% Copyright 2007 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.

% This file loads all the parsing, functions and operator stuff
%
% Version 1.414213 29/9/2007

\input pgfmathutil.code.tex
\input pgfmathparser.code.tex
\input pgfmathfunctions.code.tex
%\input pgfmathbase.code.tex

% \pgfmathsetlength, \pgfmathaddtolength
%
% #1 = dimension register
% #2 = expression
%
% Description:
%
% These functions work similar to \setlength and \addtolength. Only,
% they allow #2 to contain an expression, which is evaluated before
% assignment. Furthermore, the font is setup before the assignment is
% done, so that dimensions like 1em are evaluated correctly.
%
% If #2 starts with "+", then a simple assignment is done (but the
% font is still setup). This is orders of magnitude faster than a
% parsed assignment.

\def\pgfmathsetlength#1#2{%
	\expandafter\pgfmath@onquick#2\pgfmath@%
	{%
		% Ok, quick version:
		\begingroup%
			\pgfmath@selectfont%
			\pgfmath@x#2\unskip%
			\pgfmath@returnone\pgfmath@x%
		\endgroup%
		#1\pgfmathresult pt\relax%
	}%
	{%
		\pgfmathparse{#2}%
		#1\pgfmathresult pt\relax%
	}%
	\ignorespaces%
}

% \pgfmathaddtolength
%
% Add to #1 the result of evaluating #2.
%
% #1 - a dimension register
% #2 - an expression
%
\def\pgfmathaddtolength#1#2{%
	\expandafter\pgfmath@onquick#2\pgfmath@%
  {%
  	\begingroup%
  		\pgfmath@selectfont%
  		\pgfmath@x#1\relax%
  		\advance\pgfmath@x#2\unskip%
  		\pgfmath@returnone\pgfmath@x%
    \endgroup%
    #1\pgfmathresult pt\relax%
  }%
  {%
  	\pgfmathparse{#2}%
  	\advance#1\pgfmathresult pt\relax%
  }%
  \ignorespaces%
}

% \pgfmathsetcount
%
% Assign #1 the truncated evaluation of #2.
%
% #1 - a count register
% #2 - an expression
%
\def\pgfmathsetcount#1#2{%
  \expandafter\pgfmath@onquick#2\pgfmath@%
  {%
    \afterassignment\pgfmath@gobbletilpgfmath@%
    #1#2\relax\pgfmath@%
  }%
  {%
    \pgfmathparse{#2}%
    \afterassignment\pgfmath@gobbletilpgfmath@%
    #1\pgfmathresult\relax\pgfmath@%
  }%
  \ignorespaces%
}

% \pgfmathaddtocount
%
% Add to #1 the truncated evaluation of #2.
%
% #1 - a count register
% #2 - an expression
%
\def\pgfmathaddtocount#1#2{%
  \expandafter\pgfmath@onquick#2\pgfmath@%
  {%
    \edef\pgfmath@addtocounttemp{\the#1}%
    \afterassignment\pgfmath@gobbletilpgfmath@%
    #1#2\relax\pgfmath@%
    \advance#1\pgfmath@addtocounttemp\relax%
  }%
  {%
    \edef\pgfmath@addtocounttemp{\the#1}%
    \pgfmathparse{#2}%
    \afterassignment\pgfmath@gobbletilpgfmath@%
    #1\pgfmathresult\relax\pgfmath@%
    \advance#1\pgfmath@addtocounttemp\relax%
  }%
  \ignorespaces%
}

% \pgfmathnewcounter
%
% LaTeX style counter which also works in plain TeX. Defines
% \c@<name> as a count register and also defines \the<name>.
%
% #1 the name of the counter.
%
% Example:
%
% \pgfmathnewcounter{counter}
% \pgfmathsetcounter{counter}{12}
% \thecounter  (same as \the\c@counter)
%
\def\pgfmathnewcounter#1{%
	\expandafter\ifx\csname c@#1\endcsname\relax%
		\def\pgfmath@marshal{\csname newcount\endcsname}% Ha! Who cares about \outer?
		\expandafter\pgfmath@marshal\csname c@#1\endcsname%
		\expandafter\def\csname the#1\endcsname{\expandafter\the\csname c@#1\endcsname}%
	\fi%
}

