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% 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 defines the trigonometric functions/functions.
%
% Much of this file is based on ideas and code (particularly
% the old \pgfcoremath.code.tex) due to Till Tantau.
%
% Version 1.414213 29/9/2007

% \pgfmathpi
%
\pgfmathdeclarefunction{pi}{0}{\def\pgfmathresult{3.141592654}}

\pgfkeys{
    /pgf/trig format/.is choice,
    % attention: the luamath library will hook into these code keys.
    /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
}%

% \pgfmathradians
% (for compatibility with 1.18 beta, will be deprecated)
%
% Convert #1 from radians to degrees (accurate to 1 deg).
%
\pgfmathdeclarefunction{radians}{1}{%
  \begingroup%
    \expandafter\pgfmath@x#1pt\relax%
    \pgfmath@x57.29577\pgfmath@x\relax% 57.29577 = 360/(2*pi)
    \pgfmath@returnone\pgfmath@x%
  \endgroup%
}%

% \pgfmathdeg
%
% Convert #1 from radians to degrees.
%
\pgfmathdeclarefunction{deg}{1}{%
  \begingroup%
    \expandafter\pgfmath@x#1pt\relax%
    \pgfmath@scale@rad@to@deg\pgfmath@x
    \pgfmath@returnone\pgfmath@x%
  \endgroup%
}%

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

% \pgfmathrad
%
% Convert #1 from degrees to radians.
%
\pgfmathdeclarefunction{rad}{1}{%
  \begingroup%
    \expandafter\pgfmath@x#1pt\relax%
    \pgfmath@scale@deg@to@rad\pgfmath@x
    \pgfmath@returnone\pgfmath@x%
  \endgroup%
}%

\def\pgfmath@scale@deg@to@rad#1{%
    #1=3.14159#1%
    \divide#1180\relax%
}%

% \pgfmathsin
%
% Calculate the sine of #1 (in degrees).
%
\pgfmathdeclarefunction{sin}{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<0pt\relax\pgfmath@x-\pgfmath@x\fi%
    \ifdim\pgfmath@x<180pt\relax%
    \else
      \pgfmath@x-\pgfmath@x%
      \advance\pgfmath@x360pt\relax%
    \fi%
    % Now 0 <= x < 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).
%
\pgfmathdeclarefunction{cos}{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<0pt\relax\pgfmath@x-\pgfmath@x\fi%
    \ifdim\pgfmath@x<180pt\relax%
    \else%
      \pgfmath@x-\pgfmath@x%
      \advance\pgfmath@x360pt\relax%
    \fi%
    % Now 0 <= x < 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%
}

% \pgfmathsincos
%
% Calculate the sin and cosine of #1 (in degrees).
%
\def\pgfmathsincos#1{%
  \pgfmathparse{#1}%
  \expandafter\pgfmathsincos@\expandafter{\pgfmathresult}}
\def\pgfmathsincos@#1{%
  \edef\pgfmath@temparg{#1}%
  \pgfmathsin@{\pgfmath@temparg}\edef\pgfmathresulty{\pgfmathresult}%
  \pgfmathcos@{\pgfmath@temparg}\edef\pgfmathresultx{\pgfmathresult}%
}

% \pgfmathtan
%
% Calculate the tangent of #1 (in degrees).
%
\pgfmathdeclarefunction{tan}{1}{%
  \begingroup%
    \edef\pgfmath@temparg{#1}%
    \pgfmathcos@{\pgfmath@temparg}%
    \expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}%
    \edef\pgfmath@tantemp{\pgfmathresult}%
    \pgfmathsin@{\pgfmath@temparg}%
    \pgfmath@x\pgfmathresult pt\relax%
    \pgfmath@x\pgfmath@tantemp\pgfmath@x%
    \pgfmath@returnone\pgfmath@x%
  \endgroup%
}

% \pgfmathcosec
%
% Calculate the cosec of #1 (in degrees).
%
\pgfmathdeclarefunction{cosec}{1}{%
  \expandafter\pgfmathsin@\expandafter{#1}%
  \pgfmathreciprocal@{\pgfmathresult}%
}

