pgfmath: add pTeX-specific units and pdfTeX-specific units

20200119-pgfmath-unit.tex

\documentclass[dvipdfmx]{article}
\usepackage{tikz}

\makeatletter % TEX CODE BEGIN
%
\usepackage{etoolbox}
%
% missing for pdfTeX and LuaTeX:
\pgfmath@tokens@make{unit}{{nc}{nd}}% double character units are ok
%
% missing for pTeX and friends:
\pgfmath@tokens@make{unit}{{zh}{zw}}% double character units are ok
\pgfmath@tokens@make{unit}{{H}{Q}} % single character units; see below
%
% hack to support single-character units
\patchcmd{\pgfmath@parse@@number}{%
        % It isn't numeric (i.e., 012345679.), so it might be units...
        \expandafter\ifx\csname pgfmath@token@unit@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax%
  }{%
        % It isn't numeric (i.e., 012345679.), so it might be units...
        \expandafter\ifx\csname pgfmath@token@unit@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax%
        \expandafter\ifx\csname pgfmath@token@unit@\pgfmath@token\endcsname\relax%
  }{}{}
\patchcmd{\pgfmath@parse@@number}{%
        \else% ...but here it is units.
          \global\pgfmathunitsdeclaredtrue%
          \pgfmath@dimen=\pgfmath@number\pgfmath@token\pgfmath@token@next\relax%
          \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
          \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
          \let\pgfmath@parse@next=\pgfmath@parse@@operator%
        \fi%
  }{%
        \else% ...but here it is units.
          \global\pgfmathunitsdeclaredtrue%
          \pgfmath@dimen=\pgfmath@number\pgfmath@token\relax%
          \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
          \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
          \let\pgfmath@parse@next=\pgfmath@parse@@operator%
        \fi%
        \else% ...but here it is units.
          \global\pgfmathunitsdeclaredtrue%
          \pgfmath@dimen=\pgfmath@number\pgfmath@token\pgfmath@token@next\relax%
          \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}%
          \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}%
          \let\pgfmath@parse@next=\pgfmath@parse@@operator%
        \fi%
  }{}{}
%
\makeatletter % TEX CODE END

\begin{document}

\begin{tikzpicture}
  \draw (0,0) rectangle (3,3);
  \node[yshift=\dimexpr1zw\relax] at (0,0) {Hello!}; % OK
\end{tikzpicture}

\begin{tikzpicture}
  \draw (0,0) rectangle (3,3);
  \node[yshift=1zw] at (0,0) {Hello!}; % !!
\end{tikzpicture}
% without patch,
% => ! Package PGF Math Error: Unknown operator `z' or `zw' (in '1zw').

\begin{tikzpicture}
  \draw (0,0) rectangle (3,3);
  \node[yshift=1Q] at (0,0) {Hello!}; % !!
\end{tikzpicture}
% without patch,
% => ! Package PGF Math Error: Unknown operator `Q' or `Q@' (in '1Q').

\begin{tikzpicture}
  \draw (0,0) rectangle (3,3);
  \node[yshift=1nd] at (0,0) {Hello!}; % error expected
\end{tikzpicture}
% => ! Illegal unit of measure (pt inserted).

\end{document}

See pgf-tikz/pgf#827