% Copyright 2019 by Mark Wibrow
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Public License.
%
% See the file doc/generic/pgf/licenses/LICENSE for more details.

\usetikzlibrary{fpu}

\edef\tikz@math@at@catcode{\the\catcode`\@}%
\catcode`\@=11

\def\tikz@math@gobblespaces#1{\pgfutil@ifnextchar x{#1}{#1}}%

\def\tikz@math@meaning@macro{macro}%
\def\tikz@math@meaning@dimen{dimen}%
\def\tikz@math@meaning@count{count}%
\def\tikz@math@meaning@null{null}%

\def\tikz@math@getmeaning#1{\expandafter\tikz@math@@getmeaning\meaning#1\tikz@math@getmeaning@stop}%

\def\tikz@math@@getmeaning#1#2#3#4#5\tikz@math@getmeaning@stop{%
    \if#1u% undefined
        \let\tikz@math@meaning=\tikz@math@meaning@macro%
    \else%
        \if#1m%
            \let\tikz@math@meaning=\tikz@math@meaning@macro%
        \else%
            \if#2d%
                \let\tikz@math@meaning=\tikz@math@meaning@dimen%
            \else%
                \if#2c%
                    \let\tikz@math@meaning=\tikz@math@meaning@count%
                \else%
                    \if#3k% A skip. Treat like a dimen.
                        \let\tikz@math@meaning=\tikz@math@meaning@dimen%
                    \else%
                        \let\tikz@math@meaning=\tikz@math@meaning@null%
                    \fi%
                \fi%
            \fi%
        \fi%
    \fi%
}%

\def\tikz@math@firstoftwo#1#2{#1}%
\def\tikz@math@secondoftwo#1#2{#2}%


\def\tikz@math@getvarstring#1{%
    \begingroup%
        \escapechar=-1\relax%
        \expandafter\tikz@math@@getvarstring\string#1\tikz@math}%

\def\tikz@math@@getvarstring#1\tikz@math#2{%
    \endgroup%
    \def#2{#1}%
}%

\long\def\tikz@math@collecttosemicolon@other#1#2;{%
    \def\tikz@math@collected{#2}#1}%
\def\tikz@math@semicolon@other{;}%

{\catcode`\;=13
\long\gdef\tikz@math@collecttosemicolon@active#1#2;{%
    \def\tikz@math@collected{#2}#1}%
\gdef\tikz@math@semicolon@active{;}%
}%


\def\tikz@math@setvartype#1#2{%
    \expandafter\let\csname tikz@math@var@vartype@\string#1\endcsname=#2%
}%


\def\tikz@math@getvartype#1#2{%
    \def\tikz@math@marshal{\let#1=}%
    \expandafter\tikz@math@marshal\csname
    tikz@math@var@vartype@\string#2\endcsname%
}%



\def\tikz@math@ifvarcoordinate#1{%
    \expandafter\ifx\csname
    tikz@math@var@vartype@\string#1\endcsname\tikz@math@keyword@coordinate%
        \let\tikz@math@next=\tikz@math@firstoftwo%
    \else%
        \let\tikz@math@next=\tikz@math@secondoftwo%
    \fi%
    \tikz@math@next%
}%

\def\tikz@math@ifvarinteger#1{%
    \expandafter\ifx\csname
    tikz@math@var@vartype@\string#1\endcsname\tikz@math@keyword@integer%
        \let\tikz@math@next=\tikz@math@firstoftwo%
    \else%
        \let\tikz@math@next=\tikz@math@secondoftwo%
    \fi%
    \tikz@math@next%
}%


\def\tikz@math@setvarindexed#1{%
    \expandafter\let\csname
    tikz@math@var@subtype@\string#1\endcsname=\tikz@math@subtype@indexed%
}%

\def\tikz@math@clearvarindexed#1{%
    \expandafter\let\csname tikz@math@var@subtype@\string#1\endcsname=\relax%
}%

\def\tikz@math@ifvarindexed#1{%
    \expandafter\ifx\csname tikz@math@var@subtype@\string#1\endcsname\relax%
        \let\tikz@math@next=\tikz@math@secondoftwo%
    \else%
        \let\tikz@math@next=\tikz@math@firstoftwo%
    \fi%
    \tikz@math@next%
}%