% \pgfmathsec
%
% Calculate the sec of #1 (in degrees).
%
\pgfmathdeclarefunction{sec}{1}{%
  \expandafter\pgfmathcos@\expandafter{#1}%
  \pgfmathreciprocal@{\pgfmathresult}%
}

% \pgfmathcot
%
% Calculate the cotangent of #1 (in degrees).
%
\pgfmathdeclarefunction{cot}{1}{%
  \begingroup%
    \edef\pgfmath@temparg{#1}%
    \pgfmathsin@{\pgfmath@temparg}%
    \expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}%
    \edef\pgfmath@tantemp{\pgfmathresult}%
    \pgfmathcos@{\pgfmath@temparg}%
    \pgfmath@x\pgfmathresult pt\relax%
    \pgfmath@x\pgfmath@tantemp\pgfmath@x%
    \pgfmath@returnone\pgfmath@x%
  \endgroup%
}

\def\pgfmath@multiply@thousand#1.#2#3#4#5\relax{%
  \edef\pgfmathresult{#1#2#3#4.#5}%
}%

% \pgfmathasin
%
% The asin of #1
%
\pgfmathdeclarefunction{asin}{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<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<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%
}

% 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<#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
}%

% \pgfmathacos
%
% The acos of #1
%
\pgfmathdeclarefunction{acos}{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<0pt\relax%
      \pgfmath@x-\pgfmath@x%
    \fi%
    \pgfmath@table@lookup{\pgfmath@x}{pgfmath@acos@}{1001}%
    \ifdim\pgfmath@xa<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%
}

\pgfmathdeclarefunction{atan}{1}{%
  \begingroup%
    \expandafter\pgfmath@x#1pt\relax%
    \pgfmath@xa\pgfmath@x%
    \ifdim\pgfmath@x<0pt\relax%
      \pgfmath@x-\pgfmath@x%
    \fi%
    \pgfmath@xb\pgfmath@x%
    \ifdim\pgfmath@x>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>1pt\relax%
      \pgfmath@x=-\pgfmath@x%
      \advance\pgfmath@x90pt%
    \fi%
    \ifdim\pgfmath@xa<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%
}

\pgfmathdeclarefunction{atan2}{2}{%
  % Note: first parameter is y (!), second is x (!)
  \begingroup%
    \let\pgfmath@trig@format@choice@@=\pgfmath@trig@format@choice
    \def\pgfmath@trig@format@choice{0}%
    \pgfmath@y=#1pt\relax%
    \ifdim\pgfmath@y<0pt\relax%
      \pgfmath@y=-\pgfmath@y%
    \fi%
    \ifdim\pgfmath@y<0.001pt\relax%
      \ifdim#2pt<0pt\relax%
        \pgfmath@x=+180pt\relax%
      \else%
        \ifdim#2pt>0pt\relax%
          \pgfmath@x=0pt\relax%
        \else%
          \ifdim#1pt<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>\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<0pt%
          \advance\pgfmath@x by180pt\relax%
        \fi%
      \fi%
      \ifdim#1pt<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%
}

% This is needed since \pgfmathatan2 is not a legal macro name
\expandafter\let\expandafter\pgfmathatantwo\csname pgfmathatan2\endcsname
\expandafter\let\expandafter\pgfmathatantwo@\csname pgfmathatan2@\endcsname

