<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">% This file contains patches to support 'trig format'
%
%%% This file is a copy of some part of PGF/Tikz.
%%% It has been copied here to provide :
%%%  - compatibility with older PGF versions
%%%  - availability of PGF contributions by Christian Feuersaenger
%%%    which are necessary or helpful for pgfplots.
%%%
%%% This file contains just the functionality for trig format (written by Christian Feuersaenger).
%%% 
% Support for the contents of this file will NOT be done by the PGF/TikZ team. 
% Please contact the author and/or maintainer of pgfplots (Christian Feuersaenger) if you need assistance in conjunction
% with the deployment of this patch or partial content of PGF. Note that the author and/or maintainer of pgfplots has no obligation to fix anything:
% This file comes without any warranty as the rest of pgfplots; there is no obligation for help.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\pgfkeys{
	/pgf/trig format/.is choice,
	/pgf/trig format/deg/.code={\def\pgfmath@trig@format@choice{0}},
	/pgf/trig format/rad/.code={\def\pgfmath@trig@format@choice{1}},
	/pgf/trig format/deg,
}

% Executes #1 if 'trig format=deg' and #2 otherwise.
\def\pgfmathiftrigonometricusesdeg#1#2{%
	\if0\pgfmath@trig@format@choice
		#1%
	\else
		#2%
	\fi
}%

\pgfutil@ifundefined{pgfmath@multiply@thousand}{%
	% Oh - we are working against PGF 2.10 . Apply more patches:
	%
	\def\pgfmath@multiply@thousand#1.#2#3#4#5\relax{%
	  \edef\pgfmathresult{#1#2#3#4.#5}%
	}%
	% Defines \pgfmath@x to be the result of the table lookup for value
	% '#1' in table '#2'
	%
	% #1: a value for which lookup should be performed
	% #2: the table's prefix name
	% #3: the table's size
	\def\pgfmath@table@lookup#1#2#3{%
	  \pgfmath@x=#1\relax
	  \expandafter\pgfmath@table@lookup@\the\pgfmath@x\relax{#2}{#3}%
	}
	\def\pgfmath@table@lookup@#1.#2\relax#3#4{%
	  \edef\pgf@temp{\Pgf@geT#2}% strip 'pt' suffix.
	  %
	  % prepare constant interpolant (i.e. the value at node '#1'):
	  \pgfmath@x=\csname #3#1\endcsname pt %
	  %
	  \c@pgfmath@countc=#1 %
	  \advance\c@pgfmath@countc by1 %
	  \ifnum\c@pgfmath@countc&lt;#4 %
		% Ah - we have enough elements in the table.
		%
		% perform linear interpolation:
		\pgfmath@ya=\csname #3\the\c@pgfmath@countc\endcsname pt %
		\advance\pgfmath@ya by-\pgfmath@x %
		\advance\pgfmath@x by0.\pgf@temp\pgfmath@ya
	  \fi
	}%
}{}%



\def\pgfmath@scale@rad@to@deg#1{%
    #1=57.29577#1\relax% 57.29577 = 360/(2*pi)
}%
\def\pgfmath@scale@deg@to@rad#1{%
    #1=3.14159#1% 
    \divide#1180\relax%
}%

\def\pgfmathsin@#1{%
  % Let #1 = a.b
  % Then sin(#1) \approx (1-b)*sin(a) + b*sin(a+1)
  %
  \begingroup%
    \expandafter\pgfmath@x#1pt\relax%
	\if1\pgfmath@trig@format@choice
		% trig format=rad
		\pgfmath@scale@rad@to@deg\pgfmath@x
	\fi
    \advance\pgfmath@x-90pt\relax%
    \afterassignment\pgfmath@gobbletilpgfmath@
    \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@
    \divide\c@pgfmath@counta360\relax%
    \multiply\c@pgfmath@counta-360\relax%
    \advance\pgfmath@x\c@pgfmath@counta pt\relax%
    \ifdim\pgfmath@x&lt;0pt\relax\pgfmath@x-\pgfmath@x\fi%
    \ifdim\pgfmath@x&lt;180pt\relax%
    \else
      \pgfmath@x-\pgfmath@x%
      \advance\pgfmath@x360pt\relax%
    \fi%
    % Now 0 &lt;= x &lt; 179. So split x into integer and decimal...
    %
    \afterassignment\pgfmath@xa%
    \expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
    %
    % ...if #1 is an integer, don't do anything fancy.
    \ifdim\pgfmath@xa=0pt%
      \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname pt\relax%
    \else%
      \pgfmath@x-\pgfmath@xa%
      \advance\pgfmath@x1pt\relax%
      \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@x%
      \advance\c@pgfmath@counta1\relax%
      \ifnum\c@pgfmath@counta=181\relax\c@pgfmath@counta179\relax\fi%
      \expandafter\advance\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@xa%
    \fi%
    \pgfmath@returnone\pgfmath@x%
  \endgroup
}