\def\tikz@math@stop{@}%

\let\tikz@math@parse@hook@before=\pgfutil@empty
\let\tikz@math@parse@hook@after=\pgfutil@empty

\def\tikz@math{%
    \ifnum\catcode`\;=13\relax%
        \let\tikz@math@semicolon=\tikz@math@semicolon@active%
        \let\tikz@math@collecttosemicolon=\tikz@math@collecttosemicolon@active%
    \else%
        \let\tikz@math@semicolon=\tikz@math@semicolon@other%
        \let\tikz@math@collecttosemicolon=\tikz@math@collecttosemicolon@other%
    \fi%
    \tikz@math@parse@hook@before%
    \tikz@@math}%




\long\def\tikz@@math#1{%
    \def\tikz@math@marshal{\tikz@math@parse#1}%
    \expandafter\expandafter\expandafter\tikz@math@marshal\expandafter\tikz@math@stop\tikz@math@semicolon}%

\def\tikz@math@parse{\pgfutil@ifnextchar\bgroup\tikz@math@@parse@bgroup\tikz@math@@parse@nobgroup}%


\def\tikz@math@@parse@bgroup{%
    \tikz@math@collecttosemicolon{%
        % MW: Don't know how reliable this test is.
        \ifx\pgf@selectfontorig\tikz@math@undefined%
            \begingroup\tikz@math@collected\endgroup%
        \else%
            \begingroup\csname nullfont\endcsname\tikz@math@collected\endgroup%
        \fi\tikz@math@parse}}%



\def\tikz@math@@parse@nobgroup{\tikz@math@collecttosemicolon{\tikz@math@@parse@@nobgroup}}%

\def\tikz@math@@parse@@nobgroup{%
    \let\tikz@math@tmp=\tikz@math@collected%
    \ifx\tikz@math@tmp\tikz@math@stop%
        \def\tikz@math@next{\expandafter\tikz@math@parse@finish\tikz@math@semicolon}%
    \else%
        \def\tikz@math@next{\expandafter\expandafter\expandafter\tikz@math@parse@keyword@check\expandafter\tikz@math@tmp\tikz@math@semicolon}%
    \fi%
    \tikz@math@next%
}%

\def\tikz@math@parse@finish{%
    \tikz@math@collecttosemicolon{\tikz@math@parse@hook@after}%
}%



\newif\iftikz@math@let
\def\tikz@math@parse@keyword@check#1{%
    \tikz@math@letfalse%
    \tikz@math@getmeaning{#1}%
    \ifx\tikz@math@meaning\tikz@math@meaning@null%
        \let\tikz@math@next=\tikz@math@parse@keyword%
    \else%
        \let\tikz@math@next=\tikz@math@parse@nokeyword%
    \fi%
    \tikz@math@next#1}%


\def\tikz@math@parse@keyword{%
    \let\tikz@math@parsed@keyword=\pgfutil@empty%
    \futurelet\tikz@math@parse@token\tikz@math@@parse@keyword}%

\def\tikz@math@@parse@keyword{%
    \ifx\tikz@math@parse@token\pgfutil@sptoken%
        \let\tikz@math@next=\tikz@math@@@parse@keyword%
    \else%
        \ifx\tikz@math@parse@token(%
            \let\tikz@math@next=\tikz@math@@@parse@keyword%
        \else%
            \ifx\tikz@math@parse@token\bgroup%
                \let\tikz@math@next=\tikz@math@@@parse@keyword%
            \else%
                \let\tikz@math@next=\tikz@math@@@@parse@keyword%
            \fi%
        \fi%
    \fi%
    \tikz@math@next}%

