%% %% 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 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 1979 2010-07-08 19:51:19Z joseph $ {L3 Experimental floating-point operations} \ProvidesExplPackage {\filename}{\filedate}{\fileversion}{\filedescription} \package_check_loaded_expl: \int_new:N \l_fp_input_a_integer_int \int_new:N \l_fp_input_a_decimal_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_a_sign_int \int_new:N \l_fp_input_b_sign_int \int_new:N \l_fp_split_sign_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_div_count_int \int_new:N \l_fp_div_offset_int \int_new:N \l_fp_output_sign_int \int_new:N \l_fp_output_integer_int \int_new:N \l_fp_output_decimal_int \bool_new:N \l_fp_round_carry_bool \tl_new:N \l_fp_round_decimal_tl \int_new:N \l_fp_round_discard_int \int_new:N \l_fp_round_position_int \int_new:N \l_fp_tmp_int \tl_new:N \l_fp_tmp_tl \tl_new:N \c_zero_fp \tl_set:Nn \c_zero_fp { + 0.000000000 } \tl_new:N \c_undefined_fp \tl_set:Nn \c_undefined_fp { X 0.000000000 } \tl_new:N \c_infinity_fp \tl_set:Nn \c_infinity_fp { +2147483647.2147483647 } \tl_new:N \c_minus_infinity_fp \tl_set:Nn \c_minus_infinity_fp { -2147483647.2147483647 } \int_new:N \c_one_hundred_million \int_set:Nn \c_one_hundred_million { 100000000 } \int_new:N \c_one_thousand_million \int_set:Nn \c_one_thousand_million { 1000000000 } \prg_new_conditional:Npnn \fp_if_infinite:N #1 { p , T , F , TF } { \tex_ifx:D #1 \c_infinity_fp \prg_return_true: \tex_else:D \tex_ifx:D #1 \c_minus_infinity_fp \prg_return_true: \tex_else:D \prg_return_false: \tex_fi:D \tex_fi:D } \prg_new_conditional:Npnn \fp_if_plus_infinity:N #1 { p , T , F , TF } { \tex_ifx:D #1 \c_infinity_fp \prg_return_true: \tex_else:D \prg_return_false: \tex_fi:D } \prg_new_conditional:Npnn \fp_if_minus_infinity:N #1 { p , T , F , TF } { \tex_ifx:D #1 \c_minus_infinity_fp \prg_return_true: \tex_else:D \prg_return_false: \tex_fi:D } \prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF } { \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 { p , T , F , TF } { \tex_ifx:D #1 \c_zero_fp \prg_return_true: \tex_else:D \prg_return_false: \tex_fi:D } \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_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} \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 . \exp_after:wN \use_none:n \int_use:N \l_fp_input_a_decimal_int } \exp_after:wN \group_end: \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl } } \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_dim \etex_dimexpr:D #3 \scan_stop: \fp_split:Nn a { \exp_after:wN \fp_set_from_dim_aux:w \dim_use:N \l_fp_tmp_dim } \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 . \exp_after:wN \use_none:n \int_use:N \l_fp_input_a_decimal_int } \exp_after:wN \group_end: \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl } } \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 \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_eq:NN \fp_use:N \tl_use:N \cs_new_eq:NN \fp_use:c \tl_use:c \cs_new_protected_nopar:Npn \fp_read:N #1 { \exp_after:wN \fp_read_aux:w #1 \q_stop } \cs_new_protected_nopar:Npn \fp_read_aux:w #1#2 . #3 \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: } \cs_new_protected_nopar:Npn \fp_split:Nn #1#2 { \tl_set:Nx \l_fp_tmp_tl {#2} \l_fp_split_sign_int \c_one \fp_split_sign: \use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int \tex_afterassignment:D \fp_split_aux_i:w \use:c { l_fp_input_ #1 _integer_int } \etex_numexpr:D 0 \l_fp_tmp_tl . . \q_stop #1 } \cs_new_protected_nopar:Npn \fp_split_sign: { \tex_ifnum:D \pdf_strcmp:D { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_nil } { - } = \c_zero \tl_set:Nx \l_fp_tmp_tl { \exp_after:wN \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_nil } \l_fp_split_sign_int -\l_fp_split_sign_int \exp_after:wN \fp_split_sign: \tex_else:D \tex_ifnum:D \pdf_strcmp:D { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_nil } { + } = \c_zero \tl_set:Nx \l_fp_tmp_tl { \exp_after:wN \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_nil } \exp_after:wN \exp_after:wN \exp_after:wN \fp_split_sign: \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_split_aux_i:w #1 . #2 . #3 \q_stop { \fp_split_aux_ii:w #2 000000000 \q_stop } \cs_new_protected_nopar:Npn \fp_split_aux_ii:w #1#2#3#4#5#6#7#8#9 { \fp_split_aux_iii:w {#1#2#3#4#5#6#7#8#9} } \cs_new_protected_nopar:Npn \fp_split_aux_iii:w #1#2 \q_stop { \l_fp_tmp_int 1 #1 \scan_stop: \exp_after:wN \fp_split_decimal:w \int_use:N \l_fp_tmp_int 000000000 \q_stop } \cs_new_protected_nopar:Npn \fp_split_decimal:w #1#2#3#4#5#6#7#8#9 { \fp_split_decimal_aux:w {#2#3#4#5#6#7#8#9} } \cs_new_protected_nopar:Npn \fp_split_decimal_aux:w #1#2#3 \q_stop #4 { \use:c { l_fp_input_ #4 _decimal_int } #1#2 \scan_stop: \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 } \cs_new_protected_nopar:Npn \fp_abs:N { \fp_abs:NN \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gabs:N { \fp_abs: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: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 { + \int_use:N \l_fp_input_a_integer_int . \exp_after:wN \use_none:n \int_use:N \l_fp_input_a_decimal_int } \exp_after:wN \group_end: \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl } } \cs_new_protected_nopar:Npn \fp_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 . \exp_after:wN \use_none:n \int_use:N \l_fp_input_a_decimal_int } \exp_after:wN \group_end: \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl } } \cs_new_protected_nopar:Npn \fp_add:Nn { \fp_add_aux:NNn \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gadd:Nn { \fp_add_aux:NNn \tl_gset:Nn } \cs_generate_variant:Nn \fp_add:Nn { c } \cs_generate_variant:Nn \fp_gadd:Nn { c } \cs_new_protected_nopar:Npn \fp_add_aux:NNn #1#2#3 { \group_begin: \fp_read:N #2 \fp_split:Nn b {#3} \fp_add_core: \exp_after:wN \group_end: \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl } } \cs_new_protected_nopar:Npn \fp_add_core: { \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_sign_int * \l_fp_input_b_sign_int \scan_stop: > \c_zero \exp_after:wN \fp_add_sum: \tex_else:D \exp_after:wN \fp_add_difference: \tex_fi:D \tl_set:Nx \l_fp_tmp_tl { \tex_ifnum:D \l_fp_output_sign_int < \c_zero - \tex_else:D + \tex_fi:D \int_use:N \l_fp_output_integer_int . \exp_after:wN \use_none:n \int_use:N \l_fp_output_decimal_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_advance:D \l_fp_output_decimal_int \c_one_thousand_million \tex_else:D \tex_advance:D \l_fp_output_integer_int \c_one \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 \tex_ifnum:D \etex_numexpr:D \l_fp_output_integer_int + \l_fp_output_decimal_int \scan_stop: = \c_zero \l_fp_output_sign_int \c_one \tex_fi:D \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million } \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} \tex_multiply:D \l_fp_input_b_sign_int \c_minus_one \fp_add_core: \exp_after:wN \group_end: \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl } } \cs_new_protected_nopar:Npn \fp_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_mul_split:NNNN \l_fp_input_a_integer_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_a_decimal_int \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int \fp_mul_split:NNNN \l_fp_input_b_integer_int \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int \fp_mul_split:NNNN \l_fp_input_b_decimal_int \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_iv_int \l_fp_mul_b_vi_int \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_v_int \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_iv_int \tex_divide:D \l_fp_mul_output_int \c_thousand \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_vi_int \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_v_int \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_iv_int \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_iii_int \fp_mul_end_level: \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_vi_int \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_v_int \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_iv_int \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_iii_int \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_ii_int \fp_mul_end_level: \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 \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_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: \l_fp_output_integer_int 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: \tex_ifnum:D \l_fp_mul_output_tl = \c_zero \tex_else:D \exp_after:wN \fp_msg_overflow: \tex_fi:D \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million \tl_set:Nx \l_fp_tmp_tl { \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_sign_int * \l_fp_input_b_sign_int \scan_stop: < \c_zero \tex_ifnum:D \etex_numexpr:D \l_fp_output_integer_int + \l_fp_output_decimal_int \scan_stop: = \c_one_thousand_million + \tex_else:D - \tex_fi:D \tex_else:D + \tex_fi:D \int_use:N \l_fp_output_integer_int . \exp_after:wN \use_none:n \int_use:N \l_fp_output_decimal_int } \exp_after:wN \group_end: \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl } } \cs_new_protected_nopar:Npn \fp_mul_split:NNNN #1#2#3#4 { \tex_advance:D #1 \c_one_thousand_million \cs_set_protected_nopar:Npn \fp_mul_split_aux:w ##1##2##3##4##5##6##7##8##9 \q_stop { #2 ##2##3##4 \scan_stop: #3 ##5##6##7 \scan_stop: #4 ##8##9 \scan_stop: } \exp_after:wN \fp_mul_split_aux:w \int_use:N #1 \q_stop } \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 \exp_after:wN \fp_mul_end_level:w \int_use:N \l_fp_mul_output_int \q_stop } \cs_new_protected_nopar:Npn \fp_mul_end_level:w #1#2#3#4#5#6#7#8#9 \q_stop { \tl_set:Nx \l_fp_mul_output_tl { #8#9 \l_fp_mul_output_tl } \l_fp_mul_output_int #5#6#7 \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} \tex_ifnum:D \etex_numexpr:D \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int \scan_stop: = \c_zero \tl_set_eq:NN \l_fp_tmp_tl \c_undefined_fp \tex_else:D \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int \scan_stop: = \c_zero \tl_set_eq:NN \l_fp_tmp_tl \c_zero_fp \tex_else:D \exp_after:wN \exp_after:wN \exp_after:wN \fp_div_aux: \tex_fi:D \tex_fi:D \exp_after:wN \group_end: \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl } } \cs_new_protected_nopar:Npn \fp_div_aux: { \l_fp_div_offset_int \c_one \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero \exp_after:wN \fp_div_offset_create: \tex_fi:D \l_fp_output_integer_int \c_zero \l_fp_output_decimal_int \c_one_thousand_million \cs_set_eq:NN \fp_div_store: \fp_div_store_integer: \fp_div_loop: \tl_set:Nx \l_fp_tmp_tl { \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_sign_int * \l_fp_input_b_sign_int \scan_stop: < \c_zero \tex_ifnum:D \etex_numexpr:D \l_fp_output_integer_int + \l_fp_output_decimal_int \scan_stop: = \c_one_thousand_million + \tex_else:D - \tex_fi:D \tex_else:D + \tex_fi:D \int_use:N \l_fp_output_integer_int . \exp_after:wN \use_none:n \int_use:N \l_fp_output_decimal_int } } \cs_new_protected_nopar:Npn \fp_div_offset_create: { \tex_ifnum:D \l_fp_input_b_integer_int = \c_zero \tex_advance:D \l_fp_input_b_decimal_int \c_one_thousand_million \exp_after:wN \fp_div_offset_create_aux:w \int_use:N \l_fp_input_b_decimal_int \q_stop \exp_after:wN \fp_div_offset_create: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_div_offset_create_aux:w #1#2#3#4#5#6#7#8#9 \q_stop { \l_fp_input_b_integer_int #2 \scan_stop: \l_fp_input_b_decimal_int #3#4#5#6#7#8#9 0 \scan_stop: \tex_multiply:D \l_fp_div_offset_int \c_ten } \cs_new_protected_nopar:Npn \fp_div_loop: { \l_fp_div_count_int \c_zero \fp_div_divide: \tex_divide:D \l_fp_input_b_decimal_int \c_ten \tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million \exp_after:wN \fp_div_loop_aux_i:w \int_use:N \l_fp_input_b_integer_int \fp_div_store: \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 \exp_after:wN \exp_after:wN \exp_after:wN \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 \exp_after:wN \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 \exp_after:wN \exp_after:wN \exp_after:wN \exp_after:wN \exp_after:wN \exp_after:wN \exp_after:wN \fp_div_divide_aux: \tex_fi:D \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_div_loop_aux_i:w #1#2#3#4#5#6#7#8#9 { \fp_div_loop_aux_ii:w #2#3#4#5#6#7#8#9 } \cs_new_protected_nopar:Npn \fp_div_loop_aux_ii:w #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: \l_fp_input_b_decimal_int \etex_numexpr:D \l_fp_input_b_decimal_int + \c_one_hundred_million * #9 \scan_stop: } \cs_new_protected_nopar:Npn \fp_div_divide_aux: { \tex_advance:D \l_fp_div_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 \etex_numexpr:D \l_fp_output_integer_int + \l_fp_div_count_int * \l_fp_div_offset_int \scan_stop: \tex_ifnum:D \l_fp_div_offset_int > \c_one \tex_divide:D \l_fp_div_offset_int \c_ten \tex_else:D \cs_set_eq:NN \fp_div_store: \fp_div_store_decimal: \l_fp_div_offset_int \c_one_hundred_million \tex_fi:D } \cs_new_protected_nopar:Npn \fp_div_store_decimal: { \l_fp_output_decimal_int \etex_numexpr:D \l_fp_output_decimal_int + \l_fp_div_count_int * \l_fp_div_offset_int \scan_stop: \tex_divide:D \l_fp_div_offset_int \c_ten } \prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3 { T , F , TF } { \group_begin: \fp_split:Nn a {#1} \fp_split:Nn b {#3} \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 \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 \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 } \cs_new_protected_nopar:cpn { fp_compare_>: } { \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_a < b: } \tex_fi:D \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:cpn { fp_compare_<: } { \tex_ifnum:D \l_fp_input_b_sign_int > \l_fp_input_a_sign_int \group_end: \prg_return_true: \tex_else:D \tex_ifnum:D \l_fp_input_b_sign_int < \l_fp_input_a_sign_int \group_end: \prg_return_false: \tex_else:D \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero \use:c { fp_compare_absolute_a < b: } \tex_else:D \use:c { fp_compare_absolute_a > b: } \tex_fi:D \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:cpn { fp_compare_absolute_a > b: } { \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 } \cs_new_protected_nopar:cpn { fp_compare_absolute_a < b: } { \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 } \keys_define:nn { fp } { precision .int_set:N = \l_fp_round_precision_int , remove-trailing-zeros .bool_set:N = \l_fp_remove_zeros_bool , round-mode .choice: , round-mode / half-even .tl_set:N = \l_fp_round_mode_tl , round-mode / half-from-zero .tl_set:N = \l_fp_round_mode_tl , round-mode / none .tl_set:N = \l_fp_round_mode_tl , round-mode / truncate .tl_set:N = \l_fp_round_mode_tl , } \keys_set:nn { fp } { precision = 9 , remove-trailing-zeros = true , round-mode = none , } \cs_new_protected_nopar:Npn \fp_to_tl:NN { \fp_to_tl_aux:NNN \tl_set:Nn } \cs_new_protected_nopar:Npn \fp_gto_tl:NN { \fp_to_tl_aux:NNN \tl_gset:Nn } \cs_generate_variant:Nn \fp_to_tl:NN { Nc } \cs_generate_variant:Nn \fp_to_tl:NN { c } \cs_generate_variant:Nn \fp_to_tl:NN { cc } \cs_generate_variant:Nn \fp_gto_tl:NN { Nc } \cs_generate_variant:Nn \fp_gto_tl:NN { c } \cs_generate_variant:Nn \fp_gto_tl:NN { cc } \cs_new_protected_nopar:Npn \fp_to_tl_aux:NNN #1#2#3 { \group_begin: \fp_read:N #2 \use:c { fp_round_ \l_fp_round_mode_tl :} \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_fi:D \int_use:N \l_fp_input_a_integer_int \intexpr_compare:nNnT { \l_fp_round_precision_int } > { \c_zero } { . \bool_if:NTF \l_fp_remove_zeros_bool { \exp_after:wN \use_i:nn \exp_after:wN \fp_remove_zeros:NNNNNNNNN } { \exp_after:wN \use_none:n } \int_use:N \l_fp_input_a_decimal_int } } \exp_after:wN \group_end: \exp_after:wN #1 \exp_after:wN #3 \exp_after:wN { \l_fp_tmp_tl } } \cs_new_nopar:Npn \fp_remove_zeros:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \fp_remove_zeros_aux:w #1#2#3#4#5#6#7#8#9 \q_stop 1 } \cs_new_nopar:Npn \fp_remove_zeros_aux:w #1#2 \q_stop #3 { #1 \intexpr_compare:nNnTF { 0 #2 } = { \c_zero } { \intexpr_compare:nNnF { \l_fp_round_precision_int } < { #3 + 1 } { \intexpr_compare:nNnT {#3} < { 9 } { \fp_remove_zeros_aux:w #2 \q_stop { #3 + 1 } } } } { \intexpr_compare:nNnT {#3} < { 9 } { \fp_remove_zeros_aux:w #2 \q_stop { #3 + 1 } } } } \cs_new_protected_nopar:cpn { fp_round_half-from-zero: } { \tex_ifnum:D \l_fp_round_precision_int < \c_nine \exp_after:wN \fp_round_from_zero: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_round_from_zero: { \bool_set_false:N \l_fp_round_carry_bool \l_fp_round_position_int \c_eight \tl_clear:N \l_fp_round_decimal_tl \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \exp_after:wN \use_i:nn \exp_after:wN \fp_round_from_zero_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int } \cs_new_protected_nopar:Npn \fp_round_from_zero_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \fp_round_from_zero_decimal:N #9#8#7#6#5#4#3#2#1 \fp_round_from_zero_integer: } \cs_new_protected_nopar:Npn \fp_round_from_zero_decimal:N #1 { \tex_ifnum:D \l_fp_round_position_int < \l_fp_round_precision_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_precision_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 \exp_after:wN \fp_round_from_zero_decimal:N \tex_fi:D } \cs_new_protected_nopar:Npn \fp_round_from_zero_integer: { \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: } \cs_new_protected_nopar:cpn { fp_round_half-even: } { \tex_ifnum:D \l_fp_round_precision_int < \c_nine \exp_after:wN \fp_round_even: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_round_even: { \bool_set_false:N \l_fp_round_carry_bool \l_fp_round_position_int \c_eight \tl_clear:N \l_fp_round_decimal_tl \int_zero:N \l_fp_round_discard_int \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \exp_after:wN \use_i:nn \exp_after:wN \fp_round_even_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int } \cs_new_protected_nopar:Npn \fp_round_even_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \fp_round_even_decimal:N #9#8#7#6#5#4#3#2#1 \fp_round_even_integer: } \cs_new_protected_nopar:Npn \fp_round_even_decimal:N #1 { \tex_ifnum:D \l_fp_round_position_int < \l_fp_round_precision_int \bool_if:NTF \l_fp_round_carry_bool { \tex_ifnum:D \l_fp_round_discard_int = \c_zero \l_fp_round_discard_int \c_one \tex_ifodd:D #1 \scan_stop: \l_fp_tmp_int \etex_numexpr:D #1 + \c_one \scan_stop: \tex_else:D \l_fp_tmp_int \etex_numexpr:D #1 \scan_stop: \tex_fi:D \tex_else:D \l_fp_tmp_int \etex_numexpr:D #1 + \c_one \scan_stop: \tex_fi:D } { \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_precision_int \tex_ifnum:D #1 > \c_four \bool_set_true:N \l_fp_round_carry_bool \tex_ifnum:D #1 = \c_five \tex_else:D \l_fp_round_discard_int \c_one \tex_fi:D \tex_fi:D \tex_else:D \tex_advance:D \l_fp_round_discard_int #1 \scan_stop: \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 \exp_after:wN \fp_round_even_decimal:N \tex_fi:D } \cs_new_protected_nopar:Npn \fp_round_even_integer: { \bool_if:NT \l_fp_round_carry_bool { \tex_ifnum:D \l_fp_round_discard_int = \c_zero \tex_ifodd:D \l_fp_input_a_integer_int \tex_advance:D \l_fp_input_a_integer_int \c_one \tex_fi:D \tex_else:D \tex_advance:D \l_fp_input_a_integer_int \c_one \tex_fi:D } \l_fp_input_a_decimal_int \l_fp_round_decimal_tl \scan_stop: } \cs_new_protected_nopar:Npn \fp_round_none: { \l_fp_round_precision_int \c_one } \cs_new_protected_nopar:Npn \fp_round_truncate: { \intexpr_compare:nNnF { \l_fp_round_precision_int } > { 8 } { \intexpr_compare:nNnTF { \l_fp_round_precision_int } < { 1 } { \l_fp_input_a_decimal_int \c_zero \scan_stop: } { \int_set:Nn \l_fp_tmp_int { \prg_replicate:nn { 9 - \l_fp_round_precision_int } { 10 * } 1 } \tex_divide:D \l_fp_input_a_decimal_int \l_fp_tmp_int \tex_multiply:D \l_fp_input_a_decimal_int \l_fp_tmp_int } } } \cs_new_protected_nopar:Npn \fp_msg_overflow: { \msg_kernel_error:nn { fpu } { overflow } } \msg_kernel_new:nnnn { fpu } { overflow } { Arithmetic~overflow. } { The~calculation~requested~exceeds~the~capacity \\ of~the~fixed-point~unit. } %% %% %% End of file `l3fp.sty'.