%%
%% This is file `l3fp.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% l3fp.dtx  (with options: `package')
%% l3fp-aux.dtx  (with options: `package')
%% l3fp-traps.dtx  (with options: `package')
%% l3fp-round.dtx  (with options: `package')
%% l3fp-parse.dtx  (with options: `package')
%% l3fp-logic.dtx  (with options: `package')
%% l3fp-basics.dtx  (with options: `package')
%% l3fp-extended.dtx  (with options: `package')
%% l3fp-expo.dtx  (with options: `package')
%% l3fp-trig.dtx  (with options: `package')
%% l3fp-convert.dtx  (with options: `package')
%% l3fp-assign.dtx  (with options: `package')
%% l3fp-old.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) 2011-2012 The 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 "l3kernel 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 LaTeX3 Project Team.
%%
%% -----------------------------------------------------------------------
%%
\RequirePackage{l3bootstrap}
\GetIdInfo$Id: l3fp.dtx 4151 2012-08-28 11:51:52Z bruno $
  {L3 Floating points}
\ProvidesExplPackage
  {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
\__expl_package_check:
%% File: l3fp-aux.dtx Copyright(C) 2011-2012 The 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 "l3kernel 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.
%%
%% -----------------------------------------------------------------------
%%
\cs_new:Npn \__fp_use_none_stop_f:n #1 { \exp_stop_f: }
\cs_new:Npn \__fp_use_s:n #1 { #1; }
\cs_new:Npn \__fp_use_s:nn #1#2 { #1#2; }
\cs_new:Npn \__fp_use_none_until_s:w #1; { }
\cs_new:Npn \__fp_use_i_until_s:nw #1#2; {#1}
\cs_new:Npn \__fp_use_ii_until_s:nnw #1#2#3; {#2}
\cs_new:Npn \__fp_reverse_args:Nww #1 #2; #3; { #1 #3; #2; }
\__scan_new:N \s__fp
\cs_new_protected:Npn \__fp_chk:w #1 ;
  {
    \__msg_kernel_error:nnx { kernel } { misused-fp }
      { \fp_to_tl:n { \s__fp \__fp_chk:w #1 ; } }
  }
\__scan_new:N \s__fp_mark
\__scan_new:N \s__fp_stop
\__scan_new:N \s__fp_invalid
\__scan_new:N \s__fp_underflow
\__scan_new:N \s__fp_overflow
\__scan_new:N \s__fp_division
\__scan_new:N \s__fp_exact
\tl_const:Nn \c_zero_fp       { \s__fp \__fp_chk:w 0 0 \s__fp_exact ; }
\tl_const:Nn \c_minus_zero_fp { \s__fp \__fp_chk:w 0 2 \s__fp_exact ; }
\tl_const:Nn \c_inf_fp        { \s__fp \__fp_chk:w 2 0 \s__fp_exact ; }
\tl_const:Nn \c_minus_inf_fp  { \s__fp \__fp_chk:w 2 2 \s__fp_exact ; }
\tl_const:Nn \c_nan_fp        { \s__fp \__fp_chk:w 3 1 \s__fp_exact ; }
\int_const:Nn \c__fp_max_exponent_int { 10000 }
\cs_new:Npn \__fp_zero_fp:N #1 { \s__fp \__fp_chk:w 0 #1 \s__fp_underflow ; }
\cs_new:Npn \__fp_inf_fp:N #1  { \s__fp \__fp_chk:w 2 #1 \s__fp_overflow ; }
\cs_new:Npn \__fp_min_fp:N #1
  {
    \s__fp \__fp_chk:w 1 #1
      { \int_eval:n { - \c__fp_max_exponent_int } }
      {1000} {0000} {0000} {0000} ;
  }
\cs_new:Npn \__fp_max_fp:N #1
  {
    \s__fp \__fp_chk:w 1 #1
      { \int_use:N \c__fp_max_exponent_int }
      {9999} {9999} {9999} {9999} ;
  }
\cs_new:Npn \__fp_exponent:w \s__fp \__fp_chk:w #1
  {
    \if_meaning:w 1 #1
      \exp_after:wN \__fp_use_ii_until_s:nnw
    \else:
      \exp_after:wN \__fp_use_i_until_s:nw
      \exp_after:wN 0
    \fi:
  }
\cs_new:Npn \__fp_neg_sign:N #1
  { \__int_eval:w \c_two - #1 \__int_eval_end: }
\cs_new:Npn \__fp_sanitize:Nw #1 #2;
  {
    \if_case:w \if_int_compare:w #2 > \c__fp_max_exponent_int \c_one \else:
               \if_int_compare:w #2 < - \c__fp_max_exponent_int \c_two \else:
               \if_meaning:w 1 #1 \c_three \else: \c_zero \fi: \fi: \fi:
    \or: \exp_after:wN \__fp_overflow:w
    \or: \exp_after:wN \__fp_underflow:w
    \or: \exp_after:wN \__fp_sanitize_zero:w
    \fi:
    \s__fp \__fp_chk:w 1 #1 {#2}
  }
\cs_new:Npn \__fp_sanitize:wN #1; #2 { \__fp_sanitize:Nw #2 #1; }
\cs_new:Npn \__fp_sanitize_zero:w \s__fp \__fp_chk:w #1 #2 #3; { \c_zero_fp }
\cs_new:Npn \__fp_exp_after_o:w \s__fp \__fp_chk:w #1
  {
    \if_meaning:w 1 #1
      \exp_after:wN \__fp_exp_after_normal:nNNw
    \else:
      \exp_after:wN \__fp_exp_after_special:nNNw
    \fi:
    { }
    #1
  }
\cs_new:Npn \__fp_exp_after_o:nw #1 \s__fp \__fp_chk:w #2
  {
    \if_meaning:w 1 #2
      \exp_after:wN \__fp_exp_after_normal:nNNw
    \else:
      \exp_after:wN \__fp_exp_after_special:nNNw
    \fi:
    { #1 }
    #2
  }
\cs_new:Npn \__fp_exp_after_f:nw #1 \s__fp \__fp_chk:w #2
  {
    \if_meaning:w 1 #2
      \exp_after:wN \__fp_exp_after_normal:nNNw
    \else:
      \exp_after:wN \__fp_exp_after_special:nNNw
    \fi:
    { \tex_romannumeral:D -`0 #1 }
    #2
  }
\cs_new:Npn \__fp_exp_after_special:nNNw #1#2#3#4;
  {
    \exp_after:wN \s__fp
    \exp_after:wN \__fp_chk:w
    \exp_after:wN #2
    \exp_after:wN #3
    \exp_after:wN #4
    \exp_after:wN ;
    #1
  }
\cs_new:Npn \__fp_exp_after_normal:nNNw #1 1 #2 #3 #4#5#6#7;
  {
    \exp_after:wN \__fp_exp_after_normal:Nwwwww
    \exp_after:wN #2
    \__int_value:w #3   \exp_after:wN ;
    \__int_value:w 1 #4 \exp_after:wN ;
    \__int_value:w 1 #5 \exp_after:wN ;
    \__int_value:w 1 #6 \exp_after:wN ;
    \__int_value:w 1 #7 \exp_after:wN ; #1
  }
\cs_new:Npn \__fp_exp_after_normal:Nwwwww
    #1 #2; 1 #3 ; 1 #4 ; 1 #5 ; 1 #6 ;
  { \s__fp \__fp_chk:w 1 #1 {#2} {#3} {#4} {#5} {#6} ; }
\cs_new:Npn \__fp_exp_after_array_f:w #1
  {
    \cs:w __fp_exp_after \__fp_type_from_scan:N #1 _f:nw \cs_end:
      { \__fp_exp_after_array_f:w }
    #1
  }
\cs_new_eq:NN \__fp_exp_after_stop_f:nw \use_none:nn
\int_const:Nn \c__fp_leading_shift_int  { - 5 0000 }
\int_const:Nn \c__fp_middle_shift_int   { 5 0000 *  9999 }
\int_const:Nn \c__fp_trailing_shift_int { 5 0000 * 10000 }
\cs_new:Npn \__fp_pack:NNNNNw #1 #2#3#4#5 #6; { + #1#2#3#4#5 ; {#6} }
\cs_new:Npn \__fp_pack:NNNNNwn #1 #2#3#4#5 #6; #7
  { + #1#2#3#4#5 ; {#7} {#6} }
\int_const:Nn \c__fp_big_leading_shift_int  { - 15 2374 }
\int_const:Nn \c__fp_big_middle_shift_int   { 15 2374 *  9999 }
\int_const:Nn \c__fp_big_trailing_shift_int { 15 2374 * 10000 }
\cs_new:Npn \__fp_pack_big:NNNNNNw #1#2 #3#4#5#6 #7;
  { + #1#2#3#4#5#6 ; {#7} }
\cs_new:Npn \__fp_pack_big:NNNNNNwn #1#2 #3#4#5#6 #7; #8
  { + #1#2#3#4#5#6 ; {#8} {#7} }
\int_const:Nn \c__fp_Bigg_leading_shift_int  { - 20 0000 }
\int_const:Nn \c__fp_Bigg_middle_shift_int   { 20 0000 *  9999 }
\int_const:Nn \c__fp_Bigg_trailing_shift_int { 20 0000 * 10000 }
\cs_new:Npn \__fp_pack_Bigg:NNNNNNw #1#2 #3#4#5#6 #7;
  { + #1#2#3#4#5#6 ; {#7} }
\cs_new:Npn \__fp_pack_twice_four:wNNNNNNNN #1; #2#3#4#5 #6#7#8#9
  { #1 {#2#3#4#5} {#6#7#8#9} ; }
\cs_new:Npn \__fp_pack_eight:wNNNNNNNN #1; #2#3#4#5 #6#7#8#9
  { #1 {#2#3#4#5#6#7#8#9} ; }
\cs_new:Npn \__fp_decimate:nNnnnn #1
  {
    \cs:w
      __fp_decimate_
      \if_int_compare:w \__int_eval:w #1 > \c_sixteen
        tiny
      \else:
        \tex_romannumeral:D \__int_eval:w #1
      \fi:
      :Nnnnn
    \cs_end:
  }
\cs_new:Npn \__fp_decimate_:Nnnnn #1 #2#3#4#5
  { #1 0 {#2#3} {#4#5} ; }
\cs_new:Npn \__fp_decimate_tiny:Nnnnn #1 #2#3#4#5
  { #1 1 { 0000 0000 } { 0000 0000 } 0 #2#3#4#5 ; }
\cs_new:Npn \__fp_tmp:w #1 #2 #3
  {
    \cs_new:cpn { __fp_decimate_ #1 :Nnnnn } ##1 ##2##3##4##5
      {
        \exp_after:wN ##1
        \__int_value:w
          \exp_after:wN \__fp_round_digit:Nw #2 ;
        \__fp_decimate_pack:nnnnnnnnnnw #3 ;
      }
  }
\__fp_tmp:w {i}   {\use_none:nnn      #50} {    0{#2}#3{#4}#5                }
\__fp_tmp:w {ii}  {\use_none:nn       #5 } {    00{#2}#3{#4}#5               }
\__fp_tmp:w {iii} {\use_none:n        #5 } {    000{#2}#3{#4}#5              }
\__fp_tmp:w {iv}  {                   #5 } {   {0000}#2{#3}#4 #5             }
\__fp_tmp:w {v}   {\use_none:nnn    #4#5 } {   0{0000}#2{#3}#4 #5            }
\__fp_tmp:w {vi}  {\use_none:nn     #4#5 } {   00{0000}#2{#3}#4 #5           }
\__fp_tmp:w {vii} {\use_none:n      #4#5 } {   000{0000}#2{#3}#4 #5          }
\__fp_tmp:w {viii}{                 #4#5 } {  {0000}0000{#2}#3 #4 #5         }
\__fp_tmp:w {ix}  {\use_none:nnn  #3#4+#5} {  0{0000}0000{#2}#3 #4 #5        }
\__fp_tmp:w {x}   {\use_none:nn   #3#4+#5} {  00{0000}0000{#2}#3 #4 #5       }
\__fp_tmp:w {xi}  {\use_none:n    #3#4+#5} {  000{0000}0000{#2}#3 #4 #5      }
\__fp_tmp:w {xii} {               #3#4+#5} { {0000}0000{0000}#2 #3 #4 #5     }
\__fp_tmp:w {xiii}{\use_none:nnn#2#3+#4#5} { 0{0000}0000{0000}#2 #3 #4 #5    }
\__fp_tmp:w {xiv} {\use_none:nn #2#3+#4#5} { 00{0000}0000{0000}#2 #3 #4 #5   }
\__fp_tmp:w {xv}  {\use_none:n  #2#3+#4#5} { 000{0000}0000{0000}#2 #3 #4 #5  }
\__fp_tmp:w {xvi} {             #2#3+#4#5} {{0000}0000{0000}0000 #2 #3 #4 #5 }
\cs_new:Npn \__fp_decimate_pack:nnnnnnnnnnw #1#2#3#4#5
  { \__fp_decimate_pack_ii:nnnnnnw { #1#2#3#4#5 } }
\cs_new:Npn \__fp_decimate_pack_ii:nnnnnnw #1 #2#3#4#5#6
  { {#1} {#2#3#4#5#6} }
\cs_new:Npn \__fp_case_use:nw #1#2 \fi: #3 \s__fp { \fi: #1 \s__fp }
\cs_new:Npn \__fp_case_return:nw #1#2 \fi: #3 ; { \fi: #1 }
\cs_new:Npn \__fp_case_return_o:Nw #1#2 \fi: #3 \s__fp #4 ;
  { \fi: \exp_after:wN #1 }
\cs_new:Npn \__fp_case_return_same_o:w #1 \fi: #2 \s__fp
  { \fi: \__fp_exp_after_o:w \s__fp }
\cs_new:Npn \__fp_case_return_o:Nww #1#2 \fi: #3 \s__fp #4 ; #5 ;
  { \fi: \exp_after:wN #1 }
\cs_new:Npn \__fp_case_return_i_o:ww #1 \fi: #2 \s__fp #3 ; \s__fp #4 ;
  { \fi: \__fp_exp_after_o:w \s__fp #3 ; }
\cs_new:Npn \__fp_case_return_ii_o:ww #1 \fi: #2 \s__fp #3 ;
  { \fi: \__fp_exp_after_o:w }
\cs_new:Npn \__fp_small_int:wTF \s__fp \__fp_chk:w #1
  {
    \if_case:w #1 \exp_stop_f:
           \__fp_case_return:nw { \__fp_small_int_true:wTF 0 ; }
    \or:   \exp_after:wN \__fp_small_int_normal:NnwTF
    \else: \__fp_case_return:nw \use_ii:nn
    \fi:
  }
\cs_new:Npn \__fp_small_int_true:wTF #1; #2#3 { #2 {#1} }
\cs_new:Npn \__fp_small_int_normal:NnwTF #1#2#3;
  {
    \if_int_compare:w #2 > \c_zero
      \if_int_compare:w #2 > \c_eight
        \exp_after:wN \exp_after:wN
        \exp_after:wN \use_iii:nnn
      \else:
        \__fp_decimate:nNnnnn { \c_sixteen - #2 }
          \__fp_small_int_test:NnnwNTF
          #3 #1
      \fi:
    \else:
      \exp_after:wN \use_iii:nnn
    \fi:
    ;
  }
\cs_new:Npn \__fp_small_int_test:NnnwNTF #1#2#3#4; #5
  {
    \if_meaning:w 0 #1
      \exp_after:wN \__fp_small_int_true:wTF
      \__int_value:w \if_meaning:w 2 #5 - \fi: #3
    \else:
      \exp_after:wN \use_i:nn
    \fi:
  }
\cs_new:Npn \__fp_array_count:n #1
  {
    \int_use:N \__int_eval:w \c_zero
      \__fp_array_count_loop:Nw #1 { ? \__prg_break: } ;
      \__prg_break_point:
    \__int_eval_end:
  }
\cs_new:Npn \__fp_array_count_loop:Nw #1#2;
  { \use_none:n #1 + \c_one \__fp_array_count_loop:Nw }
\cs_new:Npn \__fp_expand:n #1
  {
    \__fp_expand_loop:nwnN { }
      #1 \prg_do_nothing:
      \s__fp_mark { } \__fp_expand_loop:nwnN
      \s__fp_mark { } \__fp_use_i_until_s:nw ;
  }
\cs_new:Npn \__fp_expand_loop:nwnN #1#2 \s__fp_mark #3 #4
  {
    \exp_after:wN #4 \tex_romannumeral:D -`0
    #2
    \s__fp_mark { #3 #1 } #4
  }
\__msg_kernel_new:nnnn { kernel } { misused-fp }
  { A~floating~point~with~value~'#1'~was~misused. }
  {
    To~obtain~the~value~of~a~floating~point~variable,~use~
    '\token_to_str:N \fp_to_decimal:N',~
    '\token_to_str:N \fp_to_scientific:N',~or~other~
    conversion~functions.
  }
%%
%% File: l3fp-traps.dtx Copyright (C) 2011-2012 The 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 "l3kernel 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.
%%
%% -----------------------------------------------------------------------
%%
\cs_new_protected:Npn \fp_flag_off:n #1
  { \cs_set_eq:cN { l__fp_ #1 _flag_token } \c_undefined:D }
\cs_new:Npn \fp_flag_on:n #1
  { \exp_args:Nc \use_none:n { l__fp_ #1 _flag_token } }
\prg_new_conditional:Npnn \fp_if_flag_on:n #1 { p , T , F , TF }
  {
    \if_cs_exist:w l__fp_ #1 _flag_token \cs_end:
      \prg_return_true:
    \else:
      \prg_return_false:
    \fi:
  }
\cs_new_eq:NN \l__fp_invalid_operation_flag_token \c_undefined:D
\cs_new_eq:NN \l__fp_division_by_zero_flag_token \c_undefined:D
\cs_new_eq:NN \l__fp_overflow_flag_token \c_undefined:D
\cs_new_eq:NN \l__fp_underflow_flag_token \c_undefined:D
\cs_new_protected:Npn \fp_trap:nn #1#2
  {
    \cs_if_exist_use:cF { __fp_trap_#1_set_#2: }
      {
        \clist_if_in:nnTF
          { invalid_operation , division_by_zero , overflow , underflow }
          {#1}
          {
            \__msg_kernel_error:nnxx { kernel }
              { unknown-fpu-trap-type } {#1} {#2}
          }
          { \__msg_kernel_error:nnx { kernel } { unknown-fpu-exception } {#1} }
      }
  }
\cs_new_protected_nopar:Npn \__fp_trap_invalid_operation_set_error:
  { \__fp_trap_invalid_operation_set:N \prg_do_nothing: }
\cs_new_protected_nopar:Npn \__fp_trap_invalid_operation_set_flag:
  { \__fp_trap_invalid_operation_set:N \use_none:nnnnn }
\cs_new_protected_nopar:Npn \__fp_trap_invalid_operation_set_none:
  { \__fp_trap_invalid_operation_set:N \use_none:nnnnnnn }
\cs_new_protected:Npn \__fp_trap_invalid_operation_set:N #1
  {
    \exp_args:Nno \use:n
      { \cs_set:Npn \__fp_invalid_operation:nnw ##1##2##3; }
      {
        #1
        \__fp_error:nnfn { invalid } {##2} { \fp_to_tl:n { ##3; } } { }
        \fp_flag_on:n { invalid_operation }
        ##1
      }
    \exp_args:Nno \use:n
      { \cs_set:Npn \__fp_invalid_operation_o:Nww ##1##2; ##3; }
      {
        #1
        \__fp_error:nffn { invalid-ii }
          { \fp_to_tl:n { ##2; } } { \fp_to_tl:n { ##3; } } {##1}
        \fp_flag_on:n { invalid_operation }
        \exp_after:wN \c_nan_fp
      }
    \exp_args:Nno \use:n
      { \cs_set:Npn \__fp_invalid_operation_tl_o:nf ##1##2 }
      {
        #1
        \__fp_error:nnfn { invalid } {##1} {##2} { }
        \fp_flag_on:n { invalid_operation }
        \exp_after:wN \c_nan_fp
      }
  }
\cs_new_protected_nopar:Npn \__fp_trap_division_by_zero_set_error:
  { \__fp_trap_division_by_zero_set:N \prg_do_nothing: }
\cs_new_protected_nopar:Npn \__fp_trap_division_by_zero_set_flag:
  { \__fp_trap_division_by_zero_set:N \use_none:nnnnn }
\cs_new_protected_nopar:Npn \__fp_trap_division_by_zero_set_none:
  { \__fp_trap_division_by_zero_set:N \use_none:nnnnnnn }
\cs_new_protected:Npn \__fp_trap_division_by_zero_set:N #1
  {
    \exp_args:Nno \use:n
      { \cs_set:Npn \__fp_division_by_zero_o:Nnw ##1##2##3; }
      {
        #1
        \__fp_error:nnfn { zero-div } {##2} { \fp_to_tl:n { ##3; } } { }
        \fp_flag_on:n { division_by_zero }
        \exp_after:wN ##1
      }
    \exp_args:Nno \use:n
      { \cs_set:Npn \__fp_division_by_zero_o:NNww ##1##2##3; ##4; }
      {
        #1
        \__fp_error:nffn { zero-div-ii }
          { \fp_to_tl:n { ##3; } } { \fp_to_tl:n { ##4; } } {##2}
        \fp_flag_on:n { division_by_zero }
        \exp_after:wN ##1
      }
  }
\cs_new_protected_nopar:Npn \__fp_trap_overflow_set_error:
  { \__fp_trap_overflow_set:N \prg_do_nothing: }
\cs_new_protected_nopar:Npn \__fp_trap_overflow_set_flag:
  { \__fp_trap_overflow_set:N \use_none:nnnnn }
\cs_new_protected_nopar:Npn \__fp_trap_overflow_set_none:
  { \__fp_trap_overflow_set:N \use_none:nnnnnnn }
\cs_new_protected:Npn \__fp_trap_overflow_set:N #1
  { \__fp_trap_overflow_set:NnNn #1 { overflow } \__fp_inf_fp:N { inf } }
\cs_new_protected_nopar:Npn \__fp_trap_underflow_set_error:
  { \__fp_trap_underflow_set:N \prg_do_nothing: }
\cs_new_protected_nopar:Npn \__fp_trap_underflow_set_flag:
  { \__fp_trap_underflow_set:N \use_none:nnnnn }
\cs_new_protected_nopar:Npn \__fp_trap_underflow_set_none:
  { \__fp_trap_underflow_set:N \use_none:nnnnnnn }
\cs_new_protected:Npn \__fp_trap_underflow_set:N #1
  { \__fp_trap_overflow_set:NnNn #1 { underflow } \__fp_zero_fp:N { 0 } }
\cs_new_protected:Npn \__fp_trap_overflow_set:NnNn #1#2#3#4
  {
    \exp_args:Nno \use:n
      { \cs_set:cpn { __fp_ #2 :w } \s__fp \__fp_chk:w ##1##2##3; }
      {
        #1
        \__fp_error:nffn
          { flow \if_meaning:w 1 ##1 -to \fi: }
          { \fp_to_tl:n { \s__fp \__fp_chk:w ##1##2##3; } }
          { \token_if_eq_meaning:NNF 0 ##2 { - } #4 }
          {#2}
        \fp_flag_on:n {#2}
        #3 ##2
      }
  }
\cs_new:Npn \__fp_invalid_operation:nnw #1#2#3; { }
\cs_new:Npn \__fp_invalid_operation_o:Nww #1#2; #3; { }
\cs_new:Npn \__fp_invalid_operation_tl_o:nf #1 #2 { }
\cs_new:Npn \__fp_division_by_zero_o:Nnw #1#2#3; { }
\cs_new:Npn \__fp_division_by_zero_o:NNww #1#2#3; #4; { }
\cs_new:Npn \__fp_overflow:w { }
\cs_new:Npn \__fp_underflow:w { }
\fp_trap:nn { invalid_operation } { error }
\fp_trap:nn { division_by_zero } { flag }
\fp_trap:nn { overflow } { flag }
\fp_trap:nn { underflow } { flag }
\cs_new_nopar:Npn \__fp_invalid_operation_o:nw
  { \__fp_invalid_operation:nnw { \exp_after:wN \c_nan_fp } }
\cs_new:Npn \__fp_error:nnnn #1
  { \__msg_kernel_expandable_error:nnnnn { kernel } { fp - #1 } }
\cs_generate_variant:Nn \__fp_error:nnnn { nnf, nff }
\__msg_kernel_new:nnnn { kernel } { unknown-fpu-exception }
  { The~FPU~exception~'#1'~is~not~known:~that~trap~will~never~be~triggered. }
  {
    The~only~exceptions~to~which~traps~can~be~attached~are \\
    \iow_indent:n
      {
        * ~ invalid_operation \\
        * ~ division_by_zero \\
        * ~ overflow \\
        * ~ underflow
      }
  }
\__msg_kernel_new:nnnn { kernel } { unknown-fpu-trap-type }
  { The~FPU~trap~type~'#2'~is~not~known. }
  {
    The~trap~type~must~be~one~of \\
    \iow_indent:n
      {
        * ~ error \\
        * ~ flag \\
        * ~ none
      }
  }
\__msg_kernel_new:nnn { kernel } { fp-flow }
  { An ~ #3 ~ occurred. }
\__msg_kernel_new:nnn { kernel } { fp-flow-to }
  { #1 ~ #3 ed ~ to ~ #2 . }
\__msg_kernel_new:nnn { kernel } { fp-zero-div }
  { Division~by~zero~in~ #1 (#2) }
\__msg_kernel_new:nnn { kernel } { fp-zero-div-ii }
  { Division~by~zero~in~ (#1) #3 (#2) }
\__msg_kernel_new:nnn { kernel } { fp-invalid }
  { Invalid~operation~ #1 (#2) }
\__msg_kernel_new:nnn { kernel } { fp-invalid-ii }
  { Invalid~operation~ (#1) #3 (#2) }
%% File: l3fp-round.dtx Copyright(C) 2011-2012 The 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 "l3kernel 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.