% \pgfmathsetcounter
%
% Set the counter #1 to the evaluation of #2.
%
% #1 - a counter name
% #2 - an expression
%
\def\pgfmathsetcounter#1#2{%
 	\expandafter\pgfmathsetcount\csname c@#1\endcsname{#2}%
}

% \pgfmathaddtocounter
%
% Add the counter #1 to the evaluation of #2.
%
% #1 - a counter name
% #2 - an expression
%
\def\pgfmathaddtocounter#1#2{%
  \expandafter\pgfmathaddtocount\csname c@#1\endcsname{#2}%
}

% \pgfmathmakecounterglobal
%
% Make the current value of a counter globally defined.
%
% #1 - a (valid) counter name.
%
\def\pgfmath@pgftext{pgf}
\def\pgfmath@tikztext{tikz}
\def\pgfmathmakecounterglobal#1{%
	\pgfmath@ifundefined{c@#1}{}{%
		\expandafter\pgfmath@in@\expandafter{\pgfmath@pgftext}{#1}%
		\ifpgfmath@in@%
		\else%
			\expandafter\pgfmath@in@\expandafter{\pgfmath@tikztext}{#1}%
			\ifpgfmath@in@%
			\else%
				\expandafter\global\csname c@#1\endcsname\csname c@#1\endcsname\relax%
			\fi%
		\fi%
	}%
}

% \pgfmathsetmacro
%
% \edef#1 as the result of evaluating #2.
%
% #1 - a macro
% #2 - an expression
%
\def\pgfmathsetmacro#1#2{%
	\begingroup%
		\pgfmathsetlength\pgfmath@x{#2}%
		\edef#1{\pgfmath@tonumber{\pgfmath@x}}%
		\pgfmath@smuggleone{#1}%
	\endgroup%
}

% \pgfmathsetlengthmacro
%
% \edef#1 as the result of evaluating #2 with pt.
%
% #1 - a macro
% #2 - an expression
%
\def\pgfmathsetlengthmacro#1#2{%
	\begingroup%
		\pgfmathsetlength\pgfmath@x{#2}%
		\edef#1{\the\pgfmath@x}%
		\pgfmath@smuggleone{#1}%
	\endgroup%
}

% \pgfmathtruncatemacro
%
% \edef#1 as the truncated result of evaluating #2.
%
% #1 - a macro
% #2 - an expression
%
\def\pgfmathtruncatemacro#1#2{%
	\begingroup%
		\pgfmathsetcount\c@pgfmath@counta{#2}%
		\edef#1{\the\c@pgfmath@counta}%
		\pgfmath@smuggleone{#1}%
	\endgroup%
}

% Check whether a given parameter starts with quick.
%
% The command should be followed by nonempty text, ending with
% \pgfmath@ as a stop-token. Then should follow
%
% #1 - code to execute if text starts with +
% #2 - code to execute if text does not
%
% Example:
%
% \pgfmath@onquick+0pt\pgfmath@{is quick}{is slow}

\def\pgfmath@onquick{%
  \futurelet\pgfmath@next%
  \pgfmath@@onquick}
\def\pgfmath@@onquick#1\pgfmath@{%
	\ifx\pgfmath@next+%
	  \let\pgfmath@next=\pgfmath@firstoftwo%
	\else%
	  \let\pgfmath@next=\pgfmath@secondoftwo%
	\fi%
	\pgfmath@next%
}

% *** The following commands DO NOT WORK without the rest of PGF ***
%
% (a dumping ground for stuff that doesn't really belong anywhere else)
	
