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diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty b/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty
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@@ -0,0 +1,3403 @@
+%%
+%% This is file `l3fp.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% l3fp.dtx (with options: `package')
+%%
+%% EXPERIMENTAL CODE
+%%
+%% Do not distribute this file without also distributing the
+%% source files specified above.
+%%
+%% Do not distribute a modified version of this file.
+%%
+%% File: l3fp.dtx Copyright (C) 2010,2011 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 "expl3 bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%% http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%% Snapshots taken from the repository represent work in progress and may
+%% not work or may contain conflicting material! We therefore ask
+%% people _not_ to put them into distributions, archives, etc. without
+%% prior consultation with the LaTeX3 Project.
+%%
+%% -----------------------------------------------------------------------
+\RequirePackage{l3names}
+\GetIdInfo$Id: l3fp.dtx 2478 2011-06-19 21:34:23Z joseph $
+ {L3 Experimental floating-point operations}
+\ProvidesExplPackage
+ {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
+\package_check_loaded_expl:
+\int_const:Nn \c_forty_four { 44 }
+\int_const:Nn \c_one_million { 1 000 000 }
+\int_const:Nn \c_one_hundred_million { 100 000 000 }
+\int_const:Nn \c_five_hundred_million { 500 000 000 }
+\int_const:Nn \c_one_thousand_million { 1 000 000 000 }
+\int_new:N \c_fp_pi_by_four_decimal_int
+\int_set:Nn \c_fp_pi_by_four_decimal_int { 785 398 158 }
+\int_new:N \c_fp_pi_by_four_extended_int
+\int_set:Nn \c_fp_pi_by_four_extended_int { 897 448 310 }
+\int_new:N \c_fp_pi_decimal_int
+\int_set:Nn \c_fp_pi_decimal_int { 141 592 653 }
+\int_new:N \c_fp_pi_extended_int
+\int_set:Nn \c_fp_pi_extended_int { 589 793 238 }
+\int_new:N \c_fp_two_pi_decimal_int
+\int_set:Nn \c_fp_two_pi_decimal_int { 283 185 307 }
+\int_new:N \c_fp_two_pi_extended_int
+\int_set:Nn \c_fp_two_pi_extended_int { 179 586 477 }
+\tl_const:Nn \c_e_fp { + 2.718281828 e 0 }
+\tl_const:Nn \c_one_fp { + 1.000000000 e 0 }
+\tl_const:Nn \c_pi_fp { + 3.141592654 e 0 }
+\tl_const:Nn \c_undefined_fp { X 0.000000000 e 0 }
+\tl_const:Nn \c_zero_fp { + 0.000000000 e 0 }
+\tl_new:N \l_fp_arg_tl
+\int_new:N \l_fp_count_int
+\int_new:N \l_fp_div_offset_int
+\int_new:N \l_fp_exp_integer_int
+\int_new:N \l_fp_exp_decimal_int
+\int_new:N \l_fp_exp_extended_int
+\int_new:N \l_fp_exp_exponent_int
+\int_new:N \l_fp_input_a_sign_int
+\int_new:N \l_fp_input_a_integer_int
+\int_new:N \l_fp_input_a_decimal_int
+\int_new:N \l_fp_input_a_exponent_int
+\int_new:N \l_fp_input_b_sign_int
+\int_new:N \l_fp_input_b_integer_int
+\int_new:N \l_fp_input_b_decimal_int
+\int_new:N \l_fp_input_b_exponent_int
+\int_new:N \l_fp_input_a_extended_int
+\int_new:N \l_fp_input_b_extended_int
+\int_new:N \l_fp_mul_a_i_int
+\int_new:N \l_fp_mul_a_ii_int
+\int_new:N \l_fp_mul_a_iii_int
+\int_new:N \l_fp_mul_a_iv_int
+\int_new:N \l_fp_mul_a_v_int
+\int_new:N \l_fp_mul_a_vi_int
+\int_new:N \l_fp_mul_b_i_int
+\int_new:N \l_fp_mul_b_ii_int
+\int_new:N \l_fp_mul_b_iii_int
+\int_new:N \l_fp_mul_b_iv_int
+\int_new:N \l_fp_mul_b_v_int
+\int_new:N \l_fp_mul_b_vi_int
+\int_new:N \l_fp_mul_output_int
+\tl_new:N \l_fp_mul_output_tl
+\int_new:N \l_fp_output_sign_int
+\int_new:N \l_fp_output_integer_int
+\int_new:N \l_fp_output_decimal_int
+\int_new:N \l_fp_output_exponent_int
+\int_new:N \l_fp_output_extended_int
+\bool_new:N \l_fp_round_carry_bool
+\tl_new:N \l_fp_round_decimal_tl
+\int_new:N \l_fp_round_position_int
+\int_new:N \l_fp_round_target_int
+\tl_new:N \l_fp_sign_tl
+\int_new:N \l_fp_split_sign_int
+\int_new:N \l_fp_tmp_int
+\tl_new:N \l_fp_tmp_tl
+\int_new:N \l_fp_trig_octant_int
+\int_new:N \l_fp_trig_sign_int
+\int_new:N \l_fp_trig_decimal_int
+\int_new:N \l_fp_trig_extended_int
+\cs_new_protected_nopar:Npn \fp_read:N #1
+ { \exp_after:wN \fp_read_aux:w #1 \q_stop }
+\cs_new_protected_nopar:Npn \fp_read_aux:w #1#2 . #3 e #4 \q_stop
+ {
+ \if:w #1 -
+ \l_fp_input_a_sign_int \c_minus_one
+ \else:
+ \l_fp_input_a_sign_int \c_one
+ \fi:
+ \l_fp_input_a_integer_int #2 \scan_stop:
+ \l_fp_input_a_decimal_int #3 \scan_stop:
+ \l_fp_input_a_exponent_int #4 \scan_stop:
+ }
+\cs_new_protected_nopar:Npn \fp_split:Nn #1#2
+ {
+ \tl_set:Nx \l_fp_tmp_tl {#2}
+ \tl_set_rescan:Nno \l_fp_tmp_tl { \char_set_catcode_ignore:n { 32 } }
+ { \l_fp_tmp_tl }
+ \l_fp_split_sign_int \c_one
+ \fp_split_sign:
+ \use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int
+ \exp_after:wN \fp_split_exponent:w \l_fp_tmp_tl e e \q_stop #1
+ }
+\cs_new_protected_nopar:Npn \fp_split_sign:
+ {
+ \if_int_compare:w \pdftex_strcmp:D
+ { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_stop } { - }
+ = \c_zero
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \exp_after:wN
+ \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop
+ }
+ \l_fp_split_sign_int -\l_fp_split_sign_int
+ \exp_after:wN \fp_split_sign:
+ \else:
+ \if_int_compare:w \pdftex_strcmp:D
+ { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_stop } { + }
+ = \c_zero
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \exp_after:wN
+ \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop
+ }
+ \exp_after:wN \exp_after:wN \exp_after:wN \fp_split_sign:
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_split_exponent:w #1 e #2 e #3 \q_stop #4
+ {
+ \use:c { l_fp_input_ #4 _exponent_int }
+ \int_eval:w 0 #2 \scan_stop:
+ \tex_afterassignment:D \fp_split_aux_i:w
+ \use:c { l_fp_input_ #4 _integer_int }
+ \int_eval:w 0 #1 . . \q_stop #4
+ }
+\cs_new_protected_nopar:Npn \fp_split_aux_i:w #1 . #2 . #3 \q_stop
+ { \fp_split_aux_ii:w #2 000000000 \q_stop }
+\cs_new_protected_nopar:Npn \fp_split_aux_ii:w #1#2#3#4#5#6#7#8#9
+ { \fp_split_aux_iii:w {#1#2#3#4#5#6#7#8#9} }
+\cs_new_protected_nopar:Npn \fp_split_aux_iii:w #1#2 \q_stop
+ {
+ \l_fp_tmp_int 1 #1 \scan_stop:
+ \exp_after:wN \fp_split_decimal:w
+ \int_use:N \l_fp_tmp_int 000000000 \q_stop
+ }
+\cs_new_protected_nopar:Npn \fp_split_decimal:w #1#2#3#4#5#6#7#8#9
+ { \fp_split_decimal_aux:w {#2#3#4#5#6#7#8#9} }
+\cs_new_protected_nopar:Npn \fp_split_decimal_aux:w #1#2#3 \q_stop #4
+ {
+ \use:c { l_fp_input_ #4 _decimal_int } #1#2 \scan_stop:
+ \if_int_compare:w
+ \int_eval:w
+ \use:c { l_fp_input_ #4 _integer_int } +
+ \use:c { l_fp_input_ #4 _decimal_int }
+ \scan_stop:
+ = \c_zero
+ \use:c { l_fp_input_ #4 _sign_int } \c_one
+ \fi:
+ \if_int_compare:w
+ \use:c { l_fp_input_ #4 _integer_int } < \c_one_thousand_million
+ \else:
+ \exp_after:wN \fp_overflow_msg:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_standardise:NNNN #1#2#3#4
+ {
+ \if_int_compare:w
+ \int_eval:w #2 + #3 = \c_zero
+ #1 \c_one
+ #4 \c_zero
+ \exp_after:wN \use_none:nnnn
+ \else:
+ \exp_after:wN \fp_standardise_aux:NNNN
+ \fi:
+ #1#2#3#4
+ }
+\cs_new_protected_nopar:Npn \fp_standardise_aux:NNNN #1#2#3#4
+ {
+ \cs_set_protected_nopar:Npn \fp_standardise_aux:
+ {
+ \if_int_compare:w #2 = \c_zero
+ \tex_advance:D #3 \c_one_thousand_million
+ \exp_after:wN \fp_standardise_aux:w
+ \int_use:N #3 \q_stop
+ \exp_after:wN \fp_standardise_aux:
+ \fi:
+ }
+ \cs_set_protected_nopar:Npn
+ \fp_standardise_aux:w ##1##2##3##4##5##6##7##8##9 \q_stop
+ {
+ #2 ##2 \scan_stop:
+ #3 ##3##4##5##6##7##8##9 0 \scan_stop:
+ \tex_advance:D #4 \c_minus_one
+ }
+ \fp_standardise_aux:
+ \cs_set_protected_nopar:Npn \fp_standardise_aux:
+ {
+ \if_int_compare:w #2 > \c_nine
+ \tex_advance:D #2 \c_one_thousand_million
+ \exp_after:wN \use_i:nn \exp_after:wN
+ \fp_standardise_aux:w \int_use:N #2
+ \exp_after:wN \fp_standardise_aux:
+ \fi:
+ }
+ \cs_set_protected_nopar:Npn
+ \fp_standardise_aux:w ##1##2##3##4##5##6##7##8##9
+ {
+ #2 ##1##2##3##4##5##6##7##8 \scan_stop:
+ \tex_advance:D #3 \c_one_thousand_million
+ \tex_divide:D #3 \c_ten
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ ##9
+ \exp_after:wN \use_none:n \int_use:N #3
+ }
+ #3 \l_fp_tmp_tl \scan_stop:
+ \tex_advance:D #4 \c_one
+ }
+ \fp_standardise_aux:
+ \if_int_compare:w #4 < \c_one_hundred
+ \if_int_compare:w #4 > -\c_one_hundred
+ \else:
+ #1 \c_one
+ #2 \c_zero
+ #3 \c_zero
+ #4 \c_zero
+ \fi:
+ \else:
+ \exp_after:wN \fp_overflow_msg:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_standardise_aux: { }
+\cs_new_protected_nopar:Npn \fp_standardise_aux:w { }
+\cs_new_protected_nopar:Npn \fp_level_input_exponents:
+ {
+ \if_int_compare:w \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
+ \exp_after:wN \fp_level_input_exponents_a:
+ \else:
+ \exp_after:wN \fp_level_input_exponents_b:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_level_input_exponents_a:
+ {
+ \if_int_compare:w \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
+ \tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million
+ \exp_after:wN \use_i:nn \exp_after:wN
+ \fp_level_input_exponents_a:NNNNNNNNN
+ \int_use:N \l_fp_input_b_integer_int
+ \exp_after:wN \fp_level_input_exponents_a:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_level_input_exponents_a:NNNNNNNNN
+ #1#2#3#4#5#6#7#8#9
+ {
+ \l_fp_input_b_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
+ \tex_advance:D \l_fp_input_b_decimal_int \c_one_thousand_million
+ \tex_divide:D \l_fp_input_b_decimal_int \c_ten
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ #9
+ \exp_after:wN \use_none:n
+ \int_use:N \l_fp_input_b_decimal_int
+ }
+ \l_fp_input_b_decimal_int \l_fp_tmp_tl \scan_stop:
+ \tex_advance:D \l_fp_input_b_exponent_int \c_one
+ }
+\cs_new_protected_nopar:Npn \fp_level_input_exponents_b:
+ {
+ \if_int_compare:w \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int
+ \tex_advance:D \l_fp_input_a_integer_int \c_one_thousand_million
+ \exp_after:wN \use_i:nn \exp_after:wN
+ \fp_level_input_exponents_b:NNNNNNNNN
+ \int_use:N \l_fp_input_a_integer_int
+ \exp_after:wN \fp_level_input_exponents_b:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_level_input_exponents_b:NNNNNNNNN
+ #1#2#3#4#5#6#7#8#9
+ {
+ \l_fp_input_a_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \tex_divide:D \l_fp_input_a_decimal_int \c_ten
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ #9
+ \exp_after:wN \use_none:n
+ \int_use:N \l_fp_input_a_decimal_int
+ }
+ \l_fp_input_a_decimal_int \l_fp_tmp_tl \scan_stop:
+ \tex_advance:D \l_fp_input_a_exponent_int \c_one
+ }
+\cs_new_protected_nopar:Npn \fp_tmp:w #1#2 { }
+\cs_new_protected_nopar:Npn \fp_new:N #1
+ {
+ \tl_new:N #1
+ \tl_gset_eq:NN #1 \c_zero_fp
+ }
+\cs_generate_variant:Nn \fp_new:N { c }
+\cs_new_protected_nopar:Npn \fp_const:Nn #1#2
+ {
+ \fp_new:N #1
+ \fp_gset:Nn #1 {#2}
+ }
+\cs_generate_variant:Nn \fp_const:Nn { c }
+\cs_new_protected_nopar:Npn \fp_zero:N #1
+ { \tl_set_eq:NN #1 \c_zero_fp }
+\cs_new_protected_nopar:Npn \fp_gzero:N #1
+ { \tl_gset_eq:NN #1 \c_zero_fp }
+\cs_generate_variant:Nn \fp_zero:N { c }
+\cs_generate_variant:Nn \fp_gzero:N { c }
+\cs_new_protected_nopar:Npn \fp_set:Nn { \fp_set_aux:NNn \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gset:Nn { \fp_set_aux:NNn \tl_gset:Nn }
+\cs_new_protected_nopar:Npn \fp_set_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
+ -
+ \else:
+ +
+ \fi:
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_use:N \l_fp_input_a_decimal_int
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ }
+ \fp_tmp:w
+ }
+\cs_generate_variant:Nn \fp_set:Nn { c }
+\cs_generate_variant:Nn \fp_gset:Nn { c }
+\cs_new_protected_nopar:Npn \fp_set_from_dim:Nn
+ { \fp_set_from_dim_aux:NNn \tl_set:Nx }
+\cs_new_protected_nopar:Npn \fp_gset_from_dim:Nn
+ { \fp_set_from_dim_aux:NNn \tl_gset:Nx }
+\cs_new_protected_nopar:Npn \fp_set_from_dim_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \l_fp_tmp_skip \etex_glueexpr:D #3 \scan_stop:
+ \l_fp_tmp_dim \l_fp_tmp_skip
+ \fp_split:Nn a
+ {
+ \exp_after:wN \fp_set_from_dim_aux:w
+ \dim_use:N \l_fp_tmp_dim
+ }
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
+ -
+ \else:
+ +
+ \fi:
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_use:N \l_fp_input_a_decimal_int
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ }
+ \fp_tmp:w
+ }
+\cs_set_protected_nopar:Npx \fp_set_from_dim_aux:w
+ {
+ \cs_set_nopar:Npn \exp_not:N \fp_set_from_dim_aux:w
+ ##1 \tl_to_str:n { pt } {##1}
+ }
+\fp_set_from_dim_aux:w
+\cs_generate_variant:Nn \fp_set_from_dim:Nn { c }
+\cs_generate_variant:Nn \fp_gset_from_dim:Nn { c }
+\dim_new:N \l_fp_tmp_dim
+\skip_new:N \l_fp_tmp_skip
+\cs_new_eq:NN \fp_set_eq:NN \tl_set_eq:NN
+\cs_new_eq:NN \fp_set_eq:cN \tl_set_eq:cN
+\cs_new_eq:NN \fp_set_eq:Nc \tl_set_eq:Nc
+\cs_new_eq:NN \fp_set_eq:cc \tl_set_eq:cc
+\cs_new_eq:NN \fp_gset_eq:NN \tl_gset_eq:NN
+\cs_new_eq:NN \fp_gset_eq:cN \tl_gset_eq:cN
+\cs_new_eq:NN \fp_gset_eq:Nc \tl_gset_eq:Nc
+\cs_new_eq:NN \fp_gset_eq:cc \tl_gset_eq:cc
+\cs_new_eq:NN \fp_show:N \tl_show:N
+\cs_new_eq:NN \fp_show:c \tl_show:c
+\cs_new_nopar:Npn \fp_use:N #1
+ { \exp_after:wN \fp_use_aux:w #1 \q_stop }
+\cs_generate_variant:Nn \fp_use:N { c }
+\cs_new_nopar:Npn \fp_use_aux:w #1#2 e #3 \q_stop
+ {
+ \if:w #1 -
+ -
+ \fi:
+ \if_int_compare:w #3 > \c_zero
+ \exp_after:wN \fp_use_large:w
+ \else:
+ \if_int_compare:w #3 < \c_zero
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \fp_use_small:w
+ \else:
+ \exp_after:wN \exp_after:wN \exp_after:wN \fp_use_none:w
+ \fi:
+ \fi:
+ #2 e #3 \q_stop
+ }
+\cs_new_nopar:Npn \fp_use_none:w #1 e #2 \q_stop {#1}
+\cs_new_nopar:Npn \fp_use_small:w #1 . #2 e #3 \q_stop
+ {
+ 0 .
