How can I globally set pgfmathsetlength?

Question

How can I declare a length via pgfmathsetlength global?

The example results in 20pt -- 5pt -- 20pt But I had expected: 20pt -- 5pt -- 5pt

\documentclass[10pt]{article}
\parindent0pt
\usepackage{tikz}
\newlength\testl
\pgfmathsetlength\testl{20pt}
\begin{document}
\the\testl

{\global\pgfmathsetlength\testl{5pt}\the\testl}

\the\testl
\end{document}

I don't want to discuss possibilities with \setlength or \deflength.

Answer 1

You can use \global like this :

 {\pgfmathsetlength{\global\testl}{5pt}}\the\testl

Some remarks : Egreg notices this code is very similar to

\setlength{\global\testl}{5pt}

It may be interesting to know what the macro pgfmathsetlength provides. In the file pgfmathcalc.code.tes we can read :

% #1 = dimension register
% #2 = expression
%
% Description:
%
% These functions work similar to \setlength and \addtolength. Only,
% they allow #2 to contain an expression, which is evaluated before
% assignment. Furthermore, the font is setup before the assignment is
% done, so that dimensions like 1em are evaluated correctly.
%
% If #2 starts with "+", then a simple assignment is done (but the
% font is still setup). This is orders of magnitude faster than a
% parsed assignment.

Another possibility to declare a length global is to redefine pgfmathsetlength but it's bad or to use a new macro :globalpgfmathsetlength based on pgfmathsetlength. We need to add \global in two lines but simplest is my first answer.

 \makeatletter
 \def\globalpgfmathsetlength#1#2{%
    \expandafter\pgfmath@onquick#2\pgfmath@%
    {%
        % Ok, quick version:
        \begingroup%
            \pgfmath@selectfont%
            \pgfmath@x#2\unskip%
            \pgfmath@returnone\pgfmath@x%
        \endgroup%
        \global#1\pgfmathresult pt\relax% here add \global before #1
    }%
    {%
        \pgfmathparse{#2}%
        \global#1\pgfmathresult pt\relax% and here
    }%
    \ignorespaces%
}  

Answer 2

Use a scratch dimension

{\dimendef\temp=0
 \pgfmathsetlength\temp{5pt}\global\testl=\temp}

Note. I wouldn't use \testl in place of \temp, in order to avoid "save stack buildup".