% This is taken from Donald Arseneau
% http://groups.google.com/group/comp.text.tex/browse_thread
%   /thread/95b55bc557d96b5/4daa67ff2a027d37

\def\pointless#1{\expandafter\remove@PT\the#1}

{\catcode`p=12 \catcode`t=12 \gdef\remove@PT#1pt{#1}} 

\let\mul\pointless

% Example: \area=\pointless\hsize\baselineskip

\newcount\FPD@hi \FPD@hi=67108863
\def\AbsVal#1{\ifnum#1<\z@ -\fi#1}
\def\AbsValD#1{\ifdim#1<\z@ -\fi#1}

\def\MaxD#1#2{\ifdim#1>#2#1\else#2\fi}

% Approximate Fixed Point Division of two dimensions
% 3.14159/2.71828 = 1.15573
% Two parameters: Numerator and denominator.  The answer is returned
% in the numerator (which must be a register).  The denominator is
% unchanged (it may be a numeric string, "123").
% \@tempcntb is used and altered.
%
\newif\ifFPD@overflow
\newdimen\FBD@denom
\def\fpdivide#1#2{%
  \FPD@overflowfalse
  \ifdim\AbsValD#2<1\p@
    \begingroup\FBD@denom\ifdim#2<\z@-\fi5000#2%
    \let\next\@empty
    \ifdim\AbsValD#1>\FBD@denom
      \def\next{%
        \FPD@overflowtrue
        \debug2{Overflow dividing \the#1 by \the#2 -> inf}%
        #1=5000\p@}%
    \fi
    \ifdim\AbsValD#2<.001\p@\ifdim\AbsValD#2<.001\p@
      \def\next{%
        \FPD@overflowtrue
        \debug2{Overflow dividing \the#1 by \the#2 -> 0}%
        #1=0\p@}%
    \fi\fi
    \expandafter\endgroup\next
  \fi
  \ifFPD@overflow\else
    \let\FPD@nume#1\@tempcntb#2\relax
    \FPD@scale\FPD@scale\FPD@scale\FPD@scale
    \divide#1\@tempcntb
  \fi
}

% Rescale numbers to preserve accuracy.  The number 16 is the level of
% uncertainty. Use a lower power of 2 for more accuracy (2 is most precise).
% But if you change it, you must change the repetions of \FPD@scale in
% \fpdivide above: magic_number^repetitions = 65536 (16^4 = 65536).
%
\def\FPD@scale{\ifnum\AbsVal\FPD@nume<\FPD@hi
    \multiply\FPD@nume\sixt@@n
  \else
    \divide\@tempcntb\sixt@@n
  \fi
}

% The syntax is
%   \fpdivide\dimenA\dimenB
% equivalent to
%   \divide\counterA \counterB 

\let\div\fpdivide

%%%%%%%%%%%%%%%
% Here is sqrt code I stole from Kevin Hamlen:

\def\sqrt#1{%
  \begingroup
  \dimen@#1\relax
  \@tempdima#1\relax
  \loop % temp1 := sqrt(arg1)
    \@tempdimb=#1%
    \div\@tempdimb \@tempdima%
    \advance\@tempdimb by\@tempdima%
    \divide\@tempdimb by\tw@%
  \ifdim\@tempdimb<\@tempdima%
    \@tempdima=\@tempdimb\repeat%
  \xa\endgroup\xa#1\the\@tempdima\relax
}

\def\pythag#1#2#3{% WATCH OVERFLOW HERE!!!
  % #3 = sqrt(#1^2+#2^2)
  %#3=\mul#1#1 \advance#3\mul#2#2
  \xa\xa\xa\ifdim\xa\AbsValD\xa#1\xa<\AbsValD#2%
    %this should be safer...
    \ifdim\AbsValD#1<.001\p@#3#2\else
      #3=#1\relax \div#3#2\relax
      #3=\mul#3#3\relax \advance#31\p@
      \sqrt#3\relax #3\mul#2#3%
    \fi
  \else
    \ifdim\AbsValD#2<.001\p@#3#1\else
      #3=#2\relax \div#3#1\relax
      #3=\mul#3#3\relax \advance#31\p@
      \sqrt#3\relax #3\mul#1#3%
    \fi
  \fi
  \ifdim#3<\z@#3-#3\fi % MUST BE POSITIVE!
}

\def\unitvector#1#2#3{% #3 is temp space
  \pythag#1#2#3%
  \div#1#3\div#2#3%
}

\def\sumsq#1#2#3{% this is probably not safe!
  % #3 = sqrt(#1^2+#2^2)
  #3=\mul#1#1\advance#3\mul#2#2%
}