% This is file `numerica.sty'. % % This work may be distributed and/or modified under the conditions % of the LaTeX Project Public License, either version 1.3c of this % license or any later version; see % http://www.latex-project.org/lppl.txt % % Andrew Parsloe (ajparsloe@gmail.com) % \RequirePackage{l3keys2e} \RequirePackage{amsmath,mathtools,etoolbox} \ProvidesExplPackage {numerica} {2021/12/07} {2.0.0} {Numerically evaluate mathematical expressions in their LaTeX form} % needs amsmath \cs_if_free:NT \arccsc { \DeclareMathOperator{\arccsc}{arccsc} } \cs_if_free:NT \arcsec { \DeclareMathOperator{\arcsec}{arcsec} } \cs_if_free:NT \arccot { \DeclareMathOperator{\arccot}{arccot} } \cs_if_free:NT \csch { \DeclareMathOperator{\csch}{csch} } \cs_if_free:NT \sech { \DeclareMathOperator{\sech}{sech} } \cs_if_free:NT \asinh { \DeclareMathOperator{\asinh}{asinh} } \cs_if_free:NT \acosh { \DeclareMathOperator{\acosh}{acosh} } \cs_if_free:NT \atanh { \DeclareMathOperator{\atanh}{atanh} } \cs_if_free:NT \acsch { \DeclareMathOperator{\acsch}{acsch} } \cs_if_free:NT \asech { \DeclareMathOperator{\asech}{asech} } \cs_if_free:NT \acoth { \DeclareMathOperator{\acoth}{acoth} } \cs_if_free:NT \sgn { \DeclareMathOperator{\sgn}{sgn} } \cs_if_free:NT \lb { \DeclareMathOperator{\lb}{lb} } % needs mathtools \cs_if_free:NT \abs {\DeclarePairedDelimiter{\abs}{\lvert}{\rvert} } \cs_if_free:NT \ceil { \DeclarePairedDelimiter{\ceil}{\lceil}{\rceil} } \cs_if_free:NT \floor { \DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor} } % \RenewDocumentCommand \land {} { \,\wedge\, } \RenewDocumentCommand \lor {} { \,\vee\, } \NewDocumentCommand \Q {} { \prg_do_nothing: } % Qleave apart \NewDocumentCommand \q {} { \prg_do_nothing: } % qleave to % \int_const:Nn \c__nmc_and_int { 0 } \int_const:Nn \c__nmc_cmp_int { 1 } \int_const:Nn \c__nmc_sum_int { 2 } \int_const:Nn \c__nmc_trg_int { 3 } \int_const:Nn \c__nmc_uny_int { 4 } \int_const:Nn \c__nmc_prn_int { 5 } \int_const:Nn \c__nmc_srd_int { 6 } \int_new:N \l__nmc_trg_int \int_new:N \l__nmc_num_sgn_int % tables \tl_new:N \l__nmc_toss_tl \seq_new:N \l_tmpc_seq % \prg_new_conditional:Npnn \int_if_zero:n #1 { p,T,F,TF } { \int_compare:nNnTF { #1 } = { 0 } { \prg_return_true: } { \prg_return_false: } } \prg_new_conditional:Npnn \__nmc_if_mod_zero:nn #1#2 { p,T,F,TF } { \bool_if:nTF { !\int_compare_p:nNn { #1 } = { 0 } && \int_compare_p:nNn { \int_mod:nn { #1 } { #2 } } = { 0 } } { \prg_return_true: } { \prg_return_false: } } % fpify & delim property lists \prop_new:N \g__nmc_class_prop % latex tokens % #1(clist) tokens; #2(tl) { fpify: delim: } routines \cs_new_protected:Npn \__nmc_fill_class:nn #1#2 { \clist_map_inline:nn { #1 } { \prop_gput:Nnn \g__nmc_class_prop { ##1 } { #2 } } } % \__nmc_fill_class:nn { 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, . } { \__nmc_fpify_dec: \__nmc_delim_dec: } \__nmc_fill_class:nn { e, \pi, \gamma, \phi, \deg, \infty } { \__nmc_fpify_const: \__nmc_delim_const: } % arith \__nmc_fill_class:nn { +, - } { \__nmc_fpify_arith: \__nmc_delim_pm: } \prop_put:Nnn \g__nmc_class_prop { * } { \__nmc_fpify_arith: \__nmc_delim_arith: } \prop_put:Nnn \g__nmc_class_prop { / } { \__nmc_fpify_slash: \__nmc_delim_arith: } \__nmc_fill_class:nn { \times, \cdot, \div } { \__nmc_fpify_arith_alt: \__nmc_delim_arith: } \prop_put:Nnn \g__nmc_class_prop { ^ } { \__nmc_fpify_power: \__nmc_delim_power: } \__nmc_fill_class:nn { \frac, \dfrac } { \__nmc_fpify_frac: \__nmc_delim_frac: } \prop_put:Nnn \g__nmc_class_prop { \tfrac } { \__nmc_fpify_frac: \__nmc_delim_tfrac: } % comparisons \__nmc_fill_class:nn { =, <, >, \ne, \neq, \nless, \ngtr, \ge, \geq, \geqq, \geqslant, \le, \leq, \leqq, \leqslant, \ngeq, \ngeqq, \ngeqslant, nleq, \nleqq, \nleqslant, } { \__nmc_fpify_comparison: \__nmc_delim_comparison: } % logic, surd \__nmc_fill_class:nn { \wedge, \land, \vee, \lor } { \__nmc_fpify_andor: \__nmc_delim_andor: } \__nmc_fill_class:nn { \surd, \neg, \lnot } { \__nmc_fpify_surd: \__nmc_delim_surd: } % left \__nmc_fill_class:nn { (, [, \{, \lparen, \lbrack, \lbrace } { \__nmc_fpify_lparen: \__nmc_delim_lparen: } \__nmc_fill_class:nn { |, \lvert, \lfloor, \lceil } { \__nmc_fpify_lvert: \__nmc_delim_lvert: } \__nmc_fill_class:nn { \left, \bigl, \Bigl, \biggl, \Biggl } { \__nmc_fpify_lmod: \__nmc_delim_lmod: } % right \__nmc_fill_class:nn { \right, \bigr, \Bigr, \biggr, \Biggr } { \prg_do_nothing: \__nmc_delim_rparen: } % unary fns: f \__nmc_fill_class:nn { \sin, \cos, \tan, \csc, \sec, \cot } { { \__nmc_fpify_unary:n { \l__nmc_trg_int } } { \__nmc_delim_unary:n { \l__nmc_trg_int } } } \__nmc_fill_class:nn { \arcsin, \arccos, \arctan, \arccsc, \arcsec, \arccot, \sinh, \cosh, \tanh, \csch, \sech, \coth, \asinh, \acosh, \atanh, \acsch, \asech, \acoth, \exp, \ln, \lg, \lb, \sgn } { { \__nmc_fpify_unary:n { \c__nmc_uny_int } } { \__nmc_delim_unary:n { \c__nmc_uny_int } } } % f! \prop_put:Nnn \g__nmc_class_prop { ! } { \__nmc_fpify_fact: \__nmc_delim_fact: } % f{} \__nmc_fill_class:nn { \sqrt, \abs, \floor, \ceil } { \__nmc_fpify_unarybrace: \__nmc_delim_unarybrace: } % binary ( f_{arg1}{arg2}, f{arg1}{arg2} ) \prop_put:Nnn \g__nmc_class_prop { \log } { \__nmc_fpify_unarysub: \__nmc_delim_log: } \__nmc_fill_class:nn { \tbinom, \binom, \dbinom } { \__nmc_fpify_binom: \__nmc_delim_frac: } % nary f(arg1,...) \__nmc_fill_class:nn { \min, \max, \gcd } { \__nmc_fpify_nary: \__nmc_delim_nary: } \prop_put:Nnn \g__nmc_class_prop { , } { \__nmc_fpify_comma: \__nmc_delim_comma: } % fontlike (ignore cmd; heed {arg} ) \__nmc_fill_class:nn { \mathrm, \mathit, \mathcal, \mathtt, \mathbf, \mathbb, \mathsf, \mathfrak, \mathscr, \mathnormal, \boldsymbol, \ensuremath, \smash, \textrm, \textsf, \texttt } { \__nmc_fpify_font: \__nmc_delim_font: } % ignore cmd, [arg1], {arg2}; heed {arg3} \prop_put:Nnn \g__nmc_class_prop { \textcolor } { \__nmc_fpify_color: \__nmc_delim_color: } % splitfrac ( ignore cmd, heed {arg1}{arg2} ) \__nmc_fill_class:nn { \splitfrac, \splitdfrac } { \__nmc_fpify_splitfrac: \__nmc_delim_append_twobraced: } % absorb \__nmc_fill_class:nn { {{}}, \\, &, \to, \q_nil, \dots, \ldots, \cdots, \quad, \qquad, \hfill, \hfil, \mathstrut, $, \(, \), \[, \], \ , \,, \;, \:, \!, \>, \thinspace, \medspace, \thickspace, \negthinspace, \negmedspace, \negthickspace, \displaystyle, \textstyle, \scriptstyle, \scriptscriptstyle, } { \prg_do_nothing: \__nmc_delim_absorb: } \__nmc_fill_class:nn { \vphantom, \hphantom, \phantom, \label, \mspace, \mbox, \text } { \__nmc_fpify_absorb_m: \__nmc_delim_absorb_i: } \__nmc_fill_class:nn { \hspace } { \__nmc_fpify_absorb_sm: \__nmc_delim_absorb_ii: } \__nmc_fill_class:nn { \xmathstrut, \color } { \__nmc_fpify_absorb_om: \__nmc_delim_absorb_ii: } % ams environs f{arg1} (& f{arg1}{arg2} for aligned, aligned*) \__nmc_fill_class:nn { \begin, \end } { \__nmc_fpify_BE: \__nmc_delim_BE: } % cleave \__nmc_fill_class:nn { \q, \Q } { \prg_do_nothing: \__nmc_delim_cleave: } % sum, prod \__nmc_fill_class:nn { \sum, \prod } { \__nmc_fpify_sum: \__nmc_delim_sum: } % nmcFn \__nmc_fill_class:nn { \eval, \nmcEvaluate, \iter, \nmcIterate, \solve, \nmcSolve, \recur, \nmcRecur, \tabulate, \nmcTabulate, \info, \nmcInfo, \constants, \nmcConstants, \reuse, \nmcReuse } { \__nmc_fpify_cmd: \__nmc_delim_cmd: } % substitution classes %%%%%%%%%%%%%%%%%%%%%%%%%% \prop_new:N \l__nmc_subst_var_prop % variables \prop_new:N \g__nmc_subst_var_prop % macros (user & reuse) \prop_new:N \g__nmc_subst_fpfn_prop % math toks for l3fp eval \prop_new:N \g__nmc_subst_misc_prop % misc subst % #1 prop; #2 seq (keys); #3 seq (values) \cs_new_protected:Npn \__nmc_subst:NNN #1#2#3 { \cs_set_protected:Npn \__nmc_substitutions:nn ##1##2 { \prop_gput:Nnn #1 { ##1 } { ##2 } } \seq_mapthread_function:NNN #2 #3 \__nmc_substitutions:nn } \seq_set_from_clist:Nn \l_tmpa_seq { e, \pi, \gamma, \phi, \deg, \infty, \sin, \cos, \tan, \csc, \sec, \cot, \arcsin, \arccos, \arctan, \arccsc, \arcsec, \arccot, \sinh, \cosh, \tanh, \csch, \sech, \coth, \asinh, \acosh, \atanh, \acsch, \asech, \acoth, \exp, \ln, \lg, \lb, \sgn, \max, \min, \surd, \sqrt, \times, \cdot, \div, \abs, \floor, \ceil, \lvert, \lfloor, \lceil, \neg, \lnot, \wedge, \land, \vee, \lor, \le, \leq, \leqq, \leqslant, \ge, \geq, \geqq, \geqslant, \ne, \neq, \nless, \ngtr, \nleq, \nleqq,\nleqslant, \ngeq, \ngeqq, \ngeqslant } \seq_set_from_clist:Nn \l_tmpb_seq { exp(1), (pi), (0.5772156649015329), (1.618033988749895), (0.0174532925199433), inf, sin\__nmc_deg:, cos\__nmc_deg:, tan\__nmc_deg:, csc\__nmc_deg:, sec\__nmc_deg:, cot\__nmc_deg:, asin\__nmc_deg:, acos\__nmc_deg:, atan\__nmc_deg:, acsc\__nmc_deg:, asec\__nmc_deg:, acot\__nmc_deg:, sinh, cosh, tanh, csch, sech, coth, asinh, acosh, atanh, acsch, asech, acoth, exp, ln, (0.4342944819032518)ln, (1.442695040888963)ln, sign, max, min, sqrt, sqrt, *, *, /, abs, floor, ceil, abs, floor, ceil, !, !, &&, &&, ||, ||, <=, <=, <=, <=, >=, >=, >=, >=, !=, !=, !<, !>, !<=, !<=, !<=, !>=, !>=, !>= } \__nmc_subst:NNN \g__nmc_subst_fpfn_prop \l_tmpa_seq \l_tmpb_seq \seq_set_from_clist:Nn \l_tmpa_seq { \cosh, \sinh, \tanh, \csch, \sech, \coth, (, [, \{, \lparen, \lbrack, \lbrace, \left, \bigl, \Bigl, \biggl, \Biggl, \lvert, \lceil, \lfloor, sum, prod, deriv, integ, iter, solve, \eval, \nmcEvaluate, \iter, \nmcIterate, \solve, \nmcSolve, \recur, \nmcRecur, \tabulate, \nmcTabulate, \info, \nmcInfo, \constants, \nmcConstants, \reuse, \nmcReuse } \seq_set_from_clist:Nn \l_tmpb_seq { acosh, asinh, atanh, acsch, asech, acoth, ), ], \}, \rparen, \rbrack, \rbrace, \right, \bigr, \Bigr, \biggr, \Biggr, \rvert, \rceil, \rfloor, term, factor, bisection, subdivision, iteration, step, eval, eval, iter, iter, solve, solve, recur, recur, table, table, info, info, consts, consts, reuse, reuse } \__nmc_subst:NNN \g__nmc_subst_misc_prop \l_tmpa_seq \l_tmpb_seq % base function variants %%%%%%%%%%%%%%%%%%%%%%%% \cs_generate_variant:Nn \tl_if_head_eq_meaning:nNTF { V } \cs_generate_variant:Nn \tl_if_head_eq_meaning:nNF { V } \cs_generate_variant:Nn \tl_if_head_eq_meaning_p:nN { V } \cs_generate_variant:Nn \tl_if_head_eq_charcode:nNTF { V } \cs_generate_variant:Nn \tl_if_head_eq_charcode:nNT { V } \cs_generate_variant:Nn \tl_if_head_eq_charcode:nNF { V } \cs_generate_variant:Nn \tl_if_head_is_group:nTF { V } \cs_generate_variant:Nn \tl_if_in:NnTF { NV } \cs_generate_variant:Nn \tl_if_in:NnT { NV } \cs_generate_variant:Nn \tl_if_in:nnTF { nV } \cs_generate_variant:Nn \tl_if_eq:nnTF { V } \cs_generate_variant:Nn \tl_if_eq:nnT { V } \cs_generate_variant:Nn \tl_if_eq:nnF { V } \cs_generate_variant:Nn \tl_replace_once:Nnn { Nnx } \cs_generate_variant:Nn \tl_count_tokens:n { V } \cs_generate_variant:Nn \int_compare:nNnTF { v } \cs_generate_variant:Nn \int_compare:nNnT { v } \cs_generate_variant:Nn \int_case:nnTF { v } \cs_generate_variant:Nn \clist_pop:NN { cc } \cs_generate_variant:Nn \prop_put_if_new:Nnn { No } \cs_generate_variant:Nn \iow_open:Nn { NV } \cs_generate_variant:Nn \iow_now:Nn { NV } \cs_generate_variant:Nn \keys_set_known:nn { x } \cs_generate_variant:Nn \file_get:nnN { V } \cs_generate_variant:Nn \file_get:nnNT { V } \cs_generate_variant:Nn \file_get:nnNTF { V } % general purpose routines %%%%%%%%%%%%%%%%%%%%%% % \tl_new:N \l__nmc_A_tl etc. \clist_map_inline:nn { A,B,C,L,R } { \tl_new:c { l__nmc_#1_tl } } % prune head from A, put in B; record new head of A in C \cs_new_protected:Npn \__nmc_next: { \exp_last_unbraced:NV\__nmc_next:w \l__nmc_A_tl\q_stop } \cs_new_protected:Npn \__nmc_next:w #1#2#3\q_stop { \__nmc_assign_vals:nnnN {#1} {#2} {#3} \l__nmc_B_tl } % get |arg| \cs_new_protected:Npn \__nmc_absval_arg:N #1 { \exp_last_unbraced:NV \__nmc_absval_arg:wN \l__nmc_A_tl\q_stop #1 } \cs_new_protected:Npn \__nmc_absval_arg:wN #1|#2#3\q_stop #4 { \__nmc_assign_vals:nnnN {#1} {#2} {#3} #4 } \cs_new_protected:Npn \__nmc_assign_vals:nnnN #1#2#3#4 { \tl_if_single:nTF { #2 } { \tl_set:Nn \l__nmc_A_tl { #2#3 } } { \tl_set:Nn \l__nmc_A_tl { {#2}#3 } } \tl_set:Nn #4 { #1 } \tl_set:Nn \l__nmc_C_tl { #2 } } \cs_new_protected:Npn \__nmc_parenth:N #1 { \tl_set:Nx #1 { ( \exp_not:o #1 ) } } \cs_new_protected:Npn \__nmc_accum_fn_parenth:NNn #1#2#3 { \tl_put_right:Nx #1 { #3( \exp_not:o #2 ) } } % (fpify) #2, append to #1 \cs_new_protected:Npn \__nmc_accum_fpify_parenth:NN #1#2 { \group_begin: \tl_clear:N \l_tmpa_tl \__nmc_fpify:VN #2 \l_tmpa_tl \exp_args:NNNV \group_end: \__nmc_accum_fn_parenth:NNn #1\l_tmpa_tl{} } % (fp-ify) next braced arg, append to #1 \cs_new_protected:Npn \__nmc_fpify_next_braced:N #1 { \__nmc_next: \__nmc_accum_fpify_parenth:NN #1 \l__nmc_B_tl } % wrap #3 in #2 & #4, & append to #1 \cs_new_protected:Npn \__nmc_put_right_wrap:NnNn #1#2#3#4 { \tl_put_right:Nx #1 { #2 \exp_not:o #3 #4 } } \cs_new_protected:Npn \__nmc_get_arg_L:nN #1#2 { \tl_set:Nn \l__nmc_L_tl { #1 } \prop_get:NnN \g__nmc_subst_misc_prop { #1 } \l__nmc_R_tl \__nmc_get_arg_L_aux:NNV #1#2 \l__nmc_R_tl } \cs_generate_variant:Nn \__nmc_get_arg_L:nN { V } \cs_new_protected:Npn \__nmc_get_arg_L_aux:NNn #1#2#3 { \__nmc_get_arg_LR:NNN #1#2#3 } \cs_generate_variant:Nn \__nmc_get_arg_L_aux:NNn { NNV } % #1 ldelim; #2 <-- arg (delims *not* included) % #3 rdelim (*must* differ from #1) \cs_new_protected:Npn \__nmc_get_arg_LR:NNN #1#2#3 { \int_set:Nn \l_tmpa_int { 1 } \tl_map_inline:Nn \l__nmc_A_tl { \str_case:nn { ##1 } { { #1 } { \int_incr:N \l_tmpa_int } { #3 } { \__nmc_get_arg_LR_rdelim: } { \q_nil } { \__nmc_get_arg_LR_qnil:N #1 } } \__nmc_next: \tl_if_single:nTF { ##1 } { \tl_put_right:Nn #2 { ##1 } } { \tl_put_right:Nn #2 { {##1} } } } } \cs_new_protected:Npn \__nmc_get_arg_LR_rdelim: { \int_decr:N \l_tmpa_int \int_if_zero:nT { \l_tmpa_int } { \__nmc_next: \tl_map_break: } } \cs_new_protected:Npn \__nmc_get_arg_LR_qnil:N #1 { \__nmc_error_what:n { Unmatched~\__nmc_verb:n { #1 }{}~in } \tl_map_break: } % #1 <== multi-char num poss. in sci notation % #2 delim: vs fpify: bool \cs_new_protected:Npn \__nmc_get_dec:NN #1#2 { \tl_set:NV #1 \l__nmc_B_tl \__nmc_get_dec_digits:Nn #1 { 1234567890. } \bool_lazy_and:nnT { \l__nmc_sci_num_in_bool } { \tl_if_eq_p:NN \l__nmc_C_tl \l__nmc_sci_num_in_tl } { \__nmc_get_dec_aux:NN #1#2 } } \cs_new_protected:Npn \__nmc_get_dec_aux:NN #1#2 { % l3fp uses "e" \__nmc_next: \tl_if_eq:VnTF \l__nmc_C_tl { - } { \__nmc_next: \__nmc_get_dec_aux:NNn #1#2 { e- } } { \__nmc_get_dec_aux:NNn #1#2 { e } } } \cs_new_protected:Npn \__nmc_get_dec_aux:NNn #1#2#3 { \tl_if_in:nVTF { 123456789 } \l__nmc_C_tl { \bool_if:NTF #2 { \tl_put_right:NV #1 \l__nmc_sci_num_in_tl } { \tl_put_right:Nn #1 { #3 } } \__nmc_get_dec_digits:Nn #1 { -1234567890 } } { \tl_set_eq:NN \l__nmc_C_tl \l__nmc_sci_num_in_tl \str_if_in:nnT { #3 } { - } { \tl_put_left:Nn \l__nmc_A_tl { - } } \tl_put_left:NV \l__nmc_A_tl \l__nmc_sci_num_in_tl } } \cs_new_protected:Npn \__nmc_get_dec_digits:Nn #1#2 { \tl_map_inline:Nn \l__nmc_A_tl { \tl_if_in:nnTF { #2 } { ##1 } { \tl_put_right:Nn #1 { ##1 } \__nmc_next: } { \tl_map_break: } } } % intify fp (for !, binom, n-th root, sum/prod) % #2(e.g. = 0,1,-1) <= #1(tl) <-- int \cs_new_protected:Npn \__nmc_intify:Nn #1#2 { \fp_compare:nTF { { #2 } <= round(#1+0,\l__nmc_intify_round_tl) = round(#1+0) } { \tl_set:Nx #1 { \fp_eval:n { round(#1+0) } } } { \fp_compare:nNnTF { #2 } = { -inf } { \__nmc_error_what:n { Integer~required~in } } { \__nmc_error_what:n { Integer~$\ge#2$~required~in } } } } % calc fn vals; explicit/implicit eval. of vv-list % #1(tl) var; #2(tl) fn; #3(fp) var val; #4(fp) <-- fn val % mode 0 (no vals in vv-list change) \cs_new_protected:Npn \__nmc_calc_fn_val:nNnN #1#2#3#4 { \prop_put:Nnx \l__nmc_subst_var_prop { #1 } { \fp_to_tl:n { #3 } } \__nmc_fpify_set:NV #4 #2 } \cs_generate_variant:Nn \__nmc_calc_fn_val:nNnN { V } \cs_new_protected:Npn \__nmc_calc_mode:n #1 { \tl_set:Nx \l__nmc_mode_tl { \int_eval:n { #1 } } \str_case:Vn \l__nmc_mode_tl { { 1 } { \cs_set_eq:NN \__nmc_calc_fn_val:nNnN \__nmc_calc_fn_vali:nNnN } { 2 } { \cs_set_eq:NN \__nmc_calc_fn_val:nNnN \__nmc_calc_fn_valii:nNnN } } } \cs_generate_variant:Nn \__nmc_calc_mode:n { V } % mode 1 (all vals in vv-list may change) \cs_new_protected:Npn \__nmc_calc_fn_vali:nNnN #1#2#3#4 { \prop_put:Nnx \l__nmc_vv_change_prop { #1 } { \fp_to_tl:n { #3 } } \__nmc_vv_get_vars_vals:NN \l__nmc_calc_fn_seq \l__nmc_vv_change_prop \__nmc_fpify_set:NV #4 #2 } % mode 2 (some vals in vv-list held const.) \cs_new_protected:Npn \__nmc_calc_fn_valii:nNnN #1#2#3#4 { \prop_put:Nnx \l__nmc_vv_change_prop { #1 } { \fp_to_tl:n { #3 } } \clist_map_inline:Nn \g__nmc_unchanged_clist { \prop_get:NnN \l__nmc_subst_var_prop { ##1 } \l__nmc_subst_tl \prop_put:NnV \l__nmc_vv_change_prop { ##1 } \l__nmc_subst_tl } \__nmc_vv_get_vars_vals:NN \l__nmc_calc_fn_seq \l__nmc_vv_change_prop \__nmc_fpify_set:NV #4 #2 } % fp-set #1 to fpified #2 \cs_new_protected:Npn \__nmc_fpify_set:Nn #1#2 { \group_begin: \tl_clear:N \l_tmpa_tl \__nmc_fpify:nN { #2 } \l_tmpa_tl \exp_args:NNNV \group_end: \tl_set:Nn \l__nmc_fp_exprn_tl \l_tmpa_tl \fp_set:Nn #1 { \l__nmc_fp_exprn_tl } \__nmc_error_fpflag: } \cs_generate_variant:Nn \__nmc_fpify_set:Nn { NV, cv } \cs_new:Npn \__nmc_verb:n #1 { \texttt{\string #1} } \cs_generate_variant:Nn \__nmc_verb:n { V } \cs_new:Npn \__nmc_verb:N #1 { \texttt{\string #1} } \cs_generate_variant:Nn \__nmc_verb:N { c } % Error handling %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \seq_new:N \g__nmc_error_where_seq \bool_new:N \g__nmc_error_bool \cs_new_protected:Npn \__nmc_error_where:n #1 { \seq_gpush:Nn \g__nmc_error_where_seq { #1 \int_compare:nNnT { \l__nmc_depth_int } > { 1 } { ~(\int_eval:n { (\l__nmc_depth_int-1)/2 } ) } } } \cs_new_protected:Npn \__nmc_error_what:n #1 { \bool_gset_true:N \g__nmc_error_bool \tl_gclear:N \g__nmc_reuse_tl \__nmc_error_msg:n { #1 } } \cs_new_protected:Npn \__nmc_error_msg:n #1 { \tl_set:Nn \l_tmpa_tl { ??? } \seq_if_empty:NF \g__nmc_error_where_seq { \seq_gpop:NN \g__nmc_error_where_seq \l_tmpa_tl \hbox:n { !!!~ #1 :~\l_tmpa_tl.~!!! } } } % l3fp exceptions; ln(1),cos(90),sin(360) underflow ignored! % Invalid op --> LaTeX *error*, hence \fp_trap:nn { invalid_operation } { flag } \cs_new_protected:Npn \__nmc_error_fpflag: { \flag_if_raised:nTF { fp_overflow } { \__nmc_flag:n { 1 } } { \flag_if_raised:nTF { fp_division_by_zero } { \__nmc_flag:n { 2 } } { \flag_if_raised:nT { fp_invalid_operation } { \__nmc_flag:n { 3 } } } } } \cs_new_protected:Npn \__nmc_flag:n #1 { \__nmc_error_what:n { \__nmc_verb:n{l3fp}~error~` \clist_item:nn { Overflow, Division~by~zero, Invalid~operation }{ #1 }'~in } } %%%%%%%% multi-tok --> single token vars %%%%%%%% % no math delims; #1(seq) vv-list; #2(tl) formula \int_new:N \g__nmc_prep_multitok_int \tl_new:N \l_nmc_multitoka_tl \tl_new:N \l_nmc_multitokb_tl \cs_new_protected:Npn \__nmc_prep_multitok:NN #1#2 { \seq_clear:N \l_tmpa_seq \seq_map_inline:Nn #1 { \seq_set_split:Nnn \l_tmpb_seq { = } { ##1 } \seq_pop:NN \l_tmpb_seq \l_tmpb_tl \int_compare:nNnT { \tl_count_tokens:V \l_tmpb_tl } > { 1 } { \seq_push:NV \l_tmpa_seq \l_tmpb_tl } } \seq_sort:Nn \l_tmpa_seq { % big --> small \int_compare:nNnTF { \tl_count:n {##2} } > { \tl_count:n { ##1 } } { \sort_return_swapped: } { \sort_return_same: } } \seq_map_inline:Nn \l_tmpa_seq { % multitoks => \nmc_a, \nmc_b, etc \int_gincr:N \g__nmc_prep_multitok_int \tl_set:Nn \l_nmc_multitoka_tl { ##1 } \tl_set:Nx \l_nmc_multitokb_tl { \cs:w nmc_\int_to_alph:n { \g__nmc_prep_multitok_int } \cs_end: } \tl_set:cn { nmc_\int_to_alph:n { \g__nmc_prep_multitok_int } } { ##1 } \regex_replace_all:nnN { \u{l_nmc_multitoka_tl} } { \u{l_nmc_multitokb_tl} } #1 \regex_replace_all:nnN { \u{l_nmc_multitoka_tl} } { \u{l_nmc_multitokb_tl} } #2 } } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \int_new:N \l__nmc_depth_int \tl_new:N \l__nmc_mode_tl \tl_new:N \l_nmc_formula_tl \fp_new:N \l__nmc_result_fp \tl_new:N \l_nmc_result_tl \tl_new:N \l__nmc_formula_dup_tl \tl_new:N \l__nmc_fp_expr_tl \tl_new:N \l__nmc_fp_exprn_tl \bool_new:N \l__nmc_dbg_count_bool \tl_new:N \l__nmc_dbg_vv_tl \tl_new:N \l__nmc_dbg_idii_tl \tl_new:N \l__nmc_dbg_idiii_tl \tl_new:N \l__nmc_dbg_idv_tl \seq_new:N \l__nmc_dbg_stored_seq \int_new:N \l__nmc_round_int \int_new:N \l__nmc_sci_expon_int \int_new:N \l__nmc_num_alt_int \tl_new:N \l__nmc_bool_F_tl \tl_new:N \l__nmc_bool_T_tl \bool_new:N \l__nmc_TF_out_bool \bool_new:N \l__nmc_allow_TF_out_bool \bool_new:N \l__nmc_sci_num_x_bool \bool_new:N \l__nmc_sci_num_table_bool \bool_new:N \l__nmc_vv_val_only_bool \bool_new:N \l__nmc_vv_invisible_bool \clist_new:N \l__nmc_vv_clist \seq_new:N \l__nmc_vv_visible_seq \seq_new:N \l__nmc_vv_no_consts_seq \seq_new:N \l__nmc_vv_all_seq \seq_new:N \l__nmc_calc_fn_seq \prop_new:N \l__nmc_vv_change_prop \tl_new:N \l__nmc_eq_var_tl \tl_new:N \l__nmc_eq_val_tl \tl_new:N \l__nmc_vv_fp_expr_tl \tl_new:N \l__nmc_punc_tl \tl_new:N \l__nmc_math_delimi_tl \tl_new:N \l__nmc_math_delimii_tl \bool_new:N \l__nmc_wraps_math_bool % ##1 = number-only switch, ##2 = keyval settings, % ##3 = formula, ##4 = vv-list, ##5 = number-format spec., % #1 = \nmcCommand, #2 = cmd id, #3 = short-name cmd \cs_new_protected:Npn \nmc_define:NnN #1#2#3 { \NewDocumentCommand #1 { s O{} m O{} O{} } { \group_begin: \__nmc_initialize:Nn ##1 { #2 } \__nmc_inputs_get:nnnnn { #2 } { ##2 } { ##3 } {##4 } {##5 } \bool_if:NF \g__nmc_error_bool { \use:c { __nmc_#2_process: } } \int_if_zero:nTF { \l__nmc_dbg_int } { \bool_if:NF \g__nmc_error_bool { \use:c { __nmc_#2_display: } } } { \__nmc_dbg_display:nn { \l__nmc_dbg_int } { #2 } } \group_end: } \ProvideDocumentCommand #3 {} { #1 } \cs_new_protected:cpn { __nmc_#2_vv_digest:N } ##1 { } \clist_map_inline:nn { initialize, settings_digest, process, display } { \cs_new_protected:cpn { __nmc_#2_##1: } { \prg_do_nothing: } } } \nmc_define:NnN \nmcEvaluate { eval } \eval %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \cs_new_protected:Npn \__nmc_initialize:Nn #1#2 { \bool_gset_false:N \g__nmc_error_bool \bool_set_eq:NN \l__nmc_num_only_bool #1 \bool_set_false:N \l__nmc_sci_num_out_bool \bool_set_false:N \l__nmc_sci_num_x_bool \bool_set_false:N \l__nmc_sci_num_table_bool \int_incr:N \l__nmc_depth_int \int_compare:nNnT \l__nmc_depth_int > { 1 } % for nesting { \bool_set_true:N \l__nmc_num_only_bool } \prop_concat:NNN \l__nmc_subst_var_prop \g__nmc_subst_var_prop \l__nmc_subst_var_prop \tl_set:Nn \l__nmc_dbg_idii_tl { vv-list } \use:c { __nmc_#2_initialize: } } \cs_new_protected:Npn \__nmc_inputs_get:nnnnn #1#2#3#4#5 { \__nmc_error_where:n { settings } \tl_if_empty:nF { #2 } { \keys_set_known:nn { numerica/generic } { #2 } \keys_set_known:xn { numerica/#1 }{ #2 } } \use:c { __nmc_#1_settings_digest: } \seq_gpop:NN \g__nmc_error_where_seq \l__nmc_toss_tl \bool_if:NF \g__nmc_error_bool { \mode_if_math:TF { \tl_set:Nn \l_nmc_formula_tl { #3 } } { \__nmc_math_delims:n { #3 } } \tl_set_eq:NN \l__nmc_formula_dup_tl \l_nmc_formula_tl } \bool_if:NF \g__nmc_error_bool { \tl_if_in:nnTF { #4 } { = }% vv-list { \__nmc_get_num_format:n { #5 } \__nmc_error_where:n { variable\,=\,value~list } \__nmc_vv_extract_visible:nN { #4 } \l__nmc_vv_clist \use:c { __nmc_#1_vv_digest:N } \l__nmc_vv_clist } { % empty vv-list \__nmc_get_num_format:n { #4#5 } \use:c { __nmc_#1_vv_digest:N } \c_empty_clist \tl_clear:N \l__nmc_vv_inline_tl \tl_clear:N \l__nmc_vv_display_tl \bool_set_true:N \l__nmc_vv_invisible_bool } \seq_gpop:NN \g__nmc_error_where_seq \l__nmc_toss_tl } } %%%%%%%%%%%%%%%%% debug routines %%%%%%%%%%%%%%%% \cs_new_protected:Npn \__nmc_dbg_display:nn #1#2 { \__nmc_dbg_display:xnn { \mode_if_math:TF { ed }{ * } } { #1 } { #2 } } \cs_new_protected:Npn \__nmc_dbg_display:nnn #1#2#3 { % #2 dbg int, #3 fn id \seq_reverse:N \l__nmc_vv_all_seq \raggedright \begin{ align#1 } \__nmc_if_mod_zero:nnT { #2 } { 2 } { \__nmc_dbg:Nnn \l__nmc_dbg_vv_tl { #2 } \l__nmc_dbg_idii_tl } \__nmc_if_mod_zero:nnT { #2 } { 3 } { \__nmc_dbg:Nnn \l_nmc_formula_tl { #2 } \l__nmc_dbg_idiii_tl } \__nmc_if_mod_zero:nnT { #2 } { 5 } { \__nmc_dbg_stored: \__nmc_dbg:Nnn \l_tmpa_tl { #2 } \l__nmc_dbg_idv_tl } \__nmc_if_mod_zero:nnT { #2 } { 7 } { \__nmc_dbg:Nnn \l__nmc_fp_expr_tl { #2 } { fp-form } \bool_if:nT { !