\newdimen\pgfmath@dimen \newcount\pgfmath@count \newbox\pgfmath@box \newtoks\pgfmath@toks \newif\ifpgfmath@quickparse \newif\ifpgfmathfloat \newif\ifpgfmathunitsdeclared \newif\ifpgfmathmathunitsdeclared \newif\ifpgfmathignoreunitscale \let\pgfmath@protected@edef=\edef \ifcsname protected@edef\endcsname \let\pgfmath@protected@edef=\protected@edef \fi \def\pgfmathprint#1{\pgfmathparse{#1}\pgfmathresult} \def\pgfmathparse{% \begingroup \pgfmath@catcodes \pgfmath@quickparsefalse % Test for the fpu library \ifpgfmathfloat \let\pgfmath@parse@next=\pgfmathfloatparsenumber \else \let\pgfmath@parse@next=\pgfmathparse@ \fi \pgfmath@parse@next} \def\pgfmath@catcodes{% Maybe unnecessary. \catcode`\==12 % \catcode`\,=12 % \catcode`\|=12 % \catcode`\&=12 % } \def\pgfmathqparse{% \begingroup \pgfmath@catcodes \pgfmath@quickparsetrue \pgfmathparse@} \def\pgfmathparse@#1{% % No (math) units yet. \global\pgfmathunitsdeclaredfalse \global\pgfmathmathunitsdeclaredfalse % Expand expression so any remaining CSs are registers % or box dimensions (i.e. |\wd|, |\ht|, |\dp|). \pgfmath@protected@edef\pgfmath@expression{#1}% % \expandafter\pgfmathparse@trynumber@loop\pgfmath@expression\pgfmath@parse@stop % % this here is the _real_ parser. it is invoked by % \pgfmathparse@trynumber@loop if that says "this is no number" %\pgfmathparse@@\pgfmath@parse@stop% } \def\pgfmath@parse@stop{\pgfmath@parse@stop}% equals only itself \def\pgfmathparse@trynumber@token{numeric} \begingroup \def\\{\global\let\pgf@let@space@token= } \\ % now, \pgf@let@space@token is a space token \endgroup % This a "fast-lane": if the expressions consist merely of number % tokens, we can simply return the number as-is. % % This is significantly faster and should resemble the 80% use-case. % % #1 a single token \def\pgfmathparse@trynumber@loop{% \futurelet\pgfmath@token@let\pgfmathparse@trynumber@loop@ }% \def\pgfmathparse@trynumber@loop@#1{% \ifx\pgfmath@token@let\pgf@let@space@token % Hm. we found a white space... and we have no support for % trimming. That means we have to assume that the white space % occurred somewhere in the middle - and fall back to the % expensive method. \def\pgfmath@parse@next{\pgfmathparse@@#1}% \else \ifx\pgfmath@token@let\bgroup% % oh! We found '{' #1. % Well, these braces appear to be special; fall back to % the complicated routine... \let\pgfmath@parse@next=\pgfmathparse@@ \else \ifx\pgfmath@token@let\pgfmath@parse@stop % Ah: we have passed the check! The expression consists only % of 0123456789. , so do not parse anything and return it % as-is! \let\pgfmath@parse@next=\pgfmathparse@expression@is@number \else \expandafter\ifx\csname pgfmath@token@\pgfmathparse@trynumber@token @\string#1\endcsname\relax% % hm. It is none of 0123456789. \let\pgfmath@parse@next=\pgfmathparse@@ \else % continue... we only found one of 0123456789. so % far... \let\pgfmath@parse@next=\pgfmathparse@trynumber@loop \fi \fi \fi \fi \pgfmath@parse@next }% \def\pgfmathparse@expression@is@number{% \let\pgfmathresult=\pgfmath@expression \pgfmath@smuggleone\pgfmathresult% \endgroup \ignorespaces }% \def\pgfmathparse@@#1\pgfmath@parse@stop{% % We are inside a group (opened in |\pgfmathparse| or % |\pgfmathqparse|). % Stuff for calc compatibility. \let\real=\pgfmath@calc@real \let\minof=\pgfmath@calc@minof \let\maxof=\pgfmath@calc@maxof \let\ratio=\pgfmath@calc@ratio \let\widthof=\pgfmath@calc@widthof \let\heightof=\pgfmath@calc@heightof \let\depthof=\pgfmath@calc@depthof % Restore font (defined in pgfmathutil.code.tex) \pgfmath@selectfont % Set up stack. \pgfmath@stack@operation={{}{}{}}% \pgfmath@stack@operand={{}{}{}}% \let\pgfmath@stack@operation@top=\pgfmath@stack@empty \let\pgfmath@stack@operand@top=\pgfmath@stack@empty % An expression always begins with an operand. \expandafter\pgfmath@bgroup@strip\expandafter{\pgfmath@expression}% % |\pgfmath@bgroup@stripped| is the result of % |\pgfmath@bgroup@strip| \expandafter\pgfmath@parse@@operand\pgfmath@bgroup@stripped @@@@\pgfmath@parse@stop% } \def\pgfmath@parse@end#1\pgfmath@parse@stop{% \pgfmathpostparse \pgfmath@smuggleone\pgfmathresult% \endgroup \ignorespaces} \let\pgfmathpostparse=\relax % For compatibility with older version. % \def\pgfmathscaleresult{% \ifpgfmathunitsdeclared \else \ifpgfmathignoreunitscale \else \afterassignment\pgfmath@gobbletilpgfmath@% \pgfmath@x\pgfmathresultunitscale pt\relax\pgfmath@% \expandafter\pgfmath@x\pgfmathresult\pgfmath@x% \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}% \fi \fi } \def\pgfmathsetresultunitscale#1{\def\pgfmathresultunitscale{#1}} \def\pgfmathresultunitscale{1} % A utility function which evaluates expression '#1' and invokes '#2' % if the expression is true and '#3' if it is false. \def\pgfmathifexpression#1#2#3{% \pgfmathparse{#1}% \pgfmath@iftrue{#2}{#3}% }% % Executes '#1' if \pgfmathresult is 'true', '#2' otherwise. % WARNING : overwritten in fpu lib! \def\pgfmath@iftrue{% \ifdim\pgfmathresult pt=1.0pt % \let\pgfmath@next=\pgfutil@firstoftwo \else \let\pgfmath@next=\pgfutil@secondoftwo \fi \pgfmath@next% }% % Stuff for computability with the calc package. % \def\pgfmath@calc@real#1{#1} \def\pgfmath@calc@minof#1#2{min(#1,#2)} \def\pgfmath@calc@maxof#1#2{max(#1,#2)} \def\pgfmath@calc@ratio#1#2{#1/#2} \def\pgfmath@calc@widthof#1{width("#1")} \def\pgfmath@calc@heightof#1{height("#1")} \def\pgfmath@calc@depthof#1{depth("#1")} \def\pgfmath@bgroup{\string\pgfmath@bgroup} \def\pgfmath@egroup{\string\pgfmath@egroup} \def\pgfmath@egroup@token{\pgfmath@egroup} \def\pgfmath@text@@{@} \def\pgfmath@text@operator{operator} \def\pgfmath@text@function{function} \def\pgfmath@dots{...} \def\pgfmath@char@zero{0} \def\pgfmath@char@quote{"} \def\pgfmath@char@exclamation{!} \def\pgfmath@char@plus{+} \def\pgfmath@char@minus{-} \def\pgfmath@char@period{.} \def\pgfmath@char@leftangle{<} \def\pgfmath@char@leftbracket{[} \pgfmath@toks={#} \edef\pgfmath@char@hash{\the\pgfmath@toks} \def\pgfmath@tokens@make#1#2{% % Defines for each token or balanced text in |#2| a control sequence % |\pgfmath@token@<#1>@\string| and stores |#2| % in it. \def\pgfmath@prefix{#1}% % Note the empty group |{}| at the end that ends the loop in % |\pgfmath@token@@make|. \expandafter\pgfmath@tokens@@make#2{}} \def\pgfmath@tokens@@make#1{% \def\pgfmath@token{#1}% \ifx\pgfmath@token\pgfmath@empty % End of loop: all tokens or balanced texts were parsed. \else \pgfmath@namedef{pgfmath@token@\pgfmath@prefix @\string#1}{#1}% \expandafter\pgfmath@tokens@@make% \fi} \pgfmath@tokens@make{box}{\wd\ht\dp} \ifx\dimexpr\@undefined\else % needed for classic tex \pgfmath@tokens@make{dimexpr}{\dimexpr\glueexpr} \fi \pgfmath@tokens@make{unit}{{bp}{cc}{cm}{dd}{em}{ex}{in}{mm}{pc}{pt}{sp}} \ifx\pdftexversion\@undefined\else % for pdfTeX \pgfmath@tokens@make{unit}{{nc}{nd}{px}} \fi \ifx\directlua\@undefined\else % for LuaTeX \pgfmath@tokens@make{unit}{{nc}{nd}{px}} \fi \ifx\kanjiskip\@undefined\else % for pTeX, upTeX \pgfmath@tokens@make{unit}{{H}{Q}{zh}{zw}} \fi % \pgfmath@tokens@make{mathunit}{{mu}} \pgfmath@tokens@make{numeric}{.0123456789} \pgfmath@tokens@make{number}{0123456789} \pgfmath@tokens@make{functional}{_abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ} \pgfmath@tokens@make{exponent}{eE} \pgfmath@tokens@make{group}{{()}{[]}{\pgfmath@bgroup\pgfmath@egroup}} \pgfmath@tokens@make{specials}{@)]\pgfmath@egroup} \pgfmath@tokens@make{hexadecimal}{0123456789ABCDEFabcdef} \pgfmath@tokens@make{octal}{01234567} \pgfmath@tokens@make{binary}{01} \pgfmath@namedef{pgfmath@base@0x}{16} \pgfmath@namedef{pgfmath@base@0X}{16} \pgfmath@namedef{pgfmath@base@0b}{2} \pgfmath@namedef{pgfmath@base@0B}{2} % Determine if a register is a count or a dimension/skip register. \newif\ifpgfmath@dimen@ \def\pgfmath@dimen@#1{% \begingroup \afterassignment\pgfmath@dimen@@% #1=0.0pt\relax\pgfmath@} \def\pgfmath@dimen@@#1#2\pgfmath@{% \endgroup \ifx#1.