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+%% $Id: pst-fp.tex 112 2009-04-17 19:21:56Z herbert $
+%%
+%%
+%% This is file `pst-fp.tex',
+%%
+%% IMPORTANT NOTICE:
+%%
+%% Package `pst-fp.tex'
+%%
+%% Herbert Voss <Herbert.Voss _at_ pstricks.de>
+%% stolen from the fp package by Michael Mehlich
+%%
+%% This program can be redistributed and/or modified under the terms
+%% of the LaTeX Project Public License Distributed from CTAN archives
+%% in directory macros/latex/base/lppl.txt.
+%%
+%% DESCRIPTION:
+%% `pst-fp' is a PSTricks related package for a division
+%%
+\csname PSTFPloaded\endcsname
+\let\PSTFPloaded\endinput
+%
+% Requires some packages
+\ifx\PSTricksLoaded\endinput\else\input pstricks \fi
+%
+\def\fileversion{0.02}
+\def\filedate{2009/04/02}
+\message{`pst-fp' v\fileversion, \filedate\space (hv)}
+%
+\edef\PstAtCode{\the\catcode`\@} \catcode`\@=11\relax
+
+%fixed point arithmetic with values between (including)
+% -999999999999999999.999999999999999999
+% and +999999999999999999.999999999999999999
+
+\def\pstFPdiv#1#2#3{\pstFP@callc\pstFP@div#1{#2}{#3}} % #1 := #2/#3
+
+\countdef\pstFP@actcounter=10 % register 0 for counter
+\ifnum\pstFP@actcounter<60\relax \pstFP@actcounter=60\fi
+
+\newcount\pstFP@xs %sign of 1st value
+\newcount\pstFP@xia%integer part of 1st value
+\newcount\pstFP@xib%integer part of 1st value
+\newcount\pstFP@xfa%fractional part of 1st value
+\newcount\pstFP@xfb%fractional part of 1st value
+
+\countdef\pstFP@ys=5 %sign of 2nd value
+\countdef\pstFP@yia=6%integer part of 2nd value
+\countdef\pstFP@yib=7%integer part of 2nd value
+\countdef\pstFP@yfa=8%fractional part of 2nd value
+\countdef\pstFP@yfb=9%fractional part of 2nd value
+
+\countdef\pstFP@xk=10 %registers for splitting 1st value
+\countdef\pstFP@xl=11
+\countdef\pstFP@xm=12
+\countdef\pstFP@xn=13
+\countdef\pstFP@xo=14
+\countdef\pstFP@xp=15
+\countdef\pstFP@xq=16
+\countdef\pstFP@xr=17
+\countdef\pstFP@xz=18
+\countdef\pstFP@xt=19
+\countdef\pstFP@xu=20
+\countdef\pstFP@xv=21
+
+\countdef\pstFP@yk=22 %registers for splitting 2nd value
+\countdef\pstFP@yl=23
+\countdef\pstFP@ym=24
+\countdef\pstFP@yn=25
+\countdef\pstFP@yo=26
+\countdef\pstFP@yp=27
+\countdef\pstFP@yq=28
+\countdef\pstFP@yr=29
+\countdef\pstFP@yz=30
+\countdef\pstFP@yt=31
+\countdef\pstFP@yu=32
+\countdef\pstFP@yv=33
+
+\newcount\pstFP@rega %auxiliary registers
+\newcount\pstFP@regb
+\countdef\pstFP@regc=36
+\countdef\pstFP@regd=37
+\countdef\pstFP@rege=38
+
+\countdef\pstFP@rs=39 %result registers
+\countdef\pstFP@ria=40
+\countdef\pstFP@rib=41
+\countdef\pstFP@rfa=42
+\countdef\pstFP@rfb=43
+
+\newcount\pstFP@regs %local auxiliary registers
+\countdef\pstFP@count=45
+\countdef\pstFP@res=46
+\countdef\pstFP@shift=47
+\newcount\pstFP@times
+
+%auxiliary macros which may be used in all of the following macros
+\newif\ifpstFP@test
+
+\def\pstFP@ignorenext#1{}
+\def\pstFP@first#1#2\relax{#1}
+\def\pstFP@swallow#1\relax{}
+%
+\def\ifpstFP@zero#1{%
+ \ifnum%
+ \expandafter\ifnum\csname pstFP@#1ia\endcsname=0 0\else1\fi%
+ \expandafter\ifnum\csname pstFP@#1ib\endcsname=0 0\else1\fi%
+ \expandafter\ifnum\csname pstFP@#1fa\endcsname=0 0\else1\fi%
+ \expandafter\ifnum\csname pstFP@#1fb\endcsname=0 0\else1\fi%