+ \prg_replicate:nn { -#3 - 1 } { 0 }
+ #1#2
+ }
+\cs_new_nopar:Npn \fp_use_large:w #1 . #2 e #3 \q_stop
+ {
+ \if_int_compare:w #3 < \c_ten
+ \exp_after:wN \fp_use_large_aux_i:w
+ \else:
+ \exp_after:wN \fp_use_large_aux_ii:w
+ \fi:
+ #1#2 e #3 \q_stop
+ }
+\cs_new_nopar:Npn \fp_use_large_aux_i:w #1#2 e #3 \q_stop
+ {
+ #1
+ \use:c { fp_use_large_aux_ #3 :w } #2 \q_stop
+ }
+\cs_new_nopar:cpn { fp_use_large_aux_1:w } #1#2 \q_stop { #1 . #2 }
+\cs_new_nopar:cpn { fp_use_large_aux_2:w } #1#2#3 \q_stop
+ { #1#2 . #3 }
+\cs_new_nopar:cpn { fp_use_large_aux_3:w } #1#2#3#4 \q_stop
+ { #1#2#3 . #4 }
+\cs_new_nopar:cpn { fp_use_large_aux_4:w } #1#2#3#4#5 \q_stop
+ { #1#2#3#4 . #5 }
+\cs_new_nopar:cpn { fp_use_large_aux_5:w } #1#2#3#4#5#6 \q_stop
+ { #1#2#3#4#5 . #6 }
+\cs_new_nopar:cpn { fp_use_large_aux_6:w } #1#2#3#4#5#6#7 \q_stop
+ { #1#2#3#4#5#6 . #7 }
+\cs_new_nopar:cpn { fp_use_large_aux_7:w } #1#2#3#4#5#6#7#8 \q_stop
+ { #1#2#3#4#6#7 . #8 }
+\cs_new_nopar:cpn { fp_use_large_aux_8:w } #1#2#3#4#5#6#7#8#9 \q_stop
+ { #1#2#3#4#5#6#7#8 . #9 }
+\cs_new_nopar:cpn { fp_use_large_aux_9:w } #1 \q_stop { #1 . }
+\cs_new_nopar:Npn \fp_use_large_aux_ii:w #1 e #2 \q_stop
+ {
+ #1
+ \prg_replicate:nn { #2 - 9 } { 0 }
+ .
+ }
+\cs_new_nopar:Npn \fp_to_dim:N #1 { \fp_use:N #1 pt }
+\cs_generate_variant:Nn \fp_to_dim:N { c }
+\cs_new_nopar:Npn \fp_to_int:N #1
+ { \exp_after:wN \fp_to_int_aux:w #1 \q_stop }
+\cs_generate_variant:Nn \fp_to_int:N { c }
+\cs_new_nopar:Npn \fp_to_int_aux:w #1#2 e #3 \q_stop
+ {
+ \if:w #1 -
+ -
+ \fi:
+ \if_int_compare:w #3 < \c_zero
+ \exp_after:wN \fp_to_int_small:w
+ \else:
+ \exp_after:wN \fp_to_int_large:w
+ \fi:
+ #2 e #3 \q_stop
+ }
+\cs_new_nopar:Npn \fp_to_int_small:w #1 . #2 e #3 \q_stop
+ {
+ \if_int_compare:w #3 > \c_one
+ \else:
+ \if_int_compare:w #1 < \c_five
+ 0
+ \else:
+ 1
+ \fi:
+ \fi:
+ }
+\cs_new_nopar:Npn \fp_to_int_large:w #1 . #2 e #3 \q_stop
+ {
+ \if_int_compare:w #3 < \c_ten
+ \exp_after:wN \fp_to_int_large_aux_i:w
+ \else:
+ \exp_after:wN \fp_to_int_large_aux_ii:w
+ \fi:
+ #1#2 e #3 \q_stop
+ }
+\cs_new_nopar:Npn \fp_to_int_large_aux_i:w #1#2 e #3 \q_stop
+ { \use:c { fp_to_int_large_aux_ #3 :w } #2 \q_stop {#1} }
+\cs_new_nopar:cpn { fp_to_int_large_aux_1:w } #1#2 \q_stop
+ { \fp_to_int_large_aux:nnn { #2 0 } {#1} }
+\cs_new_nopar:cpn { fp_to_int_large_aux_2:w } #1#2#3 \q_stop
+ { \fp_to_int_large_aux:nnn { #3 00 } {#1#2} }
+\cs_new_nopar:cpn { fp_to_int_large_aux_3:w } #1#2#3#4 \q_stop
+ { \fp_to_int_large_aux:nnn { #4 000 } {#1#2#3} }
+\cs_new_nopar:cpn { fp_to_int_large_aux_4:w } #1#2#3#4#5 \q_stop
+ { \fp_to_int_large_aux:nnn { #5 0000 } {#1#2#3#4} }
+\cs_new_nopar:cpn { fp_to_int_large_aux_5:w } #1#2#3#4#5#6 \q_stop
+ { \fp_to_int_large_aux:nnn { #6 00000 } {#1#2#3#4#5} }
+\cs_new_nopar:cpn { fp_to_int_large_aux_6:w } #1#2#3#4#5#6#7 \q_stop
+ { \fp_to_int_large_aux:nnn { #7 000000 } {#1#2#3#4#5#6} }
+\cs_new_nopar:cpn { fp_to_int_large_aux_7:w } #1#2#3#4#5#6#7#8 \q_stop
+ { \fp_to_int_large_aux:nnn { #8 0000000 } {#1#2#3#4#5#6#7} }
+\cs_new_nopar:cpn { fp_to_int_large_aux_8:w } #1#2#3#4#5#6#7#8#9 \q_stop
+ { \fp_to_int_large_aux:nnn { #9 00000000 } {#1#2#3#4#5#6#7#8} }
+\cs_new_nopar:cpn { fp_to_int_large_aux_9:w } #1 \q_stop {#1}
+\cs_new_nopar:Npn \fp_to_int_large_aux:nnn #1#2#3
+ {
+ \if_int_compare:w #1 < \c_five_hundred_million
+ #3#2
+ \else:
+ \int_value:w \int_eval:w #3#2 + 1 \int_eval_end:
+ \fi:
+ }
+\cs_new_nopar:Npn \fp_to_int_large_aux_ii:w #1 e #2 \q_stop
+ {
+ #1
+ \prg_replicate:nn { #2 - 9 } { 0 }
+ }
+\cs_new_nopar:Npn \fp_to_tl:N #1
+ { \exp_after:wN \fp_to_tl_aux:w #1 \q_stop }
+\cs_generate_variant:Nn \fp_to_tl:N { c }
+\cs_new_nopar:Npn \fp_to_tl_aux:w #1#2 e #3 \q_stop
+ {
+ \if:w #1 -
+ -
+ \fi:
+ \if_int_compare:w #3 < \c_zero
+ \exp_after:wN \fp_to_tl_small:w
+ \else:
+ \exp_after:wN \fp_to_tl_large:w
+ \fi:
+ #2 e #3 \q_stop
+ }
+\cs_new_nopar:Npn \fp_to_tl_large:w #1 e #2 \q_stop
+ {
+ \if_int_compare:w #2 < \c_ten
+ \exp_after:wN \fp_to_tl_large_aux_i:w
+ \else:
+ \exp_after:wN \fp_to_tl_large_aux_ii:w
+ \fi:
+ #1 e #2 \q_stop
+ }
+\cs_new_nopar:Npn \fp_to_tl_large_aux_i:w #1 e #2 \q_stop
+ { \use:c { fp_to_tl_large_ #2 :w } #1 \q_stop }
+\cs_new_nopar:Npn \fp_to_tl_large_aux_ii:w #1 . #2 e #3 \q_stop
+ {
+ #1
+ \fp_to_tl_large_zeros:NNNNNNNNN #2
+ e #3
+ }
+\cs_new_nopar:cpn { fp_to_tl_large_0:w } #1 . #2 \q_stop
+ {
+ #1
+ \fp_to_tl_large_zeros:NNNNNNNNN #2
+ }
+\cs_new_nopar:cpn { fp_to_tl_large_1:w } #1 . #2#3 \q_stop
+ {
+ #1#2
+ \fp_to_tl_large_zeros:NNNNNNNNN #3 0
+ }
+\cs_new_nopar:cpn { fp_to_tl_large_2:w } #1 . #2#3#4 \q_stop
+ {
+ #1#2#3
+ \fp_to_tl_large_zeros:NNNNNNNNN #4 00
+ }
+\cs_new_nopar:cpn { fp_to_tl_large_3:w } #1 . #2#3#4#5 \q_stop
+ {
+ #1#2#3#4
+ \fp_to_tl_large_zeros:NNNNNNNNN #5 000
+ }
+\cs_new_nopar:cpn { fp_to_tl_large_4:w } #1 . #2#3#4#5#6 \q_stop
+ {
+ #1#2#3#4#5
+ \fp_to_tl_large_zeros:NNNNNNNNN #6 0000
+ }
+\cs_new_nopar:cpn { fp_to_tl_large_5:w } #1 . #2#3#4#5#6#7 \q_stop
+ {
+ #1#2#3#4#5#6
+ \fp_to_tl_large_zeros:NNNNNNNNN #7 00000
+ }
+\cs_new_nopar:cpn { fp_to_tl_large_6:w } #1 . #2#3#4#5#6#7#8 \q_stop
+ {
+ #1#2#3#4#5#6#7
+ \fp_to_tl_large_zeros:NNNNNNNNN #8 000000
+ }
+\cs_new_nopar:cpn { fp_to_tl_large_7:w } #1 . #2#3#4#5#6#7#8#9 \q_stop
+ {
+ #1#2#3#4#5#6#7#8
+ \fp_to_tl_large_zeros:NNNNNNNNN #9 0000000
+ }
+\cs_new_nopar:cpn { fp_to_tl_large_8:w } #1 .
+ {
+ #1
+ \use:c { fp_to_tl_large_8_aux:w }
+ }
+\cs_new_nopar:cpn { fp_to_tl_large_8_aux:w } #1#2#3#4#5#6#7#8#9 \q_stop
+ {
+ #1#2#3#4#5#6#7#8
+ \fp_to_tl_large_zeros:NNNNNNNNN #9 00000000
+ }
+\cs_new_nopar:cpn { fp_to_tl_large_9:w } #1 . #2 \q_stop {#1#2}
+\cs_new_nopar:Npn \fp_to_tl_small:w #1 e #2 \q_stop
+ {
+ \if_int_compare:w #2 = \c_minus_one
+ \exp_after:wN \fp_to_tl_small_one:w
+ \else:
+ \if_int_compare:w #2 = -\c_two
+ \exp_after:wN \exp_after:wN \exp_after:wN \fp_to_tl_small_two:w
+ \else:
+ \exp_after:wN \exp_after:wN \exp_after:wN \fp_to_tl_small_aux:w
+ \fi:
+ \fi:
+ #1 e #2 \q_stop
+ }
+\cs_new_nopar:Npn \fp_to_tl_small_one:w #1 . #2 e #3 \q_stop
+ {
+ \if_int_compare:w \fp_use_ix:NNNNNNNNN #2 > \c_four
+ \if_int_compare:w
+ \int_eval:w #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
+ < \c_one_thousand_million
+ 0.
+ \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN
+ \int_value:w \int_eval:w
+ #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
+ \int_eval_end:
+ \else:
+ 1
+ \fi:
+ \else:
+ 0. #1
+ \fp_to_tl_small_zeros:NNNNNNNNN #2
+ \fi:
+ }
+\cs_new_nopar:Npn \fp_to_tl_small_two:w #1 . #2 e #3 \q_stop
+ {
+ \if_int_compare:w \fp_use_iix_ix:NNNNNNNNN #2 > \c_forty_four
+ \if_int_compare:w
+ \int_eval:w #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
+ < \c_one_thousand_million
+ 0.0
+ \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN
+ \int_value:w \int_eval:w
+ #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
+ \int_eval_end:
+ \else:
+ 0.1
+ \fi:
+ \else:
+ 0.0
+ #1
+ \fp_to_tl_small_zeros:NNNNNNNNN #2
+ \fi:
+ }
+\cs_new_nopar:Npn \fp_to_tl_small_aux:w #1 . #2 e #3 \q_stop
+ {
+ #1
+ \fp_to_tl_large_zeros:NNNNNNNNN #2
+ e #3
+ }
+\cs_new_nopar:Npn \fp_to_tl_large_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+ {
+ \if_int_compare:w #9 = \c_zero
+ \if_int_compare:w #8 = \c_zero
+ \if_int_compare:w #7 = \c_zero
+ \if_int_compare:w #6 = \c_zero
+ \if_int_compare:w #5 = \c_zero
+ \if_int_compare:w #4 = \c_zero
+ \if_int_compare:w #3 = \c_zero
+ \if_int_compare:w #2 = \c_zero
+ \if_int_compare:w #1 = \c_zero
+ \else:
+ . #1
+ \fi:
+ \else:
+ . #1#2
+ \fi:
+ \else:
+ . #1#2#3
+ \fi:
+ \else:
+ . #1#2#3#4
+ \fi:
+ \else:
+ . #1#2#3#4#5
+ \fi:
+ \else:
+ . #1#2#3#4#5#6
+ \fi:
+ \else:
+ . #1#2#3#4#5#6#7
+ \fi:
+ \else:
+ . #1#2#3#4#5#6#7#8
+ \fi:
+ \else:
+ . #1#2#3#4#5#6#7#8#9
+ \fi:
+ }
+\cs_new_nopar:Npn \fp_to_tl_small_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+ {
+ \if_int_compare:w #9 = \c_zero
+ \if_int_compare:w #8 = \c_zero
+ \if_int_compare:w #7 = \c_zero
+ \if_int_compare:w #6 = \c_zero
+ \if_int_compare:w #5 = \c_zero
+ \if_int_compare:w #4 = \c_zero
+ \if_int_compare:w #3 = \c_zero
+ \if_int_compare:w #2 = \c_zero
+ \if_int_compare:w #1 = \c_zero
+ \else:
+ #1
+ \fi:
+ \else:
+ #1#2
+ \fi:
+ \else:
+ #1#2#3
+ \fi:
+ \else:
+ #1#2#3#4
+ \fi:
+ \else:
+ #1#2#3#4#5
+ \fi:
+ \else:
+ #1#2#3#4#5#6
+ \fi:
+ \else:
+ #1#2#3#4#5#6#7
+ \fi:
+ \else:
+ #1#2#3#4#5#6#7#8
+ \fi:
+ \else:
+ #1#2#3#4#5#6#7#8#9
+ \fi:
+ }
+\cs_new_nopar:Npn \fp_use_iix_ix:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {#8#9}
+\cs_new_nopar:Npn \fp_use_ix:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {#9}
+\cs_new_nopar:Npn \fp_use_i_to_vii:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+ {#1#2#3#4#5#6#7}
+\cs_new_nopar:Npn \fp_use_i_to_iix:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+ {#1#2#3#4#5#6#7#8}
+\cs_new_protected_nopar:Npn \fp_round_figures:Nn
+ { \fp_round_figures_aux:NNn \tl_set:Nn }
+\cs_generate_variant:Nn \fp_round_figures:Nn { c }
+\cs_new_protected_nopar:Npn \fp_ground_figures:Nn
+ { \fp_round_figures_aux:NNn \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_ground_figures:Nn { c }
+\cs_new_protected_nopar:Npn \fp_round_figures_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_read:N #2
+ \int_set:Nn \l_fp_round_target_int { #3 - 1 }
+ \if_int_compare:w \l_fp_round_target_int < \c_ten
+ \exp_after:wN \fp_round:
+ \fi:
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
+ -
+ \else:
+ +
+ \fi:
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_use:N \l_fp_input_a_decimal_int
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ }
+ \fp_tmp:w
+ }
+\cs_new_protected_nopar:Npn \fp_round_places:Nn
+ { \fp_round_places_aux:NNn \tl_set:Nn }
+\cs_generate_variant:Nn \fp_round_places:Nn { c }
+\cs_new_protected_nopar:Npn \fp_ground_places:Nn
+ { \fp_round_places_aux:NNn \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_ground_places:Nn { c }
+\cs_new_protected_nopar:Npn \fp_round_places_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_read:N #2
+ \int_set:Nn \l_fp_round_target_int
+ { #3 + \l_fp_input_a_exponent_int }
+ \if_int_compare:w \l_fp_round_target_int < \c_ten
+ \exp_after:wN \fp_round:
+ \fi:
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
+ -
+ \else:
+ +
+ \fi:
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_use:N \l_fp_input_a_decimal_int
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ }
+ \fp_tmp:w
+ }
+\cs_new_protected_nopar:Npn \fp_round:
+ {
+ \bool_set_false:N \l_fp_round_carry_bool
+ \l_fp_round_position_int \c_eight
+ \tl_clear:N \l_fp_round_decimal_tl
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \exp_after:wN \use_i:nn \exp_after:wN
+ \fp_round_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int
+ }
+\cs_new_protected_nopar:Npn \fp_round_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+ {
+ \fp_round_loop:N #9#8#7#6#5#4#3#2#1
+ \bool_if:NT \l_fp_round_carry_bool
+ { \tex_advance:D \l_fp_input_a_integer_int \c_one }
+ \l_fp_input_a_decimal_int \l_fp_round_decimal_tl \scan_stop:
+ \if_int_compare:w \l_fp_input_a_integer_int < \c_ten
+ \else:
+ \l_fp_input_a_integer_int \c_one
+ \tex_divide:D \l_fp_input_a_decimal_int \c_ten
+ \tex_advance:D \l_fp_input_a_exponent_int \c_one
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_round_loop:N #1
+ {
+ \if_int_compare:w \l_fp_round_position_int < \l_fp_round_target_int
+ \bool_if:NTF \l_fp_round_carry_bool
+ { \l_fp_tmp_int \int_eval:w #1 + \c_one \scan_stop: }
+ { \l_fp_tmp_int \int_eval:w #1 \scan_stop: }
+ \if_int_compare:w \l_fp_tmp_int = \c_ten
+ \l_fp_tmp_int \c_zero
+ \else:
+ \bool_set_false:N \l_fp_round_carry_bool
+ \fi:
+ \tl_set:Nx \l_fp_round_decimal_tl
+ { \int_use:N \l_fp_tmp_int \l_fp_round_decimal_tl }
+ \else:
+ \tl_set:Nx \l_fp_round_decimal_tl { 0 \l_fp_round_decimal_tl }
+ \if_int_compare:w \l_fp_round_position_int = \l_fp_round_target_int
+ \if_int_compare:w #1 > \c_four
+ \bool_set_true:N \l_fp_round_carry_bool
+ \fi:
+ \fi:
+ \fi:
+ \tex_advance:D \l_fp_round_position_int \c_minus_one
+ \if_int_compare:w \l_fp_round_position_int > \c_minus_one
+ \exp_after:wN \fp_round_loop:N
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_abs:N { \fp_abs_aux:NN \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gabs:N { \fp_abs_aux:NN \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_abs:N { c }
+\cs_generate_variant:Nn \fp_gabs:N { c }
+\cs_new_protected_nopar:Npn \fp_abs_aux:NN #1#2
+ {
+ \group_begin:
+ \fp_read:N #2
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2
+ {
+ +
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_use:N \l_fp_input_a_decimal_int
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ }
+ \fp_tmp:w
+ }
+\cs_new_protected_nopar:Npn \fp_neg:N { \fp_neg_aux:NN \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gneg:N { \fp_neg_aux:NN \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_neg:N { c }
+\cs_generate_variant:Nn \fp_gneg:N { c }
+\cs_new_protected_nopar:Npn \fp_neg_aux:NN #1#2
+ {
+ \group_begin:
+ \fp_read:N #2
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
+ +
+ \else:
+ -
+ \fi:
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_use:N \l_fp_input_a_decimal_int
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ \exp_after:wN \group_end: \exp_after:wN
+ #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+ }
+\cs_new_protected_nopar:Npn \fp_add:Nn { \fp_add_aux:NNn \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gadd:Nn { \fp_add_aux:NNn \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_add:Nn { c }
+\cs_generate_variant:Nn \fp_gadd:Nn { c }
+\cs_new_protected_nopar:Npn \fp_add_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_read:N #2
+ \fp_split:Nn b {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_b_sign_int
+ \l_fp_input_b_integer_int
+ \l_fp_input_b_decimal_int
+ \l_fp_input_b_exponent_int
+ \fp_add_core:
+ \fp_tmp:w #1#2
+ }
+\cs_new_protected_nopar:Npn \fp_add_core:
+ {
+ \fp_level_input_exponents:
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
+ > \c_zero
+ \exp_after:wN \fp_add_sum:
+ \else:
+ \exp_after:wN \fp_add_difference:
+ \fi:
+ \l_fp_output_exponent_int \l_fp_input_a_exponent_int
+ \fp_standardise:NNNN
+ \l_fp_output_sign_int
+ \l_fp_output_integer_int
+ \l_fp_output_decimal_int
+ \l_fp_output_exponent_int
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2
+ {
+ \if_int_compare:w \l_fp_output_sign_int < \c_zero
+ -
+ \else:
+ +
+ \fi:
+ \int_use:N \l_fp_output_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+ }
+ }
+\cs_new_protected_nopar:Npn \fp_add_sum:
+ {
+ \l_fp_output_sign_int \l_fp_input_a_sign_int
+ \l_fp_output_integer_int
+ \int_eval:w
+ \l_fp_input_a_integer_int + \l_fp_input_b_integer_int
+ \scan_stop:
+ \l_fp_output_decimal_int
+ \int_eval:w
+ \l_fp_input_a_decimal_int + \l_fp_input_b_decimal_int
+ \scan_stop:
+ \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
+ \else:
+ \tex_advance:D \l_fp_output_integer_int \c_one
+ \tex_advance:D \l_fp_output_decimal_int -\c_one_thousand_million
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_add_difference:
+ {
+ \l_fp_output_integer_int
+ \int_eval:w
+ \l_fp_input_a_integer_int - \l_fp_input_b_integer_int
+ \scan_stop:
+ \l_fp_output_decimal_int
+ \int_eval:w
+ \l_fp_input_a_decimal_int - \l_fp_input_b_decimal_int
+ \scan_stop:
+ \if_int_compare:w \l_fp_output_decimal_int < \c_zero
+ \tex_advance:D \l_fp_output_integer_int \c_minus_one
+ \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+ \fi:
+ \if_int_compare:w \l_fp_output_integer_int < \c_zero
+ \l_fp_output_sign_int \l_fp_input_b_sign_int
+ \if_int_compare:w \l_fp_output_decimal_int = \c_zero
+ \l_fp_output_integer_int -\l_fp_output_integer_int
+ \else:
+ \l_fp_output_decimal_int
+ \int_eval:w
+ \c_one_thousand_million - \l_fp_output_decimal_int
+ \scan_stop:
+ \l_fp_output_integer_int
+ \int_eval:w
+ - \l_fp_output_integer_int - \c_one
+ \scan_stop:
+ \fi:
+ \else:
+ \l_fp_output_sign_int \l_fp_input_a_sign_int
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_sub:Nn { \fp_sub_aux:NNn \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gsub:Nn { \fp_sub_aux:NNn \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_sub:Nn { c }
+\cs_generate_variant:Nn \fp_gsub:Nn { c }
+\cs_new_protected_nopar:Npn \fp_sub_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_read:N #2
+ \fp_split:Nn b {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_b_sign_int
+ \l_fp_input_b_integer_int
+ \l_fp_input_b_decimal_int
+ \l_fp_input_b_exponent_int
+ \tex_multiply:D \l_fp_input_b_sign_int \c_minus_one
+ \fp_add_core:
+ \fp_tmp:w #1#2
+ }
+\cs_new_protected_nopar:Npn \fp_mul:Nn { \fp_mul_aux:NNn \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gmul:Nn { \fp_mul_aux:NNn \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_mul:Nn { c }
+\cs_generate_variant:Nn \fp_gmul:Nn { c }
+\cs_new_protected_nopar:Npn \fp_mul_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_read:N #2
+ \fp_split:Nn b {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_b_sign_int
+ \l_fp_input_b_integer_int
+ \l_fp_input_b_decimal_int
+ \l_fp_input_b_exponent_int
+ \fp_mul_internal:
+ \l_fp_output_exponent_int
+ \int_eval:w
+ \l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int
+ \scan_stop:
+ \fp_standardise:NNNN
+ \l_fp_output_sign_int
+ \l_fp_output_integer_int
+ \l_fp_output_decimal_int
+ \l_fp_output_exponent_int
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2
+ {
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
+ < \c_zero
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_output_integer_int + \l_fp_output_decimal_int
+ = \c_zero
+ +
+ \else:
+ -
+ \fi:
+ \else:
+ +
+ \fi:
+ \int_use:N \l_fp_output_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+ }
+ \fp_tmp:w
+ }
+\cs_new_protected_nopar:Npn \fp_mul_internal:
+ {
+ \fp_mul_split:NNNN \l_fp_input_a_decimal_int
+ \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
+ \fp_mul_split:NNNN \l_fp_input_b_decimal_int
+ \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
+ \l_fp_mul_output_int \c_zero
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_i_int
+ \tex_divide:D \l_fp_mul_output_int \c_one_thousand
+ \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_input_b_integer_int
+ \fp_mul_end_level:
+ \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_input_b_integer_int
+ \fp_mul_end_level:
+ \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_input_b_integer_int
+ \fp_mul_end_level:
+ \l_fp_output_decimal_int 0 \l_fp_mul_output_tl \scan_stop:
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_input_b_integer_int
+ \fp_mul_end_level:
+ \l_fp_output_integer_int 0 \l_fp_mul_output_tl \scan_stop:
+ }
+\cs_new_protected_nopar:Npn \fp_mul_split:NNNN #1#2#3#4
+ {
+ \tex_advance:D #1 \c_one_thousand_million
+ \cs_set_protected_nopar:Npn \fp_mul_split_aux:w
+ ##1##2##3##4##5##6##7##8##9 \q_stop {
+ #2 ##2##3##4 \scan_stop:
+ #3 ##5##6##7 \scan_stop:
+ #4 ##8##9 \scan_stop:
+ }
+ \exp_after:wN \fp_mul_split_aux:w \int_use:N #1 \q_stop
+ \tex_advance:D #1 -\c_one_thousand_million
+ }
+\cs_new_protected_nopar:Npn \fp_mul_product:NN #1#2
+ {
+ \l_fp_mul_output_int
+ \int_eval:w \l_fp_mul_output_int + #1 * #2 \scan_stop:
+ }
+\cs_new_protected_nopar:Npn \fp_mul_end_level:
+ {
+ \tex_advance:D \l_fp_mul_output_int \c_one_thousand_million
+ \exp_after:wN \use_i:nn \exp_after:wN
+ \fp_mul_end_level:NNNNNNNNN \int_use:N \l_fp_mul_output_int
+ }
+\cs_new_protected_nopar:Npn \fp_mul_end_level:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+ {
+ \tl_set:Nx \l_fp_mul_output_tl { #7#8#9 \l_fp_mul_output_tl }
+ \l_fp_mul_output_int #1#2#3#4#5#6 \scan_stop:
+ }
+\cs_new_protected_nopar:Npn \fp_div:Nn { \fp_div_aux:NNn \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gdiv:Nn { \fp_div_aux:NNn \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_div:Nn { c }
+\cs_generate_variant:Nn \fp_gdiv:Nn { c }
+\cs_new_protected_nopar:Npn \fp_div_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_read:N #2
+ \fp_split:Nn b {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_b_sign_int
+ \l_fp_input_b_integer_int
+ \l_fp_input_b_decimal_int
+ \l_fp_input_b_exponent_int
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+ = \c_zero
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ #1 \exp_not:N #2 { \c_undefined_fp }
+ }
+ \else:
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+ = \c_zero
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ #1 \exp_not:N #2 { \c_zero_fp }
+ }
+ \else:
+ \exp_after:wN \exp_after:wN \exp_after:wN \fp_div_internal:
+ \fi:
+ \fi:
+ \fp_tmp:w #1#2
+ }
+\cs_new_protected_nopar:Npn \fp_div_internal: {
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
+ \l_fp_div_offset_int \c_one_hundred_million
+ \fp_div_loop:
+ \l_fp_output_exponent_int
+ \int_eval:w
+ \l_fp_input_a_exponent_int - \l_fp_input_b_exponent_int
+ \scan_stop:
+ \fp_standardise:NNNN
+ \l_fp_output_sign_int
+ \l_fp_output_integer_int
+ \l_fp_output_decimal_int
+ \l_fp_output_exponent_int
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2
+ {
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
+ < \c_zero
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_output_integer_int + \l_fp_output_decimal_int
+ = \c_zero
+ +
+ \else:
+ -
+ \fi:
+ \else:
+ +
+ \fi:
+ \int_use:N \l_fp_output_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ \int_eval_end:
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+ }
+}
+\cs_new_protected_nopar:Npn \fp_div_loop:
+ {
+ \l_fp_count_int \c_zero
+ \fp_div_divide:
+ \fp_div_store:
+ \tex_multiply:D \l_fp_input_a_integer_int \c_ten
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \exp_after:wN \fp_div_loop_step:w
+ \int_use:N \l_fp_input_a_decimal_int \q_stop
+ \if_int_compare:w
+ \int_eval:w \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+ > \c_zero
+ \if_int_compare:w \l_fp_div_offset_int > \c_zero
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \fp_div_loop:
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_div_divide:
+ {
+ \if_int_compare:w \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
+ \exp_after:wN \fp_div_divide_aux:
+ \else:
+ \if_int_compare:w \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
+ \else:
+ \if_int_compare:w
+ \l_fp_input_a_decimal_int < \l_fp_input_b_decimal_int
+ \else:
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \fp_div_divide_aux:
+ \fi:
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_div_divide_aux:
+ {
+ \tex_advance:D \l_fp_count_int \c_one
+ \tex_advance:D \l_fp_input_a_integer_int -\l_fp_input_b_integer_int
+ \tex_advance:D \l_fp_input_a_decimal_int -\l_fp_input_b_decimal_int
+ \if_int_compare:w \l_fp_input_a_decimal_int < \c_zero
+ \tex_advance:D \l_fp_input_a_integer_int \c_minus_one
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \fi:
+ \fp_div_divide:
+ }
+\cs_new_protected_nopar:Npn \fp_div_store: { }
+\cs_new_protected_nopar:Npn \fp_div_store_integer:
+ {
+ \l_fp_output_integer_int \l_fp_count_int
+ \cs_set_eq:NN \fp_div_store: \fp_div_store_decimal:
+ }
+\cs_new_protected_nopar:Npn \fp_div_store_decimal:
+ {
+ \l_fp_output_decimal_int
+ \int_eval:w
+ \l_fp_output_decimal_int +
+ \l_fp_count_int * \l_fp_div_offset_int
+ \int_eval_end:
+ \tex_divide:D \l_fp_div_offset_int \c_ten
+ }
+\cs_new_protected_nopar:Npn \fp_div_loop_step:w #1#2#3#4#5#6#7#8#9 \q_stop
+ {
+ \l_fp_input_a_integer_int
+ \int_eval:w #2 + \l_fp_input_a_integer_int \int_eval_end:
+ \l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
+ }
+\cs_new_protected_nopar:Npn \fp_add:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+ {
+ #7 \int_eval:w #1 + #4 \int_eval_end:
+ #8 \int_eval:w #2 + #5 \int_eval_end:
+ #9 \int_eval:w #3 + #6 \int_eval_end:
+ \if_int_compare:w #9 < \c_one_thousand_million
+ \else:
+ \tex_advance:D #8 \c_one
+ \tex_advance:D #9 -\c_one_thousand_million
+ \fi:
+ \if_int_compare:w #8 < \c_one_thousand_million
+ \else:
+ \tex_advance:D #7 \c_one
+ \tex_advance:D #8 -\c_one_thousand_million
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_sub:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+ {
+ #7 \int_eval:w #1 - #4 \int_eval_end:
+ #8 \int_eval:w #2 - #5 \int_eval_end:
+ #9 \int_eval:w #3 - #6 \int_eval_end:
+ \if_int_compare:w #9 < \c_zero
+ \tex_advance:D #8 \c_minus_one
+ \tex_advance:D #9 \c_one_thousand_million
+ \fi:
+ \if_int_compare:w #8 < \c_zero
+ \tex_advance:D #7 \c_minus_one
+ \tex_advance:D #8 \c_one_thousand_million
+ \fi:
+ \if_int_compare:w #7 < \c_zero
+ \if_int_compare:w \int_eval:w #8 + #9 = \c_zero
+ #7 -#7
+ \else:
+ \tex_advance:D #7 \c_one
+ #8 \int_eval:w \c_one_thousand_million - #8 \int_eval_end:
+ #9 \int_eval:w \c_one_thousand_million - #9 \int_eval_end:
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_mul:NNNNNN #1#2#3#4#5#6
+ {
+ \fp_mul_split:NNNN #1
+ \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
+ \fp_mul_split:NNNN #2
+ \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
+ \fp_mul_split:NNNN #3
+ \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
+ \fp_mul_split:NNNN #4
+ \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int
+ \l_fp_mul_output_int \c_zero
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_vi_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_v_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_i_int
+ \tex_divide:D \l_fp_mul_output_int \c_one_thousand
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_v_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_i_int
+ \fp_mul_end_level:
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_i_int
+ \fp_mul_end_level:
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_i_int
+ \fp_mul_end_level:
+ #6 0 \l_fp_mul_output_tl \scan_stop:
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_i_int
+ \fp_mul_end_level:
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_i_int
+ \fp_mul_end_level:
+ \fp_mul_end_level:
+ #5 0 \l_fp_mul_output_tl \scan_stop:
+ }
+\cs_new_protected_nopar:Npn \fp_mul:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+ {
+ \fp_mul_split:NNNN #2
+ \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
+ \fp_mul_split:NNNN #3
+ \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
+ \fp_mul_split:NNNN #5
+ \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
+ \fp_mul_split:NNNN #6
+ \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int
+ \l_fp_mul_output_int \c_zero
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_vi_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_v_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_i_int
+ \tex_divide:D \l_fp_mul_output_int \c_one_thousand
+ \fp_mul_product:NN #1 \l_fp_mul_b_vi_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_v_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_vi_int #4
+ \fp_mul_end_level:
+ \fp_mul_product:NN #1 \l_fp_mul_b_v_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_v_int #4
+ \fp_mul_end_level:
+ \fp_mul_product:NN #1 \l_fp_mul_b_iv_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_iv_int #4
+ \fp_mul_end_level:
+ #9 0 \l_fp_mul_output_tl \scan_stop:
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN #1 \l_fp_mul_b_iii_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_iii_int #4
+ \fp_mul_end_level:
+ \fp_mul_product:NN #1 \l_fp_mul_b_ii_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_ii_int #4
+ \fp_mul_end_level:
+ \fp_mul_product:NN #1 \l_fp_mul_b_i_int
+ \fp_mul_product:NN \l_fp_mul_a_i_int #4
+ \fp_mul_end_level:
+ #8 0 \l_fp_mul_output_tl \scan_stop:
+ \tl_clear:N \l_fp_mul_output_tl
+ \fp_mul_product:NN #1 #4
+ \fp_mul_end_level:
+ #7 0 \l_fp_mul_output_tl \scan_stop:
+ }
+\cs_new_protected_nopar:Npn \fp_div_integer:NNNNN #1#2#3#4#5
+ {
+ \l_fp_tmp_int #1
+ \tex_divide:D \l_fp_tmp_int #3
+ \l_fp_tmp_int \int_eval:w #1 - \l_fp_tmp_int * #3 \int_eval_end:
+ #4 #1
+ \tex_divide:D #4 #3
+ #5 #2
+ \tex_divide:D #5 #3
+ \tex_multiply:D \l_fp_tmp_int \c_one_thousand
+ \tex_divide:D \l_fp_tmp_int #3
+ #5 \int_eval:w #5 + \l_fp_tmp_int * \c_one_million \int_eval_end:
+ \if_int_compare:w #5 > \c_one_thousand_million
+ \tex_advance:D #4 \c_one
+ \tex_advance:D #5 -\c_one_thousand_million
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_extended_normalise:
+ {
+ \fp_extended_normalise_aux_i:
+ \fp_extended_normalise_aux_ii:
+ }
+\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_i:
+ {
+ \if_int_compare:w \l_fp_input_a_exponent_int > \c_zero
+ \tex_multiply:D \l_fp_input_a_integer_int \c_ten
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \exp_after:wN \fp_extended_normalise_aux_i:w
+ \int_use:N \l_fp_input_a_decimal_int \q_stop
+ \exp_after:wN \fp_extended_normalise_aux_i:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_i:w
+ #1#2#3#4#5#6#7#8#9 \q_stop
+ {
+ \l_fp_input_a_integer_int
+ \int_eval:w \l_fp_input_a_integer_int + #2 \scan_stop:
+ \l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
+ \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
+ \exp_after:wN \fp_extended_normalise_aux_ii:w
+ \int_use:N \l_fp_input_a_extended_int \q_stop
+ }
+\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_ii:w
+ #1#2#3#4#5#6#7#8#9 \q_stop
+ {
+ \l_fp_input_a_decimal_int
+ \int_eval:w \l_fp_input_a_decimal_int + #2 \scan_stop:
+ \l_fp_input_a_extended_int #3#4#5#6#7#8#9 0 \scan_stop:
+ \tex_advance:D \l_fp_input_a_exponent_int \c_minus_one
+ }
+\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_ii:
+ {
+ \if_int_compare:w \l_fp_input_a_exponent_int < \c_zero
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \exp_after:wN \use_i:nn \exp_after:wN
+ \fp_extended_normalise_ii_aux:NNNNNNNNN
+ \int_use:N \l_fp_input_a_decimal_int
+ \exp_after:wN \fp_extended_normalise_aux_ii:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_extended_normalise_ii_aux:NNNNNNNNN
+ #1#2#3#4#5#6#7#8#9
+ {
+ \if_int_compare:w \l_fp_input_a_integer_int = \c_zero
+ \l_fp_input_a_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
+ \else:
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \int_use:N \l_fp_input_a_integer_int
+ #1#2#3#4#5#6#7#8
+ }
+ \l_fp_input_a_integer_int \c_zero
+ \l_fp_input_a_decimal_int \l_fp_tmp_tl \scan_stop:
+ \fi:
+ \tex_divide:D \l_fp_input_a_extended_int \c_ten
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ #9
+ \int_use:N \l_fp_input_a_extended_int
+ }
+ \l_fp_input_a_extended_int \l_fp_tmp_tl \scan_stop:
+ \tex_advance:D \l_fp_input_a_exponent_int \c_one
+ }
+\cs_new_protected_nopar:Npn \fp_extended_normalise_output:
+ {
+ \if_int_compare:w \l_fp_output_integer_int > \c_nine
+ \tex_advance:D \l_fp_output_integer_int \c_one_thousand_million
+ \exp_after:wN \use_i:nn \exp_after:wN
+ \fp_extended_normalise_output_aux_i:NNNNNNNNN
+ \int_use:N \l_fp_output_integer_int
+ \exp_after:wN \fp_extended_normalise_output:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_extended_normalise_output_aux_i:NNNNNNNNN
+ #1#2#3#4#5#6#7#8#9
+ {
+ \l_fp_output_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
+ \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ #9
+ \exp_after:wN \use_none:n
+ \int_use:N \l_fp_output_decimal_int
+ }
+ \exp_after:wN \fp_extended_normalise_output_aux_ii:NNNNNNNNN
+ \l_fp_tmp_tl
+ }
+\cs_new_protected_nopar:Npn \fp_extended_normalise_output_aux_ii:NNNNNNNNN
+ #1#2#3#4#5#6#7#8#9
+ {
+ \l_fp_output_decimal_int #1#2#3#4#5#6#7#8#9 \scan_stop:
+ \fp_extended_normalise_output_aux:N
+ }
+\cs_new_protected_nopar:Npn \fp_extended_normalise_output_aux:N #1
+ {
+ \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million
+ \tex_divide:D \l_fp_output_extended_int \c_ten
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ #1
+ \exp_after:wN \use_none:n
+ \int_use:N \l_fp_output_extended_int
+ }
+ \l_fp_output_extended_int \l_fp_tmp_tl \scan_stop:
+ \tex_advance:D \l_fp_output_exponent_int \c_one
+ }
+\cs_new_protected_nopar:Npn \fp_trig_normalise:
+ {
+ \if_int_compare:w \l_fp_input_a_exponent_int < \c_ten
+ \l_fp_input_a_extended_int \c_zero