% \pgfmathcos
% 
% Calculate the cosine of #1 (in degrees).
%
\def\pgfmathcos@#1{%
  % Let x = a.b
  % Then cos(x) \approx (1-b)*cos(a) + b*cos(a+1)
  %
  \begingroup%
    \expandafter\pgfmath@x#1pt\relax%
	\if1\pgfmath@trig@format@choice
		% trig format=rad
		\pgfmath@scale@rad@to@deg\pgfmath@x
	\fi
    \afterassignment\pgfmath@gobbletilpgfmath@%
    \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@% 
    \divide\c@pgfmath@counta360\relax%
    \multiply\c@pgfmath@counta-360\relax%
    \advance\pgfmath@x\c@pgfmath@counta pt\relax%
    \ifdim\pgfmath@x&lt;0pt\relax\pgfmath@x-\pgfmath@x\fi%
    \ifdim\pgfmath@x&lt;180pt\relax%
    \else%
      \pgfmath@x-\pgfmath@x%
      \advance\pgfmath@x360pt\relax%
    \fi%
    % Now 0 &lt;= x &lt; 179. So split x into integer and decimal...
    %
    \afterassignment\pgfmath@xa%
    \expandafter\c@pgfmath@counta\the\pgfmath@x\relax%
    %
    % ...if #1 is an integer, don't do anything fancy.
    \ifdim\pgfmath@xa=0pt%
      \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname pt%
    \else%
      \pgfmath@x-\pgfmath@xa%
      \advance\pgfmath@x1pt\relax%
      \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@x%
      \advance\c@pgfmath@counta1\relax%
      \ifnum\c@pgfmath@counta=181\relax\c@pgfmath@counta179\relax\fi%
      \expandafter\advance\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@xa%
    \fi%
    \pgfmath@returnone\pgfmath@x%
  \endgroup%
}

\def\pgfmathasin@#1{%
  \begingroup%
    \pgfmath@x=#1pt %
    \pgfmath@xa\pgfmath@x%
    \edef\pgf@temp{\pgf@sys@tonumber\pgfmath@x}%
    % compute lossless '*1000' operation:
    \expandafter\pgfmath@multiply@thousand\pgf@temp 000\relax
    \pgfmath@x=\pgfmathresult pt %
    \ifdim\pgfmath@x&lt;0pt\relax%
      \pgfmath@x-\pgfmath@x%
    \fi%
    \pgfmath@table@lookup{\pgfmath@x}{pgfmath@acos@}{1001}%
    \pgfmath@x=-\pgfmath@x
    \advance\pgfmath@x90pt\relax%
    \ifdim\pgfmath@xa&lt;0pt\relax%
      \pgfmath@x-\pgfmath@x%
    \fi%
	\if1\pgfmath@trig@format@choice
		% trig format=rad
		\pgfmath@scale@deg@to@rad\pgfmath@x
	\fi
    \pgfmath@returnone\pgfmath@x%
  \endgroup%
}
\def\pgfmathacos@#1{%
  \begingroup%
    \pgfmath@x#1pt\relax%
    \pgfmath@xa\pgfmath@x%
    \edef\pgf@temp{\pgf@sys@tonumber\pgfmath@x}%
    % compute lossless '*1000' operation:
    \expandafter\pgfmath@multiply@thousand\pgf@temp 000\relax
    \pgfmath@x=\pgfmathresult pt %
    \ifdim\pgfmath@x&lt;0pt\relax%
      \pgfmath@x-\pgfmath@x%
    \fi%
    \pgfmath@table@lookup{\pgfmath@x}{pgfmath@acos@}{1001}%
    \ifdim\pgfmath@xa&lt;0pt\relax%
      \pgfmath@x-\pgfmath@x%
      \advance\pgfmath@x by180pt\relax%
    \fi%
	\if1\pgfmath@trig@format@choice
		% trig format=rad
		\pgfmath@scale@deg@to@rad\pgfmath@x
	\fi
    \pgfmath@returnone\pgfmath@x%
  \endgroup%
}

