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%%
%% 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 4449 2013-01-19 23:55:05Z 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:nnnnnnw { #1#2#3#4#5 } }
\cs_new:Npn \__fp_decimate_pack: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 } \tex_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 \tex_undefined:D
\cs_new_eq:NN \l__fp_division_by_zero_flag_token \tex_undefined:D
\cs_new_eq:NN \l__fp_overflow_flag_token \tex_undefined:D
\cs_new_eq:NN \l__fp_underflow_flag_token \tex_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:NnnwNNnn #5 #1 #3 {#4} {#2}
}
\cs_new:Npn \__fp_round_normal:NnnwNNnn #1#2#3#4; #5#6
{
\exp_after:wN \__fp_round_normal: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: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_aux:N
\tex_romannumeral:D
\else:
0 \__fp_parse_return_semicolon:w #1
\fi:
\__fp_parse_expand:w
}
\cs_new:Npn \__fp_parse_exponent_aux: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_aux: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_aux: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_auxii: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.
%%
%% -----------------------------------------------------------------------
%%
\prg_new_eq_conditional:NNn \fp_if_exist:N \cs_if_exist:N { TF , T , F , p }
\prg_new_eq_conditional:NNn \fp_if_exist:c \cs_if_exist:c { TF , T , F , p }
\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_auxi:ww
\else:
\__fp_minmax_auxii: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_auxii:ww
\else:
\__fp_minmax_auxi: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_auxi:ww #1 \fi: \fi: #2 \s__fp #3 ; \s__fp #4;
{ \fi: \fi: #2 \s__fp #3 ; }
\cs_new:Npn \__fp_minmax_auxii: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_auxi: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_auxii: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_auxi: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_auxii: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:wnN
#1; {#7} \__fp_fixed_div_int_auxi:wnn
#2; {#7} \__fp_fixed_div_int_auxi:wnn
#3; {#7} \__fp_fixed_div_int_auxi:wnn
#4; {#7} \__fp_fixed_div_int_auxi:wnn
#5; {#7} \__fp_fixed_div_int_auxi:wnn
#6; {#7} \__fp_fixed_div_int_auxii:wnn ;
}
\cs_new:Npn \__fp_fixed_div_int: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_auxi: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:wnN
\int_use:N \__int_eval:w #3 - #1*#2 \__int_eval_end:
}
\cs_new:Npn \__fp_fixed_div_int_auxii: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:Nnnnnwnn + }
\cs_new_nopar:Npn \__fp_fixed_sub:wwn { \__fp_fixed_add:Nnnnnwnn - }
\cs_new:Npn \__fp_fixed_add: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:nnNnnnwn #6 #1
}
\cs_new:Npn \__fp_fixed_add: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:nnnnnnnwn #5 {#6}{#7} {#1}{#2}
}
\cs_new:Npn \__fp_fixed_mul: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: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: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:Nwnnnwnnn -
; #2 ; #1 ; #2 ; -
; {#3} ;
}
\cs_new:Npn \__fp_fixed_mul_add: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:nnnnwnnnn {#7}{#8}{#9}
}
\cs_new:Npn \__fp_fixed_mul_add: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: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: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_auxi:ww
#1#3 0000 0000 0000 0000 0000 0000 ;
}
\cs_new:Npn \__fp_fixed_dtf_zeros_auxi:ww
{
\__fp_pack_twice_four:wNNNNNNNN
\__fp_pack_twice_four:wNNNNNNNN
\__fp_pack_twice_four:wNNNNNNNN
\__fp_fixed_dtf_zeros_auxii:ww
;
}
\cs_new:Npn \__fp_fixed_dtf_zeros_auxii:ww #1; #2; #3 { #3 #1; }
\cs_new:Npn \__fp_fixed_dtf_approx:n #1
{
\exp_after:wN \__fp_fixed_dtf_approx:wnn
\int_use:N \__int_eval:w 10 0000 0000 / ( #1 + \c_one ) ;
{#1}
}
\cs_new:Npn \__fp_fixed_dtf_approx:wnn #1; #2#3
{
\exp_after:wN \__fp_fixed_dtf_approx: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: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: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: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:www #2; #3 ; #1; }
\cs_new:Npn \__fp_trig_large:www #1; #2; #3;
{
\if_meaning:w 0 #3 \__fp_trig_large_break:w \fi:
\exp_after:wN \__fp_trig_large_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_o:wnnnn #1; #2#3#4#5
{
\exp_after:wN \__fp_trig_large: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:wNNnnnnnn ;
#2 000 0000 00 {10}987654321; #1
}
\cs_new:Npn \__fp_from_dim:wNNnnnnnn #1; #2#3#4#5#6#7#8#9
{ \__fp_from_dim:wnnnnwN #1 {#2#300} {0000} ; }
\cs_new:Npn \__fp_from_dim: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_max:nn #1#2
{ \fp_to_decimal:n { max ( \__fp_parse:n {#1} , \__fp_parse:n {#2} ) } }
\cs_new:Npn \fp_min:nn #1#2
{ \fp_to_decimal:n { min ( \__fp_parse:n {#1} , \__fp_parse:n {#2} ) } }
\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:n { > ~ \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:n { > ~ \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'.