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% File: pgfmath-xfp.dtx Copyright (C) 2021 Jonathan P. Spratte
%
% This work  may be  distributed and/or  modified under  the conditions  of the
% LaTeX Project Public License (LPPL),  either version 1.3c  of this license or
% (at your option) any later version.  The latest version of this license is in
% the file:
%
%   http://www.latex-project.org/lppl.txt
%
% ------------------------------------------------------------------------------
%
%&lt;*driver&gt;^^A&gt;&gt;=
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\preamble

--------------------------------------------------------------
pgfmath-xfp -- define pgfmath functions using xfp
E-mail: jspratte@yahoo.de
Released under the LaTeX Project Public License v1.3c or later
See http://www.latex-project.org/lppl.txt
--------------------------------------------------------------

Copyright (C) 2020-2021 Jonathan P. Spratte

This  work may be  distributed and/or  modified under  the conditions  of the
LaTeX Project Public License (LPPL),  either version 1.3c  of this license or
(at your option) any later version.  The latest version of this license is in
the file:

  http://www.latex-project.org/lppl.txt

This work is "maintained" (as per LPPL maintenance status) by
  Jonathan P. Spratte.

This work consists of the file  pgfmath-xfp.dtx
and the derived files           pgfmath-xfp.pdf
                                pgfmath-xfp.sty

\endpreamble
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\postamble
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\generate{\file{pgfmath-xfp.sty}{\from{pgfmath-xfp.dtx}{pkg}}}
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%
\IfFileExists{pgfmath-xfp.sty}{\RequirePackage{pgfmath-xfp}}{}
\ProvidesFile{pgfmath-xfp.dtx}
  [\csname pgfmxfpDate\endcsname\space define pgfmath functions using xfp]
\PassOptionsToPackage{full}{textcomp}
\documentclass{l3doc}
\RequirePackage{pgfplots}
\pgfplotsset{compat=1.18}
\RequirePackage[oldstylenums,nott]{kpfonts}
\input{glyphtounicode}
\pdfgentounicode=1
\RequirePackage{listings}
\RequirePackage{xcolor}
\RequirePackage{microtype}
\RequirePackage{accsupp}
\lstset
  {
    ,flexiblecolumns=false
    ,basewidth=.53em
    ,gobble=2
    ,basicstyle=\fontfamily{jkp}^^A\itshape
    ,morekeywords=^^A
      {^^A
      }
    ,morecomment=[l]\%
    ,commentstyle=\color[gray]{0.4}
    ,literate={\{}{{\CodeSymbol\{}}{1}
              {\}}{{\CodeSymbol\}}}{1}
    ^^A,literate=*{&lt;key&gt;}{\key}{4}{&lt;set&gt;}{\set}{4}
  }
\newcommand*\CodeSymbol[1]{\textbf{#1}}
\RequirePackage{randtext}
\let\metaORIG\meta
\protected\def\meta #1{\texttt{\metaORIG{#1}}}
\renewcommand*\thefootnote{\fnsymbol{footnote}}
\makeatletter
\definecolor{xfpred}{HTML}{9F393D}
\colorlet{pgfgray}{black!75}
\newcommand*\pgfmxfplogo
  {^^A
    \begingroup
      \rmfamily
      \bfseries
      {\color{pgfgray}\scshape pgfmath}^^A
      {\color{black}\textendash}^^A
      {\color{xfpred}xfp}^^A
    \endgroup
  }
\newcommand*\pgfmxfp
  {^^A
    \texorpdfstring
      {^^A
        \mbox
          {^^A
            \BeginAccSupp{ActualText=pgfmath-xfp}^^A
            \href{https://github.com/Skillmon/ltx_pgfmath-xfp}{\pgfmxfplogo}^^A
            \EndAccSupp{}^^A
          }^^A
      }
      {pgfmath-xfp}^^A
  }
\hypersetup{linkcolor=red!80!black,urlcolor=purple!80!black}
\DoNotIndex{}
\DoNotIndex{}
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^^A\@gobble\fi ^^A ignoring \ifx and \ifcsname, but only one \fi
