%% $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 %% 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