\g__nmc_error_bool && !\str_if_eq_p:nn { #3 } { table } } { \\ \text{result:} & \quad \text{\l_nmc_result_tl } } } \end{ align#1 } \bool_set_false:N \l__nmc_dbg_count_bool } \cs_generate_variant:Nn \__nmc_dbg_display:nnn { x } \cs_new_protected:Npn \__nmc_dbg_vv_view:n #1 { \seq_set_eq:NN \l__nmc_vv_no_consts_seq \l__nmc_vv_all_seq \int_step_inline:nn { \seq_count:N \g__nmc_consts_vv_seq } { \seq_pop:NN \l__nmc_vv_no_consts_seq \l__nmc_toss_tl } \seq_reverse:N \l__nmc_vv_no_consts_seq \int_step_inline:nn { #1 } { \seq_pop:NN \l__nmc_vv_no_consts_seq \l__nmc_toss_tl } \tl_gset:Nx \l__nmc_dbg_vv_tl { \seq_use:Nn \l__nmc_vv_no_consts_seq {,~} } } \cs_new_protected:Npn \__nmc_dbg_get_data: { \seq_clear:N \l__nmc_dbg_stored_seq \__nmc_dbg_vv_view:n { 0 } \seq_map_inline:Nn \l__nmc_vv_no_consts_seq { \__nmc_split_eq:w ##1\q_stop \prop_get:NVN \l__nmc_subst_var_prop \l__nmc_eq_var_tl \l_tmpa_tl \tl_put_left:Nn \l_tmpa_tl { = } \tl_put_left:NV \l_tmpa_tl \l__nmc_eq_var_tl \seq_put_right:NV \l__nmc_dbg_stored_seq \l_tmpa_tl } } \cs_new_protected:Npn \__nmc_dbg_stored: { \seq_clear:N \l_tmpa_seq \seq_map_inline:Nn \l__nmc_dbg_stored_seq { \prop_get:NnNTF \l__nmc_subst_var_prop { ##1 } \l_tmpa_tl { \tl_put_left:Nn \l_tmpa_tl { ##1= } \seq_put_right:NV \l_tmpa_seq \l_tmpa_tl } { \seq_put_right:Nn \l_tmpa_seq { ##1 } } } \tl_gset:Nx \l_tmpa_tl { \seq_use:Nn \l_tmpa_seq {,~} } } \cs_new:Npn \__nmc_dbg:Nnn #1#2#3 { \bool_if:NT \l__nmc_dbg_count_bool { \\ } \hbox:n { #3:} & \quad \int_compare:nNnTF { #2 } > { 0 } { \vbox_top:n } { \hbox:n } { \tl_to_str:N #1 } \bool_set_true:N \l__nmc_dbg_count_bool } \cs_generate_variant:Nn \__nmc_dbg_display:nnnn { V, x } %%%%%%%%%%%%%% formula, delimiters %%%%%%%%%%%%%% \cs_new_protected:Npn \__nmc_math_delims:n #1 { % #1 formula \tl_set:Nn \l_nmc_formula_tl { #1 } \tl_trim_spaces:N \l_nmc_formula_tl \bool_set_true:N \l__nmc_wraps_math_bool % $ ? \tl_if_head_eq_meaning:VNTF \l_nmc_formula_tl $ { \__nmc_math_delims_aux:n { 1 } } { \tl_if_head_eq_meaning:VNTF \l_nmc_formula_tl \( { \__nmc_math_delims_aux:n { 1 } } { % \[ ? \tl_if_head_eq_meaning:VNTF \l_nmc_formula_tl \[ { \__nmc_math_delims_aux:n { 1 } } { %\begin{environ} ? \tl_if_head_eq_meaning:VNTF \l_nmc_formula_tl \begin { \__nmc_math_delims_aux:n { 2 } } { \__nmc_math_delims_aux:nn { \[ } { \] } \bool_set_false:N \l__nmc_wraps_math_bool } } } } \tl_trim_spaces:N \l_nmc_formula_tl \bool_if:NTF \l__nmc_num_only_bool { \__nmc_math_delims_aux:nn {}{} } { \bool_if:NT \l__nmc_vv_multline_bool { \__nmc_math_delims_mliner:V \l__nmc_eqn_num_tl } } } \cs_new:Npn \__nmc_math_delims_mliner:n #1 { \bool_if:nT { \l__nmc_wraps_math_bool || !\mode_if_math_p: } { \tl_set:Nn \l__nmc_math_delimi_tl { \begin{multline#1} } \tl_set:Nn \l__nmc_math_delimii_tl { \end{multline#1} } } } \cs_generate_variant:Nn \__nmc_math_delims_mliner:n { V } \cs_new_protected:Npn \__nmc_math_delims_aux:n #1 { \__nmc_math_delims_aux:xx { \tl_range:Nnn \l_nmc_formula_tl { 1 } { #1 } } { \tl_range:Nnn \l_nmc_formula_tl { -#1 } { -1 } } \int_set:Nn \l_tmpa_int { #1 + 1 } \tl_set:Nx \l_nmc_formula_tl { \tl_range:Nnn \l_nmc_formula_tl { \l_tmpa_int } { -\l_tmpa_int } } } \cs_new_protected:Npn \__nmc_math_delims_aux:nn #1#2 { \tl_set:Nn \l__nmc_math_delimi_tl { #1 } \tl_set:Nn \l__nmc_math_delimii_tl { #2 } } \cs_generate_variant:Nn \__nmc_math_delims_aux:nn { xx } %%%%%%%%%% number-formatting routines %%%%%%%%%%% \cs_new_protected:Npn \__nmc_get_num_format:n #1 { \__nmc_error_where:n { result~format~spec. } \str_set:Nn \l_tmpa_str { #1 } \tl_clear:N \l_tmpa_tl \int_zero:N \l__nmc_num_alt_int \str_if_in:NnTF \l_tmpa_str { ? } { \__nmc_num_bool_spec: } { \str_if_in:NnT \l_tmpa_str { * } { \bool_set_true:N \l__nmc_pad_zeros_bool \str_remove_all:Nn \l_tmpa_str { * } } } \str_map_inline:Nn \l_tmpa_str { \str_if_in:nnTF { 1234567890- } { ##1 } { \tl_put_right:Nn \l_tmpa_tl { ##1 } } { \__nmc_num_sci_spec:n { ##1 } } } \tl_if_empty:NF \l_tmpa_tl { \int_set:Nn \l__nmc_round_int \l_tmpa_tl } \int_compare:nNnT { \l__nmc_depth_int } > { 2 } { \__nmc_num_deep_output:N \l_tmpa_tl } \bool_if:NF \g__nmc_error_bool { \seq_gpop:NN \g__nmc_error_where_seq \l__nmc_toss_tl } } \cs_new_protected:Npn \__nmc_num_bool_spec: { \bool_set_eq:NN \l__nmc_TF_out_bool \l__nmc_allow_TF_out_bool \int_incr:N \l__nmc_num_alt_int \str_remove_once:Nn \l_tmpa_str { ? } \str_if_in:NnT \l_tmpa_str { ? } { \int_incr:N \l__nmc_num_alt_int \str_remove_once:Nn \l_tmpa_str { ? } \str_if_in:NnT \l_tmpa_str { ? } { \int_incr:N \l__nmc_num_alt_int \str_remove_all:Nn \l_tmpa_str { ? } } } \bool_if:NT \l__nmc_num_only_bool { \int_set:Nn \l__nmc_num_alt_int { 1 } } } \cs_new_protected:Npn \__nmc_num_sci_spec:n #1 { \str_case:nn { #1 } { { x } { \bool_set_true:N \l__nmc_sci_num_x_bool } { t } { \bool_set_true:N \l__nmc_sci_num_table_bool } } \tl_set:Nn \l__nmc_sci_num_out_tl { #1 } \bool_set_true:N \l__nmc_sci_num_out_bool \int_incr:N \l__nmc_num_alt_int } \cs_new_protected:Npn \__nmc_num_deep_output:N #1 { \bool_set_true:N \l__nmc_sci_num_out_bool \bool_set_false:N \l__nmc_sci_num_x_bool \bool_set_false:N \l__nmc_sci_num_table_bool \tl_set:Nn \l__nmc_sci_num_out_tl { e } \bool_set_false:N \l__nmc_pad_zeros_bool \int_zero:N \l__nmc_num_alt_int } %%%%%%%%%% % #1=fpify-ed in; #2=tl fmt'ed out; #3=int rnd; #4 sci bool \cs_new_protected:Npn \__nmc_num_format:nNnN #1#2#3#4 { \bool_if:NTF \l__nmc_TF_out_bool { \__nmc_num_bool_out:nNn { #1 } #2 { \l__nmc_num_alt_int } } { \bool_if:NTF #4 { \exp_last_unbraced:Nx \__nmc_sci_output_aux:wNn { \fp_to_scientific:n { #1 } } \q_stop #2 { #3 } } { \__nmc_num_format_decimal:nNn { #1 } #2 { #3 } } } } \cs_new_protected:Npn \__nmc_num_bool_out:nNn #1#2#3 { \fp_compare:nNnTF { 0 } = { #1 } { \tl_set:Nx #2 { \clist_item:nn {0,F,\texttt{F}} { #3 } } } { \tl_set:Nx #2 { \clist_item:nn {1,T,\texttt{T}} { #3 } } } } \cs_new_protected:Npn \__nmc_num_format_decimal:nNn #1#2#3 { \tl_set:Nx #2 { \fp_eval:n { 0 + round( #1, #3 ) } } \__nmc_error_fpflag: \bool_if:NF \g__nmc_error_bool { \int_set:Nn \l__nmc_num_sgn_int { \fp_sign:n { #2 } } \bool_lazy_and:nnT { \l__nmc_pad_zeros_bool } { \int_compare_p:nNn { #3 } > { 0 } } { \__nmc_num_pad:Nn #2 { #3 } } } } \cs_new_protected:Npn \__nmc_num_pad:Nn #1#2 { \tl_if_in:NnTF #1 { . } { \tl_set:Nx #1 { \__nmc_num_pad_aux:Vn #1 { #2 } } } { \tl_set:Nx #1 { \__nmc_num_pad_aux:Vn { #1.} { #2 } } } } \cs_new:Npn \__nmc_num_pad_aux:nn #1#2 { \__nmc_num_pad:wN #1\q_stop { #2 } } \cs_generate_variant:Nn \__nmc_num_pad_aux:nn { V } \cs_new:Npn \__nmc_num_pad:wN #1.#2\q_stop#3 { \int_if_zero:nTF { #3 } { #1 } { #1.#2\prg_replicate:nn { #3 - \tl_count:n { #2 } } { 0 } } } \cs_new_protected:Npn \__nmc_sci_output_aux:wNn #1e#2\q_stop#3#4 { % #1e#2=fp input; #3=formatted tl out; #4 = rounding \tl_set:Nx #3 { \fp_eval:n { 0 + round( #1, #4 ) } } \__nmc_error_fpflag: \bool_if:NF \g__nmc_error_bool { \int_set:Nn \l__nmc_sci_expon_int { #2 } \tl_if_eq:VnT #3 { 10 } { \int_incr:N \l__nmc_sci_expon_int \tl_set:Nn #3 { 1 } } \bool_if:NT \l__nmc_pad_zeros_bool { \__nmc_num_pad:Nn #3 { #4 } } \bool_lazy_or:nnT { !\int_if_zero_p:n { \l__nmc_sci_expon_int } } { \int_compare_p:nNn { \l__nmc_num_alt_int } > { 1 } } { \bool_if:NTF \l__nmc_sci_num_table_bool { \tl_put_left:Nx #3 { \__nmc_sci_num_table:n { #2 } } } { \tl_put_right:Nx #3 { \__nmc_sci_write:n { \int_use:N \l__nmc_sci_expon_int } } } } } \int_set:Nn \l__nmc_num_sgn_int { \fp_sign:n { #1 } } % tables } \cs_new:Npn \__nmc_sci_write:n #1 { % #1 exponent \int_compare:nNnTF { \l__nmc_depth_int } > { 2 } { e#1 } { \bool_if:NTF \l__nmc_sci_num_x_bool { \exp_not:N \times 10^{#1} } { \hbox:n { \l__nmc_sci_num_out_tl {#1} } } } } \cs_new:Npn \__nmc_sci_num_table:n #1 { (#1)\exp_not:n {\,} } % vv-list routines %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \cs_new_protected:Npn \__nmc_vv_extract_visible:nN #1#2 { % #2 reverses #1 \seq_clear:N \l__nmc_vv_visible_seq \clist_set:Nn \l_tmpa_clist { #1 } \mode_if_math:F { \__nmc_vv_remove_delims:N \l_tmpa_clist \tl_trim_spaces:N \l_tmpa_clist } \clist_clear:N #2 \clist_map_inline:Nn \l_tmpa_clist % to remove { } { \tl_if_head_is_group:nTF { ##1 } { \clist_put_left:Nx #2 { \tl_head:n { ##1 } \tl_tail:n { ##1 } } } { \seq_put_right:Nn \l__nmc_vv_visible_seq { ##1 } \clist_put_left:Nn #2 { ##1 } } } \__nmc_vv_subst_style: } \cs_new_protected:Npn \__nmc_vv_remove_delims:N #1 { \exp_args:Nx\str_case:nn { \tl_head:N #1 } { { $ } { \tl_remove_all:Nn #1 { $ } } { \( } { \tl_map_inline:nn {\(\)} { \tl_remove_once:Nn #1 { ##1 } } } { \[ } { \tl_map_inline:nn {\[\]} { \tl_remove_once:Nn #1 { ##1 } } } } } \cs_new_protected:Npn \__nmc_vv_subst_style: { \seq_if_empty:NTF \l__nmc_vv_visible_seq { \bool_set_true:N \l__nmc_vv_invisible_bool } { \tl_map_inline:nn { \l__nmc_vv_inline_tl \l__nmc_vv_display_tl } { \tl_replace_once:Nnx ##1 { vv } { \seq_use:Nn \l__nmc_vv_visible_seq { , } } } } } \cs_new_protected:Npn \__nmc_vv_digest:N #1 { \seq_set_from_clist:NN \l__nmc_vv_all_seq #1 \seq_concat:NNN \l__nmc_vv_all_seq \g__nmc_consts_vv_seq \l__nmc_vv_all_seq \bool_if:NT \l__nmc_multitok_bool { \__nmc_prep_multitok:NN \l__nmc_vv_all_seq \l_nmc_formula_tl } \__nmc_vv_get_vars_vals:NN \l__nmc_vv_all_seq \c_empty_prop } % #1(seq) vv-list;#2(prop) changed vars (implicit-mode) \cs_new_protected:Npn \__nmc_vv_get_vars_vals:NN #1#2 { \seq_set_eq:NN \l_tmpa_seq #1 \seq_clear:N \l__nmc_calc_fn_seq \seq_map_inline:Nn \l_tmpa_seq { \__nmc_vv_split_item:n { ##1 } \bool_if:NT \g__nmc_error_bool { \seq_map_break: } \__nmc_vv_record:NVN \l__nmc_eq_var_tl \l__nmc_eq_val_tl #2 \bool_if:NTF \g__nmc_error_bool { \seq_map_break: } { \seq_put_right:Nn \l__nmc_calc_fn_seq { ##1 } } } } \cs_new_protected:Npn \__nmc_vv_get_vars_vals_lims:NN #1#2 { % for summation, integration limits \__nmc_vv_split_item:V #1 \bool_if:NF \g__nmc_error_bool { \__nmc_vv_record:NVN \l__nmc_eq_var_tl \l__nmc_eq_val_tl #2 } } % changed `var=vals in prop #3 \cs_new_protected:Npn \__nmc_vv_record:NnN #1#2#3 { \prop_get:NVNF #3 #1 \l__nmc_vv_fp_expr_tl { \tl_clear:N \l__nmc_vv_fp_expr_tl \__nmc_fpify:nN { #2 } \l__nmc_vv_fp_expr_tl } \bool_if:nF { \l__nmc_vv_val_only_bool || \g__nmc_error_bool } { \__nmc_vv_write:VN #1 \l__nmc_vv_fp_expr_tl } } \cs_generate_variant:Nn \__nmc_vv_record:NnN { NV } % #1 = var; #2 = val as fp expr. \cs_new_protected:Npn \__nmc_vv_write:nN #1#2 { \tl_if_empty:NF #2 { \tl_if_eq:VnTF #2 { inf } { \prop_put:Nnn \l__nmc_subst_var_prop { #1 } { inf } } { \prop_put:Nnx \l__nmc_subst_var_prop { #1 } { \fp_to_tl:n {#2} } } \__nmc_error_fpflag: } } \cs_generate_variant:Nn \__nmc_vv_write:nN { V } \cs_new_protected:Npn \__nmc_vv_split_item:n #1 { \bool_set_false:N \l__nmc_vv_val_only_bool \tl_if_in:nnTF { #1 } { = } { \__nmc_split_eq:w #1\q_stop \tl_if_empty:NT \l__nmc_eq_val_tl { \__nmc_error_what:n { No~value~for~$\l__nmc_eq_var_tl$~in } } } { \bool_set_true:N \l__nmc_vv_val_only_bool \tl_set:Nn \l__nmc_eq_val_tl { #1 } } } \cs_generate_variant:Nn \__nmc_vv_split_item:n { V } \cs_new_protected:Npn \__nmc_split_eq:w #1=#2\q_stop { \tl_set:Nn \l__nmc_eq_var_tl { #1 } \tl_trim_spaces:N \l__nmc_eq_var_tl \tl_set:Nn \l__nmc_eq_val_tl { #2 } } % eval-specific routines %%%%%%%%%%%%%%%%%%%%%%%% \cs_gset_protected:Npn \__nmc_eval_initialize: { \tl_set:Nn \l__nmc_dbg_idiii_tl { formula } \tl_set:Nn \l__nmc_dbg_idv_tl { stored } } \cs_gset_protected:Npn \__nmc_eval_settings_digest: { \bool_set_true:N \l__nmc_allow_TF_out_bool } \cs_gset_eq:NN \__nmc_eval_vv_digest:N \__nmc_vv_digest:N \cs_gset_protected:Npn \__nmc_eval_process: { \__nmc_error_where:n { formula } \tl_clear:N \l__nmc_fp_expr_tl \__nmc_fpify:VN \l_nmc_formula_tl \l__nmc_fp_expr_tl \bool_if:NF \g__nmc_error_bool { \tl_set:Nx \l_nmc_result_tl { \fp_to_tl:n { \l__nmc_fp_expr_tl } } \__nmc_error_fpflag: } \int_if_zero:nF \l__nmc_dbg_int { \__nmc_dbg_get_data: } } \cs_gset_protected:Npn \__nmc_eval_display: { \__nmc_num_format:nNnN { \l_nmc_result_tl } \l_nmc_result_tl { \l__nmc_round_int } \l__nmc_sci_num_out_bool \tl_gset_eq:NN \g__nmc_reuse_tl \l_nmc_result_tl \bool_if:NF \l__nmc_num_only_bool { \tl_set:Nx \l_nmc_result_tl { \exp_not:o \l__nmc_math_delimi_tl \bool_if:NT \l__nmc_wraps_math_bool { \exp_not:o \l__nmc_formula_dup_tl \bool_if:NTF \l__nmc_TF_out_bool { \rightarrow } { = } } \exp_not:o \l_nmc_result_tl \bool_if:NTF \l__nmc_vv_multline_bool { \exp_not:o \l__nmc_vv_display_tl } { \bool_if:NF \l__nmc_vv_invisible_bool { \mathchoice{ \exp_not:o \l__nmc_vv_display_tl } { \exp_not:o \l__nmc_vv_inline_tl }{}{} } } \l__nmc_punc_tl \exp_not:o \l__nmc_math_delimii_tl } \int_if_zero:nT { \l__nmc_eval_reuse_int } { \tl_gset_eq:NN \g__nmc_reuse_tl \l_nmc_result_tl } } \l_nmc_result_tl } % fpify LaTeX math expr %%%%%%%%%%%%%%%%%%%%%%%%% \bool_new:N \l__nmc_insert_aster_bool \tl_new:N \l__nmc_subst_tl \tl_new:N \l__nmc_accum_tl \tl_new:N \l__nmc_arg_tl % unary functions \tl_new:N \l__nmc_fn_tl \tl_new:N \l__nmc_fn_arg_tl \tl_new:N \l__nmc_power_arg_tl \bool_new:N \l__nmc_hyperbolic_bool % factorial \fp_new:N \l__nmc_fact_fp \tl_new:N \l__nmc_fact_arg_tl % n-ary \int_new:N \l_tmpc_int \int_new:N \l_tmpd_int \bool_new:N \l__nmc_comma_nary_bool % sqrt \tl_new:N \l__nmc_ubrace_n_tl % binom \tl_new:N \l__nmc_binom_top_tl \tl_new:N \l__nmc_binom_bot_tl % sum/prod \tl_new:N \l__nmc_sum_var_tl \tl_new:N \l__nmc_summand_tl \tl_new:N \l__nmc_sum_op_tl \tl_new:N \l__nmc_sum_type_tl \tl_new:N \g__nmc_sum_A_tl \bool_new:N \l__nmc_sum_bool \int_new:N \l__nmc_sum_index_int \int_new:N \l__nmc_sum_end_int \int_new:N \l__nmc_sum_round_int \int_new:N \l__nmc_suma_int \int_new:N \l__nmc_sumb_int \fp_new:N \l__nmc_sum_total_fp \fp_new:N \l__nmc_sum_prev_fp \fp_new:N \l__nmc_sum_rounded_fp % #1 = latex expr #2 = fp-ified result \cs_new_protected:Npn \__nmc_fpify:nN #1#2 { \group_begin: \bool_set_false:N \l__nmc_superscript_bool \bool_set_false:N \l__nmc_insert_aster_bool \tl_clear:N \l__nmc_accum_tl \tl_clear:N \l__nmc_C_tl \tl_set:Nn \l__nmc_A_tl { #1\q_nil } \tl_if_empty:nT { #1 } { \__nmc_error_what:n { Empty~argument~to~fp-ify~in } } \bool_until_do:nn { \quark_if_nil_p:N \l__nmc_C_tl || \g__nmc_error_bool } { \tl_clear:N \l__nmc_arg_tl \__nmc_next: \prop_get:NVNTF \g__nmc_class_prop \l__nmc_B_tl \l_tmpb_tl { \exp_last_unbraced:NV \use_i:nn \l_tmpb_tl } { \__nmc_fpify_var: } } \exp_args:NNNV \group_end: \tl_put_right:Nn #2 \l__nmc_accum_tl } \cs_generate_variant:Nn \__nmc_fpify:nN { V } \cs_new_protected:Npn \__nmc_fpify_unknown: { \tl_if_in:nVTF { )]\}\rbrace } \l__nmc_B_tl { \__nmc_error_what:n { Unmatched~\__nmc_verb:V \l__nmc_B_tl{}~in } } { \__nmc_error_what:n { Unknown~token~\__nmc_verb:V \l__nmc_B_tl{}~in } } } % to avoid e.g. 34 instead of 3*4 \cs_new_protected:Npn \__nmc_insert_aster: { \bool_if:NT \l__nmc_insert_aster_bool { \tl_put_right:Nn \l__nmc_accum_tl { * } } } \cs_new_protected:Npn \__nmc_fpify_dec: { \__nmc_get_dec:NN \l__nmc_fact_arg_tl \c_false_bool \tl_if_eq:VnF \l__nmc_C_tl { ! } { \__nmc_insert_aster: \tl_put_right:NV \l__nmc_accum_tl \l__nmc_fact_arg_tl \bool_set_true:N \l__nmc_insert_aster_bool } } \cs_new_protected:Npn \__nmc_fpify_var: { % ( ) in case var < 0 raised to power \prop_get:NVNTF \l__nmc_subst_var_prop \l__nmc_B_tl \l__nmc_subst_tl { \tl_set_eq:NN \l__nmc_fact_arg_tl \l__nmc_subst_tl \tl_if_in:noF { ! } \l__nmc_C_tl { \__nmc_accum_fn_parenth:NNn \l__nmc_accum_tl \l__nmc_subst_tl {} \bool_set_true:N \l__nmc_insert_aster_bool } } { \__nmc_fpify_unknown: } } \cs_new_protected:Npn \__nmc_fpify_const: { % if const used as var \prop_get:NVNTF \l__nmc_subst_var_prop \l__nmc_B_tl \l__nmc_subst_tl { \__nmc_fpify_var: } { \prop_get:NVN \g__nmc_subst_fpfn_prop \l__nmc_B_tl \l__nmc_subst_tl \tl_if_eq:VnTF \l__nmc_C_tl { ! } { \tl_clear:N \l__nmc_fact_arg_tl } { \tl_put_right:NV \l__nmc_accum_tl \l__nmc_subst_tl } \bool_set_true:N \l__nmc_insert_aster_bool } } \cs_new_protected:Npn \__nmc_fpify_arith: { \tl_put_right:NV \l__nmc_accum_tl \l__nmc_B_tl \bool_set_false:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_slash: { \tl_put_right:NV \l__nmc_accum_tl \l__nmc_B_tl \__nmc_delim_arg:Nnn \l__nmc_arg_tl { 1 } { \c__nmc_uny_int } \__nmc_accum_fpify_parenth:NN \l__nmc_accum_tl \l__nmc_arg_tl \bool_set_true:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_arith_alt: { \prop_get:NVN \g__nmc_subst_fpfn_prop \l__nmc_B_tl \l__nmc_B_tl \tl_put_right:NV \l__nmc_accum_tl \l__nmc_B_tl \bool_set_false:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_comparison: { \tl_if_in:noTF { <=> } \l__nmc_C_tl { \__nmc_error_what:n { Multi-token~comparison~in } } { \prop_get:NVNF \g__nmc_subst_fpfn_prop \l__nmc_B_tl \l_tmpa_tl { \tl_set_eq:NN \l_tmpa_tl \l__nmc_B_tl } % < = > \__nmc_delim_arg:Nnn \l__nmc_arg_tl { 1 } { \c__nmc_cmp_int } \tl_clear:N \l_tmpb_tl \__nmc_fpify:VN \l__nmc_arg_tl \l_tmpb_tl \bool_if:NF \g__nmc_error_bool { \__nmc_accum_fn_parenth:NNn \l__nmc_accum_tl \l_tmpb_tl { - } \tl_set:Nx \l__nmc_accum_tl { round( \l__nmc_accum_tl, \int_use:N \l__nmc_round_int ) } \tl_put_right:NV \l__nmc_accum_tl \l_tmpa_tl \tl_put_right:Nn \l__nmc_accum_tl { 0 } } } } \cs_new_protected:Npn \__nmc_fpify_andor: { \prop_get:NVN \g__nmc_subst_fpfn_prop \l__nmc_B_tl \l_tmpa_tl \tl_put_right:NV \l__nmc_accum_tl \l_tmpa_tl \__nmc_delim_arg:Nnn \l__nmc_arg_tl { 1 } { \c__nmc_and_int } \tl_clear:N \l_tmpa_tl \__nmc_fpify:VN \l__nmc_arg_tl \l_tmpa_tl \tl_put_right:NV \l__nmc_accum_tl \l_tmpa_tl \bool_set_false:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_lparen: { \__nmc_get_arg_L:VN \l__nmc_B_tl \l__nmc_arg_tl \tl_set_eq:NN \l__nmc_fact_arg_tl \l__nmc_arg_tl \tl_if_eq:VnTF \l__nmc_C_tl { ! } { \bool_set_false:N \l__nmc_insert_aster_bool } { \__nmc_accum_fpify_parenth:NN \l__nmc_accum_tl \l__nmc_arg_tl \bool_set_true:N \l__nmc_insert_aster_bool } } \cs_new_protected:Npn \__nmc_fpify_lvert: { \tl_if_eq:VnTF \l__nmc_B_tl { | } { \tl_set:Nn \l__nmc_L_tl { \lvert } \__nmc_absval_arg:N \l__nmc_arg_tl \tl_set:Nn \l__nmc_R_tl { \rvert } } { \tl_set_eq:NN \l__nmc_L_tl \l__nmc_B_tl \__nmc_get_arg_L:VN \l__nmc_B_tl \l__nmc_arg_tl } \__nmc_fpify_lvert_aux: } \cs_new_protected:Npn \__nmc_fpify_lvert_aux: { \tl_if_eq:VnTF \l__nmc_C_tl { ! } { \tl_set:NV \l__nmc_fact_arg_tl \l__nmc_L_tl \tl_put_right:NV \l__nmc_fact_arg_tl \l__nmc_arg_tl \tl_put_right:NV \l__nmc_fact_arg_tl \l__nmc_R_tl } { \tl_clear:N \l_tmpa_tl \__nmc_fpify:VN \l__nmc_arg_tl \l_tmpa_tl \str_case:onF \l__nmc_L_tl { { \lvert } { \tl_put_right:Nn \l__nmc_accum_tl { abs( } } { \lceil } { \tl_put_right:Nn \l__nmc_accum_tl { ceil( } } { \lfloor } { \tl_put_right:Nn \l__nmc_accum_tl { floor( } } { | } { \tl_put_right:Nn \l__nmc_accum_tl { abs( } } { / } { \tl_put_right:Nn \l__nmc_accum_tl { / } } } { \tl_put_right:Nn \l__nmc_accum_tl { ( } } \tl_put_right:NV \l__nmc_accum_tl \l_tmpa_tl \tl_if_eq:VnF \l__nmc_R_tl { . } { \tl_put_right:Nn \l__nmc_accum_tl { ) } \bool_set_true:N \l__nmc_insert_aster_bool } } } \cs_new_protected:Npn \__nmc_fpify_lmod: { \tl_set_eq:NN \l__nmc_L_tl \l__nmc_B_tl \prop_get:NVN \g__nmc_subst_misc_prop \l__nmc_L_tl \l__nmc_R_tl \str_case:on \l__nmc_C_tl { { | } { \__nmc_fpify_lmod_abs:V \l__nmc_L_tl } { . } { \__nmc_fpify_lmod_aux:V \l__nmc_L_tl } { / } { \tl_put_right:Nn \l__nmc_accum_tl { / } \__nmc_fpify_lmod_aux:V \l__nmc_L_tl } } } \cs_new_protected:Npn \__nmc_fpify_lmod_abs:n #1 { \__nmc_next: \tl_put_right:Nn \l__nmc_accum_tl { abs( } \exp_args:NNNV\__nmc_get_arg_LR:NNN { #1 } \l__nmc_arg_tl \l__nmc_R_tl \__nmc_next: \tl_clear:N \l_tmpa_tl \__nmc_fpify:VN \l__nmc_arg_tl \l_tmpa_tl \tl_put_right:NV \l__nmc_accum_tl \l_tmpa_tl \tl_put_right:Nn \l__nmc_accum_tl { ) } \bool_set_true:N \l__nmc_insert_aster_bool } \cs_generate_variant:Nn \__nmc_fpify_lmod_abs:n { V } \cs_new_protected:Npn \__nmc_fpify_lmod_aux:n #1 { \__nmc_next: \exp_args:NNNV\__nmc_get_arg_LR:NNN #1 \l__nmc_arg_tl \l__nmc_R_tl \tl_if_eq:VnT \l__nmc_C_tl { . } { \__nmc_next: } \tl_clear:N \l_tmpa_tl \__nmc_fpify:VN \l__nmc_arg_tl \l_tmpa_tl \tl_put_right:NV \l__nmc_accum_tl \l_tmpa_tl \bool_set_true:N \l__nmc_insert_aster_bool } \cs_generate_variant:Nn \__nmc_fpify_lmod_aux:n { V } \cs_new_protected:Npn \__nmc_fpify_rmod: { \tl_if_eq:VnT \l__nmc_C_tl { . } { \__nmc_next: } } \cs_new_protected:Npn \__nmc_fpify_unary:n #1 { \tl_set:NV \l__nmc_fn_tl \l__nmc_B_tl \tl_if_eq:VnTF \l__nmc_C_tl { ^ } { \__nmc_fpify_unary_superscript: } { \prop_get:NVN \g__nmc_subst_fpfn_prop \l__nmc_fn_tl \l__nmc_fn_tl } \str_if_in:NnTF \l__nmc_fn_tl { h } { \bool_set_true:N \l__nmc_hyperbolic_bool } { \bool_set_false:N \l__nmc_hyperbolic_bool } % get fn arg \__nmc_delim_arg:Nnn \l__nmc_arg_tl { 1 } { #1 } \tl_clear:N \l__nmc_fn_arg_tl \__nmc_fpify:VN \l__nmc_arg_tl \l__nmc_fn_arg_tl \bool_if:NT \l__nmc_hyperbolic_bool { \tl_set:Nx \l__nmc_fn_tl { \__nmc_fpify_unary_hyperbolic:N \l__nmc_fn_arg_tl } } % append fn \bool_if:NTF \l__nmc_hyperbolic_bool { \tl_put_right:NV \l__nmc_accum_tl \l__nmc_fn_tl } { \__nmc_accum_fn_parenth:NNn \l__nmc_accum_tl \l__nmc_fn_arg_tl \l__nmc_fn_tl } \bool_if:NT \l__nmc_superscript_bool { % e.g. \sin^{2} \tl_put_right:Nn \l__nmc_accum_tl { ^ } \tl_put_right:NV \l__nmc_accum_tl \l__nmc_power_arg_tl \bool_set_false:N \l__nmc_superscript_bool } \bool_set_true:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_unary_superscript: { \__nmc_next: \tl_clear:N \l__nmc_power_arg_tl \__nmc_fpify_next_braced:N \l__nmc_power_arg_tl \tl_if_eq:VnTF \l__nmc_power_arg_tl { (-1) } { % inverse