pgfplots and calculations; without fpu 'dimension too large', with fpu 'Illegal unit of measure (pt inserted)'

Question

I'm trying to multiply some numbers that will end up in the legend of a plot. I can't get it to work:

1. If I naively try \pgfmathmultiply, I get a dimension too large error, with the code in MWE 1 (see below). I understand this is because TeX doesn't count beyond 18 inch (or so). All right, I need to load fpu, as explained in section 36 of the pgfmanual (version 2.10).

2. If I pass /pgf/fpu to an axis-environment, compilation fails with Illegal unit of measure (pt inserted) (with MWE 2). Even if the axis-environment is completely empty. According to " How do I use pgfmathdeclarefunction to create define a new pgf function?", pgfplots uses fpu internally, so I don't really understand why I can't load it.

3. Maybe I'm using a wrong function, I thought. On page 362 of the PGF-manual, I read The installation exchanges any routines of the standard math parser with those of the FPU: \pgfmathadd will be replaced with \pgfmathfloatadd and so on. Furthermore, any number will be parsed with \pgfmathfloatparsenumber. So, if I already have the FPU, maybe I need to use \pgfmathfloatmultiply instead? I tried with MWE 3, but this time it fails to compile with: ! Package PGF Math Error: Sorry, an internal routine of the floating point unit got an ill-formatted floating point number '1000'. The unreadable part was near '1000'... Maybe \pgfmathmultiply is not meant to be used by the user, or so.

How do I multiply large numbers and show the result in my pgfplot?

Related yet different questions:

• How do I use pgfmathdeclarefunction to create define a new pgf function?
• How can I avoid the "Dimension too large" error when plotting in newer PGF versions?
• Dimension too large while plotting with pgfplots

MWE 1:

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.5}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
    title={\pgfmathmultiply{1000}{1000}}
          ]
\addplot coordinates {(0, 0) (1, 1) (2, 2)};
\end{axis}
\end{tikzpicture}
\end{document}

MWE 2

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.5}
\begin{document}
\begin{tikzpicture}
\begin{axis}[/pgf/fpu,
    title={\pgfmathmultiply{1000}{1000}}
          ]
\addplot coordinates {(0, 0) (1, 1) (2, 2)};
\end{axis}
\end{tikzpicture}
\end{document}

MWE 3:

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.5}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
    title={\pgfmathfloatmultiply{1000}{1000}}
          ]
\addplot coordinates {(0, 0) (1, 1) (2, 2)};
\end{axis}
\end{tikzpicture}
\end{document}

Answer 1

PGFplots uses the fpu library internally, but not for everything. At the user level, the fpu library is not activated. You can do that by hand by setting \pgfkeys{/pgf/fpu=true} before you do your maths using the normal \pgfmathparse{...} command. After you're done, you need to switch the fpu library back off again, otherwise PGFplots will get confused, since the fpu library uses a floating point representation of numbers, not a fixed point one. You can see what that looks like by saying

\pgfkeys{/pgf/fpu=true}
\pgfmathparse{1000*1000}
\pgfmathresult
\pgfkeys{/pgf/fpu=false}

which will print 1Y1.0e6]. You probably don't want that representation in your title, so you should either set \pgfkeys{/pgf/fpu=true,/pgf/fpu/output format=fixed}, which will make the output of maths operations fixed point, or use \pgfmathprintnumber{\pgfmathresult} for printing the result, which will use a fixed point representation even for floating point input.

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.5}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
    title={\pgfkeys{/pgf/fpu=true}
        \pgfmathparse{1000*1000}
        \pgfmathprintnumber{\pgfmathresult}
        \pgfkeys{/pgf/fpu=false}}
          ]
\addplot coordinates {(0, 0) (1, 1) (2, 2)};
\end{axis}
\end{tikzpicture}
\end{document}