%%
%% -----------------------------------------------------------------------
%%
\cs_new:Npn \__fp_round_return_one:
  { \exp_after:wN \c_one \tex_romannumeral:D }
\cs_new:Npn \__fp_round_to_ninf:NNN #1 #2 #3
  {
    \if_meaning:w 2 #1
      \if_int_compare:w #3 > \c_zero
        \__fp_round_return_one:
      \fi:
    \fi:
    \c_zero
  }
\cs_new:Npn \__fp_round_to_zero:NNN #1 #2 #3 { \c_zero }
\cs_new:Npn \__fp_round_to_pinf:NNN #1 #2 #3
  {
    \if_meaning:w 0 #1
      \if_int_compare:w #3 > \c_zero
        \__fp_round_return_one:
      \fi:
    \fi:
    \c_zero
  }
\cs_new:Npn \__fp_round_to_nearest:NNN #1 #2 #3
  {
    \if_int_compare:w #3 > \c_five
      \__fp_round_return_one:
    \else:
      \if_meaning:w 5 #3
        \if_int_odd:w #2 \exp_stop_f:
          \__fp_round_return_one:
        \fi:
      \fi:
    \fi:
    \c_zero
  }
\cs_new_eq:NN \__fp_round:NNN \__fp_round_to_nearest:NNN
\cs_new:Npn \__fp_round_s:NNNw #1 #2 #3 #4;
  {
    \exp_after:wN \__fp_round:NNN
    \exp_after:wN #1
    \exp_after:wN #2
    \int_use:N \__int_eval:w
      \if_int_odd:w 0 \if_meaning:w 0 #3 1 \fi:
                      \if_meaning:w 5 #3 1 \fi:
                \exp_stop_f:
        \if_int_compare:w \__int_eval:w #4 > \c_zero
          1 +
        \fi:
      \fi:
      #3
    ;
  }
\cs_new:Npn \__fp_round_digit:Nw #1 #2;
  {
    \if_int_odd:w \if_meaning:w 0 #1 \c_one \else:
                  \if_meaning:w 5 #1 \c_one \else:
                  \c_zero \fi: \fi:
      \if_int_compare:w \__int_eval:w #2 > \c_zero
        \__int_eval:w \c_one +
      \fi:
    \fi:
    #1
  }
\cs_new:Npn \__fp_round_to_ninf_neg:NNN #1 #2 #3
  {
    \if_meaning:w 0 #1
      \if_int_compare:w #3 > \c_zero
        \__fp_round_return_one:
      \fi:
    \fi:
    \c_zero
  }
\cs_new:Npn \__fp_round_to_zero_neg:NNN #1 #2 #3
  {
    \if_int_compare:w #3 > \c_zero
      \__fp_round_return_one:
    \fi:
    \c_zero
  }
\cs_new:Npn \__fp_round_to_pinf_neg:NNN #1 #2 #3
  {
    \if_meaning:w 2 #1
      \if_int_compare:w #3 > \c_zero
        \__fp_round_return_one:
      \fi:
    \fi:
    \c_zero
  }
\cs_new_eq:NN \__fp_round_to_nearest_neg:NNN \__fp_round_to_nearest:NNN
\cs_new_eq:NN \__fp_round_neg:NNN \__fp_round_to_nearest_neg:NNN
\cs_new:Npn \__fp_round:Nww #1#2 ; #3 ;
  {
    \__fp_small_int:wTF #3; { \__fp_round:Nwn #1#2; }
      {
        \__fp_invalid_operation_tl_o:nf
          { round } { \__fp_array_to_clist:n { #2; #3; } }
      }
  }
\cs_new:Npn \__fp_round:Nwn #1 \s__fp \__fp_chk:w #2#3#4; #5
  {
    \if_meaning:w 1 #2
      \exp_after:wN \__fp_round_normal:NwNNnw
      \exp_after:wN #1
      \__int_value:w #5
    \else:
      \exp_after:wN \__fp_exp_after_o:w
    \fi:
    \s__fp \__fp_chk:w #2#3#4;
  }
\cs_new:Npn \__fp_round_normal:NwNNnw #1#2 \s__fp \__fp_chk:w 1#3#4#5;
  {
    \__fp_decimate:nNnnnn { \c_sixteen - #4 - #2 }
      \__fp_round_normal_ii:NnnwNNnn #5 #1 #3 {#4} {#2}
  }
\cs_new:Npn \__fp_round_normal_ii:NnnwNNnn #1#2#3#4; #5#6
  {
    \exp_after:wN \__fp_round_normal_iii:NNwNnn
    \int_use:N \__int_eval:w
      \if_int_compare:w #2 > \c_zero
        1 \__int_value:w #2
        \exp_after:wN \__fp_round_pack:Nw
        \int_use:N \__int_eval:w 1#3 +
      \else:
        \if_int_compare:w #3 > \c_zero
          1 \__int_value:w #3 +
        \fi:
      \fi:
      \exp_after:wN #5
      \exp_after:wN #6
      \use_none:nnnnnnn #3
      #1
      \__int_eval_end:
      0000 0000 0000 0000 ; #6
  }
\cs_new:Npn \__fp_round_pack:Nw #1
  { \if_meaning:w 2 #1 + \c_one \fi: \__int_eval_end: }
\cs_new:Npn \__fp_round_normal_iii:NNwNnn #1 #2
  {
    \if_meaning:w 0 #2
      \exp_after:wN \__fp_round_special:NwwNnn
      \exp_after:wN #1
    \fi:
    \__fp_pack_twice_four:wNNNNNNNN
    \__fp_pack_twice_four:wNNNNNNNN
    \__fp_round_normal_end:wwNnn
    ; #2
  }
\cs_new:Npn \__fp_round_normal_end:wwNnn #1;#2;#3#4#5
  {
    \exp_after:wN \__fp_exp_after_o:w \tex_romannumeral:D -`0
    \__fp_sanitize:Nw #3 #4 ; #1 ;
  }
\cs_new:Npn \__fp_round_special:NwwNnn #1#2;#3;#4#5#6
  {
    \if_meaning:w 0 #1
      \__fp_case_return:nw
        { \exp_after:wN \__fp_zero_fp:N \exp_after:wN #4 }
    \else:
      \exp_after:wN \__fp_round_special_aux:Nw
      \exp_after:wN #4
      \int_use:N \__int_eval:w \c_one
        \if_meaning:w 1 #1 -#6 \else: +#5 \fi:
    \fi:
    ;
  }
\cs_new:Npn \__fp_round_special_aux:Nw #1#2;
  {
    \exp_after:wN \__fp_exp_after_o:w \tex_romannumeral:D -`0
    \__fp_sanitize:Nw #1#2; {1000}{0000}{0000}{0000};
  }
%% File: l3fp-parse.dtx Copyright (C) 2011-2012 The 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 "l3kernel 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.
%%
%% -----------------------------------------------------------------------
%%
\cs_new:Npn \__fp_parse_expand:w #1 { -`0 #1 }
\cs_new:Npn \__fp_parse_return_semicolon:w
    #1 \fi: \__fp_parse_expand:w { \fi: ; #1 }
\group_begin:
\char_set_catcode_other:N \S
\char_set_catcode_other:N \F
\char_set_catcode_other:N \P
\char_set_lccode:nn { `\- } { `\_ }
\tl_to_lowercase:n
  {
    \group_end:
    \cs_new:Npn \__fp_type_from_scan:N #1
      {
        \exp_after:wN \__fp_type_from_scan:w
        \token_to_str:N #1 \q_mark S--FP-? \q_mark \q_stop
      }
    \cs_new:Npn \__fp_type_from_scan:w #1 S--FP #2 \q_mark #3 \q_stop {#2}
  }
\cs_set_protected:Npn \__fp_tmp:w #1 #2 #3
  {
    \cs_new:cpn { __fp_parse_digits_ #1 :N } ##1
      {
        \if_int_compare:w \c_nine < 1 \token_to_str:N ##1 \exp_stop_f:
          \token_to_str:N ##1 \exp_after:wN #2 \tex_romannumeral:D
        \else:
          \__fp_parse_return_semicolon:w #3 ##1
        \fi:
        \__fp_parse_expand:w
      }
  }
\__fp_tmp:w {vii}  \__fp_parse_digits_vi:N   { 0000000 ; 7 }
\__fp_tmp:w {vi}   \__fp_parse_digits_v:N    { 000000 ; 6 }
\__fp_tmp:w {v}    \__fp_parse_digits_iv:N   { 00000 ; 5 }
\__fp_tmp:w {iv}   \__fp_parse_digits_iii:N  { 0000 ; 4 }
\__fp_tmp:w {iii}  \__fp_parse_digits_ii:N   { 000 ; 3 }
\__fp_tmp:w {ii}   \__fp_parse_digits_i:N    { 00 ; 2 }
\__fp_tmp:w {i}    \__fp_parse_digits_:N     { 0 ; 1 }
\cs_new_nopar:Npn \__fp_parse_digits_:N { ; ; 0 }
\cs_new:Npn \__fp_parse_operand:Nw #1 #2
  {
    \if_catcode:w \tex_relax:D #2
      \if_meaning:w \tex_relax:D #2
        \exp_after:wN \exp_after:wN
        \exp_after:wN \__fp_parse_operand_relax:NN
      \else:
        \exp_after:wN \exp_after:wN
        \exp_after:wN \__fp_parse_operand_register:NN
      \fi:
    \else:
      \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f:
        \exp_after:wN \exp_after:wN
        \exp_after:wN \__fp_parse_operand_digit:NN
      \else:
        \exp_after:wN \exp_after:wN
        \exp_after:wN \__fp_parse_operand_other:NN
      \fi:
    \fi:
    #1 #2
  }
\group_begin:
\char_set_catcode_other:N \P
\char_set_catcode_other:N \T
\tl_to_lowercase:n
  {
    \group_end:
    \cs_new:Npn \__fp_parse_operand_register:NN #1#2
      {
        \exp_after:wN \__fp_parse_infix_after_operand:NwN
        \exp_after:wN #1
        \tex_romannumeral:D -`0
          \exp_after:wN \__fp_parse_operand_register_aux:www
          \tex_the:D
            \exp_after:wN #2
            \exp_after:wN P
            \exp_after:wN T
            \exp_after:wN \q_stop
          \__int_value:w \__fp_parse_exponent:N
      }
    \cs_new:Npn \__fp_parse_operand_register_aux:www #1 PT #2 \q_stop #3 ;
      { \__fp_parse:n { #1 e #3 } }
  }
\cs_new:Npn \__fp_parse_operand_relax:NN #1#2
  {
    \cs:w __fp_parse_exp_after \__fp_type_from_scan:N #2 _f:nw \cs_end:
      {
        \exp_after:wN \__fp_parse_infix:NN
        \exp_after:wN #1 \tex_romannumeral:D \__fp_parse_expand:w
      }
    #2
  }
\cs_new_eq:NN \__fp_parse_exp_after_f:nw \__fp_exp_after_f:nw
\cs_new:Npn \__fp_parse_exp_after_mark_f:nw #1
  {
    \__msg_kernel_expandable_error:nn { kernel } { fp-early-end }
    \exp_after:wN \c_nan_fp
    \tex_romannumeral:D -`0 #1
  }
\cs_new:cpn { __fp_parse_exp_after_?_f:nw } #1#2
  {
    \__msg_kernel_expandable_error:nnn
      { kernel } { bad-variable } {#2}
    \exp_after:wN \c_nan_fp
    \tex_romannumeral:D -`0 #1
  }
\cs_new:Npn \__fp_parse_operand_other:NN #1 #2
  {
    \if_int_compare:w
        \__int_eval:w \tex_uccode:D `#2 / 26 = \c_three
      \exp_after:wN \__fp_parse_operand_other_word_aux:Nw
      \exp_after:wN #1
      \tex_romannumeral:D
        \exp_after:wN \__fp_parse_letters:NN
        \exp_after:wN #2
        \tex_romannumeral:D
    \else:
      \exp_after:wN \__fp_parse_operand_other_prefix_aux:NNN
      \exp_after:wN #1
      \exp_after:wN #2
      \cs:w __fp_parse_prefix_#2:Nw \exp_after:wN \cs_end:
      \tex_romannumeral:D
    \fi:
    \__fp_parse_expand:w
  }

\cs_new:Npn \__fp_parse_letters:NN #1#2
  {
    \exp_after:wN \c_zero
    \exp_after:wN #1
    \tex_romannumeral:D
      \if_int_compare:w
          \if_catcode:w \tex_relax:D #2
            \c_zero
          \else:
            \__int_eval:w \tex_uccode:D `#2 / 26
          \fi:
          = \c_three
        \exp_after:wN \__fp_parse_letters:NN
        \exp_after:wN #2
        \tex_romannumeral:D
        \exp_after:wN \__fp_parse_expand:w
      \else:
        \exp_after:wN \c_zero
        \exp_after:wN ;
        \exp_after:wN #2
      \fi:
  }
\cs_new:Npn \__fp_parse_operand_other_word_aux:Nw #1 #2;
  {
    \cs_if_exist_use:cF { __fp_parse_word_#2:N }
      {
        \__msg_kernel_expandable_error:nnn
          { kernel } { unknown-fp-word } {#2}
        \exp_after:wN \c_nan_fp
        \tex_romannumeral:D -`0
          \__fp_parse_infix:NN
      }
      #1
  }
\cs_new_eq:NN \s__fp_unknown \tex_relax:D
\cs_new:Npn \__fp_parse_operand_other_prefix_aux:NNN #1#2#3
  {
    \if_meaning:w \tex_relax:D #3
      \exp_after:wN \__fp_parse_operand_other_prefix_unknown:NNN
      \exp_after:wN #2
    \fi:
    #3 #1
  }
\cs_new:Npn \__fp_parse_operand_other_prefix_unknown:NNN #1#2#3
  {
    \cs_if_exist:cTF { __fp_parse_infix_#1:N }
      {
        \__msg_kernel_expandable_error:nnn
          { kernel } { fp-missing-number } {#1}
        \exp_after:wN \c_nan_fp
        \tex_romannumeral:D -`0
          \__fp_parse_infix:NN #3 #1
      }
      {
        \__msg_kernel_expandable_error:nnn
          { kernel } { fp-unknown-symbol } {#1}
        \__fp_parse_operand:Nw #3
      }
  }
\cs_new:Npn \__fp_parse_operand_digit:NN #1
  {
    \exp_after:wN \__fp_parse_infix_after_operand:NwN
    \exp_after:wN #1
    \tex_romannumeral:D -`0
      \exp_after:wN \__fp_sanitize:wN
      \int_use:N \__int_eval:w \c_zero \__fp_parse_trim_zeros:N
  }
\cs_new:Npn \__fp_parse_trim_zeros:N #1
  {
    \if:w 0 #1
      \exp_after:wN \__fp_parse_trim_zeros:N
      \tex_romannumeral:D
    \else:
      \if:w . #1
        \exp_after:wN \__fp_parse_strim_zeros:N
        \tex_romannumeral:D
      \else:
        \__fp_parse_trim_end:w #1
      \fi:
    \fi:
    \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_trim_end:w #1 \fi: \fi: \__fp_parse_expand:w
  {
      \fi:
    \fi:
    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
      \exp_after:wN \__fp_parse_large:N
    \else:
      \exp_after:wN \__fp_parse_zero:
    \fi:
    #1
  }
\cs_new:Npn \__fp_parse_strim_zeros:N #1
  {
    \if:w 0 #1
      - \c_one
      \exp_after:wN \__fp_parse_strim_zeros:N
      \tex_romannumeral:D
    \else:
      \__fp_parse_strim_end:w #1
    \fi:
    \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_strim_end:w #1 \fi: \__fp_parse_expand:w
  {
    \fi:
    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
      \exp_after:wN \__fp_parse_small:N
    \else:
      \exp_after:wN \__fp_parse_zero:
    \fi:
    #1
  }
\cs_new:Npn \__fp_parse_zero:
  {
    \exp_after:wN ; \exp_after:wN 1
    \__int_value:w \__fp_parse_exponent:N
  }
\cs_new:Npn \__fp_parse_small:N #1
  {
    \exp_after:wN \__fp_parse_pack_leading:NNNNNww
    \int_use:N \__int_eval:w 1 \token_to_str:N #1
      \exp_after:wN \__fp_parse_small_leading:wwNN
      \__int_value:w 1
        \exp_after:wN \__fp_parse_digits_vii:N
        \tex_romannumeral:D \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_small_leading:wwNN 1 #1 ; #2; #3 #4
  {
    #1 #2
    \exp_after:wN \__fp_parse_pack_trailing:NNNNNNww
    \exp_after:wN \c_zero
    \int_use:N \__int_eval:w 1
      \if_int_compare:w \c_nine < 1 \token_to_str:N #4 \exp_stop_f:
        \token_to_str:N #4
        \exp_after:wN \__fp_parse_small_trailing:wwNN
        \__int_value:w 1
          \exp_after:wN \__fp_parse_digits_vi:N
          \tex_romannumeral:D
      \else:
        0000 0000 \__fp_parse_exponent:Nw #4
      \fi:
      \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_small_trailing:wwNN 1 #1 ; #2; #3 #4
  {
    #1 #2
    \if_int_compare:w \c_nine < 1 \token_to_str:N #4 \exp_stop_f:
      \token_to_str:N #4
      \exp_after:wN \__fp_parse_small_round:NN
      \exp_after:wN #4
      \tex_romannumeral:D
    \else:
      0 \__fp_parse_exponent:Nw #4
    \fi:
    \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_pack_trailing:NNNNNNww #1 #2 #3#4#5#6 #7; #8 ;
  {
    \if_meaning:w 2 #2 + \c_one \fi:
    ; #8 + #1 ; {#3#4#5#6} {#7};
  }
\cs_new:Npn \__fp_parse_pack_leading:NNNNNww #1 #2#3#4#5 #6; #7;
  {
    + #7
    \if_meaning:w 2 #1 \__fp_parse_pack_carry:w \fi:
    ; 0 {#2#3#4#5} {#6}
  }
\cs_new:Npn \__fp_parse_pack_carry:w \fi: ; 0 #1
  { \fi: + \c_one ; 0 {1000} }
\cs_new:Npn \__fp_parse_large:N #1
  {
    \exp_after:wN \__fp_parse_large_leading:wwNN
    \__int_value:w 1 \token_to_str:N #1
      \exp_after:wN \__fp_parse_digits_vii:N
      \tex_romannumeral:D \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_large_leading:wwNN 1 #1 ; #2; #3 #4
  {
    + \c_eight - #3
    \exp_after:wN \__fp_parse_pack_leading:NNNNNww
    \int_use:N \__int_eval:w 1 #1
      \if_int_compare:w \c_nine < 1 \token_to_str:N #4 \exp_stop_f:
        \exp_after:wN \__fp_parse_large_trailing:wwNN
        \__int_value:w 1 \token_to_str:N #4
          \exp_after:wN \__fp_parse_digits_vi:N
          \tex_romannumeral:D
      \else:
        \if:w . #4
          \exp_after:wN \__fp_parse_small_leading:wwNN
          \__int_value:w 1
            \cs:w
              __fp_parse_digits_
              \tex_romannumeral:D #3
              :N \exp_after:wN
            \cs_end:
            \tex_romannumeral:D
        \else:
          #2
          \exp_after:wN \__fp_parse_pack_trailing:NNNNNNww
          \exp_after:wN \c_zero
          \__int_value:w 1 0000 0000
          \__fp_parse_exponent:Nw #4
        \fi:
      \fi:
      \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_large_trailing:wwNN 1 #1 ; #2; #3 #4
  {
    \if_int_compare:w \c_nine < 1 \token_to_str:N #4 \exp_stop_f:
      \exp_after:wN \__fp_parse_pack_trailing:NNNNNNww
      \exp_after:wN \c_eight
      \int_use:N \__int_eval:w 1 #1 \token_to_str:N #4
        \exp_after:wN \__fp_parse_large_round:NN
        \exp_after:wN #4
        \tex_romannumeral:D
    \else:
      \exp_after:wN \__fp_parse_pack_trailing:NNNNNNww
      \int_use:N \__int_eval:w \c_seven - #3 \exp_stop_f:
      \int_use:N \__int_eval:w 1 #1
        \if:w . #4
          \exp_after:wN \__fp_parse_small_trailing:wwNN
          \__int_value:w 1
            \cs:w
              __fp_parse_digits_
              \tex_romannumeral:D #3
              :N \exp_after:wN
            \cs_end:
            \tex_romannumeral:D
        \else:
          #2 0 \__fp_parse_exponent:Nw #4
        \fi:
    \fi:
    \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_exponent:Nw #1 #2 \__fp_parse_expand:w
  {
    \exp_after:wN ;
    \__int_value:w #2 \__fp_parse_exponent:N #1
  }
\cs_new:Npn \__fp_parse_exponent:N #1
  {
    \if:w e #1
      \exp_after:wN \__fp_parse_exponent_ii:N
      \tex_romannumeral:D
    \else:
      0 \__fp_parse_return_semicolon:w #1
    \fi:
    \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_exponent_ii:N #1
  {
    \if_int_compare:w \if_catcode:w \tex_relax:D #1
                \c_zero \else: `#1 \fi: > `9 \exp_stop_f:
      0 \exp_after:wN ; \exp_after:wN e
    \else:
      \exp_after:wN \__fp_parse_exponent_sign:N
    \fi:
    #1
  }
\cs_new:Npn \__fp_parse_exponent_sign:N #1
  {
    \if:w + \if:w - #1 + \fi: \token_to_str:N #1
      \exp_after:wN \__fp_parse_exponent_sign:N
      \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
    \else:
      \exp_after:wN \__fp_parse_exponent_body:N
      \exp_after:wN #1
    \fi:
  }
\cs_new:Npn \__fp_parse_exponent_body:N #1
  {
    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
      \token_to_str:N #1
      \exp_after:wN \__fp_parse_exponent_digits:N
      \tex_romannumeral:D
    \else:
      \__fp_parse_exponent_keep:NTF #1
        { \__fp_parse_return_semicolon:w #1 }
        {
          \exp_after:wN ;
          \tex_romannumeral:D
        }
    \fi:
    \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_exponent_digits:N #1
  {
    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
      \token_to_str:N #1
      \exp_after:wN \__fp_parse_exponent_digits:N
      \tex_romannumeral:D
    \else:
      \__fp_parse_return_semicolon:w #1
    \fi:
    \__fp_parse_expand:w
  }
\prg_new_conditional:Npnn \__fp_parse_exponent_keep:N #1 { TF }
  {
    \if_catcode:w \tex_relax:D #1
      \if_meaning:w \tex_relax:D #1
        \if_int_compare:w \pdftex_strcmp:D { \s__fp } { #1 } = \c_zero
          0
          \__msg_kernel_expandable_error:nnn
            { kernel } { fp-after-e } { floating~point~ }
          \prg_return_true:
        \else:
          0
          \__msg_kernel_expandable_error:nnn
            { kernel } { bad-variable } {#1}
          \prg_return_false:
        \fi:
      \else:
        \if_int_compare:w
            \pdftex_strcmp:D { \__int_value:w #1 } { \tex_the:D #1 }
            = \c_zero
          \__int_value:w #1
        \else:
          0
          \__msg_kernel_expandable_error:nnn
            { kernel } { fp-after-e } { dimension~#1 }
        \fi:
        \prg_return_false:
      \fi:
    \else:
      0
      \__msg_kernel_expandable_error:nnn
        { kernel } { fp-missing } { exponent }
      \prg_return_true:
    \fi:
  }
\cs_new:Npn \__fp_cfs_round_loop:N #1
  {
    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
      + \c_one
      \if:w 0 #1
        \exp_after:wN \__fp_cfs_round_loop:N
        \tex_romannumeral:D
      \else:
        \exp_after:wN \__fp_cfs_round_up:N
        \tex_romannumeral:D
      \fi:
    \else:
