\newdimen\pgfmath@dimen
\newcount\pgfmath@count
\newbox\pgfmath@box
\newtoks\pgfmath@toks

\newif\ifpgfmath@quickparse
\newif\ifpgfmathfloat
\newif\ifpgfmathunitsdeclared
\newif\ifpgfmathignoreunitscale

\def\pgfmathprint#1{\pgfmathparse{#1}\pgfmathresult}

\def\pgfmathparse{%
	\begingroup%
		\pgfmath@catcodes%
		\pgfmath@quickparsefalse%
		\ifpgfmathfloat%
			\let\pgfmath@parse@next=\pgfmathfloatparsenumber%
		\else%
			\let\pgfmath@parse@next=\pgfmathparse@%
		\fi%
		\pgfmath@parse@next}

\def\pgfmath@catcodes{% Maybe unecessary.
	\catcode`\==12%
	\catcode`\,=12%
	\catcode`\|=12%
	\catcode`\&=12%
}

\def\pgfmathqparse{%
	\begingroup%
		\pgfmath@catcodes%
		\pgfmath@quickparsetrue%
		\pgfmathparse@}
	
\def\pgfmathparse@#1{%
		% Stuff for calc compatiability.
		\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.
    \pgfmath@selectfont%
    % Expand expression so any reamining CSs are registers
    % or box dimensions (i.e., \wd, \ht, \dp).
    \edef\pgfmath@expression{#1}%
    % No units yet. 
    \global\pgfmathunitsdeclaredfalse%
    % 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}%
		\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 compatiability 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}

% Stuff for compatability 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{%
	\def\pgfmath@prefix{#1}%
	\expandafter\pgfmath@tokens@@make#2{}}
	
\def\pgfmath@tokens@@make#1{%
	\def\pgfmath@token{#1}%
	\ifx\pgfmath@token\pgfmath@empty%
	\else%
		\pgfmath@namedef{pgfmath@token@\pgfmath@prefix @\string#1}{#1}%
		\expandafter\pgfmath@tokens@@make%
	\fi}

\pgfmath@tokens@make{box}{\wd\ht\dp}
\pgfmath@tokens@make{unit}{{bp}{cc}{cm}{dd}{em}{ex}{in}{mm}{pc}{pt}{sp}}
\pgfmath@tokens@make{numeric}{.0123456789}
\pgfmath@tokens@make{number}{0123456789}
\pgfmath@tokens@make{functional}{_abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNPQRSTUVWXYZ}
\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%
		\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}

\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}%

\def\pgfmath@parse@@operand{\pgfmath@parse@ifbgroup{\pgfmath@parse@@operand}{\pgfmath@parse@@operand@}}

\def\pgfmath@parse@@operand@#1{%
	\def\pgfmath@token{#1}%
	\ifx\pgfmath@token\pgfmath@char@plus% Ignore.
		\let\pgfmath@parse@next=\pgfmath@parse@@operand%
	\else%
		\ifx\pgfmath@token\pgfmath@char@minus%
			\pgfmath@stack@push@operation{neg}% Unary minus.
			\let\pgfmath@parse@next=\pgfmath@parse@@operand%
		\else%
			\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.
							\def\pgfmath@base{8}%
						\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, hexadeciaml, 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@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%
		\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...
				\expandafter\ifx\csname pgfmath@token@unit@\pgfmath@token\expandafter\string\pgfmath@token@next\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%
							% ...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 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 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 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 elsehwere).
%
\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 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{%
	\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}%
}

\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{!=}{notequalto}{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{\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}}%