% \pgfmathanglebetweenpoints
%
% Define \pgfmathresult as the angle between points #1 and #2
% Should get the quadrants right as well.
%
\def\pgfmathanglebetweenpoints#1#2{%
	\begingroup%
		\pgf@process{\pgfpointdiff{#1}{#2}}%
		%
		% First approximate the angle of the external point...
		%
		\pgf@xa\pgf@x%
		\pgf@ya\pgf@y%
		\pgf@xb\pgf@x%
		\pgf@yb\pgf@y%
		\ifdim\pgf@xa<0pt\relax%
			\pgf@xa-\pgf@xa%
		\fi%
		\ifdim\pgf@ya<0pt\relax%
			\pgf@ya-\pgf@ya%
		\fi%
		\ifdim\pgf@ya>\pgf@xa%
			\pgf@x\pgf@xa%
			\pgf@y\pgf@ya%
		\else%
			\pgf@x\pgf@ya%
			\pgf@y\pgf@xa%
		\fi%
		\ifdim\pgf@y=0pt\relax%
			\pgf@x0pt%
		\else%
			\pgfmathreciprocal@{\pgfmath@tonumber{\pgf@y}}%
			\pgf@x\pgfmathresult\pgf@x%
		\fi%
		\multiply\pgf@x1000\relax%
		\afterassignment\pgfmath@gobbletilpgfmath@%
		\expandafter\c@pgf@counta\the\pgf@x\relax\pgfmath@%
		\expandafter\pgf@x\csname pgfmath@atan@\the\c@pgf@counta\endcsname pt\relax%
		\ifdim\pgfmath@ya>\pgfmath@xa\relax%
			\pgf@x-\pgf@x%
			\advance\pgf@x90pt%
		\fi%
		\ifdim\pgf@xb<0pt%
			\ifdim\pgf@yb>0pt%
				\pgf@x-\pgf@x%
			\fi%
			\advance\pgf@x180pt\relax%
		\else%
			\ifdim\pgf@yb<0pt%
			\pgf@x-\pgf@x%
			\advance\pgf@x360pt\relax%
		\fi\fi%
		\pgfmath@returnone\pgf@x%
	\endgroup%
}

%
% \pgfmathrotatepointaround
%
% Rotate point #1 about point #2 by #3 degrees.
%
\def\pgfmathrotatepointaround#1#2#3{%
	\pgf@process{%
		\pgf@process{#1}%
		\pgf@xc=\pgf@x%
		\pgf@yc=\pgf@y%
		\pgf@process{#2}%
		\pgf@xa\pgf@x%
		\pgf@ya\pgf@y%
		\pgf@xb\pgf@x%
		\pgf@yb\pgf@y%
		\pgf@x=\pgf@xc%
		\pgf@y=\pgf@yc%
		\advance\pgf@x-\pgf@xa%
		\advance\pgf@y-\pgf@ya%
		\pgfmathsetmacro\angle{#3}%
		\pgfmathsin@{\angle}%
		\let\sineangle\pgfmathresult%
		\pgfmathcos@{\angle}%
		\let\cosineangle\pgfmathresult%
		\pgf@xa\cosineangle\pgf@x%
		\advance\pgf@xa-\sineangle\pgf@y%
		\pgf@ya\sineangle\pgf@x%
		\advance\pgf@ya\cosineangle\pgf@y%
		\pgf@x\pgf@xb%
		\pgf@y\pgf@yb%
		\advance\pgf@x\pgf@xa%
		\advance\pgf@y\pgf@ya%
	}%
}

% \pgfmathanglebetweenlines
%
% Calculate the clockwise angle between a line from point #1
% to point #2 and a line from #3 to point #4.
%
\def\pgfmathanglebetweenlines#1#2#3#4{%
	\begingroup%
		\pgfmathanglebetweenpoints{#1}{#2}%
		\let\firstangle\pgfmathresult%
		\pgfmathanglebetweenpoints{#3}{#4}%
		\let\secondangle\pgfmathresult%
		\ifdim\firstangle pt>\secondangle pt\relax%
			\pgfmathadd@{\secondangle}{360}%
			\let\secondangle\pgfmathresult%
		\fi%
		\pgfmathsubtract@{\secondangle}{\firstangle}%
		\pgfmath@smuggleone\pgfmathresult%
	\endgroup%
}