trig/hyp. function? \prop_get:NVNF \g__nmc_subst_misc_prop \l__nmc_fn_tl \l__nmc_fn_tl { \prop_get:NVN \g__nmc_subst_fpfn_prop \l__nmc_fn_tl \l__nmc_subst_tl \tl_concat:NNN \l__nmc_fn_tl a \l__nmc_subst_tl } } { % not inverse fn \prop_get:NVN \g__nmc_subst_fpfn_prop \l__nmc_fn_tl \l__nmc_fn_tl \bool_set_true:N \l__nmc_superscript_bool } } \cs_new:Npn \__nmc_fpify_unary_hyperbolic:N #1 { \str_case:on \l__nmc_fn_tl { { sinh } { ( 0.5( exp(#1)- exp(-(#1)) ) ) } { cosh } { ( 0.5( exp(#1) + exp(-(#1)) ) ) } { tanh } { ( (exp(2(#1))-1)/(exp(2(#1))+1) ) } { asinh } { ln( #1 + sqrt((#1)^2+1) ) } { acosh } { ln( #1 + sqrt((#1)^2-1) ) } { atanh } { ( 0.5 ln( (1+(#1))/(1-(#1)) ) ) } { csch } { 1/( 0.5( exp(#1)- exp(-(#1)) ) ) } { sech } { 1/( 0.5( exp(#1) + exp(-(#1)) ) ) } { coth } { ( (exp(2(#1))+1)/(exp(2(#1))-1) ) } { acsch } { ( ln(1/(#1)+sqrt(1/(#1)^2+1)) ) } { asech } { ( ln(1/(#1)+sqrt(1/(#1)^2-1)) ) } { acoth } { ( 0.5 ln( ((#1)+1)/((#1)-1) ) ) } } } \cs_new_protected:Npn \__nmc_fpify_power: { \tl_put_right:Nn \l__nmc_accum_tl { ^ } \__nmc_fpify_next_braced:N \l__nmc_accum_tl \bool_set_true:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_frac: { \tl_put_right:Nn \l__nmc_accum_tl { ( } \__nmc_fpify_next_braced:N \l__nmc_accum_tl \tl_put_right:Nn \l__nmc_accum_tl { / } \__nmc_fpify_next_braced:N \l__nmc_accum_tl \tl_put_right:Nn \l__nmc_accum_tl { ) } \bool_set_true:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_unarybrace: { \prop_get:NVN \g__nmc_subst_fpfn_prop \l__nmc_B_tl \l__nmc_subst_tl \tl_if_eq:VnT \l__nmc_C_tl { * } { \__nmc_next: } \tl_if_eq:VnTF \l__nmc_C_tl { [ } { % n-th root \tl_if_eq:VnTF \l__nmc_subst_tl { sqrt } { \__nmc_next: \__nmc_fpify_ubrace_n: } { \__nmc_next: \__nmc_next: \__nmc_next: \__nmc_fpify_ubrace_aux: } } { \__nmc_fpify_ubrace_aux: } \bool_set_true:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_ubrace_aux: { \tl_set_eq:NN \l_tmpa_tl \l__nmc_subst_tl \__nmc_fpify_next_braced:N \l_tmpa_tl \tl_if_eq:VnTF \l__nmc_C_tl { ! } { \__nmc_fpify_ubrace_fact: } { \tl_put_right:NV \l__nmc_accum_tl \l_tmpa_tl } } \cs_new_protected:Npn \__nmc_fpify_ubrace_n: { \__nmc_error_where:n { [~]~argument~of~\__nmc_verb:n { \sqrt } } \tl_clear:N \l__nmc_arg_tl \tl_clear:N \l__nmc_ubrace_n_tl \__nmc_get_arg_LR:NNN [ \l__nmc_arg_tl ] \__nmc_fpify:VN \l__nmc_arg_tl \l__nmc_ubrace_n_tl \__nmc_intify:Nn \l__nmc_ubrace_n_tl { 1 } \bool_if:NF \g__nmc_error_bool { \seq_gpop:NN \g__nmc_error_where_seq \l__nmc_toss_tl \__nmc_next: \tl_clear:N \l_tmpa_tl \__nmc_fpify:VN \l__nmc_B_tl \l_tmpa_tl \bool_if:nTF { \fp_compare_p:nNn { \l_tmpa_tl } < { 0 } && \int_if_even_p:n { \l__nmc_ubrace_n_tl } } { \flag_raise:n { fp_invalid_operation } \__nmc_error_fpflag: } { \tl_put_right:Nx \l__nmc_accum_tl { \__nmc_fpify_ubrace_n_aux:VV {\l_tmpa_tl}{ \l__nmc_ubrace_n_tl }} } } } \cs_new:Npn \__nmc_fpify_ubrace_n_aux:nn #1#2 { sign( #1 )( abs( #1 ) )^( 1/( #2 ) ) } \cs_generate_variant:Nn \__nmc_fpify_ubrace_n_aux:nn { VV } \cs_new_protected:Npn \__nmc_fpify_ubrace_fact: { \tl_if_eq:VnF \l__nmc_subst_tl { sqrt } { \str_case:onT \l__nmc_subst_tl { { abs } { \tl_set:Nn \l__nmc_fact_arg_tl { \abs } } { ceil } { \tl_set:Nn \l__nmc_fact_arg_tl { \ceil } } { floor} { \tl_set:Nn \l__nmc_fact_arg_tl { \floor } } } { \tl_put_right:Nx \l__nmc_fact_arg_tl { { \exp_not:o \l__nmc_B_tl } } } } } \cs_new_protected:Npn \__nmc_fpify_unarysub: { % e.g. \log_{10} \str_if_eq:VnTF \l__nmc_C_tl { _ } { \__nmc_next: \__nmc_next: \__nmc_fpify_unarysub:N \l__nmc_B_tl } { \__nmc_fpify_unarysub:N \l__nmc_log_base_tl } } \cs_new_protected:Npn \__nmc_fpify_unarysub:N #1 { \__nmc_fpify:VN #1 \l__nmc_arg_tl \bool_if:NF \g__nmc_error_bool { \fp_compare:nF { 0 < \l__nmc_arg_tl != 1 } { \__nmc_error_what:n { Valid~base~required~for~\__nmc_verb:n { \log }~in } } } \bool_if:NF \g__nmc_error_bool { \tl_set:Nx \l_tmpa_tl { \fp_eval:n { 1/(ln(\l__nmc_arg_tl)) } } \__nmc_error_fpflag: } \bool_if:NF \g__nmc_error_bool { \__nmc_accum_fn_parenth:NNn \l__nmc_accum_tl \l_tmpa_tl {} \tl_put_left:Nn \l__nmc_A_tl { \ln } } } \cs_new_protected:Npn \__nmc_fpify_surd: { \prop_get:NVN \g__nmc_subst_fpfn_prop \l__nmc_B_tl \l__nmc_subst_tl \tl_put_right:NV \l__nmc_accum_tl \l__nmc_subst_tl \tl_clear:N \l__nmc_arg_tl \__nmc_delim_arg:Nnn \l__nmc_arg_tl { 1 } { \c__nmc_srd_int } \__nmc_parenth:N \l__nmc_arg_tl \__nmc_fpify:VN \l__nmc_arg_tl \l__nmc_accum_tl \bool_set_true:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_fact: { \__nmc_error_where:n { factorial } \tl_clear:N \l_tmpa_tl \__nmc_fpify:VN \l__nmc_fact_arg_tl \l_tmpa_tl \tl_if_eq:VnTF \l__nmc_C_tl { ! } { \__nmc_fpify_fact_repeated: } { \__nmc_intify:Nn \l_tmpa_tl { 0 } \bool_if:NF \g__nmc_error_bool { \seq_gpop:NN \g__nmc_error_where_seq \l__nmc_toss_tl \__nmc_accum_fn_parenth:NNn \l__nmc_accum_tl \l_tmpa_tl { fact } } } \bool_set_true:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_fact_repeated: { \__nmc_intify:Nn \l_tmpa_tl { -1 } \bool_if:NF \g__nmc_error_bool { \seq_gpop:NN \g__nmc_error_where_seq \l__nmc_toss_tl \__nmc_fpify_double_fact:N \l_tmpa_tl \tl_set:Nx \l_tmpa_tl { \fp_use:N \l__nmc_fact_fp } \tl_if_eq:VnTF \l__nmc_C_tl { ! } { \tl_set_eq:NN \l__nmc_fact_arg_tl \l_tmpa_tl } { \__nmc_accum_fn_parenth:NNn \l__nmc_accum_tl \l_tmpa_tl {} } } } \cs_new_protected:Npn \__nmc_fpify_double_fact:N #1 { \__nmc_next: \int_compare:nNnTF { #1 } > { 0 } { \int_if_even:nTF { #1 } { \__nmc_fpify_fact_do:nNn { 2 } #1 { 2 } } { \__nmc_fpify_fact_do:nNn { 1 } #1 { 2 } } } { \fp_set:Nn \l__nmc_fact_fp { 1 } } } % multiply nos from #1 to #2, put in \l__nmc_fact_fp % #3 = 1 (!), = 2 (!!) \cs_new_protected:Npn \__nmc_fpify_fact_do:nNn #1#2#3 { \fp_set:Nn \l_tmpa_fp { #1 } \fp_set:Nn \l_tmpb_fp { #2 } \int_set:Nn \l_tmpb_int { #3 } \fp_set_eq:NN \l__nmc_fact_fp \l_tmpa_fp \fp_while_do:nNnn { \l_tmpa_fp } < { \l_tmpb_fp } { \fp_add:Nn \l_tmpa_fp { \l_tmpb_int } \fp_set:Nn \l__nmc_fact_fp { \l__nmc_fact_fp * \l_tmpa_fp } } } \cs_new_protected:Npn \__nmc_fpify_nary: { \bool_set_true:N \l__nmc_comma_nary_bool \str_case:on \l__nmc_B_tl { { \gcd } { \__nmc_fpify_nary_gcd: } { \max } { \__nmc_fpify_nary_maxmin: } { \min } { \__nmc_fpify_nary_maxmin: } } \bool_set_false:N \l__nmc_comma_nary_bool } \cs_new_protected:Npn \__nmc_fpify_nary_gcd: { \__nmc_insert_aster: \__nmc_delim_arg:Nnn \l__nmc_arg_tl { 1 } { \c_max_int } \tl_set:Nx \l__nmc_arg_tl { \tl_range:Nnn \l__nmc_arg_tl { 2 } { -2 } } \tl_clear:N \l_tmpa_tl \__nmc_fpify:VN \l__nmc_arg_tl \l_tmpa_tl \seq_set_split:NnV \l_tmpa_seq {,} \l_tmpa_tl % eval. 1st expr. \seq_pop:NN \l_tmpa_seq \l_tmpb_tl \int_set:Nn \l_tmpb_int { \fp_to_int:n \l_tmpb_tl } \seq_map_inline:Nn \l_tmpa_seq { \int_set:Nn \l_tmpd_int { \fp_to_int:n { ##1 } } \int_set:Nn \l_tmpa_int { \int_max:nn { \l_tmpd_int } { \l_tmpb_int } } \int_set:Nn \l_tmpb_int { \int_min:nn { \l_tmpd_int } { \l_tmpb_int } } \int_set:Nn \l_tmpc_int { \int_mod:nn { \l_tmpa_int } { \l_tmpb_int } } \int_until_do:nNnn { \l_tmpc_int } = { 0 } { \int_set_eq:NN \l_tmpa_int \l_tmpb_int \int_set_eq:NN \l_tmpb_int \l_tmpc_int \int_set:Nn \l_tmpc_int { \int_mod:nn { \l_tmpa_int } { \l_tmpb_int } } } } \tl_put_right:Nx \l__nmc_accum_tl { \int_use:N \l_tmpb_int } \bool_set_false:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_nary_maxmin: { \prop_get:NVN \g__nmc_subst_fpfn_prop \l__nmc_B_tl \l__nmc_subst_tl \__nmc_delim_arg:Nnn \l__nmc_arg_tl { 1 } { \c_max_int } \tl_clear:N \l_tmpa_tl \__nmc_fpify:VN \l__nmc_arg_tl \l_tmpa_tl % em-brace in case nested \tl_put_right:Nx \l__nmc_accum_tl { { \l__nmc_subst_tl \exp_not:o \l_tmpa_tl } } \bool_set_true:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_comma: { \tl_put_right:Nn \l__nmc_accum_tl { , } \bool_set_false:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_binom: { \__nmc_fpify_next_braced:N \l__nmc_binom_top_tl \__nmc_fpify_next_braced:N \l__nmc_binom_bot_tl \__nmc_error_where:n { 2nd~argument~of~\__nmc_verb:n { \binom } } \__nmc_intify:Nn \l__nmc_binom_bot_tl { 0 } \bool_if:NF \g__nmc_error_bool { \seq_gpop:NN \g__nmc_error_where_seq \l__nmc_toss_tl \__nmc_fpify_binom_calc:NN \l__nmc_binom_top_tl \l__nmc_binom_bot_tl } } \cs_new_protected:Npn \__nmc_fpify_binom_calc:NN #1 #2 { \tl_put_right:Nn \l__nmc_accum_tl { ( } \int_if_zero:nTF { #2 } { \tl_put_right:Nn \l__nmc_accum_tl { 1 } } { % calc. top \__nmc_fpify_binom_calc_do:nN { #1 - #2 + 1 } #1 \tl_put_right:Nn \l__nmc_accum_tl { / } \__nmc_fpify_binom_calc_do:nN { 1 } #2 % calc. bot. } \tl_put_right:Nn \l__nmc_accum_tl { ) } } \cs_new_protected:Npn \__nmc_fpify_binom_calc_do:nN #1 #2 { \__nmc_fpify_fact_do:nNn { #1 } #2 { 1 } \tl_put_right:Nx \l__nmc_accum_tl { \fp_use:N \l__nmc_fact_fp } } \cs_new_protected:Npn \__nmc_fpify_font: { \__nmc_next: \__nmc_accum_fpify_parenth:NN \l__nmc_accum_tl \l__nmc_B_tl } \cs_new_protected:Npn \__nmc_fpify_splitfrac: { \__nmc_next: \tl_set_eq:NN \l_tmpb_tl \l__nmc_B_tl \__nmc_next: \tl_put_right:NV \l_tmpb_tl \l__nmc_B_tl \__nmc_accum_fpify_parenth:NN \l__nmc_accum_tl \l_tmpb_tl } % \cs { m }, \cs { o m }, \cs { * m } \cs_new_protected:Npn \__nmc_fpify_absorb_m: { \__nmc_next: } \cs_new_protected:Npn \__nmc_fpify_absorb_om: { \str_if_eq:VnT \l__nmc_C_tl { [ } { \__nmc_next: \__nmc_get_arg_LR:NNN [ \l__nmc_toss_tl ] } \__nmc_next: } \cs_new_protected:Npn \__nmc_fpify_absorb_sm: { \str_if_eq:VnT \l__nmc_C_tl { * } { \__nmc_next: } \__nmc_next: } \cs_new_protected:Npn \__nmc_fpify_color: { \__nmc_fpify_absorb_om: \__nmc_fpify_next_braced:N \l__nmc_accum_tl \bool_set_true:N \l__nmc_insert_aster_bool } \cs_new_protected:Npn \__nmc_fpify_BE: { \__nmc_next: \tl_if_in:VnT \l__nmc_B_tl { alignat } { \__nmc_next: } } \cs_new_protected:Npn \__nmc_fpify_cmd: { \__nmc_insert_aster: \prop_get:NoNT \g__nmc_subst_misc_prop \l__nmc_B_tl \l_tmpa_tl { \exp_args:NV \__nmc_cmd:n \l_tmpa_tl \bool_set_false:N \l__nmc_insert_aster_bool \bool_set_false:N \l__nmc_wraps_math_bool } } \cs_new_protected:Npn \__nmc_cmd:n #1 { % \cm { s O m O O } \tl_set:Nn \l__nmc_delim_arg_tl { { #1 } } % cmd \tl_if_eq:VnT \l__nmc_C_tl { * } { \__nmc_next: } \bool_set_true:N \l__nmc_num_only_bool \__nmc_append_sqbrarg: % settings \__nmc_next: \tl_put_right:Nx \l__nmc_delim_arg_tl { { \exp_not:o \l__nmc_B_tl } } \__nmc_append_sqbrarg: % vv-list \__nmc_append_sqbrarg: % num format \tl_put_right:Nn \l__nmc_accum_tl { ( } \group_begin: \int_add:Nn \l__nmc_depth_int { 2 } \exp_last_unbraced:No \__nmc_inputs_get:nnnnn \l__nmc_delim_arg_tl \bool_if:NF \g__nmc_error_bool { \use:c { __nmc_#1_process: } } \exp_args:NNNV \group_end: \tl_put_right:Nn \l__nmc_accum_tl \l_nmc_result_tl \tl_put_right:Nn \l__nmc_accum_tl { ) } } \cs_new_protected:Npn \__nmc_append_sqbrarg: { \tl_if_eq:VnTF \l__nmc_C_tl { [ } { \__nmc_append_sqbrarg_aux: } { \tl_put_right:Nx \l__nmc_delim_arg_tl { {} } } } \cs_new_protected:Npn \__nmc_append_sqbrarg_aux: { \__nmc_next: \tl_clear:N \l_tmpa_tl \__nmc_get_arg_LR:NNN [ \l_tmpa_tl ] \tl_put_right:Nx \l__nmc_delim_arg_tl { { \exp_not:o \l_tmpa_tl } } } % sum/prod %%%%%%%%%%%%%%%%%% \cs_new_protected:Npn \__nmc_fpify_sum: { \__nmc_insert_aster: \group_begin: \tl_if_eq:VnTF \l__nmc_B_tl { \sum } { % sum \tl_set:Nn \l__nmc_sum_op_tl { + } \fp_zero:N \l__nmc_sum_total_fp \fp_set:Nn \l__nmc_sum_prev_fp { 1 } \tl_set:Nn \l__nmc_sum_type_tl { sum } \bool_set_true:N \l__nmc_sum_bool } { % product \tl_set:Nn \l__nmc_sum_op_tl { * } \fp_set:Nn \l__nmc_sum_total_fp { 1 } \fp_set:Nn \l__nmc_sum_prev_fp { 2 } \tl_set:Nn \l__nmc_sum_type_tl { prod } \bool_set_false:N \l__nmc_sum_bool } \__nmc_error_where:n { \l__nmc_sum_type_tl } \bool_if:NF \g__nmc_error_bool { \__nmc_error_where:n { \l__nmc_sum_type_tl~\ limits } \__nmc_sum_get_limits:NNN \l__nmc_sum_var_tl \l__nmc_sum_index_int \l__nmc_sum_end_int \seq_gpop:NN \g__nmc_error_where_seq \l__nmc_toss_tl } \bool_if:NTF \g__nmc_error_bool { \group_end: } { % get the summand/multiplicand \__nmc_delim_arg:Nnn \l__nmc_arg_tl { 1 } { \c__nmc_sum_int } \tl_if_eq:VnF \l__nmc_C_tl { ( } { \__nmc_parenth:N \l__nmc_arg_tl } \tl_set_eq:NN \l__nmc_summand_tl \l__nmc_arg_tl % do the sum/prod \__nmc_error_where:n { \l__nmc_sum_type_tl } \__nmc_sum_do:nn { \l__nmc_sum_index_int } { \l__nmc_sum_end_int } \tl_gset_eq:NN \g_tmpa_tl \l__nmc_A_tl \tl_gset_eq:NN \g_tmpb_tl \l__nmc_C_tl \exp_args:NNNV \group_end: \fp_set:Nn \l__nmc_sum_total_fp { \l__nmc_sum_total_fp } \tl_set_eq:NN \l__nmc_A_tl \g_tmpa_tl \tl_set_eq:NN \l__nmc_C_tl \g_tmpb_tl \tl_put_right:Nx \l__nmc_accum_tl { \fp_use:N \l__nmc_sum_total_fp } \bool_set_true:N \l__nmc_insert_aster_bool \seq_gpop:NN \g__nmc_error_where_seq \l__nmc_toss_tl } } \cs_new_protected:Npn \__nmc_sum_get_limits:NNN #1#2#3 { % #1 (tl) sum var #2, #3 (ints) lower, upper limits \str_if_eq:VnTF \l__nmc_C_tl { _ } { \__nmc_sum_limit_lower:NN #1#2 \bool_if:NF \g__nmc_error_bool { \__nmc_sum_limit_upper:N #3 } } { \__nmc_sum_limit_upper:N #3 \__nmc_sum_limit_lower:NN #1#2 } } \cs_new_protected:Npn \__nmc_sum_limit_lower:NN #1#2 { \__nmc_next: \__nmc_next: \bool_if:NT \l__nmc_multitok_bool { % may not be in vv-list \seq_clear:N \l_tmpc_seq \seq_push:NV \l_tmpc_seq \l__nmc_B_tl \__nmc_prep_multitok:NN \l_tmpc_seq \l__nmc_A_tl \seq_pop:NN \l_tmpc_seq \l__nmc_B_tl } \str_if_in:NnTF \l__nmc_B_tl { = } { \__nmc_vv_get_vars_vals_lims:NN \l__nmc_B_tl \c_empty_prop \tl_set_eq:NN #1 \l__nmc_eq_var_tl \__nmc_sum_limit_assign:NN #2 \l__nmc_vv_fp_expr_tl \seq_if_in:NVF \l__nmc_calc_fn_seq \l__nmc_B_tl { \seq_put_left:NV \l__nmc_calc_fn_seq \l__nmc_B_tl } } { \__nmc_error_what:n { No~\__nmc_verb:V \l__nmc_sum_type_tl\ variable~in } } } \cs_new_protected:Npn \__nmc_sum_limit_upper:N #1 { \__nmc_next: \__nmc_next: \__nmc_vv_get_vars_vals_lims:NN \l__nmc_B_tl \c_empty_prop \bool_if:NF \g__nmc_error_bool { \__nmc_sum_limit_assign:NN #1 \l__nmc_vv_fp_expr_tl } } \cs_new_protected:Npn \__nmc_sum_limit_assign:NN #1#2 { \tl_if_in:VnTF #2 { inf } { \int_set:Nn #1 { \fp_sign:n { #2 } * \c_max_int } } { \fp_compare:nNnTF { abs(#2) } > { \c_max_int } { \int_set:Nn #1 { \fp_sign:n { #2 } * \c_max_int } } { \__nmc_intify:Nn #2 { -inf } \bool_if:NF \g__nmc_error_bool { \int_set:Nn #1 { #2 } } } } } % #1#2 lower/upper limits (int); result in \l__nmc_sum_total_fp \cs_new_protected:Npn \__nmc_sum_do:nn #1#2 { \int_compare:nNnTF { \c_max_int } = { \int_max:nn { \int_abs:n { #1 } } { \int_abs:n { #2 } } } { \bool_if:NTF \l__nmc_sum_bool { \__nmc_sum_do_infinite:Nn #1 { sum } } { \__nmc_sum_do_infinite:Nn #1 { prod } } } { \int_step_function:nnnN { #1 } { 1 } { #2 } \__nmc_sum_eval:n } \bool_if:NF \g__nmc_error_bool { \int_compare:nNnT { #2 } < { #1 } { \tl_if_eq:VnTF \l__nmc_sum_op_tl { * } { \fp_set:Nn \l__nmc_sum_total_fp { 1 } } { \fp_set:Nn \l__nmc_sum_total_fp { 0 } } } } } \cs_set:Npn \__nmc_sum_do_infinite:Nn #1#2 { \int_set:Nn \l__nmc_sum_round_int { \l__nmc_round_int + \use:c { l__nmc_#2_extra_int } } \int_set:Nn \l__nmc_suma_int { #1 - 1 } % check loop \bool_do_while:nn { \l__nmc_sum_cont_bool } { % main loop \bool_set_false:N \l__nmc_sum_cont_bool \fp_until_do:nNnn { \l__nmc_sum_prev_fp } = { \l__nmc_sum_rounded_fp } { \int_incr:N \l__nmc_suma_int \fp_set_eq:NN \l__nmc_sum_prev_fp \l__nmc_sum_rounded_fp \__nmc_sum_eval:n { \l__nmc_suma_int } \fp_set:Nn \l__nmc_sum_rounded_fp { round( \l__nmc_sum_total_fp, \l__nmc_sum_round_int ) } } % query terms \int_set:Nn \l__nmc_sumb_int { \l__nmc_suma_int + \use:c { l__nmc_#2_query_int } } \int_while_do:nNnn { \l__nmc_suma_int } < { \l__nmc_sumb_int } { \int_incr:N \l__nmc_suma_int \__nmc_sum_query:n { \l__nmc_suma_int } } } \tl_gset:cx { g__nmc_info_\tl_range:Nnn \l__nmc_sum_type_tl{1}{4} _tl } { \int_eval:n { \l__nmc_suma_int - #1 - \use:c { l__nmc_#2_query_int } } } } \cs_new_protected:Npn \__nmc_sum_eval:n #1 { \__nmc_calc_fn_val:VNnN \l__nmc_sum_var_tl \l__nmc_summand_tl { #1 } \l_tmpb_fp \fp_set:Nn \l__nmc_sum_total_fp { \l__nmc_sum_total_fp \l__nmc_sum_op_tl \l_tmpb_fp } } \cs_new_protected:Npn \__nmc_sum_query:n #1 { \__nmc_sum_eval:n { #1 } \fp_set:Nn \l__nmc_sum_rounded_fp { round( \l__nmc_sum_total_fp, \l__nmc_sum_round_int ) } \fp_compare:nNnF { \l__nmc_sum_prev_fp } = { \l__nmc_sum_rounded_fp } { \bool_set_true:N \l__nmc_sum_cont_bool \int_set_eq:NN \l__nmc_sumb_int \l__nmc_suma_int } } % delimit math args %%%%%%%%%%%%%%%%%%% \tl_new:N \l__nmc_delim_arg_tl \tl_new:N \l__nmc_delim_argi_tl \int_new:N \l__nmc_delim_pas_int \int_new:N \l__nmc_delim_pos_int \bool_new:N \l__nmc_delim_stop_bool \bool_new:N \l__nmc_delim_lmod_bool \prg_new_conditional:Npnn \__nmc_if_pospas_gtr:nn #1#2 { p, TF } { \bool_if:nTF { \int_compare_p:nNn { \l__nmc_delim_pos_int } > { #1 } && \int_compare_p:nNn { \l__nmc_delim_pas_int } > { #2 } } { \prg_return_true: } { \prg_return_false: } } % #1 <-- \l__nmc_delim_arg_tl; % #2 (int) initial pos % #3 (int) parsing state \cs_new_protected:Npn \__nmc_delim_arg:Nnn #1#2#3 { \group_begin: \bool_set_false:N \__nmc_delim_stop_bool \bool_set_false:N \l__nmc_delim_lmod_bool \int_set:Nn \l__nmc_delim_pos_int { #2 } \int_set:Nn \l__nmc_delim_pas_int { #3 } \tl_clear:N \l__nmc_delim_arg_tl \bool_until_do:nn { \l__nmc_delim_stop_bool || \quark_if_nil_p:N \l__nmc_C_tl } { \prop_get:NVNTF \g__nmc_class_prop \l__nmc_C_tl \l__nmc_class_tl { \exp_last_unbraced:NV \use_ii:nn \l__nmc_class_tl } { \__nmc_delim_var: } \int_incr:N \l__nmc_delim_pos_int } \tl_gset_eq:NN \g_tmpa_tl \l__nmc_A_tl \tl_gset_eq:NN \g_tmpb_tl \l__nmc_delim_arg_tl \exp_args:NNNV \group_end: \tl_set:Nn \l__nmc_C_tl \l__nmc_C_tl \tl_set_eq:NN \l__nmc_A_tl \g_tmpa_tl \tl_set_eq:NN #1 \g_tmpb_tl } % delimit arg routines %%%%%%%%%%%%%%%% \cs_new_protected:Npn \__nmc_delim_stop: { \tl_if_eq:VnTF \l__nmc_C_tl { \q } { \bool_set_false:N \l__nmc_delim_stop_bool } { \bool_set_true:N \l__nmc_delim_stop_bool } } \cs_new_protected:Npn \__nmc_delim_stop_if_gtr:n #1 { \int_compare:nNnT { \l__nmc_delim_pas_int } > { #1 } { \__nmc_delim_stop: } } \cs_new_protected:Npn \__nmc_delim_append: { \__nmc_next: \tl_put_right:NV \l__nmc_delim_arg_tl \l__nmc_B_tl } \cs_new_protected:Npn \__nmc_delim_append_braced: { \__nmc_next: \tl_put_right:Nx \l__nmc_delim_arg_tl { { \exp_not:o\l__nmc_B_tl } } } \cs_new_protected:Npn \__nmc_delim_append_twobraced: { \__nmc_delim_append: \__nmc_delim_append_braced: \__nmc_delim_append_braced: } \cs_new_protected:Npn \__nmc_delim_append_sqbra: { \__nmc_next: \tl_clear:N \l_tmpa_tl \__nmc_get_arg_LR:NNN [ \l_tmpa_tl ] \__nmc_put_right_wrap:NnNn \l__nmc_delim_arg_tl { [ } \l_tmpa_tl { ] } } \cs_new_protected:Npn \__nmc_delim_dec: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_uny_int } { \__nmc_delim_stop: } { \__nmc_next: \__nmc_get_dec:NN \l_tmpa_tl \c_true_bool \tl_put_right:NV \l__nmc_delim_arg_tl \l_tmpa_tl } } \cs_new_protected:Npn \__nmc_delim_var: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_uny_int } { \__nmc_delim_stop: } { \__nmc_delim_append: } } \cs_new_protected:Npn \__nmc_delim_const: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_uny_int } { \__nmc_delim_stop: } { \__nmc_delim_append: } } \cs_new_protected:Npn \__nmc_delim_arith: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_sum_int } { \__nmc_delim_stop: } { \__nmc_delim_append: } } \cs_new_protected:Npn \__nmc_delim_pm: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_cmp_int } { \__nmc_delim_stop: } { \__nmc_delim_append: } } \cs_new_protected:Npn \__nmc_delim_comparison: { \int_compare:nNnT { \l__nmc_delim_pas_int } = { \c__nmc_cmp_int } { \tl_put_left:NV \l__nmc_A_tl \l__nmc_delim_arg_tl \tl_put_left:Nn \l__nmc_A_tl { \land } \tl_put_left:Nn \l__nmc_C_tl { \land } } \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_and_int } { \__nmc_delim_stop: } { \__nmc_delim_append: \__nmc_delim_arg:Nnn \l__nmc_delim_argi_tl { 1 } { \c__nmc_cmp_int } \tl_put_right:NV \l__nmc_delim_arg_tl \l__nmc_delim_argi_tl } } \cs_new_protected:Npn \__nmc_delim_andor: { \__nmc_delim_stop: } \cs_new_protected:Npn \__nmc_delim_lparen: { \bool_lazy_or:nnTF { \__nmc_if_pospas_gtr_p:nn { 1 } { \c__nmc_trg_int } } { \__nmc_if_pospas_gtr_p:nn { \l__nmc_posi_int } { \c__nmc_sum_int } } { \__nmc_delim_stop: } { \__nmc_next: \str_case:on \l__nmc_B_tl { { ( } { \__nmc_delim_lparen:nn { ( } { ) } } { [ } { \__nmc_delim_lparen:nn { [ } { ] } } { \{ } { \__nmc_delim_lparen:nn {\{ } {\} } } { \lparen } { \__nmc_delim_lparen:nn { \lparen } { \rparen } } { \lbrack } { \__nmc_delim_lparen:nn { \lbrack } { \rbrack } } { \lbrace } { \__nmc_delim_lparen:nn { \lbrace } { \rbrace } } } \__nmc_delim_lparen_auxi:n { \l__nmc_posi_int } } } \cs_new_protected:Npn \__nmc_delim_lparen:nn #1#2 { \tl_put_right:Nn \l__nmc_delim_arg_tl { ( } \__nmc_get_arg_LR:NNN #1 \l__nmc_delim_arg_tl #2 \bool_if:NT \l__nmc_delim_lmod_bool { \tl_set:Nx \l__nmc_delim_arg_tl { \tl_range:Nnn \l__nmc_delim_arg_tl { 1 } { -2 } } } \tl_put_right:Nn \l__nmc_delim_arg_tl { ) } \int_incr:N \l__nmc_delim_pos_int } \cs_generate_variant:Nn \__nmc_delim_lparen:nn { VV } \cs_new_protected:Npn \__nmc_delim_lparen_auxi:n #1 { % #1 is first pos. \int_compare:nNnTF { \l__nmc_delim_pas_int } = { \c__nmc_trg_int } { % +1 to prevent ( )( ) \__nmc_delim_arg:Nnn \l__nmc_delim_argi_tl { #1 + 1 } { \c__nmc_trg_int } } { \int_compare:nNnT { \l__nmc_delim_pas_int } = { \c__nmc_uny_int } { \__nmc_delim_arg:Nnn \l__nmc_delim_argi_tl { 2 } { \c__nmc_prn_int } } } \tl_put_right:NV \l__nmc_delim_arg_tl \l__nmc_delim_argi_tl \__nmc_delim_stop_if_gtr:n { \c__nmc_sum_int } } \cs_new_protected:Npn \__nmc_delim_rparen: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_cmp_int } { \__nmc_delim_stop: } { \__nmc_next: \tl_put_right:NV \l__nmc_delim_arg_tl \l__nmc_B_tl } } \cs_new_protected:Npn \__nmc_delim_lvert: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_sum_int } { \__nmc_delim_stop: } { \__nmc_next: \tl_put_right:NV \l__nmc_delim_arg_tl \l__nmc_B_tl \str_case:on \l__nmc_B_tl { { \lvert } { \__nmc_delim_lvert:nn { \lvert } { \rvert } } { \lceil } { \__nmc_delim_lvert:nn { \lceil } { \rceil } } { \lfloor } { \__nmc_delim_lvert:nn { \lfloor } { \rfloor } } { | } { \__nmc_absval_arg:N \l__nmc_delim_arg_tl \tl_put_right:Nn \l__nmc_delim_arg_tl { | } } } \__nmc_delim_lparen_auxi:n { 0 } } } \cs_new_protected:Npn \__nmc_delim_lvert:nn #1#2 { \__nmc_delim_lparen:nn { #1 } { #2 } \tl_put_right:Nn \l__nmc_delim_arg_tl { #2 } } \cs_new_protected:Npn \__nmc_delim_lmod: { \bool_lazy_and:nnT { \int_compare_p:nNn { \l__nmc_posi_int } < { 3 } } { \int_compare_p:nNn { \l__nmc_delim_pas_int } = { \l__nmc_trg_int } } { \int_incr:N \l__nmc_delim_pas_int } \__nmc_if_pospas_gtr:nnTF { \l__nmc_posi_int } { \l__nmc_trg_int } { \__nmc_delim_stop: } { \__nmc_next: \tl_if_in:nVTF { |./ } \l__nmc_C_tl { \prop_get:NVN \g__nmc_subst_misc_prop \l__nmc_B_tl \l_tmpb_tl \__nmc_delim_lparen:VV \l__nmc_B_tl \l_tmpb_tl \__nmc_next: \tl_put_right:NV \l__nmc_delim_arg_tl \l__nmc_B_tl \tl_if_eq:VnTF \l__nmc_C_tl { | } { \__nmc_delim_lparen_auxi:n { 0 } } { \__nmc_next: \tl_put_right:NV \l__nmc_delim_arg_tl \l__nmc_B_tl \__nmc_delim_stop: } } { \int_decr:N \l__nmc_delim_pos_int \bool_set_true:N \l__nmc_delim_lmod_bool } } } \cs_new_protected:Npn \__nmc_delim_unary:n #1 { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_sum_int } { \__nmc_delim_stop: } { \__nmc_delim_append: \tl_if_eq:VnT \l__nmc_C_tl { ^ } { \__nmc_delim_append: \__nmc_delim_append_braced: } \__nmc_delim_arg:Nnn \l__nmc_delim_argi_tl { 1 } { #1 } \tl_put_right:NV \l__nmc_delim_arg_tl \l__nmc_delim_argi_tl } } \cs_new_protected:Npn \__nmc_delim_power: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_prn_int } { \__nmc_delim_stop: } { \__nmc_delim_append: \__nmc_delim_append_braced: \__nmc_delim_stop_if_gtr:n { \c__nmc_sum_int } } } \cs_new_protected:Npn \__nmc_delim_tfrac: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_uny_int } { \__nmc_delim_stop: } { \__nmc_delim_append_twobraced: } } \cs_new_protected:Npn \__nmc_delim_frac: % also \(d)binom { \int_compare:nNnTF { \l__nmc_posi_int } = { 3 } { \__nmc_delim_tfrac: } { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_sum_int } { \__nmc_delim_stop: } { \__nmc_delim_append_twobraced: \__nmc_delim_stop_if_gtr:n { \c__nmc_sum_int } } } } \cs_new_protected:Npn \__nmc_delim_unarybrace: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_sum_int } { \__nmc_delim_stop: } { \__nmc_delim_append: \str_case:on \l__nmc_C_tl { { * } { \__nmc_delim_append: } { [ } { \__nmc_delim_append_sqbra: } } \__nmc_delim_append_braced: \__nmc_delim_arg:Nnn \l__nmc_delim_argi_tl { 2 } { \c__nmc_prn_int } \tl_put_right:NV \l__nmc_delim_arg_tl \l__nmc_delim_argi_tl \__nmc_delim_stop_if_gtr:n { \c__nmc_sum_int } } } \cs_new_protected:Npn \__nmc_delim_log: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_sum_int } { \__nmc_delim_stop: } { \__nmc_delim_append: \__nmc_delim_append: \__nmc_delim_append_braced: \__nmc_delim_arg:Nnn \l__nmc_delim_argi_tl { 1 } { \c__nmc_uny_int } \__nmc_accum_fn_parenth:NNn \l__nmc_delim_arg_tl \l__nmc_delim_argi_tl {} } } \cs_new_protected:Npn \__nmc_delim_surd: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_uny_int } { \__nmc_delim_stop: } { \__nmc_delim_append: \tl_clear:N \l__nmc_delim_argi_tl \tl_if_eq:VnT \l__nmc_B_tl { \prod } { \prg_replicate:nn { 2 } { \__nmc_delim_append: \__nmc_delim_append_braced: } } \__nmc_delim_arg:Nnn \l__nmc_delim_argi_tl { 1 } { \c__nmc_srd_int } \tl_put_right:NV \l__nmc_delim_arg_tl \l__nmc_delim_argi_tl \__nmc_delim_stop_if_gtr:n { \c__nmc_sum_int } } } \cs_new_protected:Npn \__nmc_delim_fact: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_prn_int } { \__nmc_delim_stop: } { \__nmc_delim_append: \tl_if_eq:VnT \l__nmc_C_tl { ! } { \__nmc_delim_append: } \__nmc_delim_stop_if_gtr:n { \c__nmc_sum_int } } } \cs_new_protected:Npn \__nmc_delim_cleave: { \__nmc_next: \tl_if_eq:VnTF \l__nmc_B_tl { \q } { \int_zero:N \l__nmc_delim_pos_int } % adhere { \bool_set_true:N \l__nmc_delim_stop_bool } % sever } \cs_new_protected:Npn \__nmc_delim_nary: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_sum_int } { \__nmc_delim_stop: } { \__nmc_delim_append: \__nmc_get_arg_LR:NNN ( \l__nmc_B_tl ) \__nmc_put_right_wrap:NnNn \l__nmc_delim_arg_tl { ( } \l__nmc_B_tl { ) } \__nmc_delim_stop_if_gtr:n { \c__nmc_sum_int } } } \cs_new_protected:Npn \__nmc_delim_comma: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_cmp_int } { \__nmc_delim_stop: } { \__nmc_delim_append: } } \cs_new_protected:Npn \__nmc_delim_sum: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_sum_int } { \__nmc_delim_stop: } { \__nmc_delim_append: \__nmc_delim_append: \__nmc_delim_append_braced: \__nmc_delim_append: \__nmc_delim_append_braced: \__nmc_delim_arg:Nnn \l__nmc_delim_argi_tl { 1 } { \c__nmc_sum_int } \tl_put_right:NV \l__nmc_delim_arg_tl \l__nmc_delim_argi_tl \__nmc_delim_stop_if_gtr:n { \c__nmc_cmp_int } } } \cs_new_protected:Npn \__nmc_delim_absorb: { \__nmc_next: \int_decr:N \l__nmc_delim_pos_int } \cs_new_protected:Npn \__nmc_delim_absorb_i: { \__nmc_delim_absorb: \__nmc_next: } \cs_new_protected:Npn \__nmc_delim_absorb_ii: { \__nmc_delim_absorb_i: \str_case:VnT \l__nmc_B_tl { { * } { } { [ } { \__nmc_get_arg_LR:NNN [ \l__nmc_toss_tl ] } } { \__nmc_next: } } \cs_new_protected:Npn \__nmc_delim_color: { \__nmc_next: \str_if_eq:VnT \l__nmc_C_tl { [ } { \__nmc_next: \__nmc_get_arg_LR:NNN [ \l__nmc_toss_tl ] } \__nmc_delim_font: } \cs_new_protected:Npn \__nmc_delim_font: { \__nmc_next: \__nmc_next: \tl_put_left:NV \l__nmc_A_tl \l__nmc_B_tl \tl_set:Nx \l__nmc_C_tl { \tl_head:N \l__nmc_B_tl } \int_decr:N \l__nmc_delim_pos_int } \cs_new_protected:Npn \__nmc_delim_BE: { \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_cmp_int } { \__nmc_delim_stop: } { \__nmc_next: \__nmc_next: \str_if_in:VnTF \l__nmc_B_tl { alignat } { \__nmc_next: } \tl_put_right:Nn \l__nmc_delim_arg_tl { \c_group_begin_token } \__nmc_get_arg_LR:NNN \begin \l__nmc_delim_arg_tl \end \tl_put_right:Nn \l__nmc_delim_arg_tl { \c_group_end_token } \__nmc_next: } } \cs_new_protected:Npn \__nmc_delim_cmd: { % \cmd { s O m O O } \__nmc_if_pospas_gtr:nnTF { 1 } { \c__nmc_sum_int } { \__nmc_delim_stop: } { \tl_put_right:NV \l__nmc_delim_arg_tl \l__nmc_C_tl \__nmc_next: \tl_if_eq:VnT \l__nmc_C_tl { * } { \__nmc_next: } \tl_put_right:Nn \l__nmc_delim_arg_tl { * } \__nmc_delim_nmcfn_aux:NN [ ] \__nmc_next: \tl_put_right:Nx \l__nmc_delim_arg_tl { { \exp_not:o \l__nmc_B_tl } } \__nmc_delim_nmcfn_aux:NN [ ] \__nmc_delim_nmcfn_aux:NN [ ] } } \cs_new_protected:Npn \__nmc_delim_nmcfn_aux:NN #1#2 { \tl_if_eq:VnT \l__nmc_C_tl { [ } { \__nmc_next: \tl_clear:N \l_tmpa_tl \__nmc_get_arg_LR:NNN #1 \l_tmpa_tl ] \__nmc_put_right_wrap:NnNn \l__nmc_delim_arg_tl { #1 } \l_tmpa_tl { #2 } } } %%%%%%%%% info on "infinite" processes %%%%%%%%%% \nmc_define:NnN \nmcInfo { info } \info \clist_map_inline:nn { sum,prod } { \tl_new:c { g__nmc_info_#1_tl } \tl_gset:cn { g__nmc_info_#1_tl } { 0 } } \clist_new:N \g__nmc_info_proc_clist \clist_gset:Nn \g__nmc_info_proc_clist { sum, prod } \cs_gset_protected:Npn \__nmc_info_initialize: { \seq_clear:N \l_tmpa_seq \tl_set:Nn \l__nmc_dbg_idii_tl { process } \clist_map_inline:Nn \g__nmc_info_proc_clist { \seq_put_right:Nx \l_tmpa_seq { ##1~{ \use:c { g__nmc_info_##1_tl } } } } \tl_set:Nx \l__nmc_dbg_vv_tl { \seq_use:Nn \l_tmpa_seq {,~} } } \cs_gset_protected:Npn \__nmc_info_process: { \tl_set_eq:Nc \l_nmc_result_tl { g__nmc_info_\l_nmc_formula_tl _tl } } \cs_gset_protected:Npn \__nmc_info_display: { \bool_if:NTF \l__nmc_num_only_bool { \l_nmc_result_tl } { \prop_if_in:NVTF \g__nmc_subst_misc_prop \l_nmc_formula_tl { \tl_if_empty:cT { g__nmc_info_\l_nmc_formula_tl _tl } { \tl_set:Nn \l_nmc_result_tl { 0 } } \tl_use:N \l_nmc_result_tl \prop_get:NVN \g__nmc_subst_misc_prop \l_nmc_formula_tl \l_tmpb_tl \ \l_tmpb_tl % pluralise? \int_if_zero:nF { \l_nmc_result_tl - 1 } { s } \seq_gpop:NN \g__nmc_error_where_seq \l__nmc_toss_tl } { \__nmc_error_where:n { \__nmc_verb:n {\nmcInfo}~command } \__nmc_error_what:n { Unknown~process~\__nmc_verb:V \l_nmc_formula_tl\ in } } } } %%%%%%%%%%%%% user-defined macros %%%%%%%%%%%%%%% \clist_new:N \g__nmc_macros_clist \bool_new:N \l__nmc_macros_free_bool \nmc_define:NnN \nmcMacros { macros } \macros \cs_gset_protected:Npn \__nmc_macros_initialize: { \tl_set:Nn \l__nmc_dbg_idiii_tl { macros } \tl_set:Nn \l__nmc_dbg_idv_tl { stored } } \cs_gset_protected:Npn \__nmc_macros_vv_digest:N #1 { \__nmc_error_where:n { \__nmc_verb:n { \nmcMacros }\ command } \clist_set:No \l_tmpa_clist \l_nmc_formula_tl \clist_clear:N \l_tmpb_clist \clist_map_inline:Nn \l_tmpa_clist { \cs_if_exist:NTF ##1 { \clist_put_right:Nx \l_tmpb_clist {\exp_not:N ##1 {~\exp_not:f ##1} } } { \__nmc_error_what:n { Undefined~macro~\__nmc_verb:n {##1}\ in } \clist_map_break: } } \bool_if:NF \g__nmc_error_bool { \tl_set:No \l_nmc_formula_tl \l_tmpb_clist \__nmc_vv_digest:N #1 \int_if_zero:nF \l__nmc_dbg_int { \__nmc_dbg_vv_view:n { 0 } } \clist_set:No \l_tmpb_clist \l_nmc_formula_tl } } \cs_gset_protected:Npn \__nmc_macros_process: { \bool_if:NTF \l__nmc_macros_free_bool { \__nmc_macros_deregister:N \l_tmpa_clist } { \__nmc_macros_register:N \l_tmpb_clist } \clist_gremove_duplicates:N \g__nmc_macros_clist \bool_if:NT \l__nmc_num_only_bool { \tl_set:Nx \l_nmc_result_tl { \int_eval:n { \clist_count:N \g__nmc_macros_clist } } } } \cs_gset:Npn \__nmc_macros_display: { \bool_if:NT \l__nmc_num_only_bool { \l_nmc_result_tl } } %%%%%%%%%% \cs_gset_protected:Npn \__nmc_macros_deregister:N #1 { \clist_if_empty:NT #1 { \clist_set_eq:NN #1 \g__nmc_macros_clist \tl_set:No \l_nmc_formula_tl \g__nmc_macros_clist } \clist_map_inline:Nn #1 { \cs_if_exist:NT ##1 { \clist_gremove_all:Nn \g__nmc_macros_clist { ##1 } \prop_gremove:NV \g__nmc_subst_var_prop { ##1 } } } \__nmc_macros_reg_dbg_aux:Nn \c_true_bool { freed } } \cs_gset_protected:Npn \__nmc_macros_register:N #1 { \__nmc_error_where:n { \__nmc_verb:n { \nmcMacros } } \clist_reverse:N #1 \clist_map_inline:Nn #1 { \__nmc_macros_reg_split:w ##1\q_stop \bool_if:NT \g__nmc_error_bool { \clist_map_break: } } \bool_if:NF \g__nmc_error_bool { \__nmc_macros_reg_props: } } \cs_new_protected:Npn \__nmc_macros_reg_split:w #1#2\q_stop { \tl_clear:N \l__nmc_vv_fp_expr_tl \__nmc_fpify:nN { #2 } \l__nmc_vv_fp_expr_tl \bool_if:NF \g__nmc_error_bool { \prop_put:Nnx \l__nmc_subst_var_prop { #1 } { \fp_eval:n \l__nmc_vv_fp_expr_tl } \__nmc_error_fpflag: } } \cs_new_protected:Npn \__nmc_macros_reg_props: { \clist_gconcat:NNN \g__nmc_macros_clist \l_tmpa_clist \g__nmc_macros_clist \clist_remove_duplicates:N \g__nmc_macros_clist \clist_map_inline:Nn \l_tmpa_clist { \prop_get:NnN \l__nmc_subst_var_prop { ##1 } \l_tmpa_tl \prop_gput:Nno \g__nmc_subst_var_prop { ##1 } \l_tmpa_tl } \seq_gpop:NN \g__nmc_error_where_seq \l__nmc_toss_tl \int_if_zero:nF { \l__nmc_dbg_int } { \__nmc_macros_reg_dbg: } } \cs_new_protected:Npn \__nmc_macros_reg_dbg: { \tl_if_empty:NTF \l_nmc_formula_tl { \__nmc_macros_reg_dbg_aux:Nn \c_true_bool { macros } \clist_clear:N \l_tmpb_clist \clist_map_inline:Nn \g__nmc_macros_clist { \clist_put_right:Nx \l_tmpb_clist { \exp_not:N ##1 {~\exp_not:f ##1} } } \tl_set:No \l_nmc_formula_tl \l_tmpb_clist } { \__nmc_macros_reg_dbg_aux:Nn \l__nmc_macros_free_bool { added } } } \cs_new_protected:Npn \__nmc_macros_reg_dbg_aux:Nn #1#2 { \tl_set:Nn \l__nmc_dbg_idiii_tl { #2 } \bool_if:NT #1 { \int_if_zero:nF { \l__nmc_dbg_int } { \int_set:Nn \l__nmc_dbg_int { 3*5 } } } \seq_set_from_clist:NN \l__nmc_dbg_stored_seq \g__nmc_macros_clist } %%%%%%%%%%%% user-defined constants %%%%%%%%%%%%% \seq_new:N \g__nmc_consts_seq % all \seq_new:N \g__nmc_consts_vv_seq % multitok in vv-list \int_new:N \g__nmc_consts_vv_int % count multitok + 1 \bool_new:N \l__nmc_consts_add_bool \nmc_define:NnN \nmcConstants { consts } \constants \cs_gset_protected:Npn \__nmc_consts_initialize: { \__nmc_error_where:n { \__nmc_verb:n { \nmcConstants } } \tl_set:Nn \l__nmc_dbg_idiii_tl { added } \tl_set:Nn \l__nmc_dbg_idv_tl { constants } } \cs_gset_protected:Npn \__nmc_consts_vv_digest:N #1 { % #1=*reversed* vv-list \bool_if:nT { !\l__nmc_consts_add_bool && !