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+% Copyright 2013 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.
+
+
+
+\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}%
+ \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}%
+ \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