% \pgfmathpointreflectalongaxis
%
% Reflects point #2 around an axis centered on #2 at an angle #3.
%
\def\pgfmathreflectpointalongaxis#1#2#3{%
	\pgf@process{%
		\pgfmathanglebetweenpoints{#2}{#1}%
		\pgfmath@tempdima\pgfmathresult pt\relax%
		\pgfmathparse{#3}%
		\advance\pgfmath@tempdima-\pgfmathresult pt\relax%
		\pgfmath@tempdima-2.0\pgfmath@tempdima%
		\pgfmathrotatepointaround{#1}{#2}{\pgfmath@tonumber{\pgfmath@tempdima}}%
	}%
}



% \pgfmathpointintersectionoflineandarc 
%
% A bit experimental at the moment:
%
% Locates the point where a line crosses an eliptical arc. If the line
% does not cross the arc, a meaningless point will result.
%
% #1 the point of the line on the "convex" side of the arc.
% #2 the point of the line on the "concave" side of the arc.
% #3 the center of the eliptical arc.
% #4 start angle of the arc.
% #5 end angle of the arc.
% #6 radii of the arc.
%
\def\pgfmathpointintersectionoflineandarc#1#2#3#4#5#6{%
	\pgf@process{%
		%
		% Get the required angle.
		%
		\pgfmathanglebetweenpoints{#2}{#1}%
		\let\x\pgfmathresult%
		%
		% Get the radii of the arc.
		%
		\pgfmath@in@{and }{#6}%
	  \ifpgfmath@in@%
	    \pgf@polar@#6\@@%
	  \else%
	    \pgf@polar@#6 and #6\@@%
	  \fi%
	  \edef\xarcradius{\the\pgf@x}%
	  \edef\yarcradius{\the\pgf@y}% 
	   %
	  % Get the start and end angles of the arc...
	  % 
	  \pgfmathsetmacro\s{#4}%
	  \pgfmathsetmacro\e{#5}%
	  %
	  % ...and also with rounding.
	  %
	  \pgfmathmod@{\s}{360}%
	  \ifdim\pgfmathresult pt<0pt\relax%
	  	\pgfmathadd@{\pgfmathresult}{360}%
	  \fi%
	  \let\ss\pgfmathresult%
	  \pgfmathmod@{\e}{360}%
	  \ifdim\pgfmathresult pt<0pt\relax%
	  	\pgfmathadd@{\pgfmathresult}{360}%
	  \fi%
	  \let\ee\pgfmathresult%
	  %
	  % Hackery for when arc straddles zero.
	  %
	  \ifdim\ee pt<\ss pt\relax%
	  	\pgfmathadd@{\x}{180}%
	  	\pgfmathmod@{\pgfmathresult}{360}%
	  	\let\x\pgfmathresult%
	  \fi%
	  \def\m{360}% Measure of nearness.
		\pgfmathadd@{\s}{\e}%
		\pgfmathdivide@{\pgfmathresult}{2}%
		\let\n\pgfmathresult% The best estimate (default to middle of arc).
		\pgfmathloop%
			\pgfmathadd@{\s}{\e}%
			\pgfmathdivide@{\pgfmathresult}{2}%
			\let\p\pgfmathresult%
			\ifdim\p pt=\s pt\relax% 
			\else%
				\pgfmathanglebetweenpoints{#2}{%
					\pgfpointadd{#3}{%
						\pgf@x\xarcradius\relax%
						\pgfmathcos@{\p}%
						\pgf@x\pgfmathresult\pgf@x%
						\pgf@y\yarcradius\relax%
						\pgfmathsin@{\p}%
						\pgf@y\pgfmathresult\pgf@y%
					}%
				}%
				%
			  % Hackery for when arc straddles zero.
			  %
				\ifdim\ee pt<\ss pt\relax%
			  	\pgfmathadd@{\pgfmathresult}{180}%
			  	\pgfmathmod@{\pgfmathresult}{360}%
			  \fi%
				\let\q\pgfmathresult%
				%
				% More hackery...
				%
				\ifdim\x pt>335pt\relax%
					\ifdim\q pt<45pt\relax%
						\pgfmathadd@{\q}{360}%
						\let\q\pgfmathresult%
					\fi%
				\fi%
				\ifdim\x pt=\q pt% Found it!
						\pgfmathbreakloop% Breaks after current iteration is complete.
					\else
						\ifdim\x pt<\q pt\relax%
							\let\e\p%
						\else%
							\let\s\p%
						\fi%
					\fi%
					\pgfmathsubtract@{\x}{\q}%
					\pgfmathabs@{\pgfmathresult}%
					%
					% Save the estimate if it is better than any previous estimate.
					%
					\ifdim\pgfmathresult pt<\m pt\relax%
						\let\m\pgfmathresult%
						\let\n\p%
					\fi%				
		\repeatpgfmathloop%
		\pgfpointadd{#3}{\pgfpointpolar{\n}{\xarcradius and \yarcradius}}%
	}%
}