+ \fp_extended_normalise:
+ \fp_trig_normalise_aux:
+ \if_int_compare:w \l_fp_input_a_integer_int < \c_zero
+ \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
+ \fi:
+ \exp_after:wN \fp_trig_octant:
+ \else:
+ \l_fp_input_a_sign_int \c_one
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_exponent_int \c_zero
+ \exp_after:wN \fp_trig_overflow_msg:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_trig_normalise_aux:
+ {
+ \if_int_compare:w \l_fp_input_a_integer_int > \c_three
+ \fp_trig_sub:NNN
+ \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
+ \exp_after:wN \fp_trig_normalise_aux:
+ \else:
+ \if_int_compare:w \l_fp_input_a_integer_int > \c_two
+ \if_int_compare:w \l_fp_input_a_decimal_int > \c_fp_pi_decimal_int
+ \fp_trig_sub:NNN
+ \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \fp_trig_normalise_aux:
+ \fi:
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_trig_sub:NNN #1#2#3
+ {
+ \l_fp_input_a_integer_int
+ \int_eval:w \l_fp_input_a_integer_int - #1 \int_eval_end:
+ \l_fp_input_a_decimal_int
+ \int_eval:w \l_fp_input_a_decimal_int - #2 \int_eval_end:
+ \l_fp_input_a_extended_int
+ \int_eval:w \l_fp_input_a_extended_int - #3 \int_eval_end:
+ \if_int_compare:w \l_fp_input_a_extended_int < \c_zero
+ \tex_advance:D \l_fp_input_a_decimal_int \c_minus_one
+ \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
+ \fi:
+ \if_int_compare:w \l_fp_input_a_decimal_int < \c_zero
+ \tex_advance:D \l_fp_input_a_integer_int \c_minus_one
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \fi:
+ \if_int_compare:w \l_fp_input_a_integer_int < \c_zero
+ \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
+ = \c_zero
+ \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
+ \else:
+ \l_fp_input_a_integer_int
+ \int_eval:w
+ - \l_fp_input_a_integer_int - \c_one
+ \int_eval_end:
+ \l_fp_input_a_decimal_int
+ \int_eval:w
+ \c_one_thousand_million - \l_fp_input_a_decimal_int
+ \int_eval_end:
+ \l_fp_input_a_extended_int
+ \int_eval:w
+ \c_one_thousand_million - \l_fp_input_a_extended_int
+ \int_eval_end:
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_trig_octant:
+ {
+ \l_fp_trig_octant_int \c_one
+ \fp_trig_octant_aux:
+ \if_int_compare:w \l_fp_input_a_decimal_int < \c_ten
+ \l_fp_input_a_decimal_int \c_zero
+ \l_fp_input_a_extended_int \c_zero
+ \fi:
+ \if_int_odd:w \l_fp_trig_octant_int
+ \else:
+ \fp_sub:NNNNNNNNN
+ \c_zero \c_fp_pi_by_four_decimal_int \c_fp_pi_by_four_extended_int
+ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+ \l_fp_input_a_extended_int
+ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+ \l_fp_input_a_extended_int
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_trig_octant_aux:
+ {
+ \if_int_compare:w \l_fp_input_a_integer_int > \c_zero
+ \fp_sub:NNNNNNNNN
+ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+ \l_fp_input_a_extended_int
+ \c_zero \c_fp_pi_by_four_decimal_int \c_fp_pi_by_four_extended_int
+ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+ \l_fp_input_a_extended_int
+ \tex_advance:D \l_fp_trig_octant_int \c_one
+ \exp_after:wN \fp_trig_octant_aux:
+ \else:
+ \if_int_compare:w
+ \l_fp_input_a_decimal_int > \c_fp_pi_by_four_decimal_int
+ \fp_sub:NNNNNNNNN
+ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+ \l_fp_input_a_extended_int
+ \c_zero \c_fp_pi_by_four_decimal_int
+ \c_fp_pi_by_four_extended_int
+ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+ \l_fp_input_a_extended_int
+ \tex_advance:D \l_fp_trig_octant_int \c_one
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \fp_trig_octant_aux:
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_sin:Nn { \fp_sin_aux:NNn \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gsin:Nn { \fp_sin_aux:NNn \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_sin:Nn { c }
+\cs_generate_variant:Nn \fp_gsin:Nn { c }
+\cs_new_protected_nopar:Npn \fp_sin_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \tl_set:Nx \l_fp_arg_tl
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
+ -
+ \else:
+ +
+ \fi:
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_input_a_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ \if_int_compare:w \l_fp_input_a_exponent_int < -\c_five
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2 { \l_fp_arg_tl }
+ }
+ \else:
+ \if_cs_exist:w
+ c_fp_sin ( \l_fp_arg_tl ) _fp
+ \cs_end:
+ \else:
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \fp_sin_aux_i:
+ \fi:
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2
+ { \use:c { c_fp_sin ( \l_fp_arg_tl ) _fp } }
+ }
+ \fi:
+ \fp_tmp:w
+ }
+\cs_new_protected_nopar:Npn \fp_sin_aux_i:
+ {
+ \fp_trig_normalise:
+ \fp_sin_aux_ii:
+ \if_int_compare:w \l_fp_output_integer_int = \c_one
+ \l_fp_output_exponent_int \c_zero
+ \else:
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_decimal_int \l_fp_output_extended_int
+ \l_fp_output_exponent_int -\c_nine
+ \fi:
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_output_integer_int
+ \l_fp_output_decimal_int
+ \l_fp_output_exponent_int
+ \tl_new:c { c_fp_sin ( \l_fp_arg_tl ) _fp }
+ \tl_gset:cx { c_fp_sin ( \l_fp_arg_tl ) _fp }
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
+ +
+ \else:
+ -
+ \fi:
+ \int_use:N \l_fp_output_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+ }
+\cs_new_protected_nopar:Npn \fp_sin_aux_ii:
+ {
+ \if_case:w \l_fp_trig_octant_int
+ \or:
+ \exp_after:wN \fp_trig_calc_sin:
+ \or:
+ \exp_after:wN \fp_trig_calc_cos:
+ \or:
+ \exp_after:wN \fp_trig_calc_cos:
+ \or:
+ \exp_after:wN \fp_trig_calc_sin:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_cos:Nn { \fp_cos_aux:NNn \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gcos:Nn { \fp_cos_aux:NNn \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_cos:Nn { c }
+\cs_generate_variant:Nn \fp_gcos:Nn { c }
+\cs_new_protected_nopar:Npn \fp_cos_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \tl_set:Nx \l_fp_arg_tl
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
+ -
+ \else:
+ +
+ \fi:
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_input_a_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ \if_cs_exist:w c_fp_cos ( \l_fp_arg_tl ) _fp \cs_end:
+ \else:
+ \exp_after:wN \fp_cos_aux_i:
+ \fi:
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2
+ { \use:c { c_fp_cos ( \l_fp_arg_tl ) _fp } }
+ }
+ \fp_tmp:w
+ }
+\cs_new_protected_nopar:Npn \fp_cos_aux_i:
+ {
+ \fp_trig_normalise:
+ \fp_cos_aux_ii:
+ \if_int_compare:w \l_fp_output_integer_int = \c_one
+ \l_fp_output_exponent_int \c_zero
+ \else:
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_decimal_int \l_fp_output_extended_int
+ \l_fp_output_exponent_int -\c_nine
+ \fi:
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_output_integer_int
+ \l_fp_output_decimal_int
+ \l_fp_output_exponent_int
+ \tl_new:c { c_fp_cos ( \l_fp_arg_tl ) _fp }
+ \tl_gset:cx { c_fp_cos ( \l_fp_arg_tl ) _fp }
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
+ +
+ \else:
+ -
+ \fi:
+ \int_use:N \l_fp_output_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+ }
+\cs_new_protected_nopar:Npn \fp_cos_aux_ii:
+ {
+ \if_case:w \l_fp_trig_octant_int
+ \or:
+ \exp_after:wN \fp_trig_calc_cos:
+ \or:
+ \exp_after:wN \fp_trig_calc_sin:
+ \or:
+ \exp_after:wN \fp_trig_calc_sin:
+ \or:
+ \exp_after:wN \fp_trig_calc_cos:
+ \fi:
+ \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
+ \if_int_compare:w \l_fp_trig_octant_int > \c_two
+ \l_fp_input_a_sign_int \c_minus_one
+ \fi:
+ \else:
+ \if_int_compare:w \l_fp_trig_octant_int > \c_two
+ \else:
+ \l_fp_input_a_sign_int \c_one
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_trig_calc_cos:
+ {
+ \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
+ \l_fp_output_integer_int \c_one
+ \l_fp_output_decimal_int \c_zero
+ \else:
+ \l_fp_trig_sign_int \c_minus_one
+ \fp_mul:NNNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_trig_decimal_int \l_fp_trig_extended_int
+ \fp_div_integer:NNNNN
+ \l_fp_trig_decimal_int \l_fp_trig_extended_int
+ \c_two
+ \l_fp_trig_decimal_int \l_fp_trig_extended_int
+ \l_fp_count_int \c_three
+ \if_int_compare:w \l_fp_trig_extended_int = \c_zero
+ \if_int_compare:w \l_fp_trig_decimal_int = \c_zero
+ \l_fp_output_integer_int \c_one
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_extended_int \c_zero
+ \else:
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \c_one_thousand_million
+ \l_fp_output_extended_int \c_zero
+ \fi:
+ \else:
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int 999999999 \scan_stop:
+ \l_fp_output_extended_int \c_one_thousand_million
+ \fi:
+ \tex_advance:D \l_fp_output_extended_int -\l_fp_trig_extended_int
+ \tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int
+ \exp_after:wN \fp_trig_calc_Taylor:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_trig_calc_sin:
+ {
+ \l_fp_output_integer_int \c_zero
+ \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \else:
+ \l_fp_output_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_output_extended_int \l_fp_input_a_extended_int
+ \l_fp_trig_sign_int \c_one
+ \l_fp_trig_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_trig_extended_int \l_fp_input_a_extended_int
+ \l_fp_count_int \c_two
+ \exp_after:wN \fp_trig_calc_Taylor:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_trig_calc_Taylor:
+ {
+ \l_fp_trig_sign_int -\l_fp_trig_sign_int
+ \fp_mul:NNNNNN
+ \l_fp_trig_decimal_int \l_fp_trig_extended_int
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_trig_decimal_int \l_fp_trig_extended_int
+ \fp_mul:NNNNNN
+ \l_fp_trig_decimal_int \l_fp_trig_extended_int
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_trig_decimal_int \l_fp_trig_extended_int
+ \fp_div_integer:NNNNN
+ \l_fp_trig_decimal_int \l_fp_trig_extended_int
+ \l_fp_count_int
+ \l_fp_trig_decimal_int \l_fp_trig_extended_int
+ \tex_advance:D \l_fp_count_int \c_one
+ \fp_div_integer:NNNNN
+ \l_fp_trig_decimal_int \l_fp_trig_extended_int
+ \l_fp_count_int
+ \l_fp_trig_decimal_int \l_fp_trig_extended_int
+ \tex_advance:D \l_fp_count_int \c_one
+ \if_int_compare:w \l_fp_trig_decimal_int > \c_zero
+ \if_int_compare:w \l_fp_trig_sign_int > \c_zero
+ \tex_advance:D \l_fp_output_decimal_int \l_fp_trig_decimal_int
+ \tex_advance:D \l_fp_output_extended_int
+ \l_fp_trig_extended_int
+ \if_int_compare:w \l_fp_output_extended_int < \c_one_thousand_million
+ \else:
+ \tex_advance:D \l_fp_output_decimal_int \c_one
+ \tex_advance:D \l_fp_output_extended_int
+ -\c_one_thousand_million
+ \fi:
+ \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
+ \else:
+ \tex_advance:D \l_fp_output_integer_int \c_one
+ \tex_advance:D \l_fp_output_decimal_int
+ -\c_one_thousand_million
+ \fi:
+ \else:
+ \tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int
+ \tex_advance:D \l_fp_output_extended_int
+ -\l_fp_input_a_extended_int
+ \if_int_compare:w \l_fp_output_extended_int < \c_zero
+ \tex_advance:D \l_fp_output_decimal_int \c_minus_one
+ \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million
+ \fi:
+ \if_int_compare:w \l_fp_output_decimal_int < \c_zero
+ \tex_advance:D \l_fp_output_integer_int \c_minus_one
+ \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+ \fi:
+ \fi:
+ \exp_after:wN \fp_trig_calc_Taylor:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_tan:Nn { \fp_tan_aux:NNn \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gtan:Nn { \fp_tan_aux:NNn \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_tan:Nn { c }
+\cs_generate_variant:Nn \fp_gtan:Nn { c }
+\cs_new_protected_nopar:Npn \fp_tan_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \tl_set:Nx \l_fp_arg_tl
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
+ -
+ \else:
+ +
+ \fi:
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_input_a_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ \if_int_compare:w \l_fp_input_a_exponent_int < -\c_five
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2 { \l_fp_arg_tl }
+ }
+ \else:
+ \if_cs_exist:w
+ c_fp_tan ( \l_fp_arg_tl ) _fp
+ \cs_end:
+ \else:
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \fp_tan_aux_i:
+ \fi:
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2
+ { \use:c { c_fp_tan ( \l_fp_arg_tl ) _fp } }
+ }
+ \fi:
+ \fp_tmp:w
+ }
+\cs_new_protected_nopar:Npn \fp_tan_aux_i:
+ {
+ \if_int_compare:w \l_fp_input_a_exponent_int < \c_ten
+ \exp_after:wN \fp_tan_aux_ii:
+ \else:
+ \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
+ \c_zero_fp
+ \exp_after:wN \fp_trig_overflow_msg:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_tan_aux_ii:
+ {
+ \fp_trig_normalise:
+ \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
+ \if_int_compare:w \l_fp_trig_octant_int > \c_two
+ \l_fp_output_sign_int \c_minus_one
+ \else:
+ \l_fp_output_sign_int \c_one
+ \fi:
+ \else:
+ \if_int_compare:w \l_fp_trig_octant_int > \c_two
+ \l_fp_output_sign_int \c_one
+ \else:
+ \l_fp_output_sign_int \c_minus_one
+ \fi:
