% This is (almost) exact copy of

% This is (almost) exact copy of
% fp-basic.sty package (Michael Mehlich)
%
% It is patched to work with multido.sty
% FPadd -> FPfadd
% FPsub -> FPfsub

\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{pstfp}[2003/05/10]

%version information
\def\FP@basicversion{1.2d}
\message{%
`(Patched) Basic Fixed Point Arithmetic',\space\space%

Version \FP@basicversion%
\space(C) Michael Mehlich%

\space Patched by R. Stepanyan%
\space\space\space\space\space\space\space%
\space\space\space\space\space\space%
}

%fixed point arithmetic with values between (including)
% -999999999999999999.999999999999999999
% and +999999999999999999.999999999999999999

% to suppress messages
\let\FP@save@message\message
\def\message#1{}

%%%public area (macros which may be used)%%%

%introduce and print new values
\def\FPset#1#2{\FP@set[#1|#2]}
\def\FPprint#1{\FP@print[#1]}

%binary operations
\def\FPfadd#1#2#3{\FP@callc\FP@add#1{#2}{#3}+\relax} % #1 := #2+#3
\def\FPdiv#1#2#3{\FP@callc\FP@div#1{#2}{#3}} % #1 := #2/#3
\def\FPmul#1#2#3{\FP@callc\FP@mul#1{#2}{#3}} % #1 := #2*#3
\def\FPfsub#1#2#3{\FP@callc\FP@add#1{#2}{-#3}-\relax}% #1 := #2-#3
%unary operations
\def\FPabs#1#2{\FP@calld\FP@abs#1{#2}} % #1 := abs(#2)
\def\FPneg#1#2{\FP@calld\FP@neg#1{#2}} % #1 := -#2
\def\FPsgn#1#2{\FP@calld\FP@sgn#1{#2}} % #1 := sgn(#2)
%binary relations
\def\FPiflt#1#2{\FP@callb\FP@iflt{#1}{#2}+\relax} % #1 < #2 ?
\def\FPifeq#1#2{\FP@callb\FP@ifeq{#1}{#2}} % #1 = #2 ?
\def\FPifgt#1#2{\FP@callb\FP@iflt{#2}{#1}-\relax} % #1 > #2 ?
%unary relations
\def\FPifneg#1{\FP@calla\FP@ifneg{#1}} % #1 < 0 ?
\def\FPifpos#1{\FP@calla\FP@ifpos{#1}} % #1 >= 0 ?
\def\FPifzero#1{\FP@calla\FP@ifzero{#1}} % #1 = 0 ?
\def\FPifint#1{\FP@calla\FP@ifint{#1}} % #1 is integer ?
%repeat last test
%\ifFPtest % repeat last test

%%%private fp-area (don't use these macros)%%%

% To debug FP functions (enable intermediate messages on computations)
\newif\ifFPdebug
\FPdebugfalse
\def\FP@debug#1{\ifFPdebug\typeout{FP debug: #1}\fi}

%conditional printing of messages (only if \FPmessagestrue defined)
\newif\ifFPmessages
\FPmessagestrue
\def\FP@beginmessage#1{\ifFPmessages\message{( FP-#1}\fi}
\def\FP@endmessage#1{\ifFPmessages\message{)}\fi}
\def\FP@errmessage#1{\errmessage{FP error: #1!}}
\def\FP@warnmessage#1{\message{FP warning: #1!}}

%allocation of registers

\countdef\FP@actcounter=10 % register 0 for counter
\ifnum\FP@actcounter<60\relax%
\FP@actcounter=60%
\fi

\newcount\FP@xs %sign of 1st value
\newcount\FP@xia%integer part of 1st value
\newcount\FP@xib%integer part of 1st value
\newcount\FP@xfa%fractional part of 1st value
\newcount\FP@xfb%fractional part of 1st value

\countdef\FP@ys=5 %sign of 2nd value
\countdef\FP@yia=6%integer part of 2nd value
\countdef\FP@yib=7%integer part of 2nd value
\countdef\FP@yfa=8%fractional part of 2nd value
\countdef\FP@yfb=9%fractional part of 2nd value

\countdef\FP@xk=10 %registers for splitting 1st value
\countdef\FP@xl=11
\countdef\FP@xm=12
\countdef\FP@xn=13
\countdef\FP@xo=14
\countdef\FP@xp=15
\countdef\FP@xq=16
\countdef\FP@xr=17
\countdef\FP@xz=18
\countdef\FP@xt=19
\countdef\FP@xu=20
\countdef\FP@xv=21

\countdef\FP@yk=22 %registers for splitting 2nd value
\countdef\FP@yl=23
\countdef\FP@ym=24
\countdef\FP@yn=25
\countdef\FP@yo=26
\countdef\FP@yp=27
\countdef\FP@yq=28
\countdef\FP@yr=29
\countdef\FP@yz=30
\countdef\FP@yt=31
\countdef\FP@yu=32
\countdef\FP@yv=33

\newcount\FP@rega %auxiliary registers
\newcount\FP@regb
\countdef\FP@regc=36
\countdef\FP@regd=37
\countdef\FP@rege=38

