%% %% This is file `l3fp.sty', %% generated with the docstrip utility. %% %% The original source files were: %% %% l3fp.dtx (with options: `package') %% %% %% EXPERIMENTAL CODE %% %% Do not distribute this file without also distributing the %% source files specified above. %% %% Do not distribute a modified version of this file. %% %% %% File: l3fp.dtx Copyright (C) 2010-2011 LaTeX3 project %% %% It may be distributed and/or modified under the conditions of the %% LaTeX Project Public License (LPPL), either version 1.3c of this %% license or (at your option) any later version. The latest version %% of this license is in the file %% %% http://www.latex-project.org/lppl.txt %% %% This file is part of the ``expl3 bundle'' (The Work in LPPL) %% and all files in that bundle must be distributed together. %% %% The released version of this bundle is available from CTAN. %% %% ----------------------------------------------------------------------- %% %% The development version of the bundle can be found at %% %% http://www.latex-project.org/svnroot/experimental/trunk/ %% %% for those people who are interested. %% %%%%%%%%%%% %% NOTE: %% %%%%%%%%%%% %% %% Snapshots taken from the repository represent work in progress and may %% not work or may contain conflicting material! We therefore ask %% people _not_ to put them into distributions, archives, etc. without %% prior consultation with the LaTeX Project Team. %% %% ----------------------------------------------------------------------- \RequirePackage{l3names} \GetIdInfo$Id: l3fp.dtx 2178 2011-03-06 09:03:44Z mittelba $ {L3 Experimental floating-point operations} \ProvidesExplPackage {\filename}{\filedate}{\fileversion}{\filedescription} \package_check_loaded_expl: \int_const:Nn \c_forty_four { 44 } \int_const:Nn \c_one_hundred { 100 } \int_const:Nn \c_one_thousand { 1000 } \int_const:Nn \c_one_million { 1 000 000 } \int_const:Nn \c_one_hundred_million { 100 000 000 } \int_const:Nn \c_five_hundred_million { 500 000 000 } \int_const:Nn \c_one_thousand_million { 1 000 000 000 } \int_new:N \c_fp_pi_by_four_decimal_int \int_set:Nn \c_fp_pi_by_four_decimal_int { 785 398 158 } \int_new:N \c_fp_pi_by_four_extended_int \int_set:Nn \c_fp_pi_by_four_extended_int { 897 448 310 } \int_new:N \c_fp_pi_decimal_int \int_set:Nn \c_fp_pi_decimal_int { 141 592 653 } \int_new:N \c_fp_pi_extended_int \int_set:Nn \c_fp_pi_extended_int { 589 793 238 } \int_new:N \c_fp_two_pi_decimal_int \int_set:Nn \c_fp_two_pi_decimal_int { 283 185 307 } \int_new:N \c_fp_two_pi_extended_int \int_set:Nn \c_fp_two_pi_extended_int { 179 586 477 } \tl_new:N \c_e_fp \tl_set:Nn \c_e_fp { + 2.718281828 e 0 } \tl_new:N \c_one_fp \tl_set:Nn \c_one_fp { + 1.000000000 e 0 } \tl_new:N \c_pi_fp \tl_set:Nn \c_pi_fp { + 3.141592654 e 0 } \tl_new:N \c_undefined_fp \tl_set:Nn \c_undefined_fp { X 0.000000000 e 0 } \tl_new:N \c_zero_fp \tl_set:Nn \c_zero_fp { + 0.000000000 e 0 } \tl_new:N \l_fp_arg_tl \int_new:N \l_fp_count_int \int_new:N \l_fp_div_offset_int \int_new:N \l_fp_exp_integer_int \int_new:N \l_fp_exp_decimal_int \int_new:N \l_fp_exp_extended_int \int_new:N \l_fp_exp_exponent_int \int_new:N \l_fp_input_a_sign_int \int_new:N \l_fp_input_a_integer_int \int_new:N \l_fp_input_a_decimal_int \int_new:N \l_fp_input_a_exponent_int \int_new:N \l_fp_input_b_sign_int \int_new:N \l_fp_input_b_integer_int \int_new:N \l_fp_input_b_decimal_int \int_new:N \l_fp_input_b_exponent_int \int_new:N \l_fp_input_a_extended_int \int_new:N \l_fp_input_b_extended_int \int_new:N \l_fp_mul_a_i_int \int_new:N \l_fp_mul_a_ii_int \int_new:N \l_fp_mul_a_iii_int \int_new:N \l_fp_mul_a_iv_int \int_new:N \l_fp_mul_a_v_int \int_new:N \l_fp_mul_a_vi_int \int_new:N \l_fp_mul_b_i_int \int_new:N \l_fp_mul_b_ii_int \int_new:N \l_fp_mul_b_iii_int \int_new:N \l_fp_mul_b_iv_int \int_new:N \l_fp_mul_b_v_int \int_new:N \l_fp_mul_b_vi_int \int_new:N \l_fp_mul_output_int \tl_new:N \l_fp_mul_output_tl \int_new:N \l_fp_output_sign_int \int_new:N \l_fp_output_integer_int \int_new:N \l_fp_output_decimal_int \int_new:N \l_fp_output_exponent_int \int_new:N \l_fp_output_extended_int \bool_new:N \l_fp_round_carry_bool \tl_new:N \l_fp_round_decimal_tl \int_new:N \l_fp_round_position_int \int_new:N \l_fp_round_target_int \tl_new:N \l_fp_sign_tl \int_new:N \l_fp_split_sign_int \int_new:N \l_fp_tmp_int \tl_new:N \l_fp_tmp_tl \int_new:N \l_fp_trig_octant_int \int_new:N \l_fp_trig_sign_int \int_new:N \l_fp_trig_decimal_int \int_new:N \l_fp_trig_extended_int \cs_new_protected_nopar:Npn \fp_read:N #1 { \tex_expandafter:D \fp_read_aux:w #1 \q_stop } \cs_new_protected_nopar:Npn \fp_read_aux:w #1#2 . #3 e #4 \q_stop { \tex_if:D #1 - \l_fp_input_a_sign_int \c_minus_one \tex_else:D \l_fp_input_a_sign_int \c_one \tex_fi:D \l_fp_input_a_integer_int #2 \scan_stop: \l_fp_input_a_decimal_int #3 \scan_stop: \l_fp_input_a_exponent_int #4 \scan_stop: } \cs_new_protected_nopar:Npn \fp_split:Nn #1#2 { \tl_set:Nx \l_fp_tmp_tl {#2} \tl_set_rescan:Nno \l_fp_tmp_tl { \char_make_ignore:n { 32 } } { \l_fp_tmp_tl } \l_fp_split_sign_int \c_one \fp_split_sign: \use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int \tex_expandafter:D \fp_split_exponent:w \l_fp_tmp_tl e e \q_stop #1 } \cs_new_protected_nopar:Npn \fp_split_sign: { \tex_ifnum:D \pdf_strcmp:D { \tex_expandafter:D \tl_head:w \l_fp_tmp_tl ? \q_stop } { - } = \c_zero \tl_set:Nx \l_fp_tmp_tl { \tex_expandafter:D \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop } \l_fp_split_sign_int -\l_fp_split_sign_int \tex_expandafter:D \fp_split_sign: \tex_else:D \tex_ifnum:D \pdf_strcmp:D { \tex_expandafter:D \tl_head:w \l_fp_tmp_tl ? \q_stop } { + } = \c_zero \tl_set:Nx \l_fp_tmp_tl { \tex_expandafter:D \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop } \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_split_sign: \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_split_exponent:w #1 e #2 e #3 \q_stop #4 { \use:c { l_fp_input_ #4 _exponent_int } \etex_numexpr:D 0 #2 \scan_stop: \tex_afterassignment:D \fp_split_aux_i:w \use:c { l_fp_input_ #4 _integer_int } \etex_numexpr:D 0 #1 . . \q_stop #4 } \cs_new_protected_nopar:Npn \fp_split_aux_i:w #1 . #2 . #3 \q_stop { \fp_split_aux_ii:w #2 000000000 \q_stop } \cs_new_protected_nopar:Npn \fp_split_aux_ii:w #1#2#3#4#5#6#7#8#9 { \fp_split_aux_iii:w {#1#2#3#4#5#6#7#8#9} } \cs_new_protected_nopar:Npn \fp_split_aux_iii:w #1#2 \q_stop { \l_fp_tmp_int 1 #1 \scan_stop: \tex_expandafter:D \fp_split_decimal:w \int_use:N \l_fp_tmp_int 000000000 \q_stop } \cs_new_protected_nopar:Npn \fp_split_decimal:w #1#2#3#4#5#6#7#8#9 { \fp_split_decimal_aux:w {#2#3#4#5#6#7#8#9} } \cs_new_protected_nopar:Npn \fp_split_decimal_aux:w #1#2#3 \q_stop #4 { \use:c { l_fp_input_ #4 _decimal_int } #1#2 \scan_stop: \tex_ifnum:D \etex_numexpr:D \use:c { l_fp_input_ #4 _integer_int } + \use:c { l_fp_input_ #4 _decimal_int } \scan_stop: = \c_zero \use:c { l_fp_input_ #4 _sign_int } \c_one \tex_fi:D \tex_ifnum:D \use:c { l_fp_input_ #4 _integer_int } < \c_one_thousand_million \tex_else:D \tex_expandafter:D \fp_overflow_msg: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_standardise:NNNN #1#2#3#4 { \tex_ifnum:D \etex_numexpr:D #2 + #3 = \c_zero #1 \c_one #4 \c_zero \tex_expandafter:D \use_none:nnnn \tex_else:D \tex_expandafter:D \fp_standardise_aux:NNNN \tex_fi:D #1#2#3#4 } \cs_new_protected_nopar:Npn \fp_standardise_aux:NNNN #1#2#3#4 { \cs_set_protected_nopar:Npn \fp_standardise_aux: { \tex_ifnum:D #2 = \c_zero \tex_advance:D #3 \c_one_thousand_million \tex_expandafter:D \fp_standardise_aux:w \int_use:N #3 \q_stop \tex_expandafter:D \fp_standardise_aux: \tex_fi:D } \cs_set_protected_nopar:Npn \fp_standardise_aux:w ##1##2##3##4##5##6##7##8##9 \q_stop { #2 ##2 \scan_stop: #3 ##3##4##5##6##7##8##9 0 \scan_stop: \tex_advance:D #4 \c_minus_one } \fp_standardise_aux: \cs_set_protected_nopar:Npn \fp_standardise_aux: { \tex_ifnum:D #2 > \c_nine \tex_advance:D #2 \c_one_thousand_million \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_standardise_aux:w \int_use:N #2 \tex_expandafter:D \fp_standardise_aux: \tex_fi:D } \cs_set_protected_nopar:Npn \fp_standardise_aux:w ##1##2##3##4##5##6##7##8##9 { #2 ##1##2##3##4##5##6##7##8 \scan_stop: \tex_advance:D #3 \c_one_thousand_million \tex_divide:D #3 \c_ten \tl_set:Nx \l_fp_tmp_tl { ##9 \tex_expandafter:D \use_none:n \int_use:N #3 } #3 \l_fp_tmp_tl \scan_stop: \tex_advance:D #4 \c_one } \fp_standardise_aux: \tex_ifnum:D #4 < \c_one_hundred \tex_ifnum:D #4 > -\c_one_hundred \tex_else:D #1 \c_one #2 \c_zero #3 \c_zero #4 \c_zero \tex_fi:D \tex_else:D \tex_expandafter:D \fp_overflow_msg: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_standardise_aux: { } \cs_new_protected_nopar:Npn \fp_standardise_aux:w { } \cs_new_protected_nopar:Npn \fp_level_input_exponents: { \tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int \tex_expandafter:D \fp_level_input_exponents_a: \tex_else:D \tex_expandafter:D \fp_level_input_exponents_b: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_level_input_exponents_a: { \tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int \tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_level_input_exponents_a:NNNNNNNNN \int_use:N \l_fp_input_b_integer_int \tex_expandafter:D \fp_level_input_exponents_a: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_level_input_exponents_a:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \l_fp_input_b_integer_int #1#2#3#4#5#6#7#8 \scan_stop: \tex_advance:D \l_fp_input_b_decimal_int \c_one_thousand_million \tex_divide:D \l_fp_input_b_decimal_int \c_ten \tl_set:Nx \l_fp_tmp_tl { #9 \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_b_decimal_int } \l_fp_input_b_decimal_int \l_fp_tmp_tl \scan_stop: \tex_advance:D \l_fp_input_b_exponent_int \c_one } \cs_new_protected_nopar:Npn \fp_level_input_exponents_b: { \tex_ifnum:D \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int \tex_advance:D \l_fp_input_a_integer_int \c_one_thousand_million \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_level_input_exponents_b:NNNNNNNNN \int_use:N \l_fp_input_a_integer_int \tex_expandafter:D \fp_level_input_exponents_b: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_level_input_exponents_b:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \l_fp_input_a_integer_int #1#2#3#4#5#6#7#8 \scan_stop: \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \tex_divide:D \l_fp_input_a_decimal_int \c_ten \tl_set:Nx \l_fp_tmp_tl { #9 \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int } \l_fp_input_a_decimal_int \l_fp_tmp_tl \scan_stop: \tex_advance:D \l_fp_input_a_exponent_int \c_one } \cs_new_protected_nopar:Npn \fp_tmp:w #1#2 { } \cs_new_protected_nopar:Npn \fp_new:N #1 { \tl_new:N #1 \tl_gset_eq:NN #1 \c_zero_fp } \cs_generate_variant:Nn \fp_new:N { c } \cs_new_protected_nopar:Npn \fp_const:Nn #1#2 { \cs_if_free:NTF #1 { \fp_new:N #1 \fp_gset:Nn #1 {#2} } { \msg_kernel_error:nx { variable-already-defined } { \token_to_str:N #1 } } } \cs_generate_variant:Nn \fp_const:Nn { c } \cs_new_protected_nopar:Npn \fp_zero:N #1 { \tl_set_eq:NN #1 \c_zero_fp } \cs_new_protected_nopar:Npn \fp_gzero:N #1 { \tl_gset_eq:NN #1 \c_zero_fp } \cs_generate_variant:Nn \fp_zero:N { c } \cs_generate_variant:Nn \fp_gzero:N { c } \cs_new_protected_nopar:Npn \fp_set:Nn { \fp_set_aux:NNn \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gset:Nn { \fp_set_aux:NNn \tl_gset:Nn } \cs_new_protected_nopar:Npn \fp_set_aux:NNn #1#2#3 { \group_begin: \fp_split:Nn a {#3} \fp_standardise:NNNN \l_fp_input_a_sign_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 { \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero - \tex_else:D + \tex_fi:D \int_use:N \l_fp_input_a_integer_int . \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int e \int_use:N \l_fp_input_a_exponent_int } } \fp_tmp:w } \cs_generate_variant:Nn \fp_set:Nn { c } \cs_generate_variant:Nn \fp_gset:Nn { c } \cs_new_protected_nopar:Npn \fp_set_from_dim:Nn { \fp_set_from_dim_aux:NNn \tl_set:Nx } \cs_new_protected_nopar:Npn \fp_gset_from_dim:Nn { \fp_set_from_dim_aux:NNn \tl_gset:Nx } \cs_new_protected_nopar:Npn \fp_set_from_dim_aux:NNn #1#2#3 { \group_begin: \l_fp_tmp_skip \etex_glueexpr:D #3 \scan_stop: \l_fp_tmp_dim \l_fp_tmp_skip \fp_split:Nn a { \tex_expandafter:D \fp_set_from_dim_aux:w \dim_use:N \l_fp_tmp_dim } \fp_standardise:NNNN \l_fp_input_a_sign_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 { \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero - \tex_else:D + \tex_fi:D \int_use:N \l_fp_input_a_integer_int . \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int e \int_use:N \l_fp_input_a_exponent_int } } \fp_tmp:w } \cs_set_protected_nopar:Npx \fp_set_from_dim_aux:w { \cs_set_nopar:Npn \exp_not:N \fp_set_from_dim_aux:w ##1 \tl_to_str:n { pt } {##1} } \fp_set_from_dim_aux:w \cs_generate_variant:Nn \fp_set_from_dim:Nn { c } \cs_generate_variant:Nn \fp_gset_from_dim:Nn { c } \dim_new:N \l_fp_tmp_dim \skip_new:N \l_fp_tmp_skip \cs_new_eq:NN \fp_set_eq:NN \tl_set_eq:NN \cs_new_eq:NN \fp_set_eq:cN \tl_set_eq:cN \cs_new_eq:NN \fp_set_eq:Nc \tl_set_eq:Nc \cs_new_eq:NN \fp_set_eq:cc \tl_set_eq:cc \cs_new_eq:NN \fp_gset_eq:NN \tl_gset_eq:NN \cs_new_eq:NN \fp_gset_eq:cN \tl_gset_eq:cN \cs_new_eq:NN \fp_gset_eq:Nc \tl_gset_eq:Nc \cs_new_eq:NN \fp_gset_eq:cc \tl_gset_eq:cc \cs_new_eq:NN \fp_show:N \tl_show:N \cs_new_eq:NN \fp_show:c \tl_show:c \cs_new_nopar:Npn \fp_use:N #1 { \tex_expandafter:D \fp_use_aux:w #1 \q_stop } \cs_generate_variant:Nn \fp_use:N { c } \cs_new_nopar:Npn \fp_use_aux:w #1#2 e #3 \q_stop { \tex_if:D #1 - - \tex_fi:D \tex_ifnum:D #3 > \c_zero \tex_expandafter:D \fp_use_large:w \tex_else:D \tex_ifnum:D #3 < \c_zero \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_use_small:w \tex_else:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_use_none:w \tex_fi:D \tex_fi:D #2 e #3 \q_stop } \cs_new_nopar:Npn \fp_use_none:w #1 e #2 \q_stop {#1} \cs_new_nopar:Npn \fp_use_small:w #1 . #2 e #3 \q_stop { 0 . \prg_replicate:nn { -#3 - 1 } { 0 } #1#2 } \cs_new_nopar:Npn \fp_use_large:w #1 . #2 e #3 \q_stop { \tex_ifnum:D #3 < \c_ten \tex_expandafter:D \fp_use_large_aux_i:w \tex_else:D \tex_expandafter:D \fp_use_large_aux_ii:w \tex_fi:D #1#2 e #3 \q_stop } \cs_new_nopar:Npn \fp_use_large_aux_i:w #1#2 e #3 \q_stop { #1 \use:c { fp_use_large_aux_ #3 :w } #2 \q_stop } \cs_new_nopar:cpn { fp_use_large_aux_1:w } #1#2 \q_stop { #1 . #2 } \cs_new_nopar:cpn { fp_use_large_aux_2:w } #1#2#3 \q_stop { #1#2 . #3 } \cs_new_nopar:cpn { fp_use_large_aux_3:w } #1#2#3#4 \q_stop { #1#2#3 . #4 } \cs_new_nopar:cpn { fp_use_large_aux_4:w } #1#2#3#4#5 \q_stop { #1#2#3#4 . #5 } \cs_new_nopar:cpn { fp_use_large_aux_5:w } #1#2#3#4#5#6 \q_stop { #1#2#3#4#5 . #6 } \cs_new_nopar:cpn { fp_use_large_aux_6:w } #1#2#3#4#5#6#7 \q_stop { #1#2#3#4#5#6 . #7 } \cs_new_nopar:cpn { fp_use_large_aux_7:w } #1#2#3#4#5#6#7#8 \q_stop { #1#2#3#4#6#7 . #8 } \cs_new_nopar:cpn { fp_use_large_aux_8:w } #1#2#3#4#5#6#7#8#9 \q_stop { #1#2#3#4#5#6#7#8 . #9 } \cs_new_nopar:cpn { fp_use_large_aux_9:w } #1 \q_stop { #1 . } \cs_new_nopar:Npn \fp_use_large_aux_ii:w #1 e #2 \q_stop { #1 \prg_replicate:nn { #2 - 9 } { 0 } . } \cs_new_nopar:Npn \fp_to_dim:N #1 { \fp_use:N #1 pt } \cs_generate_variant:Nn \fp_to_dim:N { c } \cs_new_nopar:Npn \fp_to_int:N #1 { \tex_expandafter:D \fp_to_int_aux:w #1 \q_stop } \cs_generate_variant:Nn \fp_to_int:N { c } \cs_new_nopar:Npn \fp_to_int_aux:w #1#2 e #3 \q_stop { \tex_if:D #1 - - \tex_fi:D \tex_ifnum:D #3 < \c_zero \tex_expandafter:D \fp_to_int_small:w \tex_else:D \tex_expandafter:D \fp_to_int_large:w \tex_fi:D #2 e #3 \q_stop } \cs_new_nopar:Npn \fp_to_int_small:w #1 . #2 e #3 \q_stop { \tex_ifnum:D #3 > \c_one \tex_else:D \tex_ifnum:D #1 < \c_five 0 \tex_else:D 1 \tex_fi:D \tex_fi:D } \cs_new_nopar:Npn \fp_to_int_large:w #1 . #2 e #3 \q_stop { \tex_ifnum:D #3 < \c_ten \tex_expandafter:D \fp_to_int_large_aux_i:w \tex_else:D \tex_expandafter:D \fp_to_int_large_aux_ii:w \tex_fi:D #1#2 e #3 \q_stop } \cs_new_nopar:Npn \fp_to_int_large_aux_i:w #1#2 e #3 \q_stop { \use:c { fp_to_int_large_aux_ #3 :w } #2 \q_stop {#1} } \cs_new_nopar:cpn { fp_to_int_large_aux_1:w } #1#2 \q_stop { \fp_to_int_large_aux:nnn { #2 0 } {#1} } \cs_new_nopar:cpn { fp_to_int_large_aux_2:w } #1#2#3 \q_stop { \fp_to_int_large_aux:nnn { #3 00 } {#1#2} } \cs_new_nopar:cpn { fp_to_int_large_aux_3:w } #1#2#3#4 \q_stop { \fp_to_int_large_aux:nnn { #4 000 } {#1#2#3} } \cs_new_nopar:cpn { fp_to_int_large_aux_4:w } #1#2#3#4#5 \q_stop { \fp_to_int_large_aux:nnn { #5 0000 } {#1#2#3#4} } \cs_new_nopar:cpn { fp_to_int_large_aux_5:w } #1#2#3#4#5#6 \q_stop { \fp_to_int_large_aux:nnn { #6 00000 } {#1#2#3#4#5} } \cs_new_nopar:cpn { fp_to_int_large_aux_6:w } #1#2#3#4#5#6#7 \q_stop { \fp_to_int_large_aux:nnn { #7 000000 } {#1#2#3#4#5#6} } \cs_new_nopar:cpn { fp_to_int_large_aux_7:w } #1#2#3#4#5#6#7#8 \q_stop { \fp_to_int_large_aux:nnn { #8 0000000 } {#1#2#3#4#5#6#7} } \cs_new_nopar:cpn { fp_to_int_large_aux_8:w } #1#2#3#4#5#6#7#8#9 \q_stop { \fp_to_int_large_aux:nnn { #9 00000000 } {#1#2#3#4#5#6#7#8} } \cs_new_nopar:cpn { fp_to_int_large_aux_9:w } #1 \q_stop {#1} \cs_new_nopar:Npn \fp_to_int_large_aux:nnn #1#2#3 { \tex_ifnum:D #1 < \c_five_hundred_million #3#2 \tex_else:D \tex_number:D \etex_numexpr:D #3#2 + 1 \scan_stop: \tex_fi:D } \cs_new_nopar:Npn \fp_to_int_large_aux_ii:w #1 e #2 \q_stop { #1 \prg_replicate:nn { #2 - 9 } { 0 } } \cs_new_nopar:Npn \fp_to_tl:N #1 { \tex_expandafter:D \fp_to_tl_aux:w #1 \q_stop } \cs_generate_variant:Nn \fp_to_tl:N { c } \cs_new_nopar:Npn \fp_to_tl_aux:w #1#2 e #3 \q_stop { \tex_if:D #1 - - \tex_fi:D \tex_ifnum:D #3 < \c_zero \tex_expandafter:D \fp_to_tl_small:w \tex_else:D \tex_expandafter:D \fp_to_tl_large:w \tex_fi:D #2 e #3 \q_stop } \cs_new_nopar:Npn \fp_to_tl_large:w #1 e #2 \q_stop { \tex_ifnum:D #2 < \c_ten \tex_expandafter:D \fp_to_tl_large_aux_i:w \tex_else:D \tex_expandafter:D \fp_to_tl_large_aux_ii:w \tex_fi:D #1 e #2 \q_stop } \cs_new_nopar:Npn \fp_to_tl_large_aux_i:w #1 e #2 \q_stop { \use:c { fp_to_tl_large_ #2 :w } #1 \q_stop } \cs_new_nopar:Npn \fp_to_tl_large_aux_ii:w #1 . #2 e #3 \q_stop { #1 \fp_to_tl_large_zeros:NNNNNNNNN #2 e #3 } \cs_new_nopar:cpn { fp_to_tl_large_0:w } #1 . #2 \q_stop { #1 \fp_to_tl_large_zeros:NNNNNNNNN #2 } \cs_new_nopar:cpn { fp_to_tl_large_1:w } #1 . #2#3 \q_stop { #1#2 \fp_to_tl_large_zeros:NNNNNNNNN #3 0 } \cs_new_nopar:cpn { fp_to_tl_large_2:w } #1 . #2#3#4 \q_stop { #1#2#3 \fp_to_tl_large_zeros:NNNNNNNNN #4 00 } \cs_new_nopar:cpn { fp_to_tl_large_3:w } #1 . #2#3#4#5 \q_stop { #1#2#3#4 \fp_to_tl_large_zeros:NNNNNNNNN #5 000 } \cs_new_nopar:cpn { fp_to_tl_large_4:w } #1 . #2#3#4#5#6 \q_stop { #1#2#3#4#5 \fp_to_tl_large_zeros:NNNNNNNNN #6 0000 } \cs_new_nopar:cpn { fp_to_tl_large_5:w } #1 . #2#3#4#5#6#7 \q_stop { #1#2#3#4#5#6 \fp_to_tl_large_zeros:NNNNNNNNN #7 00000 } \cs_new_nopar:cpn { fp_to_tl_large_6:w } #1 . #2#3#4#5#6#7#8 \q_stop { #1#2#3#4#5#6#7 \fp_to_tl_large_zeros:NNNNNNNNN #8 000000 } \cs_new_nopar:cpn { fp_to_tl_large_7:w } #1 . #2#3#4#5#6#7#8#9 \q_stop { #1#2#3#4#5#6#7#8 \fp_to_tl_large_zeros:NNNNNNNNN #9 0000000 } \cs_new_nopar:cpn { fp_to_tl_large_8:w } #1 . { #1 \use:c { fp_to_tl_large_8_aux:w } } \cs_new_nopar:cpn { fp_to_tl_large_8_aux:w } #1#2#3#4#5#6#7#8#9 \q_stop { #1#2#3#4#5#6#7#8 \fp_to_tl_large_zeros:NNNNNNNNN #9 00000000 } \cs_new_nopar:cpn { fp_to_tl_large_9:w } #1 . #2 \q_stop {#1#2} \cs_new_nopar:Npn \fp_to_tl_small:w #1 e #2 \q_stop { \tex_ifnum:D #2 = \c_minus_one \tex_expandafter:D \fp_to_tl_small_one:w \tex_else:D \tex_ifnum:D #2 = -\c_two \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_to_tl_small_two:w \tex_else:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_to_tl_small_aux:w \tex_fi:D \tex_fi:D #1 e #2 \q_stop } \cs_new_nopar:Npn \fp_to_tl_small_one:w #1 . #2 e #3 \q_stop { \tex_ifnum:D \fp_use_ix:NNNNNNNNN #2 > \c_four \tex_ifnum:D \etex_numexpr:D #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1 < \c_one_thousand_million 0. \tex_expandafter:D \fp_to_tl_small_zeros:NNNNNNNNN \tex_number:D \etex_numexpr:D #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1 \scan_stop: \tex_else:D 1 \tex_fi:D \tex_else:D 0. #1 \fp_to_tl_small_zeros:NNNNNNNNN #2 \tex_fi:D } \cs_new_nopar:Npn \fp_to_tl_small_two:w #1 . #2 e #3 \q_stop { \tex_ifnum:D \fp_use_iix_ix:NNNNNNNNN #2 > \c_forty_four \tex_ifnum:D \etex_numexpr:D #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten < \c_one_thousand_million 0.0 \tex_expandafter:D \fp_to_tl_small_zeros:NNNNNNNNN \tex_number:D \etex_numexpr:D #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten \scan_stop: \tex_else:D 0.1 \tex_fi:D \tex_else:D 0.0 #1 \fp_to_tl_small_zeros:NNNNNNNNN #2 \tex_fi:D } \cs_new_nopar:Npn \fp_to_tl_small_aux:w #1 . #2 e #3 \q_stop { #1 \fp_to_tl_large_zeros:NNNNNNNNN #2 e #3 } \cs_new_nopar:Npn \fp_to_tl_large_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \tex_ifnum:D #9 = \c_zero \tex_ifnum:D #8 = \c_zero \tex_ifnum:D #7 = \c_zero \tex_ifnum:D #6 = \c_zero \tex_ifnum:D #5 = \c_zero \tex_ifnum:D #4 = \c_zero \tex_ifnum:D #3 = \c_zero \tex_ifnum:D #2 = \c_zero \tex_ifnum:D #1 = \c_zero \tex_else:D . #1 \tex_fi:D \tex_else:D . #1#2 \tex_fi:D \tex_else:D . #1#2#3 \tex_fi:D \tex_else:D . #1#2#3#4 \tex_fi:D \tex_else:D . #1#2#3#4#5 \tex_fi:D \tex_else:D . #1#2#3#4#5#6 \tex_fi:D \tex_else:D . #1#2#3#4#5#6#7 \tex_fi:D \tex_else:D . #1#2#3#4#5#6#7#8 \tex_fi:D \tex_else:D . #1#2#3#4#5#6#7#8#9 \tex_fi:D } \cs_new_nopar:Npn \fp_to_tl_small_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \tex_ifnum:D #9 = \c_zero \tex_ifnum:D #8 = \c_zero \tex_ifnum:D #7 = \c_zero \tex_ifnum:D #6 = \c_zero \tex_ifnum:D #5 = \c_zero \tex_ifnum:D #4 = \c_zero \tex_ifnum:D #3 = \c_zero \tex_ifnum:D #2 = \c_zero \tex_ifnum:D #1 = \c_zero \tex_else:D #1 \tex_fi:D \tex_else:D #1#2 \tex_fi:D \tex_else:D #1#2#3 \tex_fi:D \tex_else:D #1#2#3#4 \tex_fi:D \tex_else:D #1#2#3#4#5 \tex_fi:D \tex_else:D #1#2#3#4#5#6 \tex_fi:D \tex_else:D #1#2#3#4#5#6#7 \tex_fi:D \tex_else:D #1#2#3#4#5#6#7#8 \tex_fi:D \tex_else:D #1#2#3#4#5#6#7#8#9 \tex_fi:D } \cs_new_nopar:Npn \fp_use_iix_ix:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {#8#9} \cs_new_nopar:Npn \fp_use_ix:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {#9} \cs_new_nopar:Npn \fp_use_i_to_vii:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { #1#2#3#4#5#6#7 } \cs_new_nopar:Npn \fp_use_i_to_iix:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { #1#2#3#4#5#6#7#8 } \cs_new_protected_nopar:Npn \fp_round_figures:Nn { \fp_round_figures_aux:NNn \tl_set:Nn } \cs_generate_variant:Nn \fp_round_figures:Nn { c } \cs_new_protected_nopar:Npn \fp_ground_figures:Nn { \fp_round_figures_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_ground_figures:Nn { c } \cs_new_protected_nopar:Npn \fp_round_figures_aux:NNn #1#2#3 { \group_begin: \fp_read:N #2 \int_set:Nn \l_fp_round_target_int { #3 - 1 } \tex_ifnum:D \l_fp_round_target_int < \c_ten \tex_expandafter:D \fp_round: \tex_fi:D \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 { \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero - \tex_else:D + \tex_fi:D \int_use:N \l_fp_input_a_integer_int . \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int e \int_use:N \l_fp_input_a_exponent_int } } \fp_tmp:w } \cs_new_protected_nopar:Npn \fp_round_places:Nn { \fp_round_places_aux:NNn \tl_set:Nn } \cs_generate_variant:Nn \fp_round_places:Nn { c } \cs_new_protected_nopar:Npn \fp_ground_places:Nn { \fp_round_places_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_ground_places:Nn { c } \cs_new_protected_nopar:Npn \fp_round_places_aux:NNn #1#2#3 { \group_begin: \fp_read:N #2 \int_set:Nn \l_fp_round_target_int { #3 + \l_fp_input_a_exponent_int } \tex_ifnum:D \l_fp_round_target_int < \c_ten \tex_expandafter:D \fp_round: \tex_fi:D \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 { \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero - \tex_else:D + \tex_fi:D \int_use:N \l_fp_input_a_integer_int . \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int e \int_use:N \l_fp_input_a_exponent_int } } \fp_tmp:w } \cs_new_protected_nopar:Npn \fp_round: { \bool_set_false:N \l_fp_round_carry_bool \l_fp_round_position_int \c_eight \tl_clear:N \l_fp_round_decimal_tl \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_round_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int } \cs_new_protected_nopar:Npn \fp_round_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \fp_round_loop:N #9#8#7#6#5#4#3#2#1 \bool_if:NT \l_fp_round_carry_bool { \tex_advance:D \l_fp_input_a_integer_int \c_one } \l_fp_input_a_decimal_int \l_fp_round_decimal_tl \scan_stop: \tex_ifnum:D \l_fp_input_a_integer_int < \c_ten \tex_else:D \l_fp_input_a_integer_int \c_one \tex_divide:D \l_fp_input_a_decimal_int \c_ten \tex_advance:D \l_fp_input_a_exponent_int \c_one \tex_fi:D } \cs_new_protected_nopar:Npn \fp_round_loop:N #1 { \tex_ifnum:D \l_fp_round_position_int < \l_fp_round_target_int \bool_if:NTF \l_fp_round_carry_bool { \l_fp_tmp_int \etex_numexpr:D #1 + \c_one \scan_stop: } { \l_fp_tmp_int \etex_numexpr:D #1 \scan_stop: } \tex_ifnum:D \l_fp_tmp_int = \c_ten \l_fp_tmp_int \c_zero \tex_else:D \bool_set_false:N \l_fp_round_carry_bool \tex_fi:D \tl_set:Nx \l_fp_round_decimal_tl { \int_use:N \l_fp_tmp_int \l_fp_round_decimal_tl } \tex_else:D \tl_set:Nx \l_fp_round_decimal_tl { 0 \l_fp_round_decimal_tl } \tex_ifnum:D \l_fp_round_position_int = \l_fp_round_target_int \tex_ifnum:D #1 > \c_four \bool_set_true:N \l_fp_round_carry_bool \tex_fi:D \tex_fi:D \tex_fi:D \tex_advance:D \l_fp_round_position_int \c_minus_one \tex_ifnum:D \l_fp_round_position_int > \c_minus_one \tex_expandafter:D \fp_round_loop:N \tex_fi:D } \cs_new_protected_nopar:Npn \fp_abs:N { \fp_abs_aux:NN \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gabs:N { \fp_abs_aux:NN \tl_gset:Nn } \cs_generate_variant:Nn \fp_abs:N { c } \cs_generate_variant:Nn \fp_gabs:N { c } \cs_new_protected_nopar:Npn \fp_abs_aux:NN #1#2 { \group_begin: \fp_read:N #2 \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 { + \int_use:N \l_fp_input_a_integer_int . \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int e \int_use:N \l_fp_input_a_exponent_int } } \fp_tmp:w } \cs_new_protected_nopar:Npn \fp_neg:N { \fp_neg_aux:NN \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gneg:N { \fp_neg_aux:NN \tl_gset:Nn } \cs_generate_variant:Nn \fp_neg:N { c } \cs_generate_variant:Nn \fp_gneg:N { c } \cs_new_protected_nopar:Npn \fp_neg_aux:NN #1#2 { \group_begin: \fp_read:N #2 \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \tl_set:Nx \l_fp_tmp_tl { \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero + \tex_else:D - \tex_fi:D \int_use:N \l_fp_input_a_integer_int . \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int e \int_use:N \l_fp_input_a_exponent_int } \tex_expandafter:D \group_end: \tex_expandafter:D #1 \tex_expandafter:D #2 \tex_expandafter:D { \l_fp_tmp_tl } } \cs_new_protected_nopar:Npn \fp_add:Nn { \fp_add_aux:NNn \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gadd:Nn { \fp_add_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_add:Nn { c } \cs_generate_variant:Nn \fp_gadd:Nn { c } \cs_new_protected_nopar:Npn \fp_add_aux:NNn #1#2#3 { \group_begin: \fp_read:N #2 \fp_split:Nn b {#3} \fp_standardise:NNNN \l_fp_input_b_sign_int \l_fp_input_b_integer_int \l_fp_input_b_decimal_int \l_fp_input_b_exponent_int \fp_add_core: \fp_tmp:w #1#2 } \cs_new_protected_nopar:Npn \fp_add_core: { \fp_level_input_exponents: \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_sign_int * \l_fp_input_b_sign_int \scan_stop: > \c_zero \tex_expandafter:D \fp_add_sum: \tex_else:D \tex_expandafter:D \fp_add_difference: \tex_fi:D \l_fp_output_exponent_int \l_fp_input_a_exponent_int \fp_standardise:NNNN \l_fp_output_sign_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_exponent_int \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: ##1 ##2 { \tex_ifnum:D \l_fp_output_sign_int < \c_zero - \tex_else:D + \tex_fi:D \int_use:N \l_fp_output_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million e \int_use:N \l_fp_output_exponent_int } } } \cs_new_protected_nopar:Npn \fp_add_sum: { \l_fp_output_sign_int \l_fp_input_a_sign_int \l_fp_output_integer_int \etex_numexpr:D \l_fp_input_a_integer_int + \l_fp_input_b_integer_int \scan_stop: \l_fp_output_decimal_int \etex_numexpr:D \l_fp_input_a_decimal_int + \l_fp_input_b_decimal_int \scan_stop: \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million \tex_else:D \tex_advance:D \l_fp_output_integer_int \c_one \tex_advance:D \l_fp_output_decimal_int -\c_one_thousand_million \tex_fi:D } \cs_new_protected_nopar:Npn \fp_add_difference: { \l_fp_output_integer_int \etex_numexpr:D \l_fp_input_a_integer_int - \l_fp_input_b_integer_int \scan_stop: \l_fp_output_decimal_int \etex_numexpr:D \l_fp_input_a_decimal_int - \l_fp_input_b_decimal_int \scan_stop: \tex_ifnum:D \l_fp_output_decimal_int < \c_zero \tex_advance:D \l_fp_output_integer_int \c_minus_one \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million \tex_fi:D \tex_ifnum:D \l_fp_output_integer_int < \c_zero \l_fp_output_sign_int \l_fp_input_b_sign_int \tex_ifnum:D \l_fp_output_decimal_int = \c_zero \l_fp_output_integer_int -\l_fp_output_integer_int \tex_else:D \l_fp_output_decimal_int \etex_numexpr:D \c_one_thousand_million - \l_fp_output_decimal_int \scan_stop: \l_fp_output_integer_int \etex_numexpr:D - \l_fp_output_integer_int - \c_one \scan_stop: \tex_fi:D \tex_else:D \l_fp_output_sign_int \l_fp_input_a_sign_int \tex_fi:D } \cs_new_protected_nopar:Npn \fp_sub:Nn { \fp_sub_aux:NNn \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gsub:Nn { \fp_sub_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_sub:Nn { c } \cs_generate_variant:Nn \fp_gsub:Nn { c } \cs_new_protected_nopar:Npn \fp_sub_aux:NNn #1#2#3 { \group_begin: \fp_read:N #2 \fp_split:Nn b {#3} \fp_standardise:NNNN \l_fp_input_b_sign_int \l_fp_input_b_integer_int \l_fp_input_b_decimal_int \l_fp_input_b_exponent_int \tex_multiply:D \l_fp_input_b_sign_int \c_minus_one \fp_add_core: \fp_tmp:w #1#2 } \cs_new_protected_nopar:Npn \fp_mul:Nn { \fp_mul_aux:NNn \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gmul:Nn { \fp_mul_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_mul:Nn { c } \cs_generate_variant:Nn \fp_gmul:Nn { c } \cs_new_protected_nopar:Npn \fp_mul_aux:NNn #1#2#3 { \group_begin: \fp_read:N #2 \fp_split:Nn b {#3} \fp_standardise:NNNN \l_fp_input_b_sign_int \l_fp_input_b_integer_int \l_fp_input_b_decimal_int \l_fp_input_b_exponent_int \fp_mul_internal: \l_fp_output_exponent_int \etex_numexpr:D \l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int \scan_stop: \fp_standardise:NNNN \l_fp_output_sign_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_exponent_int \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 { \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_sign_int * \l_fp_input_b_sign_int < \c_zero \tex_ifnum:D \etex_numexpr:D \l_fp_output_integer_int + \l_fp_output_decimal_int = \c_zero + \tex_else:D - \tex_fi:D \tex_else:D + \tex_fi:D \int_use:N \l_fp_output_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million e \int_use:N \l_fp_output_exponent_int } } \fp_tmp:w } \cs_new_protected_nopar:Npn \fp_mul_internal: { \fp_mul_split:NNNN \l_fp_input_a_decimal_int \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int \fp_mul_split:NNNN \l_fp_input_b_decimal_int \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int \l_fp_mul_output_int \c_zero \tl_clear:N \l_fp_mul_output_tl \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iii_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_i_int \tex_divide:D \l_fp_mul_output_int \c_one_thousand \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_iii_int \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_i_int \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_input_b_integer_int \fp_mul_end_level: \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_i_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_input_b_integer_int \fp_mul_end_level: \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_mul_b_i_int \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_input_b_integer_int \fp_mul_end_level: \l_fp_output_decimal_int 0 \l_fp_mul_output_tl \scan_stop: \tl_clear:N \l_fp_mul_output_tl \fp_mul_product:NN \l_fp_input_a_integer_int \l_fp_input_b_integer_int \fp_mul_end_level: \l_fp_output_integer_int 0 \l_fp_mul_output_tl \scan_stop: } \cs_new_protected_nopar:Npn \fp_mul_split:NNNN #1#2#3#4 { \tex_advance:D #1 \c_one_thousand_million \cs_set_protected_nopar:Npn \fp_mul_split_aux:w ##1##2##3##4##5##6##7##8##9 \q_stop { #2 ##2##3##4 \scan_stop: #3 ##5##6##7 \scan_stop: #4 ##8##9 \scan_stop: } \tex_expandafter:D \fp_mul_split_aux:w \int_use:N #1 \q_stop \tex_advance:D #1 -\c_one_thousand_million } \cs_new_protected_nopar:Npn \fp_mul_product:NN #1#2 { \l_fp_mul_output_int \etex_numexpr:D \l_fp_mul_output_int + #1 * #2 \scan_stop: } \cs_new_protected_nopar:Npn \fp_mul_end_level: { \tex_advance:D \l_fp_mul_output_int \c_one_thousand_million \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_mul_end_level:NNNNNNNNN \int_use:N \l_fp_mul_output_int } \cs_new_protected_nopar:Npn \fp_mul_end_level:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \tl_set:Nx \l_fp_mul_output_tl { #7#8#9 \l_fp_mul_output_tl } \l_fp_mul_output_int #1#2#3#4#5#6 \scan_stop: } \cs_new_protected_nopar:Npn \fp_div:Nn { \fp_div_aux:NNn \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gdiv:Nn { \fp_div_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_div:Nn { c } \cs_generate_variant:Nn \fp_gdiv:Nn { c } \cs_new_protected_nopar:Npn \fp_div_aux:NNn #1#2#3 { \group_begin: \fp_read:N #2 \fp_split:Nn b {#3} \fp_standardise:NNNN \l_fp_input_b_sign_int \l_fp_input_b_integer_int \l_fp_input_b_decimal_int \l_fp_input_b_exponent_int \tex_ifnum:D \etex_numexpr:D \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int = \c_zero \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: #1 \exp_not:N #2 { \c_undefined_fp } } \tex_else:D \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int = \c_zero \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: #1 \exp_not:N #2 { \c_zero_fp } } \tex_else:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_div_internal: \tex_fi:D \tex_fi:D \fp_tmp:w #1#2 } \cs_new_protected_nopar:Npn \fp_div_internal: { \l_fp_output_integer_int \c_zero \l_fp_output_decimal_int \c_zero \cs_set_eq:NN \fp_div_store: \fp_div_store_integer: \l_fp_div_offset_int \c_one_hundred_million \fp_div_loop: \l_fp_output_exponent_int \etex_numexpr:D \l_fp_input_a_exponent_int - \l_fp_input_b_exponent_int \scan_stop: \fp_standardise:NNNN \l_fp_output_sign_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_exponent_int \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: ##1 ##2 { \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_sign_int * \l_fp_input_b_sign_int < \c_zero \tex_ifnum:D \etex_numexpr:D \l_fp_output_integer_int + \l_fp_output_decimal_int = \c_zero + \tex_else:D - \tex_fi:D \tex_else:D + \tex_fi:D \int_use:N \l_fp_output_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million \scan_stop: e \int_use:N \l_fp_output_exponent_int } } } \cs_new_protected_nopar:Npn \fp_div_loop: { \l_fp_count_int \c_zero \fp_div_divide: \fp_div_store: \tex_multiply:D \l_fp_input_a_integer_int \c_ten \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \tex_expandafter:D \fp_div_loop_step:w \int_use:N \l_fp_input_a_decimal_int \q_stop \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int > \c_zero \tex_ifnum:D \l_fp_div_offset_int > \c_zero \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_div_loop: \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_div_divide: { \tex_ifnum:D \l_fp_input_a_integer_int > \l_fp_input_b_integer_int \tex_expandafter:D \fp_div_divide_aux: \tex_else:D \tex_ifnum:D \l_fp_input_a_integer_int < \l_fp_input_b_integer_int \tex_else:D \tex_ifnum:D \l_fp_input_a_decimal_int < \l_fp_input_b_decimal_int \tex_else:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_div_divide_aux: \tex_fi:D \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_div_divide_aux: { \tex_advance:D \l_fp_count_int \c_one \tex_advance:D \l_fp_input_a_integer_int -\l_fp_input_b_integer_int \tex_advance:D \l_fp_input_a_decimal_int -\l_fp_input_b_decimal_int \tex_ifnum:D \l_fp_input_a_decimal_int < \c_zero \tex_advance:D \l_fp_input_a_integer_int \c_minus_one \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \tex_fi:D \fp_div_divide: } \cs_new_protected_nopar:Npn \fp_div_store: { } \cs_new_protected_nopar:Npn \fp_div_store_integer: { \l_fp_output_integer_int \l_fp_count_int \cs_set_eq:NN \fp_div_store: \fp_div_store_decimal: } \cs_new_protected_nopar:Npn \fp_div_store_decimal: { \l_fp_output_decimal_int \etex_numexpr:D \l_fp_output_decimal_int + \l_fp_count_int * \l_fp_div_offset_int \scan_stop: \tex_divide:D \l_fp_div_offset_int \c_ten } \cs_new_protected_nopar:Npn \fp_div_loop_step:w #1#2#3#4#5#6#7#8#9 \q_stop { \l_fp_input_a_integer_int \etex_numexpr:D #2 + \l_fp_input_a_integer_int \scan_stop: \l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop: } \cs_new_protected_nopar:Npn \fp_add:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { #7 \etex_numexpr:D #1 + #4 \scan_stop: #8 \etex_numexpr:D #2 + #5 \scan_stop: #9 \etex_numexpr:D #3 + #6 \scan_stop: \tex_ifnum:D #9 < \c_one_thousand_million \tex_else:D \tex_advance:D #8 \c_one \tex_advance:D #9 -\c_one_thousand_million \tex_fi:D \tex_ifnum:D #8 < \c_one_thousand_million \tex_else:D \tex_advance:D #7 \c_one \tex_advance:D #8 -\c_one_thousand_million \tex_fi:D } \cs_new_protected_nopar:Npn \fp_sub:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { #7 \etex_numexpr:D #1 - #4 \scan_stop: #8 \etex_numexpr:D #2 - #5 \scan_stop: #9 \etex_numexpr:D #3 - #6 \scan_stop: \tex_ifnum:D #9 < \c_zero \tex_advance:D #8 \c_minus_one \tex_advance:D #9 \c_one_thousand_million \tex_fi:D \tex_ifnum:D #8 < \c_zero \tex_advance:D #7 \c_minus_one \tex_advance:D #8 \c_one_thousand_million \tex_fi:D \tex_ifnum:D #7 < \c_zero \tex_ifnum:D \etex_numexpr:D #8 + #9 = \c_zero #7 -#7 \tex_else:D \tex_advance:D #7 \c_one #8 \etex_numexpr:D \c_one_thousand_million - #8 \scan_stop: #9 \etex_numexpr:D \c_one_thousand_million - #9 \scan_stop: \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_mul:NNNNNN #1#2#3#4#5#6 { \fp_mul_split:NNNN #1 \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int \fp_mul_split:NNNN #2 \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int \fp_mul_split:NNNN #3 \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int \fp_mul_split:NNNN #4 \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int \l_fp_mul_output_int \c_zero \tl_clear:N \l_fp_mul_output_tl \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_vi_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_v_int \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iv_int \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_iii_int \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_i_int \tex_divide:D \l_fp_mul_output_int \c_one_thousand \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_v_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iv_int \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iii_int \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_i_int \fp_mul_end_level: \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iv_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iii_int \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_i_int \fp_mul_end_level: \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iii_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_i_int \fp_mul_end_level: #6 0 \l_fp_mul_output_tl \scan_stop: \tl_clear:N \l_fp_mul_output_tl \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_i_int \fp_mul_end_level: \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_i_int \fp_mul_end_level: \fp_mul_end_level: #5 0 \l_fp_mul_output_tl \scan_stop: } \cs_new_protected_nopar:Npn \fp_mul:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \fp_mul_split:NNNN #2 \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int \fp_mul_split:NNNN #3 \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int \fp_mul_split:NNNN #5 \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int \fp_mul_split:NNNN #6 \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int \l_fp_mul_output_int \c_zero \tl_clear:N \l_fp_mul_output_tl \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_vi_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_v_int \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iv_int \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_iii_int \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_i_int \tex_divide:D \l_fp_mul_output_int \c_one_thousand \fp_mul_product:NN #1 \l_fp_mul_b_vi_int \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_v_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iv_int \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iii_int \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_i_int \fp_mul_product:NN \l_fp_mul_a_vi_int #4 \fp_mul_end_level: \fp_mul_product:NN #1 \l_fp_mul_b_v_int \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iv_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iii_int \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_i_int \fp_mul_product:NN \l_fp_mul_a_v_int #4 \fp_mul_end_level: \fp_mul_product:NN #1 \l_fp_mul_b_iv_int \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iii_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_i_int \fp_mul_product:NN \l_fp_mul_a_iv_int #4 \fp_mul_end_level: #9 0 \l_fp_mul_output_tl \scan_stop: \tl_clear:N \l_fp_mul_output_tl \fp_mul_product:NN #1 \l_fp_mul_b_iii_int \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_i_int \fp_mul_product:NN \l_fp_mul_a_iii_int #4 \fp_mul_end_level: \fp_mul_product:NN #1 \l_fp_mul_b_ii_int \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_i_int \fp_mul_product:NN \l_fp_mul_a_ii_int #4 \fp_mul_end_level: \fp_mul_product:NN #1 \l_fp_mul_b_i_int \fp_mul_product:NN \l_fp_mul_a_i_int #4 \fp_mul_end_level: #8 0 \l_fp_mul_output_tl \scan_stop: \tl_clear:N \l_fp_mul_output_tl \fp_mul_product:NN #1 #4 \fp_mul_end_level: #7 0 \l_fp_mul_output_tl \scan_stop: } \cs_new_protected_nopar:Npn \fp_div_integer:NNNNN #1#2#3#4#5 { \l_fp_tmp_int #1 \tex_divide:D \l_fp_tmp_int #3 \l_fp_tmp_int \etex_numexpr:D #1 - \l_fp_tmp_int * #3 \scan_stop: #4 #1 \tex_divide:D #4 #3 #5 #2 \tex_divide:D #5 #3 \tex_multiply:D \l_fp_tmp_int \c_one_thousand \tex_divide:D \l_fp_tmp_int #3 #5 \etex_numexpr:D #5 + \l_fp_tmp_int * \c_one_million \scan_stop: \tex_ifnum:D #5 > \c_one_thousand_million \tex_advance:D #4 \c_one \tex_advancd:D #5 -\c_one_thousand_million \tex_fi:D } \cs_new_protected_nopar:Npn \fp_extended_normalise: { \fp_extended_normalise_aux_i: \fp_extended_normalise_aux_ii: } \cs_new_protected_nopar:Npn \fp_extended_normalise_aux_i: { \tex_ifnum:D \l_fp_input_a_exponent_int > \c_zero \tex_multiply:D \l_fp_input_a_integer_int \c_ten \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \tex_expandafter:D \fp_extended_normalise_aux_i:w \int_use:N \l_fp_input_a_decimal_int \q_stop \tex_expandafter:D \fp_extended_normalise_aux_i: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_extended_normalise_aux_i:w #1#2#3#4#5#6#7#8#9 \q_stop { \l_fp_input_a_integer_int \etex_numexpr:D \l_fp_input_a_integer_int + #2 \scan_stop: \l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop: \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million \tex_expandafter:D \fp_extended_normalise_aux_ii:w \int_use:N \l_fp_input_a_extended_int \q_stop } \cs_new_protected_nopar:Npn \fp_extended_normalise_aux_ii:w #1#2#3#4#5#6#7#8#9 \q_stop { \l_fp_input_a_decimal_int \etex_numexpr:D \l_fp_input_a_decimal_int + #2 \scan_stop: \l_fp_input_a_extended_int #3#4#5#6#7#8#9 0 \scan_stop: \tex_advance:D \l_fp_input_a_exponent_int \c_minus_one } \cs_new_protected_nopar:Npn \fp_extended_normalise_aux_ii: { \tex_ifnum:D \l_fp_input_a_exponent_int < \c_zero \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_extended_normalise_ii_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int \tex_expandafter:D \fp_extended_normalise_aux_ii: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_extended_normalise_ii_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \tex_ifnum:D \l_fp_input_a_integer_int = \c_zero \l_fp_input_a_decimal_int #1#2#3#4#5#6#7#8 \scan_stop: \tex_else:D \tl_set:Nx \l_fp_tmp_tl { \int_use:N \l_fp_input_a_integer_int #1#2#3#4#5#6#7#8 } \l_fp_input_a_integer_int \c_zero \l_fp_input_a_decimal_int \l_fp_tmp_tl \scan_stop: \tex_fi:D \tex_divide:D \l_fp_input_a_extended_int \c_ten \tl_set:Nx \l_fp_tmp_tl { #9 \int_use:N \l_fp_input_a_extended_int } \l_fp_input_a_extended_int \l_fp_tmp_tl \scan_stop: \tex_advance:D \l_fp_input_a_exponent_int \c_one } \cs_new_protected_nopar:Npn \fp_extended_normalise_output: { \tex_ifnum:D \l_fp_output_integer_int > \c_nine \tex_advance:D \l_fp_output_integer_int \c_one_thousand_million \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_extended_normalise_output_aux_i:NNNNNNNNN \int_use:N \l_fp_output_integer_int \tex_expandafter:D \fp_extended_normalise_output: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_extended_normalise_output_aux_i:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \l_fp_output_integer_int #1#2#3#4#5#6#7#8 \scan_stop: \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million \tl_set:Nx \l_fp_tmp_tl { #9 \tex_expandafter:D \use_none:n \int_use:N \l_fp_output_decimal_int } \tex_expandafter:D \fp_extended_normalise_output_aux_ii:NNNNNNNNN \l_fp_tmp_tl } \cs_new_protected_nopar:Npn \fp_extended_normalise_output_aux_ii:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \l_fp_output_decimal_int #1#2#3#4#5#6#7#8#9 \scan_stop: \fp_extended_normalise_output_aux:N } \cs_new_protected_nopar:Npn \fp_extended_normalise_output_aux:N #1 { \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million \tex_divide:D \l_fp_output_extended_int \c_ten \tl_set:Nx \l_fp_tmp_tl { #1 \tex_expandafter:D \use_none:n \int_use:N \l_fp_output_extended_int } \l_fp_output_extended_int \l_fp_tmp_tl \scan_stop: \tex_advance:D \l_fp_output_exponent_int \c_one } \cs_new_protected_nopar:Npn \fp_trig_normalise: { \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten \l_fp_input_a_extended_int \c_zero \fp_extended_normalise: \fp_trig_normalise_aux: \tex_ifnum:D \l_fp_input_a_integer_int < \c_zero \l_fp_input_a_sign_int -\l_fp_input_a_sign_int \l_fp_input_a_integer_int -\l_fp_input_a_integer_int \tex_fi:D \tex_expandafter:D \fp_trig_octant: \tex_else:D \l_fp_input_a_sign_int \c_one \l_fp_output_integer_int \c_zero \l_fp_output_decimal_int \c_zero \l_fp_output_exponent_int \c_zero \tex_expandafter:D \fp_trig_overflow_msg: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_trig_normalise_aux: { \tex_ifnum:D \l_fp_input_a_integer_int > \c_three \fp_trig_sub:NNN \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int \tex_expandafter:D \fp_trig_normalise_aux: \tex_else:D \tex_ifnum:D \l_fp_input_a_integer_int > \c_two \tex_ifnum:D \l_fp_input_a_decimal_int > \c_fp_pi_decimal_int \fp_trig_sub:NNN \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_trig_normalise_aux: \tex_fi:D \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_trig_sub:NNN #1#2#3 { \l_fp_input_a_integer_int \etex_numexpr:D \l_fp_input_a_integer_int - #1 \scan_stop: \l_fp_input_a_decimal_int \etex_numexpr:D \l_fp_input_a_decimal_int - #2 \scan_stop: \l_fp_input_a_extended_int \etex_numexpr:D \l_fp_input_a_extended_int - #3 \scan_stop: \tex_ifnum:D \l_fp_input_a_extended_int < \c_zero \tex_advance:D \l_fp_input_a_decimal_int \c_minus_one \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million \tex_fi:D \tex_ifnum:D \l_fp_input_a_decimal_int < \c_zero \tex_advance:D \l_fp_input_a_integer_int \c_minus_one \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \tex_fi:D \tex_ifnum:D \l_fp_input_a_integer_int < \c_zero \l_fp_input_a_sign_int -\l_fp_input_a_sign_int \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int = \c_zero \l_fp_input_a_integer_int -\l_fp_input_a_integer_int \tex_else:D \l_fp_input_a_integer_int \etex_numexpr:D - \l_fp_input_a_integer_int - \c_one \scan_stop: \l_fp_input_a_decimal_int \etex_numexpr:D \c_one_thousand_million - \l_fp_input_a_decimal_int \scan_stop: \l_fp_input_a_extended_int \etex_numexpr:D \c_one_thousand_million - \l_fp_input_a_extended_int \scan_stop: \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_trig_octant: { \l_fp_trig_octant_int \c_one \fp_trig_octant_aux: \tex_ifnum:D \l_fp_input_a_decimal_int < \c_ten \l_fp_input_a_decimal_int \c_zero \l_fp_input_a_extended_int \c_zero \tex_fi:D \tex_ifodd:D \l_fp_trig_octant_int \tex_else:D \fp_sub:NNNNNNNNN \c_zero \c_fp_pi_by_four_decimal_int \c_fp_pi_by_four_extended_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \tex_fi:D } \cs_new_protected_nopar:Npn \fp_trig_octant_aux: { \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero \fp_sub:NNNNNNNNN \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \c_zero \c_fp_pi_by_four_decimal_int \c_fp_pi_by_four_extended_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \tex_advance:D \l_fp_trig_octant_int \c_one \tex_expandafter:D \fp_trig_octant_aux: \tex_else:D \tex_ifnum:D \l_fp_input_a_decimal_int > \c_fp_pi_by_four_decimal_int \fp_sub:NNNNNNNNN \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \c_zero \c_fp_pi_by_four_decimal_int \c_fp_pi_by_four_extended_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \tex_advance:D \l_fp_trig_octant_int \c_one \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_trig_octant_aux: \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_sin:Nn { \fp_sin_aux:NNn \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gsin:Nn { \fp_sin_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_sin:Nn { c } \cs_generate_variant:Nn \fp_gsin:Nn { c } \cs_new_protected_nopar:Npn \fp_sin_aux:NNn #1#2#3 { \group_begin: \fp_split:Nn a {#3} \fp_standardise:NNNN \l_fp_input_a_sign_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int \tl_set:Nx \l_fp_arg_tl { \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero - \tex_else:D + \tex_fi:D \int_use:N \l_fp_input_a_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_input_a_decimal_int + \c_one_thousand_million e \int_use:N \l_fp_input_a_exponent_int } \tex_ifnum:D \l_fp_input_a_exponent_int < -\c_five \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 { \l_fp_arg_tl } } \tex_else:D \etex_ifcsname:D c_fp_sin ( \l_fp_arg_tl ) _fp \tex_endcsname:D \tex_else:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_sin_aux_i: \tex_fi:D \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 { \use:c { c_fp_sin ( \l_fp_arg_tl ) _fp } } } \tex_fi:D \fp_tmp:w } \cs_new_protected_nopar:Npn \fp_sin_aux_i: { \fp_trig_normalise: \fp_sin_aux_ii: \tex_ifnum:D \l_fp_output_integer_int = \c_one \l_fp_output_exponent_int \c_zero \tex_else:D \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_decimal_int \l_fp_output_extended_int \l_fp_output_exponent_int -\c_nine \tex_fi:D \fp_standardise:NNNN \l_fp_input_a_sign_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_exponent_int \tl_new:c { c_fp_sin ( \l_fp_arg_tl ) _fp } \tl_gset:cx { c_fp_sin ( \l_fp_arg_tl ) _fp } { \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero + \tex_else:D - \tex_fi:D \int_use:N \l_fp_output_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million \scan_stop: e \int_use:N \l_fp_output_exponent_int } } \cs_new_protected_nopar:Npn \fp_sin_aux_ii: { \tex_ifcase:D \l_fp_trig_octant_int \tex_or:D \tex_expandafter:D \fp_trig_calc_sin: \tex_or:D \tex_expandafter:D \fp_trig_calc_cos: \tex_or:D \tex_expandafter:D \fp_trig_calc_cos: \tex_or:D \tex_expandafter:D \fp_trig_calc_sin: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_cos:Nn { \fp_cos_aux:NNn \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gcos:Nn { \fp_cos_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_cos:Nn { c } \cs_generate_variant:Nn \fp_gcos:Nn { c } \cs_new_protected_nopar:Npn \fp_cos_aux:NNn #1#2#3 { \group_begin: \fp_split:Nn a {#3} \fp_standardise:NNNN \l_fp_input_a_sign_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int \tl_set:Nx \l_fp_arg_tl { \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero - \tex_else:D + \tex_fi:D \int_use:N \l_fp_input_a_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_input_a_decimal_int + \c_one_thousand_million e \int_use:N \l_fp_input_a_exponent_int } \etex_ifcsname:D c_fp_cos ( \l_fp_arg_tl ) _fp \tex_endcsname:D \tex_else:D \tex_expandafter:D \fp_cos_aux_i: \tex_fi:D \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 { \use:c { c_fp_cos ( \l_fp_arg_tl ) _fp } } } \fp_tmp:w } \cs_new_protected_nopar:Npn \fp_cos_aux_i: { \fp_trig_normalise: \fp_cos_aux_ii: \tex_ifnum:D \l_fp_output_integer_int = \c_one \l_fp_output_exponent_int \c_zero \tex_else:D \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_decimal_int \l_fp_output_extended_int \l_fp_output_exponent_int -\c_nine \tex_fi:D \fp_standardise:NNNN \l_fp_input_a_sign_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_exponent_int \tl_new:c { c_fp_cos ( \l_fp_arg_tl ) _fp } \tl_gset:cx { c_fp_cos ( \l_fp_arg_tl ) _fp } { \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero + \tex_else:D - \tex_fi:D \int_use:N \l_fp_output_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million \scan_stop: e \int_use:N \l_fp_output_exponent_int } } \cs_new_protected_nopar:Npn \fp_cos_aux_ii: { \tex_ifcase:D \l_fp_trig_octant_int \tex_or:D \tex_expandafter:D \fp_trig_calc_cos: \tex_or:D \tex_expandafter:D \fp_trig_calc_sin: \tex_or:D \tex_expandafter:D \fp_trig_calc_sin: \tex_or:D \tex_expandafter:D \fp_trig_calc_cos: \tex_fi:D \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero \tex_ifnum:D \l_fp_trig_octant_int > \c_two \l_fp_input_a_sign_int \c_minus_one \tex_fi:D \tex_else:D \tex_ifnum:D \l_fp_trig_octant_int > \c_two \tex_else:D \l_fp_input_a_sign_int \c_one \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_trig_calc_cos: { \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero \l_fp_output_integer_int \c_one \l_fp_output_decimal_int \c_zero \tex_else:D \l_fp_trig_sign_int \c_minus_one \fp_mul:NNNNNN \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \l_fp_trig_decimal_int \l_fp_trig_extended_int \fp_div_integer:NNNNN \l_fp_trig_decimal_int \l_fp_trig_extended_int \c_two \l_fp_trig_decimal_int \l_fp_trig_extended_int \l_fp_count_int \c_three \tex_ifnum:D \l_fp_trig_extended_int = \c_zero \tex_ifnum:D \l_fp_trig_decimal_int = \c_zero \l_fp_output_integer_int \c_one \l_fp_output_decimal_int \c_zero \l_fp_output_extended_int \c_zero \tex_else:D \l_fp_output_integer_int \c_zero \l_fp_output_decimal_int \c_one_thousand_million \l_fp_output_extended_int \c_zero \tex_fi:D \tex_else:D \l_fp_output_integer_int \c_zero \l_fp_output_decimal_int 999999999 \scan_stop: \l_fp_output_extended_int \c_one_thousand_million \tex_fi:D \tex_advance:D \l_fp_output_extended_int -\l_fp_trig_extended_int \tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int \tex_expandafter:D \fp_trig_calc_Taylor: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_trig_calc_sin: { \l_fp_output_integer_int \c_zero \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero \l_fp_output_decimal_int \c_zero \tex_else:D \l_fp_output_decimal_int \l_fp_input_a_decimal_int \l_fp_output_extended_int \l_fp_input_a_extended_int \l_fp_trig_sign_int \c_one \l_fp_trig_decimal_int \l_fp_input_a_decimal_int \l_fp_trig_extended_int \l_fp_input_a_extended_int \l_fp_count_int \c_two \tex_expandafter:D \fp_trig_calc_Taylor: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_trig_calc_Taylor: { \l_fp_trig_sign_int -\l_fp_trig_sign_int \fp_mul:NNNNNN \l_fp_trig_decimal_int \l_fp_trig_extended_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \l_fp_trig_decimal_int \l_fp_trig_extended_int \fp_mul:NNNNNN \l_fp_trig_decimal_int \l_fp_trig_extended_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \l_fp_trig_decimal_int \l_fp_trig_extended_int \fp_div_integer:NNNNN \l_fp_trig_decimal_int \l_fp_trig_extended_int \l_fp_count_int \l_fp_trig_decimal_int \l_fp_trig_extended_int \tex_advance:D \l_fp_count_int \c_one \fp_div_integer:NNNNN \l_fp_trig_decimal_int \l_fp_trig_extended_int \l_fp_count_int \l_fp_trig_decimal_int \l_fp_trig_extended_int \tex_advance:D \l_fp_count_int \c_one \tex_ifnum:D \l_fp_trig_decimal_int > \c_zero \tex_ifnum:D \l_fp_trig_sign_int > \c_zero \tex_advance:D \l_fp_output_decimal_int \l_fp_trig_decimal_int \tex_advance:D \l_fp_output_extended_int \l_fp_trig_extended_int \tex_ifnum:D \l_fp_output_extended_int < \c_one_thousand_million \tex_else:D \tex_advance:D \l_fp_output_decimal_int \c_one \tex_advance:D \l_fp_output_extended_int -\c_one_thousand_million \tex_fi:D \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million \tex_else:D \tex_advance:D \l_fp_output_integer_int \c_one \tex_advance:D \l_fp_output_decimal_int -\c_one_thousand_million \tex_fi:D \tex_else:D \tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int \tex_advance:D \l_fp_output_extended_int -\l_fp_input_a_extended_int \tex_ifnum:D \l_fp_output_extended_int < \c_zero \tex_advance:D \l_fp_output_decimal_int \c_minus_one \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million \tex_fi:D \tex_ifnum:D \l_fp_output_decimal_int < \c_zero \tex_advance:D \l_fp_output_integer_int \c_minus_one \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million \tex_fi:D \tex_fi:D \tex_expandafter:D \fp_trig_calc_Taylor: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_tan:Nn { \fp_tan_aux:NNn \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gtan:Nn { \fp_tan_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_tan:Nn { c } \cs_generate_variant:Nn \fp_gtan:Nn { c } \cs_new_protected_nopar:Npn \fp_tan_aux:NNn #1#2#3 { \group_begin: \fp_split:Nn a {#3} \fp_standardise:NNNN \l_fp_input_a_sign_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int \tl_set:Nx \l_fp_arg_tl { \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero - \tex_else:D + \tex_fi:D \int_use:N \l_fp_input_a_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_input_a_decimal_int + \c_one_thousand_million e \int_use:N \l_fp_input_a_exponent_int } \tex_ifnum:D \l_fp_input_a_exponent_int < -\c_five \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 { \l_fp_arg_tl } } \tex_else:D \etex_ifcsname:D c_fp_tan ( \l_fp_arg_tl ) _fp \tex_endcsname:D \tex_else:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_tan_aux_i: \tex_fi:D \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 { \use:c { c_fp_tan ( \l_fp_arg_tl ) _fp } } } \tex_fi:D \fp_tmp:w } \cs_new_protected_nopar:Npn \fp_tan_aux_i: { \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten \tex_expandafter:D \fp_tan_aux_ii: \tex_else:D \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp } \c_zero_fp \tex_expandafter:D \fp_trig_overflow_msg: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_tan_aux_ii: { \fp_trig_normalise: \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero \tex_ifnum:D \l_fp_trig_octant_int > \c_two \l_fp_output_sign_int \c_minus_one \tex_else:D \l_fp_output_sign_int \c_one \tex_fi:D \tex_else:D \tex_ifnum:D \l_fp_trig_octant_int > \c_two \l_fp_output_sign_int \c_one \tex_else:D \l_fp_output_sign_int \c_minus_one \tex_fi:D \tex_fi:D \fp_cos_aux_ii: \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero \tex_ifnum:D \l_fp_input_a_integer_int = \c_zero \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp } \c_undefined_fp \tex_else:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_tan_aux_iii: \tex_fi:D \tex_else:D \tex_expandafter:D \fp_tan_aux_iii: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_tan_aux_iii: { \l_fp_input_b_integer_int \l_fp_output_decimal_int \l_fp_input_b_decimal_int \l_fp_output_extended_int \l_fp_input_b_exponent_int -\c_nine \fp_standardise:NNNN \l_fp_input_b_sign_int \l_fp_input_b_integer_int \l_fp_input_b_decimal_int \l_fp_input_b_exponent_int \fp_sin_aux_ii: \l_fp_input_a_integer_int \l_fp_output_decimal_int \l_fp_input_a_decimal_int \l_fp_output_extended_int \l_fp_input_a_exponent_int -\c_nine \fp_standardise:NNNN \l_fp_input_a_sign_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero \tex_ifnum:D \l_fp_input_a_integer_int = \c_zero \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp } \c_zero_fp \tex_else:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_tan_aux_iv: \tex_fi:D \tex_else:D \tex_expandafter:D \fp_tan_aux_iv: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_tan_aux_iv: { \l_fp_output_integer_int \c_zero \l_fp_output_decimal_int \c_zero \cs_set_eq:NN \fp_div_store: \fp_div_store_integer: \l_fp_div_offset_int \c_one_hundred_million \fp_div_loop: \l_fp_output_exponent_int \etex_numexpr:D \l_fp_input_a_exponent_int - \l_fp_input_b_exponent_int \scan_stop: \fp_standardise:NNNN \l_fp_output_sign_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_exponent_int \tl_new:c { c_fp_tan ( \l_fp_arg_tl ) _fp } \tl_gset:cx { c_fp_tan ( \l_fp_arg_tl ) _fp } { \tex_ifnum:D \l_fp_output_sign_int > \c_zero + \tex_else:D - \tex_fi:D \int_use:N \l_fp_output_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million \scan_stop: e \int_use:N \l_fp_output_exponent_int } } \tl_new:c { c_fp_exp_1_tl } \tl_set:cn { c_fp_exp_1_tl } { { 2 } { 718281828 } { 459045235 } { 0 } } \tl_new:c { c_fp_exp_2_tl } \tl_set:cn { c_fp_exp_2_tl } { { 7 } { 389056098 } { 930650227 } { 0 } } \tl_new:c { c_fp_exp_3_tl } \tl_set:cn { c_fp_exp_3_tl } { { 2 } { 008553692 } { 318766774 } { 1 } } \tl_new:c { c_fp_exp_4_tl } \tl_set:cn { c_fp_exp_4_tl } { { 5 } { 459815003 } { 314423908 } { 1 } } \tl_new:c { c_fp_exp_5_tl } \tl_set:cn { c_fp_exp_5_tl } { { 1 } { 484131591 } { 025766034 } { 2 } } \tl_new:c { c_fp_exp_6_tl } \tl_set:cn { c_fp_exp_6_tl } { { 4 } { 034287934 } { 927351226 } { 2 } } \tl_new:c { c_fp_exp_7_tl } \tl_set:cn { c_fp_exp_7_tl } { { 1 } { 096633158 } { 428458599 } { 3 } } \tl_new:c { c_fp_exp_8_tl } \tl_set:cn { c_fp_exp_8_tl } { { 2 } { 980957987 } { 041728275 } { 3 } } \tl_new:c { c_fp_exp_9_tl } \tl_set:cn { c_fp_exp_9_tl } { { 8 } { 103083927 } { 575384008 } { 3 } } \tl_new:c { c_fp_exp_10_tl } \tl_set:cn { c_fp_exp_10_tl } { { 2 } { 202646579 } { 480671652 } { 4 } } \tl_new:c { c_fp_exp_20_tl } \tl_set:cn { c_fp_exp_20_tl } { { 4 } { 851651954 } { 097902280 } { 8 } } \tl_new:c { c_fp_exp_30_tl } \tl_set:cn { c_fp_exp_30_tl } { { 1 } { 068647458 } { 152446215 } { 13 } } \tl_new:c { c_fp_exp_40_tl } \tl_set:cn { c_fp_exp_40_tl } { { 2 } { 353852668 } { 370199854 } { 17 } } \tl_new:c { c_fp_exp_50_tl } \tl_set:cn { c_fp_exp_50_tl } { { 5 } { 184705528 } { 587072464 } { 21 } } \tl_new:c { c_fp_exp_60_tl } \tl_set:cn { c_fp_exp_60_tl } { { 1 } { 142007389 } { 815684284 } { 26 } } \tl_new:c { c_fp_exp_70_tl } \tl_set:cn { c_fp_exp_70_tl } { { 2 } { 515438670 } { 919167006 } { 30 } } \tl_new:c { c_fp_exp_80_tl } \tl_set:cn { c_fp_exp_80_tl } { { 5 } { 540622384 } { 393510053 } { 34 } } \tl_new:c { c_fp_exp_90_tl } \tl_set:cn { c_fp_exp_90_tl } { { 1 } { 220403294 } { 317840802 } { 39 } } \tl_new:c { c_fp_exp_100_tl } \tl_set:cn { c_fp_exp_100_tl } { { 2 } { 688117141 } { 816135448 } { 43 } } \tl_new:c { c_fp_exp_200_tl } \tl_set:cn { c_fp_exp_200_tl } { { 7 } { 225973768 } { 125749258 } { 86 } } \tl_new:c { c_fp_exp_-1_tl } \tl_set:cn { c_fp_exp_-1_tl } { { 3 } { 678794411 } { 71442322 } { -1 } } \tl_new:c { c_fp_exp_-2_tl } \tl_set:cn { c_fp_exp_-2_tl } { { 1 } { 353352832 } { 366132692 } { -1 } } \tl_new:c { c_fp_exp_-3_tl } \tl_set:cn { c_fp_exp_-3_tl } { { 4 } { 978706836 } { 786394298 } { -2 } } \tl_new:c { c_fp_exp_-4_tl } \tl_set:cn { c_fp_exp_-4_tl } { { 1 } { 831563888 } { 873418029 } { -2 } } \tl_new:c { c_fp_exp_-5_tl } \tl_set:cn { c_fp_exp_-5_tl } { { 6 } { 737946999 } { 085467097 } { -3 } } \tl_new:c { c_fp_exp_-6_tl } \tl_set:cn { c_fp_exp_-6_tl } { { 2 } { 478752176 } { 666358423 } { -3 } } \tl_new:c { c_fp_exp_-7_tl } \tl_set:cn { c_fp_exp_-7_tl } { { 9 } { 118819655 } { 545162080 } { -4 } } \tl_new:c { c_fp_exp_-8_tl } \tl_set:cn { c_fp_exp_-8_tl } { { 3 } { 354626279 } { 025118388 } { -4 } } \tl_new:c { c_fp_exp_-9_tl } \tl_set:cn { c_fp_exp_-9_tl } { { 1 } { 234098040 } { 866795495 } { -4 } } \tl_new:c { c_fp_exp_-10_tl } \tl_set:cn { c_fp_exp_-10_tl } { { 4 } { 539992976 } { 248451536 } { -5 } } \tl_new:c { c_fp_exp_-20_tl } \tl_set:cn { c_fp_exp_-20_tl } { { 2 } { 061153622 } { 438557828 } { -9 } } \tl_new:c { c_fp_exp_-30_tl } \tl_set:cn { c_fp_exp_-30_tl } { { 9 } { 357622968 } { 840174605 } { -14 } } \tl_new:c { c_fp_exp_-40_tl } \tl_set:cn { c_fp_exp_-40_tl } { { 4 } { 248354255 } { 291588995 } { -18 } } \tl_new:c { c_fp_exp_-50_tl } \tl_set:cn { c_fp_exp_-50_tl } { { 1 } { 928749847 } { 963917783 } { -22 } } \tl_new:c { c_fp_exp_-60_tl } \tl_set:cn { c_fp_exp_-60_tl } { { 8 } { 756510762 } { 696520338 } { -27 } } \tl_new:c { c_fp_exp_-70_tl } \tl_set:cn { c_fp_exp_-70_tl } { { 3 } { 975449735 } { 908646808 } { -31 } } \tl_new:c { c_fp_exp_-80_tl } \tl_set:cn { c_fp_exp_-80_tl } { { 1 } { 804851387 } { 845415172 } { -35 } } \tl_new:c { c_fp_exp_-90_tl } \tl_set:cn { c_fp_exp_-90_tl } { { 8 } { 194012623 } { 990515430 } { -40 } } \tl_new:c { c_fp_exp_-100_tl } \tl_set:cn { c_fp_exp_-100_tl } { { 3 } { 720075976 } { 020835963 } { -44 } } \tl_new:c { c_fp_exp_-200_tl } \tl_set:cn { c_fp_exp_-200_tl } { { 1 } { 383896526 } { 736737530 } { -87 } } \cs_new_protected_nopar:Npn \fp_exp:Nn { \fp_exp_aux:NNn \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gexp:Nn { \fp_exp_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_exp:Nn { c } \cs_generate_variant:Nn \fp_gexp:Nn { c } \cs_new_protected_nopar:Npn \fp_exp_aux:NNn #1#2#3 { \group_begin: \fp_split:Nn a {#3} \fp_standardise:NNNN \l_fp_input_a_sign_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int \l_fp_input_a_extended_int \c_zero \tl_set:Nx \l_fp_arg_tl { \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero - \tex_else:D + \tex_fi:D \int_use:N \l_fp_input_a_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_input_a_decimal_int + \c_one_thousand_million e \int_use:N \l_fp_input_a_exponent_int } \etex_ifcsname:D c_fp_exp ( \l_fp_arg_tl ) _fp \tex_endcsname:D \tex_else:D \tex_expandafter:D \fp_exp_internal: \tex_fi:D \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 { \etex_ifcsname:D c_fp_exp ( \l_fp_arg_tl ) _fp \tex_endcsname:D \use:c { c_fp_exp ( \l_fp_arg_tl ) _fp } \tex_else:D \c_zero_fp \tex_fi:D } } \fp_tmp:w } \cs_new_protected_nopar:Npn \fp_exp_internal: { \tex_ifnum:D \l_fp_input_a_exponent_int < \c_three \fp_extended_normalise: \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero \tex_ifnum:D \l_fp_input_a_integer_int < 230 \scan_stop: \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_exp_aux: \tex_else:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_exp_overflow_msg: \tex_fi:D \tex_else:D \tex_ifnum:D \l_fp_input_a_integer_int < 230 \scan_stop: \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_exp_aux: \tex_else:D \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp } { \c_zero_fp } \tex_fi:D \tex_fi:D \tex_else:D \tex_expandafter:D \fp_exp_overflow_msg: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_exp_aux: { \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero \tex_expandafter:D \fp_exp_integer: \tex_else:D \l_fp_output_integer_int \c_one \l_fp_output_decimal_int \c_zero \l_fp_output_extended_int \c_zero \l_fp_output_exponent_int \c_zero \tex_expandafter:D \fp_exp_decimal: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_exp_integer: { \tex_ifnum:D \l_fp_input_a_integer_int < \c_one_hundred \l_fp_exp_integer_int \c_one \l_fp_exp_decimal_int \c_zero \l_fp_exp_extended_int \c_zero \l_fp_exp_exponent_int \c_zero \tex_expandafter:D \fp_exp_integer_tens: \tex_else:D \tl_set:Nx \l_fp_tmp_tl { \tex_expandafter:D \use_i:nnn \int_use:N \l_fp_input_a_integer_int } \l_fp_input_a_integer_int \etex_numexpr:D \l_fp_input_a_integer_int - \l_fp_tmp_tl 00 \scan_stop: \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero \tex_ifnum:D \l_fp_output_integer_int > 200 \scan_stop: \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp } { \c_zero_fp } \tex_else:D \fp_exp_integer_const:n { - \l_fp_tmp_tl 00 } \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_exp_integer_tens: \tex_fi:D \tex_else:D \fp_exp_integer_const:n { \l_fp_tmp_tl 00 } \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_exp_integer_tens: \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_exp_integer_tens: { \l_fp_output_integer_int \l_fp_exp_integer_int \l_fp_output_decimal_int \l_fp_exp_decimal_int \l_fp_output_extended_int \l_fp_exp_extended_int \l_fp_output_exponent_int \l_fp_exp_exponent_int \tex_ifnum:D \l_fp_input_a_integer_int > \c_nine \tl_set:Nx \l_fp_tmp_tl { \tex_expandafter:D \use_i:nn \int_use:N \l_fp_input_a_integer_int } \l_fp_input_a_integer_int \etex_numexpr:D \l_fp_input_a_integer_int - \l_fp_tmp_tl 0 \scan_stop: \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero \fp_exp_integer_const:n { \l_fp_tmp_tl 0 } \tex_else:D \fp_exp_integer_const:n { - \l_fp_tmp_tl 0 } \tex_fi:D \fp_mul:NNNNNNNNN \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_extended_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_extended_int \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int \fp_extended_normalise_output: \tex_fi:D \fp_exp_integer_units: } \cs_new_protected_nopar:Npn \fp_exp_integer_units: { \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero \fp_exp_integer_const:n { \int_use:N \l_fp_input_a_integer_int } \tex_else:D \fp_exp_integer_const:n { - \int_use:N \l_fp_input_a_integer_int } \tex_fi:D \fp_mul:NNNNNNNNN \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_extended_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_extended_int \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int \fp_extended_normalise_output: \tex_fi:D \fp_exp_decimal: } \cs_new_protected_nopar:Npn \fp_exp_integer_const:n #1 { \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_exp_integer_const:nnnn \tex_csname:D c_fp_exp_ #1 _tl \tex_endcsname:D } \cs_new_protected_nopar:Npn \fp_exp_integer_const:nnnn #1#2#3#4 { \l_fp_exp_integer_int #1 \scan_stop: \l_fp_exp_decimal_int #2 \scan_stop: \l_fp_exp_extended_int #3 \scan_stop: \l_fp_exp_exponent_int #4 \scan_stop: } \cs_new_protected_nopar:Npn \fp_exp_decimal: { \tex_ifnum:D \l_fp_input_a_decimal_int > \c_zero \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero \l_fp_exp_integer_int \c_one \l_fp_exp_decimal_int \l_fp_input_a_decimal_int \l_fp_exp_extended_int \l_fp_input_a_extended_int \tex_else:D \l_fp_exp_integer_int \c_zero \tex_ifnum:D \l_fp_exp_extended_int = \c_zero \l_fp_exp_decimal_int \etex_numexpr:D \c_one_thousand_million - \l_fp_input_a_decimal_int \scan_stop: \l_fp_exp_extended_int \c_zero \tex_else:D \l_fp_exp_decimal_int \etex_numexpr:D 999999999 - \l_fp_input_a_decimal_int \scan_stop: \l_fp_exp_extended_int \etex_numexpr:D \c_one_thousand_million - \l_fp_input_a_extended_int \scan_stop: \tex_fi:D \tex_fi:D \l_fp_input_b_sign_int \l_fp_input_a_sign_int \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int \l_fp_input_b_extended_int \l_fp_input_a_extended_int \l_fp_count_int \c_one \fp_exp_Taylor: \fp_mul:NNNNNNNNN \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_extended_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_extended_int \tex_fi:D \tex_ifnum:D \l_fp_output_extended_int < \c_five_hundred_million \tex_else:D \tex_advance:D \l_fp_output_decimal_int \c_one \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million \tex_else:D \l_fp_output_decimal_int \c_zero \tex_advance:D \l_fp_output_integer_int \c_one \tex_fi:D \tex_fi:D \fp_standardise:NNNN \l_fp_output_sign_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_exponent_int \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp } { + \int_use:N \l_fp_output_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million \scan_stop: e \int_use:N \l_fp_output_exponent_int } } \cs_new_protected_nopar:Npn \fp_exp_Taylor: { \tex_advance:D \l_fp_count_int \c_one \tex_multiply:D \l_fp_input_b_sign_int \l_fp_input_a_sign_int \fp_mul:NNNNNN \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \l_fp_input_b_decimal_int \l_fp_input_b_extended_int \l_fp_input_b_decimal_int \l_fp_input_b_extended_int \fp_div_integer:NNNNN \l_fp_input_b_decimal_int \l_fp_input_b_extended_int \l_fp_count_int \l_fp_input_b_decimal_int \l_fp_input_b_extended_int \tex_ifnum:D \etex_numexpr:D \l_fp_input_b_decimal_int + \l_fp_input_b_extended_int > \c_zero \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero \tex_advance:D \l_fp_exp_decimal_int \l_fp_input_b_decimal_int \tex_advance:D \l_fp_exp_extended_int \l_fp_input_b_extended_int \tex_ifnum:D \l_fp_exp_extended_int < \c_one_thousand_million \tex_else:D \tex_advance:D \l_fp_exp_decimal_int \c_one \tex_advance:D \l_fp_exp_extended_int -\c_one_thousand_million \tex_fi:D \tex_ifnum:D \l_fp_exp_decimal_int < \c_one_thousand_million \tex_else:D \tex_advance:D \l_fp_exp_integer_int \c_one \tex_advance:D \l_fp_exp_decimal_int -\c_one_thousand_million \tex_fi:D \tex_else:D \tex_advance:D \l_fp_exp_decimal_int -\l_fp_input_b_decimal_int \tex_advance:D \l_fp_exp_extended_int -\l_fp_input_a_extended_int \tex_ifnum:D \l_fp_exp_extended_int < \c_zero \tex_advance:D \l_fp_exp_decimal_int \c_minus_one \tex_advance:D \l_fp_exp_extended_int \c_one_thousand_million \tex_fi:D \tex_ifnum:D \l_fp_exp_decimal_int < \c_zero \tex_advance:D \l_fp_exp_integer_int \c_minus_one \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million \tex_fi:D \tex_fi:D \tex_expandafter:D \fp_exp_Taylor: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_exp_const:Nx #1#2 { \tl_new:N #1 \tl_gset:Nx #1 {#2} } \cs_generate_variant:Nn \fp_exp_const:Nx { c } \tl_new:c { c_fp_ln_10_1_tl } \tl_set:cn { c_fp_ln_10_1_tl } { { 2 } { 302585092 } { 994045684 } { 0 } } \tl_new:c { c_fp_ln_10_2_tl } \tl_set:cn { c_fp_ln_10_2_tl } { { 4 } { 605170185 } { 988091368 } { 0 } } \tl_new:c { c_fp_ln_10_3_tl } \tl_set:cn { c_fp_ln_10_3_tl } { { 6 } { 907755278 } { 982137052 } { 0 } } \tl_new:c { c_fp_ln_10_4_tl } \tl_set:cn { c_fp_ln_10_4_tl } { { 9 } { 210340371 } { 976182736 } { 0 } } \tl_new:c { c_fp_ln_10_5_tl } \tl_set:cn { c_fp_ln_10_5_tl } { { 1 } { 151292546 } { 497022842 } { 1 } } \tl_new:c { c_fp_ln_10_6_tl } \tl_set:cn { c_fp_ln_10_6_tl } { { 1 } { 381551055 } { 796427410 } { 1 } } \tl_new:c { c_fp_ln_10_7_tl } \tl_set:cn { c_fp_ln_10_7_tl } { { 1 } { 611809565 } { 095831979 } { 1 } } \tl_new:c { c_fp_ln_10_8_tl } \tl_set:cn { c_fp_ln_10_8_tl } { { 1 } { 842068074 } { 395226547 } { 1 } } \tl_new:c { c_fp_ln_10_9_tl } \tl_set:cn { c_fp_ln_10_9_tl } { { 2 } { 072326583 } { 694641116 } { 1 } } \tl_new:c { c_fp_ln_2_1_tl } \tl_set:cn { c_fp_ln_2_1_tl } { { 0 } { 693147180 } { 559945309 } { 0 } } \tl_new:c { c_fp_ln_2_2_tl } \tl_set:cn { c_fp_ln_2_2_tl } { { 1 } { 386294361 } { 119890618 } { 0 } } \tl_new:c { c_fp_ln_2_3_tl } \tl_set:cn { c_fp_ln_2_3_tl } { { 2 } { 079441541 } { 679835928 } { 0 } } \cs_new_protected_nopar:Npn \fp_ln:Nn { \fp_ln_aux:NNn \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gln:Nn { \fp_ln_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_ln:Nn { c } \cs_generate_variant:Nn \fp_gln:Nn { c } \cs_new_protected_nopar:Npn \fp_ln_aux:NNn #1#2#3 { \group_begin: \fp_split:Nn a {#3} \fp_standardise:NNNN \l_fp_input_a_sign_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int > \c_zero \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_ln_aux: \tex_else:D \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: ##1 \exp_not:N ##2 { \c_zero_fp } } \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_ln_error_msg: \tex_fi:D \tex_else:D \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: ##1 \exp_not:N ##2 { \c_zero_fp } } \tex_expandafter:D \fp_ln_error_msg: \tex_fi:D \fp_tmp:w #1 #2 } \cs_new_protected_nopar:Npn \fp_ln_aux: { \tl_set:Nx \l_fp_arg_tl { + \int_use:N \l_fp_input_a_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_input_a_decimal_int + \c_one_thousand_million e \int_use:N \l_fp_input_a_exponent_int } \etex_ifcsname:D c_fp_ln ( \l_fp_arg_tl ) _fp \tex_endcsname:D \tex_else:D \tex_expandafter:D \fp_ln_exponent: \tex_fi:D \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: ##1 \exp_not:N ##2 { \use:c { c_fp_ln ( \l_fp_arg_tl ) _fp } } } } \cs_new_protected_nopar:Npn \fp_ln_exponent: { \fp_ln_internal: \tex_ifnum:D \l_fp_output_extended_int < \c_five_hundred_million \tex_else:D \tex_advance:D \l_fp_output_decimal_int \c_one \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million \tex_else:D \l_fp_output_decimal_int \c_zero \tex_advance:D \l_fp_output_integer_int \c_one \tex_fi:D \tex_fi:D \fp_standardise:NNNN \l_fp_output_sign_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_exponent_int \tl_new:c { c_fp_ln ( \l_fp_arg_tl ) _fp } \tl_gset:cx { c_fp_ln ( \l_fp_arg_tl ) _fp } { \tex_ifnum:D \l_fp_output_sign_int > \c_zero + \tex_else:D - \tex_fi:D \int_use:N \l_fp_output_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million \scan_stop: e \int_use:N \l_fp_output_exponent_int } } \cs_new_protected_nopar:Npn \fp_ln_internal: { \tex_ifnum:D \l_fp_input_a_exponent_int < \c_zero \l_fp_input_a_exponent_int -\l_fp_input_a_exponent_int \l_fp_output_sign_int \c_minus_one \tex_else:D \l_fp_output_sign_int \c_one \tex_fi:D \tex_ifnum:D \l_fp_input_a_exponent_int > \c_nine \tl_set:Nx \l_fp_tmp_tl { \tex_expandafter:D \use_i:nn \int_use:N \l_fp_input_a_exponent_int } \l_fp_input_a_exponent_int \etex_numexpr:D \l_fp_input_a_exponent_int - \l_fp_tmp_tl 0 \scan_stop: \fp_ln_const:nn { 10 } { \l_fp_tmp_tl } \tex_advance:D \l_fp_exp_exponent_int \c_one \l_fp_output_integer_int \l_fp_exp_integer_int \l_fp_output_decimal_int \l_fp_exp_decimal_int \l_fp_output_extended_int \l_fp_exp_extended_int \l_fp_output_exponent_int \l_fp_exp_exponent_int \tex_else:D \l_fp_output_integer_int \c_zero \l_fp_output_decimal_int \c_zero \l_fp_output_extended_int \c_zero \l_fp_output_exponent_int \c_zero \tex_fi:D \fp_ln_exponent_units: } \cs_new_protected_nopar:Npn \fp_ln_exponent_units: { \tex_ifnum:D \l_fp_input_a_exponent_int > \c_zero \fp_ln_const:nn { 10 } { \int_use:N \l_fp_input_a_exponent_int } \fp_ln_normalise: \fp_add:NNNNNNNNN \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_extended_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_extended_int \tex_fi:D \fp_ln_mantissa: } \cs_new_protected_nopar:Npn \fp_ln_normalise: { \tex_ifnum:D \l_fp_exp_exponent_int < \l_fp_output_exponent_int \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_ln_normalise_aux:NNNNNNNNN \int_use:N \l_fp_exp_decimal_int \tex_expandafter:D \fp_ln_normalise: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_ln_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \tex_ifnum:D \l_fp_exp_integer_int = \c_zero \l_fp_exp_decimal_int #1#2#3#4#5#6#7#8 \scan_stop: \tex_else:D \tl_set:Nx \l_fp_tmp_tl { \int_use:N \l_fp_exp_integer_int #1#2#3#4#5#6#7#8 } \l_fp_exp_integer_int \c_zero \l_fp_exp_decimal_int \l_fp_tmp_tl \scan_stop: \tex_fi:D \tex_divide:D \l_fp_exp_extended_int \c_ten \tl_set:Nx \l_fp_tmp_tl { #9 \int_use:N \l_fp_exp_extended_int } \l_fp_exp_extended_int \l_fp_tmp_tl \scan_stop: \tex_advance:D \l_fp_exp_exponent_int \c_one } \cs_new_protected_nopar:Npn \fp_ln_mantissa: { \l_fp_count_int \c_zero \l_fp_input_a_extended_int \c_zero \fp_ln_mantissa_aux: \tex_ifnum:D \l_fp_count_int > \c_zero \fp_ln_const:nn { 2 } { \int_use:N \l_fp_count_int } \fp_ln_normalise: \tex_ifnum:D \l_fp_output_sign_int > \c_zero \tex_expandafter:D \fp_add:NNNNNNNNN \tex_else:D \tex_expandafter:D \fp_sub:NNNNNNNNN \tex_fi:D \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_extended_int \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_extended_int \tex_fi:D \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int > \c_one \scan_stop: \tex_expandafter:D \fp_ln_Taylor: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_ln_mantissa_aux: { \tex_ifnum:D \l_fp_input_a_integer_int > \c_one \tex_advance:D \l_fp_count_int \c_one \fp_ln_mantissa_divide_two: \tex_expandafter:D \fp_ln_mantissa_aux: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_ln_mantissa_divide_two: { \tex_ifodd:D \l_fp_input_a_decimal_int \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million \tex_fi:D \tex_ifodd:D \l_fp_input_a_integer_int \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \tex_fi:D \tex_divide:D \l_fp_input_a_integer_int \c_two \tex_divide:D \l_fp_input_a_decimal_int \c_two \tex_divide:D \l_fp_input_a_extended_int \c_two } \cs_new_protected_nopar:Npn \fp_ln_const:nn #1#2 { \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_exp_integer_const:nnnn \tex_csname:D c_fp_ln_ #1 _ #2 _tl \tex_endcsname:D } \cs_new_protected_nopar:Npn \fp_ln_Taylor: { \group_begin: \l_fp_input_a_integer_int \c_zero \l_fp_input_a_exponent_int \c_zero \l_fp_input_b_integer_int \c_two \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int \l_fp_input_b_exponent_int \c_zero \fp_div_internal: \fp_ln_fixed: \l_fp_input_a_integer_int \l_fp_output_integer_int \l_fp_input_a_decimal_int \l_fp_output_decimal_int \l_fp_input_a_exponent_int \l_fp_output_exponent_int \l_fp_input_a_extended_int \c_zero \l_fp_output_decimal_int \c_zero \l_fp_output_decimal_int \l_fp_input_a_decimal_int \l_fp_output_extended_int \l_fp_input_a_extended_int \fp_mul:NNNNNN \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \l_fp_input_b_decimal_int \l_fp_input_b_extended_int \l_fp_count_int \c_one \fp_ln_Taylor_aux: \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: \exp_not:N \l_fp_exp_decimal_int \int_use:N \l_fp_output_decimal_int \scan_stop: \exp_not:N \l_fp_exp_extended_int \int_use:N \l_fp_output_extended_int \scan_stop: \exp_not:N \l_fp_exp_exponent_int \int_use:N \l_fp_output_exponent_int \scan_stop: } \fp_tmp:w \tex_advance:D \l_fp_exp_decimal_int \l_fp_exp_decimal_int \tex_ifnum:D \l_fp_exp_extended_int < \c_five_hundred_million \tex_else:D \tex_advance:D \l_fp_exp_extended_int -\c_five_hundred_million \tex_advance:D \l_fp_exp_decimal_int \c_one \tex_fi:D \tex_advance:D \l_fp_exp_extended_int \l_fp_exp_extended_int \tex_ifnum:D \l_fp_output_sign_int > \c_zero \tex_expandafter:D \fp_add:NNNNNNNNN \tex_else:D \tex_expandafter:D \fp_sub:NNNNNNNNN \tex_fi:D \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_extended_int \c_zero \l_fp_exp_decimal_int \l_fp_exp_extended_int \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_extended_int } \cs_new_protected_nopar:Npn \fp_ln_fixed: { \tex_ifnum:D \l_fp_output_exponent_int < \c_zero \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_ln_fixed_aux:NNNNNNNNN \int_use:N \l_fp_output_decimal_int \tex_expandafter:D \fp_ln_fixed: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_ln_fixed_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \tex_ifnum:D \l_fp_output_integer_int = \c_zero \l_fp_output_decimal_int #1#2#3#4#5#6#7#8 \scan_stop: \tex_else:D \tl_set:Nx \l_fp_tmp_tl { \int_use:N \l_fp_output_integer_int #1#2#3#4#5#6#7#8 } \l_fp_output_integer_int \c_zero \l_fp_output_decimal_int \l_fp_tmp_tl \scan_stop: \tex_fi:D \tex_advance:D \l_fp_output_exponent_int \c_one } \cs_new_protected_nopar:Npn \fp_ln_Taylor_aux: { \tex_advance:D \l_fp_count_int \c_two \fp_mul:NNNNNN \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \l_fp_input_b_decimal_int \l_fp_input_b_extended_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int > \c_zero \fp_div_integer:NNNNN \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \l_fp_count_int \l_fp_exp_decimal_int \l_fp_exp_extended_int \tex_advance:D \l_fp_output_decimal_int \l_fp_exp_decimal_int \tex_advance:D \l_fp_output_extended_int \l_fp_exp_extended_int \tex_ifnum:D \l_fp_output_extended_int < \c_one_thousand_million \tex_else:D \tex_advance:D \l_fp_output_decimal_int \c_one \tex_advance:D \l_fp_output_extended_int -\c_one_thousand_million \tex_fi:D \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million \tex_else:D \tex_advance:D \l_fp_output_integer_int \c_one \tex_advance:D \l_fp_output_decimal_int -\c_one_thousand_million \tex_fi:D \tex_expandafter:D \fp_ln_Taylor_aux: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_pow:Nn { \fp_pow_aux:NNn \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gpow:Nn { \fp_pow_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_pow:Nn { c } \cs_generate_variant:Nn \fp_gpow:Nn { c } \cs_new_protected_nopar:Npn \fp_pow_aux:NNn #1#2#3 { \group_begin: \fp_read:N #2 \l_fp_input_b_sign_int \l_fp_input_a_sign_int \l_fp_input_b_integer_int \l_fp_input_a_integer_int \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int \fp_split:Nn a {#3} \fp_standardise:NNNN \l_fp_input_a_sign_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int \tex_ifnum:D \etex_numexpr:D \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int = \c_zero \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int = \c_zero \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: ##1 ##2 { \c_undefined_fp } } \tex_else:D \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: ##1 ##2 { \c_zero_fp } } \tex_fi:D \tex_else:D \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int = \c_zero \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: ##1 ##2 { \c_one_fp } } \tex_else:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_pow_aux_i: \tex_fi:D \tex_fi:D \fp_tmp:w #1 #2 } \cs_new_protected_nopar:Npn \fp_pow_aux_i: { \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero \tl_set:Nn \l_fp_sign_tl { + } \tex_expandafter:D \fp_pow_aux_ii: \tex_else:D \l_fp_input_a_extended_int \c_zero \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten \group_begin: \fp_extended_normalise: \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int = \c_zero \group_end: \tl_set:Nn \l_fp_sign_tl { - } \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_pow_aux_ii: \tex_else:D \group_end: \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: ##1 ##2 { \c_undefined_fp } } \tex_fi:D \tex_else:D \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: ##1 ##2 { \c_undefined_fp } } \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_pow_aux_ii: { \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero \tex_expandafter:D \fp_pow_aux_iv: \tex_else:D \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten \group_begin: \l_fp_input_a_extended_int \c_zero \fp_extended_normalise: \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero \tex_ifnum:D \l_fp_input_a_integer_int > \c_ten \group_end: \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_pow_aux_iv: \tex_else:D \group_end: \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_pow_aux_iii: \tex_fi:D \tex_else:D \group_end: \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_pow_aux_iv: \tex_fi:D \tex_else:D \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_pow_aux_iv: \tex_fi:D \tex_fi:D \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 { \group_end: ##1 ##2 { \l_fp_sign_tl \int_use:N \l_fp_output_integer_int . \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million \scan_stop: e \int_use:N \l_fp_output_exponent_int } } } \cs_new_protected_nopar:Npn \fp_pow_aux_iii: { \l_fp_input_a_sign_int \c_one \fp_pow_aux_iv: \l_fp_input_a_integer_int \c_one \l_fp_input_a_decimal_int \c_zero \l_fp_input_a_exponent_int \c_zero \l_fp_input_b_integer_int \l_fp_output_integer_int \l_fp_input_b_decimal_int \l_fp_output_decimal_int \l_fp_input_b_exponent_int \l_fp_output_exponent_int \fp_div_internal: } \cs_new_protected_nopar:Npn \fp_pow_aux_iv: { \group_begin: \l_fp_input_a_integer_int \l_fp_input_b_integer_int \l_fp_input_a_decimal_int \l_fp_input_b_decimal_int \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int \fp_ln_internal: \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: \exp_not:N \l_fp_input_b_sign_int \int_use:N \l_fp_output_sign_int \scan_stop: \exp_not:N \l_fp_input_b_integer_int \int_use:N \l_fp_output_integer_int \scan_stop: \exp_not:N \l_fp_input_b_decimal_int \int_use:N \l_fp_output_decimal_int \scan_stop: \exp_not:N \l_fp_input_b_extended_int \int_use:N \l_fp_output_extended_int \scan_stop: \exp_not:N \l_fp_input_b_exponent_int \int_use:N \l_fp_output_exponent_int \scan_stop: } \fp_tmp:w \l_fp_input_a_extended_int \c_zero \fp_mul:NNNNNNNNN \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \l_fp_input_b_integer_int \l_fp_input_b_decimal_int \l_fp_input_b_extended_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \tex_advance:D \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int \l_fp_output_integer_int \c_zero \l_fp_output_decimal_int \c_zero \l_fp_output_exponent_int \c_zero \cs_set_eq:NN \fp_exp_const:Nx \use_none:nn \fp_exp_internal: } \prg_new_conditional:Npnn \fp_if_undefined:N #1 { T , F , TF , p } { \tex_ifx:D #1 \c_undefined_fp \prg_return_true: \tex_else:D \prg_return_false: \tex_fi:D } \prg_new_conditional:Npnn \fp_if_zero:N #1 { T , F , TF , p } { \tex_ifx:D #1 \c_zero_fp \prg_return_true: \tex_else:D \prg_return_false: \tex_fi:D } \prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3 { T , F , TF } { \group_begin: \fp_split:Nn a {#1} \fp_standardise:NNNN \l_fp_input_a_sign_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int \fp_split:Nn b {#3} \fp_standardise:NNNN \l_fp_input_b_sign_int \l_fp_input_b_integer_int \l_fp_input_b_decimal_int \l_fp_input_b_exponent_int \fp_compare_aux:N #2 } \prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3 { T , F , TF } { \group_begin: \fp_read:N #3 \l_fp_input_b_sign_int \l_fp_input_a_sign_int \l_fp_input_b_integer_int \l_fp_input_a_integer_int \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int \fp_read:N #1 \fp_compare_aux:N #2 } \cs_new_protected_nopar:Npn \fp_compare_aux:N #1 { \cs_if_exist:cTF { fp_compare_#1: } { \use:c { fp_compare_#1: } } { \group_end: \prg_return_false: } } \cs_new_protected_nopar:cpn { fp_compare_=: } { \tex_ifnum:D \l_fp_input_a_sign_int = \l_fp_input_b_sign_int \tex_ifnum:D \l_fp_input_a_integer_int = \l_fp_input_b_integer_int \tex_ifnum:D \l_fp_input_a_decimal_int = \l_fp_input_b_decimal_int \tex_ifnum:D \l_fp_input_a_exponent_int = \l_fp_input_b_exponent_int \group_end: \prg_return_true: \tex_else:D \group_end: \prg_return_false: \tex_fi:D \tex_else:D \group_end: \prg_return_false: \tex_fi:D \tex_else:D \group_end: \prg_return_false: \tex_fi:D \tex_else:D \group_end: \prg_return_false: \tex_fi:D } \cs_new_protected_nopar:cpn { fp_compare_>: } { \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int = \c_zero \tex_ifnum:D \etex_numexpr:D \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int = \c_zero \group_end: \prg_return_false: \tex_else:D \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero \group_end: \prg_return_false: \tex_else:D \group_end: \prg_return_true: \tex_fi:D \tex_fi:D \tex_else:D \tex_ifnum:D \etex_numexpr:D \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int = \c_zero \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero \group_end: \prg_return_true: \tex_else:D \group_end: \prg_return_false: \tex_fi:D \tex_else:D \use:c { fp_compare_>_aux: } \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:cpn { fp_compare_>_aux: } { \tex_ifnum:D \l_fp_input_a_sign_int > \l_fp_input_b_sign_int \group_end: \prg_return_true: \tex_else:D \tex_ifnum:D \l_fp_input_a_sign_int < \l_fp_input_b_sign_int \group_end: \prg_return_false: \tex_else:D \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero \use:c { fp_compare_absolute_a>b: } \tex_else:D \use:c { fp_compare_absolute_ab: } { \tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int \group_end: \prg_return_true: \tex_else:D \tex_ifnum:D \l_fp_input_a_exponent_int < \l_fp_input_b_exponent_int \group_end: \prg_return_false: \tex_else:D \tex_ifnum:D \l_fp_input_a_integer_int > \l_fp_input_b_integer_int \group_end: \prg_return_true: \tex_else:D \tex_ifnum:D \l_fp_input_a_integer_int < \l_fp_input_b_integer_int \group_end: \prg_return_false: \tex_else:D \tex_ifnum:D \l_fp_input_a_decimal_int > \l_fp_input_b_decimal_int \group_end: \prg_return_true: \tex_else:D \group_end: \prg_return_false: \tex_fi:D \tex_fi:D \tex_fi:D \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:cpn { fp_compare_absolute_a \l_fp_input_a_exponent_int \group_end: \prg_return_true: \tex_else:D \tex_ifnum:D \l_fp_input_b_exponent_int < \l_fp_input_a_exponent_int \group_end: \prg_return_false: \tex_else:D \tex_ifnum:D \l_fp_input_b_integer_int > \l_fp_input_a_integer_int \group_end: \prg_return_true: \tex_else:D \tex_ifnum:D \l_fp_input_b_integer_int < \l_fp_input_a_integer_int \group_end: \prg_return_false: \tex_else:D \tex_ifnum:D \l_fp_input_b_decimal_int > \l_fp_input_a_decimal_int \group_end: \prg_return_true: \tex_else:D \group_end: \prg_return_false: \tex_fi:D \tex_fi:D \tex_fi:D \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:cpn { fp_compare_<: } { \tl_set:Nx \l_fp_tmp_tl { \int_set:Nn \exp_not:N \l_fp_input_a_sign_int { \int_use:N \l_fp_input_b_sign_int } \int_set:Nn \exp_not:N \l_fp_input_a_integer_int { \int_use:N \l_fp_input_b_integer_int } \int_set:Nn \exp_not:N \l_fp_input_a_decimal_int { \int_use:N \l_fp_input_b_decimal_int } \int_set:Nn \exp_not:N \l_fp_input_a_exponent_int { \int_use:N \l_fp_input_b_exponent_int } \int_set:Nn \exp_not:N \l_fp_input_b_sign_int { \int_use:N \l_fp_input_a_sign_int } \int_set:Nn \exp_not:N \l_fp_input_b_integer_int { \int_use:N \l_fp_input_a_integer_int } \int_set:Nn \exp_not:N \l_fp_input_b_decimal_int { \int_use:N \l_fp_input_a_decimal_int } \int_set:Nn \exp_not:N \l_fp_input_b_exponent_int { \int_use:N \l_fp_input_a_exponent_int } } \l_fp_tmp_tl \use:c { fp_compare_>: } } \msg_kernel_new:nnnn { fpu } { overflow } { Number~too~big. } { The~input~given~is~too~big~for~the~LaTeX~floating~point~unit. \\ Further~errors~may~well~occur! } \cs_new_protected_nopar:Npn \fp_overflow_msg: { \msg_kernel_error:nn { fpu } { overflow } } \msg_kernel_new:nnnn { fpu } { exponent-overflow } { Number~too~big~for~exponent~unit. } { The~exponent~of~the~input~given~is~too~big~for~the~floating~point~ unit:~the~maximum~input~value~for~an~exponent~is~230. } \cs_new_protected_nopar:Npn \fp_exp_overflow_msg: { \msg_kernel_error:nn { fpu } { exponent-overflow } } \msg_kernel_new:nnnn { fpu } { logarithm-input-error } { Invalid~input~to~ln~function. } { Logarithms~can~only~be~calculated~for~positive~numbers. } \cs_new_protected_nopar:Npn \fp_ln_error_msg: { \msg_kernel_error:nn { fpu } { logarithm-input-error } } \msg_kernel_new:nnnn { fpu } { trigonometric-overflow } { Number~too~big~for~trigonometry~unit. } { The~trigonometry~code~can~only~work~with~numbers~smaller~ than~1000000000. } \cs_new_protected_nopar:Npn \fp_trig_overflow_msg: { \msg_kernel_error:nn { fpu } { trigonometric-overflow } } %% %% %% End of file `l3fp.sty'.