { 1 } }
-\tl_new:c { c_fp_ln_10_7_tl }
-\tl_set:cn { c_fp_ln_10_7_tl }
-  { { 1 } { 611809565 } { 095831979 } { 1 } }
-\tl_new:c { c_fp_ln_10_8_tl }
-\tl_set:cn { c_fp_ln_10_8_tl }
-  { { 1 } { 842068074 } { 395226547 } { 1 } }
-\tl_new:c { c_fp_ln_10_9_tl }
-\tl_set:cn { c_fp_ln_10_9_tl }
-  { { 2 } { 072326583 } { 694641116 } { 1 } }
-\tl_new:c { c_fp_ln_2_1_tl }
-\tl_set:cn { c_fp_ln_2_1_tl }
-  { { 0 } { 693147180 } { 559945309 } { 0 } }
-\tl_new:c { c_fp_ln_2_2_tl }
-\tl_set:cn { c_fp_ln_2_2_tl }
-  { { 1 } { 386294361 } { 119890618 } { 0 } }
-\tl_new:c { c_fp_ln_2_3_tl }
-\tl_set:cn { c_fp_ln_2_3_tl }
-  { { 2 } { 079441541 } { 679835928 } { 0 } }
-\cs_new_protected_nopar:Npn \fp_ln:Nn {
-  \fp_ln_aux:NNn \tl_set:Nn
-}
-\cs_new_protected_nopar:Npn \fp_gln:Nn {
-  \fp_ln_aux:NNn \tl_gset:Nn
-}
-\cs_generate_variant:Nn \fp_ln:Nn  { c }
-\cs_generate_variant:Nn \fp_gln:Nn { c }
-\cs_new_protected_nopar:Npn \fp_ln_aux:NNn #1#2#3 {
-  \group_begin:
-    \fp_split:Nn a {#3}
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int
-      \l_fp_input_a_decimal_int
-      \l_fp_input_a_exponent_int
-    \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
-      \tex_ifnum:D
-        \etex_numexpr:D
-          \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-          > \c_zero
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \fp_ln_aux:
-      \tex_else:D
-        \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-          {
-            \group_end:
-            ##1 \exp_not:N ##2 { \c_zero_fp }
-          }
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \fp_ln_error_msg:
-      \tex_fi:D
-    \tex_else:D
-      \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-        {
-          \group_end:
-          ##1 \exp_not:N ##2 { \c_zero_fp }
-        }
-      \tex_expandafter:D \fp_ln_error_msg:
-    \tex_fi:D
-  \fp_tmp:w #1 #2
-}
-\cs_new_protected_nopar:Npn \fp_ln_aux: {
-  \tl_set:Nx \l_fp_arg_tl
-    {
-      +
-      \int_use:N \l_fp_input_a_integer_int
-      .
-      \tex_expandafter:D \use_none:n
-        \tex_number:D \etex_numexpr:D
-           \l_fp_input_a_decimal_int + \c_one_thousand_million
-      e
-      \int_use:N \l_fp_input_a_exponent_int
-    }
-  \etex_ifcsname:D c_fp_ln ( \l_fp_arg_tl ) _fp \tex_endcsname:D
-  \tex_else:D
-    \tex_expandafter:D \fp_ln_exponent:
-  \tex_fi:D
-  \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-    {
-      \group_end:
-      ##1 \exp_not:N ##2
-        { \use:c { c_fp_ln ( \l_fp_arg_tl ) _fp } }
-    }
-}
-\cs_new_protected_nopar:Npn \fp_ln_exponent: {
-  \fp_ln_internal:
-  \tex_ifnum:D \l_fp_output_extended_int < \c_five_hundred_million
-  \tex_else:D
-    \tex_advance:D \l_fp_output_decimal_int \c_one
-    \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
-    \tex_else:D
-      \l_fp_output_decimal_int \c_zero
-      \tex_advance:D \l_fp_output_integer_int \c_one
-    \tex_fi:D
-  \tex_fi:D
-  \fp_standardise:NNNN
-    \l_fp_output_sign_int
-    \l_fp_output_integer_int
-    \l_fp_output_decimal_int
-    \l_fp_output_exponent_int
-  \tl_new:c { c_fp_ln ( \l_fp_arg_tl ) _fp }
-  \tl_gset:cx { c_fp_ln ( \l_fp_arg_tl ) _fp }
-    {
-      \tex_ifnum:D \l_fp_output_sign_int > \c_zero
-        +
-      \tex_else:D
-        -
-      \tex_fi:D
-      \int_use:N \l_fp_output_integer_int
-      .
-      \tex_expandafter:D \use_none:n
-        \tex_number:D \etex_numexpr:D
-           \l_fp_output_decimal_int + \c_one_thousand_million
-         \scan_stop:
-      e
-      \int_use:N \l_fp_output_exponent_int
-    }
-}
-\cs_new_protected_nopar:Npn \fp_ln_internal: {
-  \tex_ifnum:D \l_fp_input_a_exponent_int < \c_zero
-    \l_fp_input_a_exponent_int -\l_fp_input_a_exponent_int
-    \l_fp_output_sign_int \c_minus_one
-  \tex_else:D
-    \l_fp_output_sign_int \c_one
-  \tex_fi:D
-  \tex_ifnum:D \l_fp_input_a_exponent_int > \c_nine
-    \tl_set:Nx \l_fp_tmp_tl
-      {
-        \tex_expandafter:D \use_i:nn
-          \int_use:N \l_fp_input_a_exponent_int
-      }
-    \l_fp_input_a_exponent_int
-      \etex_numexpr:D
-        \l_fp_input_a_exponent_int - \l_fp_tmp_tl 0
-      \scan_stop:
-    \fp_ln_const:nn { 10 } { \l_fp_tmp_tl }
-    \tex_advance:D \l_fp_exp_exponent_int \c_one
-    \l_fp_output_integer_int  \l_fp_exp_integer_int
-    \l_fp_output_decimal_int  \l_fp_exp_decimal_int
-    \l_fp_output_extended_int \l_fp_exp_extended_int
-    \l_fp_output_exponent_int \l_fp_exp_exponent_int
-  \tex_else:D
-    \l_fp_output_integer_int  \c_zero
-    \l_fp_output_decimal_int  \c_zero
-    \l_fp_output_extended_int \c_zero
-    \l_fp_output_exponent_int \c_zero
-  \tex_fi:D
-  \fp_ln_exponent_units:
-}
-\cs_new_protected_nopar:Npn \fp_ln_exponent_units: {
-  \tex_ifnum:D \l_fp_input_a_exponent_int > \c_zero
-    \fp_ln_const:nn { 10 } { \int_use:N \l_fp_input_a_exponent_int }
-    \fp_ln_normalise:
-    \fp_add:NNNNNNNNN
-      \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-      \l_fp_output_integer_int \l_fp_output_decimal_int
-        \l_fp_output_extended_int
-  \tex_fi:D
-  \fp_ln_mantissa:
-}
-\cs_new_protected_nopar:Npn \fp_ln_normalise: {
-  \tex_ifnum:D \l_fp_exp_exponent_int < \l_fp_output_exponent_int
-    \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
-    \tex_expandafter:D \use_i:nn \tex_expandafter:D
-      \fp_ln_normalise_aux:NNNNNNNNN
-      \int_use:N \l_fp_exp_decimal_int
-     \tex_expandafter:D \fp_ln_normalise:
-   \tex_fi:D
-}
-\cs_new_protected_nopar:Npn
-  \fp_ln_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  \tex_ifnum:D \l_fp_exp_integer_int = \c_zero
-    \l_fp_exp_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
-  \tex_else:D
-    \tl_set:Nx \l_fp_tmp_tl
-      {
-        \int_use:N \l_fp_exp_integer_int
-        #1#2#3#4#5#6#7#8
-      }
-    \l_fp_exp_integer_int \c_zero
-    \l_fp_exp_decimal_int \l_fp_tmp_tl \scan_stop:
-  \tex_fi:D
-  \tex_divide:D \l_fp_exp_extended_int \c_ten
-  \tl_set:Nx \l_fp_tmp_tl
-    {
-      #9
-      \int_use:N \l_fp_exp_extended_int
-    }
-  \l_fp_exp_extended_int \l_fp_tmp_tl \scan_stop:
-  \tex_advance:D \l_fp_exp_exponent_int \c_one
-}
-\cs_new_protected_nopar:Npn \fp_ln_mantissa: {
-  \l_fp_count_int \c_zero
-  \l_fp_input_a_extended_int \c_zero
-  \fp_ln_mantissa_aux:
-  \tex_ifnum:D \l_fp_count_int > \c_zero
-    \fp_ln_const:nn { 2 } { \int_use:N \l_fp_count_int }
-    \fp_ln_normalise:
-    \tex_ifnum:D \l_fp_output_sign_int > \c_zero
-      \tex_expandafter:D \fp_add:NNNNNNNNN
-    \tex_else:D
-      \tex_expandafter:D \fp_sub:NNNNNNNNN
-    \tex_fi:D
-    \l_fp_output_integer_int \l_fp_output_decimal_int
-      \l_fp_output_extended_int
-    \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
-    \l_fp_output_integer_int \l_fp_output_decimal_int
-      \l_fp_output_extended_int
-  \tex_fi:D
-  \tex_ifnum:D
-    \etex_numexpr:D
-      \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int > \c_one
-    \scan_stop:
-    \tex_expandafter:D \fp_ln_Taylor:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_ln_mantissa_aux: {
-  \tex_ifnum:D \l_fp_input_a_integer_int > \c_one
-    \tex_advance:D \l_fp_count_int \c_one
-    \fp_ln_mantissa_divide_two:
-    \tex_expandafter:D \fp_ln_mantissa_aux:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_ln_mantissa_divide_two: {
-  \tex_ifodd:D \l_fp_input_a_decimal_int
-    \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
-  \tex_fi:D
-  \tex_ifodd:D \l_fp_input_a_integer_int
-    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-  \tex_fi:D
-  \tex_divide:D \l_fp_input_a_integer_int  \c_two
-  \tex_divide:D \l_fp_input_a_decimal_int  \c_two
-  \tex_divide:D \l_fp_input_a_extended_int \c_two
-}
-\cs_new_protected_nopar:Npn \fp_ln_const:nn #1#2 {
-  \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-    \fp_exp_integer_const:nnnn
-    \tex_csname:D c_fp_ln_ #1 _ #2 _tl \tex_endcsname:D
-}
-\cs_new_protected_nopar:Npn \fp_ln_Taylor: {
-  \group_begin:
-    \l_fp_input_a_integer_int \c_zero
-    \l_fp_input_a_exponent_int \c_zero
-    \l_fp_input_b_integer_int \c_two
-    \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
-    \l_fp_input_b_exponent_int \c_zero
-    \fp_div_internal:
-    \fp_ln_fixed:
-    \l_fp_input_a_integer_int  \l_fp_output_integer_int
-    \l_fp_input_a_decimal_int  \l_fp_output_decimal_int
-    \l_fp_input_a_exponent_int \l_fp_output_exponent_int
-    \l_fp_input_a_extended_int \c_zero
-    \l_fp_output_decimal_int \c_zero
-    \l_fp_output_decimal_int  \l_fp_input_a_decimal_int
-    \l_fp_output_extended_int \l_fp_input_a_extended_int
-    \fp_mul:NNNNNN
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-    \l_fp_count_int \c_one
-    \fp_ln_Taylor_aux:
-    \cs_set_protected_nopar:Npx \fp_tmp:w
-      {
-        \group_end:
-        \exp_not:N \l_fp_exp_decimal_int
-          \int_use:N \l_fp_output_decimal_int \scan_stop:
-        \exp_not:N \l_fp_exp_extended_int
-          \int_use:N \l_fp_output_extended_int \scan_stop:
-        \exp_not:N \l_fp_exp_exponent_int
-          \int_use:N \l_fp_output_exponent_int \scan_stop:
-      }
-  \fp_tmp:w
-  \tex_advance:D \l_fp_exp_decimal_int \l_fp_exp_decimal_int
-  \tex_ifnum:D \l_fp_exp_extended_int < \c_five_hundred_million
-  \tex_else:D
-    \tex_advance:D \l_fp_exp_extended_int -\c_five_hundred_million
-    \tex_advance:D \l_fp_exp_decimal_int \c_one
-  \tex_fi:D
-  \tex_advance:D \l_fp_exp_extended_int \l_fp_exp_extended_int
-  \tex_ifnum:D \l_fp_output_sign_int > \c_zero
-    \tex_expandafter:D \fp_add:NNNNNNNNN
-  \tex_else:D
-    \tex_expandafter:D \fp_sub:NNNNNNNNN
-  \tex_fi:D
-  \l_fp_output_integer_int \l_fp_output_decimal_int
-    \l_fp_output_extended_int