\def\tikz@math@error#1{\pgfutil@packageerror{tikz}{tikz math library: #1}{}}%

\def\tikz@math@@@parse@keyword{%
        \expandafter\ifx\csname tikz@math@process@keyword@\tikz@math@parsed@keyword\endcsname\relax%
            \expandafter\ifx\csname pgfmath\tikz@math@parsed@keyword\endcsname\relax%
                    \tikz@math@error{Unknown function or keyword '\tikz@math@parsed@keyword'}%
            \else%
                \def\tikz@math@next{\tikz@math@collecttosemicolon{\tikz@math@function@noassign}}%
            \fi%
        \else%
            \expandafter\def\expandafter\tikz@math@next\expandafter{\csname tikz@math@process@keyword@\tikz@math@parsed@keyword\endcsname}%
        \fi%
    \tikz@math@next}%

\def\tikz@math@@@@parse@keyword#1{%
    \edef\tikz@math@parsed@keyword{\tikz@math@parsed@keyword#1}%
    \futurelet\tikz@math@parse@token\tikz@math@@parse@keyword%
}%

\def\tikz@math@function@noassign{%
    \pgfmathparse{\tikz@math@parsed@keyword\tikz@math@collected}%
    \tikz@math@parse%
}%




\def\tikz@math@process@keyword@count{\tikz@math@collecttosemicolon{\tikz@math@process@keyword@@count}}%
\def\tikz@math@process@keyword@@count{%
\def\tikz@math@assign@register{\csname newcount\endcsname}%
\expandafter\tikz@math@gobblespaces\expandafter\tikz@math@process@registers\tikz@math@collected,@,}%

\def\tikz@math@process@keyword@length{\tikz@math@collecttosemicolon{\tikz@math@process@keyword@@length}}%
\def\tikz@math@process@keyword@@length{%
\def\tikz@math@assign@register{\csname newdimen\endcsname}%
\show\tikz@math@collected
\expandafter\tikz@math@gobblespaces\expandafter\tikz@math@process@registers\tikz@math@collected,@,}%


\def\tikz@math@process@registers#1#2,{%
    \def\tikz@math@var{#1}%
    \ifx\tikz@math@var\tikz@math@stop%
        \let\tikz@math@next=\tikz@math@parse%
    \else%
        \tikz@math@assign@register#1\relax%
        \let\tikz@math@next=\tikz@math@process@registers%
    \fi%
    \tikz@math@gobblespaces\tikz@math@next%
}%


\def\tikz@math@process@keyword@if#1then{%
    \def\tikz@math@if@condition{#1}%
    \tikz@math@gobblespaces\tikz@math@parse@if@iftrue%
}%
\def\tikz@math@parse@if@iftrue#1{%
    \def\tikz@math@if@trueaction{#1}%
    \pgfutil@ifnextchar e{\tikz@math@parse@else}{\tikz@math@if@doif}}%

\def\tikz@math@parse@else else{\tikz@math@gobblespaces\tikz@math@if@doifelse}%

\def\tikz@math@if@doif{\tikz@math@collecttosemicolon{\tikz@math@if@@doif}}%

\def\tikz@math@if@@doif{%
    \pgfmathparse{\tikz@math@if@condition}%
    \ifpgfmathfloatparseactive%
        \pgfmathfloattofixed{\pgfmathresult}%
    \fi%
    \ifdim\pgfmathresult pt=0pt\relax%
    \else%
        \expandafter\tikz@math\expandafter{\tikz@math@if@trueaction}%
    \fi%
    \tikz@math@parse%
}%
\def\tikz@math@if@doifelse{\tikz@math@collecttosemicolon{\tikz@math@if@@doifelse}}%
\def\tikz@math@if@@doifelse{%
    \pgfmathparse{\tikz@math@if@condition}%
    \ifpgfmathfloatparseactive%
        \pgfmathfloattofixed{\pgfmathresult}%
    \fi%
    \let\tikz@math@if@falseaction=\tikz@math@collected%
    \ifdim\pgfmathresult pt=0pt\relax%
        \expandafter\tikz@math\expandafter{\tikz@math@if@falseaction}%
    \else%
        \expandafter\tikz@math\expandafter{\tikz@math@if@trueaction}%
    \fi%
    \tikz@math@parse%
}%
\def\tikz@math@process@keyword@let{%
    \tikz@math@lettrue%
    \tikz@math@gobblespaces\tikz@math@parse@nokeyword%
}%