      \__fp_parse_return_semicolon:w \c_zero #1
    \fi:
    \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_cfs_round_up:N #1
  {
    \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f:
      + 1
      \exp_after:wN \__fp_cfs_round_up:N
      \tex_romannumeral:D
    \else:
      \__fp_parse_return_semicolon:w \c_one #1
    \fi:
    \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_large_round:NN #1#2
  {
    \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f:
      +
      \exp_after:wN \__fp_round_s:NNNw
      \exp_after:wN 0
      \exp_after:wN #1
      \exp_after:wN #2
      \int_use:N \__int_eval:w
        \exp_after:wN \__fp_parse_large_round_after:wNN
        \int_use:N \__int_eval:w \c_one
          \exp_after:wN \__fp_cfs_round_loop:N
    \else: %^^A could be dot, or e, or other
      \exp_after:wN \__fp_parse_large_round_dot_test:NNw
      \exp_after:wN #1
      \exp_after:wN #2
    \fi:
  }
\cs_new:Npn \__fp_parse_large_round_dot_test:NNw #1#2
  {
    \if:w . #2
      \exp_after:wN \__fp_parse_small_round:NN
      \exp_after:wN #1
      \tex_romannumeral:D
    \else:
      \__fp_parse_exponent:Nw #2
    \fi:
    \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_large_round_after:wNN #1 ; #2 #3
  {
    \if:w . #3
      \exp_after:wN \__fp_parse_large_round_after_ii:wN
      \int_use:N \__int_eval:w #1 +
        \c_zero * \__int_eval:w \c_zero
          \exp_after:wN \__fp_cfs_round_loop:N
          \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
    \else:
      + #2
      \exp_after:wN ;
      \int_use:N \__int_eval:w #1 +
        \exp_after:wN \__fp_parse_exponent:N
        \exp_after:wN #3
    \fi:
  }
\cs_new:Npn \__fp_parse_large_round_after_ii:wN #1 ; #2
  {
    + #2
    \exp_after:wN ;
    \int_use:N \__int_eval:w #1 +
      \__fp_parse_exponent:N
  }
\cs_new:Npn \__fp_parse_small_round:NN #1#2
  {
    \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f:
      +
      \exp_after:wN \__fp_round_s:NNNw
      \exp_after:wN 0
      \exp_after:wN #1
      \exp_after:wN #2
      \int_use:N \__int_eval:w
        \exp_after:wN \__fp_parse_small_round_after:wN
        \int_use:N \__int_eval:w \c_zero
          \exp_after:wN \__fp_cfs_round_loop:N
          \tex_romannumeral:D
    \else:
      \__fp_parse_exponent:Nw #2
    \fi:
    \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_small_round_after:wN #1; #2
  {
    + #2 \exp_after:wN ;
    \__int_value:w \__fp_parse_exponent:N
  }
\cs_new:Npn \__fp_parse:n #1
  {
    \tex_romannumeral:D
      \exp_after:wN \__fp_parse_after:ww
      \tex_romannumeral:D
        \__fp_parse_until:Nw \c_minus_one
        \__fp_parse_expand:w #1 \s__fp_mark
      \s__fp_stop
  }
\cs_new:Npn \__fp_parse_after:ww #1@ #2 \s__fp_stop
  {
    \c_zero #1
  }
\cs_new:Npn \__fp_parse_until:Nw #1
  {
    -`0
    \exp_after:wN \__fp_parse_until_test:NwN
    \exp_after:wN #1
    \tex_romannumeral:D -`0
    \exp_after:wN \__fp_parse_operand:Nw
    \exp_after:wN #1
    \tex_romannumeral:D
  }
\cs_new:Npn \__fp_parse_until_test:NwN #1 #2 @ #3 { #3 #1 #2 @ }
\cs_new_eq:NN \__fp_parse_stop_until:N \use_none:n
\cs_new:Npn \__fp_parse_infix_after_operand:NwN #1 #2;
  {
    \__fp_exp_after_f:nw { \__fp_parse_infix:NN #1 }
    #2;
  }
\group_begin:
  \char_set_catcode_letter:N \*
  \cs_new:Npn \__fp_parse_infix:NN #1 #2
    {
      \if_catcode:w \tex_relax:D #2
        \if_int_compare:w
            \pdftex_strcmp:D { \s__fp_mark } { #2 }
            = \c_zero
          \exp_after:wN \exp_after:wN
          \exp_after:wN \__fp_parse_infix_end:N
        \else:
          \exp_after:wN \exp_after:wN
          \exp_after:wN \__fp_parse_infix_juxtapose:N
        \fi:
      \else:
        \if_int_compare:w
            \__int_eval:w \tex_uccode:D `#2 / 26
            = \c_three
          \exp_after:wN \exp_after:wN
          \exp_after:wN \__fp_parse_infix_juxtapose:N
        \else:
          \exp_after:wN \__fp_parse_infix_check:NNN
          \cs:w
            __fp_parse_infix_#2:N
            \exp_after:wN \exp_after:wN \exp_after:wN
          \cs_end:
        \fi:
      \fi:
      #1
      #2
    }
  \cs_new:Npn \__fp_parse_infix_check:NNN #1#2#3
    {
      \if_meaning:w \tex_relax:D #1
        \__msg_kernel_expandable_error:nnn { kernel } { fp-missing } { * }
        \exp_after:wN \__fp_parse_infix_*:N
        \exp_after:wN #2
        \exp_after:wN #3
      \else:
        \exp_after:wN #1
        \exp_after:wN #2
        \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
      \fi:
    }
\group_end:
\cs_new:Npn \__fp_parse_apply_binary:NwNwN #1 #2#3@ #4 #5#6@ #7
  {
    \exp_after:wN \__fp_parse_until_test:NwN
    \exp_after:wN #1
    \tex_romannumeral:D -`0
      \cs:w
        __fp
        \__fp_type_from_scan:N #2
        _ #4
        \__fp_type_from_scan:N #5
        _o:ww
      \cs_end:
      #2#3 #5#6
    \tex_romannumeral:D -`0 #7 #1
  }
\cs_new:Npn \__fp_parse_apply_unary_array:NNwN #1#2#3@#4
  {
    #2 #3 @
    \tex_romannumeral:D -`0 #4 #1
  }
\cs_new:Npn \__fp_parse_apply_unary:NNwN #1#2#3@#4
  {
    #2 #3
    \tex_romannumeral:D -`0 #4 #1
  }
\cs_new:Npn \__fp_parse_unary_type:N #1
  { \__fp_type_from_scan:N #1 _o:w \cs_end: #1 }
\cs_set_protected:Npn \__fp_tmp:w #1 #2
  {
    \cs_new_nopar:cpn { __fp_parse_word_#1:N }
      { \exp_after:wN #2 \tex_romannumeral:D -`0 \__fp_parse_infix:NN }
  }
\__fp_tmp:w { inf } \c_inf_fp
\__fp_tmp:w { nan } \c_nan_fp
\__fp_tmp:w { pi  } \c_pi_fp
\__fp_tmp:w { deg } \c_one_degree_fp
\__fp_tmp:w { true } \c_one_fp
\__fp_tmp:w { false } \c_zero_fp
\__fp_tmp:w { pt } \c_one_fp
\cs_set_protected:Npn \__fp_tmp:w #1 #2
  {
    \cs_new_nopar:cpn { __fp_parse_word_#1:N }
      {
        \__fp_exp_after_f:nw { \__fp_parse_infix:NN }
        \s__fp \__fp_chk:w 10 #2 ;
      }
  }
\__fp_tmp:w {in} { {2} {7227} {0000} {0000} {0000} }
\__fp_tmp:w {pc} { {2} {1200} {0000} {0000} {0000} }
\__fp_tmp:w {cm} { {2} {2845} {2755} {9055} {1181} }
\__fp_tmp:w {mm} { {1} {2845} {2755} {9055} {1181} }
\__fp_tmp:w {dd} { {1} {1070} {0085} {6496} {0630} }
\__fp_tmp:w {cc} { {2} {1284} {0102} {7795} {2756} }
\__fp_tmp:w {nd} { {1} {1066} {9783} {4645} {6693} }
\__fp_tmp:w {nc} { {2} {1280} {3740} {1574} {8031} }
\__fp_tmp:w {bp} { {1} {1003} {7500} {0000} {0000} }
\__fp_tmp:w {sp} { {-4} {1525} {8789} {0625} {0000} }
\tl_map_inline:nn { {em} {ex} }
  {
    \cs_new_nopar:cpn { __fp_parse_word_#1:N }
      {
        \exp_after:wN \dim_to_fp:n \exp_after:wN
          { \dim_use:N \__dim_eval:w 1 #1 \exp_after:wN }
        \tex_romannumeral:D -`0 \__fp_parse_infix:NN
      }
  }
\tl_map_inline:nn
  { {abs} {cos} {cot} {csc} {exp} {ln} {sec} {sin} {tan} }
  {
    \cs_new:cpn { __fp_parse_word_#1:N } ##1
      {
        \exp_after:wN \__fp_parse_apply_unary:NNwN
        \exp_after:wN ##1
        \cs:w __fp_ #1 \exp_after:wN \__fp_parse_unary_type:N
        \tex_romannumeral:D
        \__fp_parse_until:Nw \c_fifteen
        \__fp_parse_expand:w
      }
  }
\cs_set_protected:Npn \__fp_tmp:w #1#2
  {
    \cs_new:Npn #1 ##1
      {
        \exp_after:wN \__fp_parse_apply_unary_array:NNwN
        \exp_after:wN ##1
        \exp_after:wN #2
        \tex_romannumeral:D
        \__fp_parse_until:Nw \c_sixteen \__fp_parse_expand:w
      }
  }
\__fp_tmp:w \__fp_parse_word_max:N \__fp_max_o:w
\__fp_tmp:w \__fp_parse_word_min:N \__fp_min_o:w
\cs_new:Npn \__fp_parse_word_round:N #1#2
  {
    \if_meaning:w + #2
      \__fp_parse_round:Nw \__fp_round_to_pinf:NNN
    \else:
      \if_meaning:w 0 #2
        \__fp_parse_round:Nw \__fp_round_to_zero:NNN
      \else:
        \if_meaning:w - #2
          \__fp_parse_round:Nw \__fp_round_to_ninf:NNN
        \fi:
      \fi:
    \fi:
    \exp_after:wN \__fp_parse_apply_round:NNwN
    \exp_after:wN #1
    \exp_after:wN \__fp_round_to_nearest:NNN
    \tex_romannumeral:D
    \__fp_parse_until:Nw \c_sixteen \__fp_parse_expand:w #2
  }
\cs_new:Npn \__fp_parse_round:Nw
    #1 #2 \__fp_round_to_nearest:NNN #3 \__fp_parse_expand:w #4
  { #2 #1 #3 \__fp_parse_expand:w }
\cs_new:Npn \__fp_parse_apply_round:NNwN #1#2#3@#4
  {
    \if_case:w \__int_eval:w \__fp_array_count:n {#3} - \c_one \__int_eval_end:
         \__fp_round:Nwn #2 #3 {0} \tex_romannumeral:D
    \or: \__fp_round:Nww #2 #3 \tex_romannumeral:D
    \else:
      \__msg_kernel_expandable_error:nnnnn
        { kernel } { fp-num-args } { round() } { 1 } { 2 }
      \exp_after:wN \c_nan_fp \tex_romannumeral:D
    \fi:
    -`0 #4 #1
  }
\cs_new_eq:cN { __fp_parse_prefix_+:Nw } \__fp_parse_operand:Nw
\cs_set_protected:Npn \__fp_tmp:w #1#2
  {
    \cs_new:cpn { __fp_parse_prefix_#1:Nw } ##1
      {
        \exp_after:wN \__fp_parse_apply_unary:NNwN
        \exp_after:wN ##1
        \cs:w __fp_ #2 \exp_after:wN \__fp_parse_unary_type:N
        \tex_romannumeral:D
        \if_int_compare:w \c_twelve < ##1
          \__fp_parse_until:Nw ##1
        \else:
          \__fp_parse_until:Nw \c_twelve
        \fi:
        \__fp_parse_expand:w
      }
  }
\__fp_tmp:w - { - }
\__fp_tmp:w ! { ! }
\group_begin:
  \char_set_catcode_letter:N \)
  \cs_new:cpn { __fp_parse_prefix_(:Nw } #1
    {
      \exp_after:wN \__fp_parse_lparen_after:NwN
      \exp_after:wN #1
      \tex_romannumeral:D
      \if_int_compare:w #1 = \c_sixteen
        \__fp_parse_until:Nw \c_one
      \else:
        \__fp_parse_until:Nw \c_zero
      \fi:
      \__fp_parse_expand:w
    }
  \cs_new:Npn \__fp_parse_lparen_after:NwN #1#2@#3
    {
      \token_if_eq_meaning:NNTF #3 \__fp_parse_infix_):N
        {
          \__fp_exp_after_array_f:w #2 \s__fp_stop
          \exp_after:wN \__fp_parse_infix:NN
          \exp_after:wN #1
          \tex_romannumeral:D \__fp_parse_expand:w
        }
        {
          \__msg_kernel_expandable_error:nnn { kernel } { fp-missing } { ) }
          #2 @ \__fp_parse_stop_until:N #3
        }
    }
\group_end:
\cs_new:cpn {__fp_parse_prefix_.:Nw} #1
  {
    \exp_after:wN \__fp_parse_infix_after_operand:NwN
    \exp_after:wN #1
    \tex_romannumeral:D -`0
      \exp_after:wN \__fp_sanitize:wN
      \int_use:N \__int_eval:w \c_zero \__fp_parse_strim_zeros:N
  }
\cs_set_protected:Npn \__fp_tmp:w #1#2#3#4
  {
    \cs_new:Npn #1 ##1
      {
        \if_int_compare:w ##1 < #3
          \exp_after:wN @
          \exp_after:wN \__fp_parse_apply_binary:NwNwN
          \exp_after:wN #2
          \tex_romannumeral:D
          \__fp_parse_until:Nw #4
          \exp_after:wN \__fp_parse_expand:w
        \else:
          \exp_after:wN @
          \exp_after:wN \__fp_parse_stop_until:N
          \exp_after:wN #1
        \fi:
      }
  }
\group_begin:
  \char_set_catcode_other:N \&
  \__fp_tmp:w \__fp_parse_infix_juxtapose:N * \c_thirty_two \c_thirty_two
  \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_ / :N } / \c_ten \c_ten
  \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_mul:N } * \c_ten \c_ten
  \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_ - :N } - \c_nine \c_nine
  \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_ + :N } + \c_nine \c_nine
  \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_and:N } & \c_five \c_five
  \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_ or:N } | \c_four \c_four
\group_end:
\group_begin:
  \char_set_catcode_letter:N ^
  \__fp_tmp:w \__fp_parse_infix_^:N ^ \c_fifteen \c_fourteen
  \cs_new:cpn { __fp_parse_infix_*:N } #1#2
    {
      \if:w * #2
        \exp_after:wN \__fp_parse_infix_^:N
        \exp_after:wN #1
      \else:
        \exp_after:wN \__fp_parse_infix_mul:N
        \exp_after:wN #1
        \exp_after:wN #2
      \fi:
    }
\group_end:
\group_begin:
  \char_set_catcode_letter:N \|
  \char_set_catcode_letter:N \&
  \cs_new:Npn \__fp_parse_infix_|:N #1#2
    {
      \if:w | #2
        \exp_after:wN \__fp_parse_infix_|:N
        \exp_after:wN #1
        \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
      \else:
        \exp_after:wN \__fp_parse_infix_or:N
        \exp_after:wN #1
        \exp_after:wN #2
      \fi:
    }
  \cs_new:Npn \__fp_parse_infix_&:N #1#2
    {
      \if:w & #2
        \exp_after:wN \__fp_parse_infix_&:N
        \exp_after:wN #1
        \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
      \else:
        \exp_after:wN \__fp_parse_infix_and:N
        \exp_after:wN #1
        \exp_after:wN #2
      \fi:
    }
\group_end:
\cs_new:cpn { __fp_parse_infix_<:N } #1
  {
    \__fp_infix_compare:N #1 \c_one_fp
      \c_zero_fp  \c_zero_fp \c_zero_fp \c_zero_fp <
  }
\cs_new:cpn { __fp_parse_infix_=:N } #1
  {
    \__fp_infix_compare:N #1 \c_one_fp
      \c_zero_fp \c_zero_fp \c_zero_fp \c_zero_fp =
  }
\cs_new:cpn { __fp_parse_infix_>:N } #1
  {
    \__fp_infix_compare:N #1 \c_one_fp
      \c_zero_fp \c_zero_fp \c_zero_fp \c_zero_fp >
  }
\cs_new:cpn { __fp_parse_infix_!:N } #1
  {
    \exp_after:wN \__fp_parse_infix_excl_aux:NN
    \exp_after:wN #1 \tex_romannumeral:D \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_infix_excl_aux:NN #1#2
  {
    \__fp_infix_compare:N #1 \c_zero_fp
      \c_one_fp \c_one_fp \c_one_fp \c_one_fp #2
  }
\cs_new:Npn \__fp_parse_infix_excl_error:
  {
    \__msg_kernel_expandable_error:nnnn
      { kernel } { fp-missing } { = } { ~after~!. }
  }
\cs_new:Npn \__fp_infix_compare:N #1
  {
    \if_int_compare:w #1 < \c_seven
      \exp_after:wN \__fp_parse_compare:NNNNNNw
      \exp_after:wN \__fp_parse_infix_excl_error:
    \else:
      \exp_after:wN @
      \exp_after:wN \__fp_parse_stop_until:N
      \exp_after:wN \__fp_infix_compare:N
    \fi:
  }
\cs_new:Npn \__fp_parse_compare:NNNNNNw #1#2#3#4#5#6#7
  {
    \if_case:w
          \if_catcode:w \tex_relax:D #7
            \c_minus_one
          \else:
            \__int_eval:w `#7 - `< \__int_eval_end:
          \fi:
         \__fp_parse_compare_expand:NNNNNw #2#2#4#5#6
    \or: \__fp_parse_compare_expand:NNNNNw #2#3#2#5#6
    \or: \__fp_parse_compare_expand:NNNNNw #2#3#4#2#6
    \or: \__fp_parse_compare_expand:NNNNNw #2#3#4#5#2
    \else: #1 \__fp_parse_compare_end:NNNN #3#4#5#6#7
    \fi:
  }
\cs_new:Npn \__fp_parse_compare_expand:NNNNNw #1#2#3#4#5
  {
    \exp_after:wN \__fp_parse_compare:NNNNNNw
    \exp_after:wN \prg_do_nothing:
    \exp_after:wN #1
    \exp_after:wN #2
    \exp_after:wN #3
    \exp_after:wN #4
    \exp_after:wN #5
    \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
  }
\cs_new:Npn \__fp_parse_compare_end:NNNN #1#2#3#4#5 \fi:
  {
    \fi:
    \exp_after:wN @
    \exp_after:wN \__fp_parse_apply_compare:NwNNNNwN
    \exp_after:wN #1
    \exp_after:wN #2
    \exp_after:wN #3
    \exp_after:wN #4
    \tex_romannumeral:D
    \__fp_parse_until:Nw \c_seven \__fp_parse_expand:w #5
  }
\cs_new:Npn \__fp_parse_apply_compare:NwNNNNwN #1 #2@ #3#4#5#6 #7@ #8
  {
    \exp_after:wN \__fp_parse_until_test:NwN
    \exp_after:wN #1
    \tex_romannumeral:D -`0
      \exp_after:wN \exp_after:wN
      \exp_after:wN \exp_after:wN
      \exp_after:wN \exp_after:wN
      \if_case:w \__fp_compare_back:ww #7 #2 \exp_stop_f:
             #4
      \or:   #5
      \or:   #6
      \else: #3
      \fi:
    \tex_romannumeral:D -`0 #8 #1
  }
\group_begin:
  \char_set_catcode_letter:N \?
  \cs_new:Npn \__fp_parse_infix_?:N #1
    {
      \if_int_compare:w #1 < \c_three
        \exp_after:wN @
        \exp_after:wN \__fp_ternary:NwwN
        \tex_romannumeral:D
        \__fp_parse_until:Nw \c_three
        \exp_after:wN \__fp_parse_expand:w
      \else:
        \exp_after:wN @
        \exp_after:wN \__fp_parse_stop_until:N
        \exp_after:wN \__fp_parse_infix_?:N
      \fi:
    }
  \cs_new:Npn \__fp_parse_infix_::N #1
    {
      \if_int_compare:w #1 < \c_three
        \__msg_kernel_expandable_error:nnnn
          { kernel } { fp-missing } { ? } { ~for~?: }
        \exp_after:wN @
        \exp_after:wN \__fp_ternary_ii:NwwN
        \tex_romannumeral:D
        \__fp_parse_until:Nw \c_two
        \exp_after:wN \__fp_parse_expand:w
      \else:
        \exp_after:wN @
        \exp_after:wN \__fp_parse_stop_until:N
        \exp_after:wN \__fp_parse_infix_::N
      \fi:
    }
\group_end:
\group_begin:
  \char_set_catcode_letter:N \)
  \cs_new:Npn \__fp_parse_infix_):N #1
    {
      \if_int_compare:w #1 < \c_zero
        \__msg_kernel_expandable_error:nnn { kernel } { fp-extra } { ) }
        \exp_after:wN \__fp_parse_infix:NN
        \exp_after:wN #1
        \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w
      \else:
        \exp_after:wN @
        \exp_after:wN \__fp_parse_stop_until:N
        \exp_after:wN \__fp_parse_infix_):N
      \fi:
    }
\group_end:
\cs_new:Npn \__fp_parse_infix_end:N #1
  { @ \__fp_parse_stop_until:N \__fp_parse_infix_end:N }
\group_begin:
  \char_set_catcode_letter:N \,
  \cs_new:Npn \__fp_parse_infix_,:N #1
    {
      \if_int_compare:w #1 > \c_one
        \exp_after:wN @
        \exp_after:wN \__fp_parse_stop_until:N
        \exp_after:wN \__fp_parse_infix_,:N
      \else:
        \if_int_compare:w #1 = \c_one
          \exp_after:wN \__fp_parse_infix_comma:w
          \tex_romannumeral:D
        \else:
          \exp_after:wN \__fp_parse_infix_comma_gobble:w
          \tex_romannumeral:D
        \fi:
        \__fp_parse_until:Nw \c_one
        \exp_after:wN \__fp_parse_expand:w
      \fi:
    }
  \cs_new:Npn \__fp_parse_infix_comma:w #1 @
    { #1 @ \__fp_parse_stop_until:N }
  \cs_new:Npn \__fp_parse_infix_comma_gobble:w #1 @
    {
      \__msg_kernel_expandable_error:nn { kernel } { fp-extra-comma }
      @ \__fp_parse_stop_until:N
    }
\group_end:
\__msg_kernel_new:nnn { kernel } { unknown-fp-word }
  { Unknown~fp~word~#1. }
\__msg_kernel_new:nnn { kernel } { fp-missing }
  { Missing~#1~inserted #2. }
\__msg_kernel_new:nnn { kernel } { fp-extra }
  { Extra~#1~ignored. }
\__msg_kernel_new:nnn { kernel } { fp-early-end }
  { Premature~end~in~fp~expression. }
\__msg_kernel_new:nnn { kernel } { fp-after-e }
  { Cannot~use~#1 after~'e'. }
\__msg_kernel_new:nnn { kernel } { fp-missing-number }
  { Missing~number~before~'#1'. }
\__msg_kernel_new:nnn { kernel } { fp-unknown-symbol }
  { Unknown~symbol~#1~ignored. }
\__msg_kernel_new:nnn { kernel } { fp-extra-comma }
  { Unexpected~comma:~extra~arguments~ignored. }
\__msg_kernel_new:nnn { kernel } { fp-num-args }
  { #1~expects~between~#2~and~#3~arguments. }
%% File: l3fp-logic.dtx Copyright (C) 2011-2012 The 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 "l3kernel 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.