-  \c_zero \l_fp_exp_decimal_int \l_fp_exp_extended_int
-  \l_fp_output_integer_int \l_fp_output_decimal_int
-    \l_fp_output_extended_int
-}
-\cs_new_protected_nopar:Npn \fp_ln_fixed: {
-  \tex_ifnum:D \l_fp_output_exponent_int < \c_zero
-    \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
-    \tex_expandafter:D \use_i:nn \tex_expandafter:D
-      \fp_ln_fixed_aux:NNNNNNNNN
-      \int_use:N \l_fp_output_decimal_int
-     \tex_expandafter:D \fp_ln_fixed:
-   \tex_fi:D
-}
-\cs_new_protected_nopar:Npn
-  \fp_ln_fixed_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
-  \tex_ifnum:D \l_fp_output_integer_int = \c_zero
-    \l_fp_output_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
-  \tex_else:D
-    \tl_set:Nx \l_fp_tmp_tl
-      {
-        \int_use:N \l_fp_output_integer_int
-        #1#2#3#4#5#6#7#8
-      }
-    \l_fp_output_integer_int \c_zero
-    \l_fp_output_decimal_int \l_fp_tmp_tl \scan_stop:
-  \tex_fi:D
-  \tex_advance:D \l_fp_output_exponent_int \c_one
-}
-\cs_new_protected_nopar:Npn \fp_ln_Taylor_aux: {
-  \tex_advance:D \l_fp_count_int \c_two
-  \fp_mul:NNNNNN
-    \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-    \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
-    \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-  \tex_ifnum:D
-    \etex_numexpr:D
-      \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
-      > \c_zero
-    \fp_div_integer:NNNNN
-      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
-      \l_fp_count_int
-      \l_fp_exp_decimal_int \l_fp_exp_extended_int
-      \tex_advance:D \l_fp_output_decimal_int \l_fp_exp_decimal_int
-      \tex_advance:D \l_fp_output_extended_int \l_fp_exp_extended_int
-      \tex_ifnum:D \l_fp_output_extended_int < \c_one_thousand_million
-      \tex_else:D
-        \tex_advance:D \l_fp_output_decimal_int \c_one
-        \tex_advance:D \l_fp_output_extended_int
-          -\c_one_thousand_million
-      \tex_fi:D
-      \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
-      \tex_else:D
-        \tex_advance:D \l_fp_output_integer_int \c_one
-        \tex_advance:D \l_fp_output_decimal_int
-          -\c_one_thousand_million
-      \tex_fi:D
-    \tex_expandafter:D \fp_ln_Taylor_aux:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_pow:Nn {
-  \fp_pow_aux:NNn \tl_set:Nn
-}
-\cs_new_protected_nopar:Npn \fp_gpow:Nn {
-  \fp_pow_aux:NNn \tl_gset:Nn
-}
-\cs_generate_variant:Nn \fp_pow:Nn  { c }
-\cs_generate_variant:Nn \fp_gpow:Nn { c }
-\cs_new_protected_nopar:Npn \fp_pow_aux:NNn #1#2#3 {
-  \group_begin:
-    \fp_read:N #2
-    \l_fp_input_b_sign_int     \l_fp_input_a_sign_int
-    \l_fp_input_b_integer_int  \l_fp_input_a_integer_int
-    \l_fp_input_b_decimal_int  \l_fp_input_a_decimal_int
-    \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int
-    \fp_split:Nn a {#3}
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int
-      \l_fp_input_a_decimal_int
-      \l_fp_input_a_exponent_int
-    \tex_ifnum:D
-      \etex_numexpr:D
-        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
-        = \c_zero
-       \tex_ifnum:D
-         \etex_numexpr:D
-           \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-           = \c_zero
-           \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-             {
-               \group_end:
-               ##1 ##2 { \c_undefined_fp }
-             }
-         \tex_else:D
-           \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-             {
-               \group_end:
-               ##1 ##2 { \c_zero_fp }
-             }
-        \tex_fi:D
-     \tex_else:D
-       \tex_ifnum:D
-         \etex_numexpr:D
-           \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
-           = \c_zero
-           \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-             {
-               \group_end:
-               ##1 ##2 { \c_one_fp }
-             }
-         \tex_else:D
-           \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-             \fp_pow_aux_i:
-        \tex_fi:D
-     \tex_fi:D
-  \fp_tmp:w #1 #2
-}
-\cs_new_protected_nopar:Npn \fp_pow_aux_i: {
-  \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero
-    \tl_set:Nn \l_fp_sign_tl { + }
-    \tex_expandafter:D \fp_pow_aux_ii:
-  \tex_else:D
-    \l_fp_input_a_extended_int \c_zero
-    \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
-      \group_begin:
-      \fp_extended_normalise:
-      \tex_ifnum:D
-        \etex_numexpr:D
-          \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
-          = \c_zero
-         \group_end:
-        \tl_set:Nn \l_fp_sign_tl { - }
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \fp_pow_aux_ii:
-      \tex_else:D
-        \group_end:
-        \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-          {
-            \group_end:
-            ##1 ##2 { \c_undefined_fp }
-         }
-      \tex_fi:D
-    \tex_else:D
-      \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-        {
-          \group_end:
-          ##1 ##2 { \c_undefined_fp }
-       }
-    \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_protected_nopar:Npn \fp_pow_aux_ii: {
-  \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
-    \tex_expandafter:D \fp_pow_aux_iv:
-  \tex_else:D
-    \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
-      \group_begin:
-      \l_fp_input_a_extended_int \c_zero
-      \fp_extended_normalise:
-      \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
-        \tex_ifnum:D \l_fp_input_a_integer_int > \c_ten
-          \group_end:
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-            \fp_pow_aux_iv:
-        \tex_else:D
-          \group_end:
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-            \tex_expandafter:D \fp_pow_aux_iii:
-        \tex_fi:D
-      \tex_else:D
-        \group_end:
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-            \tex_expandafter:D \fp_pow_aux_iv:
-      \tex_fi:D
-    \tex_else:D
-      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
-        \fp_pow_aux_iv:
-    \tex_fi:D
-  \tex_fi:D
-  \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
-    {
-      \group_end:
-      ##1 ##2
-        {
-          \l_fp_sign_tl
-          \int_use:N \l_fp_output_integer_int
-          .
