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Diffstat (limited to 'Master/texmf-dist/tex/latex/l3kernel/l3fp.sty')
-rw-r--r-- | Master/texmf-dist/tex/latex/l3kernel/l3fp.sty | 3403 |
1 files changed, 3403 insertions, 0 deletions
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty b/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty new file mode 100644 index 00000000000..d3f98d4353a --- /dev/null +++ b/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty @@ -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'. |