Precision in numeric calculations

Question

When using pgfmathsetmacro with very small of high exponents, it doesn't work. The example below exits by complaining a division by zero. Is there any way to increase the precision that this works or another package which handles this example?

\documentclass{article}

\usepackage{tikz}

\begin{document}

\pgfmathsetmacro{\a}{10e-32}
\pgfmathsetmacro{\b}{10e-30}

\pgfmathsetmacro{\c}{\a/\b}
\c
\pgfmathsetmacro{\c}{1/\b}
\c
\end{document}

score 15 · Accepted Answer · answered Jun 18 '16 at 20:09

The number range in the default math engine of pgf is quite restricted because of the limitations of TeX's numbers. Also the library for fixed point arithmetic does not help with these exponents, because this library only covers ten digits before and after the decimal point.

The example can be processed with the floating point unit library:

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{fpu}

\begin{document}

\pgfset{fpu}
\pgfmathsetmacro{\a}{10e-32}
\pgfmathsetmacro{\b}{10e-30}

\pgfset{fpu/output format=fixed}
\pgfmathsetmacro{\c}{\a/\b}
\c

\pgfset{fpu/output format=sci}
\pgfmathsetmacro{\c}{1/\b}
\c
\end{document}

score 12 · Answer 2 · answered Jun 18 '16 at 20:14

12

Use a better floating point management framework, the one in expl3.

\documentclass{article}
\usepackage{expl3}

\ExplSyntaxOn
\cs_set_eq:NN \fpeval \fp_eval:n
\ExplSyntaxOff

\begin{document}

\fpeval{10e-32/10e-30}

\end{document}

Note that, differently from pgf, the floating point macros are expandable.

Thus, you get the same output from

\documentclass{article}
\usepackage{expl3}

\ExplSyntaxOn
\cs_set_eq:NN \fpeval \fp_eval:n
\ExplSyntaxOff

\newcommand{\varA}{10e-32}
\newcommand{\varB}{10e-30}

\begin{document}

\fpeval{\varA/\varB}

\end{document}

Consult texdoc interface3 for more information about the supported functions and the syntax.

answered Jun 18 '16 at 20:14

egreg

1,121,712

1

Could you elaborate on why (in your opinion) this is a better floating point management framework? Better than what? – Runar Jun 18 '16 at 20:34
@runartrollet Better than pgfmath, which was the OP's choice. – egreg Jun 18 '16 at 20:35
Also better than pgfmath with fpu library? – student Jun 19 '16 at 06:25
@student It lacks random numbers, but full expandability is a plus. – egreg Jun 19 '16 at 08:50

score 6 · Answer 3 · answered Jun 18 '16 at 20:23

6

Use lualatex:

\documentclass{article}
\begin{document}    
\directlua{tex.print(10^(-32)/10^(-30))}

\directlua{tex.print(1/10^(-30))}
\end{document}

answered Jun 18 '16 at 20:23

Precision in numeric calculations

3 Answers3

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