-          \tex_expandafter:D \use_none:n
-            \tex_number:D \etex_numexpr:D
-               \l_fp_output_decimal_int + \c_one_thousand_million
-             \scan_stop:
-          e
-          \int_use:N \l_fp_output_exponent_int
-        }
-    }
-}
-\cs_new_protected_nopar:Npn \fp_pow_aux_iii: {
-  \l_fp_input_a_sign_int \c_one
-  \fp_pow_aux_iv:
-  \l_fp_input_a_integer_int  \c_one
-  \l_fp_input_a_decimal_int  \c_zero
-  \l_fp_input_a_exponent_int \c_zero
-  \l_fp_input_b_integer_int  \l_fp_output_integer_int
-  \l_fp_input_b_decimal_int  \l_fp_output_decimal_int
-  \l_fp_input_b_exponent_int \l_fp_output_exponent_int
-  \fp_div_internal:
-}
-\cs_new_protected_nopar:Npn \fp_pow_aux_iv: {
-  \group_begin:
-    \l_fp_input_a_integer_int  \l_fp_input_b_integer_int
-    \l_fp_input_a_decimal_int  \l_fp_input_b_decimal_int
-    \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int
-    \fp_ln_internal:
-    \cs_set_protected_nopar:Npx \fp_tmp:w
-      {
-        \group_end:
-        \exp_not:N \l_fp_input_b_sign_int
-          \int_use:N \l_fp_output_sign_int \scan_stop:
-        \exp_not:N \l_fp_input_b_integer_int
-          \int_use:N \l_fp_output_integer_int \scan_stop:
-        \exp_not:N \l_fp_input_b_decimal_int
-          \int_use:N \l_fp_output_decimal_int \scan_stop:
-        \exp_not:N \l_fp_input_b_extended_int
-          \int_use:N \l_fp_output_extended_int \scan_stop:
-        \exp_not:N \l_fp_input_b_exponent_int
-          \int_use:N \l_fp_output_exponent_int \scan_stop:
-      }
-  \fp_tmp:w
-  \l_fp_input_a_extended_int  \c_zero
-  \fp_mul:NNNNNNNNN
-    \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-      \l_fp_input_a_extended_int
-    \l_fp_input_b_integer_int \l_fp_input_b_decimal_int
-      \l_fp_input_b_extended_int
-    \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
-      \l_fp_input_a_extended_int
-  \tex_advance:D \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int
-  \l_fp_output_integer_int  \c_zero
-  \l_fp_output_decimal_int  \c_zero
-  \l_fp_output_exponent_int \c_zero
-  \cs_set_eq:NN \fp_exp_const:Nx \use_none:nn
-  \fp_exp_internal:
-}
-\prg_new_conditional:Npnn \fp_if_undefined:N #1 { T , F , TF , p } {
-  \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 { T , F , TF , p } {
-  \tex_ifx:D #1 \c_zero_fp
-    \prg_return_true:
-  \tex_else:D
-    \prg_return_false:
-  \tex_fi:D
-}
-\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3
-  { T , F , TF }
-  {
-  \group_begin:
-    \fp_split:Nn a {#1}
-    \fp_standardise:NNNN
-      \l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int
-      \l_fp_input_a_decimal_int
-      \l_fp_input_a_exponent_int
-    \fp_split:Nn b {#3}
-    \fp_standardise:NNNN
-      \l_fp_input_b_sign_int
-      \l_fp_input_b_integer_int
-      \l_fp_input_b_decimal_int
-      \l_fp_input_b_exponent_int
-    \fp_compare_aux:N #2
-}
-\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3
-  { T , F , TF }
-  {
-  \group_begin:
-    \fp_read:N #3
-    \l_fp_input_b_sign_int     \l_fp_input_a_sign_int
-    \l_fp_input_b_integer_int  \l_fp_input_a_integer_int
-    \l_fp_input_b_decimal_int  \l_fp_input_a_decimal_int
-    \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int
-    \fp_read:N #1
-    \fp_compare_aux:N #2
-}
-\cs_new_protected_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
-        \tex_ifnum:D
-          \l_fp_input_a_exponent_int = \l_fp_input_b_exponent_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
-  \tex_else:D
-    \group_end:
-    \prg_return_false:
-  \tex_fi:D
-}
-\cs_new_protected_nopar:cpn { fp_compare_>: } {
-  \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
-      \group_end:
-      \prg_return_false:
-    \tex_else:D