\countdef\FP@rs=39 %result registers
\countdef\FP@ria=40
\countdef\FP@rib=41
\countdef\FP@rfa=42
\countdef\FP@rfb=43

\newcount\FP@regs %local auxiliary registers
\countdef\FP@count=45
\countdef\FP@res=46
\countdef\FP@shift=47
\newcount\FP@times
\countdef\FP@prod=49

%set values
\def\FP@set[#1#2|#3#4]{%
\ifx#3\@undefined%
\expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\FP@tmp\expandafter\expandafter\expandafter{\csname #3#4\endcsname}%
\else\ifcat\noexpand#3\relax%
\expandafter\def\expandafter\FP@tmp\expandafter{#3#4}%
\else\ifcat#32\relax%
\expandafter\def\expandafter\FP@tmp\expandafter{#3#4}%
\else%
\expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\FP@tmp\expandafter\expandafter\expandafter{\csname #3#4\endcsname}%
\fi\fi\fi%
\ifx#1\@undefined%
\let#1\FP@tmp%
\else\ifcat\noexpand#1\relax%
\let#1\FP@tmp%
\else%
\expandafter\let\csname #1#2\endcsname\FP@tmp%
\fi\fi%
}

%print values
\def\FP@print[#1#2]{%
\ifx#1\@undefined%
\csname #1#2\endcsname%
\else\ifcat\noexpand#1\relax%
#1#2%
\else\ifcat#12\relax%
#1#2%
\else%
\csname #1#2\endcsname%
\fi\fi\fi%
}

%auxiliary macros which may be used in all of the following macros
\newif\ifFP@test

\def\FP@ignorenext#1{}
\def\FP@first#1#2\relax{#1}
\def\FP@swallow#1\relax{}

\def\ifFP@zero#1{%
\ifnum%
\expandafter\ifnum\csname FP@#1ia\endcsname=0 0\else1\fi%
\expandafter\ifnum\csname FP@#1ib\endcsname=0 0\else1\fi%
\expandafter\ifnum\csname FP@#1fa\endcsname=0 0\else1\fi%
\expandafter\ifnum\csname FP@#1fb\endcsname=0 0\else1\fi%
=0\relax%
}

%read value

\def\FP@correctintcounter#1\relax{%
{\edef\FP@tmp{#1}%
\FP@count=0\relax%
\loop%
\edef\FP@tmpa{\expandafter\FP@first\FP@tmp\noexpand\relax}%
\expandafter\ifx\FP@tmpa0\relax%
\advance\FP@count1\relax%
\edef\FP@tmp{\expandafter\FP@ignorenext\FP@tmp}%
\repeat%
\ifnum\FP@count>18\relax%
\FP@errmessage{Overflow}%
\fi%
\expandafter\if!\FP@tmp!%
\advance\FP@count-18\relax%
\FP@count=-\FP@count%
\loop%
\ifnum\FP@count>0\relax%
\FP@regc=\FP@rega%
\divide\FP@rega10\relax\multiply\FP@rega10\relax%
\advance\FP@regc-\FP@rega\multiply\FP@regc100000000\relax%
\divide\FP@rega10\relax%
\divide\FP@regb10\relax\advance\FP@regb\FP@regc%
\advance\FP@count-1\relax%
\repeat%
\global\FP@rega=\FP@rega%
\global\FP@regb=\FP@regb%
\else%
\FP@errmessage{Number too big}%
\fi%
}%
}
\def\FP@@setintcounter#1#2#3#4#5#6#7#8#9{%
\FP@regb=#1#2#3#4#5#6#7#8#9\relax%
\FP@correctintcounter%
}
\def\FP@setintcounter#1#2#3#4#5#6#7#8#9{%
\FP@rega=#1#2#3#4#5#6#7#8#9\relax%
\FP@@setintcounter%
}

\def\FP@@setfractcounter#1#2#3#4#5#6#7#8#9{%
\FP@regb=#1#2#3#4#5#6#7#8#9\relax%
\FP@swallow%
}
\def\FP@setfractcounter#1#2#3#4#5#6#7#8#9{%
\FP@rega=#1#2#3#4#5#6#7#8#9\relax%
\FP@@setfractcounter%
}

\def\FP@getsign#1\relax{%
{\FP@regs=1\relax%
\edef\FP@tmp{#1}%
\loop%
\edef\FP@tmpa{\expandafter\FP@first\FP@tmp\noexpand\relax}%
\expandafter\ifx\FP@tmpa-\relax%
\multiply\FP@regs-1\relax%
\fi%
\ifnum\expandafter\ifx\FP@tmpa-1\else0\fi\expandafter\ifx\FP@tmpa+1\else0\fi>0%
\edef\FP@tmp{\expandafter\FP@ignorenext\FP@tmp}%
\repeat%
\global\let\FP@tmp\FP@tmp%
\global\FP@regs=\FP@regs%
}%
}

\def\FP@removeleadingzeros#1\relax{%
{\edef\FP@tmp{#1}%
\loop%
\edef\FP@tmpa{\expandafter\FP@first\FP@tmp\noexpand\relax}%
\expandafter\ifx\FP@tmpa0\relax%
\edef\FP@tmp{\expandafter\FP@ignorenext\FP@tmp}%
\repeat%
\global\let\FP@tmp\FP@tmp%
}%
}