% \pgfmath@dimen@false \else \pgfmath@dimen@true \fi} \def\pgfmath@parse@ifbgroup#1#2{% \let\pgfmath@parse@bgroup@after=#1% \let\pgfmath@parse@nobgroup@after=#2% \futurelet\pgfmath@token@let% \pgfmath@parse@@ifbgroup} \def\pgfmath@parse@@ifbgroup{% \ifx\pgfmath@token@let\bgroup \let\pgfmath@parse@next=\pgfmath@parse@@@ifbgroup \else % |\pgfmath@sptoken| defined in \file{pgfmathutil.code.tex}. \ifx\pgfmath@token@let\pgfmath@sptoken \let\pgfmath@parse@next=\pgfmath@parse@@@@ifbgroup \else \let\pgfmath@parse@next=\pgfmath@parse@nobgroup@after \fi \fi \pgfmath@parse@next} % TT: If false, octal parsing is switched off (needed for time parsing) \newif\ifpgfmath@octalparsing \pgfmath@octalparsingtrue % I (CJ) *think* it replaces |{| and |}| by |\pgfmath@bgroup| and % |\pgfmath@egroup|? \def\pgfmath@parse@@@ifbgroup#1{% \pgfmath@parse@bgroup@after\pgfmath@bgroup#1\pgfmath@egroup} { \def\:{\pgfmath@parse@@@@ifbgroup} \expandafter\gdef\: {\futurelet\pgfmath@token@let\pgfmath@parse@@ifbgroup} } % Parse an operand. \def\pgfmath@parse@operand{% \expandafter\pgfmath@parse@@operand\pgfmath@token@next} % This is the entry point for the parser. It is called at the end of % |\pgfmathparse@| with the following syntax % |\expandafter\pgfmath@parse@@operand\pgfmath@bgroup@stripped % @@@@\pgfmath@parse@stop|. % Note: we are inside a group. \def\pgfmath@parse@@operand{% \pgfmath@parse@ifbgroup{\pgfmath@parse@@operand}{\pgfmath@parse@@operand@}} % An operand is % * |+| (unary plus), % * |-| (unary minus), % * a prefix operator \def\pgfmath@parse@@operand@#1{% \def\pgfmath@token{#1}% \ifx\pgfmath@token\pgfmath@char@plus % Unary (prefix) plus \let\pgfmath@parse@next=\pgfmath@parse@@operand% \else \ifx\pgfmath@token\pgfmath@char@minus % Unary (prefix) minus \pgfmath@stack@push@operation{neg}% \let\pgfmath@parse@next=\pgfmath@parse@@operand \else % See |\pgfmathdeclareoperator| (below). Note that |+| and |-| % that are also declared as operators have been tested before so % they should never be parsed as binary (infix) operator at this stage. \expandafter\ifx\csname pgfmath@operation@\expandafter\string\pgfmath@token @prefix\endcsname\pgfmath@token \let\pgfmath@parse@next=\pgfmath@parse@prefix@operator \else \ifpgfmath@quickparse \let\pgfmath@parse@next=\pgfmath@qparse@operand \else \let\pgfmath@number=\pgfmath@empty \expandafter\ifx\csname pgfmath@token@functional@\string#1\endcsname\relax% \let\pgfmath@base=\pgfmath@empty% \let\pgfmath@token@next=\pgfmath@token% \if#10% Check for octal prefix. \ifpgfmath@octalparsing% \def\pgfmath@base{8}% \fi% \fi% \let\pgfmath@parse@next=\pgfmath@parse@number% \else% \let\pgfmath@function=\pgfmath@token% \let\pgfmath@parse@next=\pgfmath@parse@function% \fi% \fi% \fi% \fi% \fi% \pgfmath@parse@next% } % Parse prefix operators. % \def\pgfmath@parse@prefix@operator{% \ifx\pgfmath@token\pgfmath@char@quote% Quote character. \let\pgfmath@parse@next=\pgfmath@parse@operand@quote% \else% \ifx\pgfmath@token\pgfmath@char@exclamation% Prefix !. \pgfmath@stack@push@operation{not}% \let\pgfmath@parse@next=\pgfmath@parse@@operand% \else% Anything else, just push and hope. \expandafter\pgfmath@stack@push@operation\expandafter{\pgfmath@token}% \let\pgfmath@parse@next=\pgfmath@parse@@operand% \fi% \fi% \pgfmath@parse@next% }% % Quote part of an expression. % \def\pgfmath@parse@operand@quote#1"{% \def\pgfmathresult{#1}% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \pgfmath@parse@@operator% } % Quick operand parsing. Should always have units. % No functions, base conversion, quoting or scientific notation % are permitted. \def\pgfmath@qparse@operand{% \afterassignment\pgfmath@qparse@@operand% \pgfmath@dimen\pgfmath@token} \def\pgfmath@qparse@@operand{% \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \pgfmath@parse@@operator% } % Parse a number, which can take the form: % % 1. An integer, or a decimal, with or without units. % 2. A dimension/skip or a count register. % 3. A dimension register preceded by a number or count register. % 4. A box dimension (e.g., \wd\mybox). % 5. A box dimension preceded by a number or a count register. % 6. Scientific notation (e.g., 1.234567e-10). % 7. A binary, hexadecimal, or octal