-      \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero
-        \group_end:
-        \prg_return_false:
-      \tex_else:D
-        \group_end:
-        \prg_return_true:
-      \tex_fi:D
-    \tex_fi:D
-  \tex_else:D
-    \tex_ifnum:D \etex_numexpr:D
-      \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
-      = \c_zero
-      \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
-        \group_end:
-        \prg_return_true:
-      \tex_else:D
-        \group_end:
-        \prg_return_false:
-      \tex_fi:D
-    \tex_else:D
-      \use:c { fp_compare_>_aux: }
-    \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_protected_nopar:cpn { fp_compare_>_aux: } {
-  \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_absolute_a>b: } {
-  \tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
-    \group_end:
-    \prg_return_true:
-  \tex_else:D
-    \tex_ifnum:D \l_fp_input_a_exponent_int < \l_fp_input_b_exponent_int
-      \group_end:
-      \prg_return_false:
-    \tex_else:D
-      \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
-    \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_protected_nopar:cpn { fp_compare_absolute_a<b: } {
-  \tex_ifnum:D \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int
-    \group_end:
-    \prg_return_true:
-  \tex_else:D
-    \tex_ifnum:D \l_fp_input_b_exponent_int < \l_fp_input_a_exponent_int
-      \group_end:
-      \prg_return_false:
-    \tex_else:D
-      \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
-    \tex_fi:D
-  \tex_fi:D
-}
-\cs_new_protected_nopar:cpn { fp_compare_<: } {
-  \tl_set:Nx \l_fp_tmp_tl
-    {
-      \int_set:Nn \exp_not:N \l_fp_input_a_sign_int
-        { \int_use:N \l_fp_input_b_sign_int }
-      \int_set:Nn \exp_not:N \l_fp_input_a_integer_int
-        { \int_use:N \l_fp_input_b_integer_int }
-      \int_set:Nn \exp_not:N \l_fp_input_a_decimal_int
-        { \int_use:N \l_fp_input_b_decimal_int }
-      \int_set:Nn \exp_not:N \l_fp_input_a_exponent_int
-        { \int_use:N \l_fp_input_b_exponent_int }
-      \int_set:Nn \exp_not:N \l_fp_input_b_sign_int
-        { \int_use:N \l_fp_input_a_sign_int }
-      \int_set:Nn \exp_not:N \l_fp_input_b_integer_int
-        { \int_use:N \l_fp_input_a_integer_int }
-      \int_set:Nn \exp_not:N \l_fp_input_b_decimal_int
-        { \int_use:N \l_fp_input_a_decimal_int }
-      \int_set:Nn \exp_not:N \l_fp_input_b_exponent_int
-        { \int_use:N \l_fp_input_a_exponent_int }
-    }
-  \l_fp_tmp_tl
-  \use:c { fp_compare_>: }
-}
-\msg_kernel_new:nnnn { fpu } { overflow }
-  { Number~too~big. }
-  {
-    The~input~given~is~too~big~for~the~LaTeX~floating~point~unit. \\
-    Further~errors~may~well~occur!
-  }
-\cs_new_protected_nopar:Npn \fp_overflow_msg: {
-  \msg_kernel_error:nn { fpu } { overflow }
-}
-\msg_kernel_new:nnnn { fpu } { exponent-overflow }
-  { Number~too~big~for~exponent~unit. }
-  {
-    The~exponent~of~the~input~given~is~too~big~for~the~floating~point~
-    unit:~the~maximum~input~value~for~an~exponent~is~230.
-  }
-\cs_new_protected_nopar:Npn \fp_exp_overflow_msg: {
-  \msg_kernel_error:nn { fpu } { exponent-overflow }
-}
-\msg_kernel_new:nnnn { fpu } { logarithm-input-error }
-  { Invalid~input~to~ln~function. }
-  { Logarithms~can~only~be~calculated~for~positive~numbers. }
-\cs_new_protected_nopar:Npn \fp_ln_error_msg: {
-  \msg_kernel_error:nn { fpu } { logarithm-input-error }
-}
-\msg_kernel_new:nnnn { fpu } { trigonometric-overflow }
-  { Number~too~big~for~trigonometry~unit. }
-  {
-    The~trigonometry~code~can~only~work~with~numbers~smaller~
-    than~1000000000.
-  }
-\cs_new_protected_nopar:Npn \fp_trig_overflow_msg: {
-  \msg_kernel_error:nn { fpu } { trigonometric-overflow }
-}
-%% 
-%%
-%% End of file `l3fp.sty'.