\tl_if_empty_p:N \l_nmc_formula_tl } { \__nmc_consts_clear: } \clist_set:NV \l_tmpa_clist \l_nmc_formula_tl \clist_reverse:N \l_tmpa_clist \clist_concat:NNN \l_tmpb_clist #1 \l_tmpa_clist \__nmc_vv_digest:N \l_tmpb_clist \clist_set:No \l_nmc_formula_tl \l_nmc_formula_tl \clist_reverse:N \l_nmc_formula_tl \int_if_zero:nF \l__nmc_dbg_int { \__nmc_dbg_vv_view:n { \clist_count:N \l_tmpa_clist } } } \cs_gset_protected:Npn \__nmc_consts_clear: { \seq_gclear:N \g__nmc_consts_vv_seq \seq_map_inline:Nn \g__nmc_consts_seq { \__nmc_split_eq:w ##1\q_stop \prop_gremove:NV \g__nmc_subst_var_prop \l__nmc_eq_var_tl } \seq_gclear:N \g__nmc_consts_seq } \cs_gset_protected:Npn \__nmc_consts_process: { \tl_if_empty:NF \l_nmc_formula_tl { \seq_set_from_clist:NN \l_tmpa_seq \l_nmc_formula_tl \seq_map_inline:Nn \l_tmpa_seq { \__nmc_split_eq:w ##1\q_stop \prop_get:NVN \l__nmc_subst_var_prop \l__nmc_eq_var_tl \l_tmpb_tl \clist_pop:NN \l_tmpa_clist \l_tmpa_tl \exp_last_unbraced:No\__nmc_split_eq:w \l_tmpa_tl\q_stop \int_compare:nNnTF { \tl_count:N \l__nmc_eq_var_tl } = { 1 } { \prop_gput:NVV \g__nmc_subst_var_prop \l__nmc_eq_var_tl \l_tmpb_tl \tl_put_right:Nn \l__nmc_eq_var_tl { = } \tl_put_right:NV \l__nmc_eq_var_tl \l_tmpb_tl } { \tl_put_right:Nn \l__nmc_eq_var_tl { = } \tl_set:Nx \l_tmpa_tl { \exp_not:o\l__nmc_eq_var_tl { \fp_eval:n \l_tmpb_tl } } \tl_put_right:NV \l__nmc_eq_var_tl \l_tmpb_tl \seq_gput_right:NV \g__nmc_consts_vv_seq \l_tmpa_tl } \seq_gput_right:NV \g__nmc_consts_seq \l__nmc_eq_var_tl } \int_gset:Nn \g__nmc_consts_vv_int { 1 + \seq_count:N \g__nmc_consts_vv_seq } } \bool_if:nT { (\tl_if_empty_p:N \l_nmc_formula_tl) && (\int_compare_p:nNn { \l__nmc_dbg_int } = { 30 }) } { \int_set:Nn \l__nmc_dbg_int { 5 } } \seq_set_eq:NN \l__nmc_dbg_stored_seq \g__nmc_consts_seq \bool_if:NT \l__nmc_num_only_bool { \tl_set:Nx \l_nmc_result_tl { \int_eval:n { \seq_count:N \g__nmc_consts_seq } } } } \cs_gset_protected:Npn \__nmc_consts_display: { \bool_if:NT \l__nmc_num_only_bool { \l_nmc_result_tl } } %%%%%%% save/retrieve results to/from file %%%%%% \tl_new:N \g__nmc_reuse_tl \tl_new:N \l__nmc_reuse_loaded_tl \bool_new:N \l__nmc_reuse_loaded_bool \int_new:N \l__nmc_reuse_mode_int \ior_new:N \g__nmc_ior \iow_new:N \g__nmc_iow \tl_gset:Nn \g__nmc_reuse_filename_tl { .nmc } \tl_gput_left:NV \g__nmc_reuse_filename_tl \jobname % save last \eval-uation to \#1 \nmc_define:NnN \nmcReuse { reuse } \reuse \cs_gset_protected:Npn \__nmc_reuse_settings_digest: { \tl_set:Nn \l__nmc_dbg_idii_tl { saved } \__nmc_reuse_load: } \cs_gset_protected:Npn \__nmc_reuse_process: { \__nmc_error_where:n { \__nmc_verb:n { \nmcReuse }~command } \tl_if_empty:NTF \l_nmc_formula_tl { \int_if_zero:nTF { 1 + \l__nmc_reuse_mode_int } { \__nmc_reuse_delete_all: } { \__nmc_reuse_load: } } { \__nmc_reuse_mode:Nn \l_nmc_formula_tl { \l__nmc_reuse_mode_int } } \bool_if:NT \l__nmc_num_only_bool { \tl_set:Nx \l_nmc_result_tl { \int_eval:n { \clist_count:N \l__nmc_reuse_loaded_tl } } } \__nmc_reuse_dbg_display:Nn \l_nmc_formula_tl { \l__nmc_dbg_int } } \cs_gset_protected:Npn \__nmc_reuse_display: { \bool_if:NT \l__nmc_num_only_bool { \l_nmc_result_tl } } %%%%%%%%%% \cs_new_protected:Npn \__nmc_reuse_load: { \bool_if:NF \l__nmc_reuse_loaded_bool { \file_get:VnNT \g__nmc_reuse_filename_tl {} \l_tmpa_tl { \clist_set:No \l__nmc_reuse_loaded_tl \l_tmpa_tl \bool_lazy_or:nnTF { \tl_if_blank_p:V \l__nmc_reuse_loaded_tl } { \tl_if_head_eq_meaning_p:VN \l__nmc_reuse_loaded_tl \par } { \tl_clear:N \l__nmc_reuse_loaded_tl } { \seq_set_split:NnV \l_tmpa_seq {,} \l__nmc_reuse_loaded_tl \seq_map_inline:Nn \l_tmpa_seq { \__nmc_reuse_write_props:Nn ##1 } } } \bool_set_true:N \l__nmc_reuse_loaded_bool } } \cs_new_protected:Npn \__nmc_reuse_mode:Nn #1#2 { \int_if_zero:nTF { 1 + #2 } % if #2=-1 { \__nmc_reuse_delete_one:c #1 } { \tl_if_empty:NTF \g__nmc_reuse_tl { \__nmc_error_what:n { No~result~available~for~\__nmc_verb:V #1\ in } } { \exp_args:NNc \tl_set:Nn \l_tmpa_tl #1 \prop_if_in:NVTF \g__nmc_subst_var_prop \l_tmpa_tl { \int_if_zero:nTF { #2 } { \__nmc_reuse_already_def:N \l_nmc_formula_tl } { \__nmc_reuse_delete_one:c #1 \__nmc_reuse_save:c #1 } } { \__nmc_reuse_save:c #1 } } } } \cs_new_protected:Npn \__nmc_reuse_dbg_display:Nn #1#2 { \bool_if:nTF { !\int_if_zero_p:n { #2 } && ( \int_if_zero_p:n { 1 + \l__nmc_reuse_mode_int } || \tl_if_empty_p:N #1 ) } { \tl_set:Nx \l__nmc_dbg_vv_tl { \clist_use:Nn \l__nmc_reuse_loaded_tl {,~} } } { \clist_pop:NN \l__nmc_reuse_loaded_tl \l__nmc_dbg_vv_tl } } \cs_new_protected:Npn \__nmc_reuse_save:N #1 { \__nmc_reuse_load: \tl_set:Nn \l_tmpb_tl { #1 } \tl_put_right:Nx \l_tmpb_tl { { \exp_not:o \g__nmc_reuse_tl } } \prop_get:NnNTF \l__nmc_subst_var_prop { #1 } \l_tmpa_tl { \exp_last_unbraced:NV\__nmc_reuse_defcmds:Nn \l_tmpb_tl } { \cs_if_exist:NTF #1 { \__nmc_reuse_already_def:N \l_nmc_formula_tl } { \exp_last_unbraced:NV\__nmc_reuse_defcmds:Nn \l_tmpb_tl } } } \cs_generate_variant:Nn \__nmc_reuse_save:N { c } \cs_new_protected:Npn \__nmc_reuse_defcmds:Nn #1#2 { \tl_set_rescan:Nnn #1 { \ExplSyntaxOn } { #2 } \__nmc_reuse_write_props:Nn #1{#2} \tl_if_empty:NF \l__nmc_reuse_loaded_tl { \__nmc_reuse_delete:N #1 } \clist_put_left:Nn \l__nmc_reuse_loaded_tl { #1 {#2} } \iow_open:NV \g__nmc_iow \g__nmc_reuse_filename_tl \str_set:NV \l_tmpa_str \l__nmc_reuse_loaded_tl \iow_now:NV \g__nmc_iow \l_tmpa_str \iow_close:N \g__nmc_iow } \cs_new_protected:Npn \__nmc_reuse_write_props:Nn #1#2 { \prop_gput:Nnn \g__nmc_subst_var_prop { #1 } { #2 } \tl_gset:Nn #1 { #2 } } \cs_new_protected:Npn \__nmc_reuse_delete:N #1 { \seq_clear:N \l_tmpb_seq \seq_set_split:NnV \l_tmpa_seq {,} \l__nmc_reuse_loaded_tl \seq_map_inline:Nn \l_tmpa_seq { \exp_args:No\str_if_eq:nnF { \use_i:nn ##1 } { #1 } { \seq_put_right:Nn \l_tmpb_seq { ##1 } } } \tl_set:Nx \l__nmc_reuse_loaded_tl { \seq_use:Nn \l_tmpb_seq {,} } } \cs_new_protected:Npn \__nmc_reuse_delete:Nn #1#2 { \prop_gremove:Nn \g__nmc_subst_var_prop { #1 } \cs_undefine:N #1 } \cs_new_protected:Npn \__nmc_reuse_delete_one:N #1 { \__nmc_reuse_load: \tl_if_empty:NF \l__nmc_reuse_loaded_tl { \__nmc_reuse_delete:N #1 } \__nmc_reuse_delete:Nn #1 {} \iow_open:NV \g__nmc_iow \g__nmc_reuse_filename_tl \iow_now:NV \g__nmc_iow \l__nmc_reuse_loaded_tl \iow_close:N \g__nmc_iow } \cs_generate_variant:Nn \__nmc_reuse_delete_one:N { c } \cs_new_protected:Npn \__nmc_reuse_delete_all: { \__nmc_reuse_load: \tl_if_empty:NF \l__nmc_reuse_loaded_tl { \seq_set_split:NnV \l_tmpa_seq {,} \l__nmc_reuse_loaded_tl \seq_map_inline:Nn \l_tmpa_seq { \__nmc_reuse_delete:Nn ##1 } \tl_clear:N \l__nmc_reuse_loaded_tl } \iow_open:NV \g__nmc_iow \g__nmc_reuse_filename_tl \iow_close:N \g__nmc_iow } \cs_new_protected:Npn \__nmc_reuse_already_def:N #1 { \__nmc_error_what:n { \__nmc_verb:c #1\ already~defined~in } } %%%%%%%%%%%%%%%%%%% settings %%%%%%%%%%%%%%%%%%%% \bool_new:N \l__nmc_multitok_bool \bool_new:N \l__nmc_vv_multline_bool \bool_new:N \l__nmc_deg_bool \tl_new:N \l__nmc_eqn_num_tl \int_new:N \l__nmc_posi_int \int_set:Nn \l__nmc_posi_int { 1 } \int_new:N \l__nmc_eval_reuse_int \int_new:N \l__nmc_dbg_int \cs_new_protected:Npn \__nmc_dbg_int:nn #1#2 { \int_set:Nn \l__nmc_dbg_int { \int_compare:nNnTF { \int_abs:n { #1 } } = { 1 } { \int_sign:n { #1 }*#2 } { #1 } } } \cs_new_protected:Npn \__nmc_set_trig_parsing:n #1 { % #1=1,2,3 \int_set:Nn \l__nmc_posi_int { #1 } \int_compare:nNnTF { #1 } > { 1 } { \int_set_eq:NN \l__nmc_trg_int \c__nmc_trg_int } % #1=2,3 { \int_set_eq:NN \l__nmc_trg_int \c__nmc_uny_int } % #1=1 } \cs_new:Npn \__nmc_int_to_bool:Nn #1#2 { \bool_set:Nn #1 { !\int_if_zero_p:n { #2 } } } \cs_new:Npn \__nmc_deg: { \bool_if:NT { \l__nmc_deg_bool } { d } } \keys_define:nn { numerica } { rounding .int_set:N = \l__nmc_round_int, pad .code:n = \__nmc_int_to_bool:Nn \l__nmc_pad_zeros_bool { #1 }, output-sci-notation .code:n = \__nmc_int_to_bool:Nn \l__nmc_sci_num_out_bool { #1 }, output-exponent-char .tl_set:N = \l__nmc_sci_num_out_tl, input-sci-notation .code:n = \__nmc_int_to_bool:Nn \l__nmc_sci_num_in_bool { #1 }, input-exponent-char .tl_set:N = \l__nmc_sci_num_in_tl, multitoken-variables .code:n = \__nmc_int_to_bool:Nn \l__nmc_multitok_bool { #1 }, use-degrees .code:n = \__nmc_int_to_bool:Nn \l__nmc_deg_bool { #1 }, logarithm-base .tl_set:N = \l__nmc_log_base_tl, intify-rounding .tl_set:N = \l__nmc_intify_round_tl, vv-display .tl_set:N = \l__nmc_vv_display_tl, vv-inline .tl_set:N = \l__nmc_vv_inline_tl, sum-extra-rounding .int_set:N = \l__nmc_sum_extra_int, sum-query-terms .int_set:N = \l__nmc_sum_query_int, prod-extra-rounding .int_set:N = \l__nmc_prod_extra_int, prod-query-terms .int_set:N = \l__nmc_prod_query_int, eval-reuse .int_set:N = \l__nmc_eval_reuse_int, % rounding .default:n = 6, pad .default:n = 0, output-sci-notation .default:n = 0, output-exponent-char .default:n = e, input-sci-notation .default:n = 0, input-exponent-char .default:n = e, multitoken-variables .default:n = 1, use-degrees .default:n = 0, logarithm-base .default:n = 10, intify-rounding .default:n = 14, vv-display .default:n = {,}\mskip 36mu minus 24mu(vv), vv-inline .default:n = {,}\mskip 12mu plus 6mu minus 9mu(vv), sum-extra-rounding .default:n = 2, sum-query-terms .default:n = 0, prod-extra-rounding .default:n = 2, prod-query-terms .default:n = 0, eval-reuse .default:n = 0, } \keys_set_known:nn { numerica } { rounding,pad,output-sci-notation,output-exponent-char, input-sci-notation,input-exponent-char,use-degrees, multitoken-variables,logarithm-base,intify-rounding, vv-display,vv-inline,sum-extra-rounding,sum-query-terms, prod-extra-rounding,prod-query-terms,eval-reuse } \keys_define:nn { numerica/generic } { dbg .code:n = \__nmc_dbg_int:nn { #1 } { 2*3*5*7 }, dbg .initial:n = 0, view .code:n = \__nmc_dbg_int:nn { 1 } { 2*3*5*7 }, ^ .code:n = \bool_set_true:N \l__nmc_sci_num_in_bool \tl_set:Nn \l__nmc_sci_num_in_tl { #1 }, xx .code:n = \__nmc_int_to_bool:Nn \l__nmc_multitok_bool { #1 }, () .code:n = \__nmc_set_trig_parsing:n { 2+\int_sign:n { #1-1 } }, () .initial:n = 0, o .code:n = \__nmc_int_to_bool:Nn \l__nmc_deg_bool { #1 }, o .default:n = 1, log .tl_set:N = \l__nmc_log_base_tl, vvmode .code:n = \__nmc_calc_mode:n { \int_sign:n { #1*#1 } }, vv@ .code:n = \__nmc_calc_mode:n { \int_sign:n { #1*#1 } }, vv@ .initial:n = 0, vvd .code:n = \tl_set:Nn \l__nmc_vv_display_tl { #1 } \tl_if_in:NnT \l__nmc_vv_display_tl { \\ } { \bool_set_true:N \l__nmc_vv_multline_bool }, vvi .tl_set:N = \l__nmc_vv_inline_tl, * .code:n = \tl_set:Nn \l__nmc_eqn_num_tl { * }, S+ .int_set:N = \l__nmc_sum_extra_int, S? .int_set:N = \l__nmc_sum_query_int, P+ .int_set:N = \l__nmc_prod_extra_int, P? .int_set:N = \l__nmc_prod_query_int, } \keys_define:nn { numerica/eval } { p .tl_set:N = \l__nmc_punc_tl, p .default:n = {,}, reuse .int_set:N = \l__nmc_eval_reuse_int } \keys_define:nn { numerica/info } { view .code:n = \__nmc_dbg_int:nn { 1 } { 2 } } \keys_define:nn { numerica/macros } { view .code:n = \__nmc_dbg_int:nn { 1 } { 2*3*5 }, free .code:n = \bool_set_true:N \l__nmc_macros_free_bool } \keys_define:nn { numerica/consts } { view .code:n = \__nmc_dbg_int:nn { 1 } { 2*3*5 }, add .code:n = \bool_set_true:N \l__nmc_consts_add_bool } \keys_define:nn { numerica/reuse } { view .code:n = \__nmc_dbg_int:nn { 1 } { 2 }, delete .code:n = \int_set:Nn \l__nmc_reuse_mode_int { -1 }, renew .code:n = \int_set:Nn \l__nmc_reuse_mode_int { 1 } } \file_if_exist:nT { numerica.cfg } { \file_get:nnN { numerica.cfg } {} \l_tmpa_tl \exp_args:NnV \keys_set_known:nn { numerica } \l_tmpa_tl } % end of file `numerica.sty'