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%
% Base arithmetic functions
%
\newdimen\MFF@dimenA
\newdimen\MFF@dimenB
\newdimen\MFF@dimenC
\newdimen\MFF@dimenD
%
% this code convert dimen (pt) into real value assigned to \@tempa
%
\def\MFF@convert#1{\@ovxx=#1\relax \@negargfalse
\ifdim \@ovxx<0pt \@ovxx=-\@ovxx \@negargtrue \fi
\@xarg=\@ovxx \@yarg=\@xarg
\divide\@xarg by 65536\relax
\@yyarg=\@xarg \multiply\@yyarg by 65536\relax
\advance\@yarg by -\@yyarg
\multiply\@yarg by 3125 \divide\@yarg by 2048
\ifnum \@yarg > 9999 \def\@tempa{}%
\else \ifnum \@yarg > 999 \def\@tempa{0}%
\else \ifnum \@yarg > 99 \def\@tempa{00}%
\else \ifnum \@yarg > 99 \def\@tempa{000}%
\else \def\@tempa{0000}%
\fi\fi\fi\fi
\edef\@tempa{\if@negarg -\fi \the\@xarg.\@tempa\the\@yarg}%
}
% ************************************************************
% *** The following macros are partially taken from PiCTeX ***
% ************************************************************
% DIVISION (Does long division of dimension registers)
% ** \MFF@divide{DIVIDEND}{DIVISOR}{RESULT}
% ** \MFF@divide DIVIDEND [by] DIVISOR [to get] ANSWER
% ** Divides the dimension DIVIDEND by the dimension DIVISOR, placing the
% ** quotient in the dimension register ANSWER. Values are understood to
% ** be in points. E.g. 12.5pt/1.4pt=8.92857pt.
% ** Quotient is accurate to 1/65536pt=2**[-16]pt
% ** |DIVISOR| should be < 8192pt = 113.36in
% ** --- otherwise acciracy is decreased in 2 times
\def\MFF@divide#1#2#3{%
\ifdim #2=\z@ #3=\z@\relax
\else
\MFF@dimenB=#1\relax% ** dimB holds current remainder (r)
\MFF@dimenC=#2\relax% ** dimC holds divisor (d)
\ifdim\MFF@dimenC<\z@
\MFF@dimenB=-\MFF@dimenB \MFF@dimenC=-\MFF@dimenC
\fi
\@negargfalse
\ifdim \MFF@dimenB<\z@ \MFF@dimenB=-\MFF@dimenB \@negargtrue \fi
\ifdim \MFF@dimenC<8192pt\relax
\else
\MFF@dimenB=0.5\MFF@dimenB
\MFF@dimenC=0.5\MFF@dimenC
\fi
\MFF@dimenD=\MFF@dimenB% ** dimD holds quotient q=r/d for this
\divide \MFF@dimenD \MFF@dimenC% ** step, in units of scaled pts
\MFF@dimenA=\MFF@dimenD% ** dimA eventually holds answer (a)
\multiply\MFF@dimenD \MFF@dimenC% ** r <-- r - dq
\advance\MFF@dimenB -\MFF@dimenD% ** First step complete. Have integer part
% ** of a, and corresponding remainder.
\MFF@dimenD=\MFF@dimenC% ** Temporarily use dimD to hold |d|
\ifdim\MFF@dimenD<64pt% ** Branch on the magnitude of |d|
\MFF@divstep[256]\MFF@divstep[256]%
\else
% ** The following code handles divisors d with
% ** (1) .88in = 64pt <= d < 256pt = 3.54in
% ** (2) 3.54in = 256pt <= d < 2048pt = 28.34in
% ** (3) 28.34in = 2048pt <= d < 8192pt = 113.36in
% ** Anything bigger than that may result in an overflow condition.
% ** For our purposes, we should never even see case (2) or (3).
\ifdim\MFF@dimenD<256pt
\MFF@divstep[64]\MFF@divstep[32]\MFF@divstep[32]%
\else
\ifdim\MFF@dimenD<2048pt
\MFF@divstep[8]\MFF@divstep[8]\MFF@divstep[8]%
\MFF@divstep[8]\MFF@divstep[4]\MFF@divstep[4]%
\else
\MFF@divstep[2]\MFF@divstep[2]\MFF@divstep[2]\MFF@divstep[2]%
\MFF@divstep[2]\MFF@divstep[2]\MFF@divstep[2]\MFF@divstep[2]%
\MFF@divstep[2]\MFF@divstep[2]\MFF@divstep[2]\MFF@divstep[2]%
\MFF@divstep[2]\MFF@divstep[2]\MFF@divstep[2]\MFF@divstep[2]%
\fi
\fi
\fi
\if@negarg \MFF@dimenA=-\MFF@dimenA \fi
#3=\MFF@dimenA
\fi\ignorespaces}
% ** The following macro does the real long division work.
\def\MFF@divstep[#1]{% ** #1 = "B"
\MFF@dimenB=#1\MFF@dimenB% ** r <-- B*r
\MFF@dimenD=\MFF@dimenB% ** dimD holds quotient q=r/d for this
\divide \MFF@dimenD by \MFF@dimenC% ** step, in units of scaled pts
\MFF@dimenA=#1\MFF@dimenA% ** a <-- B*a + q
\advance\MFF@dimenA by \MFF@dimenD%
\multiply\MFF@dimenD by \MFF@dimenC% ** r <-- r - dq
\advance\MFF@dimenB by -\MFF@dimenD}
% MULTIPLICATION (Does long multiplication of dimension registers)
% ** \MFF@multiply{FACTOR1}{FACTOR2}{RESULT}
% ** Result is accurate to 1/65536pt=2**[-16]pt
% ** |FACTOR2| should be < 8192pt = 113.36in
% ** --- otherwise acciracy is decreased in 2 times
\def\MFF@multiply#1#2#3{%
\MFF@dimenB=#1\relax \MFF@dimenC=#2\relax
\ifdim\MFF@dimenC<\z@
\MFF@dimenB=-\MFF@dimenB \MFF@dimenC=-\MFF@dimenC
\fi
\@negargfalse
\ifdim \MFF@dimenB<\z@ \MFF@dimenB=-\MFF@dimenB \@negargtrue \fi
\ifdim \MFF@dimenC<8192pt\relax
\else
\MFF@dimenB=2\MFF@dimenB
\MFF@dimenC=0.5\MFF@dimenC
\fi
% calculate integer part
\@yarg=\MFF@dimenC \@xarg=65536
\@yyarg=\@yarg \divide\@yyarg by \@xarg
% multiplication by integer part
\MFF@dimenA=\MFF@dimenB \multiply\MFF@dimenA by \@yyarg
% prepare fraction part
\multiply\@yyarg by \@xarg \advance\@yarg by -\@yyarg
% multiplication cycle
\ifdim\MFF@dimenB<64pt%
\MFF@mulstep[256]\MFF@mulstep[256]%
\else
\ifdim\MFF@dimenB<256pt
\MFF@mulstep[64]\MFF@mulstep[32]\MFF@mulstep[32]%
\else
\ifdim\MFF@dimenB<2048pt
\MFF@mulstep[8]\MFF@mulstep[8]\MFF@mulstep[8]%
\MFF@mulstep[8]\MFF@mulstep[4]\MFF@mulstep[4]%
\else
\MFF@mulstep[2]\MFF@mulstep[2]\MFF@mulstep[2]\MFF@mulstep[2]%
\MFF@mulstep[2]\MFF@mulstep[2]\MFF@mulstep[2]\MFF@mulstep[2]%
\MFF@mulstep[2]\MFF@mulstep[2]\MFF@mulstep[2]\MFF@mulstep[2]%
\MFF@mulstep[2]\MFF@mulstep[2]\MFF@mulstep[2]\MFF@mulstep[2]%
\fi
\fi
\fi
% assign result
\if@negarg \MFF@dimenA=-\MFF@dimenA \fi
#3=\MFF@dimenA
\ignorespaces}
% perform partial multiplication
\def\MFF@mulstep[#1]{\divide\@xarg by #1
\@yyarg=\@yarg \divide\@yyarg by \@xarg
% calculate new additive component
\MFF@dimenC=\MFF@dimenB \multiply\MFF@dimenC by \@yyarg
\divide\MFF@dimenC by #1 \advance\MFF@dimenA by \MFF@dimenC
% update fraction data
\multiply\@yyarg by \@xarg \advance\@yarg by -\@yyarg
\divide\MFF@dimenB by #1
}
% *********************************************
% ******** End of PiCTeX arith macros *********
% *********************************************
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