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Diffstat (limited to 'graphics/pstricks/base/generic/pst-fp.tex')
-rw-r--r-- | graphics/pstricks/base/generic/pst-fp.tex | 717 |
1 files changed, 717 insertions, 0 deletions
diff --git a/graphics/pstricks/base/generic/pst-fp.tex b/graphics/pstricks/base/generic/pst-fp.tex new file mode 100644 index 0000000000..2d4e748193 --- /dev/null +++ b/graphics/pstricks/base/generic/pst-fp.tex @@ -0,0 +1,717 @@ +%% $Id: pst-fp.tex 465 2017-05-22 17:50:57Z herbert $ +%% +%% +%% This is file `pst-fp.tex', +%% +%% IMPORTANT NOTICE: +%% +%% Package `pst-fp.tex' +%% +%% Herbert Voss <hvoss@tug.org> +%% 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, +%% multiplication and addition +%% +\csname PSTFPloaded\endcsname +\let\PSTFPloaded\endinput +% +% Requires some packages +\ifx\PSTricksLoaded\endinput\else\input pstricks \fi +% +\def\fileversion{0.05} +\def\filedate{2010/01/17} +\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\pstFPadd#1#2#3{\pstFP@callc\pstFP@add#1{#2}{#3}+\relax} % #1 := #2+#3 +\def\pstFPsub#1#2#3{\pstFP@callc\pstFP@add#1{#2}{-#3}-\relax}% #1 := #2-#3 +\def\pstFPmul#1#2#3{\pstFP@callc\pstFP@mul#1{#2}{#3}} % #1 := #2*#3 +\def\pstFPdiv#1#2#3{\pstFP@callc\pstFP@div#1{#2}{#3}} % #1 := #2/#3 + +\def\pst@int#1{\expandafter\pst@@int#1..\@nil} +\def\pst@@int#1.#2.\@nil{#1} +\def\pst@Int#1{% + \@tempdima=#1\relax% + \expandafter\pst@@Int\the\@tempdima\@nil} +\def\pst@@Int#1.#2\@nil{#1} + +% +\def\pstFPMul#1#2#3{\pstFP@callc\pstFP@mul#1{#2}{#3}% % #1 := int(#2*#3) + \edef#1{\pst@int{#1}}}% +\def\pstFPDiv#1#2#3{\pstFP@callc\pstFP@div#1{#2}{#3}% % #1 := int(#2/#3) + \edef#1{\pst@int{#1}}}% +\def\pstFPstripZeros#1#2{\pst@dimm=#1pt\relax \edef#2{\strip@pt\pst@dimm}} +% +\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 +\countdef\pstFP@prod=49 + +%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@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 '.' + % + {\pstFP@readvalue{x}{#2}{#3}% + \pstFP@readvalue{y}{#5}{#6}% + % + \ifnum\pstFP@xs=\pstFP@ys% + \advance\pstFP@xfb\pstFP@yfb% + \advance\pstFP@xfa\pstFP@yfa% + \ifnum\pstFP@xfb<1000000000\relax\else% + \advance\pstFP@xfb-1000000000\relax% + \advance\pstFP@xfa1\relax% + \fi% + \advance\pstFP@xib\pstFP@yib% + \ifnum\pstFP@xfa<1000000000\relax\else% + \advance\pstFP@xfa-1000000000\relax% + \advance\pstFP@xib1\relax% + \fi% + \advance\pstFP@xia\pstFP@yia% + \ifnum\pstFP@xib<1000000000\relax\else% + \advance\pstFP@xib-1000000000\relax% + \advance\pstFP@xia1\relax% + \fi% + \ifnum\pstFP@xia<1000000000\relax\else% + \pstFP@errmessage{Overflow}% + \fi% + \pstFP@store\pstFP@tmp{x}% + \else% + \advance\pstFP@xfb-\pstFP@yfb% + \ifnum\pstFP@xfb<0\relax% + \advance\pstFP@yfa1\relax% + \advance\pstFP@xfb1000000000\relax% + \fi% + \advance\pstFP@xfa-\pstFP@yfa% + \ifnum\pstFP@xfa<0\relax% + \advance\pstFP@yib1\relax% + \advance\pstFP@xfa1000000000\relax% + \fi% + \advance\pstFP@xib-\pstFP@yib% + \ifnum\pstFP@xib<0\relax% + \advance\pstFP@yia1\relax% + \advance\pstFP@xib1000000000\relax% + \fi% + \advance\pstFP@xia-\pstFP@yia% + \ifnum\pstFP@xia<0\relax% + \pstFP@xs=-\pstFP@xs% + \ifnum\pstFP@xfb=0\relax\else% + \advance\pstFP@xfb-1000000000\relax\pstFP@xfb=-\pstFP@xfb% + \advance\pstFP@xfa1\relax% + \fi% + \ifnum\pstFP@xfa=0\relax\else% + \advance\pstFP@xfa-1000000000\relax\pstFP@xfa=-\pstFP@xfa% + \advance\pstFP@xib1\relax% + \fi% + \ifnum\pstFP@xib=0\relax\else% + \advance\pstFP@xib-1000000000\relax\pstFP@xib=-\pstFP@xib% + \advance\pstFP@xia1\relax% + \fi% + \relax\pstFP@xia=-\pstFP@xia% + \fi% + \pstFP@store\pstFP@tmp{x}% + \fi% + \global\let\pstFP@tmp\pstFP@tmp% + }% +% \pstFPstripZeros\pstFP@tmp{#1}% + \let#1\pstFP@tmp +} + + +\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% + % + }% +% \pstFPstripZeros\pstFP@tmp{#1}% + \let#1\pstFP@tmp +} +%multiply two values + +\def\pstFP@firstnine#1#2#3#4#5#6#7#8#9{% + \pstFP@res=#1#2#3#4#5#6#7#8#9\relax% +} +\def\pstFP@@ninesplit#1\relax#2\end#3{% + #1% + \edef#3{#2}% +} +\def\pstFP@ninesplit#1{% + \edef#1{\expandafter\pstFP@firstnine\pstFP@rd}% + \expandafter\pstFP@@ninesplit#1\end#1\relax% +} + +\def\pstFP@split#1#2#3#4{% + % #1 highest three digits + % #2 medium three digits + % #3 least three digits + % #4 counter + \pstFP@regc=#4% + \divide\pstFP@regc1000000\relax% + #1=\pstFP@regc% + \multiply\pstFP@regc-1000000\relax\advance\pstFP@regc#4% + #3=\pstFP@regc% + \divide\pstFP@regc1000\relax% + #2=\pstFP@regc% + \multiply\pstFP@regc-1000\relax\advance\pstFP@regc#3% + #3=\pstFP@regc% +} + +\def\pstFP@@mul#1#2#3{% + \pstFP@regc=\csname pstFP@x#1\endcsname% + \multiply\pstFP@regc\csname pstFP@y#2\endcsname% + \advance\pstFP@prod\pstFP@regc% + % + \ifx#3\relax% + \let\next=\relax% + \else% + \let\next=\pstFP@@mul% + \fi% + \next#3% +} + +\def\pstFP@saveshift{% + % save rightmost three digits + \pstFP@regc=\pstFP@prod% + \divide\pstFP@prod1000\relax% + \multiply\pstFP@prod1000\relax% + \advance\pstFP@regc-\pstFP@prod% + \advance\pstFP@regc1000\relax% + \edef\pstFP@rd{\expandafter\pstFP@ignorenext\the\pstFP@regc\pstFP@rd}% + % + \divide\pstFP@prod1000\relax% +} + +\def\pstFP@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 + % + {\pstFP@readvalue{x}{#2}{#3}% + \pstFP@readvalue{y}{#5}{#6}% + % + %sign + \multiply\pstFP@xs\pstFP@ys% + \pstFP@rs=\pstFP@xs% + % + % split parts + \pstFP@split\pstFP@xk\pstFP@xl\pstFP@xm\pstFP@xia\pstFP@split\pstFP@xn\pstFP@xo\pstFP@xp\pstFP@xib% + \pstFP@split\pstFP@xq\pstFP@xr\pstFP@xz\pstFP@xfa\pstFP@split\pstFP@xt\pstFP@xu\pstFP@xv\pstFP@xfb% + \pstFP@split\pstFP@yk\pstFP@yl\pstFP@ym\pstFP@yia\pstFP@split\pstFP@yn\pstFP@yo\pstFP@yp\pstFP@yib% + \pstFP@split\pstFP@yq\pstFP@yr\pstFP@yz\pstFP@yfa\pstFP@split\pstFP@yt\pstFP@yu\pstFP@yv\pstFP@yfb% + % + \pstFP@prod=0\relax% + \edef\pstFP@rd{}% + % + %compute result + \pstFP@@mul vv \relax\pstFP@saveshift% + \pstFP@@mul vu uv \relax\pstFP@saveshift% + \pstFP@@mul uu vt tv \relax\pstFP@saveshift% + \pstFP@@mul ut tu vz zv \relax\pstFP@saveshift% + \pstFP@@mul tt zu uz rv vr \relax\pstFP@saveshift% + \pstFP@@mul zt tz ur ru vq qv \relax\pstFP@saveshift% + \pstFP@@mul zz rt tr uq qu vp pv \relax\pstFP@saveshift% + \pstFP@@mul zr rz tq qt up pu vo ov \relax\pstFP@saveshift% + \pstFP@@mul rr qz zq tp pt uo ou vn nv \relax\pstFP@saveshift% + \pstFP@@mul rq qr zp pz to ot un nu vm mv \relax\pstFP@saveshift% + \pstFP@@mul qq rp pr zo oz tn nt um mu vl lv \relax\pstFP@saveshift% + \pstFP@@mul qp pq ro or zn nz tm mt ul lu kv vk \relax\pstFP@saveshift% + \pstFP@@mul pp oq qo rn nr zm mz tl lt ku uk \relax\pstFP@saveshift% + \pstFP@@mul op po nq qn rm mr zl lz tk kt \relax\pstFP@saveshift% + \pstFP@@mul oo pn np mq qm rl lr kz zk \relax\pstFP@saveshift% + \pstFP@@mul no on mp pm lq ql kr rk \relax\pstFP@saveshift% + \pstFP@@mul nn mo om pl lp qk kq \relax\pstFP@saveshift% + \pstFP@@mul mn nm lo ok pk kp \relax\pstFP@saveshift% + \pstFP@@mul mm ln nl ko ok \relax\pstFP@saveshift% + \pstFP@@mul lm ml kn nk \relax\pstFP@saveshift% + \pstFP@@mul ll km mk \relax\pstFP@saveshift% + \pstFP@@mul kl lk \relax\pstFP@saveshift% + \pstFP@@mul kk \relax\pstFP@saveshift\pstFP@saveshift% + \pstFP@ninesplit\pstFP@rd% + \ifnum\pstFP@res=0\relax% + \pstFP@ninesplit\pstFP@rd% + \ifnum\pstFP@res=0\relax% + \pstFP@ninesplit\pstFP@rd\pstFP@ria=\pstFP@res% + \pstFP@ninesplit\pstFP@rd\pstFP@rib=\pstFP@res% + \pstFP@ninesplit\pstFP@rd\pstFP@rfa=\pstFP@res% + \pstFP@ninesplit\pstFP@rd\pstFP@rfb=\pstFP@res% + \pstFP@store\pstFP@tmp{r}% + \else\typeout{pstFPmul: Overflow}\fi% + \else\typeout{pstFPmul: Overflow}\fi% + \global\let\pstFP@tmp\pstFP@tmp}% +% \pstFPstripZeros\pstFP@tmp{#1}% + \let#1\pstFP@tmp +} +% +\catcode`\@=\PstAtCode\relax +% +%% END: pst-fp.tex +\endinput |