diff options
author | Karl Berry <karl@freefriends.org> | 2006-01-12 23:51:53 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2006-01-12 23:51:53 +0000 |
commit | c11a98e10de0410a50337e5ab4e3b63b210eec13 (patch) | |
tree | 690b00bd75ff04ce9740a64e6ab1aeaed65a3836 /Master/texmf-dist/tex/latex/bardiag/pstfp.sty | |
parent | 27ac78b71207f7568bad5b936aa5b3109e5eea82 (diff) |
bardiag
git-svn-id: svn://tug.org/texlive/trunk@692 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/tex/latex/bardiag/pstfp.sty')
-rw-r--r-- | Master/texmf-dist/tex/latex/bardiag/pstfp.sty | 1137 |
1 files changed, 1137 insertions, 0 deletions
diff --git a/Master/texmf-dist/tex/latex/bardiag/pstfp.sty b/Master/texmf-dist/tex/latex/bardiag/pstfp.sty new file mode 100644 index 00000000000..a7785ac7dcd --- /dev/null +++ b/Master/texmf-dist/tex/latex/bardiag/pstfp.sty @@ -0,0 +1,1137 @@ +% 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% +} |