diff options
Diffstat (limited to 'Master/texmf-dist/tex/latex/l3kernel/l3fp.sty')
| -rw-r--r-- | Master/texmf-dist/tex/latex/l3kernel/l3fp.sty | 2298 |
1 files changed, 1482 insertions, 816 deletions
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty b/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty index 48e8d757bfe..679f97c2519 100644 --- a/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty +++ b/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty @@ -25,7 +25,7 @@ %% %% Do not distribute a modified version of this file. %% -%% File: l3fp.dtx Copyright (C) 2011-2012 The LaTeX3 Project +%% File: l3fp.dtx Copyright (C) 2011-2013 The LaTeX3 Project %% %% It may be distributed and/or modified under the conditions of the %% LaTeX Project Public License (LPPL), either version 1.3c of this @@ -59,12 +59,12 @@ %% ----------------------------------------------------------------------- %% \RequirePackage{l3bootstrap} -\GetIdInfo$Id: l3fp.dtx 4521 2013-07-09 11:45:31Z joseph $ +\GetIdInfo$Id: l3fp.dtx 4601 2013-11-18 23:13:28Z bruno $ {L3 Floating points} \ProvidesExplPackage {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription} \__expl_package_check: -%% File: l3fp-aux.dtx Copyright(C) 2011-2012 The LaTeX3 Project +%% File: l3fp-aux.dtx Copyright(C) 2011-2013 The LaTeX3 Project %% %% It may be distributed and/or modified under the conditions of the %% LaTeX Project Public License (LPPL), either version 1.3c of this @@ -99,11 +99,14 @@ %% \cs_new:Npn \__fp_use_none_stop_f:n #1 { \exp_stop_f: } \cs_new:Npn \__fp_use_s:n #1 { #1; } +\cs_new:Npn \__fp_use_braced_s:n #1 { {#1} ; } \cs_new:Npn \__fp_use_s:nn #1#2 { #1#2; } \cs_new:Npn \__fp_use_none_until_s:w #1; { } \cs_new:Npn \__fp_use_i_until_s:nw #1#2; {#1} \cs_new:Npn \__fp_use_ii_until_s:nnw #1#2#3; {#2} \cs_new:Npn \__fp_reverse_args:Nww #1 #2; #3; { #1 #3; #2; } +\cs_new:Npn \__fp_rrot:www #1; #2; #3; { #2; #3; #1; } +\cs_new:Npn \__fp_use_i:ww #1; #2; { #1; } \__scan_new:N \s__fp \cs_new_protected:Npn \__fp_chk:w #1 ; { @@ -366,7 +369,7 @@ conversion~functions. } %% -%% File: l3fp-traps.dtx Copyright (C) 2011-2012 The LaTeX3 Project +%% File: l3fp-traps.dtx Copyright (C) 2011-2013 The LaTeX3 Project %% %% It may be distributed and/or modified under the conditions of the %% LaTeX Project Public License (LPPL), either version 1.3c of this @@ -533,6 +536,7 @@ \fp_trap:nn { underflow } { flag } \cs_new_nopar:Npn \__fp_invalid_operation_o:nw { \__fp_invalid_operation:nnw { \exp_after:wN \c_nan_fp } } +\cs_generate_variant:Nn \__fp_invalid_operation_o:nw { f } \cs_new:Npn \__fp_error:nnnn #1 { \__msg_kernel_expandable_error:nnnnn { kernel } { fp - #1 } } \cs_generate_variant:Nn \__fp_error:nnnn { nnf, nff } @@ -773,7 +777,7 @@ \exp_after:wN \__fp_exp_after_o:w \tex_romannumeral:D -`0 \__fp_sanitize:Nw #1#2; {1000}{0000}{0000}{0000}; } -%% File: l3fp-parse.dtx Copyright (C) 2011-2012 The LaTeX3 Project +%% File: l3fp-parse.dtx Copyright (C) 2011-2013 The LaTeX3 Project %% %% It may be distributed and/or modified under the conditions of the %% LaTeX Project Public License (LPPL), either version 1.3c of this @@ -844,84 +848,109 @@ \__fp_tmp:w {ii} \__fp_parse_digits_i:N { 00 ; 2 } \__fp_tmp:w {i} \__fp_parse_digits_:N { 0 ; 1 } \cs_new_nopar:Npn \__fp_parse_digits_:N { ; ; 0 } -\cs_new:Npn \__fp_parse_operand:Nw #1 #2 +\cs_new:Npn \__fp_parse_one:Nw #1 #2 { - \if_catcode:w \tex_relax:D #2 - \if_meaning:w \tex_relax:D #2 + \if_catcode:w \scan_stop: \exp_not:N #2 + \if_meaning:w \scan_stop: #2 \exp_after:wN \exp_after:wN - \exp_after:wN \__fp_parse_operand_relax:NN + \exp_after:wN \__fp_parse_one_fp:NN \else: \exp_after:wN \exp_after:wN - \exp_after:wN \__fp_parse_operand_register:NN + \exp_after:wN \__fp_parse_one_register:NN \fi: \else: \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f: \exp_after:wN \exp_after:wN - \exp_after:wN \__fp_parse_operand_digit:NN + \exp_after:wN \__fp_parse_one_digit:NN \else: \exp_after:wN \exp_after:wN - \exp_after:wN \__fp_parse_operand_other:NN + \exp_after:wN \__fp_parse_one_other:NN \fi: \fi: #1 #2 } +\cs_new:Npn \__fp_parse_one_fp:NN #1#2 + { + \cs:w __fp_exp_after \__fp_type_from_scan:N #2 _f:nw \cs_end: + { + \exp_after:wN \__fp_parse_infix:NN + \exp_after:wN #1 \tex_romannumeral:D \__fp_parse_expand:w + } + #2 + } +\cs_new:Npn \__fp_exp_after_mark_f:nw #1 + { + \__msg_kernel_expandable_error:nn { kernel } { fp-early-end } + \exp_after:wN \c_nan_fp \tex_romannumeral:D -`0 #1 + } +\cs_new:cpn { __fp_exp_after_?_f:nw } #1#2 + { + \__msg_kernel_expandable_error:nnn { kernel } { bad-variable } {#2} + \exp_after:wN \c_nan_fp \tex_romannumeral:D -`0 #1 + } +\cs_new:Npn \__fp_parse_one_register:NN #1#2 + { + \exp_after:wN \__fp_parse_infix_after_operand:NwN + \exp_after:wN #1 + \tex_romannumeral:D -`0 + \exp_after:wN \__fp_parse_one_register_aux:Nw + \exp_after:wN #2 + \__int_value:w + \exp_after:wN \__fp_parse_exponent:N + \tex_romannumeral:D \__fp_parse_expand:w + } \group_begin: \char_set_catcode_other:N \P \char_set_catcode_other:N \T +\char_set_catcode_other:N \M +\char_set_catcode_other:N \U \tl_to_lowercase:n { \group_end: - \cs_new:Npn \__fp_parse_operand_register:NN #1#2 + \cs_new:Npn \__fp_parse_one_register_aux:Nw #1 { - \exp_after:wN \__fp_parse_infix_after_operand:NwN - \exp_after:wN #1 - \tex_romannumeral:D -`0 - \exp_after:wN \__fp_parse_operand_register_aux:www - \tex_the:D - \exp_after:wN #2 - \exp_after:wN P - \exp_after:wN T - \exp_after:wN \q_stop - \__int_value:w \__fp_parse_exponent:N + \exp_after:wN \use:nn + \exp_after:wN \__fp_parse_one_register_auxii:wwwNw + \exp_after:wN { \tex_the:D \exp_not:N #1 } + ; \__fp_parse_one_register_dim:ww + PT ; \__fp_parse_one_register_mu:www + . PT ; \__fp_parse_one_register_int:www + \q_stop } - \cs_new:Npn \__fp_parse_operand_register_aux:www #1 PT #2 \q_stop #3 ; - { \__fp_parse:n { #1 e #3 } } - } -\cs_new:Npn \__fp_parse_operand_relax:NN #1#2 - { - \cs:w __fp_parse_exp_after \__fp_type_from_scan:N #2 _f:nw \cs_end: - { - \exp_after:wN \__fp_parse_infix:NN - \exp_after:wN #1 \tex_romannumeral:D \__fp_parse_expand:w - } - #2 + \cs_new:Npn \__fp_parse_one_register_auxii:wwwNw + #1 . #2 PT #3 ; #4#5 \q_stop { #4 #1.#2; } + \cs_new:Npn \__fp_parse_one_register_mu:www #1 MU; #2; + { \__fp_parse_one_register_dim:ww #1; } } -\cs_new_eq:NN \__fp_parse_exp_after_f:nw \__fp_exp_after_f:nw -\cs_new:Npn \__fp_parse_exp_after_mark_f:nw #1 +\cs_new:Npn \__fp_parse_one_register_int:www #1; #2.; #3; + { \__fp_parse:n { #1 e #3 } } +\cs_new:Npn \__fp_parse_one_register_dim:ww #1; #2; { - \__msg_kernel_expandable_error:nn { kernel } { fp-early-end } - \exp_after:wN \c_nan_fp - \tex_romannumeral:D -`0 #1 + \exp_after:wN \__fp_from_dim_test:ww + \__int_value:w #2 \exp_after:wN , + \__int_value:w \__dim_eval:w #1 pt ; } -\cs_new:cpn { __fp_parse_exp_after_?_f:nw } #1#2 +\cs_new:Npn \__fp_parse_one_digit:NN #1 { - \__msg_kernel_expandable_error:nnn - { kernel } { bad-variable } {#2} - \exp_after:wN \c_nan_fp - \tex_romannumeral:D -`0 #1 + \exp_after:wN \__fp_parse_infix_after_operand:NwN + \exp_after:wN #1 + \tex_romannumeral:D -`0 + \exp_after:wN \__fp_sanitize:wN + \int_use:N \__int_eval:w \c_zero \__fp_parse_trim_zeros:N } -\cs_new:Npn \__fp_parse_operand_other:NN #1 #2 +\cs_new:Npn \__fp_parse_one_other:NN #1 #2 { \if_int_compare:w - \__int_eval:w \tex_uccode:D `#2 / 26 = \c_three - \exp_after:wN \__fp_parse_operand_other_word_aux:Nw + \__int_eval:w + ( `#2 \if_int_compare:w `#2 > `Z - \c_thirty_two \fi: ) / 26 + = \c_three + \exp_after:wN \__fp_parse_word:Nw \exp_after:wN #1 + \exp_after:wN #2 + \tex_romannumeral:D \exp_after:wN \__fp_parse_letters:N \tex_romannumeral:D - \exp_after:wN \__fp_parse_letters:NN - \exp_after:wN #2 - \tex_romannumeral:D \else: - \exp_after:wN \__fp_parse_operand_other_prefix_aux:NNN + \exp_after:wN \__fp_parse_prefix:NNN \exp_after:wN #1 \exp_after:wN #2 \cs:w __fp_parse_prefix_#2:Nw \exp_after:wN \cs_end: @@ -929,81 +958,67 @@ \fi: \__fp_parse_expand:w } - -\cs_new:Npn \__fp_parse_letters:NN #1#2 - { - \exp_after:wN \c_zero - \exp_after:wN #1 - \tex_romannumeral:D - \if_int_compare:w - \if_catcode:w \tex_relax:D #2 - \c_zero - \else: - \__int_eval:w \tex_uccode:D `#2 / 26 - \fi: - = \c_three - \exp_after:wN \__fp_parse_letters:NN - \exp_after:wN #2 - \tex_romannumeral:D - \exp_after:wN \__fp_parse_expand:w - \else: - \exp_after:wN \c_zero - \exp_after:wN ; - \exp_after:wN #2 - \fi: - } -\cs_new:Npn \__fp_parse_operand_other_word_aux:Nw #1 #2; +\cs_new:Npn \__fp_parse_word:Nw #1#2; { \cs_if_exist_use:cF { __fp_parse_word_#2:N } { \__msg_kernel_expandable_error:nnn { kernel } { unknown-fp-word } {#2} - \exp_after:wN \c_nan_fp - \tex_romannumeral:D -`0 - \__fp_parse_infix:NN + \exp_after:wN \c_nan_fp \tex_romannumeral:D -`0 + \__fp_parse_infix:NN } #1 } -\cs_new_eq:NN \s__fp_unknown \tex_relax:D -\cs_new:Npn \__fp_parse_operand_other_prefix_aux:NNN #1#2#3 +\cs_new:Npn \__fp_parse_letters:N #1 + { + -`0 + \if_int_compare:w + \if_catcode:w \scan_stop: \exp_not:N #1 + \c_zero + \else: + \__int_eval:w + ( `#1 \if_int_compare:w `#1 > `Z - \c_thirty_two \fi: ) + / 26 + \fi: + = \c_three + \exp_after:wN #1 + \tex_romannumeral:D \exp_after:wN \__fp_parse_letters:N + \tex_romannumeral:D + \else: + \__fp_parse_return_semicolon:w #1 + \fi: + \__fp_parse_expand:w + } +\cs_new:Npn \__fp_parse_prefix:NNN #1#2#3 { - \if_meaning:w \tex_relax:D #3 - \exp_after:wN \__fp_parse_operand_other_prefix_unknown:NNN + \if_meaning:w \scan_stop: #3 + \exp_after:wN \__fp_parse_prefix_unknown:NNN \exp_after:wN #2 \fi: #3 #1 } -\cs_new:Npn \__fp_parse_operand_other_prefix_unknown:NNN #1#2#3 +\cs_new:Npn \__fp_parse_prefix_unknown:NNN #1#2#3 { \cs_if_exist:cTF { __fp_parse_infix_#1:N } { \__msg_kernel_expandable_error:nnn { kernel } { fp-missing-number } {#1} - \exp_after:wN \c_nan_fp - \tex_romannumeral:D -`0 - \__fp_parse_infix:NN #3 #1 + \exp_after:wN \c_nan_fp \tex_romannumeral:D -`0 + \__fp_parse_infix:NN #3 #1 } { \__msg_kernel_expandable_error:nnn { kernel } { fp-unknown-symbol } {#1} - \__fp_parse_operand:Nw #3 + \__fp_parse_one:Nw #3 } } -\cs_new:Npn \__fp_parse_operand_digit:NN #1 - { - \exp_after:wN \__fp_parse_infix_after_operand:NwN - \exp_after:wN #1 - \tex_romannumeral:D -`0 - \exp_after:wN \__fp_sanitize:wN - \int_use:N \__int_eval:w \c_zero \__fp_parse_trim_zeros:N - } \cs_new:Npn \__fp_parse_trim_zeros:N #1 { - \if:w 0 #1 + \if:w 0 \exp_not:N #1 \exp_after:wN \__fp_parse_trim_zeros:N \tex_romannumeral:D \else: - \if:w . #1 + \if:w . \exp_not:N #1 \exp_after:wN \__fp_parse_strim_zeros:N \tex_romannumeral:D \else: @@ -1025,10 +1040,9 @@ } \cs_new:Npn \__fp_parse_strim_zeros:N #1 { - \if:w 0 #1 + \if:w 0 \exp_not:N #1 - \c_one - \exp_after:wN \__fp_parse_strim_zeros:N - \tex_romannumeral:D + \exp_after:wN \__fp_parse_strim_zeros:N \tex_romannumeral:D \else: \__fp_parse_strim_end:w #1 \fi: @@ -1119,7 +1133,7 @@ \exp_after:wN \__fp_parse_digits_vi:N \tex_romannumeral:D \else: - \if:w . #4 + \if:w . \exp_not:N #4 \exp_after:wN \__fp_parse_small_leading:wwNN \__int_value:w 1 \cs:w @@ -1151,7 +1165,7 @@ \exp_after:wN \__fp_parse_pack_trailing:NNNNNNww \int_use:N \__int_eval:w \c_seven - #3 \exp_stop_f: \int_use:N \__int_eval:w 1 #1 - \if:w . #4 + \if:w . \exp_not:N #4 \exp_after:wN \__fp_parse_small_trailing:wwNN \__int_value:w 1 \cs:w @@ -1166,6 +1180,100 @@ \fi: \__fp_parse_expand:w } +\cs_new:Npn \__fp_parse_round_loop:N #1 + { + \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f: + + \c_one + \if:w 0 \token_to_str:N #1 + \exp_after:wN \__fp_parse_round_loop:N + \tex_romannumeral:D + \else: + \exp_after:wN \__fp_parse_round_up:N + \tex_romannumeral:D + \fi: + \else: + \__fp_parse_return_semicolon:w \c_zero #1 + \fi: + \__fp_parse_expand:w + } +\cs_new:Npn \__fp_parse_round_up:N #1 + { + \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f: + + \c_one + \exp_after:wN \__fp_parse_round_up:N + \tex_romannumeral:D + \else: + \__fp_parse_return_semicolon:w \c_one #1 + \fi: + \__fp_parse_expand:w + } +\cs_new:Npn \__fp_parse_round_after:wN #1; #2 + { + + #2 \exp_after:wN ; + \int_use:N \__int_eval:w #1 + \__fp_parse_exponent:N + } +\cs_new:Npn \__fp_parse_small_round:NN #1#2 + { + \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f: + + + \exp_after:wN \__fp_round_s:NNNw + \exp_after:wN 0 + \exp_after:wN #1 + \exp_after:wN #2 + \int_use:N \__int_eval:w + \exp_after:wN \__fp_parse_round_after:wN + \int_use:N \__int_eval:w \c_zero * \__int_eval:w \c_zero + \exp_after:wN \__fp_parse_round_loop:N + \tex_romannumeral:D + \else: + \__fp_parse_exponent:Nw #2 + \fi: + \__fp_parse_expand:w + } +\cs_new:Npn \__fp_parse_large_round:NN #1#2 + { + \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f: + + + \exp_after:wN \__fp_round_s:NNNw + \exp_after:wN 0 + \exp_after:wN #1 + \exp_after:wN #2 + \int_use:N \__int_eval:w + \exp_after:wN \__fp_parse_large_round_aux:wNN + \int_use:N \__int_eval:w \c_one + \exp_after:wN \__fp_parse_round_loop:N + \else: %^^A could be dot, or e, or other + \exp_after:wN \__fp_parse_large_round_test:NN + \exp_after:wN #1 + \exp_after:wN #2 + \fi: + } +\cs_new:Npn \__fp_parse_large_round_test:NN #1#2 + { + \if:w . \exp_not:N #2 + \exp_after:wN \__fp_parse_small_round:NN + \exp_after:wN #1 + \tex_romannumeral:D + \else: + \__fp_parse_exponent:Nw #2 + \fi: + \__fp_parse_expand:w + } +\cs_new:Npn \__fp_parse_large_round_aux:wNN #1 ; #2 #3 + { + + #2 + \exp_after:wN \__fp_parse_round_after:wN + \int_use:N \__int_eval:w #1 + \if:w . \exp_not:N #3 + + \c_zero * \__int_eval:w \c_zero + \exp_after:wN \__fp_parse_round_loop:N + \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w + \else: + \exp_after:wN ; + \exp_after:wN \c_zero + \exp_after:wN #3 + \fi: + } \cs_new:Npn \__fp_parse_exponent:Nw #1 #2 \__fp_parse_expand:w { \exp_after:wN ; @@ -1173,7 +1281,7 @@ } \cs_new:Npn \__fp_parse_exponent:N #1 { - \if:w e #1 + \if:w e \exp_not:N #1 \exp_after:wN \__fp_parse_exponent_aux:N \tex_romannumeral:D \else: @@ -1183,7 +1291,7 @@ } \cs_new:Npn \__fp_parse_exponent_aux:N #1 { - \if_int_compare:w \if_catcode:w \tex_relax:D #1 + \if_int_compare:w \if_catcode:w \scan_stop: \exp_not:N #1 \c_zero \else: `#1 \fi: > `9 \exp_stop_f: 0 \exp_after:wN ; \exp_after:wN e \else: @@ -1193,7 +1301,7 @@ } \cs_new:Npn \__fp_parse_exponent_sign:N #1 { - \if:w + \if:w - #1 + \fi: \token_to_str:N #1 + \if:w + \if:w - \exp_not:N #1 + \fi: \token_to_str:N #1 \exp_after:wN \__fp_parse_exponent_sign:N \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w \else: @@ -1230,9 +1338,10 @@ } \prg_new_conditional:Npnn \__fp_parse_exponent_keep:N #1 { TF } { - \if_catcode:w \tex_relax:D #1 - \if_meaning:w \tex_relax:D #1 - \if_int_compare:w \pdftex_strcmp:D { \s__fp } { #1 } = \c_zero + \if_catcode:w \scan_stop: \exp_not:N #1 + \if_meaning:w \scan_stop: #1 + \if_int_compare:w + \pdftex_strcmp:D { \s__fp } { \exp_not:N #1 } = \c_zero 0 \__msg_kernel_expandable_error:nnn { kernel } { fp-after-e } { floating~point~ } @@ -1262,210 +1371,70 @@ \prg_return_true: \fi: } -\cs_new:Npn \__fp_cfs_round_loop:N #1 - { - \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f: - + \c_one - \if:w 0 #1 - \exp_after:wN \__fp_cfs_round_loop:N - \tex_romannumeral:D - \else: - \exp_after:wN \__fp_cfs_round_up:N - \tex_romannumeral:D - \fi: - \else: - \__fp_parse_return_semicolon:w \c_zero #1 - \fi: - \__fp_parse_expand:w - } -\cs_new:Npn \__fp_cfs_round_up:N #1 - { - \if_int_compare:w \c_nine < 1 \token_to_str:N #1 \exp_stop_f: - + 1 - \exp_after:wN \__fp_cfs_round_up:N - \tex_romannumeral:D - \else: - \__fp_parse_return_semicolon:w \c_one #1 - \fi: - \__fp_parse_expand:w - } -\cs_new:Npn \__fp_parse_large_round:NN #1#2 - { - \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f: - + - \exp_after:wN \__fp_round_s:NNNw - \exp_after:wN 0 - \exp_after:wN #1 - \exp_after:wN #2 - \int_use:N \__int_eval:w - \exp_after:wN \__fp_parse_large_round_after:wNN - \int_use:N \__int_eval:w \c_one - \exp_after:wN \__fp_cfs_round_loop:N - \else: %^^A could be dot, or e, or other - \exp_after:wN \__fp_parse_large_round_dot_test:NNw - \exp_after:wN #1 - \exp_after:wN #2 - \fi: - } -\cs_new:Npn \__fp_parse_large_round_dot_test:NNw #1#2 - { - \if:w . #2 - \exp_after:wN \__fp_parse_small_round:NN - \exp_after:wN #1 - \tex_romannumeral:D - \else: - \__fp_parse_exponent:Nw #2 - \fi: - \__fp_parse_expand:w - } -\cs_new:Npn \__fp_parse_large_round_after:wNN #1 ; #2 #3 - { - \if:w . #3 - \exp_after:wN \__fp_parse_large_round_after_aux:wN - \int_use:N \__int_eval:w #1 + - \c_zero * \__int_eval:w \c_zero - \exp_after:wN \__fp_cfs_round_loop:N - \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w - \else: - + #2 - \exp_after:wN ; - \int_use:N \__int_eval:w #1 + - \exp_after:wN \__fp_parse_exponent:N - \exp_after:wN #3 - \fi: - } -\cs_new:Npn \__fp_parse_large_round_after_aux:wN #1 ; #2 - { - + #2 - \exp_after:wN ; - \int_use:N \__int_eval:w #1 + - \__fp_parse_exponent:N - } -\cs_new:Npn \__fp_parse_small_round:NN #1#2 - { - \if_int_compare:w \c_nine < 1 \token_to_str:N #2 \exp_stop_f: - + - \exp_after:wN \__fp_round_s:NNNw - \exp_after:wN 0 - \exp_after:wN #1 - \exp_after:wN #2 - \int_use:N \__int_eval:w - \exp_after:wN \__fp_parse_small_round_after:wN - \int_use:N \__int_eval:w \c_zero - \exp_after:wN \__fp_cfs_round_loop:N - \tex_romannumeral:D - \else: - \__fp_parse_exponent:Nw #2 - \fi: - \__fp_parse_expand:w - } -\cs_new:Npn \__fp_parse_small_round_after:wN #1; #2 +\cs_new_eq:cN { __fp_parse_prefix_+:Nw } \__fp_parse_one:Nw +\cs_new:Npn \__fp_parse_apply_unary:NNNwN #1#2#3#4@#5 { - + #2 \exp_after:wN ; - \__int_value:w \__fp_parse_exponent:N + #3 #2 #4 @ + \tex_romannumeral:D -`0 #5 #1 } -\cs_new:Npn \__fp_parse:n #1 - { - \tex_romannumeral:D - \exp_after:wN \__fp_parse_after:ww - \tex_romannumeral:D - \__fp_parse_until:Nw \c_minus_one - \__fp_parse_expand:w #1 \s__fp_mark - \s__fp_stop - } -\cs_new:Npn \__fp_parse_after:ww #1@ #2 \s__fp_stop +\cs_set_protected:Npn \__fp_tmp:w #1#2#3#4 { - \c_zero #1 + \cs_new:cpn { __fp_parse_prefix_ #1 :Nw } ##1 + { + \exp_after:wN \__fp_parse_apply_unary:NNNwN + \exp_after:wN ##1 + \exp_after:wN #4 + \cs:w __fp_#3_o:w \exp_after:wN \cs_end: + \tex_romannumeral:D + \if_int_compare:w #2 < ##1 + \__fp_parse_operand:Nw ##1 + \else: + \__fp_parse_operand:Nw #2 + \fi: + \__fp_parse_expand:w + } } -\cs_new:Npn \__fp_parse_until:Nw #1 +\__fp_tmp:w - \c_twelve { set_sign } 2 +\__fp_tmp:w ! \c_twelve { not } ? +\cs_new:cpn { __fp_parse_prefix_.:Nw } #1 { - -`0 - \exp_after:wN \__fp_parse_until_test:NwN + \exp_after:wN \__fp_parse_infix_after_operand:NwN \exp_after:wN #1 \tex_romannumeral:D -`0 - \exp_after:wN \__fp_parse_operand:Nw - \exp_after:wN #1 - \tex_romannumeral:D - } -\cs_new:Npn \__fp_parse_until_test:NwN #1 #2 @ #3 { #3 #1 #2 @ } -\cs_new_eq:NN \__fp_parse_stop_until:N \use_none:n -\cs_new:Npn \__fp_parse_infix_after_operand:NwN #1 #2; - { - \__fp_exp_after_f:nw { \__fp_parse_infix:NN #1 } - #2; + \exp_after:wN \__fp_sanitize:wN + \int_use:N \__int_eval:w \c_zero \__fp_parse_strim_zeros:N } \group_begin: - \char_set_catcode_letter:N \* - \cs_new:Npn \__fp_parse_infix:NN #1 #2 + \char_set_catcode_letter:N ( + \char_set_catcode_letter:N ) + \cs_new:Npn \__fp_parse_prefix_(:Nw #1 { - \if_catcode:w \tex_relax:D #2 - \if_int_compare:w - \pdftex_strcmp:D { \s__fp_mark } { #2 } - = \c_zero - \exp_after:wN \exp_after:wN - \exp_after:wN \__fp_parse_infix_end:N - \else: - \exp_after:wN \exp_after:wN - \exp_after:wN \__fp_parse_infix_juxtapose:N - \fi: + \exp_after:wN \__fp_parse_lparen_after:NwN + \exp_after:wN #1 + \tex_romannumeral:D + \if_int_compare:w #1 = \c_sixteen + \__fp_parse_operand:Nw \c_one \else: - \if_int_compare:w - \__int_eval:w \tex_uccode:D `#2 / 26 - = \c_three - \exp_after:wN \exp_after:wN - \exp_after:wN \__fp_parse_infix_juxtapose:N - \else: - \exp_after:wN \__fp_parse_infix_check:NNN - \cs:w - __fp_parse_infix_#2:N - \exp_after:wN \exp_after:wN \exp_after:wN - \cs_end: - \fi: + \__fp_parse_operand:Nw \c_zero \fi: - #1 - #2 + \__fp_parse_expand:w } - \cs_new:Npn \__fp_parse_infix_check:NNN #1#2#3 + \cs_new:Npn \__fp_parse_lparen_after:NwN #1#2 @ #3 { - \if_meaning:w \tex_relax:D #1 - \__msg_kernel_expandable_error:nnn { kernel } { fp-missing } { * } - \exp_after:wN \__fp_parse_infix_*:N - \exp_after:wN #2 - \exp_after:wN #3 - \else: - \exp_after:wN #1 - \exp_after:wN #2 - \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w - \fi: + \token_if_eq_meaning:NNTF #3 \__fp_parse_infix_):N + { + \__fp_exp_after_array_f:w #2 \s__fp_stop + \exp_after:wN \__fp_parse_infix:NN + \exp_after:wN #1 + \tex_romannumeral:D \__fp_parse_expand:w + } + { + \__msg_kernel_expandable_error:nnn + { kernel } { fp-missing } { ) } + #2 @ \use_none:n #3 + } } \group_end: -\cs_new:Npn \__fp_parse_apply_binary:NwNwN #1 #2#3@ #4 #5#6@ #7 - { - \exp_after:wN \__fp_parse_until_test:NwN - \exp_after:wN #1 - \tex_romannumeral:D -`0 - \cs:w - __fp - \__fp_type_from_scan:N #2 - _ #4 - \__fp_type_from_scan:N #5 - _o:ww - \cs_end: - #2#3 #5#6 - \tex_romannumeral:D -`0 #7 #1 - } -\cs_new:Npn \__fp_parse_apply_unary_array:NNwN #1#2#3@#4 - { - #2 #3 @ - \tex_romannumeral:D -`0 #4 #1 - } -\cs_new:Npn \__fp_parse_apply_unary:NNwN #1#2#3@#4 - { - #2 #3 - \tex_romannumeral:D -`0 #4 #1 - } -\cs_new:Npn \__fp_parse_unary_type:N #1 - { \__fp_type_from_scan:N #1 _o:w \cs_end: #1 } \cs_set_protected:Npn \__fp_tmp:w #1 #2 { \cs_new_nopar:cpn { __fp_parse_word_#1:N } @@ -1477,7 +1446,6 @@ \__fp_tmp:w { deg } \c_one_degree_fp \__fp_tmp:w { true } \c_one_fp \__fp_tmp:w { false } \c_zero_fp -\__fp_tmp:w { pt } \c_one_fp \cs_set_protected:Npn \__fp_tmp:w #1 #2 { \cs_new_nopar:cpn { __fp_parse_word_#1:N } @@ -1486,6 +1454,7 @@ \s__fp \__fp_chk:w 10 #2 ; } } +\__fp_tmp:w {pt} { {1} {1000} {0000} {0000} {0000} } \__fp_tmp:w {in} { {2} {7227} {0000} {0000} {0000} } \__fp_tmp:w {pc} { {2} {1200} {0000} {0000} {0000} } \__fp_tmp:w {cm} { {2} {2845} {2755} {9055} {1181} } @@ -1500,37 +1469,59 @@ { \cs_new_nopar:cpn { __fp_parse_word_#1:N } { - \exp_after:wN \dim_to_fp:n \exp_after:wN - { \dim_use:N \__dim_eval:w 1 #1 \exp_after:wN } + \exp_after:wN \__fp_from_dim_test:ww + \exp_after:wN 0 \exp_after:wN , + \__int_value:w \__dim_eval:w 1 #1 \exp_after:wN ; \tex_romannumeral:D -`0 \__fp_parse_infix:NN } } +\cs_new:Npn \__fp_parse_unary_function:nNN #1#2#3 + { + \exp_after:wN \__fp_parse_apply_unary:NNNwN + \exp_after:wN #3 + \exp_after:wN #2 + \cs:w __fp_#1_o:w \exp_after:wN \cs_end: + \tex_romannumeral:D + \__fp_parse_operand:Nw \c_fifteen \__fp_parse_expand:w + } +\cs_new:Npn \__fp_parse_function:NNN #1#2#3 + { + \exp_after:wN \__fp_parse_apply_unary:NNNwN + \exp_after:wN #3 + \exp_after:wN #2 + \exp_after:wN #1 + \tex_romannumeral:D + \__fp_parse_operand:Nw \c_sixteen \__fp_parse_expand:w + } +\cs_new_nopar:Npn \__fp_parse_word_acot:N + { \__fp_parse_function:NNN \__fp_acot_o:Nw \use_i:nn } +\cs_new_nopar:Npn \__fp_parse_word_acotd:N + { \__fp_parse_function:NNN \__fp_acot_o:Nw \use_ii:nn } +\cs_new_nopar:Npn \__fp_parse_word_atan:N + { \__fp_parse_function:NNN \__fp_atan_o:Nw \use_i:nn } +\cs_new_nopar:Npn \__fp_parse_word_atand:N + { \__fp_parse_function:NNN \__fp_atan_o:Nw \use_ii:nn } +\cs_new_nopar:Npn \__fp_parse_word_max:N + { \__fp_parse_function:NNN \__fp_minmax_o:Nw 2 } +\cs_new_nopar:Npn \__fp_parse_word_min:N + { \__fp_parse_function:NNN \__fp_minmax_o:Nw 0 } +\cs_new:Npn \__fp_parse_word_abs:N + { \__fp_parse_unary_function:nNN { set_sign } 0 } +\cs_new_nopar:Npn \__fp_parse_word_exp:N + { \__fp_parse_unary_function:nNN {exp} ? } +\cs_new_nopar:Npn \__fp_parse_word_ln:N + { \__fp_parse_unary_function:nNN {ln} ? } \tl_map_inline:nn - { {abs} {cos} {cot} {csc} {exp} {ln} {sec} {sin} {tan} } { - \cs_new:cpn { __fp_parse_word_#1:N } ##1 - { - \exp_after:wN \__fp_parse_apply_unary:NNwN - \exp_after:wN ##1 - \cs:w __fp_ #1 \exp_after:wN \__fp_parse_unary_type:N - \tex_romannumeral:D - \__fp_parse_until:Nw \c_fifteen - \__fp_parse_expand:w - } + {acos} {acsc} {asec} {asin} + {cos} {cot} {csc} {sec} {sin} {tan} } -\cs_set_protected:Npn \__fp_tmp:w #1#2 { - \cs_new:Npn #1 ##1 - { - \exp_after:wN \__fp_parse_apply_unary_array:NNwN - \exp_after:wN ##1 - \exp_after:wN #2 - \tex_romannumeral:D - \__fp_parse_until:Nw \c_sixteen \__fp_parse_expand:w - } + \cs_new_nopar:cpn { __fp_parse_word_#1:N } + { \__fp_parse_unary_function:nNN {#1} \use_i:nn } + \cs_new_nopar:cpn { __fp_parse_word_#1d:N } + { \__fp_parse_unary_function:nNN {#1} \use_ii:nn } } -\__fp_tmp:w \__fp_parse_word_max:N \__fp_max_o:w -\__fp_tmp:w \__fp_parse_word_min:N \__fp_min_o:w \cs_new:Npn \__fp_parse_word_round:N #1#2 { \if_meaning:w + #2 @@ -1548,7 +1539,7 @@ \exp_after:wN #1 \exp_after:wN \__fp_round_to_nearest:NNN \tex_romannumeral:D - \__fp_parse_until:Nw \c_sixteen \__fp_parse_expand:w #2 + \__fp_parse_operand:Nw \c_sixteen \__fp_parse_expand:w #2 } \cs_new:Npn \__fp_parse_round:Nw #1 #2 \__fp_round_to_nearest:NNN #3 \__fp_parse_expand:w #4 @@ -1565,96 +1556,199 @@ \fi: -`0 #4 #1 } -\cs_new_eq:cN { __fp_parse_prefix_+:Nw } \__fp_parse_operand:Nw -\cs_set_protected:Npn \__fp_tmp:w #1#2 +\cs_new:Npn \__fp_parse:n #1 { - \cs_new:cpn { __fp_parse_prefix_#1:Nw } ##1 - { - \exp_after:wN \__fp_parse_apply_unary:NNwN - \exp_after:wN ##1 - \cs:w __fp_ #2 \exp_after:wN \__fp_parse_unary_type:N - \tex_romannumeral:D - \if_int_compare:w \c_twelve < ##1 - \__fp_parse_until:Nw ##1 + \tex_romannumeral:D + \exp_after:wN \__fp_parse_after:ww + \tex_romannumeral:D + \__fp_parse_operand:Nw \c_minus_one + \__fp_parse_expand:w #1 \s__fp_mark + \s__fp_stop + } +\cs_new:Npn \__fp_parse_after:ww + #1@ \__fp_parse_infix_end:N \s__fp_mark \s__fp_stop + { \c_zero #1 } +\cs_new:Npn \__fp_parse_operand:Nw #1 + { + -`0 + \exp_after:wN \__fp_parse_continue:NwN + \exp_after:wN #1 + \tex_romannumeral:D -`0 + \exp_after:wN \__fp_parse_one:Nw + \exp_after:wN #1 + \tex_romannumeral:D + } +\cs_new:Npn \__fp_parse_continue:NwN #1 #2 @ #3 { #3 #1 #2 @ } +\cs_new:Npn \__fp_parse_apply_binary:NwNwN #1 #2@ #3 #4@ #5 + { + \exp_after:wN \__fp_parse_continue:NwN + \exp_after:wN #1 + \tex_romannumeral:D -`0 \cs:w __fp_#3_o:ww \cs_end: #2 #4 + \tex_romannumeral:D -`0 #5 #1 + } +\cs_new:Npn \__fp_parse_infix_after_operand:NwN #1 #2; + { + \__fp_exp_after_f:nw { \__fp_parse_infix:NN #1 } + #2; + } +\group_begin: + \char_set_catcode_letter:N \* + \cs_new:Npn \__fp_parse_infix:NN #1 #2 + { + \if_catcode:w \scan_stop: \exp_not:N #2 + \if_int_compare:w + \pdftex_strcmp:D { \s__fp_mark } { \exp_not:N #2 } + = \c_zero + \exp_after:wN \exp_after:wN + \exp_after:wN \__fp_parse_infix_end:N \else: - \__fp_parse_until:Nw \c_twelve + \exp_after:wN \exp_after:wN + \exp_after:wN \__fp_parse_infix_juxtapose:N \fi: - \__fp_parse_expand:w - } - } -\__fp_tmp:w - { - } -\__fp_tmp:w ! { ! } + \else: + \if_int_compare:w + \__int_eval:w + ( `#2 \if_int_compare:w `#2 > `Z - \c_thirty_two \fi: ) + / 26 + = \c_three + \exp_after:wN \exp_after:wN + \exp_after:wN \__fp_parse_infix_juxtapose:N + \else: + \exp_after:wN \__fp_parse_infix_check:NNN + \cs:w + __fp_parse_infix_#2:N + \exp_after:wN \exp_after:wN \exp_after:wN + \cs_end: + \fi: + \fi: + #1 + #2 + } + \cs_new:Npn \__fp_parse_infix_check:NNN #1#2#3 + { + \if_meaning:w \scan_stop: #1 + \__msg_kernel_expandable_error:nnn + { kernel } { fp-missing } { * } + \exp_after:wN \__fp_parse_infix_*:N + \exp_after:wN #2 + \exp_after:wN #3 + \else: + \exp_after:wN #1 + \exp_after:wN #2 + \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w + \fi: + } +\group_end: +\cs_new:Npn \__fp_parse_infix_end:N #1 + { @ \use_none:n \__fp_parse_infix_end:N } \group_begin: \char_set_catcode_letter:N \) - \cs_new:cpn { __fp_parse_prefix_(:Nw } #1 + \cs_new:Npn \__fp_parse_infix_):N #1 { - \exp_after:wN \__fp_parse_lparen_after:NwN - \exp_after:wN #1 - \tex_romannumeral:D - \if_int_compare:w #1 = \c_sixteen - \__fp_parse_until:Nw \c_one + \if_int_compare:w #1 < \c_zero + \__msg_kernel_expandable_error:nnn { kernel } { fp-extra } { ) } + \exp_after:wN \__fp_parse_infix:NN + \exp_after:wN #1 + \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w \else: - \__fp_parse_until:Nw \c_zero + \exp_after:wN @ + \exp_after:wN \use_none:n + \exp_after:wN \__fp_parse_infix_):N \fi: - \__fp_parse_expand:w } - \cs_new:Npn \__fp_parse_lparen_after:NwN #1#2@#3 +\group_end: +\group_begin: + \char_set_catcode_letter:N \, + \cs_new:Npn \__fp_parse_infix_,:N #1 { - \token_if_eq_meaning:NNTF #3 \__fp_parse_infix_):N - { - \__fp_exp_after_array_f:w #2 \s__fp_stop - \exp_after:wN \__fp_parse_infix:NN - \exp_after:wN #1 - \tex_romannumeral:D \__fp_parse_expand:w - } + \if_int_compare:w #1 > \c_one + \exp_after:wN @ + \exp_after:wN \use_none:n + \exp_after:wN \__fp_parse_infix_,:N + \else: + \if_int_compare:w #1 = \c_one + \exp_after:wN \__fp_parse_infix_comma:w + \tex_romannumeral:D + \else: + \exp_after:wN \__fp_parse_infix_comma_gobble:w + \tex_romannumeral:D + \fi: + \__fp_parse_operand:Nw \c_one + \exp_after:wN \__fp_parse_expand:w + \fi: + } + \cs_new:Npn \__fp_parse_infix_comma:w #1 @ + { #1 @ \use_none:n } + \cs_new:Npn \__fp_parse_infix_comma_gobble:w #1 @ + { + \__msg_kernel_expandable_error:nn { kernel } { fp-extra-comma } + @ \use_none:n + } +\group_end: +\group_begin: + \char_set_catcode_other:N \& + \char_set_catcode_letter:N \^ + \char_set_catcode_letter:N \/ + \char_set_catcode_letter:N \- + \char_set_catcode_letter:N \+ + \cs_set_protected:Npn \__fp_tmp:w #1#2#3#4 + { + \cs_new:Npn #1 ##1 { - \__msg_kernel_expandable_error:nnn { kernel } { fp-missing } { ) } - #2 @ \__fp_parse_stop_until:N #3 + \if_int_compare:w ##1 < #3 + \exp_after:wN @ + \exp_after:wN \__fp_parse_apply_binary:NwNwN + \exp_after:wN #2 + \tex_romannumeral:D + \__fp_parse_operand:Nw #4 + \exp_after:wN \__fp_parse_expand:w + \else: + \exp_after:wN @ + \exp_after:wN \use_none:n + \exp_after:wN #1 + \fi: } } + \__fp_tmp:w \__fp_parse_infix_^:N ^ \c_fifteen \c_fourteen + \__fp_tmp:w \__fp_parse_infix_/:N / \c_ten \c_ten + \__fp_tmp:w \__fp_parse_infix_mul:N * \c_ten \c_ten + \__fp_tmp:w \__fp_parse_infix_-:N - \c_nine \c_nine + \__fp_tmp:w \__fp_parse_infix_+:N + \c_nine \c_nine + \__fp_tmp:w \__fp_parse_infix_and:N & \c_five \c_five + \__fp_tmp:w \__fp_parse_infix_or:N | \c_four \c_four \group_end: -\cs_new:cpn {__fp_parse_prefix_.:Nw} #1 +\cs_new:cpn { __fp_parse_infix_(:N } #1 + { \__fp_parse_infix_juxtapose:N #1 ( } +\cs_new:Npn \__fp_parse_infix_juxtapose:N #1 { - \exp_after:wN \__fp_parse_infix_after_operand:NwN - \exp_after:wN #1 - \tex_romannumeral:D -`0 - \exp_after:wN \__fp_sanitize:wN - \int_use:N \__int_eval:w \c_zero \__fp_parse_strim_zeros:N + \if_int_compare:w #1 < \c_thirty_two + \exp_after:wN @ + \exp_after:wN \__fp_parse_apply_juxtapose:NwwN + \tex_romannumeral:D + \__fp_parse_operand:Nw \c_thirty_two + \exp_after:wN \__fp_parse_expand:w + \else: + \exp_after:wN @ + \exp_after:wN \use_none:n + \exp_after:wN \__fp_parse_infix_juxtapose:N + \fi: } -\cs_set_protected:Npn \__fp_tmp:w #1#2#3#4 +\cs_new:Npn \__fp_parse_apply_juxtapose:NwwN #1 #2;#3@ #4;#5@ { - \cs_new:Npn #1 ##1 - { - \if_int_compare:w ##1 < #3 - \exp_after:wN @ - \exp_after:wN \__fp_parse_apply_binary:NwNwN - \exp_after:wN #2 - \tex_romannumeral:D - \__fp_parse_until:Nw #4 - \exp_after:wN \__fp_parse_expand:w - \else: - \exp_after:wN @ - \exp_after:wN \__fp_parse_stop_until:N - \exp_after:wN #1 - \fi: - } + \if_catcode:w ^ \tl_to_str:n { #3 #5 } ^ + \else: + \__fp_error:nffn { invalid-ii } + { \__fp_array_to_clist:n { #2; #3 } } + { \__fp_array_to_clist:n { #4; #5 } } + { } + \fi: + \__fp_parse_apply_binary:NwNwN #1 #2;@ * #4;@ } \group_begin: - \char_set_catcode_other:N \& - \__fp_tmp:w \__fp_parse_infix_juxtapose:N * \c_thirty_two \c_thirty_two - \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_ / :N } / \c_ten \c_ten - \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_mul:N } * \c_ten \c_ten - \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_ - :N } - \c_nine \c_nine - \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_ + :N } + \c_nine \c_nine - \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_and:N } & \c_five \c_five - \exp_args:Nc \__fp_tmp:w { __fp_parse_infix_ or:N } | \c_four \c_four -\group_end: -\group_begin: \char_set_catcode_letter:N ^ - \__fp_tmp:w \__fp_parse_infix_^:N ^ \c_fifteen \c_fourteen \cs_new:cpn { __fp_parse_infix_*:N } #1#2 { - \if:w * #2 + \if:w * \exp_not:N #2 \exp_after:wN \__fp_parse_infix_^:N \exp_after:wN #1 \else: @@ -1669,7 +1763,7 @@ \char_set_catcode_letter:N \& \cs_new:Npn \__fp_parse_infix_|:N #1#2 { - \if:w | #2 + \if:w | \exp_not:N #2 \exp_after:wN \__fp_parse_infix_|:N \exp_after:wN #1 \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w @@ -1681,7 +1775,7 @@ } \cs_new:Npn \__fp_parse_infix_&:N #1#2 { - \if:w & #2 + \if:w & \exp_not:N #2 \exp_after:wN \__fp_parse_infix_&:N \exp_after:wN #1 \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w @@ -1692,6 +1786,39 @@ \fi: } \group_end: +\group_begin: + \char_set_catcode_letter:N \? + \cs_new:Npn \__fp_parse_infix_?:N #1 + { + \if_int_compare:w #1 < \c_three + \exp_after:wN @ + \exp_after:wN \__fp_ternary:NwwN + \tex_romannumeral:D + \__fp_parse_operand:Nw \c_three + \exp_after:wN \__fp_parse_expand:w + \else: + \exp_after:wN @ + \exp_after:wN \use_none:n + \exp_after:wN \__fp_parse_infix_?:N + \fi: + } + \cs_new:Npn \__fp_parse_infix_::N #1 + { + \if_int_compare:w #1 < \c_three + \__msg_kernel_expandable_error:nnnn + { kernel } { fp-missing } { ? } { ~for~?: } + \exp_after:wN @ + \exp_after:wN \__fp_ternary_auxii:NwwN + \tex_romannumeral:D + \__fp_parse_operand:Nw \c_two + \exp_after:wN \__fp_parse_expand:w + \else: + \exp_after:wN @ + \exp_after:wN \use_none:n + \exp_after:wN \__fp_parse_infix_::N + \fi: + } +\group_end: \cs_new:cpn { __fp_parse_infix_<:N } #1 { \__fp_infix_compare:N #1 \c_one_fp @@ -1729,14 +1856,14 @@ \exp_after:wN \__fp_parse_infix_excl_error: \else: \exp_after:wN @ - \exp_after:wN \__fp_parse_stop_until:N + \exp_after:wN \use_none:n \exp_after:wN \__fp_infix_compare:N \fi: } \cs_new:Npn \__fp_parse_compare:NNNNNNw #1#2#3#4#5#6#7 { \if_case:w - \if_catcode:w \tex_relax:D #7 + \if_catcode:w \scan_stop: #7 \c_minus_one \else: \__int_eval:w `#7 - `< \__int_eval_end: @@ -1769,11 +1896,11 @@ \exp_after:wN #3 \exp_after:wN #4 \tex_romannumeral:D - \__fp_parse_until:Nw \c_seven \__fp_parse_expand:w #5 + \__fp_parse_operand:Nw \c_seven \__fp_parse_expand:w #5 } \cs_new:Npn \__fp_parse_apply_compare:NwNNNNwN #1 #2@ #3#4#5#6 #7@ #8 { - \exp_after:wN \__fp_parse_until_test:NwN + \exp_after:wN \__fp_parse_continue:NwN \exp_after:wN #1 \tex_romannumeral:D -`0 \exp_after:wN \exp_after:wN @@ -1787,85 +1914,6 @@ \fi: \tex_romannumeral:D -`0 #8 #1 } -\group_begin: - \char_set_catcode_letter:N \? - \cs_new:Npn \__fp_parse_infix_?:N #1 - { - \if_int_compare:w #1 < \c_three - \exp_after:wN @ - \exp_after:wN \__fp_ternary:NwwN - \tex_romannumeral:D - \__fp_parse_until:Nw \c_three - \exp_after:wN \__fp_parse_expand:w - \else: - \exp_after:wN @ - \exp_after:wN \__fp_parse_stop_until:N - \exp_after:wN \__fp_parse_infix_?:N - \fi: - } - \cs_new:Npn \__fp_parse_infix_::N #1 - { - \if_int_compare:w #1 < \c_three - \__msg_kernel_expandable_error:nnnn - { kernel } { fp-missing } { ? } { ~for~?: } - \exp_after:wN @ - \exp_after:wN \__fp_ternary_auxii:NwwN - \tex_romannumeral:D - \__fp_parse_until:Nw \c_two - \exp_after:wN \__fp_parse_expand:w - \else: - \exp_after:wN @ - \exp_after:wN \__fp_parse_stop_until:N - \exp_after:wN \__fp_parse_infix_::N - \fi: - } -\group_end: -\group_begin: - \char_set_catcode_letter:N \) - \cs_new:Npn \__fp_parse_infix_):N #1 - { - \if_int_compare:w #1 < \c_zero - \__msg_kernel_expandable_error:nnn { kernel } { fp-extra } { ) } - \exp_after:wN \__fp_parse_infix:NN - \exp_after:wN #1 - \tex_romannumeral:D \exp_after:wN \__fp_parse_expand:w - \else: - \exp_after:wN @ - \exp_after:wN \__fp_parse_stop_until:N - \exp_after:wN \__fp_parse_infix_):N - \fi: - } -\group_end: -\cs_new:Npn \__fp_parse_infix_end:N #1 - { @ \__fp_parse_stop_until:N \__fp_parse_infix_end:N } -\group_begin: - \char_set_catcode_letter:N \, - \cs_new:Npn \__fp_parse_infix_,:N #1 - { - \if_int_compare:w #1 > \c_one - \exp_after:wN @ - \exp_after:wN \__fp_parse_stop_until:N - \exp_after:wN \__fp_parse_infix_,:N - \else: - \if_int_compare:w #1 = \c_one - \exp_after:wN \__fp_parse_infix_comma:w - \tex_romannumeral:D - \else: - \exp_after:wN \__fp_parse_infix_comma_gobble:w - \tex_romannumeral:D - \fi: - \__fp_parse_until:Nw \c_one - \exp_after:wN \__fp_parse_expand:w - \fi: - } - \cs_new:Npn \__fp_parse_infix_comma:w #1 @ - { #1 @ \__fp_parse_stop_until:N } - \cs_new:Npn \__fp_parse_infix_comma_gobble:w #1 @ - { - \__msg_kernel_expandable_error:nn { kernel } { fp-extra-comma } - @ \__fp_parse_stop_until:N - } -\group_end: \__msg_kernel_new:nnn { kernel } { unknown-fp-word } { Unknown~fp~word~#1. } \__msg_kernel_new:nnn { kernel } { fp-missing } @@ -1884,7 +1932,7 @@ { Unexpected~comma:~extra~arguments~ignored. } \__msg_kernel_new:nnn { kernel } { fp-num-args } { #1~expects~between~#2~and~#3~arguments. } -%% File: l3fp-logic.dtx Copyright (C) 2011-2012 The LaTeX3 Project +%% File: l3fp-logic.dtx Copyright (C) 2011-2013 The LaTeX3 Project %% %% It may be distributed and/or modified under the conditions of the %% LaTeX Project Public License (LPPL), either version 1.3c of this @@ -2052,20 +2100,15 @@ \fp_while_do:nNnn {#1} #2 {#3} {#4} } } -\cs_new:Npn \__fp_max_o:w #1 @ +\cs_new:Npn \__fp_minmax_o:Nw #1#2 @ { - \exp_after:wN \__fp_minmax_loop:Nww - \exp_after:wN \c_minus_one - \c_minus_inf_fp - #1 - \s__fp \__fp_chk:w { 3 \__fp_minmax_break_o:w } ; - } -\cs_new:Npn \__fp_min_o:w #1 @ - { - \exp_after:wN \__fp_minmax_loop:Nww - \exp_after:wN \c_one - \c_inf_fp - #1 + \if_meaning:w 0 #1 + \exp_after:wN \__fp_minmax_loop:Nww \exp_after:wN \c_one + \else: + \exp_after:wN \__fp_minmax_loop:Nww \exp_after:wN \c_minus_one + \fi: + #2 + \s__fp \__fp_chk:w 2 #1 \s__fp_exact ; \s__fp \__fp_chk:w { 3 \__fp_minmax_break_o:w } ; } \cs_new:Npn \__fp_minmax_loop:Nww @@ -2098,9 +2141,9 @@ { \fi: \fi: #2 } \cs_new:Npn \__fp_minmax_break_o:w #1 \fi: \fi: #2 \s__fp #3; #4; { \fi: \__fp_exp_after_o:w \s__fp #3; } -\cs_new:cpn { __fp_!_o:w } \s__fp \__fp_chk:w #1#2; +\cs_new:cpn { __fp_not_o:w } #1 \s__fp \__fp_chk:w #2#3; @ { - \if_meaning:w 0 #1 + \if_meaning:w 0 #2 \exp_after:wN \exp_after:wN \exp_after:wN \c_one_fp \else: \exp_after:wN \exp_after:wN \exp_after:wN \c_zero_fp @@ -2131,12 +2174,12 @@ \__fp_exp_after_array_f:w #3 \s__fp_stop \exp_after:wN @ \tex_romannumeral:D - \__fp_parse_until:Nw \c_two + \__fp_parse_operand:Nw \c_two \__fp_parse_expand:w \else: \__msg_kernel_expandable_error:nnnn { kernel } { fp-missing } { : } { ~for~?: } - \exp_after:wN \__fp_parse_until_test:NwN + \exp_after:wN \__fp_parse_continue:NwN \exp_after:wN #1 \tex_romannumeral:D -`0 \__fp_exp_after_array_f:w #3 \s__fp_stop @@ -2159,7 +2202,7 @@ \cs_new:Npn \__fp_ternary_map_break: #1 \__fp_ternary_break_point:n #2 {#2} \cs_new:Npn \__fp_ternary_auxi:NwwN #1#2@#3@#4 { - \exp_after:wN \__fp_parse_until_test:NwN + \exp_after:wN \__fp_parse_continue:NwN \exp_after:wN #1 \tex_romannumeral:D -`0 \__fp_exp_after_array_f:w #2 \s__fp_stop @@ -2167,13 +2210,13 @@ } \cs_new:Npn \__fp_ternary_auxii:NwwN #1#2@#3@#4 { - \exp_after:wN \__fp_parse_until_test:NwN + \exp_after:wN \__fp_parse_continue:NwN \exp_after:wN #1 \tex_romannumeral:D -`0 \__fp_exp_after_array_f:w #3 \s__fp_stop #4 #1 } -%% File: l3fp-basics.dtx Copyright (C) 2011-2012 The LaTeX3 Project +%% File: l3fp-basics.dtx Copyright (C) 2011-2013 The LaTeX3 Project %% %% It may be distributed and/or modified under the conditions of the %% LaTeX Project Public License (LPPL), either version 1.3c of this @@ -2781,23 +2824,17 @@ \__int_value:w \__fp_round_digit:Nw #7 #8 ; \exp_after:wN ; } -\cs_new:cpn { __fp_-_o:w } #1 \s__fp \__fp_chk:w #2 #3 +\cs_new:Npn \__fp_set_sign_o:w #1 \s__fp \__fp_chk:w #2#3#4; @ { \exp_after:wN \__fp_exp_after_o:w \exp_after:wN \s__fp \exp_after:wN \__fp_chk:w \exp_after:wN #2 - \int_use:N \__int_eval:w \c_two - #3 \__int_eval_end: - } -\cs_new:Npn \__fp_abs_o:w \s__fp \__fp_chk:w #1 #2 - { - \exp_after:wN \__fp_exp_after_o:w - \exp_after:wN \s__fp - \exp_after:wN \__fp_chk:w - \exp_after:wN #1 - \__int_value:w \if_meaning:w 1 #2 1 \else: 0 \fi: \exp_stop_f: + \__int_value:w + \if_case:w #3 \exp_stop_f: #1 \or: 1 \or: 0 \fi: \exp_stop_f: + #4; } -%% File: l3fp-extended.dtx Copyright (C) 2011-2012 The LaTeX3 Project +%% File: l3fp-extended.dtx Copyright (C) 2011-2013 The LaTeX3 Project %% %% It may be distributed and/or modified under the conditions of the %% LaTeX Project Public License (LPPL), either version 1.3c of this @@ -2838,7 +2875,39 @@ \exp_after:wN #3 \exp_after:wN { \int_use:N \__int_eval:w \c_ten_thousand + #1 } #2 ; } +\cs_new:Npn \__fp_fixed_div_myriad:wn #1#2#3#4#5#6; #7 + { + \exp_after:wN \__fp_fixed_mul_after:wn + \int_use:N \__int_eval:w \c__fp_leading_shift_int + \exp_after:wN \__fp_pack:NNNNNwn + \int_use:N \__int_eval:w \c__fp_trailing_shift_int + + #1 ; {#7} {#2}{#3}{#4}{#5}; + } \cs_new:Npn \__fp_fixed_mul_after:wn #1; #2 { #2 {#1} } +\cs_new:Npn \__fp_fixed_mul_short:wwn #1#2#3#4#5#6; #7#8#9; + { + \exp_after:wN \__fp_fixed_mul_after:wn + \int_use:N \__int_eval:w \c__fp_leading_shift_int + + #1*#7 + \exp_after:wN \__fp_pack:NNNNNwn + \int_use:N \__int_eval:w \c__fp_middle_shift_int + + #1*#8 + #2*#7 + \exp_after:wN \__fp_pack:NNNNNwn + \int_use:N \__int_eval:w \c__fp_middle_shift_int + + #1*#9 + #2*#8 + #3*#7 + \exp_after:wN \__fp_pack:NNNNNwn + \int_use:N \__int_eval:w \c__fp_middle_shift_int + + #2*#9 + #3*#8 + #4*#7 + \exp_after:wN \__fp_pack:NNNNNwn + \int_use:N \__int_eval:w \c__fp_middle_shift_int + + #3*#9 + #4*#8 + #5*#7 + \exp_after:wN \__fp_pack:NNNNNwn + \int_use:N \__int_eval:w \c__fp_trailing_shift_int + + #4*#9 + #5*#8 + #6*#7 + + ( #5*#9 + #6*#8 + #6*#9 / \c_ten_thousand ) + / \c_ten_thousand + \exp_after:wN ; \__fp_use_braced_s:n + } \cs_new:Npn \__fp_fixed_div_int:wwN #1#2#3#4#5#6 ; #7 ; #8 { \exp_after:wN \__fp_fixed_div_int_after:Nw @@ -2977,10 +3046,213 @@ #9 (#4* #1 *#7) #9 (#5*#6+#4* #2 *#7+#3*#8) / \c_ten_thousand } +\cs_new:Npn \__fp_ep_to_fixed:wwn #1,#2 + { + \exp_after:wN \__fp_ep_to_fixed_auxi:www + \int_use:N \__int_eval:w 1 0000 0000 + #2 \exp_after:wN ; + \tex_romannumeral:D -`0 + \prg_replicate:nn { \c_four - \int_max:nn {#1} { -32 } } { 0 } ; + } +\cs_new:Npn \__fp_ep_to_fixed_auxi:www 1#1; #2; #3#4#5#6#7; + { + \__fp_pack_eight:wNNNNNNNN + \__fp_pack_twice_four:wNNNNNNNN + \__fp_pack_twice_four:wNNNNNNNN + \__fp_pack_twice_four:wNNNNNNNN + \__fp_ep_to_fixed_auxii:nnnnnnnwn ; + #2 #1#3#4#5#6#7 0000 ! + } +\cs_new:Npn \__fp_ep_to_fixed_auxii:nnnnnnnwn #1#2#3#4#5#6#7; #8! #9 + { #9 {#1#2}{#3}{#4}{#5}{#6}{#7}; } +\cs_new:Npn \__fp_ep_to_ep:wwN #1,#2#3#4#5#6#7; #8 + { + \exp_after:wN #8 + \int_use:N \__int_eval:w #1 + \c_four + \exp_after:wN \use_i:nn + \exp_after:wN \__fp_ep_to_ep_loop:N + \int_use:N \__int_eval:w 1 0000 0000 + #2 \__int_eval_end: + #3#4#5#6#7 ; ; ! + } +\cs_new:Npn \__fp_ep_to_ep_loop:N #1 + { + \if_meaning:w 0 #1 + - \c_one + \else: + \__fp_ep_to_ep_end:www #1 + \fi: + \__fp_ep_to_ep_loop:N + } +\cs_new:Npn \__fp_ep_to_ep_end:www + #1 \fi: \__fp_ep_to_ep_loop:N #2; #3! + { + \fi: + \if_meaning:w ; #1 + - \c_two * \c__fp_max_exponent_int + \__fp_ep_to_ep_zero:ww + \fi: + \__fp_pack_twice_four:wNNNNNNNN + \__fp_pack_twice_four:wNNNNNNNN + \__fp_pack_twice_four:wNNNNNNNN + \__fp_use_i:ww , ; + #1 #2 0000 0000 0000 0000 0000 0000 ; + } +\cs_new:Npn \__fp_ep_to_ep_zero:ww \fi: #1; #2; #3; + { \fi: , {1000}{0000}{0000}{0000}{0000}{0000} ; } +\cs_new:Npn \__fp_ep_compare:wwww #1,#2#3#4#5#6#7; + { \__fp_ep_compare_aux:wwww {#1}{#2}{#3}{#4}{#5}; #6#7; } +\cs_new:Npn \__fp_ep_compare_aux:wwww #1;#2;#3,#4#5#6#7#8#9; + { + \if_case:w + \__fp_compare_npos:nwnw #1; {#3}{#4}{#5}{#6}{#7}; \exp_stop_f: + \if_int_compare:w #2 = #8#9 \exp_stop_f: + 0 + \else: + \if_int_compare:w #2 < #8#9 - \fi: 1 + \fi: + \or: 1 + \else: -1 + \fi: + } +\cs_new:Npn \__fp_ep_mul:wwwwn #1,#2; #3,#4; + { + \__fp_ep_to_ep:wwN #3,#4; + \__fp_fixed_continue:wn + { + \__fp_ep_to_ep:wwN #1,#2; + \__fp_ep_mul_raw:wwwwN + } + \__fp_fixed_continue:wn + } +\cs_new:Npn \__fp_ep_mul_raw:wwwwN #1,#2; #3,#4; #5 + { + \__fp_fixed_mul:wwn #2; #4; + { \exp_after:wN #5 \int_use:N \__int_eval:w #1 + #3 , } + } +\cs_new:Npn \__fp_ep_div:wwwwn #1,#2; #3,#4; + { + \__fp_ep_to_ep:wwN #1,#2; + \__fp_fixed_continue:wn + { + \__fp_ep_to_ep:wwN #3,#4; + \__fp_ep_div_esti:wwwwn + } + } +\cs_new:Npn \__fp_ep_div_esti:wwwwn #1,#2#3; #4, + { + \exp_after:wN \__fp_ep_div_estii:wwnnwwn + \int_use:N \__int_eval:w 10 0000 0000 / ( #2 + \c_one ) + \exp_after:wN ; + \int_use:N \__int_eval:w #4 - #1 + \c_one , + {#2} #3; + } +\cs_new:Npn \__fp_ep_div_estii:wwnnwwn #1; #2,#3#4#5; #6; #7 + { + \exp_after:wN \__fp_ep_div_estiii:NNNNNwwwn + \int_use:N \__int_eval:w 10 0000 0000 - 1750 + + #1 000 + (10 0000 0000 / #3 - #1) * (1000 - #4 / 10) ; + {#3}{#4}#5; #6; { #7 #2, } + } +\cs_new:Npn \__fp_ep_div_estiii:NNNNNwwwn 1#1#2#3#4#5#6; #7; + { + \__fp_fixed_mul_short:wwn #7; {#1}{#2#3#4#5}{#6}; + \__fp_ep_div_epsi:wnNNNNNn {#1#2#3#4}#5#6 + \__fp_fixed_mul:wwn + } +\cs_new:Npn \__fp_ep_div_epsi:wnNNNNNn #1#2#3#4#5#6; + { + \exp_after:wN \__fp_ep_div_epsii:wwnNNNNNn + \int_use:N \__int_eval:w 1 9998 - #2 + \exp_after:wN \__fp_ep_div_eps_pack:NNNNNw + \int_use:N \__int_eval:w 1 9999 9998 - #3#4 + \exp_after:wN \__fp_ep_div_eps_pack:NNNNNw + \int_use:N \__int_eval:w 2 0000 0000 - #5#6 ; ; + } +\cs_new:Npn \__fp_ep_div_eps_pack:NNNNNw #1#2#3#4#5#6; + { + #1 ; {#2#3#4#5} {#6} } +\cs_new:Npn \__fp_ep_div_epsii:wwnNNNNNn 1#1; #2; #3#4#5#6#7#8 + { + \__fp_fixed_mul:wwn {0000}{#1}#2; {0000}{#1}#2; + \__fp_fixed_add_one:wN + \__fp_fixed_mul:wwn {10000} {#1} #2 ; + { + \__fp_fixed_mul_short:wwn {0000}{#1}#2; {#3}{#4#5#6#7}{#8000}; + \__fp_fixed_div_myriad:wn + \__fp_fixed_mul:wwn + } + \__fp_fixed_add:wwn {#3}{#4#5#6#7}{#8000}{0000}{0000}{0000}; + } +\cs_new:Npn \__fp_ep_isqrt:wwn #1,#2; + { + \__fp_ep_to_ep:wwN #1,#2; + \__fp_ep_isqrt_auxi:wwn + } +\cs_new:Npn \__fp_ep_isqrt_auxi:wwn #1, + { + \exp_after:wN \__fp_ep_isqrt_auxii:wwnnnwn + \int_use:N \__int_eval:w + \int_if_odd:nTF {#1} + { (\c_one - #1) / \c_two , 535 , { 0 } { } } + { \c_one - #1 / \c_two , 168 , { } { 0 } } + } +\cs_new:Npn \__fp_ep_isqrt_auxii:wwnnnwn #1, #2, #3#4 #5#6; #7 + { + \__fp_ep_isqrt_esti:wwwnnwn #2, 0, #5, {#3} {#4} + {#5} #6 ; { #7 #1 , } + } +\cs_new:Npn \__fp_ep_isqrt_esti:wwwnnwn #1, #2, #3, #4 + { + \if_int_compare:w #1 = #2 \exp_stop_f: + \exp_after:wN \__fp_ep_isqrt_estii:wwwnnwn + \fi: + \exp_after:wN \__fp_ep_isqrt_esti:wwwnnwn + \int_use:N \__int_eval:w + (#1 + 1 0050 0000 #4 / (#1 * #3)) / \c_two , + #1, #3, {#4} + } +\cs_new:Npn \__fp_ep_isqrt_estii:wwwnnwn #1, #2, #3, #4#5 + { + \exp_after:wN \__fp_ep_isqrt_estiii:NNNNNwwwn + \int_use:N \__int_eval:w 1000 0000 + #2 * #2 #5 * \c_five + \exp_after:wN , \int_use:N \__int_eval:w 10000 + #2 ; + } +\cs_new:Npn \__fp_ep_isqrt_estiii:NNNNNwwwn 1#1#2#3#4#5#6, 1#7#8; #9; + { + \__fp_fixed_mul_short:wwn #9; {#1} {#2#3#4#5} {#600} ; + \__fp_ep_isqrt_epsi:wN + \__fp_fixed_mul_short:wwn {#7} {#80} {0000} ; + } +\cs_new:Npn \__fp_ep_isqrt_epsi:wN #1; + { + \__fp_fixed_sub:wwn {15000}{0000}{0000}{0000}{0000}{0000}; #1; + \__fp_ep_isqrt_epsii:wwN #1; + \__fp_ep_isqrt_epsii:wwN #1; + \__fp_ep_isqrt_epsii:wwN #1; + } +\cs_new:Npn \__fp_ep_isqrt_epsii:wwN #1; #2; + { + \__fp_fixed_mul:wwn #1; #1; + \__fp_fixed_mul_sub_back:wwwn #2; + {15000}{0000}{0000}{0000}{0000}{0000}; + \__fp_fixed_mul:wwn #1; + } +\cs_new:Npn \__fp_ep_to_float:wwN #1, + { + \__int_eval:w #1 \__fp_fixed_to_float:wN } +\cs_new:Npn \__fp_ep_inv_to_float:wwN #1,#2; + { + \__fp_ep_div:wwwwn 1,{1000}{0000}{0000}{0000}{0000}{0000}; #1,#2; + \__fp_ep_to_float:wwN + } +\cs_new:Npn \__fp_fixed_inv_to_float:wN + { \__fp_ep_inv_to_float:wwN 0, } +\cs_new:Npn \__fp_fixed_to_float_rad:wN #1; + { + \__fp_fixed_mul:wwn #1; {5729}{5779}{5130}{8232}{0876}{7981}; + { \__fp_ep_to_float:wwN 2, } + } \cs_new:Npn \__fp_fixed_to_float:Nw #1#2; { \__fp_fixed_to_float:wN #2; #1 } \cs_new:Npn \__fp_fixed_to_float:wN #1#2#3#4#5#6; #7 { - + \c_four % for the 8-digit-at-the-start thing. + + \__int_eval:w \c_four % for the 8-digit-at-the-start thing. \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_to_loop:N \exp_after:wN \use_none:n @@ -3033,111 +3305,7 @@ \exp_after:wN \__fp_basics_pack_low:NNNNNw \int_use:N \__int_eval:w 1 #3#4 + \c_one ; } -\cs_new:Npn \__fp_fixed_inv_to_float:wN #1#2; #3 - { - + \__int_eval:w % ^^A todo: remove the +? - \if_int_compare:w #1 < \c_one_thousand - \__fp_fixed_dtf_zeros:wNnnnnnn - \fi: - \__fp_fixed_dtf_no_zero:Nwn + {#1} #2 \s__fp - \__fp_fixed_dtf_approx:n - {10000} {0000} {0000} {0000} {0000} {0000} ; - } -\cs_new:Npn \__fp_fixed_div_to_float:ww #1#2; #3#4; - { - \if_int_compare:w #1 < \c_one_thousand - \__fp_fixed_dtf_zeros:wNnnnnnn - \fi: - \__fp_fixed_dtf_no_zero:Nwn - {#1} #2 \s__fp - { - \if_int_compare:w #3 < \c_one_thousand - \__fp_fixed_dtf_zeros:wNnnnnnn - \fi: - \__fp_fixed_dtf_no_zero:Nwn + {#3} #4 \s__fp - \__fp_fixed_dtf_approx:n - } - } -\cs_new:Npn \__fp_fixed_dtf_no_zero:Nwn #1#2 \s__fp #3 { #3 #2; } -\cs_new:Npn \__fp_fixed_dtf_zeros:wNnnnnnn - \fi: \__fp_fixed_dtf_no_zero:Nwn #1#2#3#4#5#6#7 - { - \fi: - #1 \c_minus_one - \exp_after:wN \use_i_ii:nnn - \exp_after:wN \__fp_fixed_dtf_zeros:NN - \exp_after:wN #1 - \int_use:N \__int_eval:w 10 0000 + #2 \__int_eval_end: #3#4#5#6#7 - ; 1 ; - } -\cs_new:Npn \__fp_fixed_dtf_zeros:NN #1#2 - { - \if_meaning:w 0 #2 - #1 \c_one - \else: - \__fp_fixed_dtf_zeros_end:wNww #2 - \fi: - \__fp_fixed_dtf_zeros:NN #1 - } -\cs_new:Npn \__fp_fixed_dtf_zeros_end:wNww - #1 \fi: \__fp_fixed_dtf_zeros:NN #2 #3; #4 \s__fp - { - \fi: - \if_meaning:w ; #1 - #2 \c_two * \c__fp_max_exponent_int - \use_i_ii:nnn - \fi: - \__fp_fixed_dtf_zeros_auxi:ww - #1#3 0000 0000 0000 0000 0000 0000 ; - } -\cs_new:Npn \__fp_fixed_dtf_zeros_auxi:ww - { - \__fp_pack_twice_four:wNNNNNNNN - \__fp_pack_twice_four:wNNNNNNNN - \__fp_pack_twice_four:wNNNNNNNN - \__fp_fixed_dtf_zeros_auxii:ww - ; - } -\cs_new:Npn \__fp_fixed_dtf_zeros_auxii:ww #1; #2; #3 { #3 #1; } -\cs_new:Npn \__fp_fixed_dtf_approx:n #1 - { - \exp_after:wN \__fp_fixed_dtf_approx:wnn - \int_use:N \__int_eval:w 10 0000 0000 / ( #1 + \c_one ) ; - {#1} - } -\cs_new:Npn \__fp_fixed_dtf_approx:wnn #1; #2#3 - { - \exp_after:wN \__fp_fixed_dtf_approx:NNNNNw - \int_use:N \__int_eval:w 10 0000 0000 - 1750 - + #1000 + (10 0000 0000/#2-#1) * (1000-#3/10) ; - {#2}{#3} - } -\cs_new:Npn \__fp_fixed_dtf_approx:NNNNNw 1#1#2#3#4#5#6; #7; #8; - { - + \c_four % because of the line below "dtf_epsilon" here. - \__fp_fixed_mul:wwn {000#1}{#2#3#4#5}{#6}{0000}{0000}{0000} ; #7; - \__fp_fixed_dtf_epsilon:wN - \__fp_fixed_mul:wwn {000#1}{#2#3#4#5}{#6}{0000}{0000}{0000} ; - \__fp_fixed_mul:wwn #8; - \__fp_fixed_to_float:wN ? - } -\cs_new:Npn \__fp_fixed_dtf_epsilon:wN #1#2#3#4#5#6; - { - \exp_after:wN \__fp_fixed_dtf_epsilon:NNNNNww - \int_use:N \__int_eval:w 1 9999 9998 - #3#4 + - \exp_after:wN \__fp_fixed_dtf_epsilon_pack:NNNNNw - \int_use:N \__int_eval:w 2 0000 0000 - #5#6 ; {0000} ; - } -\cs_new:Npn \__fp_fixed_dtf_epsilon_pack:NNNNNw #1#2#3#4#5#6; - { #1 ; {#2#3#4#5} {#6} } -\cs_new:Npn \__fp_fixed_dtf_epsilon:NNNNNww #1#2#3#4#5#6; #7; - { - \__fp_fixed_mul:wwn %^^A todo: optimize to use \__fp_mul_significand. - {0000} {#2#3#4#5} {#6} #7 ; - {0000} {#2#3#4#5} {#6} #7 ; - \__fp_fixed_add_one:wN - \__fp_fixed_mul:wwn {10000} {#2#3#4#5} {#6} #7 ; - } -%% File: l3fp-expo.dtx Copyright (C) 2011-2012 The LaTeX3 Project +%% File: l3fp-expo.dtx Copyright (C) 2011-2013 The LaTeX3 Project %% %% It may be