\def\pgfmath@def#1#2#3{\expandafter\def\csname pgfmath@#1@#2\endcsname{#3}}
\pgfmath@def{cos}{0}{1.00000}    \pgfmath@def{cos}{1}{0.99985}
\pgfmath@def{cos}{2}{0.99939}    \pgfmath@def{cos}{3}{0.99863}
\pgfmath@def{cos}{4}{0.99756}    \pgfmath@def{cos}{5}{0.99619}
\pgfmath@def{cos}{6}{0.99452}    \pgfmath@def{cos}{7}{0.99255}
\pgfmath@def{cos}{8}{0.99027}    \pgfmath@def{cos}{9}{0.98769}
\pgfmath@def{cos}{10}{0.98481}    \pgfmath@def{cos}{11}{0.98163}
\pgfmath@def{cos}{12}{0.97815}    \pgfmath@def{cos}{13}{0.97437}
\pgfmath@def{cos}{14}{0.97030}    \pgfmath@def{cos}{15}{0.96593}
\pgfmath@def{cos}{16}{0.96126}    \pgfmath@def{cos}{17}{0.95630}
\pgfmath@def{cos}{18}{0.95106}    \pgfmath@def{cos}{19}{0.94552}
\pgfmath@def{cos}{20}{0.93969}    \pgfmath@def{cos}{21}{0.93358}
\pgfmath@def{cos}{22}{0.92718}    \pgfmath@def{cos}{23}{0.92050}
\pgfmath@def{cos}{24}{0.91355}    \pgfmath@def{cos}{25}{0.90631}
\pgfmath@def{cos}{26}{0.89879}    \pgfmath@def{cos}{27}{0.89101}
\pgfmath@def{cos}{28}{0.88295}    \pgfmath@def{cos}{29}{0.87462}
\pgfmath@def{cos}{30}{0.86603}    \pgfmath@def{cos}{31}{0.85717}
\pgfmath@def{cos}{32}{0.84805}    \pgfmath@def{cos}{33}{0.83867}
\pgfmath@def{cos}{34}{0.82904}    \pgfmath@def{cos}{35}{0.81915}
\pgfmath@def{cos}{36}{0.80902}    \pgfmath@def{cos}{37}{0.79864}
\pgfmath@def{cos}{38}{0.78801}    \pgfmath@def{cos}{39}{0.77715}
\pgfmath@def{cos}{40}{0.76604}    \pgfmath@def{cos}{41}{0.75471}
\pgfmath@def{cos}{42}{0.74314}    \pgfmath@def{cos}{43}{0.73135}
\pgfmath@def{cos}{44}{0.71934}    \pgfmath@def{cos}{45}{0.70711}
\pgfmath@def{cos}{46}{0.69466}    \pgfmath@def{cos}{47}{0.68200}
\pgfmath@def{cos}{48}{0.66913}    \pgfmath@def{cos}{49}{0.65606}
\pgfmath@def{cos}{50}{0.64279}    \pgfmath@def{cos}{51}{0.62932}
\pgfmath@def{cos}{52}{0.61566}    \pgfmath@def{cos}{53}{0.60182}
\pgfmath@def{cos}{54}{0.58779}    \pgfmath@def{cos}{55}{0.57358}
\pgfmath@def{cos}{56}{0.55919}    \pgfmath@def{cos}{57}{0.54464}
\pgfmath@def{cos}{58}{0.52992}    \pgfmath@def{cos}{59}{0.51504}
\pgfmath@def{cos}{60}{0.50000}    \pgfmath@def{cos}{61}{0.48481}
\pgfmath@def{cos}{62}{0.46947}    \pgfmath@def{cos}{63}{0.45399}
\pgfmath@def{cos}{64}{0.43837}    \pgfmath@def{cos}{65}{0.42262}
\pgfmath@def{cos}{66}{0.40674}    \pgfmath@def{cos}{67}{0.39073}
\pgfmath@def{cos}{68}{0.37461}    \pgfmath@def{cos}{69}{0.35837}
\pgfmath@def{cos}{70}{0.34202}    \pgfmath@def{cos}{71}{0.32557}
\pgfmath@def{cos}{72}{0.30902}    \pgfmath@def{cos}{73}{0.29237}
\pgfmath@def{cos}{74}{0.27564}    \pgfmath@def{cos}{75}{0.25882}
\pgfmath@def{cos}{76}{0.24192}    \pgfmath@def{cos}{77}{0.22495}
\pgfmath@def{cos}{78}{0.20791}    \pgfmath@def{cos}{79}{0.19081}
\pgfmath@def{cos}{80}{0.17365}    \pgfmath@def{cos}{81}{0.15643}
\pgfmath@def{cos}{82}{0.13917}    \pgfmath@def{cos}{83}{0.12187}
\pgfmath@def{cos}{84}{0.10453}    \pgfmath@def{cos}{85}{0.08716}
\pgfmath@def{cos}{86}{0.06976}    \pgfmath@def{cos}{87}{0.05234}
\pgfmath@def{cos}{88}{0.03490}    \pgfmath@def{cos}{89}{0.01745}
\pgfmath@def{cos}{90}{0.00000}    \pgfmath@def{cos}{91}{-0.01745}