\@ifdefinable\gobbledocstriptag{\def\gobbledocstriptag#1&gt;{}}
\makeatother
\begin{document}
  \title
    {^^A
      \texorpdfstring
        {^^A
          \huge\pgfmxfp
          \\[\medskipamount]
          \Large define \pkg{pgfmath} functions using \pkg{xfp}^^A
        }{pgfmath-xfp - define pgfmath functions using xfp}^^A
    }
  \date{\pgfmxfpDate\space v\pgfmxfpVersion}
  \author{Jonathan P. Spratte\thanks{\protect\randomize{jspratte@yahoo.de}}}
  \DocInput{pgfmath-xfp.dtx}
\end{document}
%&lt;/driver&gt;^^A=&lt;&lt;
% \fi
%
% \maketitle
% \renewcommand*\thefootnote{\arabic{footnote}}
%
% \begin{abstract}
% \noindent\parfillskip=0pt
% \pgfmxfp\ provides a small wrapper to define \pkg{pgfmath} functions which
% use the floating point unit of \pkg{expl3} (of which the document-level
% interface is called \pkg{xfp}).
% \end{abstract}
%
% \tableofcontents
%
% \begin{documentation}^^A&gt;&gt;=
%
% \section{Documentation}
%
% This package serves as a stopgap to allow the usage of \pkg{xfp} in
% \pkg{pgfmath} functions. It is only meant as a temporary fix to allow single
% functions using the \pkg{expl3} fpu until a more sophisticated solution to
% allow broader support for it in \textsc{pgf} is available.
%
% The defined functions should work correctly independent of the surrounding
% \pkg{pgfmath} context. This is achieved by first parsing the arguments via
% \cs{pgfmathsetmacro} with \textsc{pgf} settings applied locally to ensure
% that the resulting format is understandable by \pkg{xfp}'s fpu.
%
% Though it has both \pkg{pgfmath} and \pkg{xfp} in its name, it only loads
% \pkg{pgfmath} as a dependency, the access to \pkg{xfp}'s fpu is done at the
% \pkg{expl3} level.
%
% It was created as a result of two questions on
% \url{https://tex.stackexchange.com}:
% \href
%   {https://tex.stackexchange.com/q/597549/117050}
%   {expl3 cannot see declared functions}
% and
% \href
%   {https://tex.stackexchange.com/q/584887/117050}
%   {pgf: ���Dimension too large��� in a function which fits into a graph,
%     /pgf/fpu=true does not help}.
%
% \subsection{Document-Level Interface}
%
% \begin{function}{\pgfmxfpdeclarefunction}
%   \begin{syntax}
%     \cs{pgfmxfpdeclarefunction}\marg{name}\marg{arg-count}\oarg{process-args}\marg{fp-expression}
%   \end{syntax}
%   Define a \pkg{pgfmath} function named \meta{name} that takes
%   \meta{arg-count} arguments. The behaviour is different depending on whether
%   the optional argument was used or not.
%   \begin{description}
%     \item[If it isn't] the \meta{fp-expression} can refer to the
%       \meta{arg-count} arguments using |#1|, \emph{etc.}, and will get the
%       arguments just like they are given to the function (translated to a
%       format that \pkg{xfp} will understand by parsing them through
%       \pkg{pgfmath} once).
%     \item[If it is] use \meta{process-args} to specify any number of
%       processed arguments in a comma separated list. Inside this list you can
%       specify up to nine processed arguments using \pkg{pgfmath} functions in
%       which you can refer to the arguments passed to your new function using
%       |#1|, \emph{etc}.
%       You can refer to these processed arguments inside \meta{fp-expression}
%       using |#1|, \emph{etc}. A result of this rule is that you have to
%       explicitly use |#1| in \meta{process-args} to forward it unaltered to
%       the underlying \pkg{xfp} expression.