+ =0\relax%
+}
+%
+%read value
+%
+\def\pstFP@correctintcounter#1\relax{%
+ {\edef\pstFP@tmp{#1}%
+ \pstFP@count=0\relax%
+ \loop%
+ \edef\pstFP@tmpa{\expandafter\pstFP@first\pstFP@tmp\noexpand\relax}%
+ \expandafter\ifx\pstFP@tmpa0\relax%
+ \advance\pstFP@count1\relax%
+ \edef\pstFP@tmp{\expandafter\pstFP@ignorenext\pstFP@tmp}%
+ \repeat%
+ \ifnum\pstFP@count>18\relax%
+ \typeout{>>>> Overflow}%
+ \fi%
+ \expandafter\if!\pstFP@tmp!%
+ \advance\pstFP@count-18\relax%
+ \pstFP@count=-\pstFP@count%
+ \loop%
+ \ifnum\pstFP@count>0\relax%
+ \pstFP@regc=\pstFP@rega%
+ \divide\pstFP@rega10\relax\multiply\pstFP@rega10\relax%
+ \advance\pstFP@regc-\pstFP@rega\multiply\pstFP@regc100000000\relax%
+ \divide\pstFP@rega10\relax%
+ \divide\pstFP@regb10\relax\advance\pstFP@regb\pstFP@regc%
+ \advance\pstFP@count-1\relax%
+ \repeat%
+ \global\pstFP@rega=\pstFP@rega%
+ \global\pstFP@regb=\pstFP@regb%
+ \else%
+ \typeout{>>>>Number too big}%
+ \fi%
+ }%
+}
+\def\pstFP@@setintcounter#1#2#3#4#5#6#7#8#9{%
+ \pstFP@regb=#1#2#3#4#5#6#7#8#9\relax%
+ \pstFP@correctintcounter%
+}
+\def\pstFP@setintcounter#1#2#3#4#5#6#7#8#9{%
+ \pstFP@rega=#1#2#3#4#5#6#7#8#9\relax%
+ \pstFP@@setintcounter%
+}
+
+\def\pstFP@@setfractcounter#1#2#3#4#5#6#7#8#9{%
+ \pstFP@regb=#1#2#3#4#5#6#7#8#9\relax%
+ \pstFP@swallow%
+}
+\def\pstFP@setfractcounter#1#2#3#4#5#6#7#8#9{%
+ \pstFP@rega=#1#2#3#4#5#6#7#8#9\relax%
+ \pstFP@@setfractcounter%
+}
+
+\def\pstFP@getsign#1\relax{%
+ {\pstFP@regs=1\relax%
+ \edef\pstFP@tmp{#1}%
+ \loop%
+ \edef\pstFP@tmpa{\expandafter\pstFP@first\pstFP@tmp\noexpand\relax}%
+ \expandafter\ifx\pstFP@tmpa-\relax%
+ \multiply\pstFP@regs-1\relax%
+ \fi%
+ \ifnum\expandafter\ifx\pstFP@tmpa-1\else0\fi\expandafter\ifx\pstFP@tmpa+1\else0\fi>0%
+ \edef\pstFP@tmp{\expandafter\pstFP@ignorenext\pstFP@tmp}%
+ \repeat%
+ \global\let\pstFP@tmp\pstFP@tmp%
+ \global\pstFP@regs=\pstFP@regs%
+ }%
+}
+
+\def\pstFP@removeleadingzeros#1\relax{%
+ {\edef\pstFP@tmp{#1}%
+ \loop%
+ \edef\pstFP@tmpa{\expandafter\pstFP@first\pstFP@tmp\noexpand\relax}%
+ \expandafter\ifx\pstFP@tmpa0\relax%
+ \edef\pstFP@tmp{\expandafter\pstFP@ignorenext\pstFP@tmp}%
+ \repeat%
+ \global\let\pstFP@tmp\pstFP@tmp%
+ }%
+}
+
+\newif\ifpstFP@nonstop
+\def\pstFP@strip#1{%
+ {\edef\pstFP@tmp{#1}%
+ \edef\pstFP@tmpb{}%
+ \ifx\pstFP@tmp\@empty\else%
+ \pstFP@nonstoptrue%
+ \loop%
+ \edef\pstFP@tmpa{\expandafter\pstFP@first\pstFP@tmp\noexpand\relax}%
+ \expandafter\ifx\pstFP@tmpa-\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
+ \expandafter\ifx\pstFP@tmpa+\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
+ \expandafter\ifx\pstFP@tmpa0\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
+ \expandafter\ifx\pstFP@tmpa1\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
+ \expandafter\ifx\pstFP@tmpa2\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
+ \expandafter\ifx\pstFP@tmpa3\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
+ \expandafter\ifx\pstFP@tmpa4\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
+ \expandafter\ifx\pstFP@tmpa5\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
+ \expandafter\ifx\pstFP@tmpa6\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