\newif\ifFP@nonstop
\def\FP@strip#1{%
{\edef\FP@tmp{#1}%
\edef\FP@tmpb{}%
\ifx\FP@tmp\@empty\else%
\FP@nonstoptrue%
\loop%
\edef\FP@tmpa{\expandafter\FP@first\FP@tmp\noexpand\relax}%
\expandafter\ifx\FP@tmpa-\relax\edef\FP@tmpb{\FP@tmpb\FP@tmpa}\else%
\expandafter\ifx\FP@tmpa+\relax\edef\FP@tmpb{\FP@tmpb\FP@tmpa}\else%
\expandafter\ifx\FP@tmpa0\relax\edef\FP@tmpb{\FP@tmpb\FP@tmpa}\else%
\expandafter\ifx\FP@tmpa1\relax\edef\FP@tmpb{\FP@tmpb\FP@tmpa}\else%
\expandafter\ifx\FP@tmpa2\relax\edef\FP@tmpb{\FP@tmpb\FP@tmpa}\else%
\expandafter\ifx\FP@tmpa3\relax\edef\FP@tmpb{\FP@tmpb\FP@tmpa}\else%
\expandafter\ifx\FP@tmpa4\relax\edef\FP@tmpb{\FP@tmpb\FP@tmpa}\else%
\expandafter\ifx\FP@tmpa5\relax\edef\FP@tmpb{\FP@tmpb\FP@tmpa}\else%
\expandafter\ifx\FP@tmpa6\relax\edef\FP@tmpb{\FP@tmpb\FP@tmpa}\else%
\expandafter\ifx\FP@tmpa7\relax\edef\FP@tmpb{\FP@tmpb\FP@tmpa}\else%
\expandafter\ifx\FP@tmpa8\relax\edef\FP@tmpb{\FP@tmpb\FP@tmpa}\else%
\expandafter\ifx\FP@tmpa9\relax\edef\FP@tmpb{\FP@tmpb\FP@tmpa}\else%
\ifx\FP@tmpa\@empty\FP@nonstopfalse\else%
\ifx\FP@tmpa\space\FP@nonstopfalse\else%
\FP@errmessage{Illegal character \FP@tmpa\space found in float number}%
\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi%
\edef\FP@tmp{\expandafter\FP@ignorenext\FP@tmp}%
\ifx\FP@tmp\@empty\FP@nonstopfalse\fi%
\ifFP@nonstop%
\repeat%
\fi%
\global\let\FP@tmp\FP@tmpb%
}%
}

\def\FP@readvalue#1#2#3{%
% #1 macro family to catch the value
% #2.#3 value
%
% regular expression [+|-]*[d]_0^18.[d]*
%
\FP@strip{#2}%
%sign
\expandafter\FP@getsign\FP@tmp\relax%
\csname FP@#1s\endcsname=\FP@regs%
%
%integer part
\FP@removeleadingzeros\FP@tmp\relax%
\expandafter\FP@setintcounter\FP@tmp000000000000000000\relax%
\csname FP@#1ia\endcsname=\FP@rega%
\csname FP@#1ib\endcsname=\FP@regb%
%
%fractional part
\FP@strip{#3}%
\expandafter\FP@setfractcounter\FP@tmp000000000000000000\relax%
\csname FP@#1fa\endcsname=\FP@rega%
\csname FP@#1fb\endcsname=\FP@regb%
%
%correct sign
\ifnum\FP@rega=0\relax%
\ifnum\FP@regb=0\relax%
\expandafter\ifnum\csname FP@#1ib\endcsname=0\relax%
\expandafter\ifnum\csname FP@#1ia\endcsname=0\relax%
\csname FP@#1s\endcsname=1\relax%
\fi%
\fi%
\fi%
\fi%
}

%store value in macro

\def\FP@store#1#2{%
% #1 macro
% #2 macro family (value) to store
%
\ifFP@zero{#2}%
\csname FP@#2s\endcsname=1\relax%
\fi%
\expandafter\ifnum\csname FP@#2s\endcsname<0\relax%
\edef#1{-}%
\else%
\edef#1{}%
\fi%
\expandafter\ifnum\csname FP@#2ia\endcsname=0\relax%
\expandafter\ifnum\csname FP@#2ib\endcsname=0\relax%
\edef#1{#10}%
\else%
\edef#1{#1\expandafter\the\csname FP@#2ib\endcsname}%
\fi%
\else%
\expandafter\advance\csname FP@#2ib\endcsname1000000000\relax%
\edef#1{#1\expandafter\the\csname FP@#2ia\endcsname\expandafter\FP@ignorenext\the\csname FP@#2ib\endcsname}%
\fi%
\expandafter\advance\csname FP@#2fa\endcsname1000000000\relax%
\expandafter\advance\csname FP@#2fb\endcsname1000000000\relax%
\edef#1{#1\noexpand.\expandafter\FP@ignorenext\the\csname FP@#2fa\endcsname\expandafter\FP@ignorenext\the\csname FP@#2fb\endcsname}%
}

%macros to expand some arguments

\def\FP@calla#1#2{%
% #1 macro to call
% #2 value
% expand the value and split them into the integer and the fractional part
\edef\next{\noexpand#1#2..\noexpand\relax}%
\next%
}

\def\FP@callb#1#2#3{%
% #1 macro to call
% #2 1st value
% #3 2nd value
% expand the values and split them into the integer and the fractional parts
\edef\next{\noexpand#1#2..\noexpand\relax#3..\noexpand\relax}%
\next%
}

\def\FP@callc#1#2#3#4{%
% #1 macro to call
% #2 macro, which gets the result
% #3 1st value
% #4 2nd value
% expand the values and split them into the integer and the fractional parts
\edef\next{\noexpand#1\noexpand#2#3..\noexpand\relax#4..\noexpand\relax}%
\next%
}

\def\FP@calld#1#2#3{%
% #1 macro to call
% #2 macro, which gets the result
% #3 value
\edef\next{\noexpand#1\noexpand#2#3..\noexpand\relax}%
\next%
}

\def\FP@calle#1#2#3#4{%
% #1 macro to call
% #2 macro, which gets the first result
% #3 macro, which gets the second result
% #4 value
\edef\next{\noexpand#1\noexpand#2\noexpand#3#4..\noexpand\relax}%
\next%
}

%add two values

\def\FP@add#1#2.#3.#4\relax#5.#6.#7\relax#8\relax{%
% #1 macro, which gets the result
% #2 integer part of 1st value
% #3 fractional part of 1st value
% #4 dummy to swallow everthing after the 2nd '.'
% #5 integer part of 2nd value
% #6 fractional part of 2nd value
% #7 dummy to swallow everthing after the 2nd '.'
%
{\ifx#8+\relax%
\FP@beginmessage{ADD}%
\else%
\FP@beginmessage{SUB}%
\fi%
%
\FP@readvalue{x}{#2}{#3}%
\FP@readvalue{y}{#5}{#6}%
%
\ifnum\FP@xs=\FP@ys%
\advance\FP@xfb\FP@yfb%
\advance\FP@xfa\FP@yfa%
\ifnum\FP@xfb<1000000000\relax\else%
\advance\FP@xfb-1000000000\relax%
\advance\FP@xfa1\relax%
\fi%
\advance\FP@xib\FP@yib%
\ifnum\FP@xfa<1000000000\relax\else%
\advance\FP@xfa-1000000000\relax%
\advance\FP@xib1\relax%
\fi%
\advance\FP@xia\FP@yia%
\ifnum\FP@xib<1000000000\relax\else%
\advance\FP@xib-1000000000\relax%
\advance\FP@xia1\relax%
\fi%
\ifnum\FP@xia<1000000000\relax\else%
\FP@errmessage{Overflow}%
\fi%
\FP@store\FP@tmp{x}%
\else%
\advance\FP@xfb-\FP@yfb%
\ifnum\FP@xfb<0\relax%
\advance\FP@yfa1\relax%
\advance\FP@xfb1000000000\relax%
\fi%
\advance\FP@xfa-\FP@yfa%
\ifnum\FP@xfa<0\relax%
\advance\FP@yib1\relax%
\advance\FP@xfa1000000000\relax%
\fi%
\advance\FP@xib-\FP@yib%
\ifnum\FP@xib<0\relax%
\advance\FP@yia1\relax%
\advance\FP@xib1000000000\relax%
\fi%
\advance\FP@xia-\FP@yia%
\ifnum\FP@xia<0\relax%
\FP@xs=-\FP@xs%
\ifnum\FP@xfb=0\relax\else%
\advance\FP@xfb-1000000000\relax\FP@xfb=-\FP@xfb%
\advance\FP@xfa1\relax%
\fi%
\ifnum\FP@xfa=0\relax\else%
\advance\FP@xfa-1000000000\relax\FP@xfa=-\FP@xfa%
\advance\FP@xib1\relax%
\fi%
\ifnum\FP@xib=0\relax\else%
\advance\FP@xib-1000000000\relax\FP@xib=-\FP@xib%
\advance\FP@xia1\relax%
\fi%
\relax\FP@xia=-\FP@xia%
\fi%
\FP@store\FP@tmp{x}%
\fi%
%
\global\let\FP@tmp\FP@tmp%
%
\FP@endmessage{}%
}%
\let#1\FP@tmp%
}

%multiply two values

\def\FP@firstnine#1#2#3#4#5#6#7#8#9{%
\FP@res=#1#2#3#4#5#6#7#8#9\relax%
}
\def\FP@@ninesplit#1\relax#2\end#3{%
#1%
\edef#3{#2}%
}
\def\FP@ninesplit#1{%
\edef#1{\expandafter\FP@firstnine\FP@rd}%
\expandafter\FP@@ninesplit#1\end#1\relax%
}

\def\FP@split#1#2#3#4{%
% #1 highest three digits
% #2 medium three digits
% #3 least three digits
% #4 counter
\FP@regc=#4%
\divide\FP@regc1000000\relax%
#1=\FP@regc%
\multiply\FP@regc-1000000\relax\advance\FP@regc#4%
#3=\FP@regc%
\divide\FP@regc1000\relax%
#2=\FP@regc%
\multiply\FP@regc-1000\relax\advance\FP@regc#3%
#3=\FP@regc%
}

\def\FP@@mul#1#2#3{%
\FP@regc=\csname FP@x#1\endcsname%
\multiply\FP@regc\csname FP@y#2\endcsname%
\advance\FP@prod\FP@regc%
%
\ifx#3\relax%
\let\next=\relax%
\else%
\let\next=\FP@@mul%
\fi%
\next#3%
}

\def\FP@saveshift{%
% save rightmost three digits
\FP@regc=\FP@prod%
\divide\FP@prod1000\relax%
\multiply\FP@prod1000\relax%
\advance\FP@regc-\FP@prod%
\advance\FP@regc1000\relax%
\edef\FP@rd{\expandafter\FP@ignorenext\the\FP@regc\FP@rd}%
%
\divide\FP@prod1000\relax%
}

\def\FP@mul#1#2.#3.#4\relax#5.#6.#7\relax{%
% #1 macro, which gets the result
% #2 integer part of 1st value
% #3 fractional part of 1st value
% #4 dummy to swallow everthing after the 2nd '.'
% #5 integer part of 2nd value
% #6 fractional part of 2nd value
% #7 dummy to swallow everthing after the 2nd '.'
%
% split value in various parts
% x y = 123 456 789 123 456 789 . 123 456 789 123 456 789
% -> xk xl xm xn xo xp xq xr xs xt xu xv
% -> yk yl ym yn yo yp yq yr ys yt yu yv
% multiply these parts and save the result wrt the necessary shifts
%
{\FP@beginmessage{MUL}%
%
\FP@readvalue{x}{#2}{#3}%
\FP@readvalue{y}{#5}{#6}%
%
%sign
\multiply\FP@xs\FP@ys%
\FP@rs=\FP@xs%
%
% split parts
\FP@split\FP@xk\FP@xl\FP@xm\FP@xia\FP@split\FP@xn\FP@xo\FP@xp\FP@xib%
\FP@split\FP@xq\FP@xr\FP@xz\FP@xfa\FP@split\FP@xt\FP@xu\FP@xv\FP@xfb%
\FP@split\FP@yk\FP@yl\FP@ym\FP@yia\FP@split\FP@yn\FP@yo\FP@yp\FP@yib%
\FP@split\FP@yq\FP@yr\FP@yz\FP@yfa\FP@split\FP@yt\FP@yu\FP@yv\FP@yfb%
%
\FP@prod=0\relax%
\edef\FP@rd{}%
%
%compute result
\FP@@mul vv \relax\FP@saveshift%
\FP@@mul vu uv \relax\FP@saveshift%
\FP@@mul uu vt tv \relax\FP@saveshift%
\FP@@mul ut tu vz zv \relax\FP@saveshift%
\FP@@mul tt zu uz rv vr \relax\FP@saveshift%
\FP@@mul zt tz ur ru vq qv \relax\FP@saveshift%
\FP@@mul zz rt tr uq qu vp pv \relax\FP@saveshift%
\FP@@mul zr rz tq qt up pu vo ov \relax\FP@saveshift%
\FP@@mul rr qz zq tp pt uo ou vn nv \relax\FP@saveshift%
\FP@@mul rq qr zp pz to ot un nu vm mv \relax\FP@saveshift%
\FP@@mul qq rp pr zo oz tn nt um mu vl lv \relax\FP@saveshift%
\FP@@mul qp pq ro or zn nz tm mt ul lu kv vk \relax\FP@saveshift%
\FP@@mul pp oq qo rn nr zm mz tl lt ku uk \relax\FP@saveshift%
\FP@@mul op po nq qn rm mr zl lz tk kt \relax\FP@saveshift%
\FP@@mul oo pn np mq qm rl lr kz zk \relax\FP@saveshift%
\FP@@mul no on mp pm lq ql kr rk \relax\FP@saveshift%
\FP@@mul nn mo om pl lp qk kq \relax\FP@saveshift%
\FP@@mul mn nm lo ok pk kp \relax\FP@saveshift%
\FP@@mul mm ln nl ko ok \relax\FP@saveshift%
\FP@@mul lm ml kn nk \relax\FP@saveshift%
\FP@@mul ll km mk \relax\FP@saveshift%
\FP@@mul kl lk \relax\FP@saveshift%
\FP@@mul kk \relax\FP@saveshift\FP@saveshift%
\FP@ninesplit\FP@rd%
\ifnum\FP@res=0\relax%
\FP@ninesplit\FP@rd%
\ifnum\FP@res=0\relax%
\FP@ninesplit\FP@rd\FP@ria=\FP@res%
\FP@ninesplit\FP@rd\FP@rib=\FP@res%
\FP@ninesplit\FP@rd\FP@rfa=\FP@res%
\FP@ninesplit\FP@rd\FP@rfb=\FP@res%
\FP@store\FP@tmp{r}%
\else%
\FP@errmessage{Overflow}%
\fi%
\else%
\FP@errmessage{Overflow}%
\fi%
%
\global\let\FP@tmp\FP@tmp%
%
\FP@endmessage{}%
}%
%
\let#1\FP@tmp%
}