%   \end{description}
% \end{function}
%
% \subsection{Examples}
%
% The following are examples taken from the two questions responsible for this
% package.
%
% \begin{lstlisting}
% \pgfmxfpdeclarefunction{lognormal}{3}
%   {exp(-((ln(#1) - #2)^2) / (2 * (#3)^2)) / (#1 * #3 * sqrt(2 * pi))}
%
% \begin{tikzpicture}
% \begin{axis}[ domain=0.01:10, samples=100 ]
%   \addplot {lognormal(x,ln(5),0.2)};
% \end{axis}
% \end{tikzpicture}
% \end{lstlisting}
% \begin{minipage}{\linewidth}
% \pgfmxfpdeclarefunction{lognormal}{3}
%   {exp(-((ln(#1) - #2)^2) / (2 * (#3)^2)) / (#1 * #3 * sqrt(2 * pi))}
% \begin{tikzpicture}
% \begin{axis}[ domain=0.01:10, samples=100 ]
%   \addplot {lognormal(x,ln(5),0.2)};
% \end{axis}
% \end{tikzpicture}
% \end{minipage}
%
% Showing that a single \pkg{pgfmath} function argument can result in multiple
% arguments for the \pkg{xfp} expression. This example is suboptimal slow code,
% but could be educational.
%
% \begin{lstlisting}
% \pgfmxfpdeclarefunction{fplog}{1}{ln(#1)}
% \pgfmxfpdeclarefunction{nlogn}{1}[#1,fplog(#1)]{#1 * #2}
%
% \begin{tikzpicture}
%   \begin{axis}[ domain=0.01:10, samples=50 ]
%     \addplot {nlogn(x)};
%   \end{axis}
% \end{tikzpicture}
% \end{lstlisting}
% \begin{minipage}{\linewidth}
% \pgfmxfpdeclarefunction{fplog}{1}{ln(#1)}
% \pgfmxfpdeclarefunction{nlogn}{1}[#1,fplog(#1)]{#1 * #2}
% \begin{tikzpicture}
%   \begin{axis}[ domain=0.01:10, samples=50 ]
%     \addplot {nlogn(x)};
%   \end{axis}
% \end{tikzpicture}
% \end{minipage}
%
%
% \subsection{\pkg{expl3}-Level Interface}
%
% \begin{function}{\pgfmxfp_declare:nnn}
%   \begin{syntax}
%     \cs{pgfmxfp_declare:nnn} \marg{name} \marg{arg-count} \marg{fp-expression}
%   \end{syntax}
%   Defines a \pkg{pgfmath} function named \meta{name}, that takes
%   \marg{arg-count} arguments. The function will evaluate the
%   \meta{fp-expression} using the \pkg{l3fp} fpu and store the result for
%   \pkg{pgfmath}. The arguments can be referred using |#1|, \emph{etc}.
% \end{function}
%
% \begin{function}{\pgfmxfp_declare_processed_args:nnnn}
%   \begin{syntax}
%     \cs{pgfmxfp_declare_processed_args:nnnn} \marg{name} \marg{arg-count} \marg{processed-args} \marg{fp-expression}
%   \end{syntax}
%   Defines a \pkg{pgfmath} function named \meta{name}, that takes
%   \marg{arg-count} arguments. The arguments will be evaluated through
%   \pkg{pgfmath} according to the comma separated list of
%   \meta{processed-args} (in which you can refer to the arguments using |#1|,
%   \emph{etc.}) and the results of which will be the arguments for the
%   \meta{fp-expression} (in which you can refer to the \meta{processed-args}
%   using |#1|, \emph{etc.}).