number. % \def\pgfmath@parse@number{\pgfmath@parse@ifbgroup{\pgfmath@parse@number}{\pgfmath@parse@number@}} \def\pgfmath@parse@number@#1{% \let\pgfmath@token=\pgfmath@token@next% \def\pgfmath@token@next{#1}% \pgfmath@parse@@number} \def\pgfmath@parse@@number{% \ifx\pgfmath@token\pgfmath@egroup@token% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmath@number}% \let\pgfmath@parse@next=\pgfmath@parse@@@operator% \else% \expandafter\ifcat\pgfmath@token\relax% A CS? \expandafter\ifx\csname pgfmath@token@dimexpr@\expandafter\string\pgfmath@token\endcsname\relax% \expandafter\ifx\pgfmath@token\numexpr% \let\pgfmath@parse@next=\pgfmath@parse@numexpr% \else% \expandafter\ifx\pgfmath@token\muexpr% \let\pgfmath@parse@next=\pgfmath@parse@muexpr% \else% \expandafter\ifx\csname pgfmath@token@box@\expandafter\string\pgfmath@token\endcsname\relax% % So, is the CS is a dimension or a count register? \expandafter\pgfmath@dimen@\pgfmath@token% \ifpgfmath@dimen@% A dimension register. \global\pgfmathunitsdeclaredtrue% \pgfmath@dimen=\pgfmath@number\pgfmath@token% \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \let\pgfmath@parse@next=\pgfmath@parse@operator% \else% A count register. \pgfmath@count=\pgfmath@token% \expandafter\def\expandafter\pgfmath@number\expandafter{\the\pgfmath@count}% \expandafter\ifcat\pgfmath@token@next\relax% % A CS following a count register should be \wd, \ht or \dp. \let\pgfmath@parse@next=\pgfmath@parse@number% \else% \let\pgfmathresult=\pgfmath@number% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \let\pgfmath@parse@next=\pgfmath@parse@operator% \fi% \fi% \else% % This should be a box specification, for example, 0.5\wd\mybox. \global\pgfmathunitsdeclaredtrue% \pgfmath@dimen=\pgfmath@number\pgfmath@token\pgfmath@token@next% \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \let\pgfmath@parse@next=\pgfmath@parse@@operator% \fi% \fi% \fi% \else% \global\pgfmathunitsdeclaredtrue% \let\pgfmath@parse@next=\pgfmath@parse@dimexpr% \fi% \else% \expandafter\ifx\csname pgfmath@token@numeric@\expandafter\string\pgfmath@token\endcsname\relax% % It isn't numeric (i.e., 012345679.), so it might be units... % first double-character units... \expandafter\ifx\csname pgfmath@token@unit@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax% % then single-character units... \expandafter\ifx\csname pgfmath@token@unit@\pgfmath@token\endcsname\relax% % ...or the exponent characters... \expandafter\ifx\csname pgfmath@token@exponent@\pgfmath@token\endcsname\relax% % ...or a base prefix... \expandafter\ifx\csname pgfmath@base@\pgfmath@number\pgfmath@token\endcsname\relax% % ...or a math unit... \expandafter\ifx\csname pgfmath@token@mathunit@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax% % ...none of the above... \ifx\pgfmath@base\pgfmath@empty% \let\pgfmathresult=\pgfmath@number% \else% \ifx\pgfmath@number\pgfmath@char@zero% \let\pgfmathresult=\pgfmath@number% \else% % Convert from octal. \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\pgfmath@number}{8}{10}% \fi% \fi% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \let\pgfmath@parse@next=\pgfmath@parse@@@operator% \else% % ...here, it is a math unit (mu). Treat it as a pt. \global\pgfmathunitsdeclaredtrue% \global\pgfmathmathunitsdeclaredtrue% \pgfmath@dimen=\pgfmath@number pt\relax% \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \let\pgfmath@parse@next=\pgfmath@parse@@operator% \fi% \else% % ...here, it is a base prefix 0x, 0X, 0b or 0B \expandafter\let\expandafter\pgfmath@base\expandafter=% \csname pgfmath@base@\pgfmath@number\pgfmath@token\endcsname% \let\pgfmath@parse@next=\pgfmath@parse@base% \fi% \else% ... and here, it is the exponent characters. \let\pgfmath@parse@next=\pgfmath@parse@exponent% \fi% \else% ...but here it is single-character 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 double-character 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% It is numeric. \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgfmath@number% \expandafter\expandafter\expandafter{\expandafter\pgfmath@number\pgfmath@token}% \ifx\pgfmath@token\pgfmath@char@period% \let\pgfmath@base=\pgfmath@empty% \fi% \let\pgfmath@parse@next=\pgfmath@parse@number% \fi% \fi% \fi% \pgfmath@parse@next% } % Parse