\def\tikz@math@parse@nokeyword#1{%
    \def\tikz@math@var{#1}%
    \tikz@math@getvarstring{#1}\tikz@math@varstring%
    \let\tikz@math@vartype=\pgfutil@empty%
    \ifx\tikz@math@var\tikz@math@stop%
        \let\tikz@math@next=\tikz@math@parse@finish%
    \else%
         \ifx\tikz@math@semicolon\tikz@math@var%
            \let\tikz@math@next=\tikz@math@parse%
            \else%
                \let\tikz@math@next=\tikz@math@parse@index@check%
            \fi%
    \fi%
    \tikz@math@next}%

\def\tikz@math@parse@index@check{%
    \pgfutil@ifnextchar={\tikz@math@parse@noindex}{\tikz@math@parse@index}}%

\def\tikz@math@parse@noindex{%
    \expandafter\tikz@math@clearvarindexed\tikz@math@var%
    \let\tikz@math@current@index=\pgfutil@empty%
    \tikz@math@parse@afterindex%
}%

\def\tikz@math@parse@index#1{%
    \def\tikz@math@tmp{#1}%
    \expandafter\tikz@math@setvarindexed\tikz@math@var% {}
    \edef\tikz@math@current@index{#1}%
    \tikz@math@parse@afterindex%
}%
\def\tikz@math@parse@afterindex#1={\tikz@math@gobblespaces\tikz@math@parse@assignment}%

\def\tikz@math@parse@assignment{\tikz@math@collecttosemicolon{\tikz@math@parse@@assignment}}%
\def\tikz@math@parse@@assignment{%
    \expandafter\expandafter\expandafter\tikz@math@doassignment\expandafter\expandafter\expandafter%
        {\expandafter\tikz@math@var\expandafter}\expandafter{\tikz@math@collected}%
    \tikz@math@parse%
}%

\def\tikz@math@dollar@char{$}%
\def\tikz@math@dollar@char{$}% For annoying syntax highlighters

\def\tikz@math@doassignment#1#2{%
    \tikz@math@ifvarcoordinate{#1}{%
        \def\tikz@math@var{#1}% Unfortunately, we must do this again.
        \tikz@math@getvarstring{#1}\tikz@math@varstring% And this
        \expandafter\pgfutil@in@\tikz@math@dollar@char{#2}%
        \edef\tikz@math@expression{#2}%
        \ifpgfutil@in@%
            \expandafter\tikz@scan@one@point\expandafter\tikz@math@assign@coordinate\tikz@math@expression%
        \else%
            \expandafter\ifx\csname tikz@library@calc@loaded\endcsname\relax%
                \expandafter\tikz@scan@one@point\expandafter\tikz@math@assign@coordinate\tikz@math@expression%
            \else%
                \expandafter\tikz@scan@one@point\expandafter\tikz@math@assign@coordinate\expandafter%
                (\expandafter$\tikz@math@expression$)%
            \fi%
        \fi%
    }{%
        \iftikz@math@let% Not really a let
            \ifx\tikz@math@current@index\pgfutil@empty%
                \edef#1{#2}%
            \else%
                \edef\tikz@math@tmp{#2}%
                \expandafter\expandafter\expandafter\tikz@math@assign@index\expandafter\expandafter\expandafter%
                    {\expandafter\tikz@math@varstring\expandafter}\expandafter{\tikz@math@tmp}%
            \fi%
            \tikz@math@letfalse%
        \else%
            \ifx\tikz@math@current@index\pgfutil@empty%
                \tikz@math@getmeaning{#1}%
                \ifx\tikz@math@meaning\tikz@math@meaning@dimen%
                    \pgfmathsetlength{#1}{#2}%
                    \let\tikz@math@last@assigned@value=\pgfmathresult%
                \else%
                    \ifx\tikz@math@meaning\tikz@math@meaning@count%
                        \pgfmathsetcount{#1}{#2}%
                        \let\tikz@math@last@assigned@value=\pgfmathresult%
                    \else%
                        \tikz@math@ifvarinteger{#1}{\pgfmathparse{int(#2)}}{\pgfmathparse{#2}}%
                        \let\tikz@math@last@assigned@value=\pgfmathresult%
                        \let#1=\pgfmathresult%
                    \fi%
                \fi%
            \else%
                \tikz@math@ifvarinteger{#1}{\pgfmathparse{int(#2)}}{\pgfmathparse{#2}}%
                \expandafter\tikz@math@assign@index\expandafter{\tikz@math@varstring}\pgfmathresult%
                \let\tikz@math@last@assigned@value=\pgfmathresult%
            \fi%
        \fi%
    }%
}%



\def\tikz@math@assign@index#1#2{%
    \expandafter\def\csname#1\endcsname##1{\csname
    tikz@math@var@indexed@#1@##1\endcsname}%
    \expandafter\edef\csname
    tikz@math@var@indexed@#1@\tikz@math@current@index\endcsname{#2}\relax%
}%



\def\tikz@math@assign@coordinate#1{%
    \pgf@process{#1}%
    \ifx\tikz@math@current@index\pgfutil@empty%
        \expandafter\edef\csname\tikz@math@varstring\endcsname{\the\pgf@x,\the\pgf@y}%
        \expandafter\edef\csname\tikz@math@varstring x\endcsname{\the\pgf@x}%
        \expandafter\edef\csname\tikz@math@varstring y\endcsname{\the\pgf@y}%
    \else%
        \expandafter\tikz@math@assign@index\expandafter{\tikz@math@varstring}{\the\pgf@x,\the\pgf@y}%
        \expandafter\tikz@math@assign@index\expandafter{\tikz@math@varstring x}{\the\pgf@x}%
        \expandafter\tikz@math@assign@index\expandafter{\tikz@math@varstring y}{\the\pgf@y}%
    \fi%
}%



\def\tikz@math@keyword@coordinate{coordinate}%
\def\tikz@math@process@keyword@coordinate{%
    \let\tikz@math@vartype=\tikz@math@keyword@coordinate%
    \tikz@math@gobblespaces\tikz@math@process@vartypes%
}%

\def\tikz@math@keyword@integer{integer}%
\def\tikz@math@process@keyword@integer{%
    \let\tikz@math@vartype=\tikz@math@keyword@integer%
    \tikz@math@gobblespaces\tikz@math@process@vartypes%
}%
\def\tikz@math@process@keyword@int{%
    \tikz@math@process@keyword@integer%
}%

\def\tikz@math@keyword@real{real}%
\def\tikz@math@process@keyword@real{%
    \let\tikz@math@vartype=\tikz@math@keyword@real%
    \tikz@math@gobblespaces\tikz@math@process@vartypes%
}%

\def\tikz@math@process@keyword@point{\tikz@math@process@keyword@coordinate}%


\def\tikz@math@process@vartypes{\tikz@math@collecttosemicolon{\tikz@math@process@@vartypes}}%

\def\tikz@math@process@@vartypes{%
    \expandafter\tikz@math@@process@vartypes\tikz@math@collected,@,\tikz@math%
}%

\def\tikz@math@@process@vartypes#1#2,{%
    \def\tikz@math@var{#1}%
    \tikz@math@getvarstring{#1}\tikz@math@varstring%
    \ifx\tikz@math@var\tikz@math@stop%
        \let\tikz@math@next=\tikz@math@@@process@vartypes%
    \else%
        \expandafter\tikz@math@setvartype\tikz@math@var\tikz@math@vartype%
        \def\tikz@math@next{\tikz@math@gobblespaces\tikz@math@@process@vartypes}%
    \fi%
    \tikz@math@next%
}%

\def\tikz@math@process@keyword@print{\tikz@math@collecttosemicolon{\tikz@math@process@keyword@@print}}%
\def\tikz@math@process@keyword@@print{%
    \begingroup\tikz@math@collected\endgroup\tikz@math@parse%
}%

\def\tikz@math@@@process@vartypes#1\tikz@math{%
    \tikz@math@parse%
}%

\newcount\tikz@math@for@depth

\def\tikz@math@for@namedef#1{\expandafter\def\csname tikz@math@for@def@#1@\the\tikz@math@for@depth\endcsname}%
\def\tikz@math@for@nameedef#1{\expandafter\edef\csname tikz@math@for@def@#1@\the\tikz@math@for@depth\endcsname}%
\def\tikz@math@for@namelet#1{\expandafter\let\csname tikz@math@for@def@#1@\the\tikz@math@for@depth\endcsname}%

\def\tikz@math@for@namegetvalue#1#2{%
    \def\tikz@math@marshal{\let#2=}%
    \expandafter\tikz@math@marshal\csname tikz@math@for@def@#1@\the\tikz@math@for@depth\endcsname}%

\def\tikz@math@process@keyword@for{%
    \tikz@math@for%
}%

\def\tikz@math@for@external{%
    \ifnum\catcode`\;=13\relax%
        \let\tikz@math@semicolon=\tikz@math@semicolon@active%
        \let\tikz@math@collecttosemicolon=\tikz@math@collecttosemicolon@active%
    \else%
        \let\tikz@math@semicolon=\tikz@math@semicolon@other%
        \let\tikz@math@collecttosemicolon=\tikz@math@collecttosemicolon@other%
    \fi
    \advance\tikz@math@for@depth by1\relax%
    \tikz@math@for@namedef{execute}{\tikz@math@for@external@execute}%
    \tikz@math@for@namedef{finished}{\relax}%
    \tikz@math@gobblespaces\tikz@math@for@parsevar}%

\def\tikz@math@for@external@execute#1{#1}%

\def\tikz@math@for{%
    \advance\tikz@math@for@depth by1\relax%
    \tikz@math@for@namedef{execute}{\tikz@math}%
    \tikz@math@for@namedef{finished}{\tikz@math@parse}%
    \tikz@math@gobblespaces\tikz@math@for@parsevar}%


\def\tikz@math@for@parsevar#1{%
    \tikz@math@for@namedef{var}{#1}%
    \tikz@math@for@parsein}%

\def\tikz@math@getindex#1{%
    \tikz@math@@getindex#1\tikz@math@getindex\tikz@math@@getindex%
}%

\def\tikz@math@@getindex#1#2\tikz@math@@getindex{#1}%

\def\tikz@math@for@parsein#1in{%
    \def\tikz@math@tmp{#1}%
    \ifx\tikz@math@tmp\pgfutil@empty%
        \tikz@math@for@namedef{index}{}%
    \else%
        \tikz@math@for@nameedef{index}{\tikz@math@getindex{#1}}%
    \fi%
    \tikz@math@gobblespaces\tikz@math@for@parselist%
}%


\long\def\tikz@math@for@parselist#1{%
    \edef\tikz@math@for@list{#1}%
    \tikz@math@collecttosemicolon{\tikz@math@for@parseaction}}%

\def\tikz@math@for@parseaction{%
    \tikz@math@for@namedef{prevvalue}{}%
    \tikz@math@for@namedef{prevprevvalue}{}%
    \tikz@math@for@namelet{action}=\tikz@math@collected%
    \expandafter\tikz@math@for@scan\tikz@math@for@list,\tikz@math,\tikz@@math%
}%

\def\tikz@math@token{\tikz@math}%


\def\tikz@math@for@scan#1,{%
    \def\tikz@math@for@value{#1}%
    \ifx\tikz@math@for@value\tikz@math@token%
        \let\tikz@math@next=\tikz@math@for@scan@end%
    \else%
        \ifx\tikz@math@for@value\pgfutil@empty%
            \let\tikz@math@next=\tikz@math@for@scan@end%
        \else%
            \pgfutil@in@{...}{#1}%
            \ifpgfutil@in@%
                \let\tikz@math@next=\tikz@math@for@scan@dots%
            \else%
                \tikz@math@for@namegetvalue{var}{\tikz@math@var}%
                \tikz@math@for@namegetvalue{index}{\tikz@math@current@index}%
                \tikz@math@for@namegetvalue{action}{\tikz@math@action}%
                \expandafter\tikz@math@getvarstring\expandafter{\tikz@math@var}\tikz@math@varstring%
                \expandafter\tikz@math@doassignment\expandafter{\tikz@math@var}{#1}%
                \tikz@math@for@namelet{value}=\tikz@math@last@assigned@value%
                \tikz@math@for@namegetvalue{execute}{\tikz@math@execute}%
                \expandafter\tikz@math@execute\expandafter{\tikz@math@action}%
                \tikz@math@for@namegetvalue{prevvalue}{\tikz@math@prevvalue}%
                \tikz@math@for@namelet{prevprevvalue}=\tikz@math@prevvalue%
                \tikz@math@for@namegetvalue{value}{\tikz@math@value}%
                \tikz@math@for@namelet{prevvalue}=\tikz@math@value%
                \let\tikz@math@next=\tikz@math@for@scan%
            \fi%
        \fi%
    \fi%
    \tikz@math@next%
}%