%%
%% -----------------------------------------------------------------------
%%
\cs_new_eq:NN \fp_if_exist:NTF \cs_if_exist:NTF
\cs_new_eq:NN \fp_if_exist:NT  \cs_if_exist:NT
\cs_new_eq:NN \fp_if_exist:NF  \cs_if_exist:NF
\cs_new_eq:NN \fp_if_exist_p:N \cs_if_exist_p:N
\cs_new_eq:NN \fp_if_exist:cTF \cs_if_exist:cTF
\cs_new_eq:NN \fp_if_exist:cT  \cs_if_exist:cT
\cs_new_eq:NN \fp_if_exist:cF  \cs_if_exist:cF
\cs_new_eq:NN \fp_if_exist_p:c \cs_if_exist_p:c
\prg_new_conditional:Npnn \fp_compare:n #1 { p , T , F , TF }
  {
    \exp_after:wN \__fp_compare_return:w
    \tex_romannumeral:D -`0 \__fp_parse:n {#1}
  }
\cs_new:Npn \__fp_compare_return:w \s__fp \__fp_chk:w #1#2;
  {
    \if_meaning:w 0 #1
      \prg_return_false:
    \else:
      \prg_return_true:
    \fi:
  }
\prg_new_conditional:Npnn \fp_compare:nNn #1#2#3 { p , T , F , TF }
  {
    \if_int_compare:w
        \exp_after:wN \__fp_compare_aux:wn
          \tex_romannumeral:D -`0 \__fp_parse:n {#1} {#3}
        = \__int_eval:w `#2 - `= \__int_eval_end:
      \prg_return_true:
    \else:
      \prg_return_false:
    \fi:
  }
\cs_new:Npn \__fp_compare_aux:wn #1; #2
  {
    \exp_after:wN \__fp_compare_back:ww
      \tex_romannumeral:D -`0 \__fp_parse:n {#2} #1;
  }
\cs_new:Npn \__fp_compare_back:ww
    \s__fp \__fp_chk:w #1 #2 #3;
    \s__fp \__fp_chk:w #4 #5 #6;
  {
    \__int_value:w
      \if_meaning:w 3 #1 \exp_after:wN \__fp_compare_nan:w \fi:
      \if_meaning:w 3 #4 \exp_after:wN \__fp_compare_nan:w \fi:
      \if_meaning:w 2 #5 - \fi:
      \if_meaning:w #2 #5
        \if_meaning:w #1 #4
          \if_meaning:w 1 #1
            \__fp_compare_npos:nwnw #6; #3;
          \else:
            0
          \fi:
        \else:
          \if_int_compare:w #4 < #1 - \fi: 1
        \fi:
      \else:
        \if_int_compare:w #1#4 = \c_zero
          0
        \else:
          1
        \fi:
      \fi:
    \exp_stop_f:
  }
\cs_new:Npn \__fp_compare_nan:w #1 \exp_stop_f: { \c_two }
\cs_new:Npn \__fp_compare_npos:nwnw #1#2; #3#4;
  {
    \if_int_compare:w #1 = #3 \exp_stop_f:
      \__fp_compare_significand:nnnnnnnn #2 #4
    \else:
      \if_int_compare:w #1 < #3 - \fi: 1
    \fi:
  }
\cs_new:Npn \__fp_compare_significand:nnnnnnnn #1#2#3#4#5#6#7#8
  {
    \if_int_compare:w #1#2 = #5#6 \exp_stop_f:
      \if_int_compare:w #3#4 = #7#8 \exp_stop_f:
        0
      \else:
        \if_int_compare:w #3#4 < #7#8 - \fi: 1
      \fi:
    \else:
      \if_int_compare:w #1#2 < #5#6 - \fi: 1
    \fi:
  }
\cs_new:Npn \fp_do_until:nn #1#2
  {
    #2
    \fp_compare:nF {#1}
      { \fp_do_until:nn {#1} {#2} }
  }
\cs_new:Npn \fp_do_while:nn #1#2
  {
    #2
    \fp_compare:nT {#1}
      { \fp_do_while:nn {#1} {#2} }
  }
\cs_new:Npn \fp_until_do:nn #1#2
  {
    \fp_compare:nF {#1}
      {
        #2
        \fp_until_do:nn {#1} {#2}
      }
  }
\cs_new:Npn \fp_while_do:nn #1#2
  {
    \fp_compare:nT {#1}
      {
        #2
        \fp_while_do:nn {#1} {#2}
      }
  }
\cs_new:Npn \fp_do_until:nNnn #1#2#3#4
  {
    #4
    \fp_compare:nNnF {#1} #2 {#3}
      { \fp_do_until:nNnn {#1} #2 {#3} {#4} }
  }
\cs_new:Npn \fp_do_while:nNnn #1#2#3#4
  {
    #4
    \fp_compare:nNnT {#1} #2 {#3}
      { \fp_do_while:nNnn {#1} #2 {#3} {#4} }
  }
\cs_new:Npn \fp_until_do:nNnn #1#2#3#4
  {
    \fp_compare:nNnF {#1} #2 {#3}
      {
        #4
        \fp_until_do:nNnn {#1} #2 {#3} {#4}
      }
  }
\cs_new:Npn \fp_while_do:nNnn #1#2#3#4
  {
    \fp_compare:nNnT {#1} #2 {#3}
      {
        #4
        \fp_while_do:nNnn {#1} #2 {#3} {#4}
      }
  }
\cs_new:Npn \__fp_max_o:w #1 @
  {
    \exp_after:wN \__fp_minmax_loop:Nww
    \exp_after:wN \c_minus_one
    \c_minus_inf_fp
    #1
    \s__fp \__fp_chk:w { 3 \__fp_minmax_break_o:w } ;
  }
\cs_new:Npn \__fp_min_o:w #1 @
  {
    \exp_after:wN \__fp_minmax_loop:Nww
    \exp_after:wN \c_one
    \c_inf_fp
    #1
    \s__fp \__fp_chk:w { 3 \__fp_minmax_break_o:w } ;
  }
\cs_new:Npn \__fp_minmax_loop:Nww
    #1 \s__fp \__fp_chk:w #2#3; \s__fp \__fp_chk:w #4#5;
  {
    \if_meaning:w 3 #4
      \if_meaning:w 3 #2
        \__fp_minmax_i:ww
      \else:
        \__fp_minmax_ii:ww
      \fi:
    \else:
      \if_int_compare:w
          \__fp_compare_back:ww
            \s__fp \__fp_chk:w #4#5;
            \s__fp \__fp_chk:w #2#3;
          = #1
        \__fp_minmax_ii:ww
      \else:
        \__fp_minmax_i:ww
      \fi:
    \fi:
    \__fp_minmax_loop:Nww #1
      \s__fp \__fp_chk:w #2#3;
      \s__fp \__fp_chk:w #4#5;
  }
\cs_new:Npn \__fp_minmax_i:ww  #1 \fi: \fi: #2 \s__fp #3 ; \s__fp #4;
  { \fi: \fi: #2 \s__fp #3 ; }
\cs_new:Npn \__fp_minmax_ii:ww #1 \fi: \fi: #2 \s__fp #3 ;
  { \fi: \fi: #2 }
\cs_new:Npn \__fp_minmax_break_o:w #1 \fi: \fi: #2 \s__fp #3; #4;
  { \fi: \__fp_exp_after_o:w \s__fp #3; }
\cs_new:cpn { __fp_!_o:w } \s__fp \__fp_chk:w #1#2;
  {
    \if_meaning:w 0 #1
      \exp_after:wN \exp_after:wN \exp_after:wN \c_one_fp
    \else:
      \exp_after:wN \exp_after:wN \exp_after:wN \c_zero_fp
    \fi:
  }
\group_begin:
  \char_set_catcode_letter:N &
  \char_set_catcode_letter:N |
  \cs_new:Npn \__fp_&_o:ww #1 \s__fp \__fp_chk:w #2#3;
    {
      \if_meaning:w 0 #2 #1
        \__fp_and_return:wNw \s__fp \__fp_chk:w #2#3;
      \fi:
      \__fp_exp_after_o:w
    }
  \cs_new_nopar:Npn \__fp_|_o:ww { \__fp_&_o:ww \else: }
\group_end:
\cs_new:Npn \__fp_and_return:wNw #1; \fi: #2#3; { \fi: #2 #1; }
\cs_new:Npn \__fp_ternary:NwwN #1 #2@ #3@ #4
  {
    \if_meaning:w \__fp_parse_infix_::N #4
      \__fp_ternary_loop:Nw
        #2
        \s__fp \__fp_chk:w { \__fp_ternary_loop_break:w } ;
      \__fp_ternary_break_point:n { \exp_after:wN \__fp_ternary_i:NwwN }
      \exp_after:wN #1
      \tex_romannumeral:D -`0
      \__fp_exp_after_array_f:w #3 \s__fp_stop
      \exp_after:wN @
      \tex_romannumeral:D
        \__fp_parse_until:Nw \c_two
        \__fp_parse_expand:w
    \else:
      \__msg_kernel_expandable_error:nnnn
        { kernel } { fp-missing } { : } { ~for~?: }
      \exp_after:wN \__fp_parse_until_test:NwN
      \exp_after:wN #1
      \tex_romannumeral:D -`0
      \__fp_exp_after_array_f:w #3 \s__fp_stop
      \exp_after:wN #4
      \exp_after:wN #1
    \fi:
  }
\cs_new:Npn \__fp_ternary_loop_break:w #1 \fi: #2 \__fp_ternary_break_point:n #3
  {
    \c_zero = \c_zero \fi:
    \exp_after:wN \__fp_ternary_ii:NwwN
  }
\cs_new:Npn \__fp_ternary_loop:Nw \s__fp \__fp_chk:w #1#2;
  {
    \if_int_compare:w #1 > \c_zero
      \exp_after:wN \__fp_ternary_map_break:
    \fi:
    \__fp_ternary_loop:Nw
  }
\cs_new:Npn \__fp_ternary_map_break: #1 \__fp_ternary_break_point:n #2 {#2}
\cs_new:Npn \__fp_ternary_i:NwwN #1#2@#3@#4
  {
    \exp_after:wN \__fp_parse_until_test:NwN
    \exp_after:wN #1
    \tex_romannumeral:D -`0
    \__fp_exp_after_array_f:w #2 \s__fp_stop
    #4 #1
  }
\cs_new:Npn \__fp_ternary_ii:NwwN #1#2@#3@#4
  {
    \exp_after:wN \__fp_parse_until_test:NwN
    \exp_after:wN #1
    \tex_romannumeral:D -`0
    \__fp_exp_after_array_f:w #3 \s__fp_stop
    #4 #1
  }
%% File: l3fp-basics.dtx Copyright (C) 2011-2012 The 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 "l3kernel 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.
%%
%% -----------------------------------------------------------------------
%%
\cs_new:Npn \__fp_basics_pack_low:NNNNNw #1 #2#3#4#5 #6;
  {
    \if_meaning:w 2 #1
      + \c_one
    \fi:
    ; {#2#3#4#5} {#6} ;
  }
\cs_new:Npn \__fp_basics_pack_high:NNNNNw #1 #2#3#4#5 #6;
  {
    \if_meaning:w 2 #1
      \__fp_basics_pack_high_carry:w
    \fi:
    ; {#2#3#4#5} {#6}
  }
\cs_new:Npn \__fp_basics_pack_high_carry:w \fi: ; #1
  { \fi: + \c_one ; {1000} }
\cs_new:Npn \__fp_basics_pack_weird_low:NNNNw #1 #2#3#4 #5;
  {
    \if_meaning:w 2 #1
      + \c_one
    \fi:
    \__int_eval_end:
    #2#3#4; {#5} ;
  }
\cs_new:Npn \__fp_basics_pack_weird_high:NNNNNNNNw
   1 #1#2#3#4 #5#6#7#8 #9; { ; {#1#2#3#4} {#5#6#7#8} {#9} }
\cs_new_nopar:cpx { __fp_-_o:ww } \s__fp
  {
    \exp_not:c { __fp_+_o:ww }
    \exp_not:n { \s__fp \__fp_neg_sign:N }
  }
\cs_new:cpn { __fp_+_o:ww }
    \s__fp #1 \__fp_chk:w #2 #3 ; \s__fp \__fp_chk:w #4 #5
  {
    \if_case:w
      \if_meaning:w #2 #4
        #2 \exp_stop_f:
      \else:
        \if_int_compare:w #2 > #4 \exp_stop_f:
          \c_three
        \else:
          \c_minus_one
        \fi:
      \fi:
           \exp_after:wN \__fp_add_zeros_o:Nww \__int_value:w
    \or:   \exp_after:wN \__fp_add_normal_o:Nww \__int_value:w
    \or:   \exp_after:wN \__fp_add_inf_o:Nww \__int_value:w
    \or:   \__fp_case_return_i_o:ww
    \else: \exp_after:wN \__fp_add_return_ii_o:Nww \__int_value:w
    \fi:
    #1 #5
    \s__fp \__fp_chk:w #2 #3 ;
    \s__fp \__fp_chk:w #4 #5
  }
\cs_new:Npn \__fp_add_return_ii_o:Nww #1 #2 ; \s__fp \__fp_chk:w #3 #4
  { \__fp_exp_after_o:w \s__fp \__fp_chk:w #3 #1 }
\cs_new:Npn \__fp_add_zeros_o:Nww #1 \s__fp \__fp_chk:w 0 #2
  {
    \if_int_compare:w #2 #1 = 20 \exp_stop_f:
      \exp_after:wN \__fp_add_return_ii_o:Nww
    \else:
      \__fp_case_return_i_o:ww
    \fi:
    #1
    \s__fp \__fp_chk:w 0 #2
  }
\cs_new:Npn \__fp_add_inf_o:Nww
    #1 \s__fp \__fp_chk:w 2 #2 #3; \s__fp \__fp_chk:w 2 #4
  {
    \if_meaning:w #1 #2
      \__fp_case_return_i_o:ww
    \else:
      \__fp_case_use:nw
        {
          \if_meaning:w #1 #4
            \exp_after:wN \__fp_invalid_operation_o:Nww
            \exp_after:wN +
          \else:
            \exp_after:wN \__fp_invalid_operation_o:Nww
            \exp_after:wN -
          \fi:
        }
    \fi:
    \s__fp \__fp_chk:w 2 #2 #3;
    \s__fp \__fp_chk:w 2 #4
  }
\cs_new:Npn \__fp_add_normal_o:Nww #1 \s__fp \__fp_chk:w 1 #2
  {
    \if_meaning:w #1#2
      \exp_after:wN \__fp_add_npos_o:NnwNnw
    \else:
      \exp_after:wN \__fp_sub_npos_o:NnwNnw
    \fi:
    #2
  }
\cs_new:Npn \__fp_add_npos_o:NnwNnw #1#2#3 ; \s__fp \__fp_chk:w 1 #4 #5
  {
    \exp_after:wN \__fp_sanitize:Nw
    \exp_after:wN #1
    \int_use:N \__int_eval:w
      \if_int_compare:w #2 > #5 \exp_stop_f:
        #2
        \exp_after:wN \__fp_add_big_i_o:wNww \__int_value:w -
      \else:
        #5
        \exp_after:wN \__fp_add_big_ii_o:wNww \__int_value:w
      \fi:
      \__int_eval:w #5 - #2 ; #1 #3;
  }
\cs_new:Npn \__fp_add_big_i_o:wNww #1; #2 #3; #4;
  {
    \__fp_decimate:nNnnnn {#1}
      \__fp_add_significand_o:NnnwnnnnN
      #4
    #3
    #2
  }
\cs_new:Npn \__fp_add_big_ii_o:wNww #1; #2 #3; #4;
  {
    \__fp_decimate:nNnnnn {#1}
      \__fp_add_significand_o:NnnwnnnnN
      #3
    #4
    #2
  }
\cs_new:Npn \__fp_add_significand_o:NnnwnnnnN #1 #2#3 #4; #5#6#7#8
  {
    \exp_after:wN \__fp_add_significand_test_o:N
    \int_use:N \__int_eval:w 1#5#6 + #2
      \exp_after:wN \__fp_add_significand_pack:NNNNNNN
      \int_use:N \__int_eval:w 1#7#8 + #3 ; #1
  }
\cs_new:Npn \__fp_add_significand_pack:NNNNNNN #1 #2#3#4#5#6#7
  {
    \if_meaning:w 2 #1
      + \c_one
    \fi:
    ; #2 #3 #4 #5 #6 #7 ;
  }
\cs_new:Npn \__fp_add_significand_test_o:N #1
  {
    \if_meaning:w 2 #1
      \exp_after:wN \__fp_add_significand_carry_o:wwwNN
    \else:
      \exp_after:wN \__fp_add_significand_no_carry_o:wwwNN
    \fi:
  }
\cs_new:Npn \__fp_add_significand_no_carry_o:wwwNN
    #1; #2; #3#4 ; #5#6
  {
    \exp_after:wN \__fp_basics_pack_high:NNNNNw
    \int_use:N \__int_eval:w 1 #1
      \exp_after:wN \__fp_basics_pack_low:NNNNNw
      \int_use:N \__int_eval:w 1 #2 #3#4
        + \__fp_round:NNN #6 #4 #5
        \exp_after:wN ;
  }
\cs_new:Npn \__fp_add_significand_carry_o:wwwNN
    #1; #2; #3#4; #5#6
  {
    + \c_one
    \exp_after:wN \__fp_basics_pack_weird_high:NNNNNNNNw
    \int_use:N \__int_eval:w 1 1 #1
      \exp_after:wN \__fp_basics_pack_weird_low:NNNNw
      \int_use:N \__int_eval:w 1 #2#3 +
        \exp_after:wN \__fp_round:NNN
        \exp_after:wN #6
        \exp_after:wN #3
        \__int_value:w \__fp_round_digit:Nw #4 #5 ;
        \exp_after:wN ;
  }
\cs_new:Npn \__fp_sub_npos_o:NnwNnw #1#2#3; \s__fp \__fp_chk:w 1 #4#5#6;
  {
    \if_case:w \__fp_compare_npos:nwnw {#2} #3; {#5} #6; \exp_stop_f:
      \exp_after:wN \__fp_sub_eq_o:Nnwnw
    \or:
      \exp_after:wN \__fp_sub_npos_i_o:Nnwnw
    \else:
      \exp_after:wN \__fp_sub_npos_ii_o:Nnwnw
    \fi:
    #1 {#2} #3; {#5} #6;
  }
\cs_new:Npn \__fp_sub_eq_o:Nnwnw #1#2; #3; { \exp_after:wN \c_zero_fp }
\cs_new:Npn \__fp_sub_npos_ii_o:Nnwnw #1 #2; #3;
  {
    \exp_after:wN \__fp_sub_npos_i_o:Nnwnw
      \int_use:N \__int_eval:w \c_two - #1 \__int_eval_end:
      #3; #2;
  }
\cs_new:Npn \__fp_sub_npos_i_o:Nnwnw #1 #2#3; #4#5;
  {
    \exp_after:wN \__fp_sanitize:Nw
    \exp_after:wN #1
    \int_use:N \__int_eval:w
      #2
      \if_int_compare:w #2 = #4 \exp_stop_f:
        \exp_after:wN \__fp_sub_back_near_o:nnnnnnnnN
      \else:
        \exp_after:wN \__fp_decimate:nNnnnn \exp_after:wN
          { \int_use:N \__int_eval:w #2 - #4 - \c_one \exp_after:wN }
          \exp_after:wN \__fp_sub_back_far_o:NnnwnnnnN
      \fi:
        #5
      #3
      #1
  }
\cs_new:Npn \__fp_sub_back_near_o:nnnnnnnnN #1#2#3#4 #5#6#7#8 #9
  {
    \exp_after:wN \__fp_sub_back_near_after:wNNNNw
    \int_use:N \__int_eval:w 10#5#6 - #1#2 - \c_eleven
      \exp_after:wN \__fp_sub_back_near_pack:NNNNNNw
      \int_use:N \__int_eval:w 11#7#8 - #3#4 \exp_after:wN ;
  }
\cs_new:Npn \__fp_sub_back_near_pack:NNNNNNw #1#2#3#4#5#6#7 ;
  { + #1#2 ; {#3#4#5#6} {#7} ; }
\cs_new:Npn \__fp_sub_back_near_after:wNNNNw 10 #1#2#3#4 #5 ;
  {
    \if_meaning:w 0 #1
      \exp_after:wN \__fp_sub_back_shift:wnnnn
    \fi:
    ; {#1#2#3#4} {#5}
  }
\cs_new:Npn \__fp_sub_back_shift:wnnnn ; #1#2
  {
    \exp_after:wN \__fp_sub_back_shift_ii:ww
    \__int_value:w #1 #2 0 ;
  }
\cs_new:Npn \__fp_sub_back_shift_ii:ww #1 0 ; #2#3 ;
  {
    \if_meaning:w @ #1 @
      - \c_seven
      - \exp_after:wN \use_i:nnn
        \exp_after:wN \__fp_sub_back_shift_iii:NNNNNNNNw
        \__int_value:w #2#3 0 ~ 123456789;
    \else:
      - \__fp_sub_back_shift_iii:NNNNNNNNw #1 123456789;
    \fi:
    \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
    \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
    \exp_after:wN \__fp_sub_back_shift_iv:nnnnw
    \exp_after:wN ;
    \__int_value:w
    #1 ~ #2#3 0 ~ 0000 0000 0000 000 ;
  }
\cs_new:Npn \__fp_sub_back_shift_iii:NNNNNNNNw #1#2#3#4#5#6#7#8#9; {#8}
\cs_new:Npn \__fp_sub_back_shift_iv:nnnnw #1 ; #2 ; { ; #1 ; }
\cs_new:Npn \__fp_sub_back_far_o:NnnwnnnnN #1 #2#3 #4; #5#6#7#8
  {
    \if_case:w
      \if_int_compare:w 1 #2 = #5#6 \use_i:nnnn #7 \exp_stop_f:
        \if_int_compare:w #3 = \use_none:n #7#8 0 \exp_stop_f:
          \c_zero
        \else:
          \if_int_compare:w #3 > \use_none:n #7#8 0 - \fi: \c_one
        \fi:
      \else:
        \if_int_compare:w 1 #2 > #5#6 \use_i:nnnn #7 - \fi: \c_one
      \fi:
           \exp_after:wN \__fp_sub_back_quite_far_o:wwNN
    \or:   \exp_after:wN \__fp_sub_back_very_far_o:wwwwNN
    \else: \exp_after:wN \__fp_sub_back_not_far_o:wwwwNN
    \fi:
    #2 ~ #3 ; #5 #6 ~ #7 #8 ; #1
  }
\cs_new:Npn \__fp_sub_back_quite_far_o:wwNN #1; #2; #3#4
  {
    \exp_after:wN \__fp_sub_back_quite_far_ii:NN
    \exp_after:wN #3
    \exp_after:wN #4
  }
\cs_new:Npn \__fp_sub_back_quite_far_ii:NN #1#2
  {
    \if_case:w \__fp_round_neg:NNN #2 0 #1
      \exp_after:wN \use_i:nn
    \else:
      \exp_after:wN \use_ii:nn
    \fi:
      { ; {1000} {0000} {0000} {0000} ; }
      { - \c_one ; {9999} {9999} {9999} {9999} ; }
  }
\cs_new:Npn \__fp_sub_back_not_far_o:wwwwNN #1 ~ #2; #3 ~ #4; #5#6
  {
    - \c_one
    \exp_after:wN \__fp_sub_back_near_after:wNNNNw
    \int_use:N \__int_eval:w 1#30 - #1 - \c_eleven
      \exp_after:wN \__fp_sub_back_near_pack:NNNNNNw
      \int_use:N \__int_eval:w 11 0000 0000 + #40 - #2
        - \exp_after:wN \__fp_round_neg:NNN
          \exp_after:wN #6
          \use_none:nnnnnnn #2 #5
        \exp_after:wN ;
  }
\cs_new:Npn \__fp_sub_back_very_far_o:wwwwNN #1#2#3#4#5#6#7
  {
    \__fp_pack_eight:wNNNNNNNN
    \__fp_sub_back_very_far_ii_o:nnNwwNN
    { 0 #1#2#3 #4#5#6#7 }
    ;
  }
\cs_new:Npn \__fp_sub_back_very_far_ii_o:nnNwwNN #1#2 ; #3 ; #4 ~ #5; #6#7
  {
    \exp_after:wN \__fp_basics_pack_high:NNNNNw
    \int_use:N \__int_eval:w 1#4 - #1 - \c_one
      \exp_after:wN \__fp_basics_pack_low:NNNNNw
      \int_use:N \__int_eval:w 2#5 - #2
        - \exp_after:wN \__fp_round_neg:NNN
          \exp_after:wN #7
          \__int_value:w
            \if_int_odd:w \__int_eval:w #5 - #2 \__int_eval_end:
              1 \else: 2 \fi:
          \__int_value:w \__fp_round_digit:Nw #3 #6 ;
      \exp_after:wN ;
  }
\cs_new_nopar:cpn { __fp_*_o:ww }
  {
    \__fp_mul_cases_o:NnNnww
      *
      { - \c_two + }
      \__fp_mul_npos_o:Nww
      { }
  }
\cs_new:Npn \__fp_mul_cases_o:NnNnww
    #1#2#3#4 \s__fp \__fp_chk:w #5#6#7; \s__fp \__fp_chk:w #8#9
  {
    \if_case:w \__int_eval:w
                 \if_int_compare:w #5 #8 = \c_eleven
                   \c_one
                 \else:
                   \if_meaning:w 3 #8
                     \c_three
                   \else:
                     \if_meaning:w 3 #5
                       \c_two
                     \else:
                       \if_int_compare:w #5 #8 = \c_ten
                         \c_nine #2 - \c_two
                       \else:
                         (#5 #2 #8) / \c_two * \c_two + \c_seven
                       \fi:
                     \fi:
                   \fi:
                 \fi:
                 \if_meaning:w #6 #9 - \c_one \fi:
               \__int_eval_end:
         \__fp_case_use:nw { #3 0 }
    \or: \__fp_case_use:nw { #3 2 }
    \or: \__fp_case_return_i_o:ww
    \or: \__fp_case_return_ii_o:ww
    \or: \__fp_case_return_o:Nww \c_zero_fp
    \or: \__fp_case_return_o:Nww \c_minus_zero_fp
    \or: \__fp_case_use:nw { \__fp_invalid_operation_o:Nww #1 }
    \or: \__fp_case_use:nw { \__fp_invalid_operation_o:Nww #1 }
    \or: \__fp_case_return_o:Nww \c_inf_fp
    \or: \__fp_case_return_o:Nww \c_minus_inf_fp
    #4
    \fi:
    \s__fp \__fp_chk:w #5 #6 #7;
    \s__fp \__fp_chk:w #8 #9
  }
\cs_new:Npn \__fp_mul_npos_o:Nww
    #1 \s__fp \__fp_chk:w #2 #3 #4 #5 ; \s__fp \__fp_chk:w #6 #7 #8 #9 ;
  {
    \exp_after:wN \__fp_sanitize:Nw
    \exp_after:wN #1
    \int_use:N \__int_eval:w
      #4 + #8
      \__fp_mul_significand_o:nnnnNnnnn #5 #1 #9
  }
\cs_new:Npn \__fp_mul_significand_o:nnnnNnnnn #1#2#3#4 #5 #6#7#8#9
  {
    \exp_after:wN \__fp_mul_significand_test_f:NNN
    \exp_after:wN #5
    \int_use:N \__int_eval:w 99990000 + #1*#6 +
      \exp_after:wN \__fp_mul_significand_keep:NNNNNw
      \int_use:N \__int_eval:w 99990000 + #1*#7 + #2*#6 +
        \exp_after:wN \__fp_mul_significand_keep:NNNNNw
        \int_use:N \__int_eval:w 99990000 + #1*#8 + #2*#7 + #3*#6 +
          \exp_after:wN \__fp_mul_significand_drop:NNNNNw
          \int_use:N \__int_eval:w  99990000 + #1*#9 + #2*#8 + #3*#7 + #4*#6 +
            \exp_after:wN \__fp_mul_significand_drop:NNNNNw
            \int_use:N \__int_eval:w  99990000 + #2*#9 + #3*#8 + #4*#7 +
              \exp_after:wN \__fp_mul_significand_drop:NNNNNw
              \int_use:N \__int_eval:w  99990000 + #3*#9 + #4*#8 +
                \exp_after:wN \__fp_mul_significand_drop:NNNNNw
                \int_use:N \__int_eval:w 100000000 + #4*#9 ;
    ; \exp_after:wN ;
  }
\cs_new:Npn \__fp_mul_significand_drop:NNNNNw #1#2#3#4#5 #6;
  { #1#2#3#4#5 ; + #6 }
\cs_new:Npn \__fp_mul_significand_keep:NNNNNw #1#2#3#4#5 #6;
  { #1#2#3#4#5 ; #6 ; }
\cs_new:Npn \__fp_mul_significand_test_f:NNN #1 #2 #3
  {
    \if_meaning:w 0 #3
      \exp_after:wN \__fp_mul_significand_small_f:NNwwwN
    \else:
      \exp_after:wN \__fp_mul_significand_large_f:NwwNNNN
    \fi:
    #1 #3
  }
\cs_new:Npn \__fp_mul_significand_large_f:NwwNNNN #1 #2; #3; #4#5#6#7; +
  {
    \exp_after:wN \__fp_basics_pack_high:NNNNNw
    \int_use:N \__int_eval:w 1#2
      \exp_after:wN \__fp_basics_pack_low:NNNNNw
      \int_use:N \__int_eval:w 1#3#4#5#6#7
        + \exp_after:wN \__fp_round:NNN
          \exp_after:wN #1
          \exp_after:wN #7
          \__int_value:w \__fp_round_digit:Nw
  }
\cs_new:Npn \__fp_mul_significand_small_f:NNwwwN #1 #2#3; #4#5; #6; + #7
  {
    - \c_one
    \exp_after:wN \__fp_basics_pack_high:NNNNNw
    \int_use:N \__int_eval:w 1#3#4
      \exp_after:wN \__fp_basics_pack_low:NNNNNw
      \int_use:N \__int_eval:w 1#5#6#7
        + \exp_after:wN \__fp_round:NNN
          \exp_after:wN #1
          \exp_after:wN #7
          \__int_value:w \__fp_round_digit:Nw
  }
\cs_new_nopar:cpn { __fp_/_o:ww }
  {
    \__fp_mul_cases_o:NnNnww
      /
      { - }
      \__fp_div_npos_o:Nww
      {
        \or:
          \__fp_case_use:nw
            { \__fp_division_by_zero_o:NNww \c_inf_fp / }
        \or:
          \__fp_case_use:nw
            { \__fp_division_by_zero_o:NNww \c_minus_inf_fp / }
      }
  }
\cs_new:Npn \__fp_div_npos_o:Nww
    #1 \s__fp \__fp_chk:w 1 #2 #3 #4 ; \s__fp \__fp_chk:w 1 #5 #6 #7#8#9;
  {
    \exp_after:wN \__fp_sanitize:Nw
    \exp_after:wN #1
    \int_use:N \__int_eval:w
      #3 - #6
      \exp_after:wN \__fp_div_significand_i_o:wnnw
        \int_use:N \__int_eval:w #7 \use_i:nnnn #8 + \c_one ;
        #4
        {#7}{#8}#9 ;
        #1
  }
\cs_new:Npn \__fp_div_significand_i_o:wnnw #1 ; #2#3 #4 ;
  {
    \exp_after:wN \__fp_div_significand_test_o:w
    \int_use:N \__int_eval:w
      \exp_after:wN \__fp_div_significand_calc:wwnnnnnnn
      \int_use:N \__int_eval:w 999999 + #2 #3 0 / #1 ;
        #2 #3 ;
        #4
        { \exp_after:wN \__fp_div_significand_ii:wwn \__int_value:w #1 }
        { \exp_after:wN \__fp_div_significand_ii:wwn \__int_value:w #1 }
        { \exp_after:wN \__fp_div_significand_ii:wwn \__int_value:w #1 }
        { \exp_after:wN \__fp_div_significand_iii:wwnnnnn \__int_value:w #1 }
  }
\cs_new:Npn \__fp_div_significand_calc:wwnnnnnnn 1#1
  {
    \if_meaning:w 1 #1
      \exp_after:wN \__fp_div_significand_calc_i:wwnnnnnnn
    \else:
      \exp_after:wN \__fp_div_significand_calc_ii:wwnnnnnnn
    \fi:
  }
\cs_new:Npn \__fp_div_significand_calc_i:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
  {
    1 1 #1
    #9 \exp_after:wN ;
    \int_use:N \__int_eval:w \c__fp_Bigg_leading_shift_int
      + #2 - #1 * #5 - #5#60
      \exp_after:wN \__fp_pack_Bigg:NNNNNNw
      \int_use:N \__int_eval:w \c__fp_Bigg_middle_shift_int
        + #3 - #1 * #6 - #70
        \exp_after:wN \__fp_pack_Bigg:NNNNNNw
        \int_use:N \__int_eval:w \c__fp_Bigg_middle_shift_int
          + #4 - #1 * #7 - #80
          \exp_after:wN \__fp_pack_Bigg:NNNNNNw
          \int_use:N \__int_eval:w \c__fp_Bigg_trailing_shift_int
            - #1 * #8 ;
    {#5}{#6}{#7}{#8}
  }
\cs_new:Npn \__fp_div_significand_calc_ii:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
  {
    1 0 #1
    #9 \exp_after:wN ;
    \int_use:N \__int_eval:w \c__fp_Bigg_leading_shift_int
      + #2 - #1 * #5
      \exp_after:wN \__fp_pack_Bigg:NNNNNNw
      \int_use:N \__int_eval:w \c__fp_Bigg_middle_shift_int
        + #3 - #1 * #6
        \exp_after:wN \__fp_pack_Bigg:NNNNNNw
        \int_use:N \__int_eval:w \c__fp_Bigg_middle_shift_int
          + #4 - #1 * #7
          \exp_after:wN \__fp_pack_Bigg:NNNNNNw
          \int_use:N \__int_eval:w \c__fp_Bigg_trailing_shift_int
            - #1 * #8 ;
    {#5}{#6}{#7}{#8}
  }
\cs_new:Npn \__fp_div_significand_ii:wwn #1; #2;#3
  {
    \exp_after:wN \__fp_div_significand_pack:NNN
    \int_use:N \__int_eval:w
      \exp_after:wN \__fp_div_significand_calc:wwnnnnnnn
      \int_use:N \__int_eval:w 999999 + #2 #3 0 / #1 ; #2 #3 ;
  }
\cs_new:Npn \__fp_div_significand_iii:wwnnnnn #1; #2;#3#4#5 #6#7
  {
    0
    \exp_after:wN \__fp_div_significand_iv:wwnnnnnnn
    \int_use:N \__int_eval:w (\c_two * #2 #3) / #6 #7 ; % <- P
      #2 ; {#3} {#4} {#5}
      {#6} {#7}
  }
\cs_new:Npn \__fp_div_significand_iv:wwnnnnnnn #1; #2;#3#4#5 #6#7#8#9
  {
    + \c_five * #1
    \exp_after:wN \__fp_div_significand_vi:Nw
    \int_use:N \__int_eval:w -20 + 2*#2#3 - #1*#6#7 +
      \exp_after:wN \__fp_div_significand_v:NN
      \int_use:N \__int_eval:w 199980 + 2*#4 - #1*#8 +
        \exp_after:wN \__fp_div_significand_v:NN
        \int_use:N \__int_eval:w 200000 + 2*#5 - #1*#9 ;
  }
\cs_new:Npn \__fp_div_significand_v:NN #1#2 { #1#2 \__int_eval_end: + }
\cs_new:Npn \__fp_div_significand_vi:Nw #1#2;
  {
    \if_meaning:w 0 #1
      \if_int_compare:w \__int_eval:w #2 > \c_zero + \c_one \fi:
    \else:
      \if_meaning:w - #1 - \else: + \fi: \c_one
    \fi:
    ;
  }
\cs_new:Npn \__fp_div_significand_pack:NNN 1 #1 #2 { + #1 #2 ; }
\cs_new:Npn \__fp_div_significand_test_o:w 10 #1
  {
    \if_meaning:w 0 #1
      \exp_after:wN \__fp_div_significand_small_o:wwwNNNNwN
    \else:
      \exp_after:wN \__fp_div_significand_large_o:wwwNNNNwN
    \fi:
    #1
  }
\cs_new:Npn \__fp_div_significand_small_o:wwwNNNNwN
    0 #1; #2; #3; #4#5#6#7#8; #9
  {
    \exp_after:wN \__fp_basics_pack_high:NNNNNw
    \int_use:N \__int_eval:w 1 #1#2
      \exp_after:wN \__fp_basics_pack_low:NNNNNw
      \int_use:N \__int_eval:w 1 #3#4#5#6#7
        + \__fp_round:NNN #9 #7 #8
        \exp_after:wN ;
  }
\cs_new:Npn \__fp_div_significand_large_o:wwwNNNNwN
    #1; #2; #3; #4#5#6#7#8; #9
  {
    + \c_one
    \exp_after:wN \__fp_basics_pack_weird_high:NNNNNNNNw
    \int_use:N \__int_eval:w 1 #1 #2
      \exp_after:wN \__fp_basics_pack_weird_low:NNNNw
      \int_use:N \__int_eval:w 1 #3 #4 #5 #6 +
        \exp_after:wN \__fp_round:NNN
        \exp_after:wN #9
        \exp_after:wN #6
        \__int_value:w \__fp_round_digit:Nw #7 #8 ;
      \exp_after:wN ;
  }
\cs_new:cpn { __fp_-_o:w } #1 \s__fp \__fp_chk:w #2 #3
  {
    \exp_after:wN \__fp_exp_after_o:w
    \exp_after:wN \s__fp
    \exp_after:wN \__fp_chk:w
    \exp_after:wN #2
    \int_use:N \__int_eval:w \c_two - #3 \__int_eval_end:
  }
\cs_new:Npn \__fp_abs_o:w \s__fp \__fp_chk:w #1 #2
  {
    \exp_after:wN \__fp_exp_after_o:w
    \exp_after:wN \s__fp
    \exp_after:wN \__fp_chk:w
    \exp_after:wN #1
    \__int_value:w \if_meaning:w 1 #2 1 \else: 0 \fi: \exp_stop_f:
  }
%% File: l3fp-extended.dtx Copyright (C) 2011-2012 The 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 "l3kernel 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.
%%
%% -----------------------------------------------------------------------
%%
\tl_const:Nn \c__fp_one_fixed_tl
  { {10000} {0000} {0000} {0000} {0000} {0000} }
\cs_new:Npn \__fp_fixed_continue:wn #1; #2 { #2 #1; }
\cs_new:Npn \__fp_fixed_add_one:wN #1#2; #3
  {
    \exp_after:wN #3 \exp_after:wN
      { \int_use:N \__int_eval:w \c_ten_thousand + #1 } #2 ;
  }
\cs_new:Npn \__fp_fixed_mul_after:wn #1; #2 { #2 {#1} }
\cs_new:Npn \__fp_fixed_div_int:wwN #1#2#3#4#5#6 ; #7 ; #8
  {
    \exp_after:wN \__fp_fixed_div_int_after:Nw
    \exp_after:wN #8
    \int_use:N \__int_eval:w \c_minus_one
      \__fp_fixed_div_int_i:wnN
      #1; {#7} \__fp_fixed_div_int_ii:wnn
      #2; {#7} \__fp_fixed_div_int_ii:wnn
      #3; {#7} \__fp_fixed_div_int_ii:wnn
      #4; {#7} \__fp_fixed_div_int_ii:wnn
      #5; {#7} \__fp_fixed_div_int_ii:wnn
      #6; {#7} \__fp_fixed_div_int_iii:wnn ;
  }
\cs_new:Npn \__fp_fixed_div_int_i:wnN #1; #2 #3
  {
    \exp_after:wN #3
    \int_use:N \__int_eval:w #1 / #2 - \c_one ;
    {#2}
    {#1}
  }
\cs_new:Npn \__fp_fixed_div_int_ii:wnn #1; #2 #3
  {
    + #1
    \exp_after:wN \__fp_fixed_div_int_pack:Nw
    \int_use:N \__int_eval:w 9999
      \exp_after:wN \__fp_fixed_div_int_i:wnN
      \int_use:N \__int_eval:w #3 - #1*#2 \__int_eval_end:
  }
\cs_new:Npn \__fp_fixed_div_int_iii:wnn #1; #2 #3 { + #1 + \c_two ; }
\cs_new:Npn \__fp_fixed_div_int_pack:Nw #1 #2; { + #1; {#2} }
\cs_new:Npn \__fp_fixed_div_int_after:Nw #1 #2; { #1 {#2} }
\cs_new_nopar:Npn \__fp_fixed_add:wwn { \__fp_fixed_add_i:Nnnnnwnn + }
\cs_new_nopar:Npn \__fp_fixed_sub:wwn { \__fp_fixed_add_i:Nnnnnwnn - }
\cs_new:Npn \__fp_fixed_add_i:Nnnnnwnn #1 #2#3#4#5 #6; #7#8
  {
    \exp_after:wN \__fp_fixed_add_after:NNNNNwn
    \int_use:N \__int_eval:w 9 9999 9998 + #2#3 #1 #7#8
      \exp_after:wN \__fp_fixed_add_pack:NNNNNwn
      \int_use:N \__int_eval:w 1 9999 9998 + #4#5
        \__fp_fixed_add_ii:nnNnnnwn #6 #1
  }
\cs_new:Npn \__fp_fixed_add_ii:nnNnnnwn #1#2 #3 #4#5 #6#7 ; #8
  {
    #3 #4#5
    \exp_after:wN \__fp_fixed_add_pack:NNNNNwn
    \int_use:N \__int_eval:w 2 0000 0000 #3 #6#7 + #1#2 ; {#8} ;
  }
\cs_new:Npn \__fp_fixed_add_pack:NNNNNwn #1 #2#3#4#5 #6; #7
  { + #1 ; {#7} {#2#3#4#5} {#6} }
\cs_new:Npn \__fp_fixed_add_after:NNNNNwn 1 #1 #2#3#4#5 #6; #7
  { #7 {#1#2#3#4#5} {#6} }
\cs_new:Npn \__fp_fixed_mul:wwn #1#2#3#4 #5; #6#7#8#9
  {
    \exp_after:wN \__fp_fixed_mul_after:wn
    \int_use:N \__int_eval:w \c__fp_leading_shift_int
      \exp_after:wN \__fp_pack:NNNNNwn
      \int_use:N \__int_eval:w \c__fp_middle_shift_int
        + #1*#6
        \exp_after:wN \__fp_pack:NNNNNwn
        \int_use:N \__int_eval:w \c__fp_middle_shift_int
          + #1*#7 + #2*#6
          \exp_after:wN \__fp_pack:NNNNNwn
          \int_use:N \__int_eval:w \c__fp_middle_shift_int
            + #1*#8 + #2*#7 + #3*#6
            \exp_after:wN \__fp_pack:NNNNNwn
            \int_use:N \__int_eval:w \c__fp_middle_shift_int
              + #1*#9 + #2*#8 + #3*#7 + #4*#6
              \exp_after:wN \__fp_pack:NNNNNwn
              \int_use:N \__int_eval:w \c__fp_trailing_shift_int
                + #2*#9 + #3*#8 + #4*#7
                + ( #3*#9 + #4*#8
                  + \__fp_fixed_mul_i:nnnnnnnwn #5 {#6}{#7}  {#1}{#2}
  }
\cs_new:Npn \__fp_fixed_mul_i:nnnnnnnwn #1#2 #3#4 #5#6 #7#8 ; #9
  {
    #1*#4 + #2*#3 + #5*#8 + #6*#7 ) / \c_ten_thousand
    + #1*#3 + #5*#7 ;
    {#9} ;
  }
\cs_new:Npn \__fp_fixed_mul_add:wwwn #1; #2; #3#4#5#6#7#8; #9
  {
    \exp_after:wN \__fp_fixed_mul_after:wn
    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int
      \exp_after:wN \__fp_pack_big:NNNNNNwn
      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #3 #4
        \__fp_fixed_mul_add_i:Nwnnnwnnn +
          + #5 #6 ; #2 ; #1 ; #2 ; +
          + #7 #8 ; {#9} ;
  }
\cs_new:Npn \__fp_fixed_mul_sub_back:wwwn #1; #2; #3#4#5#6#7#8; #9
  {
    \exp_after:wN \__fp_fixed_mul_after:wn
    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int
      \exp_after:wN \__fp_pack_big:NNNNNNwn
      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #3 #4
        \__fp_fixed_mul_add_i:Nwnnnwnnn -
          + #5 #6 ; #2 ; #1 ; #2 ; -
          + #7 #8 ; {#9} ;
  }
\cs_new:Npn \__fp_fixed_one_minus_mul:wwn #1; #2; #3
  {
    \exp_after:wN \__fp_fixed_mul_after:wn
    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int
      \exp_after:wN \__fp_pack_big:NNNNNNwn
      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + 1 0000 0000
        \__fp_fixed_mul_add_i:Nwnnnwnnn -
          ; #2 ; #1 ; #2 ; -
          ; {#3} ;
  }
\cs_new:Npn \__fp_fixed_mul_add_i:Nwnnnwnnn #1 #2; #3#4#5#6; #7#8#9
  {
    #1 #7*#3
    \exp_after:wN \__fp_pack_big:NNNNNNwn
    \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
      #1 #7*#4 #1 #8*#3
      \exp_after:wN \__fp_pack_big:NNNNNNwn
      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
        #1 #7*#5 #1 #8*#4 #1 #9*#3 #2
        \exp_after:wN \__fp_pack_big:NNNNNNwn
        \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
          #1 \__fp_fixed_mul_add_ii:nnnnwnnnn {#7}{#8}{#9}
  }
\cs_new:Npn \__fp_fixed_mul_add_ii:nnnnwnnnn #1#2#3#4#5; #6#7#8#9
  {
    ( #1*#9 + #2*#8 + #3*#7 + #4*#6 )
    \exp_after:wN \__fp_pack_big:NNNNNNwn
    \int_use:N \__int_eval:w \c__fp_big_trailing_shift_int
      \__fp_fixed_mul_add_iii:nnnnwnnwN
        { #6 + #4*#7 + #3*#8 + #2*#9 + #1 }
        { #7 + #4*#8 + #3*#9 + #2 }
        {#1} #5;
        {#6}
  }
\cs_new:Npn \__fp_fixed_mul_add_iii:nnnnwnnwN #1#2 #3#4#5; #6#7#8; #9
  {
    #9 (#4* #1 *#7)
    #9 (#5*#6+#4* #2 *#7+#3*#8) / \c_ten_thousand
  }
\cs_new:Npn \__fp_fixed_to_float:Nw #1#2; { \__fp_fixed_to_float:wN #2; #1 }
\cs_new:Npn \__fp_fixed_to_float:wN #1#2#3#4#5#6; #7
  {
    + \c_four % for the 8-digit-at-the-start thing.
    \exp_after:wN \exp_after:wN
    \exp_after:wN \__fp_fixed_to_loop:N
    \exp_after:wN \use_none:n
    \int_use:N \__int_eval:w
      1 0000 0000 + #1   \exp_after:wN \__fp_use_none_stop_f:n
      \__int_value:w   1#2 \exp_after:wN \__fp_use_none_stop_f:n
      \__int_value:w 1#3#4 \exp_after:wN \__fp_use_none_stop_f:n
      \__int_value:w 1#5#6
    \exp_after:wN ;
    \exp_after:wN ;
  }
\cs_new:Npn \__fp_fixed_to_loop:N #1
  {
    \if_meaning:w 0 #1
      - \c_one
      \exp_after:wN \__fp_fixed_to_loop:N
    \else:
      \exp_after:wN \__fp_fixed_to_loop_end:w
      \exp_after:wN #1
    \fi:
  }
\cs_new:Npn \__fp_fixed_to_loop_end:w #1 #2 ;
  {
    \if_meaning:w ; #1
      \exp_after:wN \__fp_fixed_to_float_zero:w
    \else:
      \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
      \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
      \exp_after:wN \__fp_fixed_to_float_pack:ww
      \exp_after:wN ;
    \fi:
    #1 #2 0000 0000 0000 0000 ;
  }
\cs_new:Npn \__fp_fixed_to_float_zero:w ; 0000 0000 0000 0000 ;
  {
    - \c_two * \c__fp_max_exponent_int ;
    {0000} {0000} {0000} {0000} ;
  }
\cs_new:Npn \__fp_fixed_to_float_pack:ww #1 ; #2#3 ; ;
  {
    \if_int_compare:w #2 > \c_four
      \exp_after:wN \__fp_fixed_to_float_round_up:wnnnnw
    \fi:
    ; #1 ;
  }
\cs_new:Npn \__fp_fixed_to_float_round_up:wnnnnw ; #1#2#3#4 ;
  {
    \exp_after:wN \__fp_basics_pack_high:NNNNNw
    \int_use:N \__int_eval:w 1 #1#2
      \exp_after:wN \__fp_basics_pack_low:NNNNNw
      \int_use:N \__int_eval:w 1 #3#4 + \c_one ;
  }
\cs_new:Npn \__fp_fixed_inv_to_float:wN #1#2; #3
  {
    + \__int_eval:w % ^^A todo: remove the +?