\def\pgfmathatan@#1{%
  \begingroup%
    \expandafter\pgfmath@x#1pt\relax%
    \pgfmath@xa\pgfmath@x%
    \ifdim\pgfmath@x&lt;0pt\relax%
      \pgfmath@x-\pgfmath@x%
    \fi%
    \pgfmath@xb\pgfmath@x%
    \ifdim\pgfmath@x&gt;1pt\relax%
      \edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@x}}%
      \pgfmathreciprocal@{\pgfmath@temp}%
      \pgfmath@x\pgfmathresult pt\relax%
    \fi%
    % compute lossless '*1000' operation:
    \edef\pgf@temp{\pgf@sys@tonumber\pgfmath@x}%
    \expandafter\pgfmath@multiply@thousand\pgf@temp 000\relax
    \pgfmath@x=\pgfmathresult pt %
    \pgfmath@table@lookup{\pgfmath@x}{pgfmath@atan@}{1001}%xxx
    \ifdim\pgfmath@xb&gt;1pt\relax%
      \pgfmath@x=-\pgfmath@x%
      \advance\pgfmath@x90pt%
    \fi%
    \ifdim\pgfmath@xa&lt;0pt\relax%
      \pgfmath@x-\pgfmath@x%
    \fi%
	\if1\pgfmath@trig@format@choice
		% trig format=rad
		\pgfmath@scale@deg@to@rad\pgfmath@x
	\fi
    \pgfmath@returnone\pgfmath@x%
  \endgroup%
}

\expandafter\def\csname pgfmathatan2@\endcsname#1#2{%
  % Note: first parameter is y (!), second is x (!)
  \begingroup%
    \pgfmath@y=#1pt\relax%
    \ifdim\pgfmath@y&lt;0pt\relax%
      \pgfmath@y=-\pgfmath@y%
    \fi%
    \ifdim\pgfmath@y&lt;0.001pt\relax%
      \ifdim#2pt&lt;0pt\relax%
        \pgfmath@x=-180pt\relax%
      \else%
        \ifdim#2pt&gt;0pt\relax%
          \pgfmath@x=0pt\relax%
        \else%
          \ifdim#1pt&lt;0pt%
            \pgfmath@x=-90pt\relax%
          \else%
            \pgfmath@x=90pt\relax%
          \fi%
        \fi%
      \fi%
    \else%
      \pgfmathabs@{#1}\let\pgfmath@tempa\pgfmathresult%
      \pgfmathabs@{#2}\let\pgfmath@tempb\pgfmathresult%
      \ifdim\pgfmath@tempa pt&gt;\pgfmath@tempb pt%
        \pgfmathdivide@{#2}{\pgfmath@tempa}%
        \expandafter\pgfmathatan@\expandafter{\pgfmathresult}%
        \pgfmath@x=90pt%
        \advance\pgfmath@x by-\pgfmathresult pt\relax%
      \else%
        \pgfmathdivide@{\pgfmath@tempa}{#2}%
        \expandafter\pgfmathatan@\expandafter{\pgfmathresult}%
        \pgfmath@x=\pgfmathresult pt\relax%
        \ifdim#2pt&lt;0pt%
          \advance\pgfmath@x by180pt\relax%
        \fi%
      \fi%
      \ifdim#1pt&lt;0pt\relax%
        \pgfmath@x=-\pgfmath@x%
      \fi%
    \fi%
	\if1\pgfmath@trig@format@choice
		% trig format=rad
		\pgfmath@scale@deg@to@rad\pgfmath@x
	\fi
    \pgfmath@returnone\pgfmath@x%
  \endgroup%    
}

% FPU:


\let\pgfmath@basic@sin@=\pgfmathsin@
\let\pgfmath@basic@cos@=\pgfmathcos@
\let\pgfmath@basic@tan@=\pgfmathtan@
\let\pgfmath@basic@atan@=\pgfmathatan@
\let\pgfmath@basic@asin@=\pgfmathasin@
\let\pgfmath@basic@acos@=\pgfmathacos@
\let\pgfmath@basic@cot@=\pgfmathcot@
\let\pgfmath@basic@sec@=\pgfmathsec@
\let\pgfmath@basic@cosec@=\pgfmathcosec@