+ \fi:
+ \fp_cos_aux_ii:
+ \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
+ \if_int_compare:w \l_fp_input_a_integer_int = \c_zero
+ \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
+ \c_undefined_fp
+ \else:
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \fp_tan_aux_iii:
+ \fi:
+ \else:
+ \exp_after:wN \fp_tan_aux_iii:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_tan_aux_iii:
+ {
+ \l_fp_input_b_integer_int \l_fp_output_decimal_int
+ \l_fp_input_b_decimal_int \l_fp_output_extended_int
+ \l_fp_input_b_exponent_int -\c_nine
+ \fp_standardise:NNNN
+ \l_fp_input_b_sign_int
+ \l_fp_input_b_integer_int
+ \l_fp_input_b_decimal_int
+ \l_fp_input_b_exponent_int
+ \fp_sin_aux_ii:
+ \l_fp_input_a_integer_int \l_fp_output_decimal_int
+ \l_fp_input_a_decimal_int \l_fp_output_extended_int
+ \l_fp_input_a_exponent_int -\c_nine
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
+ \if_int_compare:w \l_fp_input_a_integer_int = \c_zero
+ \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
+ \c_zero_fp
+ \else:
+ \exp_after:wN \exp_after:wN \exp_after:wN \fp_tan_aux_iv:
+ \fi:
+ \else:
+ \exp_after:wN \fp_tan_aux_iv:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_tan_aux_iv:
+ {
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
+ \l_fp_div_offset_int \c_one_hundred_million
+ \fp_div_loop:
+ \l_fp_output_exponent_int
+ \int_eval:w
+ \l_fp_input_a_exponent_int - \l_fp_input_b_exponent_int
+ \int_eval_end:
+ \fp_standardise:NNNN
+ \l_fp_output_sign_int
+ \l_fp_output_integer_int
+ \l_fp_output_decimal_int
+ \l_fp_output_exponent_int
+ \tl_new:c { c_fp_tan ( \l_fp_arg_tl ) _fp }
+ \tl_gset:cx { c_fp_tan ( \l_fp_arg_tl ) _fp }
+ {
+ \if_int_compare:w \l_fp_output_sign_int > \c_zero
+ +
+ \else:
+ -
+ \fi:
+ \int_use:N \l_fp_output_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+ }
+\tl_const:cn { c_fp_exp_1_tl } { { 2 } { 718281828 } { 459045235 } { 0 } }
+\tl_const:cn { c_fp_exp_2_tl } { { 7 } { 389056098 } { 930650227 } { 0 } }
+\tl_const:cn { c_fp_exp_3_tl } { { 2 } { 008553692 } { 318766774 } { 1 } }
+\tl_const:cn { c_fp_exp_4_tl } { { 5 } { 459815003 } { 314423908 } { 1 } }
+\tl_const:cn { c_fp_exp_5_tl } { { 1 } { 484131591 } { 025766034 } { 2 } }
+\tl_const:cn { c_fp_exp_6_tl } { { 4 } { 034287934 } { 927351226 } { 2 } }
+\tl_const:cn { c_fp_exp_7_tl } { { 1 } { 096633158 } { 428458599 } { 3 } }
+\tl_const:cn { c_fp_exp_8_tl } { { 2 } { 980957987 } { 041728275 } { 3 } }
+\tl_const:cn { c_fp_exp_9_tl } { { 8 } { 103083927 } { 575384008 } { 3 } }
+\tl_const:cn { c_fp_exp_10_tl } { { 2 } { 202646579 } { 480671652 } { 4 } }
+\tl_const:cn { c_fp_exp_20_tl } { { 4 } { 851651954 } { 097902280 } { 8 } }
+\tl_const:cn { c_fp_exp_30_tl } { { 1 } { 068647458 } { 152446215 } { 13 } }
+\tl_const:cn { c_fp_exp_40_tl } { { 2 } { 353852668 } { 370199854 } { 17 } }
+\tl_const:cn { c_fp_exp_50_tl } { { 5 } { 184705528 } { 587072464 } { 21 } }
+\tl_const:cn { c_fp_exp_60_tl } { { 1 } { 142007389 } { 815684284 } { 26 } }
+\tl_const:cn { c_fp_exp_70_tl } { { 2 } { 515438670 } { 919167006 } { 30 } }
+\tl_const:cn { c_fp_exp_80_tl } { { 5 } { 540622384 } { 393510053 } { 34 } }
+\tl_const:cn { c_fp_exp_90_tl } { { 1 } { 220403294 } { 317840802 } { 39 } }
+\tl_const:cn { c_fp_exp_100_tl } { { 2 } { 688117141 } { 816135448 } { 43 } }
+\tl_const:cn { c_fp_exp_200_tl } { { 7 } { 225973768 } { 125749258 } { 86 } }
+\tl_const:cn { c_fp_exp_-1_tl } { { 3 } { 678794411 } { 71442322 } { -1 } }
+\tl_const:cn { c_fp_exp_-2_tl } { { 1 } { 353352832 } { 366132692 } { -1 } }
+\tl_const:cn { c_fp_exp_-3_tl } { { 4 } { 978706836 } { 786394298 } { -2 } }
+\tl_const:cn { c_fp_exp_-4_tl } { { 1 } { 831563888 } { 873418029 } { -2 } }
+\tl_const:cn { c_fp_exp_-5_tl } { { 6 } { 737946999 } { 085467097 } { -3 } }
+\tl_const:cn { c_fp_exp_-6_tl } { { 2 } { 478752176 } { 666358423 } { -3 } }
+\tl_const:cn { c_fp_exp_-7_tl } { { 9 } { 118819655 } { 545162080 } { -4 } }
+\tl_const:cn { c_fp_exp_-8_tl } { { 3 } { 354626279 } { 025118388 } { -4 } }
+\tl_const:cn { c_fp_exp_-9_tl } { { 1 } { 234098040 } { 866795495 } { -4 } }
+\tl_const:cn { c_fp_exp_-10_tl } { { 4 } { 539992976 } { 248451536 } { -5 } }
+\tl_const:cn { c_fp_exp_-20_tl } { { 2 } { 061153622 } { 438557828 } { -9 } }
+\tl_const:cn { c_fp_exp_-30_tl } { { 9 } { 357622968 } { 840174605 } { -14 } }
+\tl_const:cn { c_fp_exp_-40_tl } { { 4 } { 248354255 } { 291588995 } { -18 } }
+\tl_const:cn { c_fp_exp_-50_tl } { { 1 } { 928749847 } { 963917783 } { -22 } }
+\tl_const:cn { c_fp_exp_-60_tl } { { 8 } { 756510762 } { 696520338 } { -27 } }
+\tl_const:cn { c_fp_exp_-70_tl } { { 3 } { 975449735 } { 908646808 } { -31 } }
+\tl_const:cn { c_fp_exp_-80_tl } { { 1 } { 804851387 } { 845415172 } { -35 } }
+\tl_const:cn { c_fp_exp_-90_tl } { { 8 } { 194012623 } { 990515430 } { -40 } }
+\tl_const:cn { c_fp_exp_-100_tl } { { 3 } { 720075976 } { 020835963 } { -44 } }
+\tl_const:cn { c_fp_exp_-200_tl } { { 1 } { 383896526 } { 736737530 } { -87 } }
+\cs_new_protected_nopar:Npn \fp_exp:Nn { \fp_exp_aux:NNn \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gexp:Nn { \fp_exp_aux:NNn \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_exp:Nn { c }
+\cs_generate_variant:Nn \fp_gexp:Nn { c }
+\cs_new_protected_nopar:Npn \fp_exp_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \l_fp_input_a_extended_int \c_zero
+ \tl_set:Nx \l_fp_arg_tl
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
+ -
+ \else:
+ +
+ \fi:
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_input_a_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ \if_cs_exist:w c_fp_exp ( \l_fp_arg_tl ) _fp \cs_end:
+ \else:
+ \exp_after:wN \fp_exp_internal:
+ \fi:
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ #1 \exp_not:N #2
+ {
+ \if_cs_exist:w c_fp_exp ( \l_fp_arg_tl ) _fp
+ \cs_end:
+ \use:c { c_fp_exp ( \l_fp_arg_tl ) _fp }
+ \else:
+ \c_zero_fp
+ \fi:
+ }
+ }
+ \fp_tmp:w
+ }
+\cs_new_protected_nopar:Npn \fp_exp_internal:
+ {
+ \if_int_compare:w \l_fp_input_a_exponent_int < \c_three
+ \fp_extended_normalise:
+ \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
+ \if_int_compare:w \l_fp_input_a_integer_int < 230 \scan_stop:
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \fp_exp_aux:
+ \else:
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \fp_exp_overflow_msg:
+ \fi:
+ \else:
+ \if_int_compare:w \l_fp_input_a_integer_int < 230 \scan_stop:
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \fp_exp_aux:
+ \else:
+ \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+ { \c_zero_fp }
+ \fi:
+ \fi:
+ \else:
+ \exp_after:wN \fp_exp_overflow_msg:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_exp_aux:
+ {
+ \if_int_compare:w \l_fp_input_a_integer_int > \c_zero
+ \exp_after:wN \fp_exp_integer:
+ \else:
+ \l_fp_output_integer_int \c_one
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_extended_int \c_zero
+ \l_fp_output_exponent_int \c_zero
+ \exp_after:wN \fp_exp_decimal:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_exp_integer:
+ {
+ \if_int_compare:w \l_fp_input_a_integer_int < \c_one_hundred
+ \l_fp_exp_integer_int \c_one
+ \l_fp_exp_decimal_int \c_zero
+ \l_fp_exp_extended_int \c_zero
+ \l_fp_exp_exponent_int \c_zero
+ \exp_after:wN \fp_exp_integer_tens:
+ \else:
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \exp_after:wN \use_i:nnn
+ \int_use:N \l_fp_input_a_integer_int
+ }
+ \l_fp_input_a_integer_int
+ \int_eval:w
+ \l_fp_input_a_integer_int - \l_fp_tmp_tl 00
+ \int_eval_end:
+ \if_int_compare:w \l_fp_input_a_sign_int < \c_zero
+ \if_int_compare:w \l_fp_output_integer_int > 200 \scan_stop:
+ \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+ { \c_zero_fp }
+ \else:
+ \fp_exp_integer_const:n { - \l_fp_tmp_tl 00 }
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \fp_exp_integer_tens:
+ \fi:
+ \else:
+ \fp_exp_integer_const:n { \l_fp_tmp_tl 00 }
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \fp_exp_integer_tens:
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_exp_integer_tens:
+ {
+ \l_fp_output_integer_int \l_fp_exp_integer_int
+ \l_fp_output_decimal_int \l_fp_exp_decimal_int
+ \l_fp_output_extended_int \l_fp_exp_extended_int
+ \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ \if_int_compare:w \l_fp_input_a_integer_int > \c_nine
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \exp_after:wN \use_i:nn
+ \int_use:N \l_fp_input_a_integer_int
+ }
+ \l_fp_input_a_integer_int
+ \int_eval:w
+ \l_fp_input_a_integer_int - \l_fp_tmp_tl 0
+ \int_eval_end:
+ \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
+ \fp_exp_integer_const:n { \l_fp_tmp_tl 0 }
+ \else:
+ \fp_exp_integer_const:n { - \l_fp_tmp_tl 0 }
+ \fi:
+ \fp_mul:NNNNNNNNN
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ \fp_extended_normalise_output:
+ \fi:
+ \fp_exp_integer_units:
+ }
+\cs_new_protected_nopar:Npn \fp_exp_integer_units:
+ {
+ \if_int_compare:w \l_fp_input_a_integer_int > \c_zero
+ \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
+ \fp_exp_integer_const:n { \int_use:N \l_fp_input_a_integer_int }
+ \else:
+ \fp_exp_integer_const:n
+ { - \int_use:N \l_fp_input_a_integer_int }
+ \fi:
+ \fp_mul:NNNNNNNNN
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ \fp_extended_normalise_output:
+ \fi:
+ \fp_exp_decimal:
+ }
+\cs_new_protected_nopar:Npn \fp_exp_integer_const:n #1
+ {
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \fp_exp_integer_const:nnnn
+ \cs:w c_fp_exp_ #1 _tl \cs_end:
+ }
+\cs_new_protected_nopar:Npn \fp_exp_integer_const:nnnn #1#2#3#4
+ {
+ \l_fp_exp_integer_int #1 \scan_stop:
+ \l_fp_exp_decimal_int #2 \scan_stop:
+ \l_fp_exp_extended_int #3 \scan_stop:
+ \l_fp_exp_exponent_int #4 \scan_stop:
+ }
+\cs_new_protected_nopar:Npn \fp_exp_decimal:
+ {
+ \if_int_compare:w \l_fp_input_a_decimal_int > \c_zero
+ \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
+ \l_fp_exp_integer_int \c_one
+ \l_fp_exp_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_exp_extended_int \l_fp_input_a_extended_int
+ \else:
+ \l_fp_exp_integer_int \c_zero
+ \if_int_compare:w \l_fp_exp_extended_int = \c_zero
+ \l_fp_exp_decimal_int
+ \int_eval:w
+ \c_one_thousand_million - \l_fp_input_a_decimal_int
+ \int_eval_end:
+ \l_fp_exp_extended_int \c_zero
+ \else:
+ \l_fp_exp_decimal_int
+ \int_eval:w
+ 999999999 - \l_fp_input_a_decimal_int
+ \scan_stop:
+ \l_fp_exp_extended_int
+ \int_eval:w
+ \c_one_thousand_million - \l_fp_input_a_extended_int
+ \int_eval_end:
+ \fi:
+ \fi:
+ \l_fp_input_b_sign_int \l_fp_input_a_sign_int
+ \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_input_b_extended_int \l_fp_input_a_extended_int
+ \l_fp_count_int \c_one
+ \fp_exp_Taylor:
+ \fp_mul:NNNNNNNNN
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \fi:
+ \if_int_compare:w \l_fp_output_extended_int < \c_five_hundred_million
+ \else:
+ \tex_advance:D \l_fp_output_decimal_int \c_one
+ \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
+ \else:
+ \l_fp_output_decimal_int \c_zero
+ \tex_advance:D \l_fp_output_integer_int \c_one
+ \fi:
+ \fi:
+ \fp_standardise:NNNN
+ \l_fp_output_sign_int
+ \l_fp_output_integer_int
+ \l_fp_output_decimal_int
+ \l_fp_output_exponent_int
+ \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+ {
+ +
+ \int_use:N \l_fp_output_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+ }
+\cs_new_protected_nopar:Npn \fp_exp_Taylor:
+ {
+ \tex_advance:D \l_fp_count_int \c_one
+ \tex_multiply:D \l_fp_input_b_sign_int \l_fp_input_a_sign_int
+ \fp_mul:NNNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \fp_div_integer:NNNNN
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \l_fp_count_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_b_decimal_int + \l_fp_input_b_extended_int
+ > \c_zero
+ \if_int_compare:w \l_fp_input_b_sign_int > \c_zero
+ \tex_advance:D \l_fp_exp_decimal_int \l_fp_input_b_decimal_int
+ \tex_advance:D \l_fp_exp_extended_int
+ \l_fp_input_b_extended_int
+ \if_int_compare:w \l_fp_exp_extended_int < \c_one_thousand_million
+ \else:
+ \tex_advance:D \l_fp_exp_decimal_int \c_one
+ \tex_advance:D \l_fp_exp_extended_int
+ -\c_one_thousand_million
+ \fi:
+ \if_int_compare:w \l_fp_exp_decimal_int < \c_one_thousand_million
+ \else:
+ \tex_advance:D \l_fp_exp_integer_int \c_one
+ \tex_advance:D \l_fp_exp_decimal_int
+ -\c_one_thousand_million
+ \fi:
+ \else:
+ \tex_advance:D \l_fp_exp_decimal_int -\l_fp_input_b_decimal_int
+ \tex_advance:D \l_fp_exp_extended_int
+ -\l_fp_input_a_extended_int
+ \if_int_compare:w \l_fp_exp_extended_int < \c_zero
+ \tex_advance:D \l_fp_exp_decimal_int \c_minus_one
+ \tex_advance:D \l_fp_exp_extended_int \c_one_thousand_million
+ \fi:
+ \if_int_compare:w \l_fp_exp_decimal_int < \c_zero
+ \tex_advance:D \l_fp_exp_integer_int \c_minus_one
+ \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
+ \fi:
+ \fi:
+ \exp_after:wN \fp_exp_Taylor:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_exp_const:Nx #1#2