        \if_int_compare:w #1 < \c_one_thousand
          \__fp_fixed_dtf_zeros:wNnnnnnn
        \fi:
        \__fp_fixed_dtf_no_zero:Nwn + {#1} #2 \s__fp
        \__fp_fixed_dtf_approx:n
        {10000} {0000} {0000} {0000} {0000} {0000} ;
  }
\cs_new:Npn \__fp_fixed_div_to_float:ww #1#2; #3#4;
  {
    \if_int_compare:w #1 < \c_one_thousand
      \__fp_fixed_dtf_zeros:wNnnnnnn
    \fi:
    \__fp_fixed_dtf_no_zero:Nwn - {#1} #2 \s__fp
    {
      \if_int_compare:w #3 < \c_one_thousand
        \__fp_fixed_dtf_zeros:wNnnnnnn
      \fi:
      \__fp_fixed_dtf_no_zero:Nwn + {#3} #4 \s__fp
      \__fp_fixed_dtf_approx:n
    }
  }
\cs_new:Npn \__fp_fixed_dtf_no_zero:Nwn #1#2 \s__fp #3 { #3 #2; }
\cs_new:Npn \__fp_fixed_dtf_zeros:wNnnnnnn
    \fi: \__fp_fixed_dtf_no_zero:Nwn #1#2#3#4#5#6#7
  {
    \fi:
    #1 \c_minus_one
    \exp_after:wN \use_i_ii:nnn
    \exp_after:wN \__fp_fixed_dtf_zeros:NN
    \exp_after:wN #1
    \int_use:N \__int_eval:w 10 0000 + #2 \__int_eval_end: #3#4#5#6#7
    ; 1 ;
  }
\cs_new:Npn \__fp_fixed_dtf_zeros:NN #1#2
  {
    \if_meaning:w 0 #2
      #1 \c_one
    \else:
      \__fp_fixed_dtf_zeros_end:wNww #2
    \fi:
    \__fp_fixed_dtf_zeros:NN #1
  }
\cs_new:Npn \__fp_fixed_dtf_zeros_end:wNww
    #1 \fi: \__fp_fixed_dtf_zeros:NN #2 #3; #4 \s__fp
  {
    \fi:
    \if_meaning:w ; #1
      #2 \c_two * \c__fp_max_exponent_int
      \use_i_ii:nnn
    \fi:
    \__fp_fixed_dtf_zeros_ii:ww
    #1#3 0000 0000 0000 0000 0000 0000 ;
  }
\cs_new:Npn \__fp_fixed_dtf_zeros_ii:ww
  {
    \__fp_pack_twice_four:wNNNNNNNN
    \__fp_pack_twice_four:wNNNNNNNN
    \__fp_pack_twice_four:wNNNNNNNN
    \__fp_fixed_dtf_zeros_iii:ww
    ;
  }
\cs_new:Npn \__fp_fixed_dtf_zeros_iii:ww #1; #2; #3 { #3 #1; }
\cs_new:Npn \__fp_fixed_dtf_approx:n #1
  {
    \exp_after:wN \__fp_fixed_dtf_approx_ii:wnn
    \int_use:N \__int_eval:w 10 0000 0000 / ( #1 + \c_one ) ;
    {#1}
  }
\cs_new:Npn \__fp_fixed_dtf_approx_ii:wnn #1; #2#3
  {
    \exp_after:wN \__fp_fixed_dtf_approx_iii:NNNNNw
    \int_use:N \__int_eval:w 10 0000 0000 - 1750
      + #1000 + (10 0000 0000/#2-#1) * (1000-#3/10) ;
    {#2}{#3}
  }
\cs_new:Npn \__fp_fixed_dtf_approx_iii:NNNNNw 1#1#2#3#4#5#6; #7; #8;
  {
    + \c_four % because of the line below "dtf_epsilon" here.
    \__fp_fixed_mul:wwn {000#1}{#2#3#4#5}{#6}{0000}{0000}{0000} ; #7;
    \__fp_fixed_dtf_epsilon:wN
    \__fp_fixed_mul:wwn {000#1}{#2#3#4#5}{#6}{0000}{0000}{0000} ;
    \__fp_fixed_mul:wwn #8;
    \__fp_fixed_to_float:wN ?
  }
\cs_new:Npn \__fp_fixed_dtf_epsilon:wN #1#2#3#4#5#6;
  {
    \exp_after:wN \__fp_fixed_dtf_epsilon_ii:NNNNNww
    \int_use:N \__int_eval:w 1 9999 9998 - #3#4 +
      \exp_after:wN \__fp_fixed_dtf_epsilon_pack:NNNNNw
      \int_use:N \__int_eval:w 2 0000 0000 - #5#6 ; {0000} ;
  }
\cs_new:Npn \__fp_fixed_dtf_epsilon_pack:NNNNNw #1#2#3#4#5#6;
  { #1 ; {#2#3#4#5} {#6} }
\cs_new:Npn \__fp_fixed_dtf_epsilon_ii:NNNNNww #1#2#3#4#5#6; #7;
  {
    \__fp_fixed_mul:wwn %^^A todo: optimize to use \__fp_mul_significand.
      {0000} {#2#3#4#5} {#6} #7 ;
      {0000} {#2#3#4#5} {#6} #7 ;
    \__fp_fixed_add_one:wN
    \__fp_fixed_mul:wwn {10000} {#2#3#4#5} {#6} #7 ;
  }
%% File: l3fp-expo.dtx Copyright (C) 2011-2012 The 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 "l3kernel 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.
%%
%% -----------------------------------------------------------------------
%%
\tl_const:Nn \c__fp_ln_i_fixed_tl   { {0000}{0000}{0000}{0000}{0000}{0000} }
\tl_const:Nn \c__fp_ln_ii_fixed_tl  { {6931}{4718}{0559}{9453}{0941}{7232} }
\tl_const:Nn \c__fp_ln_iii_fixed_tl {{10986}{1228}{8668}{1096}{9139}{5245} }
\tl_const:Nn \c__fp_ln_iv_fixed_tl  {{13862}{9436}{1119}{8906}{1883}{4464} }
\tl_const:Nn \c__fp_ln_vi_fixed_tl  {{17917}{5946}{9228}{0550}{0081}{2477} }
\tl_const:Nn \c__fp_ln_vii_fixed_tl {{19459}{1014}{9055}{3133}{0510}{5353} }
\tl_const:Nn \c__fp_ln_viii_fixed_tl{{20794}{4154}{1679}{8359}{2825}{1696} }
\tl_const:Nn \c__fp_ln_ix_fixed_tl  {{21972}{2457}{7336}{2193}{8279}{0490} }
\tl_const:Nn \c__fp_ln_x_fixed_tl   {{23025}{8509}{2994}{0456}{8401}{7991} }
\cs_new:Npn \__fp_ln_o:w \s__fp \__fp_chk:w #1 #2
  {
    \if_meaning:w 2 #2
      \__fp_case_use:nw { \__fp_invalid_operation_o:nw { ln } }
    \fi:
    \if_case:w #1 \exp_stop_f:
      \__fp_case_use:nw
        { \__fp_division_by_zero_o:Nnw \c_minus_inf_fp { ln } }
    \or:
    \else:
      \__fp_case_return_same_o:w
    \fi:
    \__fp_ln_npos_o:w \s__fp \__fp_chk:w #1#2
  }
\cs_new:Npn \__fp_ln_npos_o:w \s__fp \__fp_chk:w 10#1#2#3;
  { %^^A todo: ln(1) should be "exact zero", not "underflow"
    \exp_after:wN \__fp_sanitize:Nw
    \__int_value:w % for the overall sign
      \if_int_compare:w #1 < \c_one
        2
      \else:
        0
      \fi:
      \exp_after:wN \exp_stop_f:
      \int_use:N \__int_eval:w % for the exponent
        \__fp_ln_significand:NNNNnnnN #2#3
        \__fp_ln_exponent:wn {#1}
  }
\cs_new:Npn \__fp_ln_significand:NNNNnnnN #1#2#3#4
  {
    \exp_after:wN \__fp_ln_x_ii:wnnnn
    \__int_value:w
      \if_case:w #1 \exp_stop_f:
      \or:
        \if_int_compare:w #2 < \c_four
          \__int_eval:w \c_ten - #2
        \else:
          6
        \fi:
      \or: 4
      \or: 3
      \or: 2
      \or: 2
      \or: 2
      \else: 1
      \fi:
    ; { #1 #2 #3 #4 }
  }
\cs_new:Npn \__fp_ln_x_ii:wnnnn #1; #2#3#4#5
  {
    \exp_after:wN \__fp_ln_div_after:Nw
    \cs:w c__fp_ln_ \tex_romannumeral:D #1 _fixed_tl \exp_after:wN \cs_end:
    \__int_value:w
      \exp_after:wN \__fp_ln_x_iv:wnnnnnnnn
      \int_use:N \__int_eval:w
        \exp_after:wN \__fp_ln_x_iii_var:NNNNNw
        \int_use:N \__int_eval:w 9999 9999 + #1*#2#3 +
          \exp_after:wN \__fp_ln_x_iii:NNNNNw
          \int_use:N \__int_eval:w 1 0000 0000 + #1*#4#5 ;
    {20000} {0000} {0000} {0000}
  } %^^A todo: reoptimize (a generalization attempt failed).
\cs_new:Npn \__fp_ln_x_iii:NNNNNw #1 #2#3#4#5 #6; { #1; {#2#3#4#5} {#6} }
\cs_new:Npn \__fp_ln_x_iii_var:NNNNNw #1 #2#3#4#5 #6;
  {
    #1#2#3#4#5 + \c_one ;
    {#1#2#3#4#5} {#6}
  }
\cs_new:Npn \__fp_ln_x_iv:wnnnnnnnn #1; #2#3#4#5 #6#7#8#9
  {
    \exp_after:wN \__fp_div_significand_pack:NNN
    \int_use:N \__int_eval:w
    \__fp_ln_div_i:w #1 ;
      #6 #7 ; {#8} {#9}
      {#2} {#3} {#4} {#5}
      { \exp_after:wN \__fp_ln_div_ii:wwn \__int_value:w #1 }
      { \exp_after:wN \__fp_ln_div_ii:wwn \__int_value:w #1 }
      { \exp_after:wN \__fp_ln_div_ii:wwn \__int_value:w #1 }
      { \exp_after:wN \__fp_ln_div_ii:wwn \__int_value:w #1 }
      { \exp_after:wN \__fp_ln_div_vi:wwn \__int_value:w #1 }
  }
\cs_new:Npn \__fp_ln_div_i:w #1;
  {
    \exp_after:wN \__fp_div_significand_calc:wwnnnnnnn
    \int_use:N \__int_eval:w 999999 + 2 0000 0000 / #1 ; % Q1
  }
\cs_new:Npn \__fp_ln_div_ii:wwn #1; #2;#3 % y; B1;B2 <- for k=1
  {
    \exp_after:wN \__fp_div_significand_pack:NNN
    \int_use:N \__int_eval:w
      \exp_after:wN \__fp_div_significand_calc:wwnnnnnnn
      \int_use:N \__int_eval:w 999999 + #2 #3 / #1 ; % Q2
      #2 #3 ;
  }
\cs_new:Npn \__fp_ln_div_vi:wwn #1; #2;#3#4#5 #6#7#8#9 %y;F1;F2F3F4x1x2x3x4
  {
    \exp_after:wN \__fp_div_significand_pack:NNN
    \int_use:N \__int_eval:w 1000000 + #2 #3 / #1 ; % Q6
  }
\cs_new:Npn \__fp_ln_div_after:Nw #1#2;
  {
    \if_meaning:w 0 #2
      \exp_after:wN \__fp_ln_t_small:Nw
    \else:
      \exp_after:wN \__fp_ln_t_large:NNw
      \exp_after:wN -
    \fi:
    #1
  }
\cs_new:Npn \__fp_ln_t_small:Nw #1 #2; #3; #4; #5; #6; #7;
  {
    \exp_after:wN \__fp_ln_t_large:NNw
    \exp_after:wN + % <sign>
    \exp_after:wN #1
    \int_use:N \__int_eval:w 9999 - #2 \exp_after:wN ;
    \int_use:N \__int_eval:w 9999 - #3 \exp_after:wN ;
    \int_use:N \__int_eval:w 9999 - #4 \exp_after:wN ;
    \int_use:N \__int_eval:w 9999 - #5 \exp_after:wN ;
    \int_use:N \__int_eval:w 9999 - #6 \exp_after:wN ;
    \int_use:N \__int_eval:w 1 0000 - #7 ;
  }
\cs_new:Npn \__fp_ln_t_large:NNw #1 #2 #3; #4; #5; #6; #7; #8;
  {
    \exp_after:wN \__fp_ln_square_t_after:w
    \int_use:N \__int_eval:w 9999 0000 + #3*#3
      \exp_after:wN \__fp_ln_square_t_pack:NNNNNw
      \int_use:N \__int_eval:w 9999 0000 + 2*#3*#4
        \exp_after:wN \__fp_ln_square_t_pack:NNNNNw
        \int_use:N \__int_eval:w 9999 0000 + 2*#3*#5 + #4*#4
          \exp_after:wN \__fp_ln_square_t_pack:NNNNNw
          \int_use:N \__int_eval:w 9999 0000 + 2*#3*#6 + 2*#4*#5
            \exp_after:wN \__fp_ln_square_t_pack:NNNNNw
            \int_use:N \__int_eval:w 1 0000 0000 + 2*#3*#7 + 2*#4*#6 + #5*#5
              + (2*#3*#8 + 2*#4*#7 + 2*#5*#6) / 1 0000
              % ; ; ;
    \exp_after:wN \__fp_ln_twice_t_after:w
    \int_use:N \__int_eval:w -1 + 2*#3
      \exp_after:wN \__fp_ln_twice_t_pack:Nw
      \int_use:N \__int_eval:w 9999 + 2*#4
        \exp_after:wN \__fp_ln_twice_t_pack:Nw
        \int_use:N \__int_eval:w 9999 + 2*#5
          \exp_after:wN \__fp_ln_twice_t_pack:Nw
          \int_use:N \__int_eval:w 9999 + 2*#6
            \exp_after:wN \__fp_ln_twice_t_pack:Nw
            \int_use:N \__int_eval:w 9999 + 2*#7
              \exp_after:wN \__fp_ln_twice_t_pack:Nw
              \int_use:N \__int_eval:w 10000 + 2*#8 ; ;
    { \__fp_ln_c:NwNw #1 }
    #2
  }
\cs_new:Npn \__fp_ln_twice_t_pack:Nw #1 #2; { + #1 ; {#2} }
\cs_new:Npn \__fp_ln_twice_t_after:w #1; { ;;; {#1} }
\cs_new:Npn \__fp_ln_square_t_pack:NNNNNw #1 #2#3#4#5 #6;
  { + #1#2#3#4#5 ; {#6} }
\cs_new:Npn \__fp_ln_square_t_after:w 1 0 #1#2#3 #4;
  { \__fp_ln_Taylor:wwNw {0#1#2#3} {#4} }
\cs_new:Npn \__fp_ln_Taylor:wwNw
  { \__fp_ln_Taylor_loop:www 21 ; {0000}{0000}{0000}{0000}{0000}{0000} ; }
\cs_new:Npn \__fp_ln_Taylor_loop:www #1; #2; #3;
  {
    \if_int_compare:w #1 = \c_one
      \__fp_ln_Taylor_break:w
    \fi:
    \exp_after:wN \__fp_fixed_div_int:wwN \c__fp_one_fixed_tl ; #1;
    \__fp_fixed_add:wwn #2;
    \__fp_fixed_mul:wwn #3;
    {
      \exp_after:wN \__fp_ln_Taylor_loop:www
      \int_use:N \__int_eval:w #1 - \c_two ;
    }
    #3;
  }
\cs_new:Npn \__fp_ln_Taylor_break:w \fi: #1 \__fp_fixed_add:wwn #2#3; #4 ;;
  {
    \fi:
    \exp_after:wN \__fp_fixed_mul:wwn
    \exp_after:wN { \int_use:N \__int_eval:w 10000 + #2 } #3;
  }
\cs_new:Npn \__fp_ln_c:NwNw #1 #2; #3
  {
    \if_meaning:w + #1
      \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_sub:wwn
    \else:
      \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_add:wwn
    \fi:
    #3 ; #2 ;
  }
\cs_new:Npn \__fp_ln_exponent:wn #1; #2
  {
    \if_case:w #2 \exp_stop_f:
      \c_zero \__fp_case_return:nw { \__fp_fixed_to_float:Nw 2 }
    \or:
      \exp_after:wN \__fp_ln_exponent_one:ww \__int_value:w
    \else:
      \if_int_compare:w #2 > \c_zero
        \exp_after:wN \__fp_ln_exponent_small:NNww
        \exp_after:wN 0
        \exp_after:wN \__fp_fixed_sub:wwn \__int_value:w
      \else:
        \exp_after:wN \__fp_ln_exponent_small:NNww
        \exp_after:wN 2
        \exp_after:wN \__fp_fixed_add:wwn \__int_value:w -
      \fi:
    \fi:
    #2; #1;
  }
\cs_new:Npn \__fp_ln_exponent_one:ww 1; #1;
  {
    \c_zero
    \exp_after:wN \__fp_fixed_sub:wwn \c__fp_ln_x_fixed_tl ; #1;
    \__fp_fixed_to_float:wN 0
  }
\cs_new:Npn \__fp_ln_exponent_small:NNww #1#2#3; #4#5#6#7#8#9;
  {
    \c_four
    \exp_after:wN \__fp_fixed_mul:wwn
      \c__fp_ln_x_fixed_tl ;
      {#3}{0000}{0000}{0000}{0000}{0000} ;
    #2
      {0000}{#4}{#5}{#6}{#7}{#8};
    \__fp_fixed_to_float:wN #1
  }
\cs_new:Npn \__fp_exp_o:w \s__fp \__fp_chk:w #1#2
  {
    \if_case:w #1 \exp_stop_f:
      \__fp_case_return_o:Nw \c_one_fp
    \or:
      \exp_after:wN \__fp_exp_normal:w
    \or:
      \if_meaning:w 0 #2
        \exp_after:wN \__fp_case_return_o:Nw
        \exp_after:wN \c_inf_fp
      \else:
        \exp_after:wN \__fp_case_return_o:Nw
        \exp_after:wN \c_zero_fp
      \fi:
    \or:
      \__fp_case_return_same_o:w
    \fi:
    \s__fp \__fp_chk:w #1#2
  }
\cs_new:Npn \__fp_exp_normal:w \s__fp \__fp_chk:w 1#1
  {
    \if_meaning:w 0 #1
      \__fp_exp_pos:NNwnw + \__fp_fixed_to_float:wN
    \else:
      \__fp_exp_pos:NNwnw - \__fp_fixed_inv_to_float:wN
    \fi:
  }
\cs_new:Npn \__fp_exp_pos:NNwnw #1#2#3 \fi: #4#5;
  {
    \fi:
    \exp_after:wN \__fp_sanitize:Nw
    \exp_after:wN 0
    \__int_value:w #1 \__int_eval:w
      \if_int_compare:w #4 < - \c_eight
        \c_one
        \exp_after:wN \__fp_add_big_i_o:wNww
        \int_use:N \__int_eval:w \c_one - #4 ;
        0 {1000}{0000}{0000}{0000} ; #5;
        \tex_romannumeral:D
      \else:
        \if_int_compare:w #4 > \c_five % cf \c__fp_max_exponent_int
          \exp_after:wN \__fp_exp_overflow:
          \tex_romannumeral:D
        \else:
          \if_int_compare:w #4 < \c_zero
            \exp_after:wN \use_i:nn
          \else:
            \exp_after:wN \use_ii:nn
          \fi:
          {
            \c_zero
            \__fp_decimate:nNnnnn { - #4 }
              \__fp_exp_Taylor:Nnnwn
          }
          {
            \__fp_decimate:nNnnnn { \c_sixteen - #4 }
              \__fp_exp_pos_large:NnnNwn
          }
          #5
          {#4}
          #1 #2 0
          \tex_romannumeral:D
        \fi:
      \fi:
    \exp_after:wN \c_zero
  }
\cs_new:Npn \__fp_exp_overflow:
  { + \c_two * \c__fp_max_exponent_int ; {1000} {0000} {0000} {0000} ; }
\cs_new:Npn \__fp_exp_Taylor:Nnnwn #1#2#3 #4; #5 #6
  {
    #6
    \__fp_pack_twice_four:wNNNNNNNN
    \__fp_pack_twice_four:wNNNNNNNN
    \__fp_pack_twice_four:wNNNNNNNN
    \__fp_exp_Taylor_ii:ww
    ; #2#3#4 0000 0000 ;
  }
\cs_new:Npn \__fp_exp_Taylor_ii:ww #1; #2;
  { \__fp_exp_Taylor_loop:www 10 ; #1 ; #1 ; \s__stop }
\cs_new:Npn \__fp_exp_Taylor_loop:www #1; #2; #3;
  {
    \if_int_compare:w #1 = \c_one
      \exp_after:wN \__fp_exp_Taylor_break:Nww
    \fi:
    \__fp_fixed_div_int:wwN #3 ; #1 ;
    \__fp_fixed_add_one:wN
    \__fp_fixed_mul:wwn #2 ;
    {
      \exp_after:wN \__fp_exp_Taylor_loop:www
      \int_use:N \__int_eval:w #1 - 1 ;
      #2 ;
    }
  }
\cs_new:Npn \__fp_exp_Taylor_break:Nww #1 #2; #3 \s__stop
  { \__fp_fixed_add_one:wN #2 ; }
\cs_new:Npn \__fp_exp_pos_large:NnnNwn #1#2#3 #4#5; #6
  {
    \exp_after:wN \exp_after:wN
    \cs:w __fp_exp_large_\tex_romannumeral:D #6:wN \exp_after:wN \cs_end:
    \exp_after:wN \c__fp_one_fixed_tl
    \exp_after:wN ;
    \__int_value:w #3 #4 \exp_stop_f:
    #5 00000 ;
  }
\cs_new:Npn \__fp_exp_large:w #1 \or: #2 \fi:
  { \fi: \__fp_fixed_mul:wwn #1; }
\cs_new:Npn \__fp_exp_large_v:wN #1; #2
  {
    \if_case:w #2 ~           \exp_after:wN \__fp_fixed_continue:wn  \or:
      +  4343 \__fp_exp_large:w {8806}{8182}{2566}{2921}{5872}{6150} \or:
      +  8686 \__fp_exp_large:w {7756}{0047}{2598}{6861}{0458}{3204} \or:
      + 13029 \__fp_exp_large:w {6830}{5723}{7791}{4884}{1932}{7351} \or:
      + 17372 \__fp_exp_large:w {6015}{5609}{3095}{3052}{3494}{7574} \or:
      + 21715 \__fp_exp_large:w {5297}{7951}{6443}{0315}{3251}{3576} \or:
      + 26058 \__fp_exp_large:w {4665}{6719}{0099}{3379}{5527}{2929} \or:
      + 30401 \__fp_exp_large:w {4108}{9724}{3326}{3186}{5271}{5665} \or:
      + 34744 \__fp_exp_large:w {3618}{6973}{3140}{0875}{3856}{4102} \or:
      + 39087 \__fp_exp_large:w {3186}{9209}{6113}{3900}{6705}{9685} \or:
    \fi:
    #1;
    \__fp_exp_large_iv:wN
  }
\cs_new:Npn \__fp_exp_large_iv:wN #1; #2
  {
    \if_case:w #2 ~          \exp_after:wN \__fp_fixed_continue:wn  \or:
      +  435 \__fp_exp_large:w {1970}{0711}{1401}{7046}{9938}{8888} \or:
      +  869 \__fp_exp_large:w {3881}{1801}{9428}{4368}{5764}{8232} \or:
      + 1303 \__fp_exp_large:w {7646}{2009}{8905}{4704}{8893}{1073} \or:
      + 1738 \__fp_exp_large:w {1506}{3559}{7005}{0524}{9009}{7592} \or:
      + 2172 \__fp_exp_large:w {2967}{6283}{8402}{3667}{0689}{6630} \or:
      + 2606 \__fp_exp_large:w {5846}{4389}{5650}{2114}{7278}{5046} \or:
      + 3041 \__fp_exp_large:w {1151}{7900}{5080}{6878}{2914}{4154} \or:
      + 3475 \__fp_exp_large:w {2269}{1083}{0850}{6857}{8724}{4002} \or:
      + 3909 \__fp_exp_large:w {4470}{3047}{3316}{5442}{6408}{6591} \or:
    \fi:
    #1;
    \__fp_exp_large_iii:wN
  }
\cs_new:Npn \__fp_exp_large_iii:wN #1; #2
  {
    \if_case:w #2 ~         \exp_after:wN \__fp_fixed_continue:wn  \or:
      +  44 \__fp_exp_large:w {2688}{1171}{4181}{6135}{4484}{1263} \or:
      +  87 \__fp_exp_large:w {7225}{9737}{6812}{5749}{2581}{7748} \or:
      + 131 \__fp_exp_large:w {1942}{4263}{9524}{1255}{9365}{8421} \or:
      + 174 \__fp_exp_large:w {5221}{4696}{8976}{4143}{9505}{8876} \or:
      + 218 \__fp_exp_large:w {1403}{5922}{1785}{2837}{4107}{3977} \or:
      + 261 \__fp_exp_large:w {3773}{0203}{0092}{9939}{8234}{0143} \or:
      + 305 \__fp_exp_large:w {1014}{2320}{5473}{5004}{5094}{5533} \or:
      + 348 \__fp_exp_large:w {2726}{3745}{7211}{2566}{5673}{6478} \or:
      + 391 \__fp_exp_large:w {7328}{8142}{2230}{7421}{7051}{8866} \or:
    \fi:
    #1;
    \__fp_exp_large_ii:wN
  }
\cs_new:Npn \__fp_exp_large_ii:wN #1; #2
  {
    \if_case:w #2 ~        \exp_after:wN \__fp_fixed_continue:wn  \or:
      +  5 \__fp_exp_large:w {2202}{6465}{7948}{0671}{6516}{9579} \or:
      +  9 \__fp_exp_large:w {4851}{6519}{5409}{7902}{7796}{9107} \or:
      + 14 \__fp_exp_large:w {1068}{6474}{5815}{2446}{2146}{9905} \or:
      + 18 \__fp_exp_large:w {2353}{8526}{6837}{0199}{8540}{7900} \or:
      + 22 \__fp_exp_large:w {5184}{7055}{2858}{7072}{4640}{8745} \or:
      + 27 \__fp_exp_large:w {1142}{0073}{8981}{5684}{2836}{6296} \or:
      + 31 \__fp_exp_large:w {2515}{4386}{7091}{9167}{0062}{6578} \or:
      + 35 \__fp_exp_large:w {5540}{6223}{8439}{3510}{0525}{7117} \or:
      + 40 \__fp_exp_large:w {1220}{4032}{9431}{7840}{8020}{0271} \or:
    \fi:
    #1;
    \__fp_exp_large_i:wN
  }
\cs_new:Npn \__fp_exp_large_i:wN #1; #2
  {
    \if_case:w #2 ~       \exp_after:wN \__fp_fixed_continue:wn  \or:
      + 1 \__fp_exp_large:w {2718}{2818}{2845}{9045}{2353}{6029} \or:
      + 1 \__fp_exp_large:w {7389}{0560}{9893}{0650}{2272}{3043} \or:
      + 2 \__fp_exp_large:w {2008}{5536}{9231}{8766}{7740}{9285} \or:
      + 2 \__fp_exp_large:w {5459}{8150}{0331}{4423}{9078}{1103} \or:
      + 3 \__fp_exp_large:w {1484}{1315}{9102}{5766}{0342}{1116} \or:
      + 3 \__fp_exp_large:w {4034}{2879}{3492}{7351}{2260}{8387} \or:
      + 4 \__fp_exp_large:w {1096}{6331}{5842}{8458}{5992}{6372} \or:
      + 4 \__fp_exp_large:w {2980}{9579}{8704}{1728}{2747}{4359} \or:
      + 4 \__fp_exp_large:w {8103}{0839}{2757}{5384}{0077}{1000} \or:
    \fi:
    #1;
    \__fp_exp_large_:wN
  }
\cs_new:Npn \__fp_exp_large_:wN #1; #2
  {
    \if_case:w #2 ~       \exp_after:wN \__fp_fixed_continue:wn  \or:
      + 1 \__fp_exp_large:w {1105}{1709}{1807}{5647}{6248}{1171} \or:
      + 1 \__fp_exp_large:w {1221}{4027}{5816}{0169}{8339}{2107} \or:
      + 1 \__fp_exp_large:w {1349}{8588}{0757}{6003}{1039}{8374} \or:
      + 1 \__fp_exp_large:w {1491}{8246}{9764}{1270}{3178}{2485} \or:
      + 1 \__fp_exp_large:w {1648}{7212}{7070}{0128}{1468}{4865} \or:
      + 1 \__fp_exp_large:w {1822}{1188}{0039}{0508}{9748}{7537} \or:
      + 1 \__fp_exp_large:w {2013}{7527}{0747}{0476}{5216}{2455} \or:
      + 1 \__fp_exp_large:w {2225}{5409}{2849}{2467}{6045}{7954} \or:
      + 1 \__fp_exp_large:w {2459}{6031}{1115}{6949}{6638}{0013} \or:
    \fi:
    #1;
    \__fp_exp_large_after:wwn
  }
\cs_new:Npn \__fp_exp_large_after:wwn #1; #2; #3
  {
    \__fp_exp_Taylor:Nnnwn ? { } { } 0 #2; {} #3
    \__fp_fixed_mul:wwn #1;
  }
\cs_new:cpn { __fp_ \iow_char:N \^ _o:ww }
    \s__fp \__fp_chk:w #1#2#3; \s__fp \__fp_chk:w #4#5#6;
  {
    \if_meaning:w 0 #4
      \__fp_case_return_o:Nw \c_one_fp
    \fi:
    \if_case:w #2 \exp_stop_f:
      \exp_after:wN \use_i:nn
    \or:
      \__fp_case_return_o:Nw \c_nan_fp
    \else:
      \exp_after:wN \__fp_pow_neg:www
      \tex_romannumeral:D -`0 \exp_after:wN \use:nn
    \fi:
    {
      \if_meaning:w 1 #1
        \exp_after:wN \__fp_pow_normal:ww
      \else:
        \exp_after:wN \__fp_pow_zero_or_inf:ww
      \fi:
      \s__fp \__fp_chk:w #1#2#3;
    }
    { \s__fp \__fp_chk:w #4#5#6; \s__fp \__fp_chk:w #1#2#3; }
    \s__fp \__fp_chk:w #4#5#6;
  }
\cs_new:Npn \__fp_pow_zero_or_inf:ww \s__fp \__fp_chk:w #1#2; \s__fp \__fp_chk:w #3#4
  {
    \if_meaning:w 1 #4
      \__fp_case_return_same_o:w
    \fi:
    \if_meaning:w #1 #4
      \__fp_case_return_o:Nw \c_zero_fp
    \fi:
    \if_meaning:w 0 #1
      \__fp_case_use:nw
        {
          \__fp_division_by_zero_o:NNww \c_inf_fp ^
            \s__fp \__fp_chk:w #1 #2 ;
        }
    \else:
      \__fp_case_return_o:Nw \c_inf_fp
    \fi:
    \s__fp \__fp_chk:w #3#4
  }
\cs_new:Npn \__fp_pow_normal:ww \s__fp \__fp_chk:w 1 #1#2#3; \s__fp \__fp_chk:w #4#5
  {
    \if_int_compare:w \pdftex_strcmp:D { #2 #3 }
              { 1 {1000} {0000} {0000} {0000} } = \c_zero
      \if_int_compare:w #4 #1 = 32 \exp_stop_f:
        \exp_after:wN \__fp_case_return_ii_o:ww
      \fi:
      \__fp_case_return_o:Nww \c_one_fp
    \fi:
    \if_case:w #4 \exp_stop_f:
    \or:
      \exp_after:wN \__fp_pow_npos:Nww
      \exp_after:wN #5
    \or:
      \if_meaning:w 2 #5 \exp_after:wN \reverse_if:N \fi:
      \if_int_compare:w #2 > \c_zero
        \exp_after:wN \__fp_case_return_o:Nww
        \exp_after:wN \c_inf_fp
      \else:
        \exp_after:wN \__fp_case_return_o:Nww
        \exp_after:wN \c_zero_fp
      \fi:
    \or:
      \__fp_case_return_ii_o:ww
    \fi:
    \s__fp \__fp_chk:w 1 #1 {#2} #3 ;
    \s__fp \__fp_chk:w #4 #5
  }
\cs_new:Npn \__fp_pow_npos:Nww #1 \s__fp \__fp_chk:w 1#2#3
  {
    \exp_after:wN \__fp_sanitize:Nw
    \exp_after:wN 0
    \__int_value:w
      \if:w #1 \if_int_compare:w #3 > \c_zero 0 \else: 2 \fi:
        \exp_after:wN \__fp_pow_npos_aux:NNnww
        \exp_after:wN +
        \exp_after:wN \__fp_fixed_to_float:wN
      \else:
        \exp_after:wN \__fp_pow_npos_aux:NNnww
        \exp_after:wN -
        \exp_after:wN \__fp_fixed_inv_to_float:wN
      \fi:
      {#3}
  }
\cs_new:Npn \__fp_pow_npos_aux:NNnww #1#2#3#4#5; \s__fp \__fp_chk:w 1#6#7#8;
  {
    #1
    \__int_eval:w
      \__fp_ln_significand:NNNNnnnN #4#5
      \__fp_pow_exponent:wnN {#3}
      \__fp_fixed_mul:wwn #8 {0000}{0000} ;
      \__fp_pow_B:wwN #7;
      #1 #2 0 % fixed_to_float:wN
  }
\cs_new:Npn \__fp_pow_exponent:wnN #1; #2
  {
    \if_int_compare:w #2 > \c_zero
      \exp_after:wN \__fp_pow_exponent:Nwnnnnnwn % n\ln(10) - (-\ln(x))
      \exp_after:wN +
    \else:
      \exp_after:wN \__fp_pow_exponent:Nwnnnnnwn % -( |n|\ln(10) + (-\ln(x)) )
      \exp_after:wN -
    \fi:
    #2; #1;
  }
\cs_new:Npn \__fp_pow_exponent:Nwnnnnnwn #1#2; #3#4#5#6#7#8; #9
  { %^^A todo: use that in ln.
    \exp_after:wN \__fp_fixed_mul_after:wn
    \int_use:N \__int_eval:w \c__fp_leading_shift_int
      \exp_after:wN \__fp_pack:NNNNNwn
      \int_use:N \__int_eval:w \c__fp_middle_shift_int
        #1#2*23025 - #1 #3
        \exp_after:wN \__fp_pack:NNNNNwn
        \int_use:N \__int_eval:w \c__fp_middle_shift_int
          #1 #2*8509 - #1 #4
          \exp_after:wN \__fp_pack:NNNNNwn
          \int_use:N \__int_eval:w \c__fp_middle_shift_int
            #1 #2*2994 - #1 #5
            \exp_after:wN \__fp_pack:NNNNNwn
            \int_use:N \__int_eval:w \c__fp_middle_shift_int
              #1 #2*0456 - #1 #6
              \exp_after:wN \__fp_pack:NNNNNwn
              \int_use:N \__int_eval:w \c__fp_trailing_shift_int
                #1 #2*8401 - #1 #7
                #1 ( #2*7991 - #8 ) / 1 0000 ; {#9} ;
  }
\cs_new:Npn \__fp_pow_B:wwN #1#2#3#4#5#6; #7;
  {
    \if_int_compare:w #7 < \c_zero
      \exp_after:wN \__fp_pow_C_neg:w \__int_value:w -
    \else:
      \if_int_compare:w #7 < 22 \exp_stop_f:
        \exp_after:wN \__fp_pow_C_pos:w \__int_value:w
      \else:
        \exp_after:wN \__fp_pow_C_overflow:w \__int_value:w
      \fi:
    \fi:
    #7 \exp_after:wN ;
    \int_use:N \__int_eval:w 10 0000 + #1 \__int_eval_end:
    #2#3#4#5#6 0000 0000 0000 0000 0000 0000 ; %^^A todo: how many 0?
  }
\cs_new:Npn \__fp_pow_C_overflow:w #1; #2; #3
  {
    + \c_two * \c__fp_max_exponent_int
    \exp_after:wN \__fp_fixed_continue:wn \c__fp_one_fixed_tl ;
  }
\cs_new:Npn \__fp_pow_C_neg:w #1 ; 1
  {
    \exp_after:wN \exp_after:wN \exp_after:wN \__fp_pow_C_pack:w
    \prg_replicate:nn {#1} {0}
  }
\cs_new:Npn \__fp_pow_C_pos:w #1; 1
  { \__fp_pow_C_pos_loop:wN #1; }
\cs_new:Npn \__fp_pow_C_pos_loop:wN #1; #2
  {
    \if_meaning:w 0 #1
      \exp_after:wN \__fp_pow_C_pack:w
      \exp_after:wN #2
    \else:
      \if_meaning:w 0 #2
        \exp_after:wN \__fp_pow_C_pos_loop:wN \__int_value:w
      \else:
        \exp_after:wN \__fp_pow_C_overflow:w \__int_value:w
      \fi:
      \__int_eval:w #1 - \c_one \exp_after:wN ;
    \fi:
  }
\cs_new:Npn \__fp_pow_C_pack:w
  { \exp_after:wN \__fp_exp_large_v:wN \c__fp_one_fixed_tl ; }
\cs_new:Npn \__fp_pow_neg:www \s__fp \__fp_chk:w #1#2; #3; #4;
  {
    \if_case:w \__fp_pow_neg_case:w #4 ;
      \cs:w __fp_-_o:w \exp_after:wN \cs_end:
    \or:
      \if_int_compare:w \__int_eval:w #1 / \c_two = \c_one
        \__fp_invalid_operation_o:Nww ^ #3; #4;
        \tex_romannumeral:D -`0
        \exp_after:wN \exp_after:wN
        \exp_after:wN \__fp_use_none_until_s:w
      \fi:
    \fi:
    \__fp_exp_after_o:w
    \s__fp \__fp_chk:w #1#2;
  }
\cs_new:Npn \__fp_pow_neg_case:w \s__fp \__fp_chk:w #1#2#3;
  {
    \if_case:w #1 \exp_stop_f:
           \c_minus_one
    \or:   \__fp_pow_neg_case_aux:nnnnn #3
    \else: \c_one
    \fi:
  }
\cs_new:Npn \__fp_pow_neg_case_aux:nnnnn #1#2#3#4#5
  {
    \if_int_compare:w #1 > \c_eight
      \if_int_compare:w #1 > \c_sixteen
        \c_minus_one
      \else:
        \exp_after:wN \exp_after:wN
        \exp_after:wN \__fp_pow_neg_case_aux:NNNNNNNNw
        \prg_replicate:nn { \c_sixteen - #1 } { 0 } #4#5 ;
      \fi:
    \else:
      \if_int_compare:w #1 > \c_zero
        \if_int_compare:w #4#5 = \c_zero
          \exp_after:wN \exp_after:wN
          \exp_after:wN \__fp_pow_neg_case_aux:NNNNNNNNw
          \prg_replicate:nn { \c_eight - #1 } { 0 } #2#3 ;
        \else:
          \c_one
        \fi:
      \else:
        \c_one
      \fi:
    \fi:
  }
\cs_new:Npn \__fp_pow_neg_case_aux:NNNNNNNNw #1#2#3#4#5#6#7#8#9;
  {
    \if_int_compare:w 0 #9 = \c_zero
      \if_int_odd:w #8 \exp_stop_f:
        \c_zero
      \else:
        \c_minus_one
      \fi:
    \else:
      \c_one
    \fi:
  }
%% File: l3fp-trig.dtx Copyright (C) 2011-2012 The 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 "l3kernel 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.
%%
%% -----------------------------------------------------------------------
%%
\cs_new:Npn \__fp_sin_o:w \s__fp \__fp_chk:w #1#2
  {
    \if_case:w #1 \exp_stop_f:
           \__fp_case_return_same_o:w
    \or:
      \__fp_case_use:nw
        {
          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_o:w
            \__fp_sin_series:NNwww \__fp_fixed_to_float:wN #2 \c_zero
        }
    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { sin } }
    \else: \__fp_case_return_same_o:w
    \fi:
    \s__fp \__fp_chk:w #1#2
  }
\cs_new:Npn \__fp_cos_o:w \s__fp \__fp_chk:w #1#2
  {
    \if_case:w #1 \exp_stop_f:
           \__fp_case_return_o:Nw \c_one_fp
    \or:
      \__fp_case_use:nw
        {
          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_one_o:w
            \__fp_sin_series:NNwww \__fp_fixed_to_float:wN 0 \c_two
        }
    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { cos } }
    \else: \__fp_case_return_same_o:w
    \fi:
    \s__fp \__fp_chk:w #1#2
  }
\cs_new:Npn \__fp_csc_o:w \s__fp \__fp_chk:w #1#2
  {
    \if_case:w #1 \exp_stop_f:
           \__fp_cot_zero_o:Nnw #2 { csc }
    \or:
      \__fp_case_use:nw
        {
          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_inv_o:w
            \__fp_sin_series:NNwww \__fp_fixed_inv_to_float:wN #2 \c_zero
        }
    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { csc } }
    \else: \__fp_case_return_same_o:w
    \fi:
    \s__fp \__fp_chk:w #1#2
  }
\cs_new:Npn \__fp_sec_o:w \s__fp \__fp_chk:w #1#2
  {
    \if_case:w #1 \exp_stop_f:
           \__fp_case_return_o:Nw \c_one_fp
    \or:
      \__fp_case_use:nw
        {
          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_one_o:w
            \__fp_sin_series:NNwww \__fp_fixed_inv_to_float:wN 0 \c_two
        }
    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { sec } }
    \else: \__fp_case_return_same_o:w
    \fi:
    \s__fp \__fp_chk:w #1#2
  }
\cs_new:Npn \__fp_tan_o:w \s__fp \__fp_chk:w #1#2
  {
    \if_case:w #1 \exp_stop_f:
           \__fp_case_return_same_o:w
    \or:
      \__fp_case_use:nw
        {
          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_o:w
            \__fp_tan_series_o:NNwww 0 #2 \c_one
        }
    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { tan } }
    \else: \__fp_case_return_same_o:w
    \fi:
    \s__fp \__fp_chk:w #1#2
  }
\cs_new:Npn \__fp_cot_o:w \s__fp \__fp_chk:w #1#2
  {
    \if_case:w #1 \exp_stop_f:
           \__fp_cot_zero_o:Nnw #2 { cot }
    \or:
      \__fp_case_use:nw
        {
          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_inv_o:w
            \__fp_tan_series_o:NNwww 2 #2 \c_three
        }
    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { cot } }
    \else: \__fp_case_return_same_o:w
    \fi:
    \s__fp \__fp_chk:w #1#2
  }
\cs_new:Npn \__fp_cot_zero_o:Nnw #1 #2 #3 \fi:
  {
    \fi:
    \if_meaning:w 0 #1
      \exp_after:wN \__fp_division_by_zero_o:Nnw \exp_after:wN \c_inf_fp
    \else:
      \exp_after:wN \__fp_division_by_zero_o:Nnw \exp_after:wN \c_minus_inf_fp
    \fi:
    {#2}
  }
\cs_new:Npn \__fp_trig_exponent:NNNNNwn #1#2#3#4#5 \s__fp \__fp_chk:w 1#6#7
  {
    \if_int_compare:w #7 > - \c_eight
      \exp_after:wN #2
      \exp_after:wN #3
      \exp_after:wN #4
      \int_use:N \__int_eval:w #5
        \if_int_compare:w #7 > \c_zero
          \exp_after:wN \__fp_trig_large:ww \__int_value:w
        \else:
          \exp_after:wN \__fp_trig_small:ww \__int_value:w
        \fi:
    \else:
      \exp_after:wN #1
      \exp_after:wN #6
    \fi:
    #7 ;
  }
\cs_new:Npn \__fp_trig_epsilon_o:w #1 #2 ;
  { \__fp_exp_after_o:w \s__fp \__fp_chk:w 1 #1 {#2} }
\cs_new:Npn \__fp_trig_epsilon_one_o:w #1 ; #2 ;
  { \exp_after:wN \c_one_fp }
\group_begin:
  \char_set_catcode_letter:N /
  \cs_new:Npn \__fp_trig_epsilon_inv_o:w #1 #2 ;
    {
      \exp_after:wN \__fp_/_o:ww
        \c_one_fp
        \s__fp \__fp_chk:w 1 #1 {#2}
    }
\group_end:
\cs_new:Npn \__fp_trig_small:ww #1; #2#3#4#5;
  {
    \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
    \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
    \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
    \exp_after:wN .
    \exp_after:wN ;
    \tex_romannumeral:D -`0
      \prg_replicate:nn { - #1 } { 0 } #2#3#4#5 0000 0000 ;
  }
\cs_new:Npn \__fp_trig_large:ww #1; #2#3;
  { \__fp_trig_large_i:www #2; #3 ;  #1; }
\cs_new:Npn \__fp_trig_large_i:www #1; #2; #3;
  {
    \if_meaning:w 0 #3 \__fp_trig_large_break:w \fi:
    \exp_after:wN \__fp_trig_large_ii_o:wnnnn
    \int_use:N \__int_eval:w ( #1 - 3141 ) / 6283 ;
    {#1} #2
    \exp_after:wN ;
    \int_use:N \__int_eval:w \c_minus_one + #3;
  }
\cs_new:Npn \__fp_trig_large_ii_o:wnnnn #1; #2#3#4#5
  {
    \exp_after:wN \__fp_trig_large_i:www
    \int_use:N \__int_eval:w \c__fp_leading_shift_int + #20 - #1*62831
      \exp_after:wN \__fp_pack:NNNNNw
      \int_use:N \__int_eval:w \c__fp_middle_shift_int + #30 - #1*8530
        \exp_after:wN \__fp_pack:NNNNNw
        \int_use:N \__int_eval:w \c__fp_middle_shift_int + #40 - #1*7179
          \exp_after:wN \__fp_pack:NNNNNw
          \int_use:N \__int_eval:w \c__fp_trailing_shift_int + #50 - #1*5880
    \exp_after:wN ;
  }
\cs_new:Npn \__fp_trig_large_break:w \fi: #1; #2;
  { \fi: \__fp_trig_octant_loop:nnnnnw #2 {0000} {0000} ; }
\cs_new:Npn \__fp_trig_octant_loop:nnnnnw #1#2#3#4#5#6;
  {
    \if_int_compare:w #1#2 < 157079633 \exp_stop_f:
      \if_int_compare:w #1#2 = 157079632 \exp_stop_f:
        \if_int_compare:w #3#4 > 67948969 \exp_stop_f:
          \use_i_ii:nnn
        \fi:
      \fi:
      \__fp_trig_octant_break:w
    \fi:
    + \c_two
    \__fp_fixed_sub:wwn
      {#1} {#2} {#3} {#4} {0000} {0000} ;
      {15707} {9632} {6794} {8970} {0000} {0000} ;
    \__fp_trig_octant_loop:nnnnnw
  }
\cs_new:Npn \__fp_trig_octant_break:w #1 \fi: + #2#3 #4#5; #6; #7;
  {
    \fi:
    \if_int_compare:w #4 < 7854 \exp_stop_f:
      \exp_after:wN \__fp_use_i_until_s:nw
      \exp_after:wN .
    \fi:
    + \c_one
    \__fp_fixed_sub:wwn #6 ; {#4} #5 ; . ;
  }
\cs_new:Npn \__fp_sin_series:NNwww #1#2#3 . #4; #5;
  {
    \__fp_fixed_mul:wwn #4; #4;
    {
      \exp_after:wN \__fp_sin_series_aux:NNnww
      \exp_after:wN #1
      \__int_value:w
        \if_int_odd:w \__int_eval:w ( #3 + \c_two ) / \c_four \__int_eval_end:
          #2
        \else:
          \if_meaning:w #2 0 2 \else: 0 \fi:
        \fi:
      {#3}
    }
    #4 ;
  }
\cs_new:Npn \__fp_sin_series_aux:NNnww #1#2#3 #4; #5;
  {
    \if_int_odd:w \__int_eval:w #3 / \c_two \__int_eval_end:
      \exp_after:wN \use_i:nn
    \else:
      \exp_after:wN \use_ii:nn
    \fi:
    { % 1/18!
      \__fp_fixed_mul_sub_back:wwwn     {0000}{0000}{0000}{0001}{5619}{2070};
                                  #4; {0000}{0000}{0000}{0477}{9477}{3324};
      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0000}{0011}{4707}{4559}{7730};
      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0000}{2087}{6756}{9878}{6810};
      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0027}{5573}{1922}{3985}{8907};
      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{2480}{1587}{3015}{8730}{1587};
      \__fp_fixed_mul_sub_back:wwwn #4; {0013}{8888}{8888}{8888}{8888}{8889};
      \__fp_fixed_mul_sub_back:wwwn #4; {0416}{6666}{6666}{6666}{6666}{6667};
      \__fp_fixed_mul_sub_back:wwwn #4; {5000}{0000}{0000}{0000}{0000}{0000};
      \__fp_fixed_mul_sub_back:wwwn #4;{10000}{0000}{0000}{0000}{0000}{0000};
    }
    { % 1/17!