distributed and/or modified under the conditions of the %% LaTeX Project Public License (LPPL), either version 1.3c of this @@ -3179,19 +3347,19 @@ \tl_const:Nn \c__fp_ln_viii_fixed_tl{{20794}{4154}{1679}{8359}{2825}{1696} } \tl_const:Nn \c__fp_ln_ix_fixed_tl {{21972}{2457}{7336}{2193}{8279}{0490} } \tl_const:Nn \c__fp_ln_x_fixed_tl {{23025}{8509}{2994}{0456}{8401}{7991} } -\cs_new:Npn \__fp_ln_o:w \s__fp \__fp_chk:w #1 #2 +\cs_new:Npn \__fp_ln_o:w #1 \s__fp \__fp_chk:w #2#3#4; @ { - \if_meaning:w 2 #2 + \if_meaning:w 2 #3 \__fp_case_use:nw { \__fp_invalid_operation_o:nw { ln } } \fi: - \if_case:w #1 \exp_stop_f: + \if_case:w #2 \exp_stop_f: \__fp_case_use:nw { \__fp_division_by_zero_o:Nnw \c_minus_inf_fp { ln } } \or: \else: \__fp_case_return_same_o:w \fi: - \__fp_ln_npos_o:w \s__fp \__fp_chk:w #1#2 + \__fp_ln_npos_o:w \s__fp \__fp_chk:w #2#3#4; } \cs_new:Npn \__fp_ln_npos_o:w \s__fp \__fp_chk:w 10#1#2#3; { %^^A todo: ln(1) should be "exact zero", not "underflow" @@ -3400,14 +3568,14 @@ {0000}{#4}{#5}{#6}{#7}{#8}; \__fp_fixed_to_float:wN #1 } -\cs_new:Npn \__fp_exp_o:w \s__fp \__fp_chk:w #1#2 +\cs_new:Npn \__fp_exp_o:w #1 \s__fp \__fp_chk:w #2#3#4; @ { - \if_case:w #1 \exp_stop_f: + \if_case:w #2 \exp_stop_f: \__fp_case_return_o:Nw \c_one_fp \or: \exp_after:wN \__fp_exp_normal:w \or: - \if_meaning:w 0 #2 + \if_meaning:w 0 #3 \exp_after:wN \__fp_case_return_o:Nw \exp_after:wN \c_inf_fp \else: @@ -3417,7 +3585,7 @@ \or: \__fp_case_return_same_o:w \fi: - \s__fp \__fp_chk:w #1#2 + \s__fp \__fp_chk:w #2#3#4; } \cs_new:Npn \__fp_exp_normal:w \s__fp \__fp_chk:w 1#1 { @@ -3783,7 +3951,7 @@ \cs_new:Npn \__fp_pow_neg:www \s__fp \__fp_chk:w #1#2; #3; #4; { \if_case:w \__fp_pow_neg_case:w #4 ; - \cs:w __fp_-_o:w \exp_after:wN \cs_end: + \exp_after:wN \__fp_pow_neg_aux:wNN \or: \if_int_compare:w \__int_eval:w #1 / \c_two = \c_one \__fp_invalid_operation_o:Nww ^ #3; #4; @@ -3795,6 +3963,14 @@ \__fp_exp_after_o:w \s__fp \__fp_chk:w #1#2; } +\cs_new:Npn \__fp_pow_neg_aux:wNN #1 \s__fp \__fp_chk:w #2#3 + { + \exp_after:wN \__fp_exp_after_o:w + \exp_after:wN \s__fp + \exp_after:wN \__fp_chk:w + \exp_after:wN #2 + \int_use:N \__int_eval:w \c_two - #3 \__int_eval_end: + } \cs_new:Npn \__fp_pow_neg_case:w \s__fp \__fp_chk:w #1#2#3; { \if_case:w #1 \exp_stop_f: @@ -3839,7 +4015,7 @@ \c_one \fi: } -%% File: l3fp-trig.dtx Copyright (C) 2011-2012 The LaTeX3 Project +%% File: l3fp-trig.dtx Copyright (C) 2011-2013 The LaTeX3 Project %% %% It may be distributed and/or modified under the conditions of the %% LaTeX Project Public License (LPPL), either version 1.3c of this @@ -3872,203 +4048,418 @@ %% %% ----------------------------------------------------------------------- %% -\cs_new:Npn \__fp_sin_o:w \s__fp \__fp_chk:w #1#2 +\cs_new:Npn \__fp_sin_o:w #1 \s__fp \__fp_chk:w #2#3#4; @ { - \if_case:w #1 \exp_stop_f: + \if_case:w #2 \exp_stop_f: \__fp_case_return_same_o:w - \or: - \__fp_case_use:nw - { - \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_o:w - \__fp_sin_series:NNwww \__fp_fixed_to_float:wN #2 \c_zero - } - \or: \__fp_case_use:nw { \__fp_invalid_operation_o:nw { sin } } + \or: \__fp_case_use:nw + { + \__fp_trig:NNNNNwn #1 \__fp_sin_series_o:NNwwww + \__fp_ep_to_float:wwN #3 \c_zero + } + \or: \__fp_case_use:nw + { \__fp_invalid_operation_o:fw { #1 { sin } { sind } } } \else: \__fp_case_return_same_o:w \fi: - \s__fp \__fp_chk:w #1#2 + \s__fp \__fp_chk:w #2 #3 #4; } -\cs_new:Npn \__fp_cos_o:w \s__fp \__fp_chk:w #1#2 +\cs_new:Npn \__fp_cos_o:w #1 \s__fp \__fp_chk:w #2#3; @ { - \if_case:w #1 \exp_stop_f: + \if_case:w #2 \exp_stop_f: \__fp_case_return_o:Nw \c_one_fp - \or: - \__fp_case_use:nw - { - \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_one_o:w - \__fp_sin_series:NNwww \__fp_fixed_to_float:wN 0 \c_two - } - \or: \__fp_case_use:nw { \__fp_invalid_operation_o:nw { cos } } + \or: \__fp_case_use:nw + { + \__fp_trig:NNNNNwn #1 \__fp_sin_series_o:NNwwww + \__fp_ep_to_float:wwN 0 \c_two + } + \or: \__fp_case_use:nw + { \__fp_invalid_operation_o:fw { #1 { cos } { cosd } } } \else: \__fp_case_return_same_o:w \fi: - \s__fp \__fp_chk:w #1#2 + \s__fp \__fp_chk:w #2 #3; } -\cs_new:Npn \__fp_csc_o:w \s__fp \__fp_chk:w #1#2 +\cs_new:Npn \__fp_csc_o:w #1 \s__fp \__fp_chk:w #2#3#4; @ { - \if_case:w #1 \exp_stop_f: - \__fp_cot_zero_o:Nnw #2 { csc } - \or: - \__fp_case_use:nw - { - \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_inv_o:w - \__fp_sin_series:NNwww \__fp_fixed_inv_to_float:wN #2 \c_zero - } - \or: \__fp_case_use:nw { \__fp_invalid_operation_o:nw { csc } } + \if_case:w #2 \exp_stop_f: + \__fp_cot_zero_o:Nfw #3 { #1 { csc } { cscd } } + \or: \__fp_case_use:nw + { + \__fp_trig:NNNNNwn #1 \__fp_sin_series_o:NNwwww + \__fp_ep_inv_to_float:wwN #3 \c_zero + } + \or: \__fp_case_use:nw + { \__fp_invalid_operation_o:fw { #1 { csc } { cscd } } } \else: \__fp_case_return_same_o:w \fi: - \s__fp \__fp_chk:w #1#2 + \s__fp \__fp_chk:w #2 #3 #4; } -\cs_new:Npn \__fp_sec_o:w \s__fp \__fp_chk:w #1#2 +\cs_new:Npn \__fp_sec_o:w #1 \s__fp \__fp_chk:w #2#3; @ { - \if_case:w #1 \exp_stop_f: + \if_case:w #2 \exp_stop_f: \__fp_case_return_o:Nw \c_one_fp - \or: - \__fp_case_use:nw - { - \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_one_o:w - \__fp_sin_series:NNwww \__fp_fixed_inv_to_float:wN 0 \c_two - } - \or: \__fp_case_use:nw { \__fp_invalid_operation_o:nw { sec } } + \or: \__fp_case_use:nw + { + \__fp_trig:NNNNNwn #1 \__fp_sin_series_o:NNwwww + \__fp_ep_inv_to_float:wwN 0 \c_two + } + \or: \__fp_case_use:nw + { \__fp_invalid_operation_o:fw { #1 { sec } { secd } } } \else: \__fp_case_return_same_o:w \fi: - \s__fp \__fp_chk:w #1#2 + \s__fp \__fp_chk:w #2 #3; } -\cs_new:Npn \__fp_tan_o:w \s__fp \__fp_chk:w #1#2 +\cs_new:Npn \__fp_tan_o:w #1 \s__fp \__fp_chk:w #2#3#4; @ { - \if_case:w #1 \exp_stop_f: + \if_case:w #2 \exp_stop_f: \__fp_case_return_same_o:w - \or: - \__fp_case_use:nw - { - \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_o:w - \__fp_tan_series_o:NNwww 0 #2 \c_one - } - \or: \__fp_case_use:nw { \__fp_invalid_operation_o:nw { tan } } + \or: \__fp_case_use:nw + { + \__fp_trig:NNNNNwn #1 + \__fp_tan_series_o:NNwwww 0 #3 \c_one + } + \or: \__fp_case_use:nw + { \__fp_invalid_operation_o:fw { #1 { tan } { tand } } } \else: \__fp_case_return_same_o:w \fi: - \s__fp \__fp_chk:w #1#2 + \s__fp \__fp_chk:w #2 #3 #4; } -\cs_new:Npn \__fp_cot_o:w \s__fp \__fp_chk:w #1#2 +\cs_new:Npn \__fp_cot_o:w #1 \s__fp \__fp_chk:w #2#3#4; @ { - \if_case:w #1 \exp_stop_f: - \__fp_cot_zero_o:Nnw #2 { cot } - \or: - \__fp_case_use:nw - { - \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_inv_o:w - \__fp_tan_series_o:NNwww 2 #2 \c_three - } - \or: \__fp_case_use:nw { \__fp_invalid_operation_o:nw { cot } } + \if_case:w #2 \exp_stop_f: + \__fp_cot_zero_o:Nfw #3 { #1 { cot } { cotd } } + \or: \__fp_case_use:nw + { + \__fp_trig:NNNNNwn #1 + \__fp_tan_series_o:NNwwww 2 #3 \c_three + } + \or: \__fp_case_use:nw + { \__fp_invalid_operation_o:fw { #1 { cot } { cotd } } } \else: \__fp_case_return_same_o:w \fi: - \s__fp \__fp_chk:w #1#2 + \s__fp \__fp_chk:w #2 #3 #4; } -\cs_new:Npn \__fp_cot_zero_o:Nnw #1 #2 #3 \fi: +\cs_new:Npn \__fp_cot_zero_o:Nfw #1#2#3 \fi: { \fi: - \if_meaning:w 0 #1 - \exp_after:wN \__fp_division_by_zero_o:Nnw \exp_after:wN \c_inf_fp - \else: - \exp_after:wN \__fp_division_by_zero_o:Nnw \exp_after:wN \c_minus_inf_fp - \fi: + \token_if_eq_meaning:NNTF 0 #1 + { \exp_args:NNf \__fp_division_by_zero_o:Nnw \c_inf_fp } + { \exp_args:NNf \__fp_division_by_zero_o:Nnw \c_minus_inf_fp } {#2} } -\cs_new:Npn \__fp_trig_exponent:NNNNNwn #1#2#3#4#5 \s__fp \__fp_chk:w 1#6#7 +\cs_new:Npn \__fp_trig:NNNNNwn #1#2#3#4#5 \s__fp \__fp_chk:w 1#6#7#8; { - \if_int_compare:w #7 > - \c_eight - \exp_after:wN #2 - \exp_after:wN #3 - \exp_after:wN #4 - \int_use:N \__int_eval:w #5 - \if_int_compare:w #7 > \c_zero - \exp_after:wN \__fp_trig_large:ww \__int_value:w - \else: - \exp_after:wN \__fp_trig_small:ww \__int_value:w - \fi: - \else: - \exp_after:wN #1 - \exp_after:wN #6 - \fi: - #7 ; + \exp_after:wN #2 + \exp_after:wN #3 + \exp_after:wN #4 + \int_use:N \__int_eval:w #5 + \exp_after:wN \exp_after:wN \exp_after:wN \exp_after:wN + \if_int_compare:w #7 > #1 \c_zero \c_one + #1 \__fp_trig_large:ww \__fp_trigd_large:ww + \else: + #1 \__fp_trig_small:ww \__fp_trigd_small:ww + \fi: + #7,#8{0000}{0000}; } -\cs_new:Npn \__fp_trig_epsilon_o:w #1 #2 ; - { \__fp_exp_after_o:w \s__fp \__fp_chk:w 1 #1 {#2} } -\cs_new:Npn \__fp_trig_epsilon_one_o:w #1 ; #2 ; - { \exp_after:wN \c_one_fp } -\group_begin: - \char_set_catcode_letter:N / - \cs_new:Npn \__fp_trig_epsilon_inv_o:w #1 #2 ; - { - \exp_after:wN \__fp_/_o:ww - \c_one_fp - \s__fp \__fp_chk:w 1 #1 {#2} - } -\group_end: -\cs_new:Npn \__fp_trig_small:ww #1; #2#3#4#5; +\cs_new:Npn \__fp_trig_small:ww #1,#2; + { \__fp_ep_to_fixed:wwn #1,#2; . #1,#2; } +\cs_new:Npn \__fp_trigd_small:ww #1,#2; { + \__fp_ep_mul_raw:wwwwN + -1,{1745}{3292}{5199}{4329}{5769}{2369}; #1,#2; + \__fp_trig_small:ww + } +\cs_new:Npn \__fp_trigd_large:ww #1, #2#3#4#5#6#7; + { + \exp_after:wN \__fp_pack_eight:wNNNNNNNN + \exp_after:wN \__fp_pack_eight:wNNNNNNNN \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN - \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN - \exp_after:wN . + \exp_after:wN \__fp_trigd_large_auxi:nnnnwNNNN \exp_after:wN ; \tex_romannumeral:D -`0 - \prg_replicate:nn { - #1 } { 0 } #2#3#4#5 0000 0000 ; + \prg_replicate:nn { \int_max:nn { 22 - #1 } { 0 } } { 0 } + #2#3#4#5#6#7 0000 0000 0000 ! } -\cs_new:Npn \__fp_trig_large:ww #1; #2#3; - { \__fp_trig_large:www #2; #3 ; #1; } -\cs_new:Npn \__fp_trig_large:www #1; #2; #3; +\cs_new:Npn \__fp_trigd_large_auxi:nnnnwNNNN #1#2#3#4#5; #6#7#8#9 { - \if_meaning:w 0 #3 \__fp_trig_large_break:w \fi: - \exp_after:wN \__fp_trig_large_o:wnnnn - \int_use:N \__int_eval:w ( #10 - 31416 ) / 62833 ; - {#1} #2 - \exp_after:wN ; - \int_use:N \__int_eval:w \c_minus_one + #3; - } -\cs_new:Npn \__fp_trig_large_o:wnnnn #1; #2#3#4#5 - { - \exp_after:wN \__fp_trig_large:www - \int_use:N \__int_eval:w \c__fp_leading_shift_int + #20 - #1*62831 - \exp_after:wN \__fp_pack:NNNNNw - \int_use:N \__int_eval:w \c__fp_middle_shift_int + #30 - #1*8530 - \exp_after:wN \__fp_pack:NNNNNw - \int_use:N \__int_eval:w \c__fp_middle_shift_int + #40 - #1*7179 - \exp_after:wN \__fp_pack:NNNNNw - \int_use:N \__int_eval:w \c__fp_trailing_shift_int + #50 - #1*5880 - \exp_after:wN ; + \exp_after:wN \__fp_trigd_large_auxii:wNw + \int_use:N \__int_eval:w #1 + #2 + - (#1 + #2 - \c_four) / \c_nine * \c_nine \__int_eval_end: + #3; + #4; #5{#6#7#8#9}; } -\cs_new:Npn \__fp_trig_large_break:w \fi: #1; #2; - { \fi: \__fp_trig_octant_loop:nnnnnw #2 {0000} {0000} ; } -\cs_new:Npn \__fp_trig_octant_loop:nnnnnw #1#2#3#4#5#6; +\cs_new:Npn \__fp_trigd_large_auxii:wNw #1; #2#3; { - \if_int_compare:w #1#2 < 157079633 \exp_stop_f: - \if_int_compare:w #1#2 = 157079632 \exp_stop_f: - \if_int_compare:w #3#4 > 67948969 \exp_stop_f: - \use_i_ii:nnn - \fi: - \fi: - \__fp_trig_octant_break:w - \fi: - + \c_two - \__fp_fixed_sub:wwn - {#1} {#2} {#3} {#4} {0000} {0000} ; - {15707} {9632} {6794} {8970} {0000} {0000} ; - \__fp_trig_octant_loop:nnnnnw + + (#1#2 - \c_four) / \c_nine * \c_two + \exp_after:wN \__fp_trigd_large_auxiii:www + \int_use:N \__int_eval:w #1#2 + - (#1#2 - \c_four) / \c_nine * \c_nine \__int_eval_end: #3 ; } -\cs_new:Npn \__fp_trig_octant_break:w #1 \fi: + #2#3 #4#5; #6; #7; +\cs_new:Npn \__fp_trigd_large_auxiii:www #1; #2; #3! { - \fi: - \if_int_compare:w #4 < 7854 \exp_stop_f: + \if_int_compare:w #1 < 4500 \exp_stop_f: \exp_after:wN \__fp_use_i_until_s:nw - \exp_after:wN . + \exp_after:wN \__fp_fixed_continue:wn + \else: + + \c_one \fi: - + \c_one - \__fp_fixed_sub:wwn #6 ; {#4} #5 ; . ; + \__fp_fixed_sub:wwn {9000}{0000}{0000}{0000}{0000}{0000}; + 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2460565661129971310275869112846043251843432691552928458573495971 ~ + 5042565399302112184947232132380516549802909919676815118022483192 ~ + 5127372199792134331067642187484426215985121676396779352982985195 ~ + 8545392106957880586853123277545433229161989053189053725391582222 ~ + 9232597278133427818256064882333760719681014481453198336237910767 ~ + 1255017528826351836492103572587410356573894694875444694018175923 ~ + 0609370828146501857425324969212764624247832210765473750568198834 ~ + 5641035458027261252285503154325039591848918982630498759115406321 ~ + 0354263890012837426155187877318375862355175378506956599570028011 ~ + 5841258870150030170259167463020842412449128392380525772514737141 ~ + 2310230172563968305553583262840383638157686828464330456805994018 ~ + 7001071952092970177990583216417579868116586547147748964716547948 ~ + 8312140431836079844314055731179349677763739898930227765607058530 ~ + 4083747752640947435070395214524701683884070908706147194437225650 ~ + 2823145872995869738316897126851939042297110721350756978037262545 ~ + 8141095038270388987364516284820180468288205829135339013835649144 ~ + 3004015706509887926715417450706686888783438055583501196745862340 ~ + 8059532724727843829259395771584036885940989939255241688378793572 ~ + 7967951654076673927031256418760962190243046993485989199060012977 ~ + 7469214532970421677817261517850653008552559997940209969455431545 ~ + 2745856704403686680428648404512881182309793496962721836492935516 ~ + 2029872469583299481932978335803459023227052612542114437084359584 ~ + 9443383638388317751841160881711251279233374577219339820819005406 ~ + 3292937775306906607415304997682647124407768817248673421685881509 ~ + 9133422075930947173855159340808957124410634720893194912880783576 ~ + 3115829400549708918023366596077070927599010527028150868897828549 ~ + 4340372642729262103487013992868853550062061514343078665396085995 ~ + 0058714939141652065302070085265624074703660736605333805263766757 ~ + 2018839497277047222153633851135483463624619855425993871933367482 ~ + 0422097449956672702505446423243957506869591330193746919142980999 ~ + 3424230550172665212092414559625960554427590951996824313084279693 ~ + 7113207021049823238195747175985519501864630940297594363194450091 ~ + 9150616049228764323192129703446093584259267276386814363309856853 ~ + 2786024332141052330760658841495858718197071242995959226781172796 ~ + 4438853796763139274314227953114500064922126500133268623021550837 + \cs_end: + } +\cs_new:Npn \__fp_trig_large:ww #1, #2#3#4#5#6; + { + \exp_after:wN \__fp_trig_large_auxi:wwwwww + \int_use:N \__int_eval:w (#1 - 32) / 64 \exp_after:wN , + \int_use:N \__int_eval:w (#1 - 4) / 8 \exp_after:wN , + \__int_value:w #1 \__fp_trig_inverse_two_pi: ; + {#2}{#3}{#4}{#5} ; + } +\cs_new:Npn \__fp_trig_large_auxi:wwwwww #1, #2, #3, #4! + { + \prg_replicate:nn {#1} { \__fp_trig_large_auxii:ww } + \prg_replicate:nn { #2 - #1 * \c_eight } + { \__fp_trig_large_auxiii:wNNNNNNNN } + \prg_replicate:nn { #3 - #2 * \c_eight } + { \__fp_trig_large_auxiv:wN } + \prg_replicate:nn { \c_eight } { \__fp_pack_twice_four:wNNNNNNNN } + \__fp_trig_large_auxv:www + ; + } +\cs_new:Npn \__fp_trig_large_auxii:ww #1; #2 ~ { #1; } +\cs_new:Npn \__fp_trig_large_auxiii:wNNNNNNNN + #1; #2#3#4#5#6#7#8#9 { #1; } +\cs_new:Npn \__fp_trig_large_auxiv:wN #1; #2 { #1; } +\cs_new:Npn \__fp_trig_large_auxv:www #1; #2; #3; + { + \exp_after:wN \__fp_use_i_until_s:nw + \exp_after:wN \__fp_trig_large_auxvii:w + \int_use:N \__int_eval:w \c__fp_leading_shift_int + \prg_replicate:nn { \c_thirteen } + { \__fp_trig_large_auxvi:wnnnnnnnn } + + \c__fp_trailing_shift_int - \c__fp_middle_shift_int + \__fp_use_i_until_s:nw + ; #3 #1 ; ; + } +\cs_new:Npn \__fp_trig_large_auxvi:wnnnnnnnn #1; #2#3#4#5#6#7#8#9 + { + \exp_after:wN \__fp_trig_large_pack:NNNNNw + \int_use:N \__int_eval:w \c__fp_middle_shift_int + + #2*#9 + #3*#8 + #4*#7 + #5*#6 + #1; {#2}{#3}{#4}{#5} {#7}{#8}{#9} + } +\cs_new:Npn \__fp_trig_large_pack:NNNNNw #1#2#3#4#5#6; + { + #1#2#3#4#5 ; #6 } +\cs_new:Npn \__fp_trig_large_auxvii:w #1#2#3 + { + \exp_after:wN \__fp_trig_large_auxviii:ww + \int_use:N \__int_eval:w (#1#2#3 - 62) / 125 ; + #1#2#3 + } +\cs_new:Npn \__fp_trig_large_auxviii:ww #1; + { + + #1 + \if_int_odd:w #1 \exp_stop_f: + \exp_after:wN \__fp_trig_large_auxix:Nw + \exp_after:wN - + \else: + \exp_after:wN \__fp_trig_large_auxix:Nw + \exp_after:wN + + \fi: + } +\cs_new_nopar:Npn \__fp_trig_large_auxix:Nw + { + \exp_after:wN \__fp_use_i_until_s:nw + \exp_after:wN \__fp_trig_large_auxxi:w + \int_use:N \__int_eval:w \c__fp_leading_shift_int + \prg_replicate:nn { \c_thirteen } + { \__fp_trig_large_auxx:wNNNNN } + + \c__fp_trailing_shift_int - \c__fp_middle_shift_int + ; + } +\cs_new:Npn \__fp_trig_large_auxx:wNNNNN #1; #2 #3#4#5#6 + { + \exp_after:wN \__fp_trig_large_pack:NNNNNw + \int_use:N \__int_eval:w \c__fp_middle_shift_int + #2 \c_eight * #3#4#5#6 + #1; #2 } -\cs_new:Npn \__fp_sin_series:NNwww #1#2#3 . #4; #5; +\cs_new:Npn \__fp_trig_large_auxxi:w #1; + { + \exp_after:wN \__fp_ep_mul_raw:wwwwN + \int_use:N \__int_eval:w \c_zero \__fp_ep_to_ep_loop:N #1 ; ; ! + 0,{7853}{9816}{3397}{4483}{0961}{5661}; + \__fp_trig_small:ww + } +\cs_new:Npn \__fp_sin_series_o:NNwwww #1#2#3. #4; { \__fp_fixed_mul:wwn #4; #4; { - \exp_after:wN \__fp_sin_series_aux:NNnww + \exp_after:wN \__fp_sin_series_aux_o:NNnwww \exp_after:wN #1 \__int_value:w \if_int_odd:w \__int_eval:w ( #3 + \c_two ) / \c_four \__int_eval_end: @@ -4078,9 +4469,8 @@ \fi: {#3} } - #4 ; } -\cs_new:Npn \__fp_sin_series_aux:NNnww #1#2#3 #4; #5; +\cs_new:Npn \__fp_sin_series_aux_o:NNnwww #1#2#3 #4; #5,#6; { \if_int_odd:w \__int_eval:w #3 / \c_two \__int_eval_end: \exp_after:wN \use_i:nn @@ -4098,6 +4488,7 @@ \__fp_fixed_mul_sub_back:wwwn #4; {0416}{6666}{6666}{6666}{6666}{6667}; \__fp_fixed_mul_sub_back:wwwn #4; {5000}{0000}{0000}{0000}{0000}{0000}; \__fp_fixed_mul_sub_back:wwwn #4;{10000}{0000}{0000}{0000}{0000}{0000}; + { \__fp_fixed_continue:wn 0, } } { % 1/17! \__fp_fixed_mul_sub_back:wwwn {0000}{0000}{0000}{0028}{1145}{7254}; @@ -4109,7 +4500,7 @@ \__fp_fixed_mul_sub_back:wwwn #4; {0083}{3333}{3333}{3333}{3333}{3333}; \__fp_fixed_mul_sub_back:wwwn #4; {1666}{6666}{6666}{6666}{6666}{6667}; \__fp_fixed_mul_sub_back:wwwn #4;{10000}{0000}{0000}{0000}{0000}{0000}; - \__fp_fixed_mul:wwn #5; + { \__fp_ep_mul:wwwwn 0, } #5,#6; } { \exp_after:wN \__fp_sanitize:Nw @@ -4118,11 +4509,11 @@ } #2 } -\cs_new:Npn \__fp_tan_series_o:NNwww #1#2#3. #4; #5; +\cs_new:Npn \__fp_tan_series_o:NNwwww #1#2#3. #4; { \__fp_fixed_mul:wwn #4; #4; { - \exp_after:wN \__fp_tan_series_aux_o:Nnww + \exp_after:wN \__fp_tan_series_aux_o:Nnwww \__int_value:w \if_int_odd:w \__int_eval:w #3 / \c_two \__int_eval_end: \exp_after:wN \reverse_if:N @@ -4130,9 +4521,8 @@ \if_meaning:w #1#2 2 \else: 0 \fi: {#3} } - #4 ; } -\cs_new:Npn \__fp_tan_series_aux_o:Nnww #1 #2 #3; #4; +\cs_new:Npn \__fp_tan_series_aux_o:Nnwww #1 #2 #3; #4,#5; { \__fp_fixed_mul_sub_back:wwwn {0000}{0000}{1527}{3493}{0856}{7059}; #3; {0000}{0159}{6080}{0274}{5257}{6472}; @@ -4140,27 +4530,302 @@ \__fp_fixed_mul_sub_back:wwwn #3; {0115}{5830}{7533}{5397}{3168}{2147}; \__fp_fixed_mul_sub_back:wwwn #3; {1929}{8245}{6140}{3508}{7719}{2982}; \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000}; - \__fp_fixed_mul:wwn #4; + { \__fp_ep_mul:wwwwn 0, } #4,#5; + { + \__fp_fixed_mul_sub_back:wwwn {0000}{0007}{0258}{0681}{9408}{4706}; + #3; {0000}{2343}{7175}{1399}{6151}{7670}; + \__fp_fixed_mul_sub_back:wwwn #3; {0019}{2638}{4588}{9232}{8861}{3691}; + \__fp_fixed_mul_sub_back:wwwn #3; {0536}{6357}{0691}{4344}{6852}{4252}; + \__fp_fixed_mul_sub_back:wwwn #3; {5263}{1578}{9473}{6842}{1052}{6315}; + \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000}; { - \__fp_fixed_mul_sub_back:wwwn {0000}{0007}{0258}{0681}{9408}{4706}; - #3; {0000}{2343}{7175}{1399}{6151}{7670}; - \__fp_fixed_mul_sub_back:wwwn #3; {0019}{2638}{4588}{9232}{8861}{3691}; - \__fp_fixed_mul_sub_back:wwwn #3; {0536}{6357}{0691}{4344}{6852}{4252}; - \__fp_fixed_mul_sub_back:wwwn #3; {5263}{1578}{9473}{6842}{1052}{6315}; - \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000}; - { - \exp_after:wN \__fp_sanitize:Nw - \exp_after:wN #1 - \int_use:N \__int_eval:w - \reverse_if:N \if_int_odd:w - \__int_eval:w (#2 - \c_one) / \c_two \__int_eval_end: - \exp_after:wN \__fp_reverse_args:Nww - \fi: - \__fp_fixed_div_to_float:ww - } + \reverse_if:N \if_int_odd:w + \__int_eval:w (#2 - \c_one) / \c_two \__int_eval_end: + \exp_after:wN \__fp_reverse_args:Nww + \fi: + \__fp_ep_div:wwwwn 0, } + } + { + \exp_after:wN \__fp_sanitize:Nw + \exp_after:wN #1 + \int_use:N \__int_eval:w \__fp_ep_to_float:wwN + } + #1 + } +\cs_new_nopar:Npn \__fp_atan_o:Nw + { + \__fp_atan_dispatch_o:NNnNw + \__fp_acotii_o:Nww \__fp_atanii_o:Nww { atan } + } +\cs_new_nopar:Npn \__fp_acot_o:Nw + { + \__fp_atan_dispatch_o:NNnNw + \__fp_atanii_o:Nww \__fp_acotii_o:Nww { acot } } -%% File: l3fp-convert.dtx Copyright(C) 2011-2012 The LaTeX3 Project +\cs_new:Npn \__fp_atan_dispatch_o:NNnNw #1#2#3#4#5@ + { + \if_case:w + \__int_eval:w \__fp_array_count:n {#5} - \c_one \__int_eval_end: + \exp_after:wN #1 \exp_after:wN #4 \c_one_fp #5 + \tex_romannumeral:D + \or: #2 #4 #5 \tex_romannumeral:D + \else: + \__msg_kernel_expandable_error:nnnnn + { kernel } { fp-num-args } { #3() } { 1 } { 2 } + \exp_after:wN \c_nan_fp \tex_romannumeral:D + \fi: + \exp_after:wN \c_zero + } +\cs_new:Npn \__fp_atanii_o:Nww + #1 \s__fp \__fp_chk:w #2#3#4; \s__fp \__fp_chk:w #5 + { + \if_meaning:w 3 #2 \__fp_case_return_i_o:ww \fi: + \if_meaning:w 3 #5 \__fp_case_return_ii_o:ww \fi: + \if_case:w + \if_meaning:w #2 #5 + \if_meaning:w 1 #2 \c_ten \else: \c_zero \fi: + \else: + \if_int_compare:w #2 > #5 \c_one \else: \c_two \fi: + \fi: + \__fp_case_return:nw { \__fp_atan_inf_o:NNNw #1 #3 \c_two } + \or: \__fp_case_return:nw { \__fp_atan_inf_o:NNNw #1 #3 \c_four } + \or: \__fp_case_return:nw { \__fp_atan_inf_o:NNNw #1 #3 \c_zero } + \fi: + \__fp_atan_normal_o:NNnwNnw #1 + \s__fp \__fp_chk:w #2#3#4; + \s__fp \__fp_chk:w #5 + } +\cs_new:Npn \__fp_acotii_o:Nww #1#2; #3; + { \__fp_atanii_o:Nww #1#3; #2; } +\cs_new:Npn \__fp_atan_inf_o:NNNw #1#2#3 \s__fp \__fp_chk:w #4#5#6; + { + \exp_after:wN \__fp_atan_combine_o:NwwwwwN + \exp_after:wN #2 + \int_use:N \__int_eval:w + \if_meaning:w 2 #5 \c_seven - \fi: #3 \exp_after:wN ; + \c__fp_one_fixed_tl ; + {0000}{0000}{0000}{0000}{0000}{0000}; + 0,{0000}{0000}{0000}{0000}{0000}{0000}; #1 + } +\cs_new_protected:Npn \__fp_atan_normal_o:NNnwNnw + #1 \s__fp \__fp_chk:w 1#2#3#4; \s__fp \__fp_chk:w 1#5#6#7; + { + \__fp_atan_test_o:NwwNwwN + #2 #3, #4{0000}{0000}; + #5 #6, #7{0000}{0000}; #1 + } +\cs_new:Npn \__fp_atan_test_o:NwwNwwN #1#2,#3; #4#5,#6; + { + \exp_after:wN \__fp_atan_combine_o:NwwwwwN + \exp_after:wN #1 + \int_use:N \__int_eval:w + \if_meaning:w 2 #4 + \c_seven - \__int_eval:w + \fi: + \if_int_compare:w + \__fp_ep_compare:wwww #2,#3; #5,#6; > \c_zero + \c_three - + \exp_after:wN \__fp_reverse_args:Nww + \fi: + \__fp_atan_div:wnwwnw #2,#3; #5,#6; + } +\cs_new:Npn \__fp_atan_div:wnwwnw #1,#2#3; #4,#5#6; + { + \if_int_compare:w + \__int_eval:w 41421 * #5 < #2 000 + \if_case:w \__int_eval:w #4 - #1 \__int_eval_end: 00 \or: 0 \fi: + \exp_stop_f: + \exp_after:wN \__fp_atan_near:wwwn + \fi: + \c_zero + \__fp_ep_div:wwwwn #1,{#2}#3; #4,{#5}#6; + \__fp_atan_auxi:ww + } +\cs_new:Npn \__fp_atan_near:wwwn + \c_zero \__fp_ep_div:wwwwn #1,#2; #3, + { + \c_one + \__fp_ep_to_fixed:wwn #1 - #3, #2; + \__fp_atan_near_aux:wwn + } +\cs_new:Npn \__fp_atan_near_aux:wwn #1; #2; + { + \__fp_fixed_add:wwn #1; #2; + { \__fp_fixed_sub:wwn #2; #1; { \__fp_ep_div:wwwwn 0, } 0, } + } +\cs_new:Npn \__fp_atan_auxi:ww #1,#2; + { \__fp_ep_to_fixed:wwn #1,#2; \__fp_atan_auxii:w #1,#2; } +\cs_new:Npn \__fp_atan_auxii:w #1; + { + \__fp_fixed_mul:wwn #1; #1; + { + \__fp_atan_Taylor_loop:www 39 ; + {0000}{0000}{0000}{0000}{0000}{0000} ; + } + ! #1; + } +\cs_new:Npn \__fp_atan_Taylor_loop:www #1; #2; #3; + { + \if_int_compare:w #1 = \c_minus_one + \__fp_atan_Taylor_break:w + \fi: + \exp_after:wN \__fp_fixed_div_int:wwN \c__fp_one_fixed_tl ; #1; + \__fp_rrot:www \__fp_fixed_mul_sub_back:wwwn #2; #3; + { + \exp_after:wN \__fp_atan_Taylor_loop:www + \int_use:N \__int_eval:w #1 - \c_two ; + } + #3; + } +\cs_new:Npn \__fp_atan_Taylor_break:w + \fi: #1 \__fp_fixed_mul_sub_back:wwwn #2; #3 ! + { \fi: ; #2 ; } +\cs_new:Npn \__fp_atan_combine_o:NwwwwwN #1 #2; #3; #4; #5,#6; #7 + { + \exp_after:wN \__fp_sanitize:Nw + \exp_after:wN #1 + \int_use:N \__int_eval:w + \if_meaning:w 0 #2 + \exp_after:wN \use_i:nn + \else: + \exp_after:wN \use_ii:nn + \fi: + { #5 \__fp_fixed_mul:wwn #3; #6; } + { + \__fp_fixed_mul:wwn #3; #4; + { + \exp_after:wN \__fp_atan_combine_aux:ww + \int_use:N \__int_eval:w #2 / \c_two ; #2; + } + } + { #7 \__fp_fixed_to_float:wN \__fp_fixed_to_float_rad:wN } + #1 + } +\cs_new:Npn \__fp_atan_combine_aux:ww #1; #2; + { + \__fp_fixed_mul_short:wwn + {7853}{9816}{3397}{4483}{0961}{5661}; + {#1}{0000}{0000}; + { + \if_int_odd:w #2 \exp_stop_f: + \exp_after:wN \__fp_fixed_sub:wwn + \else: + \exp_after:wN \__fp_fixed_add:wwn + \fi: + } + } +\cs_new:Npn \__fp_asin_o:w #1 \s__fp \__fp_chk:w #2#3; @ + { + \if_case:w #2 \exp_stop_f: + \__fp_case_return_same_o:w + \or: + \__fp_case_use:nw + { \__fp_asin_normal_o:NfwNnnnnw #1 { #1 { asin } { asind } } } + \or: + \__fp_case_use:nw + { \__fp_invalid_operation_o:fw { #1 { asin } { asind } } } + \else: + \__fp_case_return_same_o:w + \fi: + \s__fp \__fp_chk:w #2 #3; + } +\cs_new:Npn \__fp_acos_o:w #1 \s__fp \__fp_chk:w #2#3; @ + { + \if_case:w #2 \exp_stop_f: + \__fp_case_use:nw { \__fp_atan_inf_o:NNNw #1 0 \c_four } + \or: + \__fp_case_use:nw + { + \__fp_asin_normal_o:NfwNnnnnw #1 { #1 { acos } { acosd } } + \__fp_reverse_args:Nww + } + \or: + \__fp_case_use:nw + { \__fp_invalid_operation_o:fw { #1 { acos } { acosd } } } + \else: + \__fp_case_return_same_o:w + \fi: + \s__fp \__fp_chk:w #2 #3; + } +\cs_new:Npn \__fp_asin_normal_o:NfwNnnnnw + #1#2#3 \s__fp \__fp_chk:w 1#4#5#6#7#8#9; + { + \if_int_compare:w #5 < \c_one + \exp_after:wN \__fp_use_none_until_s:w + \fi: + \if_int_compare:w \__int_eval:w #5 + #6#7 + #8#9 = 1000 0001 ~ + \exp_after:wN \__fp_use_none_until_s:w + \fi: + \__fp_use_i:ww + \__fp_invalid_operation_o:fw {#2} + \s__fp \__fp_chk:w 1#4{#5}{#6}{#7}{#8}{#9}; + \__fp_asin_auxi_o:NnNww + #1 {#3} #4 #5,{#6}{#7}{#8}{#9}{0000}{0000}; + } +\cs_new:Npn \__fp_asin_auxi_o:NnNww #1#2#3#4,#5; + { + \__fp_ep_to_fixed:wwn #4,#5; + \__fp_asin_isqrt:wn + \__fp_ep_mul:wwwwn #4,#5; + \__fp_ep_to_ep:wwN + \__fp_fixed_continue:wn + { #2 \__fp_atan_test_o:NwwNwwN #3 } + 0 1,{1000}{0000}{0000}{0000}{0000}{0000}; #1 + } +\cs_new:Npn \__fp_asin_isqrt:wn #1; + { + \exp_after:wN \__fp_fixed_sub:wwn \c__fp_one_fixed_tl ; #1; + { + \__fp_fixed_add_one:wN #1; + \__fp_fixed_continue:wn { \__fp_ep_mul:wwwwn 0, } 0, + } + \__fp_ep_isqrt:wwn + } +\cs_new:Npn \__fp_acsc_o:w #1 \s__fp \__fp_chk:w #2#3#4; @ + { + \if_case:w \if_meaning:w 2 #2 #3 \fi: #2 \exp_stop_f: + \__fp_case_use:nw + { \__fp_invalid_operation_o:fw { #1 { acsc } { acscd } } } + \or: \__fp_case_use:nw + { \__fp_acsc_normal_o:NfwNnw #1 { #1 { acsc } { acscd } } } + \or: \__fp_case_return_o:Nw \c_zero_fp + \or: \__fp_case_return_same_o:w + \else: \__fp_case_return_o:Nw \c_minus_zero_fp + \fi: + \s__fp \__fp_chk:w #2 #3 #4; + } +\cs_new:Npn \__fp_asec_o:w #1 \s__fp \__fp_chk:w #2#3; @ + { + \if_case:w #2 \exp_stop_f: + \__fp_case_use:nw + { \__fp_invalid_operation_o:fw { #1 { asec } { asecd } } } + \or: + \__fp_case_use:nw + { + \__fp_acsc_normal_o:NfwNnw #1 { #1 { asec } { asecd } } + \__fp_reverse_args:Nww + } + \or: \__fp_case_use:nw { \__fp_atan_inf_o:NNNw #1 0 \c_four } + \else: \__fp_case_return_same_o:w + \fi: + \s__fp \__fp_chk:w #2 #3; + } +\cs_new:Npn \__fp_acsc_normal_o:NfwNnw #1#2#3 \s__fp \__fp_chk:w 1#4#5#6; + { + \int_compare:nNnTF {#5} < \c_one + { + \__fp_invalid_operation_o:fw {#2} + \s__fp \__fp_chk:w 1#4{#5}#6; + } + { + \__fp_ep_div:wwwwn + 1,{1000}{0000}{0000}{0000}{0000}{0000}; + #5,#6{0000}{0000}; + { \__fp_asin_auxi_o:NnNww #1 {#3} #4 } + } + } +%% File: l3fp-convert.dtx Copyright(C) 2011-2013 The LaTeX3 Project %% %% It may be distributed and/or modified under the conditions of the %% LaTeX Project Public License (LPPL), either version 1.3c of this @@ -4376,37 +5041,38 @@ } \cs_new:Npn \dim_to_fp:n #1 { - \exp_after:wN \__fp_from_dim_test:N + \exp_after:wN \__fp_from_dim_test:ww + \exp_after:wN 0 + \exp_after:wN , \__int_value:w \etex_glueexpr:D #1 ; } -\cs_new:Npn \__fp_from_dim_test:N #1 +\cs_new:Npn \__fp_from_dim_test:ww #1, #2 { - \if_meaning:w 0 #1 - \__fp_case_return:nw \c_zero_fp + \if_meaning:w 0 #2 + \__fp_case_return:nw { \exp_after:wN \c_zero_fp } \else: - \if_meaning:w - #1 - \exp_after:wN \__fp_from_dim:Nw - \exp_after:wN 2 - \__int_value:w - \else: - \exp_after:wN \__fp_from_dim:Nw - \exp_after:wN 0 - \__int_value:w #1 - \fi: + \exp_after:wN \__fp_from_dim:wNw + \int_use:N \__int_eval:w #1 - \c_four + \if_meaning:w - #2 + \exp_after:wN , \exp_after:wN 2 \__int_value:w + \else: + \exp_after:wN , \exp_after:wN 0 \__int_value:w #2 + \fi: \fi: } -\cs_new:Npn \__fp_from_dim:Nw #1 #2; +\cs_new:Npn \__fp_from_dim:wNw #1,#2#3; { \__fp_pack_twice_four:wNNNNNNNN \__fp_from_dim:wNNnnnnnn ; - #2 000 0000 00 {10}987654321; #1 + #3 000 0000 00 {10}987654321; #2 {#1} } \cs_new:Npn \__fp_from_dim:wNNnnnnnn #1; #2#3#4#5#6#7#8#9 - { \__fp_from_dim:wnnnnwN #1 {#2#300} {0000} ; } -\cs_new:Npn \__fp_from_dim:wnnnnwN #1; #2#3#4#5#6; #7 + { \__fp_from_dim:wnnnnwNn #1 {#2#300} {0000} ; } +\cs_new:Npn \__fp_from_dim:wnnnnwNn #1; #2#3#4#5#6; #7#8 { \__fp_mul_npos_o:Nww #7 \s__fp \__fp_chk:w 1 #7 {#5} #1 ; - \s__fp \__fp_chk:w 1 0 {-4} {1525} {8789} {0625} {0000} ; + \s__fp \__fp_chk:w 1 0 {#8} {1525} {8789} {0625} {0000} ; + \prg_do_nothing: } \cs_new_eq:NN \fp_use:N \fp_to_decimal:N \cs_generate_variant:Nn \fp_use:N { c } @@ -4442,7 +5108,7 @@ \exp_not:N \__fp_array_to_clist_loop:Nw } %% -%% File: l3fp-assign.dtx Copyright (C) 2011-2012 The LaTeX3 project +%% File: l3fp-assign.dtx Copyright (C) 2011-2013 The LaTeX3 project %% %% It may be distributed and/or modified under the conditions of the %% LaTeX Project Public License (LPPL), either version 1.3c of this @@ -4479,11 +5145,11 @@ { \cs_new_eq:NN #1 \c_zero_fp } \cs_generate_variant:Nn \fp_new:N {c} \cs_new_protected:Npn \fp_set:Nn #1#2 - { \tl_set:Nx #1 { \__fp_parse:n {#2} } } + { \tl_set:Nx #1 { \exp_not:f { \__fp_parse:n {#2} } } } \cs_new_protected:Npn \fp_gset:Nn #1#2 - { \tl_gset:Nx #1 { \__fp_parse:n {#2} } } + { \tl_gset:Nx #1 { \exp_not:f { \__fp_parse:n {#2} } } } \cs_new_protected:Npn \fp_const:Nn #1#2 - { \tl_const:Nx #1 { \__fp_parse:n {#2} } } + { \tl_const:Nx #1 { \exp_not:f { \__fp_parse:n {#2} } } } \cs_generate_variant:Nn \fp_set:Nn {c} \cs_generate_variant:Nn \fp_gset:Nn {c} \cs_generate_variant:Nn \fp_const:Nn {c} @@ -4525,7 +5191,7 @@ \cs_generate_variant:Nn \fp_show:N { c } \fp_const:Nn \c_e_fp { 2.718 2818 2845 9045 } \fp_const:Nn \c_one_fp { 1 } -\fp_const:Nn \c_pi_fp { 3.141 5926 5358 9794 } +\fp_const:Nn \c_pi_fp { 3.141 5926 5358 9793 } \fp_const:Nn \c_one_degree_fp { 0.0 1745 3292 5199 4330 } \fp_new:N \l_tmpa_fp \fp_new:N \l_tmpb_fp |