\pgfmath@def{cos}{92}{-0.03490}    \pgfmath@def{cos}{93}{-0.05234}
\pgfmath@def{cos}{94}{-0.06976}    \pgfmath@def{cos}{95}{-0.08716}
\pgfmath@def{cos}{96}{-0.10453}    \pgfmath@def{cos}{97}{-0.12187}
\pgfmath@def{cos}{98}{-0.13917}    \pgfmath@def{cos}{99}{-0.15643}
\pgfmath@def{cos}{100}{-0.17365}    \pgfmath@def{cos}{101}{-0.19081}
\pgfmath@def{cos}{102}{-0.20791}    \pgfmath@def{cos}{103}{-0.22495}
\pgfmath@def{cos}{104}{-0.24192}    \pgfmath@def{cos}{105}{-0.25882}
\pgfmath@def{cos}{106}{-0.27564}    \pgfmath@def{cos}{107}{-0.29237}
\pgfmath@def{cos}{108}{-0.30902}    \pgfmath@def{cos}{109}{-0.32557}
\pgfmath@def{cos}{110}{-0.34202}    \pgfmath@def{cos}{111}{-0.35837}
\pgfmath@def{cos}{112}{-0.37461}    \pgfmath@def{cos}{113}{-0.39073}
\pgfmath@def{cos}{114}{-0.40674}    \pgfmath@def{cos}{115}{-0.42262}
\pgfmath@def{cos}{116}{-0.43837}    \pgfmath@def{cos}{117}{-0.45399}
\pgfmath@def{cos}{118}{-0.46947}    \pgfmath@def{cos}{119}{-0.48481}
\pgfmath@def{cos}{120}{-0.50000}    \pgfmath@def{cos}{121}{-0.51504}
\pgfmath@def{cos}{122}{-0.52992}    \pgfmath@def{cos}{123}{-0.54464}
\pgfmath@def{cos}{124}{-0.55919}    \pgfmath@def{cos}{125}{-0.57358}
\pgfmath@def{cos}{126}{-0.58779}    \pgfmath@def{cos}{127}{-0.60182}
\pgfmath@def{cos}{128}{-0.61566}    \pgfmath@def{cos}{129}{-0.62932}
\pgfmath@def{cos}{130}{-0.64279}    \pgfmath@def{cos}{131}{-0.65606}
\pgfmath@def{cos}{132}{-0.66913}    \pgfmath@def{cos}{133}{-0.68200}
\pgfmath@def{cos}{134}{-0.69466}    \pgfmath@def{cos}{135}{-0.70711}
\pgfmath@def{cos}{136}{-0.71934}    \pgfmath@def{cos}{137}{-0.73135}
\pgfmath@def{cos}{138}{-0.74314}    \pgfmath@def{cos}{139}{-0.75471}
\pgfmath@def{cos}{140}{-0.76604}    \pgfmath@def{cos}{141}{-0.77715}
\pgfmath@def{cos}{142}{-0.78801}    \pgfmath@def{cos}{143}{-0.79864}
\pgfmath@def{cos}{144}{-0.80902}    \pgfmath@def{cos}{145}{-0.81915}
\pgfmath@def{cos}{146}{-0.82904}    \pgfmath@def{cos}{147}{-0.83867}
\pgfmath@def{cos}{148}{-0.84805}    \pgfmath@def{cos}{149}{-0.85717}
\pgfmath@def{cos}{150}{-0.86603}    \pgfmath@def{cos}{151}{-0.87462}
\pgfmath@def{cos}{152}{-0.88295}    \pgfmath@def{cos}{153}{-0.89101}
\pgfmath@def{cos}{154}{-0.89879}    \pgfmath@def{cos}{155}{-0.90631}
\pgfmath@def{cos}{156}{-0.91355}    \pgfmath@def{cos}{157}{-0.92050}
\pgfmath@def{cos}{158}{-0.92718}    \pgfmath@def{cos}{159}{-0.93358}
\pgfmath@def{cos}{160}{-0.93969}    \pgfmath@def{cos}{161}{-0.94552}
\pgfmath@def{cos}{162}{-0.95106}    \pgfmath@def{cos}{163}{-0.95630}
\pgfmath@def{cos}{164}{-0.96126}    \pgfmath@def{cos}{165}{-0.96593}
\pgfmath@def{cos}{166}{-0.97030}    \pgfmath@def{cos}{167}{-0.97437}
\pgfmath@def{cos}{168}{-0.97815}    \pgfmath@def{cos}{169}{-0.98163}
\pgfmath@def{cos}{170}{-0.98481}    \pgfmath@def{cos}{171}{-0.98769}
\pgfmath@def{cos}{172}{-0.99027}    \pgfmath@def{cos}{173}{-0.99255}
\pgfmath@def{cos}{174}{-0.99452}    \pgfmath@def{cos}{175}{-0.99619}
\pgfmath@def{cos}{176}{-0.99756}    \pgfmath@def{cos}{177}{-0.99863}
\pgfmath@def{cos}{178}{-0.99939}    \pgfmath@def{cos}{179}{-0.99985}
\pgfmath@def{cos}{180}{-1.00000}     \pgfmath@def{cos}{181}{-0.99985}

