Dimension too large with \pgfmathsetmacro

Question

I want to define varafterglowepsdown, varafterglowa and varafterglowb and use them in a tikz function like this:

\newcommand{\varafterglowepsdown}{0.0001}
\pgfmathsetmacro{\varafterglowb}{ln(\varafterglowepsdown) - ln(1 + \varafterglowepsdown)}
\pgfmathsetmacro{\varafterglowa}{(1 + \varafterglowepsdown) / exp(\varafterglowb)}

\begin{tikzpicture}[declare function={
    % some function using varafterglowa, varafterglowb, and varafterglowepsdown
    }]
    % some axis definition
\end{tikzpicture}

However on the third line I get a "Dimension too large." error.

How do I properly define varafterglowa?

Answer 1

A complementary approach to percusse's answer would be to use the LaTeX3 FPU (this provides an IEEE 754 floating point implementation in an expandable form):

\documentclass{article}
\usepackage{expl3}
\ExplSyntaxOn
\cs_new_eq:NN \fpeval \fp_eval:n
\ExplSyntaxOff
\protected\def\fpset#1#2{\edef#1{\fpeval{#2}}}
\begin{document}

\newcommand{\varafterglowepsdown}{0.0001}
\fpset{\varafterglowb}{ln(\varafterglowepsdown) - ln(1 + \varafterglowepsdown)}
\fpset{\varafterglowa}{(1 + \varafterglowepsdown) / exp(\varafterglowb)}
\varafterglowa

\end{document}

The result here is a 'pure' number so should be usable where pgf needs a number. You can use fpeval directly in many places rather than store the result.

Answer 2

There is a strict limitation in TeX about how big numbers can get which is plus minus 16384. Hence anything going above or anything that comes sufficiently close to zero in the divisor causes overflows. Here exp(-9...) is practically zero for TeX and it is done.

Instead you can use more precise calculation engines written for TeX for example FP or TikZ' internal fpu library.

\begin{tikzpicture}

\pgfkeys{/pgf/fpu}% Turn on the fp engine
\newcommand{\varafterglowepsdown}{0.0001}
\pgfmathsetmacro{\varafterglowb}{ln(\varafterglowepsdown) - ln(1 + \varafterglowepsdown)}
\pgfmathsetmacro{\varafterglowa}{(1 + \varafterglowepsdown) / exp(\varafterglowb)}
\pgfkeys{/pgf/fpu=false}% Turn it off


\node{\pgfmathfloattofixed\varafterglowa\pgfmathresult};% Show the fixed number
\end{tikzpicture}

The downside with fpu is that you have to convert the results to the fixed notation from it's own float notation.