\newdimen\tikz@math@dimen

\def\tikz@math@for@scan@dots#1,{%
    \pgfmathparse{#1}\let\tikz@math@value=\pgfmathresult%
    \tikz@math@for@nameedef{endvalue}{\tikz@math@value}%
    \tikz@math@for@namegetvalue{prevvalue}{\tikz@math@prevvalue}%
    \tikz@math@for@namegetvalue{prevprevvalue}{\tikz@math@prevprevvalue}%
    \tikz@math@dimen=\tikz@math@prevvalue pt\relax%
    \ifx\tikz@math@prevprevvalue\pgfutil@empty%
        \ifdim\tikz@math@prevvalue pt<\tikz@math@value pt\relax%%
            \def\tikz@math@step{1pt}%
        \else%
            \def\tikz@math@step{-1pt}%
        \fi%
    \else%
        \tikz@math@dimen=\tikz@math@prevvalue pt\relax%
        \advance\tikz@math@dimen by-\tikz@math@prevprevvalue pt\relax%
        \edef\tikz@math@step{\the\tikz@math@dimen}%
    \fi%
    \ifdim\tikz@math@step<0pt\relax%
        \tikz@math@for@namedef{comparitor}{<}%
    \else%
        \tikz@math@for@namedef{comparitor}{>}%
    \fi%
    \tikz@math@for@nameedef{step}{\tikz@math@step}%
    \tikz@math@for@doloop%
}%

\def\tikz@math@for@doloop{%
    \tikz@math@for@namegetvalue{prevvalue}{\tikz@math@prevvalue}%
    \tikz@math@for@namegetvalue{step}{\tikz@math@step}%
    \tikz@math@for@namegetvalue{comparitor}{\tikz@math@comparitor}%
    \tikz@math@for@namegetvalue{endvalue}{\tikz@math@endvalue}%
    \tikz@math@dimen=\tikz@math@prevvalue pt\relax%
    \advance\tikz@math@dimen by\tikz@math@step\relax%
    \ifdim\tikz@math@dimen\tikz@math@comparitor\tikz@math@endvalue pt\relax%
        \let\tikz@math@next=\tikz@math@for@endloop%
    \else%
        \tikz@math@for@nameedef{value}{\pgfmath@tonumber{\tikz@math@dimen}}%
        \tikz@math@for@namegetvalue{var}{\tikz@math@var}%
        \expandafter\tikz@math@getvarstring\expandafter{\tikz@math@var}\tikz@math@varstring%
        \tikz@math@for@namegetvalue{index}{\tikz@math@current@index}%
        \tikz@math@for@namegetvalue{action}{\tikz@math@action}%
        \tikz@math@for@namegetvalue{value}{\tikz@math@value}%
        \expandafter\expandafter\expandafter\tikz@math@doassignment\expandafter\expandafter\expandafter%
            {\expandafter\tikz@math@var\expandafter}\expandafter{\tikz@math@value}%
        \tikz@math@for@namegetvalue{execute}{\tikz@math@execute}%
        \expandafter\tikz@math@execute\expandafter{\tikz@math@action}%
        \tikz@math@for@namegetvalue{prevvalue}{\tikz@math@prevvalue}%
        \tikz@math@for@namelet{prevprevvalue}=\tikz@math@prevvalue%
        \tikz@math@for@namegetvalue{value}{\tikz@math@value}%
        \tikz@math@for@namelet{prevvalue}=\tikz@math@value%
        \let\tikz@math@next=\tikz@math@for@doloop%
    \fi%
    \tikz@math@next%
}%