\pgfmath@def{cosfrac}{0}{1.00000}    \pgfmath@def{cosfrac}{1}{0.99995}
\pgfmath@def{cosfrac}{2}{0.99980}    \pgfmath@def{cosfrac}{3}{0.99955}
\pgfmath@def{cosfrac}{4}{0.99920}    \pgfmath@def{cosfrac}{5}{0.99875}
\pgfmath@def{cosfrac}{6}{0.99820}    \pgfmath@def{cosfrac}{7}{0.99755}
\pgfmath@def{cosfrac}{8}{0.99681}    \pgfmath@def{cosfrac}{9}{0.99597}
\pgfmath@def{cosfrac}{10}{0.99503}    \pgfmath@def{cosfrac}{11}{0.99400}
\pgfmath@def{cosfrac}{12}{0.99287}    \pgfmath@def{cosfrac}{13}{0.99165}
\pgfmath@def{cosfrac}{14}{0.99034}    \pgfmath@def{cosfrac}{15}{0.98893}
\pgfmath@def{cosfrac}{16}{0.98744}    \pgfmath@def{cosfrac}{17}{0.98585}
\pgfmath@def{cosfrac}{18}{0.98418}    \pgfmath@def{cosfrac}{19}{0.98242}
\pgfmath@def{cosfrac}{20}{0.98058}    \pgfmath@def{cosfrac}{21}{0.97865}
\pgfmath@def{cosfrac}{22}{0.97664}    \pgfmath@def{cosfrac}{23}{0.97455}
\pgfmath@def{cosfrac}{24}{0.97238}    \pgfmath@def{cosfrac}{25}{0.97014}
\pgfmath@def{cosfrac}{26}{0.96782}    \pgfmath@def{cosfrac}{27}{0.96542}
\pgfmath@def{cosfrac}{28}{0.96296}    \pgfmath@def{cosfrac}{29}{0.96042}
\pgfmath@def{cosfrac}{30}{0.95782}    \pgfmath@def{cosfrac}{31}{0.95515}
\pgfmath@def{cosfrac}{32}{0.95242}    \pgfmath@def{cosfrac}{33}{0.94962}
\pgfmath@def{cosfrac}{34}{0.94677}    \pgfmath@def{cosfrac}{35}{0.94385}
\pgfmath@def{cosfrac}{36}{0.94088}    \pgfmath@def{cosfrac}{37}{0.93786}
\pgfmath@def{cosfrac}{38}{0.93478}    \pgfmath@def{cosfrac}{39}{0.93165}
\pgfmath@def{cosfrac}{40}{0.92847}    \pgfmath@def{cosfrac}{41}{0.92525}
\pgfmath@def{cosfrac}{42}{0.92198}    \pgfmath@def{cosfrac}{43}{0.91866}
\pgfmath@def{cosfrac}{44}{0.91531}    \pgfmath@def{cosfrac}{45}{0.91192}
\pgfmath@def{cosfrac}{46}{0.90849}    \pgfmath@def{cosfrac}{47}{0.90502}
\pgfmath@def{cosfrac}{48}{0.90152}    \pgfmath@def{cosfrac}{49}{0.89799}
\pgfmath@def{cosfrac}{50}{0.89442}    \pgfmath@def{cosfrac}{51}{0.89083}
\pgfmath@def{cosfrac}{52}{0.88721}    \pgfmath@def{cosfrac}{53}{0.88357}
\pgfmath@def{cosfrac}{54}{0.87990}    \pgfmath@def{cosfrac}{55}{0.87621}
\pgfmath@def{cosfrac}{56}{0.87250}    \pgfmath@def{cosfrac}{57}{0.86877}
\pgfmath@def{cosfrac}{58}{0.86503}    \pgfmath@def{cosfrac}{59}{0.86126}
\pgfmath@def{cosfrac}{60}{0.85749}    \pgfmath@def{cosfrac}{61}{0.85370}
\pgfmath@def{cosfrac}{62}{0.84990}    \pgfmath@def{cosfrac}{63}{0.84609}
\pgfmath@def{cosfrac}{64}{0.84227}    \pgfmath@def{cosfrac}{65}{0.83844}
\pgfmath@def{cosfrac}{66}{0.83460}    \pgfmath@def{cosfrac}{67}{0.83077}
\pgfmath@def{cosfrac}{68}{0.82692}    \pgfmath@def{cosfrac}{69}{0.82308}
\pgfmath@def{cosfrac}{70}{0.81923}    \pgfmath@def{cosfrac}{71}{0.81538}
\pgfmath@def{cosfrac}{72}{0.81153}    \pgfmath@def{cosfrac}{73}{0.80768}
\pgfmath@def{cosfrac}{74}{0.80384}    \pgfmath@def{cosfrac}{75}{0.80000}
\pgfmath@def{cosfrac}{76}{0.79616}    \pgfmath@def{cosfrac}{77}{0.79232}
\pgfmath@def{cosfrac}{78}{0.78850}    \pgfmath@def{cosfrac}{79}{0.78468}
\pgfmath@def{cosfrac}{80}{0.78086}    \pgfmath@def{cosfrac}{81}{0.77706}
\pgfmath@def{cosfrac}{82}{0.77326}    \pgfmath@def{cosfrac}{83}{0.76948}
\pgfmath@def{cosfrac}{84}{0.76570}    \pgfmath@def{cosfrac}{85}{0.76193}
\pgfmath@def{cosfrac}{86}{0.75818}    \pgfmath@def{cosfrac}{87}{0.75444}
\pgfmath@def{cosfrac}{88}{0.75071}    \pgfmath@def{cosfrac}{89}{0.74699}
\pgfmath@def{cosfrac}{90}{0.74329}    \pgfmath@def{cosfrac}{91}{0.73960}
\pgfmath@def{cosfrac}{92}{0.73593}    \pgfmath@def{cosfrac}{93}{0.73227}
\pgfmath@def{cosfrac}{94}{0.72862}    \pgfmath@def{cosfrac}{95}{0.72499}
\pgfmath@def{cosfrac}{96}{0.72138}    \pgfmath@def{cosfrac}{97}{0.71779}
\pgfmath@def{cosfrac}{98}{0.71421}    \pgfmath@def{cosfrac}{99}{0.71065}
\pgfmath@def{cosfrac}{100}{0.70710}

% Oh No! Some really loooooong tables.
\pgfmath@def{atan}{0}{0.00000}    \pgfmath@def{atan}{1}{0.05729}
\pgfmath@def{atan}{2}{0.11459}    \pgfmath@def{atan}{3}{0.17188}
\pgfmath@def{atan}{4}{0.22918}    \pgfmath@def{atan}{5}{0.28647}
\pgfmath@def{atan}{6}{0.34377}    \pgfmath@def{atan}{7}{0.40106}
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