calc-package prevents \headheight to change

Question

I am trying to automize setting the correct \headheight following Heiko Oberdiek's approach. It is based on the fact that the fancyhdr package usually increases the \headheight as required and saves this value at the very end to a file. The problem is that when using the calc package that value does not seem to change (although the log file still claims "We now make it that large for the rest of the document.").

I know that I could avoid the calc package by using \dimexpr and friends but I need the mathtools package which requires the calc package.

Does anyone have an idea how to get the correct value for \headheight even if the calc package is used?

\documentclass{article}
\usepackage{blindtext}
\usepackage{calc} % this suppresses fancyhdr's feature of increasing \headheight as required


% ===== save header and footer height =====
% https://tex.stackexchange.com/a/117810/120953
\usepackage{atveryend}
\makeatletter
\AtVeryEndDocument{%
    \if@filesw % respect \nofiles
        \begingroup
            % same write register as environment `filecontents` uses
            \chardef\reserved@c=15 %
            \immediate\openout\reserved@c=\jobname.heights\relax
            \immediate\write\reserved@c{%
                \string\setlength{\string\headheight}{\the\headheight}%
            }%
            \immediate\write\reserved@c{%
                \string\setlength{\string\footskip}{\the\footskip}%
            }%
            \immediate\closeout\reserved@c
        \endgroup
        \showthe\headheight
    \fi
}
\makeatother

%\InputIfFileExists{\jobname.heights}{}{} % I have commented this out for testing
\usepackage[
    includehead,
    includefoot,
    showframe,
]{geometry}


% ===== header & footer =====
\usepackage{fancyhdr}
\usepackage{lastpage}
\usepackage{graphicx}
\pagestyle{fancy}

\fancyhead{}
\fancyhead[L]{a rather long header\\ which needs to be broken into several lines}
%\fancyhead[R]{\includegraphics[height=\dimexpr\the\headheight-4.3501pt\relax]{icon}}

\fancyfoot{}
\fancyfoot[R]{page \thepage \ of \pageref{LastPage}}
\fancyfoot[L]{some footer}

\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}


% ===== test document =====
\begin{document}
    \blinddocument
\end{document}

Answer 1

fancyhdr uses \global\setlength in one place which isn't supported LaTeX syntax and it doesn't work at all if calc is loaded. It is easy to avoid it in this case just delete \setlength and use a primitive assignment.

\documentclass{article}
\usepackage{blindtext}
\usepackage{calc} % this suppresses fancyhdr's feature of increasing \headheight as required


% ===== save header and footer height =====
% http://tex.stackexchange.com/a/117810/120953
\usepackage{atveryend}
\makeatletter
\AtVeryEndDocument{%
    \if@filesw % respect \nofiles
        \begingroup
            % same write register as environment `filecontents` uses
            \chardef\reserved@c=15 %
            \immediate\openout\reserved@c=\jobname.heights\relax
            \immediate\write\reserved@c{%
                \string\setlength{\string\headheight}{\the\headheight}%
            }%
            \immediate\write\reserved@c{%
                \string\setlength{\string\footskip}{\the\footskip}%
            }%
            \immediate\closeout\reserved@c
        \endgroup
        \showthe\headheight
    \fi
}
\makeatother

%\InputIfFileExists{\jobname.heights}{}{} % I have commented this out for testing
\usepackage[
    includehead,
    includefoot,
    showframe,
]{geometry}


% ===== header & footer =====
\usepackage{fancyhdr}

\makeatletter
\def\@fancyvbox#1#2{\setbox0\vbox{#2}\ifdim\ht0>#1\@fancywarning
  {\string#1 is too small (\the#1): ^^J Make it at least \the\ht0.^^J
    We now make it that large for the rest of the document.^^J
    This may cause the page layout to be inconsistent, however\@gobble}%
  \dimen0=#1\relax
  \global#1\ht0\ht0=\dimen0\fi
  \box0}
\makeatother

\usepackage{lastpage}
\usepackage{graphicx}
\pagestyle{fancy}

\fancyhead{}
\fancyhead[L]{a rather long header\\ which needs to be broken into several lines}
%\fancyhead[R]{\includegraphics[height=\dimexpr\the\headheight-4.3501pt\relax]{icon}}

\fancyfoot{}
\fancyfoot[R]{page \thepage \ of \pageref{LastPage}}
\fancyfoot[L]{some footer}

\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}


% ===== test document =====
\begin{document}
    \blinddocument
\end{document}