      \__fp_fixed_mul_sub_back:wwwn     {0000}{0000}{0000}{0028}{1145}{7254};
                                  #4; {0000}{0000}{0000}{7647}{1637}{3182};
      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0000}{0160}{5904}{3836}{8216};
      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0002}{5052}{1083}{8544}{1719};
      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0275}{5731}{9223}{9858}{9065};
      \__fp_fixed_mul_sub_back:wwwn #4; {0001}{9841}{2698}{4126}{9841}{2698};
      \__fp_fixed_mul_sub_back:wwwn #4; {0083}{3333}{3333}{3333}{3333}{3333};
      \__fp_fixed_mul_sub_back:wwwn #4; {1666}{6666}{6666}{6666}{6666}{6667};
      \__fp_fixed_mul_sub_back:wwwn #4;{10000}{0000}{0000}{0000}{0000}{0000};
      \__fp_fixed_mul:wwn #5;
    }
    {
      \exp_after:wN \__fp_sanitize:Nw
      \exp_after:wN #2
      \int_use:N \__int_eval:w #1
    }
    #2
  }
\cs_new:Npn \__fp_tan_series_o:NNwww #1#2#3. #4; #5;
  {
    \__fp_fixed_mul:wwn #4; #4;
    {
      \exp_after:wN \__fp_tan_series_aux_o:Nnww
      \__int_value:w
        \if_int_odd:w \__int_eval:w #3 / \c_two \__int_eval_end:
          \exp_after:wN \reverse_if:N
        \fi:
        \if_meaning:w #1#2 2 \else: 0 \fi:
      {#3}
    }
    #4 ;
  }
\cs_new:Npn \__fp_tan_series_aux_o:Nnww #1 #2 #3; #4;
  {
    \__fp_fixed_mul_sub_back:wwwn     {0000}{0000}{1527}{3493}{0856}{7059};
                                #3; {0000}{0159}{6080}{0274}{5257}{6472};
    \__fp_fixed_mul_sub_back:wwwn #3; {0002}{4571}{2320}{0157}{2558}{8481};
    \__fp_fixed_mul_sub_back:wwwn #3; {0115}{5830}{7533}{5397}{3168}{2147};
    \__fp_fixed_mul_sub_back:wwwn #3; {1929}{8245}{6140}{3508}{7719}{2982};
    \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
    \__fp_fixed_mul:wwn #4;
      {
        \__fp_fixed_mul_sub_back:wwwn     {0000}{0007}{0258}{0681}{9408}{4706};
                                    #3; {0000}{2343}{7175}{1399}{6151}{7670};
        \__fp_fixed_mul_sub_back:wwwn #3; {0019}{2638}{4588}{9232}{8861}{3691};
        \__fp_fixed_mul_sub_back:wwwn #3; {0536}{6357}{0691}{4344}{6852}{4252};
        \__fp_fixed_mul_sub_back:wwwn #3; {5263}{1578}{9473}{6842}{1052}{6315};
        \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
          {
            \exp_after:wN \__fp_sanitize:Nw
            \exp_after:wN #1
            \int_use:N \__int_eval:w
              \reverse_if:N \if_int_odd:w
                  \__int_eval:w (#2 - \c_one) / \c_two \__int_eval_end:
                \exp_after:wN \__fp_reverse_args:Nww
              \fi:
              \__fp_fixed_div_to_float:ww
          }
      }
  }
%% File: l3fp-convert.dtx Copyright(C) 2011-2012 The 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 "l3kernel 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.
%%
%% -----------------------------------------------------------------------
%%
\cs_new:Npn \__fp_trim_zeros:w #1 ;
  {
    \__fp_trim_zeros_loop:w #1
      ; \__fp_trim_zeros_loop:w 0; \__fp_trim_zeros_dot:w .; \s__stop
  }
\cs_new:Npn \__fp_trim_zeros_loop:w #1 0; #2 { #2 #1 ; #2 }
\cs_new:Npn \__fp_trim_zeros_dot:w #1 .; { \__fp_trim_zeros_end:w #1 ; }
\cs_new:Npn \__fp_trim_zeros_end:w #1 ; #2 \s__stop { #1 }
\cs_new:Npn \fp_to_scientific:N #1
  { \exp_after:wN \__fp_to_scientific_dispatch:w #1 }
\cs_generate_variant:Nn \fp_to_scientific:N { c }
\cs_new_nopar:Npn \fp_to_scientific:n
  {
    \exp_after:wN \__fp_to_scientific_dispatch:w
    \tex_romannumeral:D -`0 \__fp_parse:n
  }
\group_begin:
\char_set_catcode_other:N E
\tl_to_lowercase:n
  {
    \group_end:
    \cs_new:Npn \__fp_to_scientific_dispatch:w \s__fp \__fp_chk:w #1#2
      {
        \if_meaning:w 2 #2 \exp_after:wN - \tex_romannumeral:D -`0 \fi:
        \if_case:w #1 \exp_stop_f:
             \__fp_case_return:nw { 0 }
        \or: \exp_after:wN \__fp_to_scientific_normal:wnnnnn
        \or:
          \__fp_case_use:nw
            {
              \__fp_invalid_operation:nnw
                {
                  \exp_after:wN 1
                  \exp_after:wN E
                  \int_use:N \c__fp_max_exponent_int
                }
                { fp_to_scientific }
            }
        \or:
          \__fp_case_use:nw
            {
              \__fp_invalid_operation:nnw
                { 0 }
                { fp_to_scientific }
            }
        \fi:
        \s__fp \__fp_chk:w #1 #2
      }
    \cs_new:Npn \__fp_to_scientific_normal:wnnnnn
        \s__fp \__fp_chk:w 1 #1 #2 #3#4#5#6 ;
      {
        \if_int_compare:w #2 = \c_one
          \exp_after:wN \__fp_to_scientific_normal:wNw
        \else:
          \exp_after:wN \__fp_to_scientific_normal:wNw
          \exp_after:wN E
          \int_use:N \__int_eval:w #2 - \c_one
        \fi:
        ; #3 #4 #5 #6 ;
      }
  }
\cs_new:Npn \__fp_to_scientific_normal:wNw #1 ; #2#3;
  { \__fp_trim_zeros:w #2.#3 ; #1 }
\cs_new:Npn \fp_to_decimal:N #1
  { \exp_after:wN \__fp_to_decimal_dispatch:w #1 }
\cs_generate_variant:Nn \fp_to_decimal:N { c }
\cs_new_nopar:Npn \fp_to_decimal:n
  {
    \exp_after:wN \__fp_to_decimal_dispatch:w
    \tex_romannumeral:D -`0 \__fp_parse:n
  }
\cs_new:Npn \__fp_to_decimal_dispatch:w \s__fp \__fp_chk:w #1#2
  {
    \if_meaning:w 2 #2 \exp_after:wN - \tex_romannumeral:D -`0 \fi:
    \if_case:w #1 \exp_stop_f:
         \__fp_case_return:nw { 0 }
    \or: \exp_after:wN \__fp_to_decimal_normal:wnnnnn
    \or:
      \__fp_case_use:nw
        {
          \__fp_invalid_operation:nnw
            {
              \exp_after:wN \exp_after:wN \exp_after:wN 1
              \prg_replicate:nn \c__fp_max_exponent_int 0
            }
            { fp_to_decimal }
        }
    \or:
      \__fp_case_use:nw
        {
          \__fp_invalid_operation:nnw
            { 0 }
            { fp_to_decimal }
        }
    \fi:
    \s__fp \__fp_chk:w #1 #2
  }
\cs_new:Npn \__fp_to_decimal_normal:wnnnnn
    \s__fp \__fp_chk:w 1 #1 #2 #3#4#5#6 ;
  {
    \int_compare:nNnTF {#2} > \c_zero
      {
        \int_compare:nNnTF {#2} < \c_sixteen
          {
            \__fp_decimate:nNnnnn { \c_sixteen - #2 }
              \__fp_to_decimal_large:Nnnw
          }
          {
            \exp_after:wN \exp_after:wN
            \exp_after:wN \__fp_to_decimal_huge:wnnnn
            \prg_replicate:nn { #2 - \c_sixteen } { 0 } ;
          }
        {#3} {#4} {#5} {#6}
      }
      {
        \exp_after:wN \__fp_trim_zeros:w
        \exp_after:wN 0
        \exp_after:wN .
        \tex_romannumeral:D -`0 \prg_replicate:nn { - #2 } { 0 }
        #3#4#5#6 ;
      }
  }
\cs_new:Npn \__fp_to_decimal_large:Nnnw #1#2#3#4;
  {
    \exp_after:wN \__fp_trim_zeros:w \__int_value:w
      \if_int_compare:w #2 > \c_zero
        #2
      \fi:
      \exp_stop_f:
      #3.#4 ;
  }
\cs_new:Npn \__fp_to_decimal_huge:wnnnn #1; #2#3#4#5 { #2#3#4#5 #1 }
\cs_new:Npn \fp_to_tl:N #1 { \exp_after:wN \__fp_to_tl_dispatch:w #1 }
\cs_generate_variant:Nn \fp_to_tl:N { c }
\cs_new_nopar:Npn \fp_to_tl:n
  {
    \exp_after:wN \__fp_to_tl_dispatch:w
    \tex_romannumeral:D -`0 \__fp_parse:n
  }
\cs_new:Npn \__fp_to_tl_dispatch:w \s__fp \__fp_chk:w #1#2
  {
    \if_meaning:w 2 #2 \exp_after:wN - \tex_romannumeral:D -`0 \fi:
    \if_case:w #1 \exp_stop_f:
           \__fp_case_return:nw { 0 }
    \or:   \exp_after:wN \__fp_to_tl_normal:nnnnn
    \or:   \__fp_case_return:nw { \tl_to_str:n {inf} }
    \else: \__fp_case_return:nw { \tl_to_str:n {nan} }
    \fi:
  }
\cs_new:Npn \__fp_to_tl_normal:nnnnn #1
  {
    \if_int_compare:w #1 > \c_sixteen
      \exp_after:wN \__fp_to_scientific_normal:wnnnnn
    \else:
      \if_int_compare:w #1 < - \c_two
        \exp_after:wN \exp_after:wN
        \exp_after:wN \__fp_to_scientific_normal:wnnnnn
      \else:
        \exp_after:wN \exp_after:wN
        \exp_after:wN \__fp_to_decimal_normal:wnnnnn
      \fi:
    \fi:
    \s__fp \__fp_chk:w 1 0 {#1}
  }
\cs_new:Npx \fp_to_dim:N #1
  { \exp_not:N \fp_to_decimal:N #1 \tl_to_str:n {pt} }
\cs_generate_variant:Nn \fp_to_dim:N { c }
\cs_new:Npx \fp_to_dim:n #1
  { \exp_not:N \fp_to_decimal:n {#1} \tl_to_str:n {pt} }
\cs_new:Npn \fp_to_int:N #1 { \exp_after:wN \__fp_to_int_dispatch:w #1 }
\cs_generate_variant:Nn \fp_to_int:N { c }
\cs_new_nopar:Npn \fp_to_int:n
  {
    \exp_after:wN \__fp_to_int_dispatch:w
    \tex_romannumeral:D -`0 \__fp_parse:n
  }
\cs_new:Npn \__fp_to_int_dispatch:w #1;
  {
    \exp_after:wN \__fp_to_decimal_dispatch:w \tex_romannumeral:D -`0
    \__fp_round:Nwn \__fp_round_to_nearest:NNN #1; { 0 }
  }
\cs_new:Npn \dim_to_fp:n #1
  {
    \exp_after:wN \__fp_from_dim_test:N
    \__int_value:w \etex_glueexpr:D #1 ;
  }
\cs_new:Npn \__fp_from_dim_test:N #1
  {
    \if_meaning:w 0 #1
      \__fp_case_return:nw \c_zero_fp
    \else:
      \if_meaning:w - #1
        \exp_after:wN \__fp_from_dim:Nw
        \exp_after:wN 2
        \__int_value:w
      \else:
        \exp_after:wN \__fp_from_dim:Nw
        \exp_after:wN 0
        \__int_value:w #1
      \fi:
    \fi:
  }
\cs_new:Npn \__fp_from_dim:Nw #1 #2;
  {
    \__fp_pack_twice_four:wNNNNNNNN \__fp_from_dim_ii:wNNnnnnnn ;
    #2 000 0000 00 {10}987654321; #1
  }
\cs_new:Npn \__fp_from_dim_ii:wNNnnnnnn #1; #2#3#4#5#6#7#8#9
  { \__fp_from_dim_iii:wnnnnwN #1 {#2#300} {0000} ; }
\cs_new:Npn \__fp_from_dim_iii:wnnnnwN #1; #2#3#4#5#6; #7
  {
    \__fp_mul_npos_o:Nww #7
      \s__fp \__fp_chk:w 1 #7 {#5} #1 ;
      \s__fp \__fp_chk:w 1 0 {-4} {1525} {8789} {0625} {0000} ;
  }
\cs_new_eq:NN \fp_use:N \fp_to_decimal:N
\cs_generate_variant:Nn \fp_use:N { c }
\cs_new_eq:NN \fp_eval:n \fp_to_decimal:n
\cs_new:Npn \fp_abs:n #1
  { \fp_to_decimal:n { abs \__fp_parse:n {#1} } }
\cs_new:Npn \__fp_array_to_clist:n #1
  {
    \tl_if_empty:nF {#1}
      {
        \__fp_expand:n
          {
            { \use_ii:nn }
            \__fp_array_to_clist_loop:Nw #1 { ? \__prg_break: } ;
            \__prg_break_point:
          }
      }
  }
\cs_new:Npx \__fp_array_to_clist_loop:Nw #1#2;
  {
    \exp_not:N \use_none:n #1
    \exp_not:N \exp_after:wN
                 {
    \exp_not:N     \exp_after:wN ,
    \exp_not:N     \exp_after:wN \c_space_tl
    \exp_not:N     \tex_romannumeral:D -`0
    \exp_not:N     \__fp_to_tl_dispatch:w #1 #2 ;
                 }
    \exp_not:N \__fp_array_to_clist_loop:Nw
  }
%%
%% File: l3fp-assign.dtx Copyright (C) 2011-2012 The 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 "l3kernel 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.
%%
%% -----------------------------------------------------------------------
%%
\cs_new_protected:Npn \fp_new:N #1
  { \cs_new_eq:NN #1 \c_zero_fp }
\cs_generate_variant:Nn \fp_new:N {c}
\cs_new_protected:Npn \fp_set:Nn   #1#2
  { \tl_set:Nx #1 { \__fp_parse:n {#2} } }
\cs_new_protected:Npn \fp_gset:Nn  #1#2
  { \tl_gset:Nx #1 { \__fp_parse:n {#2} } }
\cs_new_protected:Npn \fp_const:Nn #1#2
  { \tl_const:Nx #1 { \__fp_parse:n {#2} } }
\cs_generate_variant:Nn \fp_set:Nn {c}
\cs_generate_variant:Nn \fp_gset:Nn {c}
\cs_generate_variant:Nn \fp_const:Nn {c}
\cs_new_eq:NN \fp_set_eq:NN  \tl_set_eq:NN
\cs_new_eq:NN \fp_gset_eq:NN \tl_gset_eq:NN
\cs_generate_variant:Nn \fp_set_eq:NN  { c , Nc , cc }
\cs_generate_variant:Nn \fp_gset_eq:NN { c , Nc , cc }
\cs_new_protected:Npn \fp_zero:N #1 { \fp_set_eq:NN #1 \c_zero_fp }
\cs_new_protected:Npn \fp_gzero:N #1 { \fp_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:Npn \fp_zero_new:N #1
  { \fp_if_exist:NTF #1 { \fp_zero:N #1 } { \fp_new:N #1 } }
\cs_new_protected:Npn \fp_gzero_new:N #1
  { \fp_if_exist:NTF #1 { \fp_gzero:N #1 } { \fp_new:N #1 } }
\cs_generate_variant:Nn \fp_zero_new:N  { c }
\cs_generate_variant:Nn \fp_gzero_new:N { c }
\cs_new_protected_nopar:Npn \fp_add:Nn  { \__fp_add:NNNn \fp_set:Nn  + }
\cs_new_protected_nopar:Npn \fp_gadd:Nn { \__fp_add:NNNn \fp_gset:Nn + }
\cs_new_protected_nopar:Npn \fp_sub:Nn  { \__fp_add:NNNn \fp_set:Nn  - }
\cs_new_protected_nopar:Npn \fp_gsub:Nn { \__fp_add:NNNn \fp_gset:Nn - }
\cs_new_protected:Npn \__fp_add:NNNn #1#2#3#4
  { #1 #3 { #3 #2 \__fp_parse:n {#4} } }
\cs_generate_variant:Nn \fp_add:Nn  { c }
\cs_generate_variant:Nn \fp_gadd:Nn { c }
\cs_generate_variant:Nn \fp_sub:Nn  { c }
\cs_generate_variant:Nn \fp_gsub:Nn { c }
\cs_new_protected:Npn \fp_show:N #1
  {
    \fp_if_exist:NTF #1
      { \__msg_show_variable:x { > \fp_to_tl:N #1 } }
      {
        \__msg_kernel_error:nnx { kernel } { variable-not-defined }
          { \token_to_str:N #1 }
      }
  }
\cs_new_protected:Npn \fp_show:n #1
  { \__msg_show_variable:x { > \fp_to_tl:n {#1} } }
\cs_generate_variant:Nn \fp_show:N { c }
\fp_const:Nn \c_e_fp          { 2.718 2818 2845 9045 }
\fp_const:Nn \c_one_fp        { 1 }
\fp_const:Nn \c_pi_fp         { 3.141 5926 5358 9794 }
\fp_const:Nn \c_one_degree_fp { 0.0 1745 3292 5199 4330 }
\fp_new:N \l_tmpa_fp
\fp_new:N \l_tmpb_fp
\fp_new:N \g_tmpa_fp
\fp_new:N \g_tmpb_fp
%% File: l3fp-old.dtx Copyright (C) 2012 The 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 "l3kernel 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 LaTeX3 Project Team.
%%
%% -----------------------------------------------------------------------
%%
\fp_const:Nn \c_undefined_fp { nan }
\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF }
  { \exp_after:wN \__fp_if_undefined:w #1 }
\cs_new:Npn \__fp_if_undefined:w \s__fp \__fp_chk:w #1#2;
  {
    \if_int_compare:w #1 > \c_one
      \prg_return_true: \else: \prg_return_false: \fi:
  }
\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF }
  { \exp_after:wN \__fp_if_zero:w #1 }
\cs_new:Npn \__fp_if_zero:w \s__fp \__fp_chk:w #1#2;
  { \if_meaning:w #1 0 \prg_return_true: \else: \prg_return_false: \fi: }
\cs_new_protected_nopar:Npn \fp_abs:N  { \__fp_abs:NNN \tl_set:Nx  \__fp_abs_o:w }
\cs_new_protected_nopar:Npn \fp_gabs:N { \__fp_abs:NNN \tl_gset:Nx \__fp_abs_o:w }
\cs_new_protected_nopar:Npx \fp_neg:N
  {
    \exp_not:N \__fp_abs:NNN
    \exp_not:N \tl_set:Nx
    \exp_not:c { __fp_-_o:w }
  }
\cs_new_protected_nopar:Npx \fp_gneg:N
  {
    \exp_not:N \__fp_abs:NNN
    \exp_not:N \tl_gset:Nx
    \exp_not:c { __fp_-_o:w }
  }
\cs_new_protected:Npn \__fp_abs:NNN #1#2#3
  { #1 #3 { \exp_after:wN #2 #3 \prg_do_nothing: } }
\cs_generate_variant:Nn \fp_abs:N  { c }
\cs_generate_variant:Nn \fp_gabs:N { c }
\cs_generate_variant:Nn \fp_neg:N  { c }
\cs_generate_variant:Nn \fp_gneg:N { c }
\cs_new_protected_nopar:Npn \fp_mul:Nn  { \__fp_mul:NNNn \fp_set:Nn  * }
\cs_new_protected_nopar:Npn \fp_gmul:Nn { \__fp_mul:NNNn \fp_gset:Nn * }
\cs_new_protected_nopar:Npn \fp_div:Nn  { \__fp_mul:NNNn \fp_set:Nn  / }
\cs_new_protected_nopar:Npn \fp_gdiv:Nn { \__fp_mul:NNNn \fp_gset:Nn / }
\cs_new_protected_nopar:Npn \fp_pow:Nn  { \__fp_mul:NNNn \fp_set:Nn  ^ }
\cs_new_protected_nopar:Npn \fp_gpow:Nn { \__fp_mul:NNNn \fp_gset:Nn ^ }
\cs_new_protected:Npn \__fp_mul:NNNn #1#2#3#4
  { #1 #3 { #3 #2 \__fp_parse:n {#4} } }
\cs_generate_variant:Nn \fp_mul:Nn  { c }
\cs_generate_variant:Nn \fp_gmul:Nn { c }
\cs_generate_variant:Nn \fp_div:Nn  { c }
\cs_generate_variant:Nn \fp_gdiv:Nn { c }
\cs_generate_variant:Nn \fp_pow:Nn  { c }
\cs_generate_variant:Nn \fp_gpow:Nn { c }
\cs_set_protected:Npn \__fp_tmp:w #1#2#3#4#5
  {
    \cs_new_protected_nopar:Npn #1 { #5 {#4} \tl_set_eq:NN  #3 }
    \cs_new_protected_nopar:Npn #2 { #5 {#4} \tl_gset_eq:NN #3 }
    \cs_generate_variant:Nn #1 { c }
    \cs_generate_variant:Nn #2 { c }
  }
\__fp_tmp:w \fp_exp:Nn \fp_gexp:Nn \__fp_exp_o:w {exp} \__fp_assign_to:nNNNn
\__fp_tmp:w \fp_ln:Nn  \fp_gln:Nn  \__fp_ln_o:w  {ln } \__fp_assign_to:nNNNn
\__fp_tmp:w \fp_sin:Nn \fp_gsin:Nn \__fp_sin_o:w {sin} \__fp_assign_to:nNNNn
\__fp_tmp:w \fp_cos:Nn \fp_gcos:Nn \__fp_cos_o:w {cos} \__fp_assign_to:nNNNn
\__fp_tmp:w \fp_tan:Nn \fp_gtan:Nn \__fp_tan_o:w {tan} \__fp_assign_to:nNNNn
\cs_new_protected:Npn \__fp_assign_to:nNNNn #1#2#3#4#5
  {
    \exp_after:wN \__fp_assign_to_i:wNNNn
    \tex_romannumeral:D -`0 \__fp_parse:n {#5} {#1} #2#3#4
  }
\cs_new_protected:Npn \__fp_assign_to_i:wNNNn \s__fp \__fp_chk:w #1#2#3; #4
  {
    \exp_args:Nc \__fp_assign_to_ii:NnNNN
      { c__fp_ #4 [ #1 # 2 \if_meaning:w 1 #1 #3 \fi: ] _fp }
      { #1#2#3 }
  }
\cs_new_protected:Npn \__fp_assign_to_ii:NnNNN #1#2#3#4#5
  {
    \cs_if_exist:NF #1
      { \tl_const:Nx #1 { #4 \s__fp \__fp_chk:w #2; } }
    #3 #5 #1
  }
\cs_new_protected_nopar:Npn \fp_compare:NNNTF { \fp_compare:nNnTF }
\cs_new_protected_nopar:Npn \fp_compare:NNNT  { \fp_compare:nNnT  }
\cs_new_protected_nopar:Npn \fp_compare:NNNF  { \fp_compare:nNnF  }
\cs_new_protected_nopar:Npn \fp_round_places:Nn
  { \__fp_round_places:NNn \tl_set:Nx }
\cs_new_protected_nopar:Npn \fp_ground_places:Nn
  { \__fp_round_places:NNn \tl_gset:Nx }
\cs_new_protected:Npn \__fp_round_places:NNn #1#2#3
  {
    #1 #2
      {
        \exp_after:wN \exp_after:wN
        \exp_after:wN \__fp_round:Nwn
        \exp_after:wN \exp_after:wN
        \exp_after:wN \__fp_round_to_nearest:NNN
        \exp_after:wN #2
        \exp_after:wN { \int_use:N \__int_eval:w #3 }
      }
  }
\cs_generate_variant:Nn \fp_round_places:Nn { c }
\cs_generate_variant:Nn \fp_ground_places:Nn { c }
\cs_new_protected:Npn \fp_round_figures:Nn #1#2
  {
    \__fp_round_places:NNn \tl_set:Nx #1
      { #2 - \exp_after:wN \__fp_exponent:w #1 }
  }
\cs_new_protected:Npn \fp_ground_figures:Nn #1#2
  {
    \__fp_round_places:NNn \tl_gset:Nx #1
      { #2 - \exp_after:wN \__fp_exponent:w #1 }
  }
\cs_generate_variant:Nn \fp_round_figures:Nn { c }
\cs_generate_variant:Nn \fp_ground_figures:Nn { c }
%% 
%%
%% End of file `l3fp.sty'.