\pgfmathdeclarefunction and LuaLaTeX

Question

Is it possible to use LuaLaTeX in \pgfmathdeclarefunction?

I tried with sinh which seems to work in pgfmathsetmacro but not in \pgfmathparse and pgfplots. How should I declare a pgf function with Lua correctly?

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}

\makeatletter
\pgfmathdeclarefunction{luasinh}{1}{%
    \begingroup
        \edef\pgfmath@arg{#1}%
        \directlua{tex.setdimen("pgfmath@x", math.sinh(\pgfmath@arg) .. "pt")}%
        \pgfmath@returnone\pgfmath@x%
    \endgroup
}%
\makeatother


\begin{document}

\noindent
Lua: \pgfmathsetmacro\luasinh{luasinh(1)}\luasinh\\
PGF: \pgfmathsetmacro\pgfsinh{sinh(1)}\pgfsinh\\

\begin{tikzpicture}
    \begin{axis}
        \addplot {sinh(x)};
        %\addplot {luasinh(x)}; does not work
    \end{axis}
\end{tikzpicture}

\end{document}

I think being able to use Lua in LuaLaTeX when declaring pgf functions could be useful. For example, this question "Erf function in LaTeX" could maybe be answered without calling Gnuplot but simply call math.erf (if this exists?) in \directlua.

The problem is that pgfplots uses its own internal number format. Put \typeout{#1} into the luasinh definition and you will see stuff like 2Y4.5833334e0] at the terminal. Lua has no idea what to do with that. If you can convert this internal format into a 'normal' number \N then you can just use \edef\pgfmathresult{\directlua{tex.print("" .. math.sinh(\N))}} followed by \pgfmathsmuggle\pgfmathresult\endgroup. — Mark Wibrow, Oct 14 '13 at 12:53
Related question on the topic of FPU internal representation: tikz pgf - pgfplots and calculations; without fpu 'dimension too large', with fpu 'Illegal unit of measure (pt inserted)' - TeX - LaTeX Stack Exchange — user202729, Nov 23 '22 at 02:31

score 6 · Accepted Answer · edited Jul 15 '17 at 03:38

Based on @Mark Wibrow's comment, I have a working function declaration. The conversion from pgfplots internal syntax to something that is digestable by Lua feels wrong, though:

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}

\makeatletter
\pgfmathdeclarefunction{luasinh}{1}{%
    \begingroup
        \pgfkeys{/pgf/fpu,/pgf/fpu/output format=sci}%
        \pgfmathparse{#1}%
        \edef\pgfmathresult{\directlua{tex.print("" .. math.sinh(\pgfmathresult))}}%
        \pgfmathsmuggle\pgfmathresult%
    \endgroup
}%
\makeatother

\newcommand*\printtest[1]{%
    \section*{Test of $\sinh(#1)$}
    Lua: \directlua{tex.print("" .. math.sinh(#1))}~(directlua)\\
    Lua: \pgfmathsetmacro\luasinh{luasinh(#1)}\luasinh~(luasinh())\\
    Lua: \pgfmathparse{luasinh(#1)}\pgfmathresult~(pgfmathresult)\\
    %PGF: \pgfmathsetmacro\pgfsinh{sinh(#1)}\pgfsinh\\
}%

\begin{document}
\printtest{0}
\printtest{1}
\printtest{10}

\begin{tikzpicture}
    \begin{axis}[domain=-10:10]
        \addplot[mark=o] {sinh(x)};
        \addplot[mark=x] {luasinh(x)}; 
    \end{axis}
\end{tikzpicture}

\end{document}

Hi @ShreevatsaR and Martin Heller, How can I replicate this procedure to the erf function in LuaLatex?, thanks! — Alejandro Munoz Ossa, Jan 24 '21 at 15:45

\pgfmathdeclarefunction and LuaLaTeX

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