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+% Copyright 2019 by Mark Wibrow
+%
+% This file may be distributed and/or modified
+%
+% 1. under the LaTeX Project Public License and/or
+% 2. under the GNU Public License.
+%
+% See the file doc/generic/pgf/licenses/LICENSE for more details.
+
+% This file loads all the parsing, functions and operator stuff
+%
+% Version 1.414213 29/9/2007
+
+% \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%
+ #1#2\unskip%
+ \expandafter\endgroup%
+ \expandafter#1\the#1\relax%
+ }%
+ {%
+ \pgfmathparse{#2}%
+ \ifpgfmathmathunitsdeclared%
+ #1\pgfmathresult mu\relax%
+ \else%
+ #1\pgfmathresult pt\relax%
+ \fi%
+ }%
+ \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%
+ \advance#1#2\unskip%
+ \expandafter%
+ \endgroup%
+ \expandafter#1\the#1\relax%
+ }%
+ {%
+ \pgfmathparse{#2}%
+ \ifpgfmathmathunitsdeclared%
+ \advance#1\pgfmathresult mu\relax%
+ \else%
+ \advance#1\pgfmathresult pt\relax%
+ \fi%
+ }%
+ \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%
+ \pgfmathparse{#2}%
+ \let#1=\pgfmathresult
+ \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}}%
+ \edef\pgf@marshall{\expandafter\noexpand\csname pgfmathatan2@\endcsname{\expandafter\Pgf@geT\the\pgf@y}{\expandafter\Pgf@geT\the\pgf@x}}%
+ \pgf@marshall%
+ \ifdim\pgfmathresult pt<0pt%
+ \pgfmathparse{\pgfmathresult+360}%
+ \fi%
+ \expandafter%
+ \endgroup\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult}%
+}
+
+%
+% \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 #1 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%
+}
+
+
+% Local Variables:
+% tab-width: 2
+% End: