Rounding a value from a function

Question

Is possible I define a mathematical function f(x), for example, f(x) = sqrt(x), evaluate this function in a given point p=2 and round the result with 4 decimal places? I prefer use this code inside a tikz environment. My difficult is calculate the number m =1/2*f(p) with my function defined and provide the result with a given precision (4 or 5 exact decimal places). The following code does not round.

Here I provide my code:

\documentclass[tikz, border=.5cm]{article}
\usepackage{tkz-fct}   
\usepackage{multido}
\usetikzlibrary{calc,math}
\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=5}
\usepackage{xfp}
\usepackage{float}
\usepackage{amsmath}
\begin{document}
\tikzmath{
    real \a;
    real \b;
    \a = 0;
    \b = 4;
}
\foreach \p in {2,1}{
\begin{tikzpicture}[declare function = {f(\x) = (\x)^0.5;}]
\clip (-1.5,-1.5) rectangle (4.5,3.5);
\draw[help lines] (-1,-1) grid (4,3);
\draw[->,>=stealth'] (-1,0) -- (4,0) node[right] {$x$};
\draw[->,>=stealth'] (0,-1) -- (0,3) node[above] {$y$};
\foreach \j in {-1,0,1,2,3,4}{
\draw (\j,2pt)--(\j,-2pt) node[below,fill=white]{{\footnotesize $\j$}};
}
\foreach \j in {-1,0,1,2,3,}{
\draw (2pt,\j)--(-2pt,\j) node[left,] {{\footnotesize $\j$}};
}
\draw[samples=1000,thick,blue] plot[domain=\a:\b](\x,{f(\x)}) node[right]{$f$};
\draw[samples=1000,thick,red] plot[domain=-1.5+\p:1.5+\p]({\x},{f(\p) + ( 1/(2f(\p))(\x - \p)}) node[above] {$t$};
\draw[fill] (\p,{f(\p)}) circle (1pt);
\draw[dotted] (\p,0) -- (\p,{f(\p)}) node[above,rotate=atan(1/(2f(\p)))]{{\scriptsize $(\fpeval{round(\p,1)},\fpeval{round(\p^0.5,2)})$}} -- (0,{f(\p)});
\node[above] (2) at (1.5,3)  {$m = \pgfmathparse{1/(2f(\p)) }\pgfmathresult$};
\end{tikzpicture}
}
\end{document}

Answer 1

In order for your

\pgfkeys{/pgf/number format/.cd, fixed, fixed zerofill, precision=5}

to be used, you need to call \pgfmathprintnumber or \pgfmathprintnumberto, as in \pgfmathprintnumber{\pgfmathresult}. However, pgfmath is not very accurate and as you can see below, xfp (l3fp) gives a much better result:

\documentclass{article}
\usepackage{tkz-fct}
\usetikzlibrary{math}
\pgfkeys{/pgf/number format/.cd, fixed, fixed zerofill, precision=5}
\usepackage{xfp}
\begin{document}
\tikzmath{
    real \a;
    real \b;
    \a = 0;
    \b = 4;
}
\foreach \p in {2,1}{
\begin{tikzpicture}[declare function = {f(\x) = (\x)^0.5;}]
\clip (-1.5,-1.5) rectangle (4.5,3.5);
\draw[help lines] (-1,-1) grid (4,3);
\draw[->,>=stealth'] (-1,0) -- (4,0) node[right] {$x$};
\draw[->,>=stealth'] (0,-1) -- (0,3) node[above] {$y$};
\foreach \j in {-1,0,1,2,3,4}{
\draw (\j,2pt)--(\j,-2pt) node[below,fill=white]{{\footnotesize $\j$}};
}
\foreach \j in {-1,0,1,2,3,}{
\draw (2pt,\j)--(-2pt,\j) node[left,] {{\footnotesize $\j$}};
}
\draw[samples=1000,thick,blue] plot[domain=\a:\b](\x,{f(\x)}) node[right]{$f$};
\draw[samples=1000,thick,red] plot[domain=-1.5+\p:1.5+\p]({\x},{f(\p) + ( 1/(2f(\p))(\x - \p)}) node[above] {$t$};
\draw[fill] (\p,{f(\p)}) circle (1pt);
\draw[dotted] (\p,0) -- (\p,{f(\p)}) node[above,rotate=atan(1/(2f(\p)))]{{\scriptsize $(\fpeval{round(\p,1)},\fpeval{round(\p^0.5,2)})$}} -- (0,{f(\p)});
\node[above] (2) at (1.5,3)
  {$m \approx \pgfmathparse{1/(2f(\p))} \pgfmathprintnumber{\pgfmathresult}$};
\end{tikzpicture}
}
\foreach \p in {2,1}{
\begin{tikzpicture}[declare function = {f(\x) = (\x)^0.5;}]
\clip (-1.5,-1.5) rectangle (4.5,3.5);
\draw[help lines] (-1,-1) grid (4,3);
\draw[->,>=stealth'] (-1,0) -- (4,0) node[right] {$x$};
\draw[->,>=stealth'] (0,-1) -- (0,3) node[above] {$y$};
\foreach \j in {-1,0,1,2,3,4}{
\draw (\j,2pt)--(\j,-2pt) node[below,fill=white]{{\footnotesize $\j$}};
}
\foreach \j in {-1,0,1,2,3,}{
\draw (2pt,\j)--(-2pt,\j) node[left,] {{\footnotesize $\j$}};
}
\draw[samples=1000,thick,blue] plot[domain=\a:\b](\x,{f(\x)}) node[right]{$f$};
\draw[samples=1000,thick,red] plot[domain=-1.5+\p:1.5+\p]({\x},{f(\p) + ( 1/(2f(\p))(\x - \p)}) node[above] {$t$};
\draw[fill] (\p,{f(\p)}) circle (1pt);
\draw[dotted] (\p,0) -- (\p,{f(\p)}) node[above,rotate=atan(1/(2f(\p)))]{{\scriptsize $(\fpeval{round(\p,1)},\fpeval{round(\p^0.5,2)})$}} -- (0,{f(\p)});
\node[above] (2) at (1.5,3)
  {$m \approx \fpeval{round(1/(2sqrt(\p)), 5)}$};
\end{tikzpicture}
}
\end{document}

By using:

• \fpeval inside \pgfmathparse followed by \pgfmathprintnumber{\pgfmathresult}, or;

• more directly, \pgfmathprintnumber{\fpeval{1/(2*sqrt(\p))}},

you can print a fixed number of decimal places with great precision (14 correct digits here, and the 15th is correctly rounded according to what follows!):

\documentclass{article}
\usepackage{pgffor}
\usepackage{pgfmath}
\usepackage{pgf}
\usepackage{xfp}
\pgfkeys{/pgf/number format/.cd, fixed, fixed zerofill, precision=15}
\begin{document}
\foreach \p in {2,1} {%
  When $p = \p$,
  $m \approx \pgfmathprintnumber{\fpeval{1/(2*sqrt(\p))}}$.\par
}
\end{document}

Another way to format numbers (here computed with \fpeval, but this is not necessary) is to use the siunitx package:

\documentclass{article}
\usepackage{pgffor}
\usepackage{siunitx}
% See also option 'round-integer-to-decimal'.
\sisetup{round-mode = places, round-precision=15}
\usepackage{xfp}
\begin{document}
\foreach \p in {2,1} {%
  When $p = \p$,
  $m \approx \num{\fpeval{1/(2*sqrt(\p))}}$.\par
}
\end{document}