% \end{function}
%
% \end{documentation}^^A=&lt;&lt;
%
% \begin{implementation}^^A&gt;&gt;=
%
% \clearpage
%
% \section{Implementation}^^A&gt;&gt;=
%
% \gobbledocstriptag
%&lt;*pkg&gt;
% \gobbledocstriptag
%&lt;@@=pgfmxfp&gt;
%
% \subsection{General Package code}
%
% Some code for versioning support might not be available in older \LaTeXe{}
% releases.
%    \begin{macrocode}
\providecommand\DeclareRelease[3]{}
\providecommand\DeclareCurrentRelease[2]{}
%    \end{macrocode}
% Use these rollback functions to declare the current release.
%    \begin{macrocode}
\DeclareCurrentRelease{}{2021-05-19}
%    \end{macrocode}
%
% Make sure \pkg{expl3} is available and load \pkg{pgfmath} and the \textsc{pgf}
% fpu.
%    \begin{macrocode}
\@ifundefined{ExplFileDate}
  {\RequirePackage{expl3}}
  {}
\RequirePackage{pgfmath}
\usepgflibrary{fpu}
%    \end{macrocode}
%
% \begin{macro}{\pgfmxfpDate, \pgfmxfpVersion}
%   Store version and date in a macro.
%    \begin{macrocode}
\newcommand*\pgfmxfpDate{2021-05-19}
\newcommand*\pgfmxfpVersion{1.0}
%    \end{macrocode}
% \end{macro}
%
% Provide the package.
%    \begin{macrocode}
\ProvidesExplPackage
  {pgfmath-xfp}     {\pgfmxfpDate}
  {\pgfmxfpVersion} {define pgfmath functions using xfp}
%    \end{macrocode}
%
% \subsection{Document-Level Interface}
%
% \begin{macro}{\pgfmxfpdeclarefunction}
%   The document-level interface decides which of the two allocator functions
%   are used.
%    \begin{macrocode}
\NewDocumentCommand \pgfmxfpdeclarefunction { m m o m }
  {
    \IfValueTF {#3}
      { \pgfmxfp_declare_processed_args:nnnn {#1} {#2} {#3} }
      { \pgfmxfp_declare:nnn {#1} {#2} }
      {#4}
  }
%    \end{macrocode}
% \end{macro}
%
% \subsection{\pkg{expl3}-Level Interface}
%
% \begin{macro}{\pgfmxfp_declare:nnn}
%   Start building the function body. First step is to initialize it with the
%   common code. Then we add to the function body the input parsing step. For
%   this we use a loop that will place
%   \cs{pgfmathsetmacro} \meta{tmp-cs_i} |{#|\meta{i}|}|
%   in the function body.
%   Afterwards we do the real definitions. This strange construct is used to
%   normalize the input. Depending on the context in which these functions are
%   used, the arguments might be in the internal format of \textsc{pgf}'s
%   \pkg{fpu}-library or something else that \pkg{l3fp} will not understand.
%   The \cs{pgfmathsetmacro} calls will be done in a local context in which
%   \textsc{pgf}'s \pkg{fpu}-library will be activated and set up to output in
%   a format \pkg{l3fp} understands.
%    \begin{macrocode}
\cs_new_protected:Npn \pgfmxfp_declare:nnn #1#2#3
  {
    \@@_initialize_body:
    \int_step_inline:nn {#2}
      {
        \tl_put_right:Nx \l_@@_function_body_tl
          {
            \exp_not:n { \pgfmathsetmacro } \exp_not:c { @@_arg##1 }
              { \exp_not:n {####} ##1 }
          }
      }
    \@@_define_function:nnnn {#2} {#1} {#2} {#3}
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\pgfmxfp_declare_processed_args:nnnn}
%   This works mostly like \cs{pgfmxfp_declare:nnn}, but instead of
%   using an \cs{int_step_inline:nn}-loop this uses \cs{clist_map_inline:nn} to
%   map over the processed arguments. Those will be stored in the function body
%   as 
%   \cs{pgfmathsetmacro} \meta{tmp-cs_i} |{|\meta{expr_i}|}|.