% Computes #1(#2) where #1 is a trigonometric function, i.e.
% #1(#2) = #1( #2 + r*360 )
%
% #1 is a one-argument macro which assigns \pgfmathresult.
\def\pgfmathfloatTRIG@#1#2{%
	\if0\pgfmath@trig@format@choice
		% trig format=deg
		\expandafter\ifx\csname pgfmathfloatTRIG@NUM\endcsname\relax%
			% Lazy evaluation:
			\pgfmathfloatcreate{1}{3.6}{2}%
			\global\let\pgfmathfloatTRIG@NUM=\pgfmathresult
			\pgfmathfloatcreate{1}{2.77777777777778}{-3}%
			\global\let\pgfmathfloatTRIG@NUM@INV=\pgfmathresult
		\fi
		\pgfmathfloatmodknowsinverse@{#2}{\pgfmathfloatTRIG@NUM}{\pgfmathfloatTRIG@NUM@INV}%
	\else
		% trig format=rad
		\expandafter\ifx\csname pgfmathfloatTRIG@rad@NUM\endcsname\relax%
			% Lazy evaluation:
			\pgfmathfloatcreate{1}{6.28318530717959}{0}%
			\global\let\pgfmathfloatTRIG@rad@NUM=\pgfmathresult
			\pgfmathfloatcreate{1}{1.59154943091895}{-1}%
			\global\let\pgfmathfloatTRIG@rad@NUM@INV=\pgfmathresult
		\fi
		\pgfmathfloatmodknowsinverse@{#2}{\pgfmathfloatTRIG@rad@NUM}{\pgfmathfloatTRIG@rad@NUM@INV}%
	\fi
	\pgfmathfloattofixed@{\pgfmathresult}%
	\expandafter#1\expandafter{\pgfmathresult}%
	\pgfmathfloatparsenumber{\pgfmathresult}%
}%

\def\pgfmathfloatsin@#1{\pgfmathfloatTRIG@\pgfmath@basic@sin@{#1}}
\let\pgfmathfloatsin=\pgfmathfloatsin@
\def\pgfmathfloatcos@#1{\pgfmathfloatTRIG@\pgfmath@basic@cos@{#1}}
\let\pgfmathfloatcos=\pgfmathfloatcos@
\def\pgfmathfloatsec@#1{\pgfmathfloatTRIG@\pgfmath@basic@cos@{#1}\pgfmathfloatreciprocal@{\pgfmathresult}}
\let\pgfmathfloatsec=\pgfmathfloatsec@
\def\pgfmathfloatcosec@#1{\pgfmathfloatTRIG@\pgfmath@basic@sin@{#1}\pgfmathfloatreciprocal@{\pgfmathresult}}
\let\pgfmathfloatcosec=\pgfmathfloatcosec@

\def\pgfmathfloatatan@#1{%
	\begingroup
	\expandafter\ifx\csname pgfmathfloatatan@TMP\endcsname\relax% 
		\pgfmathfloatcreate{1}{1.6}{4}%
		\global\let\pgfmathfloatatan@TMP=\pgfmathresult
		\pgfmathfloatcreate{2}{1.6}{4}%
		\global\let\pgfmathfloatatan@TMPB=\pgfmathresult
	\fi
	\pgfmathfloatgreaterthan@{#1}{\pgfmathfloatatan@TMP}%
	\ifpgfmathfloatcomparison
		\pgfmathiftrigonometricusesdeg{%
			\pgfmathfloatcreate{1}{9.0}{1}%
		}{%
			\pgfmathfloatcreate{1}{1.570796326794}{0}%
		}%
	\else
		\pgfmathfloatlessthan{#1}{\pgfmathfloatatan@TMPB}%
		\ifpgfmathfloatcomparison
			\pgfmathiftrigonometricusesdeg{%
				\pgfmathfloatcreate{2}{9.0}{1}%
			}{%
				\pgfmathfloatcreate{2}{1.570796326794}{0}%
			}%
		\else
			\pgfmathfloattofixed@{#1}%
			\expandafter\pgfmath@basic@atan@\expandafter{\pgfmathresult}%
			\pgfmathfloatparsenumber{\pgfmathresult}%
		\fi
	\fi
	\pgfmath@smuggleone\pgfmathresult
	\endgroup
}%
\endinput
</pre></body></html>