% Basic trig...

% We use csnames \sin@# and \cos@# where # is int

% We could use differentials to get MUCH more accuracy
% but at the cost of expandability...

% These are not delimited - why are they scooping up
% entire numbers?!?
\def\Pos-{}
\def\Neg#1{\ifdim#11\p@<\z@\Pos#1\else-#1\fi}
%\def\Abs#1\relax{\ifnum#1<\z@\Pos#1\else#1\fi}
\def\Abs#1{\ifdim#11\p@<\z@\else#1\fi}

\def\endgroupsetdim#1#2{%
  \expandafter\endgroup\expandafter#1\the#2\relax
}

% Need atan2... how? (we could just ask perl...)
% Instead, We'll make the horrific approximation (not even
% a Taylor series) that, if 0<x<1, then atan(x)=x-x^2/5 !
\def\atan#1#2#3{% (if using \@tempdima or \dimen@ then problem)
  % #1 = y, #2 = x, #3 is result
  %\debug1{atan2(\the#1)(\the#2)}
  \begingroup
  \@testfalse % no swap (yet)
  \@tempdima#2\relax
  \dimen@#1\relax
  %\debug1{a=\the\@tempdima, @=\the\dimen@}
  \xa\xa\xa\ifdim\xa\AbsValD\xa\dimen@\xa>\AbsValD\@tempdima
    \@testtrue
    \dimen@\@tempdima
    \@tempdima#1\relax
    %\debug1{swap: a=\the\@tempdima, @=\the\dimen@}
  \fi
  \div\dimen@\@tempdima
  %\debug1{ratio: \the\dimen@}
  \@tempdima=\mul\dimen@\dimen@
  \debug5{atan2 \the#1/\the#2 -> \the\dimen@, \the\@tempdima}%
  \edef\sgn{\ifdim\dimen@<\z@+\else-\fi0.2}%
  \advance\dimen@ \sgn\@tempdima
  \dimen@=57.296\dimen@ % 180/pi -> deg
  %\debug1{atan(ratio)=\the\dimen@}
  \if@test % if we swapped...
    % dimen=90-dimen if positive, -90-dimen if negative
    \advance\dimen@\ifdim\dimen@>\z@-\fi90\p@
    \dimen@-\dimen@
    %\debug1{swapped: \the\dimen@}
  \fi
  \ifdim#2<\z@
    \advance\dimen@180\p@
    %\debug1{x<0: \the\dimen@}
  \fi
  \ifdim\dimen@<\z@
    \advance\dimen@360\p@
    %\debug1{want pos: \the\dimen@}
  \fi
  \endgroupsetdim#3\dimen@
}

% not expandable...  but more precise...
\def\dosin#1{%
  \ifdim#1<0\p@
    #1=-#1\relax\dosin#1\relax#1=-#1\relax
  \else
    \ifdim#1>45\p@
      \advance#1-90\p@
      \docos#1 % slowly work down to the right spot...!
    \else
      \begingroup
      \dimen@=.017453#1\relax %pi/180 -> rad
      \@tempdima=\mul\dimen@\dimen@
      \advance\dimen@-.12\@tempdima
      \endgroupsetdim#1\dimen@
    \fi
  \fi
}
\def\docos#1{%
  \ifdim#1<0\p@#1=-#1\relax\fi
  \ifdim#1>45\p@
    \advance#1-90\p@
    \dosin#1 % slowly work down to the right spot...!
    #1=-#1\relax
  \else
    \begingroup
    \dimen@=.017453#1\relax %pi/180 -> rad
    \dimen@=\mul\dimen@\dimen@
    \@tempdima=1\p@
    \advance\@tempdima-.48\dimen@
    \endgroupsetdim#1\@tempdima
  \fi
}

\def\normalizeangle#1{
  \ifdim#1>180\p@ \advance#1-360\p@\fi
  \ifdim#1>180\p@ \advance#1-360\p@\fi
  \ifdim#1<-180\p@ \advance#1360\p@\fi
  \ifdim#1<-180\p@ \advance#1360\p@\fi
}