+ \expandafter\ifx\pstFP@tmpa7\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
+ \expandafter\ifx\pstFP@tmpa8\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
+ \expandafter\ifx\pstFP@tmpa9\relax\edef\pstFP@tmpb{\pstFP@tmpb\pstFP@tmpa}\else%
+ \ifx\pstFP@tmpa\@empty\pstFP@nonstopfalse\else%
+ \ifx\pstFP@tmpa\space\pstFP@nonstopfalse\else%
+ \typeout{>>> Illegal character \pstFP@tmpa\space found in float number}%
+ \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi%
+ \edef\pstFP@tmp{\expandafter\pstFP@ignorenext\pstFP@tmp}%
+ \ifx\pstFP@tmp\@empty\pstFP@nonstopfalse\fi%
+ \ifpstFP@nonstop%
+ \repeat%
+ \fi%
+ \global\let\pstFP@tmp\pstFP@tmpb%
+ }%
+}
+
+\def\pstFP@readvalue#1#2#3{%
+ % #1 macro family to catch the value
+ % #2.#3 value
+ %
+ % regular expression [+|-]*[d]_0^18.[d]*
+ %
+ \pstFP@strip{#2}%
+ %sign
+ \expandafter\pstFP@getsign\pstFP@tmp\relax%
+ \csname pstFP@#1s\endcsname=\pstFP@regs%
+ %
+ %integer part
+ \pstFP@removeleadingzeros\pstFP@tmp\relax%
+ \expandafter\pstFP@setintcounter\pstFP@tmp000000000000000000\relax%
+ \csname pstFP@#1ia\endcsname=\pstFP@rega%
+ \csname pstFP@#1ib\endcsname=\pstFP@regb%
+ %
+ %fractional part
+ \pstFP@strip{#3}%
+ \expandafter\pstFP@setfractcounter\pstFP@tmp000000000000000000\relax%
+ \csname pstFP@#1fa\endcsname=\pstFP@rega%
+ \csname pstFP@#1fb\endcsname=\pstFP@regb%
+ %
+ %correct sign
+ \ifnum\pstFP@rega=0\relax%
+ \ifnum\pstFP@regb=0\relax%
+ \expandafter\ifnum\csname pstFP@#1ib\endcsname=0\relax%
+ \expandafter\ifnum\csname pstFP@#1ia\endcsname=0\relax%
+ \csname pstFP@#1s\endcsname=1\relax%
+ \fi%
+ \fi%
+ \fi%
+ \fi%
+}
+%
+%store value in macro
+%
+\def\pstFP@store#1#2{%
+ % #1 macro
+ % #2 macro family (value) to store
+ %
+ \ifpstFP@zero{#2}%
+ \csname pstFP@#2s\endcsname=1\relax%
+ \fi%
+ \expandafter\ifnum\csname pstFP@#2s\endcsname<0\relax%
+ \edef#1{-}%
+ \else%
+ \edef#1{}%
+ \fi%
+ \expandafter\ifnum\csname pstFP@#2ia\endcsname=0\relax%
+ \expandafter\ifnum\csname pstFP@#2ib\endcsname=0\relax%
+ \edef#1{#10}%
+ \else%
+ \edef#1{#1\expandafter\the\csname pstFP@#2ib\endcsname}%
+ \fi%
+ \else%
+ \expandafter\advance\csname pstFP@#2ib\endcsname1000000000\relax%
+ \edef#1{#1\expandafter\the\csname pstFP@#2ia\endcsname\expandafter\pstFP@ignorenext\the\csname pstFP@#2ib\endcsname}%
+ \fi%
+ \expandafter\advance\csname pstFP@#2fa\endcsname1000000000\relax%
+ \expandafter\advance\csname pstFP@#2fb\endcsname1000000000\relax%
+ \edef#1{#1\noexpand.\expandafter\pstFP@ignorenext\the\csname pstFP@#2fa\endcsname\expandafter\pstFP@ignorenext\the\csname pstFP@#2fb\endcsname}%
+}
+%macros to expand some arguments
+%
+\def\pstFP@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\pstFP@divten#1{%
+ \expandafter\pstFP@regc\csname pstFP@#1ia\endcsname%
+ \expandafter\divide\csname pstFP@#1ia\endcsname10\relax%
+ \expandafter\pstFP@regb\csname pstFP@#1ia\endcsname%
+ \multiply\pstFP@regb10\relax%
+ \advance\pstFP@regc-\pstFP@regb%
+ \multiply\pstFP@regc100000000\relax%
+ %
+ \expandafter\pstFP@rega\csname pstFP@#1ib\endcsname%
+ \expandafter\divide\csname pstFP@#1ib\endcsname10\relax%
+ \expandafter\pstFP@regb\csname pstFP@#1ib\endcsname%
+ \multiply\pstFP@regb10\relax%
+ \advance\pstFP@rega-\pstFP@regb%