% \pgfmathangleonellipse
% 
% Find the angle corresponding to a point on the border of an ellispe.
%
% #1 - the point on the border.
% #2 - the radii of the ellipse.
%
\def\pgfmathangleonellipse#1#2{%
	\begingroup%
		\pgfmath@in@{and }{#2}%
	  \ifpgfmath@in@%
	    \pgf@polar@#2\@@%
	  \else%
	    \pgf@polar@#2 and #2\@@%
	  \fi%
	  \pgf@xa\pgf@x%
	  \pgf@ya\pgf@y%
	  \pgf@process{#1}% 
	  \ifdim\pgf@x=0pt\relax%
			\pgfutil@tempdima1pt\relax%
		\else%
			\pgfutil@tempdima\pgf@x%
			\pgfmathdivide@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgfutil@tempdima}}%
			\pgfutil@tempdima\pgfmathresult pt\relax%
		\fi%
		\ifdim\pgf@y=0pt\relax%
			\pgfutil@tempdima1pt\relax%
		\else%
			\pgfmathdivide@{\pgfmath@tonumber{\pgf@y}}{\pgfmath@tonumber{\pgf@ya}}%
			\pgfutil@tempdima\pgfmathresult\pgfutil@tempdima%
			\pgfmathatan@{\pgfmath@tonumber{\pgfutil@tempdima}}%
		\fi%
		%
		\pgfutil@tempdima\pgfmathresult pt\relax%
		\ifdim\pgfutil@tempdima<0pt\relax%
  		\advance\pgfutil@tempdima360pt\relax%
  	\fi%
		\ifdim\pgf@x<0pt\relax%
			\ifdim\pgf@y=0pt\relax%
				\pgfutil@tempdima180pt\relax%
			\else%
				\ifdim\pgf@y<0pt\relax%
					\advance\pgfutil@tempdima180pt\relax%
				\else%
					\advance\pgfutil@tempdima-180pt\relax%
				\fi%
			\fi%
		\else%
			\ifdim\pgf@x=0pt\relax%
				\ifdim\pgf@y<0pt\relax%
					\pgfutil@tempdima270pt\relax%
				\else%
					\pgfutil@tempdima90pt\relax%
				\fi%
			\else%
				\ifdim\pgf@y=0pt\relax%
					\pgfutil@tempdima0pt\relax%
				\fi%
			\fi%				
		\fi%
		\pgfmath@returnone\pgfutil@tempdima%
	\endgroup%
}