a \dimexpr \def\pgfmath@parse@dimexpr{% \afterassignment\pgfmath@parse@dimexpr@% \expandafter\expandafter\expandafter\pgfmath@dimen\expandafter\pgfmath@token\pgfmath@token@next% } \def\pgfmath@parse@dimexpr@{% \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \pgfmath@parse@@operator% } % Parse a \muexpr \def\pgfmath@parse@muexpr{% \begingroup% \afterassignment\pgfmath@parse@muexpr@% \expandafter\expandafter\expandafter\muskip\expandafter\expandafter\expandafter0\expandafter\pgfmath@token\expandafter\pgfmath@token@next% } \def\pgfmath@parse@muexpr@{% \expandafter\endgroup% \expandafter\edef\expandafter\pgfmathresult\expandafter{\expandafter\pgfMATH@STRIPMU\the\muskip0}% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \pgfmath@parse@@operator% } { \catcode`\m=12 \catcode`\u=12 \gdef\pgfMATH@STRIPMU#1mu{#1} } % Parse a \numexpr \def\pgfmath@parse@numexpr{% \afterassignment\pgfmath@parse@numexpr@% \expandafter\expandafter\expandafter\pgfmath@count\expandafter\pgfmath@token\pgfmath@token@next% } \def\pgfmath@parse@numexpr@#1{% \expandafter\def\expandafter\pgfmath@number\expandafter{\the\pgfmath@count}% \def\pgfmath@token@next{#1}% \expandafter\ifcat\pgfmath@token@next\relax% % A CS following a count register should be \wd, \ht or \dp. \let\pgfmath@parse@next=\pgfmath@parse@number% \else% \let\pgfmathresult=\pgfmath@number% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \let\pgfmath@parse@next=\pgfmath@parse@operator% \fi% \pgfmath@parse@next% } % Parse the exponent of a number. % % REMARK: this method will be overwritten by the FPU library. Please % keep changes consistent... \def\pgfmath@parse@exponent{% \afterassignment\pgfmath@parse@@exponent% \pgfmath@count\pgfmath@token@next} \def\pgfmath@parse@@exponent{% \pgfmathscientific{\pgfmath@number}{\the\pgfmath@count}% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \pgfmath@parse@@operator% } % Parse binary or hexadecimal numbers (octal numbers done elsewhere). % \def\pgfmath@parse@base{% \ifnum\pgfmath@base=2\relax% \let\pgfmath@parse@next=\pgfmath@parse@binary% \else% \ifnum\pgfmath@base=16\relax% \let\pgfmath@parse@next=\pgfmath@parse@hexadecimal% \else% \pgfmath@error{Unexpected numerical base `\pgfmath@base'}{}% \def\pgfmathresult{0}% \let\pgfmath@parse@next=\pgfmath@parse@end% \fi% \fi% \let\pgfmath@number=\pgfmath@empty% \expandafter\pgfmath@parse@next\pgfmath@token@next% } \def\pgfmath@parse@binary#1{% \expandafter\ifx\csname pgfmath@token@binary@#1\endcsname\relax% \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\pgfmath@number}{2}{10}% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \def\pgfmath@token@next{#1}% \let\pgfmath@parse@next=\pgfmath@parse@operator% \else% \expandafter\def\expandafter\pgfmath@number\expandafter{\pgfmath@number#1}% \let\pgfmath@parse@next=\pgfmath@parse@binary% \fi% \pgfmath@parse@next% } \def\pgfmath@parse@hexadecimal#1{% \expandafter\ifx\csname pgfmath@token@hexadecimal@#1\endcsname\relax% \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\pgfmath@number}{16}{10}% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \def\pgfmath@token@next{#1}% \let\pgfmath@parse@next=\pgfmath@parse@operator% \else% \expandafter\def\expandafter\pgfmath@number\expandafter{\pgfmath@number#1}% \let\pgfmath@parse@next=\pgfmath@parse@hexadecimal% \fi% \pgfmath@parse@next% } % Parse a function. % \def\pgfmath@parse@function{\pgfmath@parse@ifbgroup{\pgfmath@parse@function}{\pgfmath@parse@@function}} \def\pgfmath@parse@function@{\futurelet\pgfmath@token@let\pgfmath@parse@@function} \def\pgfmath@parse@@function{% \ifx\pgfmath@token@let\pgfmath@sptoken% \let\pgfmath@token=\pgfmath@empty% \let\pgfmath@parse@next=\pgfmath@parse@@@@function% \else% \let\pgfmath@parse@next=\pgfmath@parse@@@function% \fi% \pgfmath@parse@next} \def\pgfmath@parse@@@function#1{% \expandafter\ifx\csname pgfmath@token@functional@\expandafter\string#1\endcsname\relax% \expandafter\ifx\csname