%divide one value by another one

\def\FP@divten#1{%
\expandafter\FP@regc\csname FP@#1ia\endcsname%
\expandafter\divide\csname FP@#1ia\endcsname10\relax%
\expandafter\FP@regb\csname FP@#1ia\endcsname%
\multiply\FP@regb10\relax%
\advance\FP@regc-\FP@regb%
\multiply\FP@regc100000000\relax%
%
\expandafter\FP@rega\csname FP@#1ib\endcsname%
\expandafter\divide\csname FP@#1ib\endcsname10\relax%
\expandafter\FP@regb\csname FP@#1ib\endcsname%
\multiply\FP@regb10\relax%
\advance\FP@rega-\FP@regb%
\multiply\FP@rega100000000\relax%
\expandafter\advance\csname FP@#1ib\endcsname\FP@regc%
%
\expandafter\FP@regc\csname FP@#1fa\endcsname%
\expandafter\divide\csname FP@#1fa\endcsname10\relax%
\expandafter\FP@regb\csname FP@#1fa\endcsname%
\multiply\FP@regb10\relax%
\advance\FP@regc-\FP@regb%
\multiply\FP@regc100000000\relax%
\expandafter\advance\csname FP@#1fa\endcsname\FP@rega%
%
\expandafter\divide\csname FP@#1fb\endcsname10\relax%
\expandafter\advance\csname FP@#1fb\endcsname\FP@regc%
}

\def\FP@multen#1{%
\expandafter\multiply\csname FP@#1ia\endcsname10\relax%
\expandafter\ifnum\csname FP@#1ib\endcsname<100000000\relax%
\else%
\expandafter\FP@regc\csname FP@#1ib\endcsname%
\divide\FP@regc100000000%
\expandafter\advance\csname FP@#1ia\endcsname\FP@regc%
\multiply\FP@regc100000000%
\expandafter\advance\csname FP@#1ib\endcsname-\FP@regc%
\fi%
\expandafter\multiply\csname FP@#1ib\endcsname10\relax%
\expandafter\ifnum\csname FP@#1fa\endcsname<100000000\relax%
\else%
\expandafter\FP@regc\csname FP@#1fa\endcsname%
\divide\FP@regc100000000%
\expandafter\advance\csname FP@#1ib\endcsname\FP@regc%
\multiply\FP@regc100000000%
\expandafter\advance\csname FP@#1fa\endcsname-\FP@regc%
\fi%
\expandafter\multiply\csname FP@#1fa\endcsname10\relax%
\expandafter\ifnum\csname FP@#1fb\endcsname<100000000\relax%
\else%
\expandafter\FP@regc\csname FP@#1fb\endcsname%
\divide\FP@regc100000000%
\expandafter\advance\csname FP@#1fa\endcsname\FP@regc%
\multiply\FP@regc100000000%
\expandafter\advance\csname FP@#1fb\endcsname-\FP@regc%
\fi%
\expandafter\multiply\csname FP@#1fb\endcsname10\relax%
}

\def\FP@counttimes{%
{\global\FP@times=0\relax%
\loop%
\ifnum%
\ifnum\FP@xia>\FP@yia1%
\else\ifnum\FP@xia<\FP@yia0%
\else%
\ifnum\FP@xib>\FP@yib1%
\else\ifnum\FP@xib<\FP@yib0%
\else%
\ifnum\FP@xfa>\FP@yfa1%
\else\ifnum\FP@xfa<\FP@yfa0%
\else%
\ifnum\FP@xfb>\FP@yfb1%
\else\ifnum\FP@xfb<\FP@yfb0%
\else%
1%
\fi\fi%
\fi\fi%
\fi\fi%
\fi\fi%
=1\relax%
\global\advance\FP@times1\relax%
\global\advance\FP@xfb-\FP@yfb%
\ifnum\FP@xfb<0\relax%
\global\advance\FP@xfb1000000000\relax%
\global\advance\FP@xfa-1\relax%
\fi%
\global\advance\FP@xfa-\FP@yfa%
\ifnum\FP@xfa<0\relax%
\global\advance\FP@xfa1000000000\relax%
\global\advance\FP@xib-1\relax%
\fi%
\global\advance\FP@xib-\FP@yib%
\ifnum\FP@xib<0\relax%
\global\advance\FP@xib1000000000\relax%
\global\advance\FP@xia-1\relax%
\fi%
\global\advance\FP@xia-\FP@yia%
\repeat%
}%
}

\def\FP@div#1#2.#3.#4\relax#5.#6.#7\relax{%
% #1 macro, which gets the result
% #2 integer part of 1st value
% #3 fractional part of 1st value
% #4 dummy to swallow everthing after the 2nd '.'
% #5 integer part of 2nd value
% #6 fractional part of 2nd value
% #7 dummy to swallow everthing after the 2nd '.'
%
% algorithmic idea (for x>0, y>0)
% - %determine \FP@shift such that y*10^\FP@shift <100000000<=y*10^(\FP@shift+1)
% - %determine \FP@shift' such that x*10^\FP@shift'<100000000<=x*10^(\FP@shift+1)
% - x=x*\FP@shift'
% - y=y*\FP@shift
% - \FP@shift=\FP@shift-\FP@shift'
% - res=0
% - while y>0 %fixed-point representation!
% - \FP@times=0
% - while x>y
% - \FP@times=\FP@times+1
% - x=x-y
% - end
% - y=y/10
% - res=10*res+\FP@times/1000000000
% - end
% - %shift the result according to \FP@shift
%
{\FP@beginmessage{DIV}%
%
\FP@readvalue{x}{#2}{#3}%
\FP@readvalue{y}{#5}{#6}%
%
%sign
\multiply\FP@xs\FP@ys%
\FP@rs=\FP@xs%
%
%compute division
\ifFP@zero{y}%
\FP@errmessage{Division by zero}%
\else%
\ifFP@zero{x}\def\next##1{\edef\FP@tmp{0}}\else\def\next##1{##1}\fi%
\next%
{\FP@shift=0\relax%
\loop%
\ifnum\FP@yia<100000000\relax%
\FP@multen{y}%
\advance\FP@shift1\relax%
\repeat%
\loop%
\ifnum\FP@xia<100000000\relax%
\FP@multen{x}%
\advance\FP@shift-1\relax%
\repeat%
\FP@ria=0\FP@rib=0\FP@rfa=0\FP@rfb=0\relax%
\loop%
\ifFP@zero{y}\else%
\FP@counttimes%divides x by \FP@times*y
\FP@divten{y}%
\FP@multen{r}%
\advance\FP@rfb\FP@times%
\ifnum\FP@rfb<1000000000\relax\else%
\advance\FP@rfa1\advance\FP@rfb-1000000000\relax%
\ifnum\FP@rfa<1000000000\relax\else%
\advance\FP@rib1\advance\FP@rfa-1000000000\relax%
\ifnum\FP@rib<1000000000\relax\else%
\advance\FP@ria1\advance\FP@rib-1000000000\relax%
\fi%
\fi%
\fi%
\repeat%
\loop%
\ifnum\FP@shift>17%
\advance\FP@shift-1\relax%
\ifnum\FP@ria<100000000\else\FP@ria=-1\fi%
\ifnum\FP@ria<0\FP@ria=-1\fi%
\FP@multen{r}%
\repeat%
\ifnum\FP@ria<1000000000\else\FP@ria=-1\fi%
\loop%
\ifnum\FP@shift<17%
\advance\FP@shift1\relax%
\FP@divten{r}%
\repeat%
\ifnum\FP@ria<0\relax%
\FP@errmessage{Overflow}%
\else%
\FP@store\FP@tmp{r}%
\fi%
}%
\fi%
%
\global\let\FP@tmp=\FP@tmp%
%
\FP@endmessage{}%
}%
\let#1\FP@tmp%
}

%absolute value

\def\FP@abs#1#2.#3.#4\relax{%
% #1 macro, which gets the result
% #2 integer part of value
% #3 fractional part of value
% #4 dummy to swallow everthing after the 2nd '.'
%
{\FP@beginmessage{ABS}%
%
\FP@readvalue{x}{#2}{#3}%
\FP@xs=1\relax%
\FP@store\FP@tmp{x}%
%
\global\let\FP@tmp\FP@tmp%
%
\FP@endmessage{}%
}%
\let#1\FP@tmp%
}

%negate value

\def\FP@neg#1#2.#3.#4\relax{%
% #1 macro, which gets the result
% #2 integer part of value
% #3 fractional part of value
% #4 dummy to swallow everthing after the 2nd '.'
%
{\FP@beginmessage{NEG}%
%
\FP@readvalue{x}{#2}{#3}%
\multiply\FP@xs-1\relax%
\FP@store\FP@tmp{x}%
%
\global\let\FP@tmp\FP@tmp%
%
\FP@endmessage{}%
}%
\let#1\FP@tmp%
}

%sign of value

\def\FP@sgn#1#2.#3.#4\relax{%
% #1 macro, which gets the result
% #2 integer part of value
% #3 fractional part of value
% #4 dummy to swallow everthing after the 2nd '.'
%
{\FP@beginmessage{SGN}%
%
\FP@readvalue{x}{#2}{#3}%
%
\ifFP@zero{x}%
\edef\FP@tmp{0}%
\else%
\edef\FP@tmp{\the\FP@xs}%
\fi%
%
\global\let\FP@tmp\FP@tmp%
%
\FP@endmessage{}%
}%
\let#1\FP@tmp%
}

%test if 1st value is less than 2nd value

\def\FP@iflt#1.#2.#3\relax#4.#5.#6\relax#7\relax{%
% #1 integer part of 1st value
% #2 fractional part of 1st value
% #3 dummy to swallow everthing after the 2nd '.'
% #4 integer part of 2nd value
% #5 fractional part of 2nd value
% #6 dummy to swallow everthing after the 2nd '.'
%
{\ifx#7+\relax%
\FP@beginmessage{LT?}%
\else%
\FP@beginmessage{GT?}%
\fi%
%
\FP@readvalue{x}{#1}{#2}%
\FP@readvalue{y}{#4}{#5}%
%
\ifnum\FP@xs<\FP@ys%
\FP@testtrue%
\else\ifnum\FP@xs>\FP@ys%
\FP@testfalse%
\else%
\ifnum\FP@xs>0\relax%
\ifnum\FP@xia<\FP@yia%
\FP@testtrue%
\else\ifnum\FP@xia>\FP@yia%
\FP@testfalse%
\else%
\ifnum\FP@xib<\FP@yib%
\FP@testtrue%
\else\ifnum\FP@xib>\FP@yib%
\FP@testfalse%
\else%
\ifnum\FP@xfa<\FP@yfa%
\FP@testtrue%
\else\ifnum\FP@xfa>\FP@yfa%
\FP@testfalse%
\else%
\ifnum\FP@xfb<\FP@yfb%
\FP@testtrue%
\else%
\FP@testfalse%
\fi%
\fi\fi%
\fi\fi%
\fi\fi%
\else%
\ifnum\FP@xia>\FP@yia%
\FP@testtrue%
\else\ifnum\FP@xia<\FP@yia%
\FP@testfalse%
\else%
\ifnum\FP@xib>\FP@yib%
\FP@testtrue%
\else\ifnum\FP@xib<\FP@yib%
\FP@testfalse%
\else%
\ifnum\FP@xfa>\FP@yfa%
\FP@testtrue%
\else\ifnum\FP@xfa<\FP@yfa%
\FP@testfalse%
\else%
\ifnum\FP@xfb>\FP@yfb%
\FP@testtrue%
\else%
\FP@testfalse%
\fi%
\fi\fi%
\fi\fi%
\fi\fi%
\fi%
\fi\fi%
%
\global\let\ifFP@test\ifFP@test%
%
\FP@endmessage{}%
}%
\let\ifFPtest\ifFP@test%
%
\ifFPtest%
}

%test if two values are equal

\def\FP@ifeq#1.#2.#3\relax#4.#5.#6\relax{%
% #1 integer part of 1st value
% #2 fractional part of 1st value
% #3 dummy to swallow everthing after the 2nd '.'
% #4 integer part of 2nd value
% #5 fractional part of 2nd value
% #6 dummy to swallow everthing after the 2nd '.'
%
{\FP@beginmessage{EQ?}%
%
\FP@readvalue{x}{#1}{#2}%
\FP@readvalue{y}{#4}{#5}%
%
\ifnum\FP@xs=\FP@ys%
\ifnum\FP@xia=\FP@yia%
\ifnum\FP@xib=\FP@yib%
\ifnum\FP@xfa=\FP@yfa%
\ifnum\FP@xfb=\FP@yfb%
\FP@testtrue%
\else%
\FP@testfalse%
\fi%
\else%
\FP@testfalse%
\fi%
\else%
\FP@testfalse%
\fi%
\else%
\FP@testfalse%
\fi%
\else%
\FP@testfalse%
\fi%
%
\global\let\ifFP@test\ifFP@test%
%
\FP@endmessage{}%
}%
\let\ifFPtest\ifFP@test%
%
\ifFPtest%
}

%test if value is negative

\def\FP@ifneg#1.#2.#3\relax{%
% #1 integer part of value
% #2 fractional part of value
% #3 dummy to swallow everthing after the 2nd '.'
%
{\FP@beginmessage{NEG?}%
%
\FP@readvalue{x}{#1}{#2}%
%
\ifnum\FP@xs<0\relax%
\FP@testtrue%
\else%
\FP@testfalse%
\fi%
%
\global\let\ifFP@test\ifFP@test%
%
\FP@endmessage{}%
}%
\let\ifFPtest\ifFP@test%
%
\ifFPtest%
}

%test if value is positive

\def\FP@ifpos#1.#2.#3\relax{%
% #1 integer part of value
% #2 fractional part of value
% #3 dummy to swallow everthing after the 2nd '.'
%
{\FP@beginmessage{POS?}%
%
\FP@readvalue{x}{#1}{#2}%
%
\ifnum\FP@xs<0\relax%
\FP@testfalse%
\else%
\FP@testtrue%
\fi%
%
\global\let\ifFP@test\ifFP@test%
%
\FP@endmessage{}%
}%
\let\ifFPtest\ifFP@test%
%
\ifFPtest%
}

%test if value is equal to zero

\def\FP@ifzero#1.#2.#3\relax{%
% #1 integer part of value
% #2 fractional part of value
% #3 dummy to swallow everthing after the 2nd '.'
%
{\FP@beginmessage{ZERO?}%
%
\FP@readvalue{x}{#1}{#2}%
%
\ifFP@zero{x}%
\FP@testtrue%
\else%
\FP@testfalse%
\fi%
%
\global\let\ifFP@test\ifFP@test%
%
\FP@endmessage{}%
}%
\let\ifFPtest\ifFP@test%
%
\ifFPtest%
}

%test if value is an integer

\def\FP@ifint#1.#2.#3\relax{%
% #1 integer part of value
% #2 fractional part of value
% #3 dummy to swallow everthing after the 2nd '.'
%
{\FP@beginmessage{INT?}%
%
\FP@readvalue{x}{#1}{#2}%
%
\ifnum\FP@xfa=0\relax%
\ifnum\FP@xfb=0\relax%
\FP@testtrue%
\else%
\FP@testfalse%
\fi%
\else%
\FP@testfalse%
\fi%
%
\global\let\ifFP@test\ifFP@test%
%
\FP@endmessage{}%
}%
\let\ifFPtest\ifFP@test%
%
\ifFPtest%
}