%    \begin{macrocode}
\cs_new_protected:Npn \pgfmxfp_declare_processed_args:nnnn #1#2#3#4
  {
    \@@_initialize_body:
    \int_zero:N \l_@@_args_int
    \clist_map_inline:nn {#3}
      {
        \int_incr:N \l_@@_args_int
        \tl_put_right:Nx \l_@@_function_body_tl
          {
            \exp_not:n { \pgfmathsetmacro }
              \exp_not:c { @@_arg \int_use:N \l_@@_args_int }
              { \exp_not:n {##1} }
          }
      }
    \exp_args:NV \@@_define_function:nnnn \l_@@_args_int {#1} {#2} {#4}
  }
%    \end{macrocode}
% \end{macro}
%
% \subsection{Internals}
%
% \begin{variable}{\l_@@_function_body_tl}
%   This token list will be used to build the function's top-level definition.
%    \begin{macrocode}
\tl_new:N \l_@@_function_body_tl
%    \end{macrocode}
% \end{variable}
%
% \begin{variable}{\l_@@_args_int}
%   In the case of \cs{pgfmxfp_declare_processed_args:nnnn} we'll have
%   to count how many arguments the auxiliary function will take. 
%    \begin{macrocode}
\int_new:N \l_@@_args_int
%    \end{macrocode}
% \end{variable}
%
% 
% \begin{macro}{\@@_initialize_body:}
%   Each function will have the same start setting up \textsc{pgf}'s \pkg{fpu}.
%    \begin{macrocode}
\cs_new_protected:Npn \@@_initialize_body:
  {
    \tl_set:Nn \l_@@_function_body_tl
      {
        \group_begin:
        \pgfkeys{/pgf/fpu=true, /pgf/fpu/output~format=sci}%
      }
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@@_define_function:nnnn, \@@_define_function_aux:n}
%   First we define the internal function. Then add to the function body some
%   code that'll use \cs{use:x} to expand the temporary macros that store the
%   input arguments and forward the results to the internal function.
%    \begin{macrocode}
\cs_new_protected:Npn \@@_define_function:nnnn #1#2#3#4
  {
    \@@_define_internal_function:nnn {#1} {#2} {#4}
    \tl_put_right:Nx \l_@@_function_body_tl
      {
        \use:x
          { 
            \exp_not:c { @@_function_ #2 _cmd }
            \int_step_function:nN {#1} \@@_define_function_aux:n
          }
      }
    \exp_args:Nnno
    \pgfmathdeclarefunction {#2} {#3} \l_@@_function_body_tl
  }
%    \end{macrocode}
%   The auxiliary is just used to build the temporary macro names and prevent
%   them from further expansion.
%    \begin{macrocode}
\cs_new:Npn \@@_define_function_aux:n #1 { { \exp_not:c { @@_arg#1 } } }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}
%   {\@@_define_internal_function:nnn, \@@_define_internal_function_aux:n}
%   The internal function is pretty straight forward, the only difficult part
%   is building the parameter list. For that we use some simple loop, a slow
%   but simplistic solution.
%    \begin{macrocode}
\cs_new_protected:Npn \@@_define_internal_function:nnn #1#2#3
  {
    \exp_last_unbraced:Nx
    \cs_set_protected:cpn
      {
        { @@_function_ #2 _cmd }
        \int_step_function:nN {#1} \@@_define_internal_function_aux:n
      }
      { \group_end: \exp_args:Nf \pgfmathparse { \fp_eval:n {#3} } }
  }
\cs_new:Npn \@@_define_internal_function_aux:n #1 { \exp_not:n {## #1} }
%    \end{macrocode}
% \end{macro}
\ExplSyntaxOff
%^^A=&lt;&lt;
%
% \end{implementation}^^A=&lt;&lt;
%
% \clearpage
% \PrintIndex
%
\endinput
%
^^A vim: ft=tex fdm=marker fmr=&gt;&gt;=,=&lt;&lt;
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