Declaring sinc in tikz

Question

I am trying to declare the sinc-function for usage in tikz. I tried two different ways:

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{math}
\begin{document}
\begin{tikzpicture}
    \tikzmath{
        function sincm(\x) {
            if abs(\x) < 0.001 then {
                return 1.0;
            } else {
                return sin(\x r)/\x;
            };
        };
    }
    \pgfmathdeclarefunction{sinc}{1}{%
        \pgfmathparse{%
            abs(#1)<0.001 ? 1 : sin(#1 r)/#1%
            }%
        }

    \draw (-1,0) -- (1,0);
    \draw[domain=0:0.5, samples=1000] plot (\x, {sincm(\x*20)});
    \draw[domain=0:0.5, samples=1000, red, dotted] plot (\x,{sinc(\x*20)});

\end{tikzpicture}
\end{document}

Both ways yield the same result. I would like to use \pgfmathdeclarefunction variante, first of all to be able to declare this function globally, maybe even for several tikz-pictures. However, if I set the start of the plotting domain to zero:

\draw[domain=0:0.5, samples=1000, red, dotted] plot (\x,{sinc(\x*20)});

I get the Error Package PGF Math Error: You've asked me to divide '0,0' by '0.0'. Somehow, in this case, the ifthenelse-structure in my declaration of sinc does not seem to work?

Answer 1

Unfortunately, when encountered with an if-then syntax, PGF evaluates both branches and then chooses hence it will divide no matter what the value of #1 is. Instead you can use it to branch off

\begin{tikzpicture}
    \pgfmathdeclarefunction{sinc}{1}{%
        \pgfmathparse{abs(#1)<0.01 ? int(1) : int(0)}%
        \ifnum\pgfmathresult>0 \pgfmathparse{1}\else\pgfmathparse{sin(#1 r)/#1}\fi%
        }

    \draw (-1,0) -- (1,0);
    \draw[domain=0:0.5, samples=250] plot (\x,{sinc(20*\x)});

\end{tikzpicture}