+ {
+ \tl_new:N #1
+ \tl_gset:Nx #1 {#2}
+ }
+\cs_generate_variant:Nn \fp_exp_const:Nx { c }
+\tl_const:cn { c_fp_ln_10_1_tl } { { 2 } { 302585092 } { 994045684 } { 0 } }
+\tl_const:cn { c_fp_ln_10_2_tl } { { 4 } { 605170185 } { 988091368 } { 0 } }
+\tl_const:cn { c_fp_ln_10_3_tl } { { 6 } { 907755278 } { 982137052 } { 0 } }
+\tl_const:cn { c_fp_ln_10_4_tl } { { 9 } { 210340371 } { 976182736 } { 0 } }
+\tl_const:cn { c_fp_ln_10_5_tl } { { 1 } { 151292546 } { 497022842 } { 1 } }
+\tl_const:cn { c_fp_ln_10_6_tl } { { 1 } { 381551055 } { 796427410 } { 1 } }
+\tl_const:cn { c_fp_ln_10_7_tl } { { 1 } { 611809565 } { 095831979 } { 1 } }
+\tl_const:cn { c_fp_ln_10_8_tl } { { 1 } { 842068074 } { 395226547 } { 1 } }
+\tl_const:cn { c_fp_ln_10_9_tl } { { 2 } { 072326583 } { 694641116 } { 1 } }
+\tl_const:cn { c_fp_ln_2_1_tl } { { 0 } { 693147180 } { 559945309 } { 0 } }
+\tl_const:cn { c_fp_ln_2_2_tl } { { 1 } { 386294361 } { 119890618 } { 0 } }
+\tl_const:cn { c_fp_ln_2_3_tl } { { 2 } { 079441541 } { 679835928 } { 0 } }
+\cs_new_protected_nopar:Npn \fp_ln:Nn { \fp_ln_aux:NNn \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gln:Nn { \fp_ln_aux:NNn \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_ln:Nn { c }
+\cs_generate_variant:Nn \fp_gln:Nn { c }
+\cs_new_protected_nopar:Npn \fp_ln_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+ > \c_zero
+ \exp_after:wN \exp_after:wN \exp_after:wN \fp_ln_aux:
+ \else:
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 \exp_not:N ##2 { \c_zero_fp }
+ }
+ \exp_after:wN \exp_after:wN \exp_after:wN \fp_ln_error_msg:
+ \fi:
+ \else:
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 \exp_not:N ##2 { \c_zero_fp }
+ }
+ \exp_after:wN \fp_ln_error_msg:
+ \fi:
+ \fp_tmp:w #1 #2
+ }
+\cs_new_protected_nopar:Npn \fp_ln_aux:
+ {
+ \tl_set:Nx \l_fp_arg_tl
+ {
+ +
+ \int_use:N \l_fp_input_a_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_input_a_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_input_a_exponent_int
+ }
+ \if_cs_exist:w c_fp_ln ( \l_fp_arg_tl ) _fp \cs_end:
+ \else:
+ \exp_after:wN \fp_ln_exponent:
+ \fi:
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 \exp_not:N ##2
+ { \use:c { c_fp_ln ( \l_fp_arg_tl ) _fp } }
+ }
+ }
+\cs_new_protected_nopar:Npn \fp_ln_exponent:
+ {
+ \fp_ln_internal:
+ \if_int_compare:w \l_fp_output_extended_int < \c_five_hundred_million
+ \else:
+ \tex_advance:D \l_fp_output_decimal_int \c_one
+ \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
+ \else:
+ \l_fp_output_decimal_int \c_zero
+ \tex_advance:D \l_fp_output_integer_int \c_one
+ \fi:
+ \fi:
+ \fp_standardise:NNNN
+ \l_fp_output_sign_int
+ \l_fp_output_integer_int
+ \l_fp_output_decimal_int
+ \l_fp_output_exponent_int
+ \tl_const:cx { c_fp_ln ( \l_fp_arg_tl ) _fp }
+ {
+ \if_int_compare:w \l_fp_output_sign_int > \c_zero
+ +
+ \else:
+ -
+ \fi:
+ \int_use:N \l_fp_output_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ \scan_stop:
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+ }
+\cs_new_protected_nopar:Npn \fp_ln_internal:
+ {
+ \if_int_compare:w \l_fp_input_a_exponent_int < \c_zero
+ \l_fp_input_a_exponent_int -\l_fp_input_a_exponent_int
+ \l_fp_output_sign_int \c_minus_one
+ \else:
+ \l_fp_output_sign_int \c_one
+ \fi:
+ \if_int_compare:w \l_fp_input_a_exponent_int > \c_nine
+ \exp_after:wN \fp_ln_exponent_tens:NN
+ \int_use:N \l_fp_input_a_exponent_int
+ \else:
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_extended_int \c_zero
+ \l_fp_output_exponent_int \c_zero
+ \fi:
+ \fp_ln_exponent_units:
+ }
+\cs_new_protected_nopar:Npn \fp_ln_exponent_tens:NN #1 #2
+ {
+ \l_fp_input_a_exponent_int #2 \scan_stop:
+ \fp_ln_const:nn { 10 } { #1 }
+ \tex_advance:D \l_fp_exp_exponent_int \c_one
+ \l_fp_output_integer_int \l_fp_exp_integer_int
+ \l_fp_output_decimal_int \l_fp_exp_decimal_int
+ \l_fp_output_extended_int \l_fp_exp_extended_int
+ \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ }
+\cs_new_protected_nopar:Npn \fp_ln_exponent_units:
+ {
+ \if_int_compare:w \l_fp_input_a_exponent_int > \c_zero
+ \fp_ln_const:nn { 10 } { \int_use:N \l_fp_input_a_exponent_int }
+ \fp_ln_normalise:
+ \fp_add:NNNNNNNNN
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \fi:
+ \fp_ln_mantissa:
+ }
+\cs_new_protected_nopar:Npn \fp_ln_normalise:
+ {
+ \if_int_compare:w \l_fp_exp_exponent_int < \l_fp_output_exponent_int
+ \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
+ \exp_after:wN \use_i:nn \exp_after:wN
+ \fp_ln_normalise_aux:NNNNNNNNN
+ \int_use:N \l_fp_exp_decimal_int
+ \exp_after:wN \fp_ln_normalise:
+ \else:
+ \l_fp_output_exponent_int \l_fp_exp_exponent_int
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_ln_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+ {
+ \if_int_compare:w \l_fp_exp_integer_int = \c_zero
+ \l_fp_exp_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
+ \else:
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \int_use:N \l_fp_exp_integer_int
+ #1#2#3#4#5#6#7#8
+ }
+ \l_fp_exp_integer_int \c_zero
+ \l_fp_exp_decimal_int \l_fp_tmp_tl \scan_stop:
+ \fi:
+ \tex_divide:D \l_fp_exp_extended_int \c_ten
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ #9
+ \int_use:N \l_fp_exp_extended_int
+ }
+ \l_fp_exp_extended_int \l_fp_tmp_tl \scan_stop:
+ \tex_advance:D \l_fp_exp_exponent_int \c_one
+ }
+\cs_new_protected_nopar:Npn \fp_ln_mantissa:
+ {
+ \l_fp_count_int \c_zero
+ \l_fp_input_a_extended_int \c_zero
+ \fp_ln_mantissa_aux:
+ \if_int_compare:w \l_fp_count_int > \c_zero
+ \fp_ln_const:nn { 2 } { \int_use:N \l_fp_count_int }
+ \fp_ln_normalise:
+ \if_int_compare:w \l_fp_output_sign_int > \c_zero
+ \exp_after:wN \fp_add:NNNNNNNNN
+ \else:
+ \exp_after:wN \fp_sub:NNNNNNNNN
+ \fi:
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \fi:
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int > \c_one
+ \exp_after:wN \fp_ln_Taylor:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_ln_mantissa_aux:
+ {
+ \if_int_compare:w \l_fp_input_a_integer_int > \c_one
+ \tex_advance:D \l_fp_count_int \c_one
+ \fp_ln_mantissa_divide_two:
+ \exp_after:wN \fp_ln_mantissa_aux:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_ln_mantissa_divide_two:
+ {
+ \if_int_odd:w \l_fp_input_a_decimal_int
+ \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
+ \fi:
+ \if_int_odd:w \l_fp_input_a_integer_int
+ \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+ \fi:
+ \tex_divide:D \l_fp_input_a_integer_int \c_two
+ \tex_divide:D \l_fp_input_a_decimal_int \c_two
+ \tex_divide:D \l_fp_input_a_extended_int \c_two
+ }
+\cs_new_protected_nopar:Npn \fp_ln_const:nn #1#2
+ {
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \fp_exp_integer_const:nnnn
+ \cs:w c_fp_ln_ #1 _ #2 _tl \cs_end:
+ }
+\cs_new_protected_nopar:Npn \fp_ln_Taylor:
+ {
+ \group_begin:
+ \l_fp_input_a_integer_int \c_zero
+ \l_fp_input_a_exponent_int \c_zero
+ \l_fp_input_b_integer_int \c_two
+ \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_input_b_exponent_int \c_zero
+ \fp_div_internal:
+ \fp_ln_fixed:
+ \l_fp_input_a_integer_int \l_fp_output_integer_int
+ \l_fp_input_a_decimal_int \l_fp_output_decimal_int
+ \l_fp_input_a_extended_int \c_zero
+ \l_fp_input_a_exponent_int \l_fp_output_exponent_int
+ \l_fp_output_decimal_int \c_zero %^^A Bug?
+ \l_fp_output_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_output_extended_int \l_fp_input_a_extended_int
+ \fp_mul:NNNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \l_fp_count_int \c_one
+ \fp_ln_Taylor_aux:
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ \l_fp_exp_integer_int \c_zero
+ \exp_not:N \l_fp_exp_decimal_int
+ \int_use:N \l_fp_output_decimal_int \scan_stop:
+ \exp_not:N \l_fp_exp_extended_int
+ \int_use:N \l_fp_output_extended_int \scan_stop:
+ \exp_not:N \l_fp_exp_exponent_int
+ \int_use:N \l_fp_output_exponent_int \scan_stop:
+ }
+ \fp_tmp:w
+ \tex_advance:D \l_fp_exp_decimal_int \l_fp_exp_decimal_int
+ \if_int_compare:w \l_fp_exp_extended_int < \c_five_hundred_million
+ \else:
+ \tex_advance:D \l_fp_exp_extended_int -\c_five_hundred_million
+ \tex_advance:D \l_fp_exp_decimal_int \c_one
+ \fi:
+ \tex_advance:D \l_fp_exp_extended_int \l_fp_exp_extended_int
+ \fp_ln_normalise:
+ \if_int_compare:w \l_fp_output_sign_int > \c_zero
+ \exp_after:wN \fp_add:NNNNNNNNN
+ \else:
+ \exp_after:wN \fp_sub:NNNNNNNNN
+ \fi:
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \c_zero \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ }
+\cs_new_protected_nopar:Npn \fp_ln_fixed:
+ {
+ \if_int_compare:w \l_fp_output_exponent_int < \c_zero
+ \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+ \exp_after:wN \use_i:nn \exp_after:wN
+ \fp_ln_fixed_aux:NNNNNNNNN
+ \int_use:N \l_fp_output_decimal_int
+ \exp_after:wN \fp_ln_fixed:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_ln_fixed_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9
+ {
+ \if_int_compare:w \l_fp_output_integer_int = \c_zero
+ \l_fp_output_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
+ \else:
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \int_use:N \l_fp_output_integer_int
+ #1#2#3#4#5#6#7#8
+ }
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \l_fp_tmp_tl \scan_stop:
+ \fi:
+ \tex_advance:D \l_fp_output_exponent_int \c_one
+ }
+\cs_new_protected_nopar:Npn \fp_ln_Taylor_aux:
+ {
+ \tex_advance:D \l_fp_count_int \c_two
+ \fp_mul:NNNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
+ > \c_zero
+ \fp_div_integer:NNNNN
+ \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+ \l_fp_count_int
+ \l_fp_exp_decimal_int \l_fp_exp_extended_int
+ \tex_advance:D \l_fp_output_decimal_int \l_fp_exp_decimal_int
+ \tex_advance:D \l_fp_output_extended_int \l_fp_exp_extended_int
+ \if_int_compare:w \l_fp_output_extended_int < \c_one_thousand_million
+ \else:
+ \tex_advance:D \l_fp_output_decimal_int \c_one
+ \tex_advance:D \l_fp_output_extended_int
+ -\c_one_thousand_million
+ \fi:
+ \if_int_compare:w \l_fp_output_decimal_int < \c_one_thousand_million
+ \else:
+ \tex_advance:D \l_fp_output_integer_int \c_one
+ \tex_advance:D \l_fp_output_decimal_int
+ -\c_one_thousand_million
+ \fi:
+ \exp_after:wN \fp_ln_Taylor_aux:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_pow:Nn { \fp_pow_aux:NNn \tl_set:Nn }
+\cs_new_protected_nopar:Npn \fp_gpow:Nn { \fp_pow_aux:NNn \tl_gset:Nn }
+\cs_generate_variant:Nn \fp_pow:Nn { c }
+\cs_generate_variant:Nn \fp_gpow:Nn { c }
+\cs_new_protected_nopar:Npn \fp_pow_aux:NNn #1#2#3
+ {
+ \group_begin:
+ \fp_read:N #2
+ \l_fp_input_b_sign_int \l_fp_input_a_sign_int
+ \l_fp_input_b_integer_int \l_fp_input_a_integer_int
+ \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int
+ \fp_split:Nn a {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+ = \c_zero
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+ = \c_zero
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_undefined_fp }
+ }
+ \else:
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_zero_fp }
+ }
+ \fi:
+ \else:
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+ = \c_zero
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_one_fp }
+ }
+ \else:
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \fp_pow_aux_i:
+ \fi:
+ \fi:
+ \fp_tmp:w #1 #2
+}
+\cs_new_protected_nopar:Npn \fp_pow_aux_i:
+ {
+ \if_int_compare:w \l_fp_input_b_sign_int > \c_zero
+ \tl_set:Nn \l_fp_sign_tl { + }
+ \exp_after:wN \fp_pow_aux_ii:
+ \else:
+ \l_fp_input_a_extended_int \c_zero
+ \if_int_compare:w \l_fp_input_a_exponent_int < \c_ten
+ \group_begin:
+ \fp_extended_normalise:
+ \if_int_compare:w
+ \int_eval:w
+ \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
+ = \c_zero
+ \group_end:
+ \tl_set:Nn \l_fp_sign_tl { - }
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \fp_pow_aux_ii:
+ \else:
+ \group_end:
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_undefined_fp }
+ }
+ \fi:
+ \else:
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2 { \c_undefined_fp }
+ }
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:Npn \fp_pow_aux_ii:
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
+ \exp_after:wN \fp_pow_aux_iv:
+ \else:
+ \if_int_compare:w \l_fp_input_a_exponent_int < \c_ten
+ \group_begin:
+ \l_fp_input_a_extended_int \c_zero
+ \fp_extended_normalise:
+ \if_int_compare:w \l_fp_input_a_decimal_int = \c_zero
+ \if_int_compare:w \l_fp_input_a_integer_int > \c_ten
+ \group_end:
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \fp_pow_aux_iv:
+ \else:
+ \group_end:
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \fp_pow_aux_iii:
+ \fi:
+ \else:
+ \group_end:
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \exp_after:wN \fp_pow_aux_iv:
+ \fi:
+ \else:
+ \exp_after:wN \exp_after:wN \exp_after:wN
+ \fp_pow_aux_iv:
+ \fi:
+ \fi:
+ \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+ {
+ \group_end:
+ ##1 ##2
+ {
+ \l_fp_sign_tl
+ \int_use:N \l_fp_output_integer_int
+ .
