diff options
author | Karl Berry <karl@freefriends.org> | 2010-12-19 00:30:41 +0000 |
---|---|---|
committer | Karl Berry <karl@freefriends.org> | 2010-12-19 00:30:41 +0000 |
commit | a3486a2d404fca82e9fc0db0a72c7d61efe4824b (patch) | |
tree | 967c74ad591a3d41a4bc66c41f9a0d582b65a704 /Master/texmf-dist/tex/latex/expl3/l3fp.sty | |
parent | 64fe2e9d7165882dc60a0c1fb71883e0b4ec2b15 (diff) |
expl3 2103 (18dec10)
git-svn-id: svn://tug.org/texlive/trunk@20793 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/tex/latex/expl3/l3fp.sty')
-rw-r--r-- | Master/texmf-dist/tex/latex/expl3/l3fp.sty | 1485 |
1 files changed, 1301 insertions, 184 deletions
diff --git a/Master/texmf-dist/tex/latex/expl3/l3fp.sty b/Master/texmf-dist/tex/latex/expl3/l3fp.sty index 65366e3af16..b5bb0661edc 100644 --- a/Master/texmf-dist/tex/latex/expl3/l3fp.sty +++ b/Master/texmf-dist/tex/latex/expl3/l3fp.sty @@ -48,25 +48,18 @@ %% %% ----------------------------------------------------------------------- \RequirePackage{l3names} -\GetIdInfo$Id: l3fp.dtx 2092 2010-11-25 20:44:04Z joseph $ +\GetIdInfo$Id: l3fp.dtx 2104 2010-12-18 09:29:34Z joseph $ {L3 Experimental floating-point operations} \ProvidesExplPackage {\filename}{\filedate}{\fileversion}{\filedescription} \package_check_loaded_expl: -\int_new:N \c_forty_four -\int_set:Nn \c_forty_four { 44 } -\int_new:N \c_one_hundred -\int_set:Nn \c_one_hundred { 100 } -\int_new:N \c_one_thousand -\int_set:Nn \c_one_thousand { 1000 } -\int_new:N \c_one_million -\int_set:Nn \c_one_million { 1 000 000 } -\int_new:N \c_one_hundred_million -\int_set:Nn \c_one_hundred_million { 100 000 000 } -\int_new:N \c_five_hundred_million -\int_set:Nn \c_five_hundred_million { 500 000 000 } -\int_new:N \c_one_thousand_million -\int_set:Nn \c_one_thousand_million { 1 000 000 000 } +\int_const:Nn \c_forty_four { 44 } +\int_const:Nn \c_one_hundred { 100 } +\int_const:Nn \c_one_thousand { 1000 } +\int_const:Nn \c_one_million { 1 000 000 } +\int_const:Nn \c_one_hundred_million { 100 000 000 } +\int_const:Nn \c_five_hundred_million { 500 000 000 } +\int_const:Nn \c_one_thousand_million { 1 000 000 000 } \int_new:N \c_fp_pi_by_four_decimal_int \int_set:Nn \c_fp_pi_by_four_decimal_int { 785 398 158 } \int_new:N \c_fp_pi_by_four_extended_int @@ -79,16 +72,23 @@ \int_set:Nn \c_fp_two_pi_decimal_int { 283 185 307 } \int_new:N \c_fp_two_pi_extended_int \int_set:Nn \c_fp_two_pi_extended_int { 179 586 477 } -\tl_new:N \c_one_fp +\tl_new:N \c_e_fp +\tl_set:Nn \c_e_fp { + 2.718281828 e 0 } +\tl_new:N \c_one_fp \tl_set:Nn \c_one_fp { + 1.000000000 e 0 } -\tl_new:N \c_pi_fp +\tl_new:N \c_pi_fp \tl_set:Nn \c_pi_fp { + 3.141592654 e 0 } -\tl_new:N \c_undefined_fp +\tl_new:N \c_undefined_fp \tl_set:Nn \c_undefined_fp { X 0.000000000 e 0 } -\tl_new:N \c_zero_fp +\tl_new:N \c_zero_fp \tl_set:Nn \c_zero_fp { + 0.000000000 e 0 } +\tl_new:N \l_fp_arg_tl \int_new:N \l_fp_count_int \int_new:N \l_fp_div_offset_int +\int_new:N \l_fp_exp_integer_int +\int_new:N \l_fp_exp_decimal_int +\int_new:N \l_fp_exp_extended_int +\int_new:N \l_fp_exp_exponent_int \int_new:N \l_fp_input_a_sign_int \int_new:N \l_fp_input_a_integer_int \int_new:N \l_fp_input_a_decimal_int @@ -122,16 +122,16 @@ \tl_new:N \l_fp_round_decimal_tl \int_new:N \l_fp_round_position_int \int_new:N \l_fp_round_target_int +\tl_new:N \l_fp_sign_tl \int_new:N \l_fp_split_sign_int \int_new:N \l_fp_tmp_int \tl_new:N \l_fp_tmp_tl -\tl_new:N \l_fp_trig_arg_tl \int_new:N \l_fp_trig_octant_int \int_new:N \l_fp_trig_sign_int \int_new:N \l_fp_trig_decimal_int \int_new:N \l_fp_trig_extended_int \cs_new_protected_nopar:Npn \fp_read:N #1 { - \exp_after:wN \fp_read_aux:w #1 \q_stop + \tex_expandafter:D \fp_read_aux:w #1 \q_stop } \cs_new_protected_nopar:Npn \fp_read_aux:w #1#2 . #3 e #4 \q_stop { \tex_if:D #1 - @@ -150,29 +150,29 @@ \l_fp_split_sign_int \c_one \fp_split_sign: \use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int - \exp_after:wN \fp_split_exponent:w \l_fp_tmp_tl e e \q_stop #1 + \tex_expandafter:D \fp_split_exponent:w \l_fp_tmp_tl e e \q_stop #1 } \cs_new_protected_nopar:Npn \fp_split_sign: { \tex_ifnum:D \pdf_strcmp:D - { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_stop } { - } + { \tex_expandafter:D \tl_head:w \l_fp_tmp_tl ? \q_stop } { - } = \c_zero \tl_set:Nx \l_fp_tmp_tl { - \exp_after:wN + \tex_expandafter:D \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop } \l_fp_split_sign_int -\l_fp_split_sign_int - \exp_after:wN \fp_split_sign: + \tex_expandafter:D \fp_split_sign: \tex_else:D \tex_ifnum:D \pdf_strcmp:D - { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_stop } { + } + { \tex_expandafter:D \tl_head:w \l_fp_tmp_tl ? \q_stop } { + } = \c_zero \tl_set:Nx \l_fp_tmp_tl { - \exp_after:wN + \tex_expandafter:D \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop } - \exp_after:wN \exp_after:wN \exp_after:wN + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_split_sign: \tex_fi:D \tex_fi:D @@ -193,7 +193,7 @@ } \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 + \tex_expandafter:D \fp_split_decimal:w \int_use:N \l_fp_tmp_int 000000000 \q_stop } \cs_new_protected_nopar:Npn \fp_split_decimal:w #1#2#3#4#5#6#7#8#9 { @@ -212,7 +212,7 @@ \tex_ifnum:D \use:c { l_fp_input_ #4 _integer_int } < \c_one_thousand_million \tex_else:D - \exp_after:wN \fp_overflow_msg: + \tex_expandafter:D \fp_overflow_msg: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_standardise:NNNN #1#2#3#4 { @@ -220,9 +220,9 @@ \etex_numexpr:D #2 + #3 = \c_zero #1 \c_one #4 \c_zero - \exp_after:wN \use_none:nnnn + \tex_expandafter:D \use_none:nnnn \tex_else:D - \exp_after:wN \fp_standardise_aux:NNNN + \tex_expandafter:D \fp_standardise_aux:NNNN \tex_fi:D #1#2#3#4 } @@ -231,9 +231,9 @@ { \tex_ifnum:D #2 = \c_zero \tex_advance:D #3 \c_one_thousand_million - \exp_after:wN \fp_standardise_aux:w + \tex_expandafter:D \fp_standardise_aux:w \int_use:N #3 \q_stop - \exp_after:wN \fp_standardise_aux: + \tex_expandafter:D \fp_standardise_aux: \tex_fi:D } \cs_set_protected_nopar:Npn @@ -248,9 +248,9 @@ { \tex_ifnum:D #2 > \c_nine \tex_advance:D #2 \c_one_thousand_million - \exp_after:wN \use_i:nn \exp_after:wN + \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_standardise_aux:w \int_use:N #2 - \exp_after:wN \fp_standardise_aux: + \tex_expandafter:D \fp_standardise_aux: \tex_fi:D } \cs_set_protected_nopar:Npn @@ -262,7 +262,7 @@ \tl_set:Nx \l_fp_tmp_tl { ##9 - \exp_after:wN \use_none:n \int_use:N #3 + \tex_expandafter:D \use_none:n \int_use:N #3 } #3 \l_fp_tmp_tl \scan_stop: \tex_advance:D #4 \c_one @@ -277,25 +277,25 @@ #4 \c_zero \tex_fi:D \tex_else:D - \exp_after:wN \fp_overflow_msg: + \tex_expandafter:D \fp_overflow_msg: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_standardise_aux: { } \cs_new_protected_nopar:Npn \fp_standardise_aux:w { } \cs_new_protected_nopar:Npn \fp_level_input_exponents: { \tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int - \exp_after:wN \fp_level_input_exponents_a: + \tex_expandafter:D \fp_level_input_exponents_a: \tex_else:D - \exp_after:wN \fp_level_input_exponents_b: + \tex_expandafter:D \fp_level_input_exponents_b: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_level_input_exponents_a: { \tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int \tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million - \exp_after:wN \use_i:nn \exp_after:wN + \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_level_input_exponents_a:NNNNNNNNN \int_use:N \l_fp_input_b_integer_int - \exp_after:wN \fp_level_input_exponents_a: + \tex_expandafter:D \fp_level_input_exponents_a: \tex_fi:D } \cs_new_protected_nopar:Npn @@ -306,7 +306,7 @@ \tl_set:Nx \l_fp_tmp_tl { #9 - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_b_decimal_int } \l_fp_input_b_decimal_int \l_fp_tmp_tl \scan_stop: @@ -315,10 +315,10 @@ \cs_new_protected_nopar:Npn \fp_level_input_exponents_b: { \tex_ifnum:D \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int \tex_advance:D \l_fp_input_a_integer_int \c_one_thousand_million - \exp_after:wN \use_i:nn \exp_after:wN + \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_level_input_exponents_b:NNNNNNNNN \int_use:N \l_fp_input_a_integer_int - \exp_after:wN \fp_level_input_exponents_b: + \tex_expandafter:D \fp_level_input_exponents_b: \tex_fi:D } \cs_new_protected_nopar:Npn @@ -329,7 +329,7 @@ \tl_set:Nx \l_fp_tmp_tl { #9 - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int } \l_fp_input_a_decimal_int \l_fp_tmp_tl \scan_stop: @@ -341,6 +341,18 @@ \tl_gset_eq:NN #1 \c_zero_fp } \cs_generate_variant:Nn \fp_new:N { c } +\cs_new_protected_nopar:Npn \fp_const:Nn #1#2 { + \cs_if_free:NTF #1 + { + \fp_new:N #1 + \fp_gset:Nn #1 {#2} + } + { + \msg_kernel_error:nx { variable-already-defined } + { \token_to_str:N #1 } + } +} +\cs_generate_variant:Nn \fp_const:Nn { c } \cs_new_protected_nopar:Npn \fp_zero:N #1 { \tl_set_eq:NN #1 \c_zero_fp } @@ -376,7 +388,7 @@ \tex_fi:D \int_use:N \l_fp_input_a_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int e \int_use:N \l_fp_input_a_exponent_int @@ -398,7 +410,7 @@ \l_fp_tmp_dim \l_fp_tmp_skip \fp_split:Nn a { - \exp_after:wN \fp_set_from_dim_aux:w + \tex_expandafter:D \fp_set_from_dim_aux:w \dim_use:N \l_fp_tmp_dim } \fp_standardise:NNNN @@ -419,7 +431,7 @@ \tex_fi:D \int_use:N \l_fp_input_a_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int e \int_use:N \l_fp_input_a_exponent_int @@ -447,7 +459,7 @@ \cs_new_eq:NN \fp_show:N \tl_show:N \cs_new_eq:NN \fp_show:c \tl_show:c \cs_new_nopar:Npn \fp_use:N #1 { - \exp_after:wN \fp_use_aux:w #1 \q_stop + \tex_expandafter:D \fp_use_aux:w #1 \q_stop } \cs_generate_variant:Nn \fp_use:N { c } \cs_new_nopar:Npn \fp_use_aux:w #1#2 e #3 \q_stop { @@ -455,13 +467,13 @@ - \tex_fi:D \tex_ifnum:D #3 > \c_zero - \exp_after:wN \fp_use_large:w + \tex_expandafter:D \fp_use_large:w \tex_else:D \tex_ifnum:D #3 < \c_zero - \exp_after:wN \exp_after:wN \exp_after:wN + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_use_small:w \tex_else:D - \exp_after:wN \exp_after:wN \exp_after:wN + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_use_none:w \tex_fi:D \tex_fi:D @@ -475,9 +487,9 @@ } \cs_new_nopar:Npn \fp_use_large:w #1 . #2 e #3 \q_stop { \tex_ifnum:D #3 < \c_ten - \exp_after:wN \fp_use_large_aux_i:w + \tex_expandafter:D \fp_use_large_aux_i:w \tex_else:D - \exp_after:wN \fp_use_large_aux_ii:w + \tex_expandafter:D \fp_use_large_aux_ii:w \tex_fi:D #1#2 e #3 \q_stop } @@ -516,7 +528,7 @@ \cs_new_nopar:Npn \fp_to_dim:N #1 { \fp_use:N #1 pt } \cs_generate_variant:Nn \fp_to_dim:N { c } \cs_new_nopar:Npn \fp_to_int:N #1 { - \exp_after:wN \fp_to_int_aux:w #1 \q_stop + \tex_expandafter:D \fp_to_int_aux:w #1 \q_stop } \cs_generate_variant:Nn \fp_to_int:N { c } \cs_new_nopar:Npn \fp_to_int_aux:w #1#2 e #3 \q_stop { @@ -524,9 +536,9 @@ - \tex_fi:D \tex_ifnum:D #3 < \c_zero - \exp_after:wN \fp_to_int_small:w + \tex_expandafter:D \fp_to_int_small:w \tex_else:D - \exp_after:wN \fp_to_int_large:w + \tex_expandafter:D \fp_to_int_large:w \tex_fi:D #2 e #3 \q_stop } @@ -542,9 +554,9 @@ } \cs_new_nopar:Npn \fp_to_int_large:w #1 . #2 e #3 \q_stop { \tex_ifnum:D #3 < \c_ten - \exp_after:wN \fp_to_int_large_aux_i:w + \tex_expandafter:D \fp_to_int_large_aux_i:w \tex_else:D - \exp_after:wN \fp_to_int_large_aux_ii:w + \tex_expandafter:D \fp_to_int_large_aux_ii:w \tex_fi:D #1#2 e #3 \q_stop } @@ -590,7 +602,7 @@ \prg_replicate:nn { #2 - 9 } { 0 } } \cs_new_nopar:Npn \fp_to_tl:N #1 { - \exp_after:wN \fp_to_tl_aux:w #1 \q_stop + \tex_expandafter:D \fp_to_tl_aux:w #1 \q_stop } \cs_generate_variant:Nn \fp_to_tl:N { c } \cs_new_nopar:Npn \fp_to_tl_aux:w #1#2 e #3 \q_stop { @@ -598,17 +610,17 @@ - \tex_fi:D \tex_ifnum:D #3 < \c_zero - \exp_after:wN \fp_to_tl_small:w + \tex_expandafter:D \fp_to_tl_small:w \tex_else:D - \exp_after:wN \fp_to_tl_large:w + \tex_expandafter:D \fp_to_tl_large:w \tex_fi:D #2 e #3 \q_stop } \cs_new_nopar:Npn \fp_to_tl_large:w #1 e #2 \q_stop { \tex_ifnum:D #2 < \c_ten - \exp_after:wN \fp_to_tl_large_aux_i:w + \tex_expandafter:D \fp_to_tl_large_aux_i:w \tex_else:D - \exp_after:wN \fp_to_tl_large_aux_ii:w + \tex_expandafter:D \fp_to_tl_large_aux_ii:w \tex_fi:D #1 e #2 \q_stop } @@ -664,13 +676,13 @@ \cs_new_nopar:cpn { fp_to_tl_large_9:w } #1 . #2 \q_stop {#1#2} \cs_new_nopar:Npn \fp_to_tl_small:w #1 e #2 \q_stop { \tex_ifnum:D #2 = \c_minus_one - \exp_after:wN \fp_to_tl_small_one:w + \tex_expandafter:D \fp_to_tl_small_one:w \tex_else:D \tex_ifnum:D #2 = -\c_two - \exp_after:wN \exp_after:wN \exp_after:wN + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_to_tl_small_two:w \tex_else:D - \exp_after:wN \exp_after:wN \exp_after:wN + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_to_tl_small_aux:w \tex_fi:D \tex_fi:D @@ -682,7 +694,7 @@ \etex_numexpr:D #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1 < \c_one_thousand_million 0. - \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN + \tex_expandafter:D \fp_to_tl_small_zeros:NNNNNNNNN \tex_number:D \etex_numexpr:D #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1 @@ -701,7 +713,7 @@ \etex_numexpr:D #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten < \c_one_thousand_million 0.0 - \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN + \tex_expandafter:D \fp_to_tl_small_zeros:NNNNNNNNN \tex_number:D \etex_numexpr:D #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten @@ -817,7 +829,7 @@ \fp_read:N #2 \int_set:Nn \l_fp_round_target_int { #3 - 1 } \tex_ifnum:D \l_fp_round_target_int < \c_ten - \exp_after:wN \fp_round: + \tex_expandafter:D \fp_round: \tex_fi:D \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \cs_set_protected_nopar:Npx \fp_tmp:w @@ -832,7 +844,7 @@ \tex_fi:D \int_use:N \l_fp_input_a_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int e \int_use:N \l_fp_input_a_exponent_int @@ -854,7 +866,7 @@ \int_set:Nn \l_fp_round_target_int { #3 + \l_fp_input_a_exponent_int } \tex_ifnum:D \l_fp_round_target_int < \c_ten - \exp_after:wN \fp_round: + \tex_expandafter:D \fp_round: \tex_fi:D \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million \cs_set_protected_nopar:Npx \fp_tmp:w @@ -869,7 +881,7 @@ \tex_fi:D \int_use:N \l_fp_input_a_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int e \int_use:N \l_fp_input_a_exponent_int @@ -882,7 +894,7 @@ \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 + \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_round_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int } \cs_new_protected_nopar:Npn \fp_round_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { @@ -919,7 +931,7 @@ \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_loop:N + \tex_expandafter:D \fp_round_loop:N \tex_fi:D } \cs_new_protected_nopar:Npn \fp_abs:N { @@ -942,7 +954,7 @@ + \int_use:N \l_fp_input_a_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int e \int_use:N \l_fp_input_a_exponent_int @@ -971,13 +983,13 @@ \tex_fi:D \int_use:N \l_fp_input_a_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \int_use:N \l_fp_input_a_decimal_int e \int_use:N \l_fp_input_a_exponent_int } - \exp_after:wN \group_end: \exp_after:wN - #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl } + \tex_expandafter:D \group_end: \tex_expandafter:D + #1 \tex_expandafter:D #2 \tex_expandafter:D { \l_fp_tmp_tl } } \cs_new_protected_nopar:Npn \fp_add:Nn { \fp_add_aux:NNn \tl_set:Nn @@ -1006,9 +1018,9 @@ \l_fp_input_a_sign_int * \l_fp_input_b_sign_int \scan_stop: > \c_zero - \exp_after:wN \fp_add_sum: + \tex_expandafter:D \fp_add_sum: \tex_else:D - \exp_after:wN \fp_add_difference: + \tex_expandafter:D \fp_add_difference: \tex_fi:D \l_fp_output_exponent_int \l_fp_input_a_exponent_int \fp_standardise:NNNN @@ -1028,7 +1040,7 @@ \tex_fi:D \int_use:N \l_fp_output_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million e @@ -1121,7 +1133,7 @@ \l_fp_input_b_integer_int \l_fp_input_b_decimal_int \l_fp_input_b_exponent_int - \fp_mul_int: + \fp_mul_internal: \l_fp_output_exponent_int \etex_numexpr:D \l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int @@ -1153,7 +1165,7 @@ \tex_fi:D \int_use:N \l_fp_output_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million e @@ -1162,7 +1174,7 @@ } \fp_tmp:w } -\cs_new_protected_nopar:Npn \fp_mul_int: { +\cs_new_protected_nopar:Npn \fp_mul_internal: { \fp_mul_split:NNNN \l_fp_input_a_decimal_int \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int \fp_mul_split:NNNN \l_fp_input_b_decimal_int @@ -1199,7 +1211,7 @@ #3 ##5##6##7 \scan_stop: #4 ##8##9 \scan_stop: } - \exp_after:wN \fp_mul_split_aux:w \int_use:N #1 \q_stop + \tex_expandafter:D \fp_mul_split_aux:w \int_use:N #1 \q_stop \tex_advance:D #1 -\c_one_thousand_million } \cs_new_protected_nopar:Npn \fp_mul_product:NN #1#2 { @@ -1208,7 +1220,7 @@ } \cs_new_protected_nopar:Npn \fp_mul_end_level: { \tex_advance:D \l_fp_mul_output_int \c_one_thousand_million - \exp_after:wN \use_i:nn \exp_after:wN + \tex_expandafter:D \use_i:nn \tex_expandafter:D \fp_mul_end_level:NNNNNNNNN \int_use:N \l_fp_mul_output_int } \cs_new_protected_nopar:Npn \fp_mul_end_level:NNNNNNNNN @@ -1224,7 +1236,6 @@ } \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 @@ -1254,13 +1265,13 @@ #1 \exp_not:N #2 { \c_zero_fp } } \tex_else:D - \exp_after:wN \exp_after:wN \exp_after:wN - \fp_div_aux: + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \fp_div_internal: \tex_fi:D \tex_fi:D \fp_tmp:w #1#2 } -\cs_new_protected_nopar:Npn \fp_div_aux: { +\cs_new_protected_nopar:Npn \fp_div_internal: { \l_fp_output_integer_int \c_zero \l_fp_output_decimal_int \c_zero \cs_set_eq:NN \fp_div_store: \fp_div_store_integer: @@ -1297,7 +1308,7 @@ \tex_fi:D \int_use:N \l_fp_output_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million \scan_stop: @@ -1312,30 +1323,30 @@ \fp_div_store: \tex_multiply:D \l_fp_input_a_integer_int \c_ten \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million - \exp_after:wN \fp_div_loop_step:w + \tex_expandafter:D \fp_div_loop_step:w \int_use:N \l_fp_input_a_decimal_int \q_stop \tex_ifnum:D \etex_numexpr:D \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int > \c_zero \tex_ifnum:D \l_fp_div_offset_int > \c_zero - \exp_after:wN \exp_after:wN \exp_after:wN + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_div_loop: \tex_fi:D \tex_fi:D } \cs_new_protected_nopar:Npn \fp_div_divide: { \tex_ifnum:D \l_fp_input_a_integer_int > \l_fp_input_b_integer_int - \exp_after:wN \fp_div_divide_aux: + \tex_expandafter:D \fp_div_divide_aux: \tex_else:D \tex_ifnum:D \l_fp_input_a_integer_int < \l_fp_input_b_integer_int \tex_else:D \tex_ifnum:D \l_fp_input_a_decimal_int < \l_fp_input_b_decimal_int \tex_else:D - \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_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \fp_div_divide_aux: \tex_fi:D \tex_fi:D \tex_fi:D @@ -1430,6 +1441,7 @@ \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 @@ -1450,6 +1462,65 @@ \fp_mul_end_level: #5 0 \l_fp_mul_output_tl \scan_stop: } +\cs_new_protected_nopar:Npn \fp_mul:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { + \fp_mul_split:NNNN #2 + \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int + \fp_mul_split:NNNN #3 + \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int + \fp_mul_split:NNNN #5 + \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int + \fp_mul_split:NNNN #6 + \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int + \l_fp_mul_output_int \c_zero + \tl_clear:N \l_fp_mul_output_tl + \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_vi_int + \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_v_int + \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iv_int + \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_iii_int + \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_ii_int + \fp_mul_product:NN \l_fp_mul_a_vi_int \l_fp_mul_b_i_int + \tex_divide:D \l_fp_mul_output_int \c_one_thousand + \fp_mul_product:NN #1 \l_fp_mul_b_vi_int + \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_v_int + \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iv_int + \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_iii_int + \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_ii_int + \fp_mul_product:NN \l_fp_mul_a_v_int \l_fp_mul_b_i_int + \fp_mul_product:NN \l_fp_mul_a_vi_int #4 + \fp_mul_end_level: + \fp_mul_product:NN #1 \l_fp_mul_b_v_int + \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iv_int + \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_iii_int + \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_ii_int + \fp_mul_product:NN \l_fp_mul_a_iv_int \l_fp_mul_b_i_int + \fp_mul_product:NN \l_fp_mul_a_v_int #4 + \fp_mul_end_level: + \fp_mul_product:NN #1 \l_fp_mul_b_iv_int + \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_iii_int + \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_ii_int + \fp_mul_product:NN \l_fp_mul_a_iii_int \l_fp_mul_b_i_int + \fp_mul_product:NN \l_fp_mul_a_iv_int #4 + \fp_mul_end_level: + #9 0 \l_fp_mul_output_tl \scan_stop: + \tl_clear:N \l_fp_mul_output_tl + \fp_mul_product:NN #1 \l_fp_mul_b_iii_int + \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_ii_int + \fp_mul_product:NN \l_fp_mul_a_ii_int \l_fp_mul_b_i_int + \fp_mul_product:NN \l_fp_mul_a_iii_int #4 + \fp_mul_end_level: + \fp_mul_product:NN #1 \l_fp_mul_b_ii_int + \fp_mul_product:NN \l_fp_mul_a_i_int \l_fp_mul_b_i_int + \fp_mul_product:NN \l_fp_mul_a_ii_int #4 + \fp_mul_end_level: + \fp_mul_product:NN #1 \l_fp_mul_b_i_int + \fp_mul_product:NN \l_fp_mul_a_i_int #4 + \fp_mul_end_level: + #8 0 \l_fp_mul_output_tl \scan_stop: + \tl_clear:N \l_fp_mul_output_tl + \fp_mul_product:NN #1 #4 + \fp_mul_end_level: + #7 0 \l_fp_mul_output_tl \scan_stop: +} \cs_new_protected_nopar:Npn \fp_div_integer:NNNNN #1#2#3#4#5 { \l_fp_tmp_int #1 \tex_divide:D \l_fp_tmp_int #3 @@ -1466,52 +1537,46 @@ \tex_advancd:D #5 -\c_one_thousand_million \tex_fi:D } -\cs_new_protected_nopar:Npn \fp_trig_normalise: { - \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten - \l_fp_input_a_extended_int \c_zero - \fp_trig_normalise_aux_i: - \fp_trig_normalise_aux_ii: - \fp_trig_normalise_aux_iii: - \tex_ifnum:D \l_fp_input_a_integer_int < \c_zero - \l_fp_input_a_sign_int -\l_fp_input_a_sign_int - \l_fp_input_a_integer_int -\l_fp_input_a_integer_int - \tex_fi:D - \exp_after:wN \fp_trig_octant: - \tex_else:D - \l_fp_input_a_sign_int \c_one - \l_fp_output_integer_int \c_zero - \l_fp_output_decimal_int \c_zero - \l_fp_output_exponent_int \c_zero - \exp_after:wN \fp_trig_overflow_msg: - \tex_fi:D +\cs_new_protected_nopar:Npn \fp_extended_normalise: { + \fp_extended_normalise_aux_i: + \fp_extended_normalise_aux_ii: } -\cs_new_protected_nopar:Npn \fp_trig_normalise_aux_i: { +\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_i: { \tex_ifnum:D \l_fp_input_a_exponent_int > \c_zero \tex_multiply:D \l_fp_input_a_integer_int \c_ten \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million - \exp_after:wN \fp_trig_normalise_aux:w + \tex_expandafter:D \fp_extended_normalise_aux_i:w \int_use:N \l_fp_input_a_decimal_int \q_stop - \exp_after:wN \fp_trig_normalise_aux_i: + \tex_expandafter:D \fp_extended_normalise_aux_i: \tex_fi:D } \cs_new_protected_nopar:Npn - \fp_trig_normalise_aux:w #1#2#3#4#5#6#7#8#9 \q_stop { + \fp_extended_normalise_aux_i:w #1#2#3#4#5#6#7#8#9 \q_stop { \l_fp_input_a_integer_int \etex_numexpr:D \l_fp_input_a_integer_int + #2 \scan_stop: \l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop: + \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million + \tex_expandafter:D \fp_extended_normalise_aux_ii:w + \int_use:N \l_fp_input_a_extended_int \q_stop +} +\cs_new_protected_nopar:Npn + \fp_extended_normalise_aux_ii:w #1#2#3#4#5#6#7#8#9 \q_stop { + \l_fp_input_a_decimal_int + \etex_numexpr:D \l_fp_input_a_decimal_int + #2 \scan_stop: + \l_fp_input_a_extended_int #3#4#5#6#7#8#9 0 \scan_stop: \tex_advance:D \l_fp_input_a_exponent_int \c_minus_one } -\cs_new_protected_nopar:Npn \fp_trig_normalise_aux_ii: { +\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_ii: { \tex_ifnum:D \l_fp_input_a_exponent_int < \c_zero \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million - \exp_after:wN \use_i:nn \exp_after:wN - \fp_trig_normalise_aux:NNNNNNNNN + \tex_expandafter:D \use_i:nn \tex_expandafter:D + \fp_extended_normalise_ii_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int - \exp_after:wN \fp_trig_normalise_aux_ii: + \tex_expandafter:D \fp_extended_normalise_aux_ii: \tex_fi:D } \cs_new_protected_nopar:Npn - \fp_trig_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { + \fp_extended_normalise_ii_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { \tex_ifnum:D \l_fp_input_a_integer_int = \c_zero \l_fp_input_a_decimal_int #1#2#3#4#5#6#7#8 \scan_stop: \tex_else:D @@ -1532,7 +1597,64 @@ \l_fp_input_a_extended_int \l_fp_tmp_tl \scan_stop: \tex_advance:D \l_fp_input_a_exponent_int \c_one } -\cs_new_protected_nopar:Npn \fp_trig_normalise_aux_iii: { +\cs_new_protected_nopar:Npn \fp_extended_normalise_output: { + \tex_ifnum:D \l_fp_output_integer_int > \c_nine + \tex_advance:D \l_fp_output_integer_int \c_one_thousand_million + \tex_expandafter:D \use_i:nn \tex_expandafter:D + \fp_extended_normalise_output_aux_i:NNNNNNNNN + \int_use:N \l_fp_output_integer_int + \tex_expandafter:D \fp_extended_normalise_output: + \tex_fi:D +} +\cs_new_protected_nopar:Npn + \fp_extended_normalise_output_aux_i:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { + \l_fp_output_integer_int #1#2#3#4#5#6#7#8 \scan_stop: + \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million + \tl_set:Nx \l_fp_tmp_tl + { + #9 + \tex_expandafter:D \use_none:n + \int_use:N \l_fp_output_decimal_int + } + \tex_expandafter:D \fp_extended_normalise_output_aux_ii:NNNNNNNNN + \l_fp_tmp_tl +} +\cs_new_protected_nopar:Npn + \fp_extended_normalise_output_aux_ii:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { + \l_fp_output_decimal_int #1#2#3#4#5#6#7#8#9 \scan_stop: + \fp_extended_normalise_output_aux:N +} +\cs_new_protected_nopar:Npn \fp_extended_normalise_output_aux:N #1 { + \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million + \tex_divide:D \l_fp_output_extended_int \c_ten + \tl_set:Nx \l_fp_tmp_tl + { + #1 + \tex_expandafter:D \use_none:n + \int_use:N \l_fp_output_extended_int + } + \l_fp_output_extended_int \l_fp_tmp_tl \scan_stop: + \tex_advance:D \l_fp_output_exponent_int \c_one +} +\cs_new_protected_nopar:Npn \fp_trig_normalise: { + \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten + \l_fp_input_a_extended_int \c_zero + \fp_extended_normalise: + \fp_trig_normalise_aux: + \tex_ifnum:D \l_fp_input_a_integer_int < \c_zero + \l_fp_input_a_sign_int -\l_fp_input_a_sign_int + \l_fp_input_a_integer_int -\l_fp_input_a_integer_int + \tex_fi:D + \tex_expandafter:D \fp_trig_octant: + \tex_else:D + \l_fp_input_a_sign_int \c_one + \l_fp_output_integer_int \c_zero + \l_fp_output_decimal_int \c_zero + \l_fp_output_exponent_int \c_zero + \tex_expandafter:D \fp_trig_overflow_msg: + \tex_fi:D +} +\cs_new_protected_nopar:Npn \fp_trig_normalise_aux: { \tex_ifnum:D \l_fp_input_a_integer_int > \c_three \fp_sub:NNNNNNNNN \l_fp_input_a_integer_int \l_fp_input_a_decimal_int @@ -1540,7 +1662,7 @@ \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int - \exp_after:wN \fp_trig_normalise_aux_iii: + \tex_expandafter:D \fp_trig_normalise_aux: \tex_else:D \tex_ifnum:D \l_fp_input_a_integer_int > \c_two \tex_ifnum:D \l_fp_input_a_decimal_int > \c_fp_pi_decimal_int @@ -1550,9 +1672,9 @@ \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int - \exp_after:wN \exp_after:wN \exp_after:wN - \exp_after:wN \exp_after:wN \exp_after:wN - \exp_after:wN \fp_trig_normalise_aux_iii: + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \fp_trig_normalise_aux: \tex_fi:D \tex_fi:D \tex_fi:D @@ -1583,7 +1705,7 @@ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \tex_advance:D \l_fp_trig_octant_int \c_one - \exp_after:wN \fp_trig_octant_aux: + \tex_expandafter:D \fp_trig_octant_aux: \tex_else:D \tex_ifnum:D \l_fp_input_a_decimal_int > \c_fp_pi_by_four_decimal_int @@ -1595,7 +1717,7 @@ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_extended_int \tex_advance:D \l_fp_trig_octant_int \c_one - \exp_after:wN \exp_after:wN \exp_after:wN + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_trig_octant_aux: \tex_fi:D \tex_fi:D @@ -1616,7 +1738,7 @@ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int - \tl_set:Nx \l_fp_trig_arg_tl + \tl_set:Nx \l_fp_arg_tl { \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero - @@ -1625,7 +1747,7 @@ \tex_fi:D \int_use:N \l_fp_input_a_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_input_a_decimal_int + \c_one_thousand_million e @@ -1635,21 +1757,21 @@ \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: - #1 \exp_not:N #2 { \l_fp_trig_arg_tl } + #1 \exp_not:N #2 { \l_fp_arg_tl } } \tex_else:D \etex_ifcsname:D - c_fp_sin ( \l_fp_trig_arg_tl ) _tl + c_fp_sin ( \l_fp_arg_tl ) _fp \tex_endcsname:D \tex_else:D - \exp_after:wN \exp_after:wN \exp_after:wN + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_sin_aux_i: \tex_fi:D \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 - { \use:c { c_fp_sin ( \l_fp_trig_arg_tl ) _tl } } + { \use:c { c_fp_sin ( \l_fp_arg_tl ) _fp } } } \tex_fi:D \fp_tmp:w @@ -1669,8 +1791,8 @@ \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_exponent_int - \tl_new:c { c_fp_sin ( \l_fp_trig_arg_tl ) _tl } - \tl_gset:cx { c_fp_sin ( \l_fp_trig_arg_tl ) _tl } + \tl_new:c { c_fp_sin ( \l_fp_arg_tl ) _fp } + \tl_gset:cx { c_fp_sin ( \l_fp_arg_tl ) _fp } { \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero + @@ -1679,7 +1801,7 @@ \tex_fi:D \int_use:N \l_fp_output_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million \scan_stop: @@ -1690,13 +1812,13 @@ \cs_new_protected_nopar:Npn \fp_sin_aux_ii: { \tex_ifcase:D \l_fp_trig_octant_int \tex_or:D - \exp_after:wN \fp_trig_calc_sin: + \tex_expandafter:D \fp_trig_calc_sin: \tex_or:D - \exp_after:wN \fp_trig_calc_cos: + \tex_expandafter:D \fp_trig_calc_cos: \tex_or:D - \exp_after:wN \fp_trig_calc_cos: + \tex_expandafter:D \fp_trig_calc_cos: \tex_or:D - \exp_after:wN \fp_trig_calc_sin: + \tex_expandafter:D \fp_trig_calc_sin: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_cos:Nn { @@ -1715,7 +1837,7 @@ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int - \tl_set:Nx \l_fp_trig_arg_tl + \tl_set:Nx \l_fp_arg_tl { \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero - @@ -1724,21 +1846,21 @@ \tex_fi:D \int_use:N \l_fp_input_a_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_input_a_decimal_int + \c_one_thousand_million e \int_use:N \l_fp_input_a_exponent_int } - \etex_ifcsname:D c_fp_cos ( \l_fp_trig_arg_tl ) _tl \tex_endcsname:D + \etex_ifcsname:D c_fp_cos ( \l_fp_arg_tl ) _fp \tex_endcsname:D \tex_else:D - \exp_after:wN \fp_cos_aux_i: + \tex_expandafter:D \fp_cos_aux_i: \tex_fi:D \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 - { \use:c { c_fp_cos ( \l_fp_trig_arg_tl ) _tl } } + { \use:c { c_fp_cos ( \l_fp_arg_tl ) _fp } } } \fp_tmp:w } @@ -1757,8 +1879,8 @@ \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_exponent_int - \tl_new:c { c_fp_cos ( \l_fp_trig_arg_tl ) _tl } - \tl_gset:cx { c_fp_cos ( \l_fp_trig_arg_tl ) _tl } + \tl_new:c { c_fp_cos ( \l_fp_arg_tl ) _fp } + \tl_gset:cx { c_fp_cos ( \l_fp_arg_tl ) _fp } { \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero + @@ -1767,7 +1889,7 @@ \tex_fi:D \int_use:N \l_fp_output_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million \scan_stop: @@ -1778,13 +1900,13 @@ \cs_new_protected_nopar:Npn \fp_cos_aux_ii: { \tex_ifcase:D \l_fp_trig_octant_int \tex_or:D - \exp_after:wN \fp_trig_calc_cos: + \tex_expandafter:D \fp_trig_calc_cos: \tex_or:D - \exp_after:wN \fp_trig_calc_sin: + \tex_expandafter:D \fp_trig_calc_sin: \tex_or:D - \exp_after:wN \fp_trig_calc_sin: + \tex_expandafter:D \fp_trig_calc_sin: \tex_or:D - \exp_after:wN \fp_trig_calc_cos: + \tex_expandafter:D \fp_trig_calc_cos: \tex_fi:D \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero \tex_ifnum:D \l_fp_trig_octant_int > \c_two @@ -1829,7 +1951,7 @@ \tex_fi:D \tex_advance:D \l_fp_output_extended_int -\l_fp_trig_extended_int \tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int - \exp_after:wN \fp_trig_calc_aux: + \tex_expandafter:D \fp_trig_calc_Taylor: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_trig_calc_sin: { @@ -1843,10 +1965,10 @@ \l_fp_trig_decimal_int \l_fp_input_a_decimal_int \l_fp_trig_extended_int \l_fp_input_a_extended_int \l_fp_count_int \c_two - \exp_after:wN \fp_trig_calc_aux: + \tex_expandafter:D \fp_trig_calc_Taylor: \tex_fi:D } -\cs_new_protected_nopar:Npn \fp_trig_calc_aux: { +\cs_new_protected_nopar:Npn \fp_trig_calc_Taylor: { \l_fp_trig_sign_int -\l_fp_trig_sign_int \fp_mul:NNNNNN \l_fp_trig_decimal_int \l_fp_trig_extended_int @@ -1896,7 +2018,7 @@ \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million \tex_fi:D \tex_fi:D - \exp_after:wN \fp_trig_calc_aux: + \tex_expandafter:D \fp_trig_calc_Taylor: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_tan:Nn { @@ -1915,7 +2037,7 @@ \l_fp_input_a_integer_int \l_fp_input_a_decimal_int \l_fp_input_a_exponent_int - \tl_set:Nx \l_fp_trig_arg_tl + \tl_set:Nx \l_fp_arg_tl { \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero - @@ -1924,7 +2046,7 @@ \tex_fi:D \int_use:N \l_fp_input_a_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_input_a_decimal_int + \c_one_thousand_million e @@ -1934,32 +2056,32 @@ \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: - #1 \exp_not:N #2 { \l_fp_trig_arg_tl } + #1 \exp_not:N #2 { \l_fp_arg_tl } } \tex_else:D \etex_ifcsname:D - c_fp_tan ( \l_fp_trig_arg_tl ) _tl + c_fp_tan ( \l_fp_arg_tl ) _fp \tex_endcsname:D \tex_else:D - \exp_after:wN \exp_after:wN \exp_after:wN + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_tan_aux_i: \tex_fi:D \cs_set_protected_nopar:Npx \fp_tmp:w { \group_end: #1 \exp_not:N #2 - { \use:c { c_fp_tan ( \l_fp_trig_arg_tl ) _tl } } + { \use:c { c_fp_tan ( \l_fp_arg_tl ) _fp } } } \tex_fi:D \fp_tmp:w } \cs_new_protected_nopar:Npn \fp_tan_aux_i: { \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten - \exp_after:wN \fp_tan_aux_ii: + \tex_expandafter:D \fp_tan_aux_ii: \tex_else:D - \cs_new_eq:cN { c_fp_tan ( \l_fp_trig_arg_tl ) _tl } + \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp } \c_zero_fp - \exp_after:wN \fp_trig_overflow_msg: + \tex_expandafter:D \fp_trig_overflow_msg: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_tan_aux_ii: { @@ -1967,14 +2089,14 @@ \fp_cos_aux_ii: \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero \tex_ifnum:D \l_fp_input_a_integer_int = \c_zero - \cs_new_eq:cN { c_fp_tan ( \l_fp_trig_arg_tl ) _tl } + \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp } \c_undefined_fp \tex_else:D - \exp_after:wN \exp_after:wN \exp_after:wN + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_tan_aux_iii: \tex_fi:D \tex_else:D - \exp_after:wN \fp_tan_aux_iii: + \tex_expandafter:D \fp_tan_aux_iii: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_tan_aux_iii: { @@ -1997,14 +2119,14 @@ \l_fp_input_a_exponent_int \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero \tex_ifnum:D \l_fp_input_a_integer_int = \c_zero - \cs_new_eq:cN { c_fp_tan ( \l_fp_trig_arg_tl ) _tl } + \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp } \c_zero_fp \tex_else:D - \exp_after:wN \exp_after:wN \exp_after:wN + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D \fp_tan_aux_iv: \tex_fi:D \tex_else:D - \exp_after:wN \fp_tan_aux_iv: + \tex_expandafter:D \fp_tan_aux_iv: \tex_fi:D } \cs_new_protected_nopar:Npn \fp_tan_aux_iv: { @@ -2027,8 +2149,563 @@ \l_fp_output_integer_int \l_fp_output_decimal_int \l_fp_output_exponent_int - \tl_new:c { c_fp_tan ( \l_fp_trig_arg_tl ) _tl } - \tl_gset:cx { c_fp_tan ( \l_fp_trig_arg_tl ) _tl } + \tl_new:c { c_fp_tan ( \l_fp_arg_tl ) _fp } + \tl_gset:cx { c_fp_tan ( \l_fp_arg_tl ) _fp } + { + \tex_ifnum:D \l_fp_output_sign_int > \c_zero + + + \tex_else:D + - + \tex_fi:D + \int_use:N \l_fp_output_integer_int + . + \tex_expandafter:D \use_none:n + \tex_number:D \etex_numexpr:D + \l_fp_output_decimal_int + \c_one_thousand_million + \scan_stop: + e + \int_use:N \l_fp_output_exponent_int + } +} +\tl_new:c { c_fp_exp_1_tl } +\tl_set:cn { c_fp_exp_1_tl } + { { 2 } { 718281828 } { 459045235 } { 0 } } +\tl_new:c { c_fp_exp_2_tl } +\tl_set:cn { c_fp_exp_2_tl } + { { 7 } { 389056098 } { 930650227 } { 0 } } +\tl_new:c { c_fp_exp_3_tl } +\tl_set:cn { c_fp_exp_3_tl } + { { 2 } { 008553692 } { 318766774 } { 1 } } +\tl_new:c { c_fp_exp_4_tl } +\tl_set:cn { c_fp_exp_4_tl } + { { 5 } { 459815003 } { 314423908 } { 1 } } +\tl_new:c { c_fp_exp_5_tl } +\tl_set:cn { c_fp_exp_5_tl } + { { 1 } { 484131591 } { 025766034 } { 2 } } +\tl_new:c { c_fp_exp_6_tl } +\tl_set:cn { c_fp_exp_6_tl } + { { 4 } { 034287934 } { 927351226 } { 2 } } +\tl_new:c { c_fp_exp_7_tl } +\tl_set:cn { c_fp_exp_7_tl } + { { 1 } { 096633158 } { 428458599 } { 3 } } +\tl_new:c { c_fp_exp_8_tl } +\tl_set:cn { c_fp_exp_8_tl } + { { 2 } { 980957987 } { 041728275 } { 3 } } +\tl_new:c { c_fp_exp_9_tl } +\tl_set:cn { c_fp_exp_9_tl } + { { 8 } { 103083927 } { 575384008 } { 3 } } +\tl_new:c { c_fp_exp_10_tl } +\tl_set:cn { c_fp_exp_10_tl } + { { 2 } { 202646579 } { 480671652 } { 4 } } +\tl_new:c { c_fp_exp_20_tl } +\tl_set:cn { c_fp_exp_20_tl } + { { 4 } { 851651954 } { 097902280 } { 8 } } +\tl_new:c { c_fp_exp_30_tl } +\tl_set:cn { c_fp_exp_30_tl } + { { 1 } { 068647458 } { 152446215 } { 13 } } +\tl_new:c { c_fp_exp_40_tl } +\tl_set:cn { c_fp_exp_40_tl } + { { 2 } { 353852668 } { 370199854 } { 17 } } +\tl_new:c { c_fp_exp_50_tl } +\tl_set:cn { c_fp_exp_50_tl } + { { 5 } { 184705528 } { 587072464 } { 21 } } +\tl_new:c { c_fp_exp_60_tl } +\tl_set:cn { c_fp_exp_60_tl } + { { 1 } { 142007389 } { 815684284 } { 26 } } +\tl_new:c { c_fp_exp_70_tl } +\tl_set:cn { c_fp_exp_70_tl } + { { 2 } { 515438670 } { 919167006 } { 30 } } +\tl_new:c { c_fp_exp_80_tl } +\tl_set:cn { c_fp_exp_80_tl } + { { 5 } { 540622384 } { 393510053 } { 34 } } +\tl_new:c { c_fp_exp_90_tl } +\tl_set:cn { c_fp_exp_90_tl } + { { 1 } { 220403294 } { 317840802 } { 39 } } +\tl_new:c { c_fp_exp_100_tl } +\tl_set:cn { c_fp_exp_100_tl } + { { 2 } { 688117141 } { 816135448 } { 43 } } +\tl_new:c { c_fp_exp_200_tl } +\tl_set:cn { c_fp_exp_200_tl } + { { 7 } { 225973768 } { 125749258 } { 86 } } +\tl_new:c { c_fp_exp_-1_tl } +\tl_set:cn { c_fp_exp_-1_tl } + { { 3 } { 678794411 } { 71442322 } { -1 } } +\tl_new:c { c_fp_exp_-2_tl } +\tl_set:cn { c_fp_exp_-2_tl } + { { 1 } { 353352832 } { 366132692 } { -1 } } +\tl_new:c { c_fp_exp_-3_tl } +\tl_set:cn { c_fp_exp_-3_tl } + { { 4 } { 978706836 } { 786394298 } { -2 } } +\tl_new:c { c_fp_exp_-4_tl } +\tl_set:cn { c_fp_exp_-4_tl } + { { 1 } { 831563888 } { 873418029 } { -2 } } +\tl_new:c { c_fp_exp_-5_tl } +\tl_set:cn { c_fp_exp_-5_tl } + { { 6 } { 737946999 } { 085467097 } { -3 } } +\tl_new:c { c_fp_exp_-6_tl } +\tl_set:cn { c_fp_exp_-6_tl } + { { 2 } { 478752176 } { 666358423 } { -3 } } +\tl_new:c { c_fp_exp_-7_tl } +\tl_set:cn { c_fp_exp_-7_tl } + { { 9 } { 118819655 } { 545162080 } { -4 } } +\tl_new:c { c_fp_exp_-8_tl } +\tl_set:cn { c_fp_exp_-8_tl } + { { 3 } { 354626279 } { 025118388 } { -4 } } +\tl_new:c { c_fp_exp_-9_tl } +\tl_set:cn { c_fp_exp_-9_tl } + { { 1 } { 234098040 } { 866795495 } { -4 } } +\tl_new:c { c_fp_exp_-10_tl } +\tl_set:cn { c_fp_exp_-10_tl } + { { 4 } { 539992976 } { 248451536 } { -5 } } +\tl_new:c { c_fp_exp_-20_tl } +\tl_set:cn { c_fp_exp_-20_tl } + { { 2 } { 061153622 } { 438557828 } { -9 } } +\tl_new:c { c_fp_exp_-30_tl } +\tl_set:cn { c_fp_exp_-30_tl } + { { 9 } { 357622968 } { 840174605 } { -14 } } +\tl_new:c { c_fp_exp_-40_tl } +\tl_set:cn { c_fp_exp_-40_tl } + { { 4 } { 248354255 } { 291588995 } { -18 } } +\tl_new:c { c_fp_exp_-50_tl } +\tl_set:cn { c_fp_exp_-50_tl } + { { 1 } { 928749847 } { 963917783 } { -22 } } +\tl_new:c { c_fp_exp_-60_tl } +\tl_set:cn { c_fp_exp_-60_tl } + { { 8 } { 756510762 } { 696520338 } { -27 } } +\tl_new:c { c_fp_exp_-70_tl } +\tl_set:cn { c_fp_exp_-70_tl } + { { 3 } { 975449735 } { 908646808 } { -31 } } +\tl_new:c { c_fp_exp_-80_tl } +\tl_set:cn { c_fp_exp_-80_tl } + { { 1 } { 804851387 } { 845415172 } { -35 } } +\tl_new:c { c_fp_exp_-90_tl } +\tl_set:cn { c_fp_exp_-90_tl } + { { 8 } { 194012623 } { 990515430 } { -40 } } +\tl_new:c { c_fp_exp_-100_tl } +\tl_set:cn { c_fp_exp_-100_tl } + { { 3 } { 720075976 } { 020835963 } { -44 } } +\tl_new:c { c_fp_exp_-200_tl } +\tl_set:cn { c_fp_exp_-200_tl } + { { 1 } { 383896526 } { 736737530 } { -87 } } +\cs_new_protected_nopar:Npn \fp_exp:Nn { + \fp_exp_aux:NNn \tl_set:Nn +} +\cs_new_protected_nopar:Npn \fp_gexp:Nn { + \fp_exp_aux:NNn \tl_gset:Nn +} +\cs_generate_variant:Nn \fp_exp:Nn { c } +\cs_generate_variant:Nn \fp_gexp:Nn { c } +\cs_new_protected_nopar:Npn \fp_exp_aux:NNn #1#2#3 { + \group_begin: + \fp_split:Nn a {#3} + \fp_standardise:NNNN + \l_fp_input_a_sign_int + \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int + \l_fp_input_a_exponent_int + \l_fp_input_a_extended_int \c_zero + \tl_set:Nx \l_fp_arg_tl + { + \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero + - + \tex_else:D + + + \tex_fi:D + \int_use:N \l_fp_input_a_integer_int + . + \tex_expandafter:D \use_none:n + \tex_number:D \etex_numexpr:D + \l_fp_input_a_decimal_int + \c_one_thousand_million + e + \int_use:N \l_fp_input_a_exponent_int + } + \etex_ifcsname:D c_fp_exp ( \l_fp_arg_tl ) _fp \tex_endcsname:D + \tex_else:D + \tex_expandafter:D \fp_exp_internal: + \tex_fi:D + \cs_set_protected_nopar:Npx \fp_tmp:w + { + \group_end: + #1 \exp_not:N #2 + { + \etex_ifcsname:D c_fp_exp ( \l_fp_arg_tl ) _fp + \tex_endcsname:D + \use:c { c_fp_exp ( \l_fp_arg_tl ) _fp } + \tex_else:D + \c_zero_fp + \tex_fi:D + } + } + \fp_tmp:w +} +\cs_new_protected_nopar:Npn \fp_exp_internal: { + \tex_ifnum:D \l_fp_input_a_exponent_int < \c_three + \fp_extended_normalise: + \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero + \tex_ifnum:D \l_fp_input_a_integer_int < 230 \scan_stop: + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \fp_exp_aux: + \tex_else:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \fp_exp_overflow_msg: + \tex_fi:D + \tex_else:D + \tex_ifnum:D \l_fp_input_a_integer_int < 230 \scan_stop: + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \fp_exp_aux: + \tex_else:D + \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp } + { \c_zero_fp } + \tex_fi:D + \tex_fi:D + \tex_else:D + \tex_expandafter:D \fp_exp_overflow_msg: + \tex_fi:D +} +\cs_new_protected_nopar:Npn \fp_exp_aux: { + \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero + \tex_expandafter:D \fp_exp_integer: + \tex_else:D + \l_fp_output_integer_int \c_one + \l_fp_output_decimal_int \c_zero + \l_fp_output_extended_int \c_zero + \l_fp_output_exponent_int \c_zero + \tex_expandafter:D \fp_exp_decimal: + \tex_fi:D +} +\cs_new_protected_nopar:Npn \fp_exp_integer: { + \tex_ifnum:D \l_fp_input_a_integer_int < \c_one_hundred + \l_fp_exp_integer_int \c_one + \l_fp_exp_decimal_int \c_zero + \l_fp_exp_extended_int \c_zero + \l_fp_exp_exponent_int \c_zero + \tex_expandafter:D \fp_exp_integer_tens: + \tex_else:D + \tl_set:Nx \l_fp_tmp_tl + { + \tex_expandafter:D \use_i:nnn + \int_use:N \l_fp_input_a_integer_int + } + \l_fp_input_a_integer_int + \etex_numexpr:D + \l_fp_input_a_integer_int - \l_fp_tmp_tl 00 + \scan_stop: + \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero + \tex_ifnum:D \l_fp_output_integer_int > 200 \scan_stop: + \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp } + { \c_zero_fp } + \tex_else:D + \fp_exp_integer_const:n { - \l_fp_tmp_tl 00 } + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \fp_exp_integer_tens: + \tex_fi:D + \tex_else:D + \fp_exp_integer_const:n { \l_fp_tmp_tl 00 } + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \fp_exp_integer_tens: + \tex_fi:D + \tex_fi:D +} +\cs_new_protected_nopar:Npn \fp_exp_integer_tens: { + \l_fp_output_integer_int \l_fp_exp_integer_int + \l_fp_output_decimal_int \l_fp_exp_decimal_int + \l_fp_output_extended_int \l_fp_exp_extended_int + \l_fp_output_exponent_int \l_fp_exp_exponent_int + \tex_ifnum:D \l_fp_input_a_integer_int > \c_nine + \tl_set:Nx \l_fp_tmp_tl + { + \tex_expandafter:D \use_i:nn + \int_use:N \l_fp_input_a_integer_int + } + \l_fp_input_a_integer_int + \etex_numexpr:D + \l_fp_input_a_integer_int - \l_fp_tmp_tl 0 + \scan_stop: + \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero + \fp_exp_integer_const:n { \l_fp_tmp_tl 0 } + \tex_else:D + \fp_exp_integer_const:n { - \l_fp_tmp_tl 0 } + \tex_fi:D + \fp_mul:NNNNNNNNN + \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int + \l_fp_output_integer_int \l_fp_output_decimal_int + \l_fp_output_extended_int + \l_fp_output_integer_int \l_fp_output_decimal_int + \l_fp_output_extended_int + \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int + \fp_extended_normalise_output: + \tex_fi:D + \fp_exp_integer_units: +} +\cs_new_protected_nopar:Npn \fp_exp_integer_units: { + \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero + \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero + \fp_exp_integer_const:n { \int_use:N \l_fp_input_a_integer_int } + \tex_else:D + \fp_exp_integer_const:n + { - \int_use:N \l_fp_input_a_integer_int } + \tex_fi:D + \fp_mul:NNNNNNNNN + \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int + \l_fp_output_integer_int \l_fp_output_decimal_int + \l_fp_output_extended_int + \l_fp_output_integer_int \l_fp_output_decimal_int + \l_fp_output_extended_int + \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int + \fp_extended_normalise_output: + \tex_fi:D + \fp_exp_decimal: +} +\cs_new_protected_nopar:Npn \fp_exp_integer_const:n #1 { + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \fp_exp_integer_const:nnnn + \tex_csname:D c_fp_exp_ #1 _tl \tex_endcsname:D +} +\cs_new_protected_nopar:Npn \fp_exp_integer_const:nnnn #1#2#3#4 { + \l_fp_exp_integer_int #1 \scan_stop: + \l_fp_exp_decimal_int #2 \scan_stop: + \l_fp_exp_extended_int #3 \scan_stop: + \l_fp_exp_exponent_int #4 \scan_stop: +} +\cs_new_protected_nopar:Npn \fp_exp_decimal: { + \tex_ifnum:D \l_fp_input_a_decimal_int > \c_zero + \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero + \l_fp_exp_integer_int \c_one + \l_fp_exp_decimal_int \l_fp_input_a_decimal_int + \l_fp_exp_extended_int \l_fp_input_a_extended_int + \tex_else:D + \l_fp_exp_integer_int \c_zero + \tex_ifnum:D \l_fp_exp_extended_int = \c_zero + \l_fp_exp_decimal_int + \etex_numexpr:D + \c_one_thousand_million - \l_fp_input_a_decimal_int + \scan_stop: + \l_fp_exp_extended_int \c_zero + \tex_else:D + \l_fp_exp_decimal_int + \etex_numexpr:D + 999999999 - \l_fp_input_a_decimal_int + \scan_stop: + \l_fp_exp_extended_int + \etex_numexpr:D + \c_one_thousand_million - \l_fp_input_a_extended_int + \scan_stop: + \tex_fi:D + \tex_fi:D + \l_fp_input_b_sign_int \l_fp_input_a_sign_int + \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int + \l_fp_input_b_extended_int \l_fp_input_a_extended_int + \l_fp_count_int \c_one + \fp_exp_Taylor: + \fp_mul:NNNNNNNNN + \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int + \l_fp_output_integer_int \l_fp_output_decimal_int + \l_fp_output_extended_int + \l_fp_output_integer_int \l_fp_output_decimal_int + \l_fp_output_extended_int + \tex_fi:D + \tex_ifnum:D \l_fp_output_extended_int < \c_five_hundred_million + \tex_else:D + \tex_advance:D \l_fp_output_decimal_int \c_one + \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million + \tex_else:D + \l_fp_output_decimal_int \c_zero + \tex_advance:D \l_fp_output_integer_int \c_one + \tex_fi:D + \tex_fi:D + \fp_standardise:NNNN + \l_fp_output_sign_int + \l_fp_output_integer_int + \l_fp_output_decimal_int + \l_fp_output_exponent_int + \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp } + { + + + \int_use:N \l_fp_output_integer_int + . + \tex_expandafter:D \use_none:n + \tex_number:D \etex_numexpr:D + \l_fp_output_decimal_int + \c_one_thousand_million + \scan_stop: + e + \int_use:N \l_fp_output_exponent_int + } +} +\cs_new_protected_nopar:Npn \fp_exp_Taylor: { + \tex_advance:D \l_fp_count_int \c_one + \tex_multiply:D \l_fp_input_b_sign_int \l_fp_input_a_sign_int + \fp_mul:NNNNNN + \l_fp_input_a_decimal_int \l_fp_input_a_extended_int + \l_fp_input_b_decimal_int \l_fp_input_b_extended_int + \l_fp_input_b_decimal_int \l_fp_input_b_extended_int + \fp_div_integer:NNNNN + \l_fp_input_b_decimal_int \l_fp_input_b_extended_int + \l_fp_count_int + \l_fp_input_b_decimal_int \l_fp_input_b_extended_int + \tex_ifnum:D + \etex_numexpr:D + \l_fp_input_b_decimal_int + \l_fp_input_b_extended_int + > \c_zero + \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero + \tex_advance:D \l_fp_exp_decimal_int \l_fp_input_b_decimal_int + \tex_advance:D \l_fp_exp_extended_int + \l_fp_input_b_extended_int + \tex_ifnum:D \l_fp_exp_extended_int < \c_one_thousand_million + \tex_else:D + \tex_advance:D \l_fp_exp_decimal_int \c_one + \tex_advance:D \l_fp_exp_extended_int + -\c_one_thousand_million + \tex_fi:D + \tex_ifnum:D \l_fp_exp_decimal_int < \c_one_thousand_million + \tex_else:D + \tex_advance:D \l_fp_exp_integer_int \c_one + \tex_advance:D \l_fp_exp_decimal_int + -\c_one_thousand_million + \tex_fi:D + \tex_else:D + \tex_advance:D \l_fp_exp_decimal_int -\l_fp_input_b_decimal_int + \tex_advance:D \l_fp_exp_extended_int + -\l_fp_input_a_extended_int + \tex_ifnum:D \l_fp_exp_extended_int < \c_zero + \tex_advance:D \l_fp_exp_decimal_int \c_minus_one + \tex_advance:D \l_fp_exp_extended_int \c_one_thousand_million + \tex_fi:D + \tex_ifnum:D \l_fp_exp_decimal_int < \c_zero + \tex_advance:D \l_fp_exp_integer_int \c_minus_one + \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million + \tex_fi:D + \tex_fi:D + \tex_expandafter:D \fp_exp_Taylor: + \tex_fi:D +} +\cs_new_protected_nopar:Npn \fp_exp_const:Nx #1#2 { + \tl_new:N #1 + \tl_gset:Nx #1 {#2} +} +\cs_generate_variant:Nn \fp_exp_const:Nx { c } +\tl_new:c { c_fp_ln_10_1_tl } +\tl_set:cn { c_fp_ln_10_1_tl } + { { 2 } { 302585092 } { 994045684 } { 0 } } +\tl_new:c { c_fp_ln_10_2_tl } +\tl_set:cn { c_fp_ln_10_2_tl } + { { 4 } { 605170185 } { 988091368 } { 0 } } +\tl_new:c { c_fp_ln_10_3_tl } +\tl_set:cn { c_fp_ln_10_3_tl } + { { 6 } { 907755278 } { 982137052 } { 0 } } +\tl_new:c { c_fp_ln_10_4_tl } +\tl_set:cn { c_fp_ln_10_4_tl } + { { 9 } { 210340371 } { 976182736 } { 0 } } +\tl_new:c { c_fp_ln_10_5_tl } +\tl_set:cn { c_fp_ln_10_5_tl } + { { 1 } { 151292546 } { 497022842 } { 1 } } +\tl_new:c { c_fp_ln_10_6_tl } +\tl_set:cn { c_fp_ln_10_6_tl } + { { 1 } { 381551055 } { 796427410 } { 1 } } +\tl_new:c { c_fp_ln_10_7_tl } +\tl_set:cn { c_fp_ln_10_7_tl } + { { 1 } { 611809565 } { 095831979 } { 1 } } +\tl_new:c { c_fp_ln_10_8_tl } +\tl_set:cn { c_fp_ln_10_8_tl } + { { 1 } { 842068074 } { 395226547 } { 1 } } +\tl_new:c { c_fp_ln_10_9_tl } +\tl_set:cn { c_fp_ln_10_9_tl } + { { 2 } { 072326583 } { 694641116 } { 1 } } +\tl_new:c { c_fp_ln_2_1_tl } +\tl_set:cn { c_fp_ln_2_1_tl } + { { 0 } { 693147180 } { 559945309 } { 0 } } +\tl_new:c { c_fp_ln_2_2_tl } +\tl_set:cn { c_fp_ln_2_2_tl } + { { 1 } { 386294361 } { 119890618 } { 0 } } +\tl_new:c { c_fp_ln_2_3_tl } +\tl_set:cn { c_fp_ln_2_3_tl } + { { 2 } { 079441541 } { 679835928 } { 0 } } +\cs_new_protected_nopar:Npn \fp_ln:Nn { + \fp_ln_aux:NNn \tl_set:Nn +} +\cs_new_protected_nopar:Npn \fp_gln:Nn { + \fp_ln_aux:NNn \tl_gset:Nn +} +\cs_generate_variant:Nn \fp_ln:Nn { c } +\cs_generate_variant:Nn \fp_gln:Nn { c } +\cs_new_protected_nopar:Npn \fp_ln_aux:NNn #1#2#3 { + \group_begin: + \fp_split:Nn a {#3} + \fp_standardise:NNNN + \l_fp_input_a_sign_int + \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int + \l_fp_input_a_exponent_int + \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero + \tex_ifnum:D + \etex_numexpr:D + \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int + > \c_zero + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \fp_ln_aux: + \tex_else:D + \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 + { + \group_end: + ##1 \exp_not:N ##2 { \c_zero_fp } + } + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \fp_ln_error_msg: + \tex_fi:D + \tex_else:D + \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 + { + \group_end: + ##1 \exp_not:N ##2 { \c_zero_fp } + } + \tex_expandafter:D \fp_ln_error_msg: + \tex_fi:D + \fp_tmp:w #1 #2 +} +\cs_new_protected_nopar:Npn \fp_ln_aux: { + \tl_set:Nx \l_fp_arg_tl + { + + + \int_use:N \l_fp_input_a_integer_int + . + \tex_expandafter:D \use_none:n + \tex_number:D \etex_numexpr:D + \l_fp_input_a_decimal_int + \c_one_thousand_million + e + \int_use:N \l_fp_input_a_exponent_int + } + \etex_ifcsname:D c_fp_ln ( \l_fp_arg_tl ) _fp \tex_endcsname:D + \tex_else:D + \tex_expandafter:D \fp_ln_exponent: + \tex_fi:D + \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 + { + \group_end: + ##1 \exp_not:N ##2 + { \use:c { c_fp_ln ( \l_fp_arg_tl ) _fp } } + } +} +\cs_new_protected_nopar:Npn \fp_ln_exponent: { + \fp_ln_internal: + \tex_ifnum:D \l_fp_output_extended_int < \c_five_hundred_million + \tex_else:D + \tex_advance:D \l_fp_output_decimal_int \c_one + \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million + \tex_else:D + \l_fp_output_decimal_int \c_zero + \tex_advance:D \l_fp_output_integer_int \c_one + \tex_fi:D + \tex_fi:D + \fp_standardise:NNNN + \l_fp_output_sign_int + \l_fp_output_integer_int + \l_fp_output_decimal_int + \l_fp_output_exponent_int + \tl_new:c { c_fp_ln ( \l_fp_arg_tl ) _fp } + \tl_gset:cx { c_fp_ln ( \l_fp_arg_tl ) _fp } { \tex_ifnum:D \l_fp_output_sign_int > \c_zero + @@ -2037,7 +2714,7 @@ \tex_fi:D \int_use:N \l_fp_output_integer_int . - \exp_after:wN \use_none:n + \tex_expandafter:D \use_none:n \tex_number:D \etex_numexpr:D \l_fp_output_decimal_int + \c_one_thousand_million \scan_stop: @@ -2045,21 +2722,445 @@ \int_use:N \l_fp_output_exponent_int } } -\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF } { +\cs_new_protected_nopar:Npn \fp_ln_internal: { + \tex_ifnum:D \l_fp_input_a_exponent_int < \c_zero + \l_fp_input_a_exponent_int -\l_fp_input_a_exponent_int + \l_fp_output_sign_int \c_minus_one + \tex_else:D + \l_fp_output_sign_int \c_one + \tex_fi:D + \tex_ifnum:D \l_fp_input_a_exponent_int > \c_nine + \tl_set:Nx \l_fp_tmp_tl + { + \tex_expandafter:D \use_i:nn + \int_use:N \l_fp_input_a_exponent_int + } + \l_fp_input_a_exponent_int + \etex_numexpr:D + \l_fp_input_a_exponent_int - \l_fp_tmp_tl 0 + \scan_stop: + \fp_ln_const:nn { 10 } { \l_fp_tmp_tl } + \tex_advance:D \l_fp_exp_exponent_int \c_one + \l_fp_output_integer_int \l_fp_exp_integer_int + \l_fp_output_decimal_int \l_fp_exp_decimal_int + \l_fp_output_extended_int \l_fp_exp_extended_int + \l_fp_output_exponent_int \l_fp_exp_exponent_int + \tex_else:D + \l_fp_output_integer_int \c_zero + \l_fp_output_decimal_int \c_zero + \l_fp_output_extended_int \c_zero + \l_fp_output_exponent_int \c_zero + \tex_fi:D + \fp_ln_exponent_units: +} +\cs_new_protected_nopar:Npn \fp_ln_exponent_units: { + \tex_ifnum:D \l_fp_input_a_exponent_int > \c_zero + \fp_ln_const:nn { 10 } { \int_use:N \l_fp_input_a_exponent_int } + \fp_ln_normalise: + \fp_add:NNNNNNNNN + \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int + \l_fp_output_integer_int \l_fp_output_decimal_int + \l_fp_output_extended_int + \l_fp_output_integer_int \l_fp_output_decimal_int + \l_fp_output_extended_int + \tex_fi:D + \fp_ln_mantissa: +} +\cs_new_protected_nopar:Npn \fp_ln_normalise: { + \tex_ifnum:D \l_fp_exp_exponent_int < \l_fp_output_exponent_int + \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million + \tex_expandafter:D \use_i:nn \tex_expandafter:D + \fp_ln_normalise_aux:NNNNNNNNN + \int_use:N \l_fp_exp_decimal_int + \tex_expandafter:D \fp_ln_normalise: + \tex_fi:D +} +\cs_new_protected_nopar:Npn + \fp_ln_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { + \tex_ifnum:D \l_fp_exp_integer_int = \c_zero + \l_fp_exp_decimal_int #1#2#3#4#5#6#7#8 \scan_stop: + \tex_else:D + \tl_set:Nx \l_fp_tmp_tl + { + \int_use:N \l_fp_exp_integer_int + #1#2#3#4#5#6#7#8 + } + \l_fp_exp_integer_int \c_zero + \l_fp_exp_decimal_int \l_fp_tmp_tl \scan_stop: + \tex_fi:D + \tex_divide:D \l_fp_exp_extended_int \c_ten + \tl_set:Nx \l_fp_tmp_tl + { + #9 + \int_use:N \l_fp_exp_extended_int + } + \l_fp_exp_extended_int \l_fp_tmp_tl \scan_stop: + \tex_advance:D \l_fp_exp_exponent_int \c_one +} +\cs_new_protected_nopar:Npn \fp_ln_mantissa: { + \l_fp_count_int \c_zero + \l_fp_input_a_extended_int \c_zero + \fp_ln_mantissa_aux: + \tex_ifnum:D \l_fp_count_int > \c_zero + \fp_ln_const:nn { 2 } { \int_use:N \l_fp_count_int } + \fp_ln_normalise: + \tex_ifnum:D \l_fp_output_sign_int > \c_zero + \tex_expandafter:D \fp_add:NNNNNNNNN + \tex_else:D + \tex_expandafter:D \fp_sub:NNNNNNNNN + \tex_fi:D + \l_fp_output_integer_int \l_fp_output_decimal_int + \l_fp_output_extended_int + \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int + \l_fp_output_integer_int \l_fp_output_decimal_int + \l_fp_output_extended_int + \tex_fi:D + \tex_ifnum:D + \etex_numexpr:D + \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int > \c_one + \scan_stop: + \tex_expandafter:D \fp_ln_Taylor: + \tex_fi:D +} +\cs_new_protected_nopar:Npn \fp_ln_mantissa_aux: { + \tex_ifnum:D \l_fp_input_a_integer_int > \c_one + \tex_advance:D \l_fp_count_int \c_one + \fp_ln_mantissa_divide_two: + \tex_expandafter:D \fp_ln_mantissa_aux: + \tex_fi:D +} +\cs_new_protected_nopar:Npn \fp_ln_mantissa_divide_two: { + \tex_ifodd:D \l_fp_input_a_decimal_int + \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million + \tex_fi:D + \tex_ifodd:D \l_fp_input_a_integer_int + \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million + \tex_fi:D + \tex_divide:D \l_fp_input_a_integer_int \c_two + \tex_divide:D \l_fp_input_a_decimal_int \c_two + \tex_divide:D \l_fp_input_a_extended_int \c_two +} +\cs_new_protected_nopar:Npn \fp_ln_const:nn #1#2 { + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \fp_exp_integer_const:nnnn + \tex_csname:D c_fp_ln_ #1 _ #2 _tl \tex_endcsname:D +} +\cs_new_protected_nopar:Npn \fp_ln_Taylor: { + \group_begin: + \l_fp_input_a_integer_int \c_zero + \l_fp_input_a_exponent_int \c_zero + \l_fp_input_b_integer_int \c_two + \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int + \l_fp_input_b_exponent_int \c_zero + \fp_div_internal: + \fp_ln_fixed: + \l_fp_input_a_integer_int \l_fp_output_integer_int + \l_fp_input_a_decimal_int \l_fp_output_decimal_int + \l_fp_input_a_exponent_int \l_fp_output_exponent_int + \l_fp_input_a_extended_int \c_zero + \l_fp_output_decimal_int \c_zero + \l_fp_output_decimal_int \l_fp_input_a_decimal_int + \l_fp_output_extended_int \l_fp_input_a_extended_int + \fp_mul:NNNNNN + \l_fp_input_a_decimal_int \l_fp_input_a_extended_int + \l_fp_input_a_decimal_int \l_fp_input_a_extended_int + \l_fp_input_b_decimal_int \l_fp_input_b_extended_int + \l_fp_count_int \c_one + \fp_ln_Taylor_aux: + \cs_set_protected_nopar:Npx \fp_tmp:w + { + \group_end: + \exp_not:N \l_fp_exp_decimal_int + \int_use:N \l_fp_output_decimal_int \scan_stop: + \exp_not:N \l_fp_exp_extended_int + \int_use:N \l_fp_output_extended_int \scan_stop: + \exp_not:N \l_fp_exp_exponent_int + \int_use:N \l_fp_output_exponent_int \scan_stop: + } + \fp_tmp:w + \tex_advance:D \l_fp_exp_decimal_int \l_fp_exp_decimal_int + \tex_ifnum:D \l_fp_exp_extended_int < \c_five_hundred_million + \tex_else:D + \tex_advance:D \l_fp_exp_extended_int -\c_five_hundred_million + \tex_advance:D \l_fp_exp_decimal_int \c_one + \tex_fi:D + \tex_advance:D \l_fp_exp_extended_int \l_fp_exp_extended_int + \tex_ifnum:D \l_fp_output_sign_int > \c_zero + \tex_expandafter:D \fp_add:NNNNNNNNN + \tex_else:D + \tex_expandafter:D \fp_sub:NNNNNNNNN + \tex_fi:D + \l_fp_output_integer_int \l_fp_output_decimal_int + \l_fp_output_extended_int + \c_zero \l_fp_exp_decimal_int \l_fp_exp_extended_int + \l_fp_output_integer_int \l_fp_output_decimal_int + \l_fp_output_extended_int +} +\cs_new_protected_nopar:Npn \fp_ln_fixed: { + \tex_ifnum:D \l_fp_output_exponent_int < \c_zero + \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million + \tex_expandafter:D \use_i:nn \tex_expandafter:D + \fp_ln_fixed_aux:NNNNNNNNN + \int_use:N \l_fp_output_decimal_int + \tex_expandafter:D \fp_ln_fixed: + \tex_fi:D +} +\cs_new_protected_nopar:Npn + \fp_ln_fixed_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 { + \tex_ifnum:D \l_fp_output_integer_int = \c_zero + \l_fp_output_decimal_int #1#2#3#4#5#6#7#8 \scan_stop: + \tex_else:D + \tl_set:Nx \l_fp_tmp_tl + { + \int_use:N \l_fp_output_integer_int + #1#2#3#4#5#6#7#8 + } + \l_fp_output_integer_int \c_zero + \l_fp_output_decimal_int \l_fp_tmp_tl \scan_stop: + \tex_fi:D + \tex_advance:D \l_fp_output_exponent_int \c_one +} +\cs_new_protected_nopar:Npn \fp_ln_Taylor_aux: { + \tex_advance:D \l_fp_count_int \c_two + \fp_mul:NNNNNN + \l_fp_input_a_decimal_int \l_fp_input_a_extended_int + \l_fp_input_b_decimal_int \l_fp_input_b_extended_int + \l_fp_input_a_decimal_int \l_fp_input_a_extended_int + \tex_ifnum:D + \etex_numexpr:D + \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int + > \c_zero + \fp_div_integer:NNNNN + \l_fp_input_a_decimal_int \l_fp_input_a_extended_int + \l_fp_count_int + \l_fp_exp_decimal_int \l_fp_exp_extended_int + \tex_advance:D \l_fp_output_decimal_int \l_fp_exp_decimal_int + \tex_advance:D \l_fp_output_extended_int \l_fp_exp_extended_int + \tex_ifnum:D \l_fp_output_extended_int < \c_one_thousand_million + \tex_else:D + \tex_advance:D \l_fp_output_decimal_int \c_one + \tex_advance:D \l_fp_output_extended_int + -\c_one_thousand_million + \tex_fi:D + \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million + \tex_else:D + \tex_advance:D \l_fp_output_integer_int \c_one + \tex_advance:D \l_fp_output_decimal_int + -\c_one_thousand_million + \tex_fi:D + \tex_expandafter:D \fp_ln_Taylor_aux: + \tex_fi:D +} +\cs_new_protected_nopar:Npn \fp_pow:Nn { + \fp_pow_aux:NNn \tl_set:Nn +} +\cs_new_protected_nopar:Npn \fp_gpow:Nn { + \fp_pow_aux:NNn \tl_gset:Nn +} +\cs_generate_variant:Nn \fp_pow:Nn { c } +\cs_generate_variant:Nn \fp_gpow:Nn { c } +\cs_new_protected_nopar:Npn \fp_pow_aux:NNn #1#2#3 { + \group_begin: + \fp_read:N #2 + \l_fp_input_b_sign_int \l_fp_input_a_sign_int + \l_fp_input_b_integer_int \l_fp_input_a_integer_int + \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int + \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int + \fp_split:Nn a {#3} + \fp_standardise:NNNN + \l_fp_input_a_sign_int + \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int + \l_fp_input_a_exponent_int + \tex_ifnum:D + \etex_numexpr:D + \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int + = \c_zero + \tex_ifnum:D + \etex_numexpr:D + \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int + = \c_zero + \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 + { + \group_end: + ##1 ##2 { \c_undefined_fp } + } + \tex_else:D + \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 + { + \group_end: + ##1 ##2 { \c_zero_fp } + } + \tex_fi:D + \tex_else:D + \tex_ifnum:D + \etex_numexpr:D + \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int + = \c_zero + \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 + { + \group_end: + ##1 ##2 { \c_one_fp } + } + \tex_else:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \fp_pow_aux_i: + \tex_fi:D + \tex_fi:D + \fp_tmp:w #1 #2 +} +\cs_new_protected_nopar:Npn \fp_pow_aux_i: { + \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero + \tl_set:Nn \l_fp_sign_tl { + } + \tex_expandafter:D \fp_pow_aux_ii: + \tex_else:D + \l_fp_input_a_extended_int \c_zero + \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten + \group_begin: + \fp_extended_normalise: + \tex_ifnum:D + \etex_numexpr:D + \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int + = \c_zero + \group_end: + \tl_set:Nn \l_fp_sign_tl { - } + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \fp_pow_aux_ii: + \tex_else:D + \group_end: + \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 + { + \group_end: + ##1 ##2 { \c_undefined_fp } + } + \tex_fi:D + \tex_else:D + \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 + { + \group_end: + ##1 ##2 { \c_undefined_fp } + } + \tex_fi:D + \tex_fi:D +} +\cs_new_protected_nopar:Npn \fp_pow_aux_ii: { + \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero + \tex_expandafter:D \fp_pow_aux_iv: + \tex_else:D + \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten + \group_begin: + \l_fp_input_a_extended_int \c_zero + \fp_extended_normalise: + \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero + \tex_ifnum:D \l_fp_input_a_integer_int > \c_ten + \group_end: + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \fp_pow_aux_iv: + \tex_else:D + \group_end: + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \fp_pow_aux_iii: + \tex_fi:D + \tex_else:D + \group_end: + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \tex_expandafter:D \fp_pow_aux_iv: + \tex_fi:D + \tex_else:D + \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D + \fp_pow_aux_iv: + \tex_fi:D + \tex_fi:D + \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2 + { + \group_end: + ##1 ##2 + { + \l_fp_sign_tl + \int_use:N \l_fp_output_integer_int + . + \tex_expandafter:D \use_none:n + \tex_number:D \etex_numexpr:D + \l_fp_output_decimal_int + \c_one_thousand_million + \scan_stop: + e + \int_use:N \l_fp_output_exponent_int + } + } +} +\cs_new_protected_nopar:Npn \fp_pow_aux_iii: { + \l_fp_input_a_sign_int \c_one + \fp_pow_aux_iv: + \l_fp_input_a_integer_int \c_one + \l_fp_input_a_decimal_int \c_zero + \l_fp_input_a_exponent_int \c_zero + \l_fp_input_b_integer_int \l_fp_output_integer_int + \l_fp_input_b_decimal_int \l_fp_output_decimal_int + \l_fp_input_b_exponent_int \l_fp_output_exponent_int + \fp_div_internal: +} +\cs_new_protected_nopar:Npn \fp_pow_aux_iv: { + \group_begin: + \l_fp_input_a_integer_int \l_fp_input_b_integer_int + \l_fp_input_a_decimal_int \l_fp_input_b_decimal_int + \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int + \fp_ln_internal: + \cs_set_protected_nopar:Npx \fp_tmp:w + { + \group_end: + \exp_not:N \l_fp_input_b_sign_int + \int_use:N \l_fp_output_sign_int \scan_stop: + \exp_not:N \l_fp_input_b_integer_int + \int_use:N \l_fp_output_integer_int \scan_stop: + \exp_not:N \l_fp_input_b_decimal_int + \int_use:N \l_fp_output_decimal_int \scan_stop: + \exp_not:N \l_fp_input_b_extended_int + \int_use:N \l_fp_output_extended_int \scan_stop: + \exp_not:N \l_fp_input_b_exponent_int + \int_use:N \l_fp_output_exponent_int \scan_stop: + } + \fp_tmp:w + \l_fp_input_a_extended_int \c_zero + \fp_mul:NNNNNNNNN + \l_fp_input_a_integer_int \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int + \l_fp_input_b_integer_int \l_fp_input_b_decimal_int + \l_fp_input_b_extended_int + \l_fp_input_a_integer_int \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int + \tex_advance:D \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int + \l_fp_output_integer_int \c_zero + \l_fp_output_decimal_int \c_zero + \l_fp_output_exponent_int \c_zero + \cs_set_eq:NN \fp_exp_const:Nx \use_none:nn + \fp_exp_internal: +} +\prg_new_conditional:Npnn \fp_if_undefined:N #1 { T , F , TF , p } { \tex_ifx:D #1 \c_undefined_fp \prg_return_true: \tex_else:D \prg_return_false: \tex_fi:D } -\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF } { +\prg_new_conditional:Npnn \fp_if_zero:N #1 { T , F , TF , p } { \tex_ifx:D #1 \c_zero_fp \prg_return_true: \tex_else:D \prg_return_false: \tex_fi:D } -\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3 { T , F , TF } +\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3 + { T , F , TF } { \group_begin: \fp_split:Nn a {#1} @@ -2076,7 +3177,8 @@ \l_fp_input_b_exponent_int \fp_compare_aux:N #2 } -\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3 { T , F , TF } +\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3 + { T , F , TF } { \group_begin: \fp_read:N #3 @@ -2265,6 +3367,21 @@ \cs_new_protected_nopar:Npn \fp_overflow_msg: { \msg_kernel_error:nn { fpu } { overflow } } +\msg_kernel_new:nnnn { fpu } { exponent-overflow } + { Number~too~big~for~exponent~unit. } + { + The~exponent~of~the~input~given~is~too~big~for~the~floating~point~ + unit:~the~maximum~input~value~for~an~exponent~is~230. + } +\cs_new_protected_nopar:Npn \fp_exp_overflow_msg: { + \msg_kernel_error:nn { fpu } { exponent-overflow } +} +\msg_kernel_new:nnnn { fpu } { logarithm-input-error } + { Invalid~input~to~ln~function. } + { Logarithms~can~only~be~calculated~for~positive~numbers. } +\cs_new_protected_nopar:Npn \fp_ln_error_msg: { + \msg_kernel_error:nn { fpu } { logarithm-input-error } +} \msg_kernel_new:nnnn { fpu } { trigonometric-overflow } { Number~too~big~for~trigonometry~unit. } { |