+ \multiply\pstFP@rega100000000\relax%
+ \expandafter\advance\csname pstFP@#1ib\endcsname\pstFP@regc%
+ %
+ \expandafter\pstFP@regc\csname pstFP@#1fa\endcsname%
+ \expandafter\divide\csname pstFP@#1fa\endcsname10\relax%
+ \expandafter\pstFP@regb\csname pstFP@#1fa\endcsname%
+ \multiply\pstFP@regb10\relax%
+ \advance\pstFP@regc-\pstFP@regb%
+ \multiply\pstFP@regc100000000\relax%
+ \expandafter\advance\csname pstFP@#1fa\endcsname\pstFP@rega%
+ %
+ \expandafter\divide\csname pstFP@#1fb\endcsname10\relax%
+ \expandafter\advance\csname pstFP@#1fb\endcsname\pstFP@regc%
+}
+%
+\def\pstFP@multen#1{%
+ \expandafter\multiply\csname pstFP@#1ia\endcsname10\relax%
+ \expandafter\ifnum\csname pstFP@#1ib\endcsname<100000000\relax%
+ \else%
+ \expandafter\pstFP@regc\csname pstFP@#1ib\endcsname%
+ \divide\pstFP@regc100000000%
+ \expandafter\advance\csname pstFP@#1ia\endcsname\pstFP@regc%
+ \multiply\pstFP@regc100000000%
+ \expandafter\advance\csname pstFP@#1ib\endcsname-\pstFP@regc%
+ \fi%
+ \expandafter\multiply\csname pstFP@#1ib\endcsname10\relax%
+ \expandafter\ifnum\csname pstFP@#1fa\endcsname<100000000\relax%
+ \else%
+ \expandafter\pstFP@regc\csname pstFP@#1fa\endcsname%
+ \divide\pstFP@regc100000000%
+ \expandafter\advance\csname pstFP@#1ib\endcsname\pstFP@regc%
+ \multiply\pstFP@regc100000000%
+ \expandafter\advance\csname pstFP@#1fa\endcsname-\pstFP@regc%
+ \fi%
+ \expandafter\multiply\csname pstFP@#1fa\endcsname10\relax%
+ \expandafter\ifnum\csname pstFP@#1fb\endcsname<100000000\relax%
+ \else%
+ \expandafter\pstFP@regc\csname pstFP@#1fb\endcsname%
+ \divide\pstFP@regc100000000%
+ \expandafter\advance\csname pstFP@#1fa\endcsname\pstFP@regc%
+ \multiply\pstFP@regc100000000%
+ \expandafter\advance\csname pstFP@#1fb\endcsname-\pstFP@regc%
+ \fi%
+ \expandafter\multiply\csname pstFP@#1fb\endcsname10\relax%
+}
+%
+\def\pstFP@counttimes{%
+ {\global\pstFP@times=0\relax%
+ \loop%
+ \ifnum%
+ \ifnum\pstFP@xia>\pstFP@yia1%
+ \else\ifnum\pstFP@xia<\pstFP@yia0%
+ \else%
+ \ifnum\pstFP@xib>\pstFP@yib1%
+ \else\ifnum\pstFP@xib<\pstFP@yib0%
+ \else%
+ \ifnum\pstFP@xfa>\pstFP@yfa1%
+ \else\ifnum\pstFP@xfa<\pstFP@yfa0%
+ \else%
+ \ifnum\pstFP@xfb>\pstFP@yfb1%
+ \else\ifnum\pstFP@xfb<\pstFP@yfb0%
+ \else%
+ 1%
+ \fi\fi%
+ \fi\fi%
+ \fi\fi%
+ \fi\fi%
+ =1\relax%
+ \global\advance\pstFP@times1\relax%
+ \global\advance\pstFP@xfb-\pstFP@yfb%
+ \ifnum\pstFP@xfb<0\relax%
+ \global\advance\pstFP@xfb1000000000\relax%
+ \global\advance\pstFP@xfa-1\relax%
+ \fi%
+ \global\advance\pstFP@xfa-\pstFP@yfa%
+ \ifnum\pstFP@xfa<0\relax%
+ \global\advance\pstFP@xfa1000000000\relax%
+ \global\advance\pstFP@xib-1\relax%
+ \fi%
+ \global\advance\pstFP@xib-\pstFP@yib%
+ \ifnum\pstFP@xib<0\relax%
+ \global\advance\pstFP@xib1000000000\relax%
+ \global\advance\pstFP@xia-1\relax%
+ \fi%
+ \global\advance\pstFP@xia-\pstFP@yia%
+ \repeat%
+ }%
+}
+%
+\def\pstFP@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 \pstFP@shift such that y*10^\pstFP@shift <100000000<=y*10^(\pstFP@shift+1)
+ % - %determine \pstFP@shift' such that x*10^\pstFP@shift'<100000000<=x*10^(\pstFP@shift+1)
+ % - x=x*\pstFP@shift'
+ % - y=y*\pstFP@shift
+ % - \pstFP@shift=\pstFP@shift-\pstFP@shift'
+ % - res=0
+ % - while y>0 %fixed-point representation!