pgfmath@token@number@\expandafter\string#1\endcsname\relax% \def\pgfmath@token{#1}% Not from A-Z, a-z, 0-9, or _. \let\pgfmath@parse@next=\pgfmath@parse@@@@function% \else% It is from 0-9. \expandafter\def\expandafter\pgfmath@function\expandafter{\pgfmath@function#1}% \let\pgfmath@parse@next=\pgfmath@parse@function@% \fi% \else% It is from A-Z, a-z, or _. \edef\pgfmath@function{\pgfmath@function#1}% \let\pgfmath@parse@next=\pgfmath@parse@function@% \fi% \pgfmath@parse@next} \def\pgfmath@parse@@@@function{% \expandafter\ifx\csname pgfmath@function@\pgfmath@function\endcsname\relax% \pgfmath@error{Unknown function `\pgfmath@function'}{}% \def\pgfmathresult{0}% \let\pgfmath@parse@next=\pgfmath@parse@end% \else% \expandafter\ifnum\csname pgfmath@operation@\pgfmath@function @arity\endcsname=0\relax% % Functions with zero arity are called directly. \csname pgfmath\pgfmath@function @\endcsname% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \let\pgfmath@parse@next=\pgfmath@parse@@operator% \else% Otherwise, they are pushed onto the operator stack \expandafter\pgfmath@stack@push@operation\expandafter{\pgfmath@function}% \let\pgfmath@parse@next=\pgfmath@parse@@operand% \fi% \fi% \expandafter\pgfmath@parse@next\pgfmath@token} % Parse an operator. % \def\pgfmath@parse@operator{\pgfmath@parse@ifbgroup{\pgfmath@parse@operator}{\pgfmath@parse@operator@}}% \def\pgfmath@parse@operator@#1{% Get one token. \let\pgfmath@token=\pgfmath@token@next% \def\pgfmath@token@next{#1}% \pgfmath@parse@@@operator} \def\pgfmath@parse@@operator{\pgfmath@parse@ifbgroup{\pgfmath@parse@@operator}{\pgfmath@parse@@operator@}}% \def\pgfmath@parse@@operator@#1{% Get first token... \def\pgfmath@token{#1}% \pgfmath@parse@ifbgroup{\pgfmath@parse@@operator@@}{\pgfmath@parse@@operator@@}}% \def\pgfmath@parse@@operator@@#1{% ...and second token. \def\pgfmath@token@next{#1}% \pgfmath@parse@@@operator} \def\pgfmath@parse@@@operator{% \expandafter\ifx\csname pgfmath@operator@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax% % Not a double character operator. \expandafter\ifx\csname pgfmath@operator@\pgfmath@token\endcsname\relax% % Not a single character operator. \pgfmath@error{Unknown operator `\pgfmath@token' or `\pgfmath@token\pgfmath@token@next'}{}% \def\pgfmathresult{0}% \let\pgfmath@parse@next=\pgfmath@parse@end% \else% \expandafter\pgfmath@operation@process\expandafter{\pgfmath@token}% \ifx\pgfmath@token\pgfmath@text@@% \let\pgfmath@parse@next=\pgfmath@parse@end% \else% \expandafter\ifx\csname pgfmath@operation@\pgfmath@token @postfix\endcsname\pgfmath@token% % Postfix operators are followed by an operator. \ifx\pgfmath@token@next\pgfmath@char@leftbracket% Except [. \let\pgfmath@parse@next=\pgfmath@parse@operand% \else% \let\pgfmath@parse@next=\pgfmath@parse@operator% \fi% \else% % Any other operator is followed by an operand. \let\pgfmath@parse@next=\pgfmath@parse@operand% \fi% \fi% \fi% \else% % A double character operator... \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter% \pgfmath@token\expandafter\expandafter\expandafter% {\expandafter\pgfmath@token\pgfmath@token@next}% \expandafter\pgfmath@operation@process\expandafter{\pgfmath@token}% % ...is always followed by an operand. \let\pgfmath@parse@next=\pgfmath@parse@@operand% \fi% \pgfmath@parse@next% } % Process an operation. % \def\pgfmath@operation@process#1{% \def\pgfmath@operator{#1}% \ifx\pgfmath@stack@operation@top\pgfmath@stack@empty% \else% \pgfmath@operation@@process% \fi% \expandafter\ifx\csname pgfmath@token@specials@#1\endcsname\relax% \pgfmath@stack@push@operation{#1}% \fi% } % Process the operation stack. % \def\pgfmath@operation@@process{% \ifx\pgfmath@stack@operation@top\pgfmath@stack@empty% \let\pgfmath@parse@next=\relax% \else% \ifnum\csname pgfmath@operation@\pgfmath@operator @precedence\endcsname>% \csname pgfmath@operation@\pgfmath@stack@operation@top @precedence\endcsname\relax% % If the precedence of the scanned operator is greater than the % precedence of the operator at the top of the stack, do