+ \exp_after:wN \use_none:n
+ \int_value:w \int_eval:w
+ \l_fp_output_decimal_int + \c_one_thousand_million
+ e
+ \int_use:N \l_fp_output_exponent_int
+ }
+ }
+ }
+\cs_new_protected_nopar:Npn \fp_pow_aux_iii:
+ {
+ \l_fp_input_a_sign_int \c_one
+ \fp_pow_aux_iv:
+ \l_fp_input_a_integer_int \c_one
+ \l_fp_input_a_decimal_int \c_zero
+ \l_fp_input_a_exponent_int \c_zero
+ \l_fp_input_b_integer_int \l_fp_output_integer_int
+ \l_fp_input_b_decimal_int \l_fp_output_decimal_int
+ \l_fp_input_b_exponent_int \l_fp_output_exponent_int
+ \fp_div_internal:
+ }
+\cs_new_protected_nopar:Npn \fp_pow_aux_iv:
+ {
+ \group_begin:
+ \l_fp_input_a_integer_int \l_fp_input_b_integer_int
+ \l_fp_input_a_decimal_int \l_fp_input_b_decimal_int
+ \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int
+ \fp_ln_internal:
+ \cs_set_protected_nopar:Npx \fp_tmp:w
+ {
+ \group_end:
+ \exp_not:N \l_fp_input_b_sign_int
+ \int_use:N \l_fp_output_sign_int \scan_stop:
+ \exp_not:N \l_fp_input_b_integer_int
+ \int_use:N \l_fp_output_integer_int \scan_stop:
+ \exp_not:N \l_fp_input_b_decimal_int
+ \int_use:N \l_fp_output_decimal_int \scan_stop:
+ \exp_not:N \l_fp_input_b_extended_int
+ \int_use:N \l_fp_output_extended_int \scan_stop:
+ \exp_not:N \l_fp_input_b_exponent_int
+ \int_use:N \l_fp_output_exponent_int \scan_stop:
+ }
+ \fp_tmp:w
+ \l_fp_input_a_extended_int \c_zero
+ \fp_mul:NNNNNNNNN
+ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+ \l_fp_input_a_extended_int
+ \l_fp_input_b_integer_int \l_fp_input_b_decimal_int
+ \l_fp_input_b_extended_int
+ \l_fp_output_integer_int \l_fp_output_decimal_int
+ \l_fp_output_extended_int
+ \l_fp_output_exponent_int
+ \int_eval:w
+ \l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int
+ \scan_stop:
+ \fp_extended_normalise_output:
+ \tex_multiply:D \l_fp_input_a_sign_int \l_fp_input_b_sign_int
+ \l_fp_input_a_integer_int \l_fp_output_integer_int
+ \l_fp_input_a_decimal_int \l_fp_output_decimal_int
+ \l_fp_input_a_extended_int \l_fp_output_extended_int
+ \l_fp_input_a_exponent_int \l_fp_output_exponent_int
+ \l_fp_output_integer_int \c_zero
+ \l_fp_output_decimal_int \c_zero
+ \l_fp_output_extended_int \c_zero
+ \l_fp_output_exponent_int \c_zero
+ \cs_set_eq:NN \fp_exp_const:Nx \use_none:nn
+ \fp_exp_internal:
+ }
+\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF }
+ {
+ \if_meaning:w #1 \c_undefined_fp
+ \prg_return_true:
+ \else:
+ \prg_return_false:
+ \fi:
+ }
+\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF }
+ {
+ \if_meaning:w #1 \c_zero_fp
+ \prg_return_true:
+ \else:
+ \prg_return_false:
+ \fi:
+ }
+\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3 { T , F , TF }
+ {
+ \group_begin:
+ \fp_split:Nn a {#1}
+ \fp_standardise:NNNN
+ \l_fp_input_a_sign_int
+ \l_fp_input_a_integer_int
+ \l_fp_input_a_decimal_int
+ \l_fp_input_a_exponent_int
+ \fp_split:Nn b {#3}
+ \fp_standardise:NNNN
+ \l_fp_input_b_sign_int
+ \l_fp_input_b_integer_int
+ \l_fp_input_b_decimal_int
+ \l_fp_input_b_exponent_int
+ \fp_compare_aux:N #2
+ }
+\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3 { T , F , TF }
+ {
+ \group_begin:
+ \fp_read:N #3
+ \l_fp_input_b_sign_int \l_fp_input_a_sign_int
+ \l_fp_input_b_integer_int \l_fp_input_a_integer_int
+ \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
+ \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int
+ \fp_read:N #1
+ \fp_compare_aux:N #2
+ }
+\cs_new_protected_nopar:Npn \fp_compare_aux:N #1
+ {
+ \cs_if_exist:cTF { fp_compare_#1: }
+ { \use:c { fp_compare_#1: } }
+ {
+ \group_end:
+ \prg_return_false:
+ }
+ }
+\cs_new_protected_nopar:cpn { fp_compare_=: }
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int = \l_fp_input_b_sign_int
+ \if_int_compare:w \l_fp_input_a_integer_int = \l_fp_input_b_integer_int
+ \if_int_compare:w \l_fp_input_a_decimal_int = \l_fp_input_b_decimal_int
+ \if_int_compare:w
+ \l_fp_input_a_exponent_int = \l_fp_input_b_exponent_int
+ \group_end:
+ \prg_return_true:
+ \else:
+ \group_end:
+ \prg_return_false:
+ \fi:
+ \else:
+ \group_end:
+ \prg_return_false:
+ \fi:
+ \else:
+ \group_end:
+ \prg_return_false:
+ \fi:
+ \else:
+ \group_end:
+ \prg_return_false:
+ \fi:
+ }
+\cs_new_protected_nopar:cpn { fp_compare_>: }
+ {
+ \if_int_compare:w \int_eval:w
+ \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+ = \c_zero
+ \if_int_compare:w \int_eval:w
+ \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+ = \c_zero
+ \group_end:
+ \prg_return_false:
+ \else:
+ \if_int_compare:w \l_fp_input_b_sign_int > \c_zero
+ \group_end:
+ \prg_return_false:
+ \else:
+ \group_end:
+ \prg_return_true:
+ \fi:
+ \fi:
+ \else:
+ \if_int_compare:w \int_eval:w
+ \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+ = \c_zero
+ \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
+ \group_end:
+ \prg_return_true:
+ \else:
+ \group_end:
+ \prg_return_false:
+ \fi:
+ \else:
+ \use:c { fp_compare_>_aux: }
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:cpn { fp_compare_>_aux: }
+ {
+ \if_int_compare:w \l_fp_input_a_sign_int > \l_fp_input_b_sign_int
+ \group_end:
+ \prg_return_true:
+ \else:
+ \if_int_compare:w \l_fp_input_a_sign_int < \l_fp_input_b_sign_int
+ \group_end:
+ \prg_return_false:
+ \else:
+ \if_int_compare:w \l_fp_input_a_sign_int > \c_zero
+ \use:c { fp_compare_absolute_a>b: }
+ \else:
+ \use:c { fp_compare_absolute_a<b: }
+ \fi:
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:cpn { fp_compare_absolute_a>b: }
+ {
+ \if_int_compare:w \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
+ \group_end:
+ \prg_return_true:
+ \else:
+ \if_int_compare:w \l_fp_input_a_exponent_int < \l_fp_input_b_exponent_int
+ \group_end:
+ \prg_return_false:
+ \else:
+ \if_int_compare:w \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
+ \group_end:
+ \prg_return_true:
+ \else:
+ \if_int_compare:w
+ \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
+ \group_end:
+ \prg_return_false:
+ \else:
+ \if_int_compare:w
+ \l_fp_input_a_decimal_int > \l_fp_input_b_decimal_int
+ \group_end:
+ \prg_return_true:
+ \else:
+ \group_end:
+ \prg_return_false:
+ \fi:
+ \fi:
+ \fi:
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:cpn { fp_compare_absolute_a<b: }
+ {
+ \if_int_compare:w \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int
+ \group_end:
+ \prg_return_true:
+ \else:
+ \if_int_compare:w \l_fp_input_b_exponent_int < \l_fp_input_a_exponent_int
+ \group_end:
+ \prg_return_false:
+ \else:
+ \if_int_compare:w \l_fp_input_b_integer_int > \l_fp_input_a_integer_int
+ \group_end:
+ \prg_return_true:
+ \else:
+ \if_int_compare:w
+ \l_fp_input_b_integer_int < \l_fp_input_a_integer_int
+ \group_end:
+ \prg_return_false:
+ \else:
+ \if_int_compare:w
+ \l_fp_input_b_decimal_int > \l_fp_input_a_decimal_int
+ \group_end:
+ \prg_return_true:
+ \else:
+ \group_end:
+ \prg_return_false:
+ \fi:
+ \fi:
+ \fi:
+ \fi:
+ \fi:
+ }
+\cs_new_protected_nopar:cpn { fp_compare_<: }
+ {
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \int_set:Nn \exp_not:N \l_fp_input_a_sign_int
+ { \int_use:N \l_fp_input_b_sign_int }
+ \int_set:Nn \exp_not:N \l_fp_input_a_integer_int
+ { \int_use:N \l_fp_input_b_integer_int }
+ \int_set:Nn \exp_not:N \l_fp_input_a_decimal_int
+ { \int_use:N \l_fp_input_b_decimal_int }
+ \int_set:Nn \exp_not:N \l_fp_input_a_exponent_int
+ { \int_use:N \l_fp_input_b_exponent_int }
+ \int_set:Nn \exp_not:N \l_fp_input_b_sign_int
+ { \int_use:N \l_fp_input_a_sign_int }
+ \int_set:Nn \exp_not:N \l_fp_input_b_integer_int
+ { \int_use:N \l_fp_input_a_integer_int }
+ \int_set:Nn \exp_not:N \l_fp_input_b_decimal_int
+ { \int_use:N \l_fp_input_a_decimal_int }
+ \int_set:Nn \exp_not:N \l_fp_input_b_exponent_int
+ { \int_use:N \l_fp_input_a_exponent_int }
+ }
+ \l_fp_tmp_tl
+ \use:c { fp_compare_>: }
+ }
+\prg_new_protected_conditional:Npnn \fp_compare:n #1 { T , F , TF }
+ {
+ \group_begin:
+ \tl_set:Nx \l_fp_tmp_tl
+ {
+ \group_end:
+ \fp_compare_aux_i:w #1 \exp_not:n { == \q_nil == \q_stop }
+ }
+ \l_fp_tmp_tl
+ }
+\cs_new_protected_nopar:Npn \fp_compare_aux_i:w #1 == #2 == #3 \q_stop
+ {
+ \quark_if_nil:nTF {#2}
+ { \fp_compare_aux_ii:w #1 != \q_nil != \q_stop }
+ { \fp_compare:nNnTF {#1} = {#2} \prg_return_true: \prg_return_false: }
+ }
+\cs_new_protected_nopar:Npn \fp_compare_aux_ii:w #1 != #2 != #3 \q_stop
+ {
+ \quark_if_nil:nTF {#2}
+ { \fp_compare_aux_iii:w #1 <= \q_nil <= \q_stop }
+ { \fp_compare:nNnTF {#1} = {#2} \prg_return_false: \prg_return_true: }
+ }
+\cs_new_protected_nopar:Npn \fp_compare_aux_iii:w #1 <= #2 <= #3 \q_stop
+ {
+ \quark_if_nil:nTF {#2}
+ { \fp_compare_aux_iv:w #1 >= \q_nil >= \q_stop }
+ { \fp_compare:nNnTF {#1} > {#2} \prg_return_false: \prg_return_true: }
+ }
+\cs_new_protected_nopar:Npn \fp_compare_aux_iv:w #1 >= #2 >= #3 \q_stop
+ {
+ \quark_if_nil:nTF {#2}
+ { \fp_compare_aux_v:w #1 = \q_nil \q_stop }
+ { \fp_compare:nNnTF {#1} < {#2} \prg_return_false: \prg_return_true: }
+ }
+\cs_new_protected_nopar:Npn \fp_compare_aux_v:w #1 = #2 = #3 \q_stop
+ {
+ \quark_if_nil:nTF {#2}
+ { \fp_compare_aux_vi:w #1 < \q_nil < \q_stop }
+ { \fp_compare:nNnTF {#1} = {#2} \prg_return_true: \prg_return_false: }
+ }
+\cs_new_protected_nopar:Npn \fp_compare_aux_vi:w #1 < #2 < #3 \q_stop
+ {
+ \quark_if_nil:nTF {#2}
+ { \fp_compare_aux_vii:w #1 > \q_nil > \q_stop }
+ { \fp_compare:nNnTF {#1} < {#2} \prg_return_true: \prg_return_false: }
+ }
+\cs_new_protected_nopar:Npn \fp_compare_aux_vii:w #1 > #2 > #3 \q_stop
+ {
+ \quark_if_nil:nTF {#2}
+ { \prg_return_false: }
+ { \fp_compare:nNnTF {#1} > {#2} \prg_return_true: \prg_return_false: }
+ }
+\msg_kernel_new:nnnn { fpu } { overflow }
+ { Number~too~big. }
+ {
+ The~input~given~is~too~big~for~the~LaTeX~floating~point~unit. \\
+ Further~errors~may~well~occur!
+ }
+\cs_new_protected_nopar:Npn \fp_overflow_msg:
+ { \msg_kernel_error:nn { fpu } { overflow } }
+\msg_kernel_new:nnnn { fpu } { exponent-overflow }
+ { Number~too~big~for~exponent~unit. }
+ {
+ The~exponent~of~the~input~given~is~too~big~for~the~floating~point~
+ unit:~the~maximum~input~value~for~an~exponent~is~230.
+ }
+\cs_new_protected_nopar:Npn \fp_exp_overflow_msg:
+ { \msg_kernel_error:nn { fpu } { exponent-overflow } }
+\msg_kernel_new:nnnn { fpu } { logarithm-input-error }
+ { Invalid~input~to~ln~function. }
+ { Logarithms~can~only~be~calculated~for~positive~numbers. }
+\cs_new_protected_nopar:Npn \fp_ln_error_msg: {
+ \msg_kernel_error:nn { fpu } { logarithm-input-error }
+}
+\msg_kernel_new:nnnn { fpu } { trigonometric-overflow }
+ { Number~too~big~for~trigonometry~unit. }
+ {
+ The~trigonometry~code~can~only~work~with~numbers~smaller~
+ than~1000000000.
+ }
+\cs_new_protected_nopar:Npn \fp_trig_overflow_msg:
+ { \msg_kernel_error:nn { fpu } { trigonometric-overflow } }
+%%
+%%
+%% End of file `l3fp.sty'.