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Diffstat (limited to 'Master/texmf-dist/source/latex-dev/l3kernel/l3fp-assign.dtx')
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diff --git a/Master/texmf-dist/source/latex-dev/l3kernel/l3fp-assign.dtx b/Master/texmf-dist/source/latex-dev/l3kernel/l3fp-assign.dtx new file mode 100644 index 00000000000..d54f0920858 --- /dev/null +++ b/Master/texmf-dist/source/latex-dev/l3kernel/l3fp-assign.dtx @@ -0,0 +1,316 @@ +% \iffalse meta-comment +% +%% File: l3fp-assign.dtx +% +% Copyright (C) 2011-2024 The LaTeX Project +% +% It may be distributed and/or modified under the conditions of the +% LaTeX Project Public License (LPPL), either version 1.3c of this +% license or (at your option) any later version. The latest version +% of this license is in the file +% +% https://www.latex-project.org/lppl.txt +% +% This file is part of the "l3kernel bundle" (The Work in LPPL) +% and all files in that bundle must be distributed together. +% +% ----------------------------------------------------------------------- +% +% The development version of the bundle can be found at +% +% https://github.com/latex3/latex3 +% +% for those people who are interested. +% +%<*driver> +\documentclass[full,kernel]{l3doc} +\begin{document} + \DocInput{\jobname.dtx} +\end{document} +%</driver> +% \fi +% +% \title{^^A +% The \pkg{l3fp-assign} module\\ +% Floating point expressions^^A +% } +% \author{^^A +% The \LaTeX{} Project\thanks +% {^^A +% E-mail: +% \href{mailto:latex-team@latex-project.org} +% {latex-team@latex-project.org}^^A +% }^^A +% } +% \date{Released 2024-04-11} +% \maketitle +% +% \begin{documentation} +% +% \end{documentation} +% +% \begin{implementation} +% +% \section{\pkg{l3fp-assign} implementation} +% +% \begin{macrocode} +%<*package> +% \end{macrocode} +% +% \begin{macrocode} +%<@@=fp> +% \end{macrocode} +% +% \subsection{Assigning values} +% +% \begin{macro}{\fp_new:N} +% Floating point variables are initialized to be $+0$. +% \begin{macrocode} +\cs_new_protected:Npn \fp_new:N #1 + { \cs_new_eq:NN #1 \c_zero_fp } +\cs_generate_variant:Nn \fp_new:N {c} +% \end{macrocode} +% \end{macro} +% +% \begin{macro} +% { +% \fp_set:Nn, \fp_set:cn, +% \fp_gset:Nn, \fp_gset:cn, +% \fp_const:Nn, \fp_const:cn +% } +% Simply use \cs{@@_parse:n} within various \texttt{f}-expanding +% assignments. +% \begin{macrocode} +\cs_new_protected:Npn \fp_set:Nn #1#2 + { \__kernel_tl_set:Nx #1 { \exp_not:f { \@@_parse:n {#2} } } } +\cs_new_protected:Npn \fp_gset:Nn #1#2 + { \__kernel_tl_gset:Nx #1 { \exp_not:f { \@@_parse:n {#2} } } } +\cs_new_protected:Npn \fp_const:Nn #1#2 + { \tl_const:Ne #1 { \exp_not:f { \@@_parse:n {#2} } } } +\cs_generate_variant:Nn \fp_set:Nn {c} +\cs_generate_variant:Nn \fp_gset:Nn {c} +\cs_generate_variant:Nn \fp_const:Nn {c} +% \end{macrocode} +% \end{macro} +% +% \begin{macro} +% { +% \fp_set_eq:NN , \fp_set_eq:cN , \fp_set_eq:Nc , \fp_set_eq:cc, +% \fp_gset_eq:NN, \fp_gset_eq:cN, \fp_gset_eq:Nc, \fp_gset_eq:cc +% } +% Copying a floating point is the same as copying the underlying token +% list. +% \begin{macrocode} +\cs_new_eq:NN \fp_set_eq:NN \tl_set_eq:NN +\cs_new_eq:NN \fp_gset_eq:NN \tl_gset_eq:NN +\cs_generate_variant:Nn \fp_set_eq:NN { c , Nc , cc } +\cs_generate_variant:Nn \fp_gset_eq:NN { c , Nc , cc } +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\fp_zero:N, \fp_zero:c, \fp_gzero:N, \fp_gzero:c} +% Setting a floating point to zero: copy \cs{c_zero_fp}. +% \begin{macrocode} +\cs_new_protected:Npn \fp_zero:N #1 { \fp_set_eq:NN #1 \c_zero_fp } +\cs_new_protected:Npn \fp_gzero:N #1 { \fp_gset_eq:NN #1 \c_zero_fp } +\cs_generate_variant:Nn \fp_zero:N { c } +\cs_generate_variant:Nn \fp_gzero:N { c } +% \end{macrocode} +% \end{macro} +% +% \begin{macro} +% {\fp_zero_new:N, \fp_zero_new:c, \fp_gzero_new:N, \fp_gzero_new:c} +% Set the floating point to zero, or define it if needed. +% \begin{macrocode} +\cs_new_protected:Npn \fp_zero_new:N #1 + { \fp_if_exist:NTF #1 { \fp_zero:N #1 } { \fp_new:N #1 } } +\cs_new_protected:Npn \fp_gzero_new:N #1 + { \fp_if_exist:NTF #1 { \fp_gzero:N #1 } { \fp_new:N #1 } } +\cs_generate_variant:Nn \fp_zero_new:N { c } +\cs_generate_variant:Nn \fp_gzero_new:N { c } +% \end{macrocode} +% \end{macro} +% +% \subsection{Updating values} +% +% These match the equivalent functions in \pkg{l3int} and \pkg{l3skip}. +% +% \begin{macro} +% { +% \fp_add:Nn, \fp_add:cn, \fp_gadd:Nn, \fp_gadd:cn, +% \fp_sub:Nn, \fp_sub:cn, \fp_gsub:Nn, \fp_gsub:cn, +% } +% \begin{macro}{\@@_add:NNNn} +% For the sake of error recovery we should not simply set |#1| to +% $|#1| \pm (|#2|)$: for instance, if |#2| is % ^^A( +% |0)+2|, the parsing error would be raised at the last closing +% parenthesis rather than at the closing parenthesis in the user +% argument. Thus we evaluate |#2| instead of just putting +% parentheses. As an optimization we use \cs{@@_parse:n} rather than +% \cs{fp_eval:n}, which would convert the result away from the +% internal representation and back. +% \begin{macrocode} +\cs_new_protected:Npn \fp_add:Nn { \@@_add:NNNn \fp_set:Nn + } +\cs_new_protected:Npn \fp_gadd:Nn { \@@_add:NNNn \fp_gset:Nn + } +\cs_new_protected:Npn \fp_sub:Nn { \@@_add:NNNn \fp_set:Nn - } +\cs_new_protected:Npn \fp_gsub:Nn { \@@_add:NNNn \fp_gset:Nn - } +\cs_new_protected:Npn \@@_add:NNNn #1#2#3#4 + { #1 #3 { #3 #2 \@@_parse:n {#4} } } +\cs_generate_variant:Nn \fp_add:Nn { c } +\cs_generate_variant:Nn \fp_gadd:Nn { c } +\cs_generate_variant:Nn \fp_sub:Nn { c } +\cs_generate_variant:Nn \fp_gsub:Nn { c } +% \end{macrocode} +% \end{macro} +% \end{macro} +% +% \subsection{Showing values} +% +% \begin{macro}{\fp_show:N, \fp_show:c, \fp_log:N, \fp_log:c, \@@_show:NN} +% This shows the result of computing its argument by +% passing the right data to \cs{tl_show:n} or \cs{tl_log:n}. +% \begin{macrocode} +\cs_new_protected:Npn \fp_show:N { \@@_show:NN \tl_show:n } +\cs_generate_variant:Nn \fp_show:N { c } +\cs_new_protected:Npn \fp_log:N { \@@_show:NN \tl_log:n } +\cs_generate_variant:Nn \fp_log:N { c } +\cs_new_protected:Npn \@@_show:NN #1#2 + { + \__kernel_chk_tl_type:NnnT #2 { fp } + { \exp_args:No \@@_show_validate:n #2 } + { \exp_args:Ne #1 { \token_to_str:N #2 = \fp_to_tl:N #2 } } + } +% \end{macrocode} +% \end{macro} +% +% \begin{macro}[EXP] +% { +% \@@_show_validate:n, \@@_show_validate_aux:n, \@@_show_validate:nn, +% } +% \begin{macro}[EXP] +% { +% \@@_show_validate:w, +% \@@_tuple_show_validate:w, +% \@@_symbolic_show_validate:w +% } +% To support symbolic expression, validation has to be done recursively. +% Two |\@@_show_validate:nn| wrappers are used to distinguish between +% initial and recursive calls, in which the former provides a demo of +% possible forms a |fp| variable would have. +% \begin{macrocode} +\cs_new:Npn \@@_show_validate:n #1 + { + \@@_show_validate:nn { #1 } + { + \s_@@ \@@_chk:w ??? ;~ or \iow_newline: + \s_@@_tuple \_@@_tuple_chk:w ? ;~ or \iow_newline: + \s_@@_symbolic \@@_symbolic_chk:w ? , ? ; + } + } +\cs_new:Npn \@@_show_validate_aux:n #1 + { + \@@_show_validate:nn { #1 } { } + } +\cs_new:Npn \@@_show_validate:nn #1#2 + { + \tl_if_empty:nF { #1 } + { + \str_case:enF { \tl_head:n { #1 } } + { + { \s_@@ } + { + \@@_show_validate:w #1 \s_@@ + \@@_chk:w ??? ; \s_@@_stop + } + { \s_@@_tuple } + { + \@@_tuple_show_validate:w #1 + \s_@@_tuple \_@@_tuple_chk:w ?? ; \s_@@_stop + } + { \s_@@_symbolic } + { + \@@_symbolic_show_validate:w #1 + \s_@@_symbolic \@@_symbolic_chk:w ? , ?? ; \s_@@_stop + } + } + { #2 } + } + } +\cs_new:Npn \@@_show_validate:w + #1 \s_@@ \@@_chk:w #2#3#4#5 ; #6 \s_@@_stop + { + \str_if_eq:nnF { #2 } {?} + { + \token_if_eq_meaning:NNTF #2 1 + { \s_@@ \@@_chk:w #2 #3 { #4 } #5 ; } + { \s_@@ \@@_chk:w #2 #3 #4 #5 ; } + \@@_show_validate_aux:n { #6 } + } + } +\cs_new:Npn \@@_tuple_show_validate:w + #1 \s_@@_tuple \_@@_tuple_chk:w #2#3 ; #4 \s_@@_stop + { + \str_if_eq:nnF { #2 } {?} + { \s_@@_tuple \@@_tuple_chk:w { \@@_show_validate_aux:n { #2 } } ; } + } +\cs_new:Npn \@@_symbolic_show_validate:w + #1 \s_@@_symbolic \@@_symbolic_chk:w #2 , #3#4 ; #5 \s_@@_stop + { + \str_if_eq:nnF { #2 } {?} + { + \s_@@_symbolic \@@_symbolic_chk:w \exp_not:n { #2 } , + { \@@_show_validate_aux:n { #3 } }; + \@@_show_validate_aux:n { #5 } + } + } +% \end{macrocode} +% \end{macro} +% \end{macro} +% +% \begin{macro}{\fp_show:n, \fp_log:n} +% Use general tools. +% \begin{macrocode} +\cs_new_protected:Npn \fp_show:n + { \__kernel_msg_show_eval:Nn \fp_to_tl:n } +\cs_new_protected:Npn \fp_log:n + { \__kernel_msg_log_eval:Nn \fp_to_tl:n } +% \end{macrocode} +% \end{macro} +% +% \subsection{Some useful constants and scratch variables} +% +% \begin{variable}{\c_one_fp, \c_e_fp} +% Some constants. +% \begin{macrocode} +\fp_const:Nn \c_e_fp { 2.718 2818 2845 9045 } +\fp_const:Nn \c_one_fp { 1 } +% \end{macrocode} +% \end{variable} +% +% \begin{variable}{\c_pi_fp, \c_one_degree_fp} +% We simply round $\pi$ to and $\pi/180$ to $16$ significant digits. +% \begin{macrocode} +\fp_const:Nn \c_pi_fp { 3.141 5926 5358 9793 } +\fp_const:Nn \c_one_degree_fp { 0.0 1745 3292 5199 4330 } +% \end{macrocode} +% \end{variable} +% +% \begin{variable}{\l_tmpa_fp, \l_tmpb_fp, \g_tmpa_fp, \g_tmpb_fp} +% Scratch variables are simply initialized there. +% \begin{macrocode} +\fp_new:N \l_tmpa_fp +\fp_new:N \l_tmpb_fp +\fp_new:N \g_tmpa_fp +\fp_new:N \g_tmpb_fp +% \end{macrocode} +% \end{variable} +% +% \begin{macrocode} +%</package> +% \end{macrocode} +% +% \end{implementation} +% +% \PrintChanges +% +% \PrintIndex |