nothing. \let\pgfmath@parse@next=\relax% \else% \let\pgfmath@stack@operation@last=\pgfmath@stack@operation@top% \expandafter\ifx\csname pgfmath@operator@\pgfmath@stack@operation@top\endcsname\relax% \pgfmath@function@@@process% \else% \pgfmath@operator@@@process% \fi% \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% \expandafter\ifx\csname pgfmath@token@group@\pgfmath@stack@operation@last\pgfmath@operator\endcsname\relax% \let\pgfmath@parse@next=\pgfmath@operation@@process% \else% \let\pgfmath@parse@next=\relax% \fi% \fi% \fi% \pgfmath@parse@next% } % Process an operator. % \def\pgfmath@operator@@@process{% Process an operator. \pgfmath@stack@pop@operation\pgfmath@@operator% \pgfmath@stack@pop@operand\pgfmath@operand@a% \ifcase\csname pgfmath@operation@\pgfmath@@operator @arity\endcsname\relax% % Zero arity operators (!). \or% \pgfmath@operator@@@@process{\pgfmath@operand@a}% \or% \pgfmath@stack@pop@operand\pgfmath@operand@b% \pgfmath@operator@@@@process{\pgfmath@operand@b}{\pgfmath@operand@a}% \or% \pgfmath@stack@pop@operand\pgfmath@operand@b% \expandafter\pgfmath@operator@@@@process\expandafter% {\expandafter\pgfmath@operand@b\expandafter}\pgfmath@operand@a% \else% % No operators with more than tenary arity. \fi% } \def\pgfmath@operator@@@@process{% \csname pgfmath% \csname pgfmath@operation@\pgfmath@@operator @name\endcsname% @\endcsname} % Process a function. % \def\pgfmath@function@@@process{% Process a function. \ifnum\csname pgfmath@operation@\pgfmath@stack@operation@top @arity\endcsname>0\relax% \pgfmath@stack@pop@operation\pgfmath@@function% \pgfmath@stack@pop@operand\pgfmath@@operand% \ifnum\csname pgfmath@operation@\pgfmath@@function @arity\endcsname>1\relax% \ifnum\csname pgfmath@operation@\pgfmath@@function @arity\endcsname>9\relax% \csname pgfmath\pgfmath@@function @\endcsname{\pgfmath@@operand}% \else% \expandafter\pgfmath@function@@@@process\pgfmath@@operand% \fi \else% \expandafter\pgfmath@function@@@@process\expandafter{\pgfmath@@operand}% \fi% \fi% } \def\pgfmath@function@@@@process{\csname pgfmath\pgfmath@@function @\endcsname} % Stack. % \newtoks\pgfmath@stack@operand \newtoks\pgfmath@stack@operation \let\pgfmath@stack@empty=\pgfmath@empty \def\pgfmath@stack@push#1#2{% \def\pgfmath@stack@top{#2}% \expandafter\expandafter\expandafter#1% \expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter% {\expandafter\pgfmath@stack@top\expandafter}\the#1}}% \def\pgfmath@stack@pop#1#2{\expandafter\pgfmath@stack@@pop\the#1\pgfmath@stack@stop{#1}{#2}} \def\pgfmath@stack@@pop#1#2#3\pgfmath@stack@stop#4#5{\def#5{#1}#4={{#2}#3}\def\pgfmath@stack@top{#2}} \def\pgfmath@stack@push@operation#1{% \pgfmath@stack@push\pgfmath@stack@operation{#1}% \let\pgfmath@stack@operation@top=\pgfmath@stack@top} \def\pgfmath@stack@pop@operation#1{% \pgfmath@stack@pop\pgfmath@stack@operation{#1}% \let\pgfmath@stack@operation@top=\pgfmath@stack@top} % REMARK: This method will be overwritten by the FPU library. Please % keep any changes consistent. \def\pgfmath@stack@push@operand#1{% \pgfmath@stack@push\pgfmath@stack@operand{#1}% \let\pgfmath@stack@operand@top=\pgfmath@stack@top} \def\pgfmath@stack@pop@operand#1{% \pgfmath@stack@pop\pgfmath@stack@operand{#1}% \let\pgfmath@stack@operand@top=\pgfmath@stack@top} % Declare an operator for the parser. % % It is not recommended that new operators be created as % the parser is not fully robust for arbitrary operators. % \def\pgfmathdeclareoperator#1#2#3#4#5{% \ifx\pgfmath@operatorlist\pgfutil@empty \edef\pgfmath@operatorlist{{\string#1}}% \else \edef\pgfmath@operatorlist{\pgfmath@operatorlist,{\string#1}}% \fi \pgfmath@namedef{pgfmath@operator@\string#1}{#1}% \pgfmath@namedef{pgfmath@operation@\string#1@name}{#2}% \pgfmath@namedef{pgfmath@operation@\string#1@arity}{#3}% \pgfmath@namedef{pgfmath@operation@\string#1@#4}{#1}% \pgfmath@namedef{pgfmath@operation@\string#1@precedence}{#5}% } \def\pgfmath@operatorlist{} \pgfmathdeclareoperator{+}{add} {2}{infix}{500} \pgfmathdeclareoperator{-}{subtract}{2}{infix}{500} \pgfmathdeclareoperator{*}{multiply}{2}{infix}{700} \pgfmathdeclareoperator{/}{divide} {2}{infix}{700} \pgfmathdeclareoperator{^}{pow} {2}{infix}{900} \pgfmathdeclareoperator{<} {} {1}{prefix} {1} \pgfmathdeclareoperator{>} {greater} {2}{infix} {250} \pgfmathdeclareoperator{<} {less} {2}{infix} {250} \pgfmathdeclareoperator{==}{equal} {2}{infix} {250} \pgfmathdeclareoperator{>=}{notless} {2}{infix} {250} \pgfmathdeclareoperator{<=}{notgreater}{2}{infix} {250} \pgfmathdeclareoperator{&&}{and} {2}{infix} {200} \pgfmathdeclareoperator{||}{or} {2}{infix} {200} \pgfmathdeclareoperator{!