+ % - \pstFP@times=0
+ % - while x>y
+ % - \pstFP@times=\pstFP@times+1
+ % - x=x-y
+ % - end
+ % - y=y/10
+ % - res=10*res+\pstFP@times/1000000000
+ % - end
+ % - %shift the result according to \pstFP@shift
+ %
+ {\pstFP@readvalue{x}{#2}{#3}%
+ \pstFP@readvalue{y}{#5}{#6}%
+ %
+ %sign
+ \multiply\pstFP@xs\pstFP@ys%
+ \pstFP@rs=\pstFP@xs%
+ %
+ %compute division
+ \ifpstFP@zero{y}%
+ \typeout{>>>>Division by zero}%
+ \else%
+ \ifpstFP@zero{x}\def\next##1{\edef\pstFP@tmp{0}}\else\def\next##1{##1}\fi%
+ \next%
+ {\pstFP@shift=0\relax%
+ \loop%
+ \ifnum\pstFP@yia<100000000\relax%
+ \pstFP@multen{y}%
+ \advance\pstFP@shift1\relax%
+ \repeat%
+ \loop%
+ \ifnum\pstFP@xia<100000000\relax%
+ \pstFP@multen{x}%
+ \advance\pstFP@shift-1\relax%
+ \repeat%
+ \pstFP@ria=0\pstFP@rib=0\pstFP@rfa=0\pstFP@rfb=0\relax%
+ \loop%
+ \ifpstFP@zero{y}\else%
+ \pstFP@counttimes%divides x by \pstFP@times*y
+ \pstFP@divten{y}%
+ \pstFP@multen{r}%
+ \advance\pstFP@rfb\pstFP@times%
+ \ifnum\pstFP@rfb<1000000000\relax\else%
+ \advance\pstFP@rfa1\advance\pstFP@rfb-1000000000\relax%
+ \ifnum\pstFP@rfa<1000000000\relax\else%
+ \advance\pstFP@rib1\advance\pstFP@rfa-1000000000\relax%
+ \ifnum\pstFP@rib<1000000000\relax\else%
+ \advance\pstFP@ria1\advance\pstFP@rib-1000000000\relax%
+ \fi%
+ \fi%
+ \fi%
+ \repeat%
+ \loop%
+ \ifnum\pstFP@shift>17%
+ \advance\pstFP@shift-1\relax%
+ \ifnum\pstFP@ria<100000000\else\pstFP@ria=-1\fi%
+ \ifnum\pstFP@ria<0\pstFP@ria=-1\fi%
+ \pstFP@multen{r}%
+ \repeat%
+ \ifnum\pstFP@ria<1000000000\else\pstFP@ria=-1\fi%
+ \loop%
+ \ifnum\pstFP@shift<17%
+ \advance\pstFP@shift1\relax%
+ \pstFP@divten{r}%
+ \repeat%
+ \ifnum\pstFP@ria<0\relax%
+ \typeout{>>>>Overflow}%
+ \else%
+ \pstFP@store\pstFP@tmp{r}%
+ \fi%
+ }%
+ \fi%
+ %
+ \global\let\pstFP@tmp=\pstFP@tmp%
+ %
+ }%
+ \let#1\pstFP@tmp%
+}
+%
+\catcode`\@=\PstAtCode\relax
+%
+%% END: pst-fp.tex
+\endinput
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-15 17:14:43 +0000