\def\tikz@math@for@endloop{%
\tikz@math@for@scan}%




\def\tikz@math@for@scan@end#1\tikz@@math{%
\tikz@math@for@namegetvalue{finished}{\tikz@math@next}%
\advance\tikz@math@for@depth by-1\relax%
\tikz@math@next}%





\def\tikz@math@process@keyword@return{%
    \tikz@math@collecttosemicolon{\pgfmathparse{\tikz@math@collected}\tikz@math@parse}}%

\def\tikz@math@process@keyword@function{\tikz@math@collecttosemicolon{\tikz@math@process@keyword@@function}}%
\def\tikz@math@process@keyword@@function{%
    \let\tikz@math@function@name=\pgfutil@empty%
    \let\tikz@math@function@arguments=\pgfutil@empty%
    \let\tikz@math@function@body=\pgfutil@empty%
    \expandafter\expandafter\expandafter\tikz@math@@declarefunction\expandafter\tikz@math@collected\tikz@math@semicolon%
}%

\def\tikz@math@@declarefunction{%
    \pgfutil@ifnextchar\bgroup\tikz@math@@@collectbody\tikz@math@@@declarefunction}%


\def\tikz@math@@@declarefunction#1{%
    \if#1(%)
        \let\tikz@math@next=\tikz@math@@@collectarguments%
    \else%
        \expandafter\def\expandafter\tikz@math@function@name\expandafter{\tikz@math@function@name#1}%
        \let\tikz@math@next=\tikz@math@@declarefunction%
    \fi%
    \tikz@math@next%
}%
\def\tikz@math@@@collectarguments#1){%
    \def\tikz@math@function@arguments{#1}%
    \tikz@math@@declarefunction%
}%

\newtoks\tikz@math@toks
\tikz@math@toks={#}%
\edef\tikz@math@char@hash{\the\tikz@math@toks}%
\tikz@math@toks={}%

\def\tikz@math@@@collectbody{\tikz@math@collecttosemicolon{\tikz@math@@@@collectbody}}%

\def\tikz@math@@@@collectbody{%
    \tikz@math@toks={}%
    \c@pgf@counta=0\relax%
    \ifx\tikz@math@function@arguments\pgfutil@empty%
    \else%
        \expandafter\tikz@math@createargumentlist\tikz@math@function@arguments,,%
        \expandafter\tikz@math@addto@toks\expandafter{\tikz@math@collected}%
    \fi%
    \edef\tikz@math@local@temp{%
        \noexpand\pgfmathdeclarefunction{\tikz@math@function@name}{\the\c@pgf@counta}%
        {\noexpand\def\noexpand\return{0}\noexpand\tikz@math{\the\tikz@math@toks}}%
    }%
    \tikz@math@local@temp
    \tikz@math@parse%
}%

\def\tikz@math@addto@toks#1{%
    \expandafter\tikz@math@toks\expandafter{\the\tikz@math@toks#1}}%

\def\tikz@math@createargumentlist{%
    \pgfutil@ifnextchar
    x\tikz@math@@createargumentlist\tikz@math@@createargumentlist}%

\def\tikz@math@comma{,}%
\def\tikz@math@@createargumentlist#1,{%
    \def\tikz@math@tmp{#1}%
    \ifx\tikz@math@tmp\pgfutil@empty%
        \let\tikz@math@next=\relax%
    \else%
        \advance\c@pgf@counta by1\relax%
        \tikz@math@addto@toks{#1=}%
        \expandafter\expandafter\expandafter\tikz@math@addto@toks\expandafter\expandafter\expandafter%
            {\expandafter\tikz@math@char@hash\the\c@pgf@counta;}%
        \let\tikz@math@next=\tikz@math@createargumentlist%
    \fi%
    \tikz@math@next%
}%



\let\tikzmath=\tikz@math
\tikzset{evaluate/.code={\tikz@math{#1}}}%
\let\tikzmathfor=\tikz@math@for@external


\catcode`\@=\tikz@math@at@catcode\relax