=}{notequal} {2}{infix} {250} \pgfmathdeclareoperator{!} {not} {1}{prefix}{975} \pgfmathdeclareoperator{?} {ifthenelse}{3}{infix} {100} \pgfmathdeclareoperator{:} {@@collect} {2}{infix}{101} \pgfmathdeclareoperator{!}{factorial}{1}{postfix}{800}% Must be defined after prefix ! operator. \pgfmathdeclareoperator{r}{deg} {1}{postfix}{600} \pgfmathdeclareoperator{,}{@collect} {2}{infix} {10} \pgfmathdeclareoperator{[}{@startindex}{2}{prefix} {7} \pgfmathdeclareoperator{]}{@endindex} {0}{postfix}{6} \pgfmathdeclareoperator{(}{@startgroup}{1}{prefix} {5} \pgfmathdeclareoperator{)}{@endgroup} {0}{postfix}{4} \pgfmathdeclareoperator{\pgfmath@bgroup}{@startarray}{1}{prefix} {3} \pgfmathdeclareoperator{\pgfmath@egroup}{@endarray} {1}{postfix}{2}% % Special operators. \pgfmathdeclareoperator{"}{}{1}{prefix}{1} \pgfmathdeclareoperator{@}{}{0}{postfix}{0} % Internal functions. % Begin and end parenthesis (). % \def\pgfmath@startgroup@#1{\pgfmath@protected@edef\pgfmathresult{#1}} \def\pgfmath@endgroup@{}% Never actually called. % Begin and end array access []. % \def\pgfmath@startindex@#1#2{% \expandafter\pgfmatharray@#1{#2}% \expandafter\pgfmath@bgroup@strip\expandafter{\pgfmathresult}% \ifx\pgfmath@token@let\bgroup% \expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{\pgfmathresult}}% \fi} \def\pgfmath@endindex@{}% Never actually called. % Begin and end array {}. % \def\pgfmath@startarray@#1{\expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{#1}}} \def\pgfmath@endarray@#1{\expandafter\def\expandafter\pgfmathresult\expandafter{#1}}% Never actually called. \def\pgfmath@@collect@#1#2{% \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter% \pgfmathresult\expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter% {\expandafter#1\expandafter}\expandafter{#2}}% } % Collect items separated by ,. % \def\pgfmath@collect@#1#2{% \expandafter\def\expandafter\pgfmath@collect@original\expandafter{#1}% \expandafter\pgfmath@bgroup@strip\expandafter{#1}% \ifx\pgfmath@token@let\bgroup% \ifx\pgfmath@collect@original\pgfmath@bgroup@stripped% \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmath@bgroup@stripped}% \else% \expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{\pgfmath@bgroup@stripped}}% \fi% \else% \expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{\pgfmath@bgroup@stripped}}% \fi% \expandafter\pgfmath@bgroup@strip\expandafter{#2}% \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter% \pgfmathresult\expandafter\expandafter\expandafter% {\expandafter\pgfmathresult\expandafter{\pgfmath@bgroup@stripped}}% } % Strip braces from a token sequence. % \def\pgfmath@bgroup@strip#1{% \def\pgfmath@bgroup@strip@last{#1}% \pgfmath@bgroup@@strip{#1}\pgfmath@\pgfmath@@\pgfmath@@@} \def\pgfmath@bgroup@strip@#1{% \def\pgfmath@bgroup@strip@last{#1}% \pgfmath@bgroup@@strip#1\pgfmath@\pgfmath@@\pgfmath@@@} \def\pgfmath@bgroup@pgfmath@{\pgfmath@} \def\pgfmath@bgroup@@strip{% \futurelet\pgfmath@token@let\pgfmath@bgroup@@@strip} \def\pgfmath@bgroup@@@strip#1#2#3\pgfmath@@@{% \ifx\pgfmath@token@let\bgroup \def\pgfmath@bgroup@test{#2}% \ifx\pgfmath@bgroup@test\pgfmath@bgroup@pgfmath@ \def\pgfmath@next{\pgfmath@bgroup@strip@{#1}}% \else \let\pgfmath@bgroup@stripped=\pgfmath@bgroup@strip@last \let\pgfmath@next=\relax \fi \else \pgfmath@bgroup@@@@strip#1#2#3% \let\pgfmath@next=\relax \fi \pgfmath@next} \def\pgfmath@bgroup@@@@strip#1\pgfmath@\pgfmath@@{% \def\pgfmath@bgroup@stripped{#1}} % Local Variables: % tab-width: 2 % End: