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| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/defpattern.sty | 31 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/fp-addons.sty | 66 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/fp-basic.sty | 1121 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/fp-eqn.sty | 382 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/fp-eval.sty | 155 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/fp-exp.sty | 500 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/fp-pas.sty | 118 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/fp-random.sty | 120 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/fp-snap.sty | 242 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/fp-trigo.sty | 1119 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/fp-upn.sty | 237 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/fp.sty | 32 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/fp/lfp.sty | 34 |
13 files changed, 4157 insertions, 0 deletions
diff --git a/Master/texmf-dist/tex/latex/fp/defpattern.sty b/Master/texmf-dist/tex/latex/fp/defpattern.sty new file mode 100644 index 00000000000..1d5787ff13f --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/defpattern.sty @@ -0,0 +1,31 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{defpattern}[1994/10/12] + +\message{% + `\string\defpattern-macro (adapted from \string\howto\space (A. Jeffrey: TeX and TUG NEWS 2(2)))'% +} + +%define a macro \defpattern for defining ML-like pattern matching macros +%adapted from the \howto-macro from tugboat + +\def\xcs#1#2{\expandafter#1\csname#2\endcsname} +\newcount\actioncount +\def\defpattern#1[#2]#3{% + \xcs\ifx{\expandafter\gobble\string#1}\relax% + \def#1{\erroraction#1}\fi% + \advance\actioncount by 1\relax% + \expandafter\defaction\expandafter{#1}{#3}{#2}% + \def\temp##1##2##3##4##5##6##7##8##9{\def\temp{[#2]}}% + \temp\empty\empty\empty\empty\empty\empty\empty\empty\empty% + \edef#1{\noexpand\doaction\xcs\noexpand% + {action-\the\actioncount}\temp}} +\def\defaction#1#2#3{% + \xcs\def{action-\the\actioncount}##1[#3]{\applyto{#1}{#2}}} +\def\gobble#1{} +\def\applyto#1#2#3{#3{#1}{#2}} +\def\doaction#1[#2][#3]{#1[#3]\success[#2]\failure[#3]} +\def\success#1#2[#3]\failure[#4]{#2} +\def\failure#1#2{#1} +\def\erroraction#1[#2]{% + \errmessage{I don't know how to \string#1[#2]}} + diff --git a/Master/texmf-dist/tex/latex/fp/fp-addons.sty b/Master/texmf-dist/tex/latex/fp/fp-addons.sty new file mode 100644 index 00000000000..d91057d2eb0 --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/fp-addons.sty @@ -0,0 +1,66 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{fp-addons}[1995/03/15] + +\def\FP@addonsversion{0.1} +\message{% + `Fixed Point Arithmetic Addons',\space% + Version \FP@addonsversion\space% + \space(C) Michael Mehlich% + \space\space\space\space\space\space\space% + \space\space\space\space\space\space\space% +} + +%%%public area (macros which may be used)%%% + +\def\FPmin#1#2#3{\FP@min#1{#2}{#3}} % #1:=min(#2,#3) +\def\FPmax#1#2#3{\FP@max#1{#2}{#3}} % #1:=max(#2,#3) + +%%%private fp-area (don't use these macros)%%% + +%compute minimum of two values +\def\FP@min#1#2#3{% + % #1 macro, which gets the result + % #2 value one + % #3 value two + \FP@beginmessage{MIN}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + % + \FPiflt{#2}{#3}% + \edef\FP@tmp{#2}% + \else% + \edef\FP@tmp{#3}% + \fi% + % + \global\let\FP@tmp\FP@tmp% + }% + % + \FP@endmessage{}% + % + \let#1\FP@tmp% +} + +%compute maximum of two values +\def\FP@max#1#2#3{% + % #1 macro, which gets the result + % #2 value one + % #3 value two + \FP@beginmessage{MAX}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + % + \FPifgt{#2}{#3}% + \edef\FP@tmp{#2}% + \else% + \edef\FP@tmp{#3}% + \fi% + % + \global\let\FP@tmp\FP@tmp% + }% + % + \FP@endmessage{}% + % + \let#1\FP@tmp% +} diff --git a/Master/texmf-dist/tex/latex/fp/fp-basic.sty b/Master/texmf-dist/tex/latex/fp/fp-basic.sty new file mode 100644 index 00000000000..8091f63b5c1 --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/fp-basic.sty @@ -0,0 +1,1121 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{fp-basic}[1996/05/13] + +%version information +\def\FP@basicversion{1.2d} +\message{% + `Basic Fixed Point Arithmetic',\space\space% + Version \FP@basicversion% + \space(C) Michael Mehlich% + \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 + + + +%%%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\FPadd#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\FPsub#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% +} diff --git a/Master/texmf-dist/tex/latex/fp/fp-eqn.sty b/Master/texmf-dist/tex/latex/fp/fp-eqn.sty new file mode 100644 index 00000000000..9841ff22565 --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/fp-eqn.sty @@ -0,0 +1,382 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{fp-eqn}[1995/04/03] + +%version information +\def\FP@eqnversion{0.4} +\message{% + `Fixed Point Equation Solver',% + \space\space\space% + Version \FP@eqnversion\space% + \space(C) Michael Mehlich% + \space\space\space\space\space\space\space% + \space\space\space\space\space\space\space% +} + +%resolve dependencies +\RequirePackage{fp} + +%%%public area (macros which may be used)%%% + +\def\FPlsolve#1#2#3{\FP@lsolve#1{#2}{#3}} % #1 := x with #2*x+#3=0 +\def\FPqsolve#1#2#3#4#5{\FP@qsolve#1#2{#3}{#4}{#5}} % #1,#2 := x with #3*x^2+#4*x+#5 = 0 +\def\FPcsolve#1#2#3#4#5#6#7{\FP@csolve#1#2#3{#4}{#5}{#6}{#7}} + % #1,#2,#3 := x with #4*x^3+#5*x^2+#6*x+#7 = 0 +\def\FPqqsolve#1#2#3#4#5#6#7#8#9{\FP@qqsolve#1#2#3#4{#5}{#6}{#7}{#8}{#9}} + % #1,#2,#3,#4 := x with #5*x^4+#6*x^3+#7*x^2+#8*x+#9 = 0 + +%%%private fp-area (don't use these macros)%%% + +%compute the solution of a*x + b = 0 +\def\FP@lsolve@warn#1{% + %value determining warning + \FPifzero{#1}% + \FP@warnmessage{Linear equation has infinitely many solutions, choosing 0}% + \edef\FP@tmp{0}% + \else% + \FP@errmessage{Linear equation does not have a solution}% + \fi% +} + +\def\FP@@lsolve#1#2{% + \FPdiv\FP@tmp{#2}{#1}% + \FPneg\FP@tmp\FP@tmp% +} + +\def\FP@lsolve#1#2#3{% + % #1 macro, which gets the result + % #2 value a + % #3 value b + % + \FP@beginmessage{LSOLVE}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + % + \FPifzero{#2}% + \FP@lsolve@warn{#3}% + \else% + \FP@@lsolve{#2}{#3}% + \fi% + % + \global\let\FP@tmp\FP@tmp% + }% + % + \let#1\FP@tmp% + % + \FP@endmessage{}% +} + +%compute the solutions of a*x^2 + b*x + c = 0 +\def\FP@@qsolve#1#2#3{% + % \FP@tmpc := 2*a + \FPadd\FP@tmpc{#1}{#1}% + % + % \FP@tmpb := b*b + \FPmul\FP@tmpd{#2}{#2}% + % + % \FP@tmpc := 4*a*c + \FPmul\FP@tmpe\FP@tmpc{#3}% + \FPadd\FP@tmpe\FP@tmpe\FP@tmpe% + % + % \FP@tmpf := b^2 - 4*a*c + \FPsub\FP@tmpf\FP@tmpd\FP@tmpe% + % + \FPifneg\FP@tmpf% + \FP@errmessage{Quadratic equation does not have a solution}% + \else% + % \FP@tmpd := sqrt(b^2 - 4*a*c) + \FProot\FP@tmpd\FP@tmpf{2}% + % + % solution 1: x = (-b + sqrt(b^2 - 4*a*c))/(2*a) + \FPsub\FP@tmp\FP@tmpd{#2}% + \FPdiv\FP@tmpe\FP@tmp\FP@tmpc% + % + % solution 2: x = (-b + sqrt(b^2 - 4*a*c))/(2*a) + \FPadd\FP@tmp\FP@tmpd{#2}% + \FPdiv\FP@tmpd\FP@tmp\FP@tmpc% + \FPneg\FP@tmpd\FP@tmpd% + \fi% +} + +\def\FP@qsolve#1#2#3#4#5{% + % #1 macro, which gets the 1st result + % #2 macro, which gets the 2nd result + % #3 value a + % #4 value b + % #5 value c + % + \FP@beginmessage{QSOLVE}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + % + \FPifzero{#3}% + \FP@warnmessage{Quadratic equation is linear}% + \FP@lsolve\FP@tmpe{#4}{#5}% + \let\FP@tmpd\FP@tmpe% + \else% + \FP@@qsolve{#3}{#4}{#5}% + \fi% + % + \global\let\FP@tmpa\FP@tmpe% + \global\let\FP@tmpb\FP@tmpd% + }% + % + \let#1\FP@tmpa% + \let#2\FP@tmpb% + % + \FP@endmessage{}% +} + +%compute the solutions of a*x^3 + b*x^2 + c*x + d = 0 +\def\FP@@csolve#1#2#3#4{% + %reducation of cubic equation + %\FPeval\FP@tmpp{(#3)/(3*(#1)) - mul(copy((#2)/(3*(#1))))}% + \FPupn\FP@tmpp{#3 3 #1 mul div #2 3 #1 mul div copy mul sub}% + %\FPeval\FP@tmpq{mul(mul(copy(copy((#2)/(3*(#1)))))) - (#2)*(#3)/(6*(#1)*(#1)) + (#4)/(2*(#1))}% + \FPupn\FP@tmpq{#2 3 #1 mul div copy copy mul mul #2 #3 mul 6 #1 mul #1 mul div sub #4 2 #1 mul div add}% + % + %check whether solution is trivial + \FPifzero\FP@tmpp% + %\FPeval\FP@tmpf{root(3,abs(2*\FP@tmpq)) * sgn(\FP@tmpq)}% + \FPupn\FP@tmpf{3 2 \FP@tmpq{} mul abs root \FP@tmpq{} sgn mul}% + \let\FP@tmpe\FP@tmpf% + \let\FP@tmpd\FP@tmpf% + \else% + %compute D + %\FPeval\FP@tmpD{mul(copy(\FP@tmpq)) + mul(mul(copy(copy(\FP@tmpp))))}% + \FPupn\FP@tmpD{\FP@tmpq{} copy mul \FP@tmpp{} copy copy mul mul add}% + \FPsgn\FP@tmp\FP@tmpD% + \expandafter\ifnum\FP@tmp=1\relax% + %only one real valued solution, compute it + \FProot\FP@tmpD\FP@tmpD{2}% + \FPsub\FP@tmpf\FP@tmpD\FP@tmpq% + \FPadd\FP@tmpe\FP@tmpD\FP@tmpq% + \FPneg\FP@tmpe\FP@tmpe% + %\FPeval\FP@tmpf{root(3,abs(\FP@tmpf)) * sgn(\FP@tmpf) + root(3,abs(\FP@tmpe)) * sgn(\FP@tmpe)}% + \FPupn\FP@tmpf{3 \FP@tmpf{} abs root \FP@tmpf{} sgn mul 3 \FP@tmpe{} abs root \FP@tmpe{} sgn mul add}% + \FP@warnmessage{Cubic equation has only one real valued solution}% + \let\FP@tmpe\FP@tmpf% + \let\FP@tmpd\FP@tmpf% + \else% + %compute r and phi/3 + %\FPeval\FP@tmpr{root(2,abs(\FP@tmpp)) * sgn(\FP@tmpq) * 2}% + \FPupn\FP@tmpr{2 \FP@tmpp{} abs root \FP@tmpq{} sgn mul}% + %\FPeval\FP@tmpp{arccos(\FP@tmpq/\FP@tmpr/\FP@tmpr/\FP@tmpr)/3}% + \FPupn\FP@tmpp{\FP@tmpq{} \FP@tmpr{} div \FP@tmpr{} div \FP@tmpr{} div arccos 3 div}% + %compute the three solutions + \FPmul\FP@tmpr{2}\FP@tmpr% + \FPeval\FP@tmpf{neg(\FP@tmpr) * cos(\FP@tmpp)}% + \FPeval\FP@tmpe{(\FP@tmpr) * cos(1.047197551196597746-(\FP@tmpp))}% + \FPeval\FP@tmpd{(\FP@tmpr) * cos(1.047197551196597746+(\FP@tmpp))}% + \fi% + \fi% + % + \FPeval\FP@tmpf{(\FP@tmpf)-(#2)/(3*(#1))}% + \FPeval\FP@tmpe{(\FP@tmpe)-(#2)/(3*(#1))}% + \FPeval\FP@tmpd{(\FP@tmpd)-(#2)/(3*(#1))}% +} + +\def\FP@csolve#1#2#3#4#5#6#7{% + % #1 macro, which gets the 1st result + % #2 macro, which gets the 2nd result + % #3 macro, which gets the 3nd result + % #4 value a + % #5 value b + % #6 value c + % #7 value d + % + \FP@beginmessage{CSOLVE}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + % + \FPifzero{#4}% + \FP@warnmessage{Cubic equation is quadratic}% + \FP@qsolve\FP@tmpe\FP@tmpf{#5}{#6}{#7}% + \let\FP@tmpd\FP@tmpe% + \else% + \FP@@csolve{#4}{#5}{#6}{#7}% + \fi% + % + \global\let\FP@tmpa\FP@tmpf% + \global\let\FP@tmpb\FP@tmpe% + \global\let\FP@tmpc\FP@tmpd% + }% + % + \let#1\FP@tmpa% + \let#2\FP@tmpb% + \let#3\FP@tmpc% + % + \FP@endmessage{}% +} + +%compute the solutions of a*x^4 + b*x^3 + c*x^2 + d*x + e = 0 +\def\FP@qqsolveAy#1#2#3{% + \FPeval\FP@tmpA{8*(\FP@tmpyc)+((#2)*(#2)/(#1)-4*(#3))/(#1)}% + \FPsgn\FP@tmp\FP@tmpA% + \expandafter\ifnum\FP@tmp>0\relax% + \let\FP@tmpy\FP@tmpyc% + \else% + \FPeval\FP@tmpA{8*(\FP@tmpyb)+((#2)*(#2)/(#1)-4*(#3))/(#1)}% + \FPsgn\FP@tmp\FP@tmpA% + \expandafter\ifnum\FP@tmp>0\relax% + \let\FP@tmpy\FP@tmpyb% + \else% + \FPeval\FP@tmpA{8*(\FP@tmpya)+((#2)*(#2)/(#1)-4*(#3))/(#1)}% + \FPsgn\FP@tmp\FP@tmpA% + \expandafter\ifnum\FP@tmp>0\relax% + \let\FP@tmpy\FP@tmpya% + \else% + \FP@errmessage{Equation of 4-th degree has no solution}% + \fi% + \fi% + \fi% + \FProot\FP@tmpA\FP@tmpA{2}% +} + +\def\FP@@qqsolve#1#2#3#4#5{% + %compute cubic equation + \FPeval\FP@tmpyb{neg(4*(#3)/(#1))}% + \FPeval\FP@tmpyc{2*(#2)*(#4)/(#1)/(#1) - 8*(#5)/(#1)}% + \FPeval\FP@tmpyd{(#5)/(#1)*(4*(#3)/(#1) - (#2)*(#2)/(#1)/(#1)) - (#4)*(#4)/(#1)/(#1)}% + %solve cubic equation + \FP@@csolve{8}\FP@tmpyb\FP@tmpyc\FP@tmpyd% + %hold an arbitrary solution + \let\FP@tmpya\FP@tmpd% + \let\FP@tmpyb\FP@tmpe% + \let\FP@tmpyc\FP@tmpf% + %compute A and y from these solutions + \FP@qqsolveAy{#1}{#2}{#3}% + %compute first quadratic equation + \FPeval\FP@tmpp{((#2)/(#1)+(\FP@tmpA))/2}% + \FPeval\FP@tmpq{(\FP@tmpy)+((#2)*(\FP@tmpy)-(#4))/(#1)/(\FP@tmpA)}% + \FP@qsolve\FP@tmpg\FP@tmpf{1}\FP@tmpp\FP@tmpq% + %compute second quadratic equation + \FPeval\FP@tmpp{((#2)/(#1)-(\FP@tmpA))/2}% + \FPeval\FP@tmpq{(\FP@tmpy)-((#2)*(\FP@tmpy)-(#4))/(#1)/(\FP@tmpA)}% + \FP@qsolve\FP@tmpe\FP@tmpd{1}\FP@tmpp\FP@tmpq% +} + +%subsolve a*x^4 + c*x^2 + e = 0 +\def\FP@qsolve@zero#1#2#3{% + \FPeval\FP@tmpy{(#2)*(#2) - 4*(#1)*(#3)}% + \FPsgn\FP@tmp\FP@tmpy% + \expandafter\ifnum\FP@tmp<0\relax% + \FP@errmessage{Equation of 4-th degree has no solution}% + \else% + %compute solutions + \FPeval\FP@tmpya{neg(root(2,\FP@tmpy)+(#2))/(2*(#1))}% + \FPeval\FP@tmpyb{(root(2,\FP@tmpy)-(#2))/(2*(#1))}% + \FPsgn\FP@tmpf\FP@tmpya% + \FPsgn\FP@tmpg\FP@tmpyb% + \ifnum\expandafter\ifnum\FP@tmpf<0 0\else1\fi\expandafter\ifnum\FP@tmpg<0 0\else1\fi=0\relax% + \FP@errmessage{Equation of 4-th degree has no solution}% + \else% + \expandafter\ifnum\FP@tmpf<0\relax% + \FP@warnmessage{Equation of 4-th degree only has two solutions}% + \let\FP@tmpya\FP@tmpyb% + \else% + \expandafter\ifnum\FP@tmpg<0\relax% + \FP@warnmessage{Equation of 4-th degree only has two solutions}% + \let\FP@tmpyb\FP@tmpya% + \fi% + \fi% + %compute solutions + \FProot\FP@tmpg\FP@tmpya{2}% + \FPneg\FP@tmpf\FP@tmpg% + \FProot\FP@tmpe\FP@tmpyb{2}% + \FPneg\FP@tmpd\FP@tmpe% + \fi% + \fi% +} + +%subsolve a*x^4 + b*x^3 + c*x^2 + b*x + a = 0 +\def\FP@qsolve@eq#1#2#3{% + \FPeval\FP@tmpy{(#2)*(#2) - 4*(#1)*(#3) + 8*(#1)*(#1)}% + \FPsgn\FP@tmp\FP@tmpy% + \expandafter\ifnum\FP@tmp<0\relax% + \FP@errmessage{Equation of 4-th degree has no solution}% + \else% + %compute solutions + \FPeval\FP@tmpya{neg(root(2,\FP@tmpy)+(#2))/(2*(#1))}% + \FPeval\FP@tmpyb{(root(2,\FP@tmpy)-(#2))/(2*(#1))}% + \FPeval\FP@tmpyc{(\FP@tmpya)*(\FP@tmpya)-4}% + \FPeval\FP@tmpyd{(\FP@tmpyb)*(\FP@tmpyb)-4}% + \FPsgn\FP@tmpf\FP@tmpyc% + \FPsgn\FP@tmpg\FP@tmpyd% + \ifnum\expandafter\ifnum\FP@tmpf<0 0\else1\fi\expandafter\ifnum\FP@tmpg<0 0\else1\fi=0\relax% + \FP@errmessage{Equation of 4-th degree has no solution}% + \else% + \expandafter\ifnum\FP@tmpf<0\relax% + \FP@warnmessage{Equation of 4-th degree only has two solutions}% + \let\FP@tmpya\FP@tmpyb% + \let\FP@tmpyc\FP@tmpyd% + \else% + \expandafter\ifnum\FP@tmpg<0\relax% + \FP@warnmessage{Equation of 4-th degree only has two solutions}% + \let\FP@tmpyb\FP@tmpya% + \let\FP@tmpyd\FP@tmpyc% + \fi% + \fi% + %compute solutions + \FPeval\FP@tmpg{((\FP@tmpya)+root(2,(\FP@tmpyc)))/2}% + \FPeval\FP@tmpf{((\FP@tmpya)-root(2,(\FP@tmpyc)))/2}% + \FPeval\FP@tmpe{((\FP@tmpyb)+root(2,(\FP@tmpyd)))/2}% + \FPeval\FP@tmpd{((\FP@tmpyb)-root(2,(\FP@tmpyd)))/2}% + \fi% + \fi% +} + +%complete solve of equation of 4-th degree +\def\FP@qqsolve#1#2#3#4#5#6#7#8#9{% + % #1 macro, which gets the 1st result + % #2 macro, which gets the 2nd result + % #3 macro, which gets the 3nd result + % #4 macro, which gets the 4th result + % #5 value a + % #6 value b + % #7 value c + % #8 value d + % #9 value e + % + \FP@beginmessage{QQSOLVE}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + % + \FPifzero{#5}% + \FP@warnmessage{Equation of 4-th degree is cubic}% + \FP@csolve\FP@tmpd\FP@tmpe\FP@tmpf{#6}{#7}{#8}{#9}% + \let\FP@tmpg\FP@tmpd% + \else% + \FPsgn\FP@tmpg{#6}% + \FPsgn\FP@tmpf{#8}% + \ifnum\expandafter\ifnum\FP@tmpg=0 0\else1\fi\expandafter\ifnum\FP@tmpf=0 0\else1\fi=0\relax% + %case b=d=0 + \FP@qsolve@zero{#5}{#7}{#9}% + \else% + \FPupn\FP@tmpg{#5 #9 sub sgn}% + \FPupn\FP@tmpf{#6 #8 sub sgn}% + \ifnum\expandafter\ifnum\FP@tmpg=0 0\else1\fi\expandafter\ifnum\FP@tmpf=0 0\else1\fi=0\relax% + %case a=e, b=d + \FP@qsolve@eq{#5}{#6}{#7}% + \else% + \FP@@qqsolve{#5}{#6}{#7}{#8}{#9}% + \fi% + \fi% + \fi% + % + \global\let\FP@tmpa\FP@tmpg% + \global\let\FP@tmpb\FP@tmpf% + \global\let\FP@tmpc\FP@tmpe% + \global\let\FP@tmpd\FP@tmpd% + }% + % + \let#1\FP@tmpa% + \let#2\FP@tmpb% + \let#3\FP@tmpc% + \let#4\FP@tmpd% + % + \FP@endmessage{}% +} diff --git a/Master/texmf-dist/tex/latex/fp/fp-eval.sty b/Master/texmf-dist/tex/latex/fp/fp-eval.sty new file mode 100644 index 00000000000..1a81f9a6ea1 --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/fp-eval.sty @@ -0,0 +1,155 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{fp-eval}[1995/04/03] + +%version information +\def\FP@evalversion{0.9a} +\message{% + `Fixed Point Calculator',% + \space\space\space\space% + \space\space\space\space% + Version \FP@evalversion% + \space(C) Michael Mehlich% + \space\space\space\space\space\space\space% + \space\space\space\space\space\space% +} + +%resolve dependencies +\RequirePackage{defpattern} +\RequirePackage{fp-upn} + +%%%public area (macros which may be used)%%% +\def\FPeval#1#2{\FP@eval{#1}{#2}} % #1 := eval(#2) + +%%%private fp-area (don't use these macros)%%% + +%%%%%make postfix notation from prefix/infix notation + +%%%handle constants and function applications + +%constants +\defpattern\FP@gen@app[#2]{#2} + +%function applications from prefix to postfix +\defpattern\FP@gen@app[add #2]{#2 add} +\defpattern\FP@gen@app[sub #2]{#2 sub} +\defpattern\FP@gen@app[mul #2]{#2 mul} +\defpattern\FP@gen@app[div #2]{#2 div} +\defpattern\FP@gen@app[abs #2]{#2 abs} +\defpattern\FP@gen@app[neg #2]{#2 neg} +\defpattern\FP@gen@app[sgn #2]{#2 sgn} +\defpattern\FP@gen@app[min #2]{#2 min} +\defpattern\FP@gen@app[max #2]{#2 max} +\defpattern\FP@gen@app[round #2]{#2 round} +\defpattern\FP@gen@app[trunc #2]{#2 trunc} +\defpattern\FP@gen@app[clip #2]{#2 clip} +\defpattern\FP@gen@app[exp #2]{#2 exp} +\defpattern\FP@gen@app[ln #2]{#2 ln} +\defpattern\FP@gen@app[pow #2]{#2 pow} +\defpattern\FP@gen@app[root #2]{#2 root} +\defpattern\FP@gen@app[seed #2]{#2 seed} +\defpattern\FP@gen@app[random #2]{#2 random} +\defpattern\FP@gen@app[sin #2]{#2 sin} +\defpattern\FP@gen@app[cos #2]{#2 cos} +\defpattern\FP@gen@app[sincos #2]{#2 sincos} +\defpattern\FP@gen@app[tan #2]{#2 tan} +\defpattern\FP@gen@app[cot #2]{#2 cot} +\defpattern\FP@gen@app[tancot #2]{#2 tancot} +\defpattern\FP@gen@app[arcsin #2]{#2 arcsin} +\defpattern\FP@gen@app[arccos #2]{#2 arccos} +\defpattern\FP@gen@app[arcsincos #2]{#2 arcsincos} +\defpattern\FP@gen@app[arctan #2]{#2 arctan} +\defpattern\FP@gen@app[arccot #2]{#2 arccot} +\defpattern\FP@gen@app[arctancot #2]{#2 arctancot} +\defpattern\FP@gen@app[pop #2]{#2 pop} +\defpattern\FP@gen@app[swap #2]{#2 swap} +\defpattern\FP@gen@app[copy #2]{#2 copy} +\defpattern\FP@gen@app[ #2]{\FP@gen@app[#2]} + +\def\FP@gen@app@handle#1{\FP@gen@app[#1]} + +%%%handle ^, right to left +\defpattern\FP@gen@exp[#2]{\FP@gen@app@handle{#2}} +\defpattern\FP@gen@exp[#2^#3]{\FP@gen@exp[#3] \FP@gen@exp[#2] pow} + +\def\FP@gen@exp@handle#1{\FP@gen@exp[#1]} + +%%%handle * and /, left to right + +%handle two or more occurrences of * and / +\defpattern\FP@gen@mul@splitted[#2|/|#3|#4|#5]{\FP@gen@mul@handle{\FP@gen@exp@handle{#2} \FP@gen@exp@handle{#3} div #4#5}} +\defpattern\FP@gen@mul@splitted[#2|*|#3|#4|#5]{\FP@gen@mul@handle{\FP@gen@exp@handle{#2} \FP@gen@exp@handle{#3} mul #4#5}} + +%split second * or / if exists +\defpattern\FP@gen@mul@split@two@div[#2|#3|#4|#5|#6]{\FP@gen@mul@splitted[#2|#3|#4|#5|#6]} +\defpattern\FP@gen@mul@split@two@div[#2|#3|#4/#5|#6|#7]{\FP@gen@mul@splitted[#2|#3|#4|/|#5#6#7]} +\defpattern\FP@gen@mul@split@two[#2|/|#3]{\FP@gen@exp@handle{#2} \FP@gen@exp@handle{#3} div} +\defpattern\FP@gen@mul@split@two[#2|*|#3]{\FP@gen@exp@handle{#2} \FP@gen@exp@handle{#3} mul} +\defpattern\FP@gen@mul@split@two[#2|#3|#4/#5]{\FP@gen@mul@splitted[#2|#3|#4|/|#5]} +\defpattern\FP@gen@mul@split@two[#2|#3|#4*#5]{\FP@gen@mul@split@two@div[#2|#3|#4|*|#5]} + +%split first * or / if exists +\defpattern\FP@gen@mul@split@one@div[#2|#3|#4]{\FP@gen@mul@split@two[#2|#3|#4]} +\defpattern\FP@gen@mul@split@one@div[#2/#3|#4|#5]{\FP@gen@mul@split@two[#2|/|#3#4#5]} +\defpattern\FP@gen@mul@split@one[#2]{\FP@gen@exp@handle{#2}} +\defpattern\FP@gen@mul@split@one[#2/#3]{\FP@gen@mul@split@two[#2|/|#3]} +\defpattern\FP@gen@mul@split@one[#2*#3]{\FP@gen@mul@split@one@div[#2|*|#3]} + +%generate code for a series of * and / +\def\FP@gen@mul@handle#1{\FP@gen@mul@split@one[#1]} + +%%%handle + and -, left to right + +%handle two or more occurrences of + and - +\defpattern\FP@gen@add@splitted[#2|-|#3|#4|#5]{\FP@gen@add@handle{\FP@gen@mul@handle{#2} \FP@gen@mul@handle{#3} sub #4#5}} +\defpattern\FP@gen@add@splitted[#2|+|#3|#4|#5]{\FP@gen@add@handle{\FP@gen@mul@handle{#2} \FP@gen@mul@handle{#3} add #4#5}} + +%split second + or - if exists +\defpattern\FP@gen@add@split@two@minus[#2|#3|#4|#5|#6]{\FP@gen@add@splitted[#2|#3|#4|#5|#6]} +\defpattern\FP@gen@add@split@two@minus[#2|#3|#4-#5|#6|#7]{\FP@gen@add@splitted[#2|#3|#4|-|#5#6#7]} +\defpattern\FP@gen@add@split@two[#2|-|#3]{\FP@gen@mul@handle{#2} \FP@gen@mul@handle{#3} sub} +\defpattern\FP@gen@add@split@two[#2|+|#3]{\FP@gen@mul@handle{#2} \FP@gen@mul@handle{#3} add} +\defpattern\FP@gen@add@split@two[#2|#3|#4-#5]{\FP@gen@add@splitted[#2|#3|#4|-|#5]} +\defpattern\FP@gen@add@split@two[#2|#3|#4+#5]{\FP@gen@add@split@two@minus[#2|#3|#4|+|#5]} + +%split first + or - if exists +\defpattern\FP@gen@add@split@one@minus[#2|#3|#4]{\FP@gen@add@split@two[#2|#3|#4]} +\defpattern\FP@gen@add@split@one@minus[#2-#3|#4|#5]{\FP@gen@add@split@two[#2|-|#3#4#5]} +\defpattern\FP@gen@add@split@one[#2]{\FP@gen@mul@handle{#2}} +\defpattern\FP@gen@add@split@one[#2-#3]{\FP@gen@add@split@two[#2|-|#3]} +\defpattern\FP@gen@add@split@one[#2+#3]{\FP@gen@add@split@one@minus[#2|+|#3]} + +%generate code for a series of + and - +\def\FP@gen@add@handle#1{\FP@gen@add@split@one[#1]} + +%%%handle , and : as argument lists for functions with surrounding ( and ) +\defpattern\FP@gen@komma[#2]{\FP@gen@add@handle{#2}} +\defpattern\FP@gen@komma[#2,#3]{\FP@gen@komma[#2] \FP@gen@komma[#3] } +\defpattern\FP@gen@komma[#2:#3]{\FP@gen@komma[#2] \FP@gen@komma[#3] } + +%%%generate code for each paranthesis +\def\FP@gen@code#1{\FP@gen@komma[#1]} + +%%%handle paranthesis +\defpattern\FP@kl@handle@one[#2|#3|#4]{\FP@kl@handle[#2 \FP@gen@code{#3}#4]} +\defpattern\FP@kl@handle@one[#2|#3(#4|#5]{\FP@kl@handle@one[#2(#3|#4|#5]} + +\defpattern\FP@kl@handle[#2]{\FP@gen@code{#2}} +\defpattern\FP@kl@handle[#2(#3)#4]{% + \FP@kl@handle@one[#2|#3|#4]% +} + +\defpattern\FP@gen[#2]{\FP@kl@handle[#2]} +\defpattern\FP@gen[#2(-#3]{\FP@gen[#2(0-#3]} +\defpattern\FP@gen[#2(+#3]{\FP@gen[#2(#3]} +\defpattern\FP@gen[#2( #3]{\FP@gen[#2(#3]} + +\def\FP@mkupn#1{% + \expandafter\FP@gen\expandafter[#1]% +} + +%%%%%compute expression via upn +\def\FP@eval#1#2{% + \FP@beginmessage{EVAL}% + \FPupn{#1}{\FP@mkupn{#2}}% + \FP@endmessage{}% +} diff --git a/Master/texmf-dist/tex/latex/fp/fp-exp.sty b/Master/texmf-dist/tex/latex/fp/fp-exp.sty new file mode 100644 index 00000000000..04a47384406 --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/fp-exp.sty @@ -0,0 +1,500 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{fp-exp}[1995/04/03] + +%version information +\def\FP@expversion{0.7e} +\message{% + `Fixed Point Exponentiation',% + \space\space\space\space% + Version \FP@expversion% + \space (C) Michael Mehlich% + \space\space\space\space\space\space\space% + \space\space\space\space\space\space% +} + +%resolve dependencies +\RequirePackage{fp-basic} + +%%%public area (macros which may be used)%%% + +%constants +\edef\FPe{2.718281828459045235} +%unary functions +\def\FPexp#1#2{\FP@calld\FP@exp#1{#2}} +\def\FPln#1#2{\FP@calld\FP@ln#1{#2}} +%binary functions +\def\FPpow#1#2#3{\FP@pow#1{#2}{#3}} +\def\FProot#1#2#3{\FP@root#1{#2}{#3}} + +%%%private fp-area (don't use these macros)%%% + +%allocation of registers + +\countdef\FP@ls=50 +\countdef\FP@lfa=51 +\countdef\FP@lfb=52 + +\countdef\FP@regd=53 +\countdef\FP@rege=54 + +%compute e pow x + +\expandafter\edef\csname FP@e0\endcsname{1.000000000000000000} +\expandafter\edef\csname FP@e1\endcsname{2.718281828459045235} +\expandafter\edef\csname FP@e2\endcsname{7.389056098930650227} +\expandafter\edef\csname FP@e3\endcsname{20.085536923187667741} +\expandafter\edef\csname FP@e4\endcsname{54.598150033144239078} +\expandafter\edef\csname FP@e5\endcsname{148.413159102576603421} +\expandafter\edef\csname FP@e6\endcsname{403.428793492735122608} +\expandafter\edef\csname FP@e7\endcsname{1096.633158428458599264} +\expandafter\edef\csname FP@e8\endcsname{2980.957987041728274744} +\expandafter\edef\csname FP@e9\endcsname{8103.083927575384007710} +\expandafter\edef\csname FP@e10\endcsname{22026.465794806716516958} +\expandafter\edef\csname FP@e11\endcsname{59874.141715197818455326} +\expandafter\edef\csname FP@e12\endcsname{162754.791419003920808005} +\expandafter\edef\csname FP@e13\endcsname{442413.392008920503326103} +\expandafter\edef\csname FP@e14\endcsname{1202604.284164776777749237} +\expandafter\edef\csname FP@e15\endcsname{3269017.372472110639301855} +\expandafter\edef\csname FP@e16\endcsname{8886110.520507872636763024} +\expandafter\edef\csname FP@e17\endcsname{24154952.753575298214775435} +\expandafter\edef\csname FP@e18\endcsname{65659969.137330511138786503} +\expandafter\edef\csname FP@e19\endcsname{178482300.963187260844910034} +\expandafter\edef\csname FP@e20\endcsname{485165195.409790277969106831} +\expandafter\edef\csname FP@e21\endcsname{1318815734.483214697209998884} +\expandafter\edef\csname FP@e22\endcsname{3584912846.131591561681159946} +\expandafter\edef\csname FP@e23\endcsname{9744803446.248902600034632685} +\expandafter\edef\csname FP@e24\endcsname{26489122129.843472294139162153} +\expandafter\edef\csname FP@e25\endcsname{72004899337.385872524161351466} +\expandafter\edef\csname FP@e26\endcsname{195729609428.838764269776397876} +\expandafter\edef\csname FP@e27\endcsname{532048240601.798616683747304341} +\expandafter\edef\csname FP@e28\endcsname{1446257064291.475173677047422997} +\expandafter\edef\csname FP@e29\endcsname{3931334297144.042074388620580844} +\expandafter\edef\csname FP@e30\endcsname{10686474581524.462146990468650741} +\expandafter\edef\csname FP@e31\endcsname{29048849665247.425231085682111680} +\expandafter\edef\csname FP@e32\endcsname{78962960182680.695160978022635108} +\expandafter\edef\csname FP@e33\endcsname{214643579785916.064624297761531261} +\expandafter\edef\csname FP@e34\endcsname{583461742527454.881402902734610391} +\expandafter\edef\csname FP@e35\endcsname{1586013452313430.728129644625774660} +\expandafter\edef\csname FP@e36\endcsname{4311231547115195.227113422292856925} +\expandafter\edef\csname FP@e37\endcsname{11719142372802611.308772939791190195} +\expandafter\edef\csname FP@e38\endcsname{31855931757113756.220328671701298646} +\expandafter\edef\csname FP@e39\endcsname{86593400423993746.953606932719264934} +\expandafter\edef\csname FP@e40\endcsname{235385266837019985.407899910749034805} +\expandafter\edef\csname FP@e41\endcsname{639843493530054949.222663403515570819} + +\expandafter\edef\csname FP@e-0\endcsname{1.000000000000000000} +\expandafter\edef\csname FP@e-1\endcsname{0.367879441171442322} +\expandafter\edef\csname FP@e-2\endcsname{0.135335283236612692} +\expandafter\edef\csname FP@e-3\endcsname{0.049787068367863943} +\expandafter\edef\csname FP@e-4\endcsname{0.018315638888734180} +\expandafter\edef\csname FP@e-5\endcsname{0.006737946999085467} +\expandafter\edef\csname FP@e-6\endcsname{0.002478752176666358} +\expandafter\edef\csname FP@e-7\endcsname{0.000911881965554516} +\expandafter\edef\csname FP@e-8\endcsname{0.000335462627902512} +\expandafter\edef\csname FP@e-9\endcsname{0.000123409804086680} +\expandafter\edef\csname FP@e-10\endcsname{0.000045399929762485} +\expandafter\edef\csname FP@e-11\endcsname{0.000016701700790246} +\expandafter\edef\csname FP@e-12\endcsname{0.000006144212353328} +\expandafter\edef\csname FP@e-13\endcsname{0.000002260329406981} +\expandafter\edef\csname FP@e-14\endcsname{0.000000831528719104} +\expandafter\edef\csname FP@e-15\endcsname{0.000000305902320502} +\expandafter\edef\csname FP@e-16\endcsname{0.000000112535174719} +\expandafter\edef\csname FP@e-17\endcsname{0.000000041399377188} +\expandafter\edef\csname FP@e-18\endcsname{0.000000015229979745} +\expandafter\edef\csname FP@e-19\endcsname{0.000000005602796438} +\expandafter\edef\csname FP@e-20\endcsname{0.000000002061153622} +\expandafter\edef\csname FP@e-21\endcsname{0.000000000758256043} +\expandafter\edef\csname FP@e-22\endcsname{0.000000000278946809} +\expandafter\edef\csname FP@e-23\endcsname{0.000000000102618796} +\expandafter\edef\csname FP@e-24\endcsname{0.000000000037751345} +\expandafter\edef\csname FP@e-25\endcsname{0.000000000013887944} +\expandafter\edef\csname FP@e-26\endcsname{0.000000000005109089} +\expandafter\edef\csname FP@e-27\endcsname{0.000000000001879529} +\expandafter\edef\csname FP@e-28\endcsname{0.000000000000691440} +\expandafter\edef\csname FP@e-29\endcsname{0.000000000000254367} +\expandafter\edef\csname FP@e-30\endcsname{0.000000000000093576} +\expandafter\edef\csname FP@e-31\endcsname{0.000000000000034425} +\expandafter\edef\csname FP@e-32\endcsname{0.000000000000012664} +\expandafter\edef\csname FP@e-33\endcsname{0.000000000000004659} +\expandafter\edef\csname FP@e-34\endcsname{0.000000000000001714} +\expandafter\edef\csname FP@e-35\endcsname{0.000000000000000631} +\expandafter\edef\csname FP@e-36\endcsname{0.000000000000000232} +\expandafter\edef\csname FP@e-37\endcsname{0.000000000000000085} +\expandafter\edef\csname FP@e-38\endcsname{0.000000000000000031} +\expandafter\edef\csname FP@e-39\endcsname{0.000000000000000012} +\expandafter\edef\csname FP@e-40\endcsname{0.000000000000000004} +\expandafter\edef\csname FP@e-41\endcsname{0.000000000000000002} +\expandafter\edef\csname FP@e-42\endcsname{0.000000000000000001} + +\def\FP@exp@mul#1#2#3#4#5#6{% + % #1 macro which gets fractional part 1 + % #2 macro which fractional part 1 + % #3 first value part 1 + % #4 first value part 2 + % #5 second value part 1 + % #6 second value part 2 + \FP@split\FP@xq\FP@xr\FP@xz{#3}\FP@split\FP@xt\FP@xu\FP@xv{#4}% + \FP@split\FP@yq\FP@yr\FP@yz{#5}\FP@split\FP@yt\FP@yu\FP@yv{#6}% + \FP@prod=0\relax% + \edef\FP@rd{}% + \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 uz zu vr rv \relax\FP@saveshift% + \FP@@mul zt tz ur ru qv vq \relax\FP@saveshift% + \FP@@mul zz rt tr qu uq \relax\FP@saveshift% + \FP@@mul rz zr qt tq \relax\FP@saveshift% + \FP@@mul rr qz zq \relax\FP@saveshift% + \FP@@mul qr rq \relax\FP@saveshift% + \FP@@mul qq \relax\FP@saveshift\FP@saveshift% + \FP@ninesplit\FP@rd#1=\FP@res% + \FP@ninesplit\FP@rd#2=\FP@res% +} + +\def\FP@exp@divn#1#2#3#4#5{% + % #1 macro which gets fractional part 1 + % #2 macro which fractional part 1 + % #3 value part 1 + % #4 value part 2 + % #5 integer (0,..,1000) + \FP@rega=#3\divide\FP@rega#5% + \FP@regd=\FP@rega% + \multiply\FP@rega#5\relax% + \advance\FP@rega-#3\relax% + \multiply\FP@rega-1000\relax% + \FP@regb=#4\divide\FP@regb1000000\relax% + \advance\FP@rega\FP@regb% + \FP@regc=\FP@rega\divide\FP@regc#5\relax% + \FP@rege=\FP@regc\multiply\FP@rege1000000\relax% + \multiply\FP@regc#5\advance\FP@rega-\FP@regc\multiply\FP@rega1000000\relax% + \multiply\FP@regb1000000\relax\advance\FP@regb-#4\relax% + \advance\FP@rega-\FP@regb% + \divide\FP@rega#5\relax% + \advance\FP@rege\FP@rega% + #1=\FP@regd% + #2=\FP@rege% +} + +%exp (for values between -1 and 1) +\def\FP@@exp#1#2#3#4{% + % #1 macro which gets the result + % #2 sign + % #3 fractional part 1 + % #4 fractional part 2 + \ifnum\ifnum#3=0 0\else1\fi\ifnum#4=0 0\else1\fi=0\relax% + \edef#1{1}% + \else% + \FP@rs=1\relax% + \FP@ria=0\relax% + \ifnum#2>0\relax% + \FP@rib=1\relax% + \FP@rfa=#3\relax% + \FP@rfb=#4\relax% + \else% + \FP@rib=0\relax% + \ifnum#4=0\relax% + \FP@rfa=1000000000\relax\FP@rfb=0\relax% + \else% + \FP@rfa=999999999\relax\FP@rfb=1000000000\relax% + \fi% + \advance\FP@rfa-#3\relax% + \advance\FP@rfb-#4\relax% + \fi% + \FP@ls=#2\relax% + \FP@lfa=#3\relax% + \FP@lfb=#4\relax% + \FP@count=1\relax% + \loop% + \advance\FP@count1\relax% + \multiply\FP@ls#2\relax% + \FP@exp@mul\FP@lfa\FP@lfb\FP@lfa\FP@lfb#3#4\relax% + \FP@exp@divn\FP@lfa\FP@lfb\FP@lfa\FP@lfb\FP@count% + \ifnum\ifnum\FP@lfa=0 0\else1\fi\ifnum\FP@lfb=0 0\else1\fi>0\relax% + \ifnum\FP@ls>0\relax% + \advance\FP@rfa\FP@lfa% + \advance\FP@rfb\FP@lfb% + \ifnum\FP@rfb<1000000000\relax\else% + \advance\FP@rfa1\relax% + \advance\FP@rfb-1000000000\relax% + \fi% + \ifnum\FP@rfa<1000000000\relax\else% + \advance\FP@rib1\relax% + \advance\FP@rfa-1000000000\relax% + \fi% + \else% + \advance\FP@rfa-\FP@lfa% + \advance\FP@rfb-\FP@lfb% + \ifnum\FP@rfb<0\relax% + \advance\FP@rfa-1\relax% + \advance\FP@rfb1000000000\relax% + \fi% + \ifnum\FP@rfa<0\relax% + \advance\FP@rib-1\relax% + \advance\FP@rfa1000000000\relax% + \fi% + \fi% + \repeat% + \FP@store#1{r}% + \fi% +} + +\def\FP@exp#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{EXP}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + \FP@readvalue{x}{#2}{#3}% + \ifnum\FP@xia=0\relax% + \ifnum\FP@xs<0\relax% + \ifnum\FP@xib>42\relax% + \edef\FP@tmp{0}% + \else% + \edef\FP@tmp{\csname FP@e-\the\FP@xib\endcsname}% + \fi% + \else% + \ifnum\FP@xib>41\relax% + \FP@errmessage{Overflow}% + \else% + \edef\FP@tmp{\csname FP@e\the\FP@xib\endcsname}% + \fi% + \fi% + \FP@@exp\FP@tmpa\FP@xs\FP@xfa\FP@xfb% + \FPmul\FP@tmp\FP@tmpa\FP@tmp% + \global\let\FP@tmp=\FP@tmp% + \else% + \FP@errmessage{Overflow}% + \fi% + }% + % + \FP@endmessage{}% + % + \let#1\FP@tmp% +} + +%compute ln x + +\expandafter\edef\csname FP@ln2-0\endcsname{0.000000000000000000} +\expandafter\edef\csname FP@ln2-1\endcsname{0.693147180559945309} +\expandafter\edef\csname FP@ln2-2\endcsname{1.386294361119890618} +\expandafter\edef\csname FP@ln2-3\endcsname{2.079441541679835928} + +\expandafter\edef\csname FP@ln10-0\endcsname{0.000000000000000000} +\expandafter\edef\csname FP@ln10-1\endcsname{2.302585092994045684} +\expandafter\edef\csname FP@ln10-2\endcsname{4.605170185988091368} +\expandafter\edef\csname FP@ln10-3\endcsname{6.907755278982137052} +\expandafter\edef\csname FP@ln10-4\endcsname{9.210340371976182736} +\expandafter\edef\csname FP@ln10-5\endcsname{11.512925464970228420} +\expandafter\edef\csname FP@ln10-6\endcsname{13.815510557964274104} +\expandafter\edef\csname FP@ln10-7\endcsname{16.118095650958319788} +\expandafter\edef\csname FP@ln10-8\endcsname{18.420680743952365472} +\expandafter\edef\csname FP@ln10-9\endcsname{20.723265836946411156} +\expandafter\edef\csname FP@ln10-10\endcsname{23.025850929940456840} +\expandafter\edef\csname FP@ln10-11\endcsname{25.328436022934502524} +\expandafter\edef\csname FP@ln10-12\endcsname{27.631021115928548208} +\expandafter\edef\csname FP@ln10-13\endcsname{29.933606208922593892} +\expandafter\edef\csname FP@ln10-14\endcsname{32.236191301916639576} +\expandafter\edef\csname FP@ln10-15\endcsname{34.538776394910685260} +\expandafter\edef\csname FP@ln10-16\endcsname{36.841361487904730944} +\expandafter\edef\csname FP@ln10-17\endcsname{39.143946580898776628} +\expandafter\edef\csname FP@ln10-18\endcsname{41.446531673892822312} + +\def\FP@ln@divtwo#1#2#3#4#5#6{% + % #1 macro which gets integer part + % #2 macro which gets fractional part 1 + % #3 macro which fractional part 2 + % #4 integer part 1 + % #5 fractional part 1 + % #6 fractional part 2 + #1=#4\relax% + #2=#5\relax\ifodd#4\advance#21000000000\relax\fi% + #3=#6\relax\ifodd#5\advance#31000000000\relax\fi% + \divide#32\relax% + \divide#22\relax% + \divide#12\relax% +} + +%ln for values between (1 and 2) +\def\FP@@ln#1#2#3#4{% + % #1 macro which gets the result + % #2 integer part (1 or 2) + % #3 fractional part 1 + % #4 fractional part 2 + {\FP@xs=1\FP@xia=0\FP@xib=#2\FP@xfa=#3\FP@xfb=#4% + {\advance\FP@xib-1\relax\FP@store\FP@tmpa{x}\global\let\FP@tmpa\FP@tmpa}% + {\advance\FP@xib+1\relax\FP@store\FP@tmpb{x}\global\let\FP@tmpb\FP@tmpb}% + \FPdiv\FP@tmpa\FP@tmpa\FP@tmpb% + % + \def\next##1.##2.##3\relax{\FP@readvalue{x}{##1}{##2}}% + \expandafter\next\FP@tmpa..\relax% + % + \FP@lfa=\FP@xfa% + \FP@lfb=\FP@xfb% + % + \FP@rs=1\relax% + \FP@ria=0\relax% + \FP@rib=0\relax% + \FP@rfa=\FP@xfa% + \FP@rfb=\FP@xfb% + % + \FP@count=1\relax% + \FP@exp@mul\FP@xfa\FP@xfb\FP@xfa\FP@xfb\FP@xfa\FP@xfb% + % + \loop% + \advance\FP@count2\relax% + \FP@exp@mul\FP@lfa\FP@lfb\FP@lfa\FP@lfb\FP@xfa\FP@xfb% + \ifnum\ifnum\FP@lfa=0 0\else1\fi\ifnum\FP@lfb=0 0\else1\fi=0\relax\else% + \FP@exp@divn\FP@yfa\FP@yfb\FP@lfa\FP@lfb\FP@count% + \advance\FP@rfb\FP@yfb% + \advance\FP@rfa\FP@yfa% + \ifnum\FP@rfb<1000000000\relax\else% + \advance\FP@rfa1\relax% + \advance\FP@rfb-1000000000\relax% + \fi% + \ifnum\FP@rfa<1000000000\relax\else% + \advance\FP@rib1\relax% + \advance\FP@rfa-1000000000\relax% + \fi% + \repeat% + % + \advance\FP@rfa\FP@rfa% + \ifnum\FP@rfb<500000000\relax\else% + \advance\FP@rfa1\relax% + \advance\FP@rfb-500000000\relax% + \fi% + \advance\FP@rfb\FP@rfb% + % + \FP@store\FP@tmpa{r}% + % + \global\let\FP@tmpa\FP@tmpa% + }% + % + \let#1\FP@tmpa% +} + +\def\FP@ln#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{LN}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + % + \FP@readvalue{x}{#2}{#3}% + % + \ifFP@zero{x}% + \FP@errmessage{Logarithm of zero}% + \else\ifnum\FP@xs<0\relax% + \FP@errmessage{Logarithm of negative value}% + \else% + \FP@count=0\relax% + \loop% + \ifnum\ifnum\FP@xia>0 1\else0\fi\ifnum\FP@xib>9 1\else0\fi>0\relax% + \advance\FP@count1\relax% + \FP@divten{x}% + \repeat% + \loop% + \ifnum\ifnum\FP@xia=0 0\else1\fi\ifnum\FP@xib=0 0\else1\fi=0\relax% + \advance\FP@count-1\relax% + \FP@multen{x}% + \repeat% + \ifnum\FP@count<0\relax% + \FP@count=-\FP@count% + \edef\FP@tmpc{-\csname FP@ln10-\the\FP@count\endcsname}% + \else% + \edef\FP@tmpc{\csname FP@ln10-\the\FP@count\endcsname}% + \fi% + \FP@count=0\relax% + \loop% + \ifnum\FP@xib<2\relax\else% + \advance\FP@count1\relax% + \FP@ln@divtwo\FP@xib\FP@xfa\FP@xfb\FP@xib\FP@xfa\FP@xfb% + \repeat% + \FPadd\FP@tmpc\FP@tmpc{\csname FP@ln2-\the\FP@count\endcsname}% + \FP@@ln\FP@tmpb\FP@xib\FP@xfa\FP@xfb% + \FPadd\FP@tmp\FP@tmpc\FP@tmpb% + \fi\fi% + % + \global\let\FP@tmp\FP@tmp% + }% + % + \FP@endmessage{}% + % + \let#1\FP@tmp% +} + +%compute x pow y + +\def\FP@pow@zero#1{% + \FPifzero{#1}% + \FP@errmessage{0-th pow of 0 not defined}% + \else% + \edef\FP@tmp{0}% + \fi% +} + +\def\FP@pow#1#2#3{ + % #1 macro, which gets the result + % #2 base + % #3 exponent + % + \FP@beginmessage{POW}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + % + \FPifzero{#2}% + \FP@pow@zero{#3}% + \else% + \FPln\FP@tmpd{#2}% + \FPmul\FP@tmpd\FP@tmpd{#3}% + \FPexp\FP@tmp\FP@tmpd% + \fi% + % + \global\let\FP@tmp\FP@tmp% + }% + % + \FP@endmessage{}% + % + \let#1\FP@tmp% +} + +%compute y-th root of x + +\def\FP@root#1#2#3{% + % #1 macro, which gets the result + % #2 base + % #3 which root + % + \FP@beginmessage{ROOT}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + % + \FPifzero{#3}% + \FP@errmessage{0-th root not defined}% + \fi% + % + \FPifzero{#2}% + \edef\FP@tmp{0}% + \else% + \FPln\FP@tmpd{#2}% + \FPdiv\FP@tmpd\FP@tmpd{#3}% + \FPexp\FP@tmp\FP@tmpd% + \fi% + % + \global\let\FP@tmp\FP@tmp% + }% + % + \FP@endmessage{}% + % + \let#1\FP@tmp% +} diff --git a/Master/texmf-dist/tex/latex/fp/fp-pas.sty b/Master/texmf-dist/tex/latex/fp/fp-pas.sty new file mode 100644 index 00000000000..8cef34d97a4 --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/fp-pas.sty @@ -0,0 +1,118 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{fp-pas}[1994/08/29] + +%version information +\def\FP@pasversion{1.0} +\message{% + `Fixed Point Pascal Triangle',% + \space\space\space% + Version \FP@pasversion\space% + \space(C) Michael Mehlich% + \space\space\space\space\space\space\space% + \space\space\space\space\space\space% +} + +%resolve dependencies +\RequirePackage{fp-basic} + +%%%public area (macros which may be used)%%% + +\def\FPpascal#1#2{\FP@pascal{#1}{#2}}%pascal triangle for lines 0,...,63 + +%%%private fp-area (don't use these macros)%%% + +%allocation of registers +\countdef\FP@pas=50 +\countdef\FP@pasc=51 + +%addition of two natural numbers +\def\FP@pasadd#1#2#3{% + % #1 macro, which gets the result + % #2 1st value + % #3 2nd value + {\FP@removeleadingzeros#2\relax% + \expandafter\FP@setintcounter\FP@tmp000000000000000000\relax% + \FP@xia=\FP@rega% + \FP@xib=\FP@regb% + % + \FP@removeleadingzeros#3\relax% + \expandafter\FP@setintcounter\FP@tmp000000000000000000\relax% + \FP@yia=\FP@rega% + \FP@yib=\FP@regb% + % + \advance\FP@xia\FP@yia% + \advance\FP@xib\FP@yib% + \ifnum\FP@xib<1000000000\relax\else% + \advance\FP@xia1\relax% + \advance\FP@xib-1000000000\relax% + \fi% + \ifnum\FP@xia<1000000000\relax\else% + \FP@errmessage{Overflow}% + \fi% + % + \ifnum\FP@xia=0\relax% + \edef\FP@tmpa{\the\FP@xib}% + \else% + \advance\FP@xib1000000000% + \edef\FP@tmpa{\the\FP@xia\expandafter\FP@ignorenext\the\FP@xib}% + \fi% + % + \global\let\FP@tmpa\FP@tmpa% + }% + % + \let#1\FP@tmpa% +} + +%the first two entries of the pascal-triangle +\expandafter\edef\csname FP@pas0\endcsname{[1]} +\expandafter\edef\csname FP@pas1\endcsname{[1,1]} + +%which is the highest line of the pascal-triangle we have already computed? +\expandafter\edef\csname FP@pascount\endcsname{1} + +%compute next line of pascal-triangle +\def\FP@pasdouble[#1]{% + % #1 previous line of pascal-triangle + \edef\FP@old{}% + \edef\FP@tmpb{}% + \@for\FP@new:=#1\do{% + \expandafter\if!\FP@old!\relax% + \edef\FP@old{\FP@new}% + \else% + \FP@pasadd{\FP@tmpa}{\FP@old}{\FP@new}% + \edef\FP@tmpb{\FP@tmpb,\FP@tmpa}% + \edef\FP@old{\FP@new}% + \fi% + }% + \global\edef\FP@tmpb{[1\FP@tmpb,1]}% +} + +%compute n-th line of pascal-triangle +\def\FP@pascomp#1{% + % #1 which line to compute + \expandafter\FP@pasc\FP@pascount\relax% + \ifnum\FP@pasc<#1\relax% + \loop% + \ifnum\FP@pasc<#1\relax% + \expandafter\expandafter\expandafter\FP@pasdouble\csname FP@pas\the\FP@pasc\endcsname% + \advance\FP@pasc1\relax% + \edef\next{\noexpand\global\noexpand\let\csname FP@pas\the\FP@pasc\endcsname\noexpand\FP@tmpb}% + \next% + \repeat% + \fi% + \global\edef\FP@pascount{\the\FP@pasc}% +} + +\def\FP@pascal#1#2{% + % #1 macro, which gets the result + % #2 which line of the pascal-triangle to compute + {\FP@beginmessage{PASCAL}% + % + \FP@pas#2\relax% + \FP@pascomp\FP@pas% + \global\edef\FP@tmp{\csname FP@pas\the\FP@pas\endcsname}% + % + \FP@endmessage{}% + }% + \let#1\FP@tmp% +} diff --git a/Master/texmf-dist/tex/latex/fp/fp-random.sty b/Master/texmf-dist/tex/latex/fp/fp-random.sty new file mode 100644 index 00000000000..72bf17f1f10 --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/fp-random.sty @@ -0,0 +1,120 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{fp-random}[1995/02/23] + +% Version information +\def\FP@randomversion{1.0a} +\message{% + `Fixed Point Random,% + \space\space\space\space\space\space% + \space\space\space\space\space\space\space% + Version \FP@randomversion% + \space(C) Denis Girou (CNRS/IDRIS)% + \space\space\space% +} + +% Resolve dependencies +\RequirePackage{fp-basic} + +% Uniform random value + +\newcount\FPseed % Seed value + +\def\FPrandom#1{% + % #1 macro, which gets the result + % + % Uniform random number generator (numbers between 0 and 1) + % + % Algorithm reproduce from a very old Fortran program (unknown origin!) + % + % double precision function RANF() + % + % integer SEED + % common /COMSEED/SEED + % * + % integer A,M,Q,R + % parameter(A=16807,M=2147483647,Q=127773,R=2836) + % * + % integer LO,HI,TEST + % * + % HI = SEED/Q + % LO = SEED-HI*Q + % TEST = A*LO-R*HI + % if(TEST.gt.0) then + % SEED = TEST + % else + % SEED = TEST+M + % endif + % * + % RANF = DFLOAT(SEED)/DFLOAT(M) + % * + % end + % + % The macro used a seed value, defined by the counter \FPseed. + % If it's unknown at first call, we used an arbitrary value. + % + % We verify that we obtain the same results as in Fortran + % + % The algorithm seems fairly good. With the Fortran version, we obtain + % typically something like 49954 numbers between 0 and 0.5 and 50046 between + % 0.5 and 1 for 100000 random numbers, depending of the seed value used. + % + % To generate a "pseudo-random" seed, you can consider to use the \time + % macro, to intialize the random numbers generator according to the time. + % Something like: + % \FPseed=\the\time + % \multiply\FPseed\the\day + % \multiply\FPseed\the\month + % \multiply\FPseed\the\year + % + % Of course, it is very slow comparing to "standard" programming + % languages. On a RS 6000 370, it's take 51s to generate 100 numbers, + % loading time of the test program included (and 0.2s for the Fortran + % version ... for 100000 numbers!) + % But you must also notice that Hans van der Meer published in TUGboat + % Vol. 15, 1, March 1994, pages 57-58, an article on "Random bit generator + % in TeX". In fact, he doesn't give a complete solution to generate uniform + % random numbers, but at least give some interesting ideas, and also the + % code of a simple but powerful macro \SRtest{choice 1}{choice 2}, which + % allow to execute the instructions of "choice 1" or those of "choice 2" + % with a probability of 1/2 each. As his method is based on shifts of bits + % with almost no computations, it's very fast (around 1000 faster than to do + % the same thing that \SRtest with \FPrandom.) + % + {\FP@beginmessage{RANDOM}% + % + \ifnum\FPseed=0% + \FPseed=123456789% + \FP@debug{random: seed value undefined! We will used \the\FPseed.^^J% + Define it if you want to generate a different sequence of random% + numbers.}% + \else% + \FP@debug{random: seed value used: \the\FPseed}% + \fi% + % + \FP@xia=\FPseed% + \divide\FP@xia by 127773% + \FP@xib=\FP@xia% + \multiply\FP@xib by 127773% + \advance\FP@xib by -\FPseed% + \FP@xib=-\FP@xib% + \multiply\FP@xia by 2836% + \FPseed=\FP@xib% + \multiply\FPseed by 16807% + \advance\FPseed by -\FP@xia% + % + \ifnum\FPseed>0% + \else% + \advance\FPseed by 2147483647% + \fi% + \FPdiv\FP@tmpa{\the\FPseed}{2147483647}% + \global\let\FP@tmp\FP@tmpa% + \global\FPseed=\FPseed% + \FP@debug{random: random number: \FP@tmp\space% + (new seed value: \the\FPseed)}% + % + \FP@endmessage{}% + }% + \let#1\FP@tmp% +} + +\endinput diff --git a/Master/texmf-dist/tex/latex/fp/fp-snap.sty b/Master/texmf-dist/tex/latex/fp/fp-snap.sty new file mode 100644 index 00000000000..f4961b7d3fd --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/fp-snap.sty @@ -0,0 +1,242 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{fp-snap}[1995/04/05] + +%version information +\def\FP@snapversion{1.0a} +\message{% + `Fixed Point Snap Off',% + \space\space\space\space\space\space\space\space\space\space% + Version \FP@snapversion% + \space(C) Michael Mehlich% + \space\space\space\space\space\space\space% + \space\space\space\space\space\space% +} + +%resolve dependencies +\RequirePackage{fp-basic} + +%%%public area (macros which may be used)%%% + +\def\FPround#1#2#3{\FP@calld\FP@round#1{#2}{#3}} +\def\FPtrunc#1#2#3{\FP@calld\FP@trunc#1{#2}{#3}} +\def\FPclip#1#2{\FP@calld\FP@clip#1{#2}} + +%%%private fp-area (don't use these macros)%%% + +%round value +\def\FP@round#1#2.#3.#4\relax#5{% + % #1 macro, which gets the result + % #2 integer part of value + % #3 fractional part of value + % #4 dummy to swallow everything after the second '.' + % #5 round position + {\FP@beginmessage{ROUND}% + % + \FP@count=#5\relax% + % + \ifnum\FP@count<0\relax% + \FP@errmessage{Rounding value before point not allowed}% + \else% + \FP@readvalue{x}{#2}{#3}% + \ifnum\FP@count=0\relax% + \ifnum\FP@xfa<500000000\relax% + \edef\FP@tmp{#2}% + \else% + \advance\FP@xib1\relax% + \ifnum\FP@xib<1000000000\relax\else% + \advance\FP@xia1\relax% + \advance\FP@xib-1000000000\relax% + \fi% + \ifnum\FP@xs<0\relax% + \edef\FP@tmp{-}% + \else% + \edef\FP@tmp{}% + \fi% + \ifnum\FP@xia=0\relax% + \edef\FP@tmp{\FP@tmp\the\FP@xib}% + \else% + \advance\FP@xib1000000000\relax% + \edef\FP@tmp{\FP@tmp\the\FP@xia\expandafter\FP@ignorenext\the\FP@xib}% + \fi% + \fi% + \else% + \ifnum\FP@count>18\relax% + \FP@count=18\relax% + \fi% + \advance\FP@xfa1000000000\relax% + \advance\FP@xfb1000000000\relax% + \edef\FP@tmp{\expandafter\FP@ignorenext\the\FP@xfa\expandafter\FP@ignorenext\the\FP@xfb}% + \edef\FP@rd{}% + \FP@shift=\FP@count% + \FP@times=1\relax% + \loop% + \ifnum\FP@count>0\relax% + \edef\FP@rd{\FP@rd\expandafter\FP@first\FP@tmp\noexpand\relax}% + \edef\FP@tmp{\expandafter\FP@ignorenext\FP@tmp}% + \advance\FP@count-1\relax% + \multiply\FP@times10\relax\ifnum\FP@times=1000000000\relax\FP@times=1\relax\fi% + \repeat% + \edef\FP@tmp{\expandafter\FP@first\FP@tmp\noexpand\relax}% + \expandafter\FP@rega\FP@tmp\relax% + \ifnum\FP@rega>4\relax% + \ifnum\FP@shift>8\relax% + \FP@ninesplit\FP@rd% + \expandafter\FP@rega\expandafter0\FP@rd\relax% + \advance\FP@rega1\relax% + \ifnum\FP@rega<\FP@times% + \advance\FP@rega\FP@times% + \advance\FP@res1000000000\relax% + \else% + \advance\FP@res1\relax% + \ifnum\FP@res<1000000000\relax% + \advance\FP@res1000000000\relax% + \else% + \advance\FP@xib1\relax% + \ifnum\FP@xib<1000000000\relax\else% + \advance\FP@xia1\relax% + \advance\FP@xib-1000000000\relax% + \fi% + \fi% + \fi% + \edef\FP@tmpa{\expandafter\FP@ignorenext\the\FP@res\expandafter\FP@ignorenext\the\FP@rega}% + \else% + \expandafter\FP@rega\FP@rd\relax% + \advance\FP@rega1\relax% + \ifnum\FP@rega<\FP@times% + \advance\FP@rega\FP@times% + \else% + \advance\FP@xib1\relax% + \ifnum\FP@xib<1000000000\relax\else% + \advance\FP@xia1\relax% + \advance\FP@xib-1000000000\relax% + \fi% + \fi% + \edef\FP@tmpa{\expandafter\FP@ignorenext\the\FP@rega}% + \fi% + \else% + \edef\FP@tmpa{\FP@rd}% + \fi% + \ifnum\FP@xs<0\relax% + \edef\FP@tmp{-}% + \else% + \edef\FP@tmp{}% + \fi% + \ifnum\FP@xia=0\relax% + \edef\FP@tmp{\FP@tmp\the\FP@xib.\FP@tmpa}% + \else% + \advance\FP@xib1000000000\relax% + \edef\FP@tmp{\FP@tmp\the\FP@xia\expandafter\FP@ignorenext\the\FP@xib.\FP@tmpa}% + \fi% + \fi% + \fi% + % + \global\let\FP@tmp\FP@tmp% + % + \FP@endmessage{}% + }% + \let#1\FP@tmp% +} + +%trunc value + +\def\FP@trunc#1#2.#3.#4\relax#5{% + % #1 macro, which gets the result + % #2 integer part of value + % #3 fractional part of value + % #4 dummy to swallow everything after the second '.' + % #5 trunc position + {\FP@beginmessage{TRUNC}% + % + \FP@count=#5\relax% + % + \ifnum\FP@count<0\relax% + \FP@errmessage{Truncating value before point not allowed}% + \else\ifnum\FP@count=0\relax% + \edef\FP@tmp{#2}% + \else% + \ifnum\FP@count>18\relax% + \FP@count=18\relax% + \fi% + \FP@readvalue{x}{#2}{#3}% + \advance\FP@xfa1000000000\relax% + \advance\FP@xfb1000000000\relax% + \edef\FP@tmp{\expandafter\FP@ignorenext\the\FP@xfa\expandafter\FP@ignorenext\the\FP@xfb}% + \edef\FP@tmpa{}% + \loop% + \ifnum\FP@count>0\relax% + \edef\FP@tmpa{\FP@tmpa\expandafter\FP@first\FP@tmp\noexpand\relax}% + \edef\FP@tmp{\expandafter\FP@ignorenext\FP@tmp}% + \advance\FP@count-1\relax% + \repeat% + \ifnum\FP@xs<0\relax% + \edef\FP@tmp{-}% + \else% + \edef\FP@tmp{}% + \fi% + \ifnum\FP@xia=0\relax% + \edef\FP@tmp{\FP@tmp\the\FP@xib.\FP@tmpa}% + \else% + \advance\FP@xib1000000000\relax% + \edef\FP@tmp{\FP@tmp\the\FP@xia\expandafter\FP@ignorenext\the\FP@xib.\FP@tmpa}% + \fi% + \fi\fi% + % + \global\let\FP@tmp\FP@tmp% + % + \FP@endmessage{}% + }% + \let#1\FP@tmp% +} + +%clip value + +\def\FP@revert#1#2{% + % #1 macro, which gets the result + % #2 value + {\edef\FP@tmpa{#2}% + \edef\FP@tmp{}% + \loop% + \expandafter\if!\FP@tmpa!\relax\else% + \edef\FP@tmpb{\expandafter\FP@first\FP@tmpa\noexpand\relax}% + \edef\FP@tmpa{\expandafter\FP@ignorenext\FP@tmpa}% + \edef\FP@tmp{\FP@tmpb\FP@tmp}% + \repeat% + \global\let\FP@tmp\FP@tmp% + }% + \let#1\FP@tmp% +} + +\def\FP@clip#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{CLIP}% + % + \FP@revert\FP@tmpb{#3}% + \FP@removeleadingzeros\FP@tmpb\relax% + \FP@revert\FP@tmpb\FP@tmp% + \edef\FP@tmpa{#2}% + \FP@removeleadingzeros\FP@tmpa\relax% + \edef\FP@tmpa{\FP@tmp}% + \expandafter\if!\FP@tmpa!\relax% + \expandafter\if!\FP@tmpb!\relax% + \edef\FP@tmp{0}% + \else% + \edef\FP@tmp{0.\FP@tmpb}% + \fi% + \else% + \expandafter\if!\FP@tmpb!\relax% + \edef\FP@tmp{\FP@tmpa}% + \else% + \edef\FP@tmp{\FP@tmpa.\FP@tmpb}% + \fi% + \fi% + % + \global\let\FP@tmp\FP@tmp% + % + \FP@endmessage{}% + }% + \let#1\FP@tmp% +} diff --git a/Master/texmf-dist/tex/latex/fp/fp-trigo.sty b/Master/texmf-dist/tex/latex/fp/fp-trigo.sty new file mode 100644 index 00000000000..06cfa30f9f8 --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/fp-trigo.sty @@ -0,0 +1,1119 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{fp-trigo}[1995/04/14] + +%version information +\def\FP@trigoversion{0.9e} +\message{% + `Fixed Point Trigonometry',% + \space\space\space\space\space\space% + Version \FP@trigoversion% + \space(C) Michael Mehlich% + \space\space\space\space\space\space\space% + \space\space\space\space\space\space% +} + +%resolve dependencies +\RequirePackage{fp-basic} + +%%%public area (macros which may be used)%%% + +%constants +\edef\FPpi{3.141592653589793238} + +%unary functions +\def\FPsin#1#2{\FP@calld\FP@sin#1{#2}} +\def\FPcos#1#2{\FP@calld\FP@cos#1{#2}} +\def\FPsincos#1#2#3{\FP@calle\FP@sincos#1#2{#3}} +\def\FPtan#1#2{\FP@calld\FP@tan#1{#2}} +\def\FPcot#1#2{\FP@calld\FP@cot#1{#2}} +\def\FPtancot#1#2#3{\FP@calle\FP@tancot#1#2{#3}} +\def\FParcsin#1#2{\FP@calld\FP@arcsin#1{#2}} +\def\FParccos#1#2{\FP@calld\FP@arccos#1{#2}} +\def\FParcsincos#1#2#3{\FP@calle\FP@arcsincos#1#2{#3}} +\def\FParctan#1#2{\FP@calld\FP@arctan#1{#2}} +\def\FParccot#1#2{\FP@calld\FP@arccot#1{#2}} +\def\FParctancot#1#2#3{\FP@calle\FP@arctancot#1#2{#3}} + +%%%private fp-area (don't use these macros)%%% + +%allocate registers + +\countdef\FP@ls=50 +\countdef\FP@lfa=51 +\countdef\FP@lfb=52 + +\countdef\FP@loops=53 +\countdef\FP@oct=54 + +\countdef\FP@@arccos=55 +\countdef\FP@oldvala=56 +\countdef\FP@oldvalb=57 +\countdef\FP@subfpih=58 + +%compute 0<=x<2pi for value 2pi*n + x + +\def\FP@modtwopi#1#2{%result is the family {x} + % #1 integer part of value + % #2 fractional part of value + \FP@readvalue{x}{#1}{#2}% + % + \ifnum\ifnum\FP@xib=0 1\else0\fi\ifnum\FP@xia<6 1\else0\fi<11\relax% + %compute modulo without caring about sign + \FP@shift=0\relax% + \FP@ys=1\FP@yia=628318530\FP@yib=717958647\FP@yfa=692528676\FP@yfb=655900577\relax%2*pi + \loop% + \ifnum\FP@xia<100000000\relax% + \FP@multen{x}% + \advance\FP@shift-1\relax% + \repeat% + \FP@loops=18\relax\advance\FP@loops\FP@shift% + \loop% + \ifnum\FP@loops=0\else% + \advance\FP@loops-1\relax% + \FP@counttimes%divides x by \FP@times*y% + \FP@divten{y}% + \repeat% + \loop% + \ifnum\FP@shift<0% + \advance\FP@shift1\relax% + \FP@divten{x}% + \repeat% + \fi% + %correct the result for negative values (modulo is positive) + \loop%should be computed only once + \ifnum\FP@xs<0\relax% + \advance\FP@xfb-179586477\relax\FP@xfb=-\FP@xfb% + \ifnum\FP@xfb<0\relax% + \advance\FP@xfb1000000000\relax% + \advance\FP@xfa1\relax% + \fi% + \advance\FP@xfa-283185307\relax\FP@xfa=-\FP@xfa% + \ifnum\FP@xfa<0\relax% + \advance\FP@xfa1000000000\relax% + \advance\FP@xib1\relax% + \fi% + \advance\FP@xib-6\relax\FP@xib=-\FP@xib% + \ifnum\FP@xib<0% + \FP@errmessage{Error in calculation: This shouldn't happen!}% + \else% + \FP@xs=1\relax% + \fi% + \repeat% +} + +%auxiliary functions + +\def\FP@trigocmpsval#1#2#3{% + % #1 macro, which gets the result + % #2 9 digits integer value + % #3 9 digits integer value + \ifnum#2<#3\relax% + #1=-1\relax% + \else\ifnum#2>#3\relax% + #1=1\relax% + \else% + #1=0\relax% + \fi\fi% +} + +\def\FP@trigocmpval#1#2#3#4#5#6#7{% + % #1 macro, which gets the result + % #2 9 digits integer value + % #3 9 digits integer value + % #4 9 digits integer value + % #5 9 digits integer value + % #6 9 digits integer value + % #7 9 digits integer value + % + \FP@trigocmpsval#1{#2}{#5}% + \ifnum#1=0\relax\FP@trigocmpsval#1{#3}{#6}\relax\fi% + \ifnum#1=0\relax\FP@trigocmpsval#1{#4}{#7}\relax\fi% +} + +\def\FP@trigosub#1#2#3#4#5#6{% + % #1 resulting fractional part one + % #2 resulting fractional part two + % #3 1st value fractional part one + % #4 1st value fractional part two + % #5 2nd value fractional part one + % #6 2nd value fractional part two + \FP@rfb=#4\relax\advance\FP@rfb-#6\relax% + \FP@rfa=#3\relax\advance\FP@rfa-#5\relax% + \ifnum\FP@rfb<0\relax% + \advance\FP@rfa-1\relax% + \advance\FP@rfb1000000000\relax% + \fi% + \ifnum\FP@rfa<0\relax% + \advance\FP@rfa1000000000\relax% + \fi% + #1=\FP@rfa% + #2=\FP@rfb% +} + +%compute octand of value and transform value to one between 0 and pi/4 + +\def\FP@octand#1#2{%resulting values \FP@oct, family {x} + % #1 integer part of value + % #2 fractional part of value + % + \FP@modtwopi{#1}{#2}% + %now it is 0<={x}<2pi + % + \FP@trigocmpval\FP@oct\FP@xib\FP@xfa\FP@xfb{3}{141592653}{589793238}% + \ifnum\FP@oct>0\relax% + \FP@trigocmpval\FP@oct\FP@xib\FP@xfa\FP@xfb{4}{712388980}{384689858}% + \ifnum\FP@oct>0\relax% + \FP@trigocmpval\FP@oct\FP@xib\FP@xfa\FP@xfb{5}{497787143}{782138167}% + \ifnum\FP@oct>0\relax% + \FP@oct=7\relax% + \FP@trigosub\FP@xfa\FP@xfb{283185307}{179586477}\FP@xfa\FP@xfb% + \else% + \FP@oct=6\relax% + \FP@trigosub\FP@xfa\FP@xfb\FP@xfa\FP@xfb{712388980}{384689858}% + \fi% + \else% + \FP@trigocmpval\FP@oct\FP@xib\FP@xfa\FP@xfb{3}{926990816}{987241548}% + \ifnum\FP@oct>0\relax% + \FP@oct=5\relax% + \FP@trigosub\FP@xfa\FP@xfb{712388980}{384689858}\FP@xfa\FP@xfb% + \else% + \FP@oct=4\relax% + \FP@trigosub\FP@xfa\FP@xfb\FP@xfa\FP@xfb{141592653}{589793238}% + \fi% + \fi% + \else% + \FP@trigocmpval\FP@oct\FP@xib\FP@xfa\FP@xfb{1}{570796326}{794896619}% + \ifnum\FP@oct>0\relax% + \FP@trigocmpval\FP@oct\FP@xib\FP@xfa\FP@xfb{2}{356194490}{192344929}% + \ifnum\FP@oct>0\relax% + \FP@oct=3\relax% + \FP@trigosub\FP@xfa\FP@xfb{141592653}{589793238}\FP@xfa\FP@xfb% + \else% + \FP@oct=2\relax% + \FP@trigosub\FP@xfa\FP@xfb\FP@xfa\FP@xfb{570796326}{794896619}% + \fi% + \else% + \FP@trigocmpval\FP@oct\FP@xib\FP@xfa\FP@xfb{0}{785398163}{397448310}% + \ifnum\FP@oct>0\relax% + \FP@oct=1\relax% + \FP@trigosub\FP@xfa\FP@xfb{570796326}{794896619}\FP@xfa\FP@xfb% + \else% + \FP@oct=0\relax% + \fi% + \fi% + \fi% + % + \FP@xib=0\relax% +} + +%auxiliary functions + +\def\FP@trigo@mul#1#2#3#4#5#6{% + % #1 macro which gets fractional part 1 + % #2 macro which fractional part 1 + % #3 first value part 1 + % #4 first value part 2 + % #5 second value part 1 + % #6 second value part 2 + \FP@split\FP@xq\FP@xr\FP@xz{#3}\FP@split\FP@xt\FP@xu\FP@xv{#4}% + \FP@split\FP@yq\FP@yr\FP@yz{#5}\FP@split\FP@yt\FP@yu\FP@yv{#6}% + \FP@prod=0\relax% + \edef\FP@rd{}% + \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 uz zu vr rv \relax\FP@saveshift% + \FP@@mul zt tz ur ru qv vq \relax\FP@saveshift% + \FP@@mul zz rt tr qu uq \relax\FP@saveshift% + \FP@@mul rz zr qt tq \relax\FP@saveshift% + \FP@@mul rr qz zq \relax\FP@saveshift% + \FP@@mul qr rq \relax\FP@saveshift% + \FP@@mul qq \relax\FP@saveshift\FP@saveshift% + \FP@ninesplit\FP@rd#1=\FP@res% + \FP@ninesplit\FP@rd#2=\FP@res% +} + +\def\FP@trigo@divn#1#2#3#4#5{% + % #1 macro which gets fractional part 1 + % #2 macro which gets fractional part 2 + % #3 value part 1 + % #4 value part 2 + % #5 integer (0,..,1000) + \FP@rega=#3\divide\FP@rega#5% + \FP@regd=\FP@rega% + \multiply\FP@rega#5\relax% + \advance\FP@rega-#3\relax% + \multiply\FP@rega-1000\relax% + \FP@regb=#4\divide\FP@regb1000000\relax% + \advance\FP@rega\FP@regb% + \FP@regc=\FP@rega\divide\FP@regc#5\relax% + \FP@rege=\FP@regc\multiply\FP@rege1000000\relax% + \multiply\FP@regc#5\advance\FP@rega-\FP@regc\multiply\FP@rega1000000\relax% + \multiply\FP@regb1000000\relax\advance\FP@regb-#4\relax% + \advance\FP@rega-\FP@regb% + \divide\FP@rega#5\relax% + \advance\FP@rege\FP@rega% + #1=\FP@regd% + #2=\FP@rege% +} + +%sine and cosine + +\def\FP@sincos@loop#1#2{% + % #1 fractional part 1 of value + % #2 fractional part 2 of value + \loop% + \FP@ls=-\FP@ls% + \FP@trigo@mul\FP@lfa\FP@lfb\FP@lfa\FP@lfb{#1}{#2}% + \FP@trigo@mul\FP@lfa\FP@lfb\FP@lfa\FP@lfb{#1}{#2}% + \FP@trigo@divn\FP@lfa\FP@lfb\FP@lfa\FP@lfb\FP@count% + \advance\FP@count1\relax% + \FP@trigo@divn\FP@lfa\FP@lfb\FP@lfa\FP@lfb\FP@count% + \advance\FP@count1\relax% + \ifnum\ifnum\FP@lfa=0 0\else1\fi\ifnum\FP@lfb=0 0\else1\fi>0\relax% + \ifnum\FP@ls>0\relax% + \advance\FP@rfa\FP@lfa% + \advance\FP@rfb\FP@lfb% + \ifnum\FP@rfb<1000000000\relax\else% + \advance\FP@rfa1\relax% + \advance\FP@rfb-1000000000\relax% + \fi% + \ifnum\FP@rfa<1000000000\relax\else% + \advance\FP@rib1\relax% + \advance\FP@rfa-1000000000\relax% + \fi% + \else% + \advance\FP@rfa-\FP@lfa% + \advance\FP@rfb-\FP@lfb% + \ifnum\FP@rfb<0\relax% + \advance\FP@rfa-1\relax% + \advance\FP@rfb1000000000\relax% + \fi% + \ifnum\FP@rfa<0\relax% + \advance\FP@rib-1\relax% + \advance\FP@rfa1000000000\relax% + \fi% + \fi% + \repeat% +} + +%sine for values 0<=v<=pi/4 +\def\FP@@sin#1#2{% + % #1 fractional part 1 + % #2 fractional part 2 + \ifnum\ifnum#1=0 0\else1\fi\ifnum#2=0 0\else1\fi=0\relax% + \FP@rs=1\FP@ria=0\FP@rib=0\FP@rfa=0\FP@rfb=0\relax% + \else% + \FP@rs=1\FP@ria=0\FP@rib=0\FP@rfa=#1\FP@rfb=#2\relax% + \FP@ls=1\FP@lfa=#1\FP@lfb=#2\relax% + \FP@count=2\relax% + \FP@sincos@loop{#1}{#2}% + \fi% +} + +%cosine for values 0<=v<=pi/4 +\def\FP@@cos#1#2{% + % #1 fractional part 1 + % #2 fractional part 2 + \ifnum\ifnum#1=0 0\else1\fi\ifnum#2=0 0\else1\fi=0\relax% + \FP@rs=1\FP@ria=0\FP@rib=1\FP@rfa=0\FP@rfb=0\relax% + \else% + \FP@ls=-1\FP@lfa=#1\FP@lfb=#2\relax% + \FP@trigo@mul\FP@lfa\FP@lfb\FP@lfa\FP@lfb\FP@lfa\FP@lfb% + \FP@trigo@divn\FP@lfa\FP@lfb\FP@lfa\FP@lfb{2}% + \FP@count=3\relax% + \FP@rs=1\FP@ria=0\relax% + \ifnum\FP@lfb=0\relax% + \ifnum\FP@lfa=0\relax% + \FP@rib=1\FP@rfa=0\FP@rfb=0\relax% + \else% + \FP@rib=0\FP@rfa=1000000000\FP@rfb=0\relax% + \fi% + \else% + \FP@rib=0\FP@rfa=999999999\FP@rfb=1000000000\relax% + \fi% + \advance\FP@rfb-\FP@lfb\advance\FP@rfa-\FP@lfa% + \FP@sincos@loop{#1}{#2}% + \fi% +} + +\def\FP@sin#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 everything after the 2nd '.' + % + \FP@beginmessage{SIN}% + % + {\FP@octand{#2}{#3}% + % + \ifnum\FP@oct<4\relax% + \ifnum\FP@oct<2\relax% + \ifnum\FP@oct<1\relax% + \FP@@sin\FP@xfa\FP@xfb% + \else% + \FP@@cos\FP@xfa\FP@xfb% + \fi% + \else% + \ifnum\FP@oct<3\relax% + \FP@@cos\FP@xfa\FP@xfb% + \else% + \FP@@sin\FP@xfa\FP@xfb% + \fi% + \fi% + \else% + \ifnum\FP@oct<6\relax% + \ifnum\FP@oct<5\relax% + \FP@@sin\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \else% + \FP@@cos\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \fi% + \else% + \ifnum\FP@oct<7\relax% + \FP@@cos\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \else% + \FP@@sin\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \fi% + \fi% + \fi% + % + \FP@store\FP@tmp{r}% + \global\let\FP@tmp\FP@tmp% + }% + % + \FP@endmessage{}% + % + \let#1\FP@tmp% +} + +\def\FP@cos#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 everything after the 2nd '.' + % + \FP@beginmessage{COS}% + % + {\FP@octand{#2}{#3}% + % + \ifnum\FP@oct<4\relax% + \ifnum\FP@oct<2\relax% + \ifnum\FP@oct<1\relax% + \FP@@cos\FP@xfa\FP@xfb% + \else% + \FP@@sin\FP@xfa\FP@xfb% + \fi% + \else% + \ifnum\FP@oct<3\relax% + \FP@@sin\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \else% + \FP@@cos\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \fi% + \fi% + \else% + \ifnum\FP@oct<6\relax% + \ifnum\FP@oct<5\relax% + \FP@@cos\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \else% + \FP@@sin\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \fi% + \else% + \ifnum\FP@oct<7\relax% + \FP@@sin\FP@xfa\FP@xfb% + \else% + \FP@@cos\FP@xfa\FP@xfb% + \fi% + \fi% + \fi% + % + \FP@store\FP@tmp{r}% + \global\let\FP@tmp\FP@tmp% + }% + % + \FP@endmessage{}% + % + \let#1\FP@tmp% +} + +\def\FP@@sincos#1#2{% + % #1 integer part of value + % #2 fractional part of value + % + \FP@octand{#1}{#2}% + % + \ifnum\FP@oct<4\relax% + \ifnum\FP@oct<2\relax% + \ifnum\FP@oct<1\relax% + \FP@@sin\FP@xfa\FP@xfb% + \FP@store\FP@tmpc{r}% + \FP@@cos\FP@xfa\FP@xfb% + \FP@store\FP@tmpb{r}% + \else% + \FP@@cos\FP@xfa\FP@xfb% + \FP@store\FP@tmpc{r}% + \FP@@sin\FP@xfa\FP@xfb% + \FP@store\FP@tmpb{r}% + \fi% + \else% + \ifnum\FP@oct<3\relax% + \FP@@cos\FP@xfa\FP@xfb% + \FP@store\FP@tmpc{r}% + \FP@@sin\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \FP@store\FP@tmpb{r}% + \else% + \FP@@sin\FP@xfa\FP@xfb% + \FP@store\FP@tmpc{r}% + \FP@@cos\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \FP@store\FP@tmpb{r}% + \fi% + \fi% + \else% + \ifnum\FP@oct<6\relax% + \ifnum\FP@oct<5\relax% + \FP@@sin\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \FP@store\FP@tmpc{r}% + \FP@@cos\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \FP@store\FP@tmpb{r}% + \else% + \FP@@cos\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \FP@store\FP@tmpc{r}% + \FP@@sin\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \FP@store\FP@tmpb{r}% + \fi% + \else% + \ifnum\FP@oct<7\relax% + \FP@@cos\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \FP@store\FP@tmpc{r}% + \FP@@sin\FP@xfa\FP@xfb% + \FP@store\FP@tmpb{r}% + \else% + \FP@@sin\FP@xfa\FP@xfb% + \FP@rs=-\FP@rs% + \FP@store\FP@tmpc{r}% + \FP@@cos\FP@xfa\FP@xfb% + \FP@store\FP@tmpb{r}% + \fi% + \fi% + \fi% +} + +\def\FP@sincos#1#2#3.#4.#5\relax{% + % #1 macro, which gets the sine result + % #2 macro, which gets the cosine result + % #3 integer part of value + % #4 fractional part of value + % #5 dummy to swallow everything after the 2nd '.' + % + {\FP@beginmessage{SINCOS}% + % + \FP@@sincos{#3}{#4}% + % + \global\let\FP@tmpc\FP@tmpc%sine + \global\let\FP@tmpb\FP@tmpb%cosine + % + \FP@endmessage{}% + }% + % + \let#1\FP@tmpc% + \let#2\FP@tmpb% + } + +%tan and cot + +\def\FP@tan#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 everything after the 2nd '.' + % + \FP@beginmessage{TAN}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + % + \FP@@sincos{#2}{#3}% + % + \FPdiv\FP@tmp\FP@tmpc\FP@tmpb% + % + \global\let\FP@tmp\FP@tmp% + }% + % + \FP@endmessage{}% + % + \let#1\FP@tmp% +} + +\def\FP@cot#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 everything after the 2nd '.' + % + \FP@beginmessage{COT}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + % + \FP@@sincos{#2}{#3}% + % + \FPdiv\FP@tmp\FP@tmpb\FP@tmpc% + % + \global\let\FP@tmp\FP@tmp% + }% + % + \FP@endmessage{}% + % + \let#1\FP@tmp% +} + +\def\FP@tancot#1#2#3.#4.#5\relax{% + % #1 macro, which gets the tan result + % #1 macro, which gets the cot result + % #3 integer part of value + % #4 fractional part of value + % #5 dummy to swallow everything after the 2nd '.' + % + \FP@beginmessage{TANCOT}% + % + {\def\FP@beginmessage##1{}% + \def\FP@endmessage##1{}% + % + \FP@@sincos{#3}{#4}% + % + \FPdiv\FP@tmpd\FP@tmpc\FP@tmpb% + \FPdiv\FP@tmp\FP@tmpb\FP@tmpc% + % + \global\let\FP@tmpd\FP@tmpd% + \global\let\FP@tmp\FP@tmp% + }% + % + \FP@endmessage{}% + % + \let#1\FP@tmpd% + \let#2\FP@tmp% +} + +%auxiliary functions + +% compute x/(x+1) for 0<=x<=1000000 +\def\FP@trigo@xy#1#2#3{% + % #1 macro, which gets fractional part 1 + % #2 macro, which gets fractional part 2 + % #3 natural number + \FP@rega=#3\relax\FP@regb=\FP@rega\advance\FP@regb1\relax% + \multiply\FP@rega1000\relax% + \FP@regc=\FP@rega\divide\FP@regc\FP@regb% + #1=\FP@regc% + \multiply\FP@regc\FP@regb\advance\FP@rega-\FP@regc% + \multiply\FP@rega1000\relax% + \FP@regc=\FP@rega\divide\FP@regc\FP@regb% + \multiply#11000\relax\advance#1\FP@regc% + \multiply\FP@regc\FP@regb\advance\FP@rega-\FP@regc% + \multiply\FP@rega1000\relax% + \FP@regc=\FP@rega\divide\FP@regc\FP@regb% + \multiply#11000\relax\advance#1\FP@regc% + \multiply\FP@regc\FP@regb\advance\FP@rega-\FP@regc% + \multiply\FP@rega1000\relax% + \FP@regc=\FP@rega\divide\FP@regc\FP@regb% + #2=\FP@regc% + \multiply\FP@regc\FP@regb\advance\FP@rega-\FP@regc% + \multiply\FP@rega1000\relax% + \FP@regc=\FP@rega\divide\FP@regc\FP@regb% + \multiply#21000\relax\advance#2\FP@regc% + \multiply\FP@regc\FP@regb\advance\FP@rega-\FP@regc% + \multiply\FP@rega1000\relax% + \FP@regc=\FP@rega\divide\FP@regc\FP@regb% + \multiply#21000\relax\advance#2\FP@regc% + \multiply\FP@regc\FP@regb\advance\FP@rega-\FP@regc% +} + +%if x<=0.707106781 then x:=y else x:=y with x^2 + y^2 = 1 +%sets \FP@@arccos to 0 if x:=y otherwise to 1 +\def\FP@sincos@transform@Rii{% + \ifnum\FP@xfa>707106781\relax% + \FP@@arccos=1\relax% + \FP@trigo@mul\FP@rfa\FP@rfb\FP@xfa\FP@xfb\FP@xfa\FP@xfb% + \FP@lfa=1000000000\relax% + \advance\FP@lfa-\FP@rfa% + \ifnum\FP@rfb>0\relax% + \advance\FP@lfa-1\relax% + \FP@lfb=1000000000\relax% + \advance\FP@lfb-\FP@rfb% + \else% + \FP@lfb=0\relax% + \fi% + \FP@xia=710000000\FP@xib0\relax% + \FP@xfa=0\FP@xfb=0\relax% + \FP@oldvala=0\FP@oldvalb=0\relax% + \loop% + \ifnum\ifnum\FP@xia=\FP@xfa0\else1\fi\ifnum\FP@xib=\FP@xfb0\else1\fi>0\relax% + \FP@rfa\FP@xia\advance\FP@rfa\FP@xfa% + \FP@rfb\FP@xib\advance\FP@rfb\FP@xfb% + \divide\FP@rfb2\relax% + \ifodd\FP@rfa\advance\FP@rfb500000000\relax\fi% + \divide\FP@rfa2\relax% + \ifnum\FP@rfb<1000000000\relax\else% + \advance\FP@rfb-1000000000\relax% + \advance\FP@rfa1\relax% + \fi% + \FP@trigo@mul\FP@ria\FP@rib\FP@rfa\FP@rfb\FP@rfa\FP@rfb% + \ifnum\FP@ria<\FP@lfa% + \FP@oct=1\relax% + \else\ifnum\FP@ria>\FP@lfa% + \FP@oct=2\relax% + \else\ifnum\FP@rib<\FP@lfb% + \FP@oct=1\relax% + \else\ifnum\FP@rib>\FP@lfb% + \FP@oct=2\relax% + \else% + \FP@oct=3\relax% + \fi\fi\fi\fi% + \ifnum\ifnum\FP@ria=\FP@oldvala0\else1\fi\ifnum\FP@rib=\FP@oldvalb0\else1\fi>0\relax% + \FP@oldvala=\FP@ria\FP@oldvalb=\FP@rib% + \else% + \FP@oct=3\relax% + \fi% + \ifodd\FP@oct% + \FP@xfa\FP@rfa\FP@xfb\FP@rfb% + \fi% + \ifnum\FP@oct>1\relax% + \FP@xia\FP@rfa\FP@xib\FP@rfb% + \fi% + \repeat% + \else% + \FP@@arccos=0\relax% + \fi% +} + +%compute arcsin(abs(x)) resp. arccos(abs(x)) for -1<=x<=1 +%\FP@@arccos determines whether arcsin or arccos has been computed +\def\FP@arcsincos@loop{% + \FP@@arccos=0\relax% + \ifnum\ifnum\FP@xia=0 1\else0\fi\ifnum\FP@xib<2 1\else 0\fi>0\relax% + \ifnum\FP@xib=1\relax% + \ifnum\ifnum\FP@xfa=0 1\else0\fi\ifnum\FP@xfb=0 1\else0\fi>10\relax% + \FP@rs=1\FP@ria=0\FP@rib=1\FP@rfa=570796326\FP@rfb=794896619\relax% + \else% + \FP@errmessage{Number too big}% + \fi% + \else% + \ifnum\ifnum\FP@xfa=0 0\else1\fi\ifnum\FP@xfb=0 0\else1\fi=0\relax% + \FP@rs=1\FP@ria=0\FP@rib=0\FP@rfa=0\FP@rfb=0\relax% + \else% + \FP@sincos@transform@Rii% + \FP@rs=1\FP@ria=0\FP@rib=0\FP@rfa=\FP@xfa\FP@rfb=\FP@xfb% + \FP@ls=1\FP@lfa=\FP@xfa\FP@lfb=\FP@xfb% + \FP@count=1\relax% + \loop% + \FP@trigo@mul\FP@lfa\FP@lfb\FP@lfa\FP@lfb\FP@xfa\FP@xfb% + \FP@trigo@mul\FP@lfa\FP@lfb\FP@lfa\FP@lfb\FP@xfa\FP@xfb% + \FP@trigo@xy\FP@yfa\FP@yfb\FP@count% + \FP@trigo@mul\FP@lfa\FP@lfb\FP@lfa\FP@lfb\FP@yfa\FP@yfb% + \advance\FP@count2\relax% + \FP@trigo@divn\FP@yfa\FP@yfb\FP@lfa\FP@lfb\FP@count% + \ifnum\ifnum\FP@yfa=0 0\else1\fi\ifnum\FP@yfb=0 0\else 1\fi>0\relax% + \advance\FP@rfa\FP@yfa\advance\FP@rfb\FP@yfb% + \ifnum\FP@rfb<1000000000\relax\else% + \advance\FP@rfb-1000000000\relax% + \advance\FP@rfa1\relax% + \fi% + \ifnum\FP@rfa<1000000000\relax\else% + \advance\FP@rfa-1000000000\relax% + \advance\FP@rib1\relax% + \fi% + \repeat% + \fi% + \fi% + \else% + \FP@errmessage{Number too big}% + \fi% +} + +%compute sign(r)*r:=#1.#2#3-abs(r) (for abs(r)<=#1.#2#3) +\def\FP@subrfrom#1#2#3{% + % #1 integer part of value to subtract from + % #2 fractional part 1 of value to subtract from + % #3 fractional part 2 of value to subtract from + \FP@ria=#1\relax\advance\FP@ria-\FP@rib\FP@rib\FP@ria% + \FP@ria=#2\relax\advance\FP@ria-\FP@rfa\FP@rfa\FP@ria% + \FP@ria=#3\relax\advance\FP@ria-\FP@rfb\FP@rfb\FP@ria% + \FP@ria=0\relax% + \ifnum\FP@rfb<0\relax% + \advance\FP@rfb1000000000\relax% + \advance\FP@rfa-1\relax% + \fi% + \ifnum\FP@rfa<0\relax% + \advance\FP@rfa1000000000\relax% + \advance\FP@rib-1\relax% + \fi% + \ifnum\FP@rib<0\relax% + \FP@errmessage{Subtraction lead to unaccepted value}% + \fi% +} + +%compute r:= pi/2 - abs(r) (for abs(r)<=pi/2) +\def\FP@pihalf@subr{\FP@subrfrom{1}{570796326}{794896619}} + +%compute sign(r)*r:= pi-abs(r) (for abs(r)<=pi) +\def\FP@pi@subr{\FP@subrfrom{3}{141592653}{589793238}} + +%compute arcsin + +\def\FP@arcsin#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 everything after the 2nd '.' + % + {\FP@beginmessage{ARCSIN}% + % + \FP@readvalue{x}{#2}{#3}% + % + \FP@arcsincos@loop% + % + \ifnum\FP@@arccos=1\relax% + \FP@pihalf@subr% + \fi% + \FP@rs=\FP@xs% + % + \FP@store\FP@tmp{r}% + % + \global\let\FP@tmp\FP@tmp% + % + \FP@endmessage{}% + }% + % + \let#1\FP@tmp% +} + +%compute arccos +\def\FP@arccos#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 everything after the 2nd '.' + % + {\FP@beginmessage{ARCCOS}% + % + \FP@readvalue{x}{#2}{#3}% + % + \FP@arcsincos@loop% + % + \ifnum\FP@@arccos=0\relax% + \FP@pihalf@subr% + \fi% + \FP@rs=1% + \ifnum\FP@xs<0\relax% + \FP@pi@subr% + \fi% + % + \FP@store\FP@tmp{r}% + % + \global\let\FP@tmp\FP@tmp% + % + \FP@endmessage{}% + }% + % + \let#1\FP@tmp% +} + +%compute arcsin and arccos +\def\FP@arcsincos#1#2#3.#4.#5\relax{% + % #1 macro, which gets the arcsin-result + % #2 macro, which gets the arccos-result + % #3 integer part of value + % #4 fractional part of value + % #5 dummy to swallow everything after the 2nd '.' + % + {\FP@beginmessage{ARCSINCOS}% + % + \FP@readvalue{x}{#3}{#4}% + % + \FP@arcsincos@loop% + % + \FP@xia\FP@ria\FP@xib\FP@rib\FP@xfa\FP@rfa\FP@xfb\FP@rfb% + % + \ifnum\FP@@arccos=1\relax% + \FP@pihalf@subr% + \fi% + \FP@rs=\FP@xs% + \FP@store\FP@tmpa{r}% + % + \FP@ria\FP@xia\FP@rib\FP@xib\FP@rfa\FP@xfa\FP@rfb\FP@xfb% + % + \ifnum\FP@@arccos=0\relax% + \FP@pihalf@subr% + \fi% + \FP@rs=1% + \ifnum\FP@xs<0\relax% + \FP@pi@subr% + \fi% + \FP@store\FP@tmpb{r}% + % + \global\let\FP@tmpa\FP@tmpa% + \global\let\FP@tmpb\FP@tmpb% + % + \FP@endmessage{}% + }% + % + \let#1\FP@tmpa% + \let#2\FP@tmpb% +} + +%compute arctan and arccot + +%compute 1/y for y>=1 +\def\FP@trigo@inv{% + \FP@shift=0\relax% + \FP@xia=1000000000\FP@xib=0\FP@xfa=0\FP@xfb=0\relax% + \loop% + \ifnum\FP@yia<100000000\relax% + \FP@multen{y}% + \advance\FP@shift1\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<35\relax% + \advance\FP@shift1\relax% + \FP@divten{r}% + \repeat% +} + +%compute 1/sqrt(1+x^2) for 0<=x<1 +\def\FP@trigo@sq\FP@xfa\FP@xfb{% + \FP@trigo@mul\FP@yfa\FP@yfb\FP@xfa\FP@xfb\FP@xfa\FP@xfb% + \ifnum\FP@yfb=0\relax\else% + \FP@yfb=-\FP@yfb% + \advance\FP@yfb1000000000\relax% + \advance\FP@yfa1\relax% + \fi% + \FP@yfa=-\FP@yfa% + \advance\FP@yfa1250000000\relax% + \FP@trigo@mul\FP@yfa\FP@yfb\FP@yfa\FP@yfb{444444444}{444444444}% + \FP@lfa=666666666\relax\FP@lfb=666666666\relax% + \FP@rs=1\FP@ria=0\FP@rib=0\FP@rfa=\FP@lfa\FP@rfb=\FP@lfb% + \FP@count=0\relax% + \loop% + \advance\FP@count2\relax% + \FP@trigo@divn\FP@yia\FP@yib{1000000000}{0}\FP@count% + \ifnum\ifnum\FP@yia=0 0\else1\fi\ifnum\FP@yib=0 0\else1\fi>0\relax% + \ifnum\FP@yib=0\relax\else% + \FP@yib=-\FP@yib% + \advance\FP@yib1000000000\relax% + \advance\FP@yia1\relax% + \fi% + \ifnum\FP@yia=0\relax\else% + \FP@yia=-\FP@yia% + \advance\FP@yia1000000000\relax% + \fi% + \FP@trigo@mul\FP@lfa\FP@lfb\FP@lfa\FP@lfb\FP@yia\FP@yib% + \fi% + \FP@trigo@mul\FP@lfa\FP@lfb\FP@lfa\FP@lfb\FP@yfa\FP@yfb% + \ifnum\ifnum\FP@lfa=0 0\else1\fi\ifnum\FP@lfb=0 0\else1\fi=0\relax\else% + \advance\FP@rfb\FP@lfb% + \ifnum\FP@rfb<1000000000\relax\else% + \advance\FP@rfa1\relax% + \advance\FP@rfb-1000000000\relax% + \fi% + \advance\FP@rfa\FP@lfa% + \ifnum\FP@rfa<1000000000\relax\else% + \advance\FP@rib1\relax% + \advance\FP@rfa-1000000000\relax% + \fi% + \repeat% +} + +%compute arctan for 0<=x<=0.5 +\def\FP@@arctan{% + \ifnum\ifnum\FP@xfa=0 0\else1\fi\ifnum\FP@xfb=0 0\else1\fi=0\relax% + \FP@rs=1\FP@ria=0\FP@rib=0\FP@rfa=0\FP@rfb=0\relax% + \else% + \FP@rs=1\FP@ria=0\FP@rib=0\FP@rfa=\FP@xfa\FP@rfb=\FP@xfb% + \FP@lfa=\FP@xfa\FP@lfb=\FP@xfb% + \FP@trigo@mul\FP@xfa\FP@xfb\FP@xfa\FP@xfb\FP@xfa\FP@xfb% + \FP@count=1\relax% + \FP@regs=1\relax% + \loop% + \FP@regs=-\FP@regs% + \advance\FP@count2\relax% + \FP@trigo@mul\FP@lfa\FP@lfb\FP@lfa\FP@lfb\FP@xfa\FP@xfb% + \FP@trigo@divn\FP@yfa\FP@yfb\FP@lfa\FP@lfb\FP@count% + \ifnum\ifnum\FP@yfa=0 0\else1\fi\ifnum\FP@yfb=0 0\else1\fi>0\relax% + \ifnum\FP@regs<0\relax% + \advance\FP@rfb-\FP@yfb% + \ifnum\FP@rfb<0\relax% + \advance\FP@rfb1000000000\relax% + \advance\FP@rfa-1\relax% + \fi% + \advance\FP@rfa-\FP@yfa% + \ifnum\FP@rfa<0\relax% + \advance\FP@rfa1000000000\relax% + \advance\FP@rib-1\relax% + \fi% + \else% + \advance\FP@rfb\FP@yfb% + \ifnum\FP@rfb<1000000000\relax\else% + \advance\FP@rfb-1000000000\relax% + \advance\FP@rfa1\relax% + \fi% + \advance\FP@rfa\FP@yfa% + \ifnum\FP@rfa<1000000000\relax\else% + \advance\FP@rfa-1000000000\relax% + \advance\FP@rib1\relax% + \fi% + \fi% + \repeat% + \fi% +} + +%compute arctan +\def\FP@@arctancot#1#2{% + % #1 integer part of value + % #2 fractional part of value + % + \FP@readvalue{x}{#1}{#2}% + % + \ifnum\ifnum\FP@xia=0 0\else1\fi\ifnum\FP@xib=1 0\else1\fi\ifnum\FP@xfa=0 0\else1\fi\ifnum\FP@xfb=0 0\else1\fi=0\relax% + \FP@ria=0\FP@rib=0\FP@rfa=785398163\FP@rfb=397448310\relax% + \FP@subfpih=0\relax% + \else% + \ifnum\ifnum\FP@xia=0 0\else1\fi\ifnum\FP@xib=0 0\else1\fi=0\relax% + \FP@subfpih=0\relax% + \else% + \FP@yia=\FP@xia\FP@yib=\FP@xib\FP@yfa=\FP@xfa\FP@yfb=\FP@xfb% + \FP@trigo@inv% + \FP@xia=\FP@ria\FP@xib=\FP@rib\FP@xfa=\FP@rfa\FP@xfb=\FP@rfb% + \FP@subfpih=1\relax% + \fi% + \ifnum\FP@xfa>880000000\relax% + \FP@trigo@sq\FP@xfa\FP@xfb% + \FP@xfa=\FP@rfa\FP@xfb=\FP@rfb% + \FP@arcsincos@loop% + \ifnum\FP@@arccos=0\relax% + \FP@pihalf@subr% + \fi% + \else% + \FP@@arctan\FP@xfa\FP@xfb% + \fi% + \fi% + % + \ifnum\FP@subfpih>0\relax% + \FP@pihalf@subr% + \fi% + % + \FP@rs=\FP@xs% +} + +%compute arctan +\def\FP@arctan#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 everything after the 2nd '.' + % + {\FP@beginmessage{ARCTAN}% + % + \FP@@arctancot{#2}{#3}% + % + \FP@store\FP@tmp{r}% + % + \global\let\FP@tmp\FP@tmp% + % + \FP@endmessage{}% + }% + % + \let#1\FP@tmp% +} + +%compute arccot +\def\FP@arccot#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 everything after the 2nd '.' + % + {\FP@beginmessage{ARCCOT}% + % + \FP@@arctancot{#2}{#3}% + \ifnum\FP@rs<0\relax% + \FP@rs=1\relax% + \FP@pihalf@subr% + \FP@pi@subr% + \else% + \FP@pihalf@subr% + \fi% + % + \FP@store\FP@tmp{r}% + % + \global\let\FP@tmp\FP@tmp% + % + \FP@endmessage{}% + }% + % + \let#1\FP@tmp% +} + +%compute arctan and arccot +\def\FP@arctancot#1#2#3.#4.#5\relax{% + % #1 macro, which gets the arcsin-result + % #2 macro, which gets the arccos-result + % #3 integer part of value + % #4 fractional part of value + % #5 dummy to swallow everything after the 2nd '.' + % + {\FP@beginmessage{ARCTANCOT}% + % + \FP@@arctancot{#3}{#4}% + \FP@xs\FP@rs\FP@xia\FP@ria\FP@xib\FP@rib\FP@xfa\FP@rfa\FP@xfb\FP@rfb% + \FP@store\FP@tmpa{x}% + % + \ifnum\FP@rs<0\relax% + \FP@rs=1\relax% + \FP@pihalf@subr% + \FP@pi@subr% + \else% + \FP@pihalf@subr% + \fi% + \FP@store\FP@tmpb{r}% + % + \global\let\FP@tmpa\FP@tmpa% + \global\let\FP@tmpb\FP@tmpb% + % + \FP@endmessage{}% + }% + % + \let#1\FP@tmpa% + \let#2\FP@tmpb% +} diff --git a/Master/texmf-dist/tex/latex/fp/fp-upn.sty b/Master/texmf-dist/tex/latex/fp/fp-upn.sty new file mode 100644 index 00000000000..2a74c50bcf4 --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/fp-upn.sty @@ -0,0 +1,237 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{fp-upn}[1996/10/21] + +%version information +\def\FP@upnversion{2.1c} +\message{% + `UPN Fixed Point Calculator',% + \space\space\space\space% + Version \FP@upnversion% + \space(C) Michael Mehlich% + \space\space\space\space\space\space\space% + \space\space\space\space\space\space% +} + +%resolve dependencies +\RequirePackage{fp} +\RequirePackage{defpattern} + +%%%public area (macros which may be used)%%% +\def\FPupn#1#2{\FP@@@upn{#1}{#2}} % #1 := eval(#2) + +%%%private fp-area (don't use these macros)%%% + +%routines for stack manipulation + +\edef\FP@stack{()} + +\defpattern\FP@@@putstack[(#2)#3]{\edef\FP@stack{(#3,#2)}} +\defpattern\FP@@@putstack[()#2]{\edef\FP@stack{(#2)}} +\def\FP@@putstack(#1)#2{\FP@@@putstack[(#1)#2]} +\def\FP@putstack#1{\expandafter\FP@@putstack\FP@stack{#1}} + +\defpattern\FP@@@getstack[(#2)#3]{\edef\FP@stack{()}\edef#2{#3}} +\defpattern\FP@@@getstack[(#2)#3,#4]{\edef\FP@stack{(#4)}\edef#2{#3}} +\defpattern\FP@@@getstack[(#2)]{\FP@errmessage{UPN stack is empty}} +\def\FP@@getstack(#1)#2{\FP@@@getstack[(#2)#1]} +\def\FP@getstack#1{\expandafter\FP@@getstack\FP@stack{#1}} + +%local debug macro +\def\FP@upn@debug#1{\FP@debug{upn: #1}} +\def\FP@upnc@debug#1{\FP@upn@debug{calculating\space\string"#1\string"}} +\def\FP@upnc@constant#1{\FP@upn@debug{constant\space\space\space\space\string"#1\string"}} +\def\FP@upnc@result#1{\FP@upn@debug{result\space\space\space\space\space\space\string"#1\string"}} + +%call fp-functions with parameters from stack +\def\FP@const#1{% + \FP@upnc@constant{#1}% + \expandafter\FP@putstack\csname FP#1\endcsname% +} +\def\FP@nullop#1{% + \FP@upnc@debug{#1()}% + \csname FP#1\endcsname\FP@valc% + \FP@upnc@result{\FP@valc}% + \FP@putstack\FP@valc% +} +\def\FP@monop#1{% + \FP@getstack\FP@vala% + \FP@upnc@debug{#1(\FP@vala)}% + \csname FP#1\endcsname\FP@valc\FP@vala% + \FP@upnc@result{\FP@valc}% + \FP@putstack\FP@valc% +} +\def\FP@monopb#1{% + \FP@getstack\FP@vala% + \FP@upnc@debug{#1(\FP@vala)}% + \csname FP#1\endcsname\FP@valc\FP@vald\FP@vala% + \FP@upnc@result{\FP@valc}% + \FP@putstack\FP@vald\FP@putstack\FP@valc% +} +\def\FP@binop#1{% + \FP@getstack\FP@vala\FP@getstack\FP@valb% + \FP@upnc@debug{\FP@vala\space #1 \FP@valb}% + \csname FP#1\endcsname\FP@valc\FP@vala\FP@valb% + \FP@upnc@result{\FP@valc}% + \FP@putstack\FP@valc% +} +\def\FP@binopv#1{% + \FP@getstack\FP@vala\FP@getstack\FP@valb% + \FP@upnc@debug{\FP@valb\space #1 \FP@vala}% + \csname FP#1\endcsname\FP@valc\FP@valb\FP@vala% + \FP@upnc@result{\FP@valc}% + \FP@putstack\FP@valc% +} +\def\FP@binopb#1{% + \FP@getstack\FP@vala\FP@getstack\FP@valb% + \FP@upnc@debug{#1(\FP@valb:\FP@vala)}% + \csname FP#1\endcsname\FP@valc\FP@valb\FP@vala% + \FP@upnc@result{\FP@valc}% + \FP@putstack\FP@valc% +} +\def\FP@binopc#1{% + \FP@getstack\FP@vala\FP@getstack\FP@valb% + \FP@upnc@debug{\FP@valb-th #1 of \FP@vala}% + \csname FP#1\endcsname\FP@valc\FP@vala\FP@valb% + \FP@upnc@result{\FP@valc}% + \FP@putstack\FP@valc% +} +\def\FP@binopd#1{% + \FP@getstack\FP@vala\FP@getstack\FP@valb% + \FP@upnc@debug{#1(\FP@valb,\FP@vala)}% + \csname FP#1\endcsname\FP@valc\FP@vala\FP@valb% + \FP@upnc@result{\FP@valc}% + \FP@putstack\FP@valc% +} + +%the calculation loop + +%put value to stack +\def\FP@put#1\@upnend{% + \FP@upnc@result{#1}% + \FP@putstack{#1}% +} + +\defpattern\FP@upn[#2#3]{% + \ifx#2\@undefined% + \FP@upnc@debug{#2#3}% + \expandafter\expandafter\expandafter\FP@put\csname #2#3\endcsname\@upnend% + \else\ifcat\noexpand#2\relax% + \FP@upnc@debug{\string#2#3}% + \expandafter\FP@put#2#3\@upnend% + \else\ifcat#22\relax% + \FP@upnc@debug{\string#2#3}% + \expandafter\FP@put#2#3\@upnend% + \else% + \FP@upnc@debug{#2#3}% + \expandafter\expandafter\expandafter\FP@put\csname #2#3\endcsname\@upnend% + \fi\fi\fi% +} + +%binary functions from fp-basic +\defpattern\FP@upn[+]{\FP@binop{add}} +\defpattern\FP@upn[add]{\FP@binopv{add}} +\defpattern\FP@upn[-]{\FP@binop{sub}} +\defpattern\FP@upn[sub]{\FP@binopv{sub}} +\defpattern\FP@upn[*]{\FP@binop{mul}} +\defpattern\FP@upn[mul]{\FP@binopv{mul}} +\defpattern\FP@upn[/]{\FP@binop{div}} +\defpattern\FP@upn[div]{\FP@binopv{div}} + +%unary functions from fp-basic +\defpattern\FP@upn[abs]{\FP@monop{abs}} +\defpattern\FP@upn[neg]{\FP@monop{neg}} +\defpattern\FP@upn[sgn]{\FP@monop{sgn}} + +%binary functions from fp-addons +\defpattern\FP@upn[min]{\FP@binopd{min}} +\defpattern\FP@upn[max]{\FP@binopd{max}} + +%functions from fp-snap +\defpattern\FP@upn[round]{\FP@binopb{round}} +\defpattern\FP@upn[trunc]{\FP@binopb{trunc}} +\defpattern\FP@upn[clip]{\FP@monop{clip}} + +%functions from fp-exp +\defpattern\FP@upn[e]{\FP@const{e}} +\defpattern\FP@upn[exp]{\FP@monop{exp}} +\defpattern\FP@upn[ln]{\FP@monop{ln}} +\defpattern\FP@upn[pow]{\FP@binopc{pow}} +\defpattern\FP@upn[root]{\FP@binopc{root}} + +%functions from fp-random +\defpattern\FP@upn[seed]{% + \FP@getstack\FP@vala\FPseed=\FP@vala% +} +\defpattern\FP@upn[random]{\FP@nullop{random}} + +%functions from fp-trigo +\defpattern\FP@upn[pi]{\FP@const{pi}} +\defpattern\FP@upn[sin]{\FP@monop{sin}} +\defpattern\FP@upn[cos]{\FP@monop{cos}} +\defpattern\FP@upn[sincos]{\FP@monopb{sincos}} +\defpattern\FP@upn[tan]{\FP@monop{tan}} +\defpattern\FP@upn[cot]{\FP@monop{cot}} +\defpattern\FP@upn[tancot]{\FP@monopb{tancot}} +\defpattern\FP@upn[arcsin]{\FP@monop{arcsin}} +\defpattern\FP@upn[arccos]{\FP@monop{arccos}} +\defpattern\FP@upn[arcsincos]{\FP@monopb{arcsincos}} +\defpattern\FP@upn[arctan]{\FP@monop{arctan}} +\defpattern\FP@upn[arccot]{\FP@monop{arccot}} +\defpattern\FP@upn[arctancot]{\FP@monopb{arctancot}} + +%stack manipulators +\defpattern\FP@upn[pop]{% + \FP@getstack\FP@vala% + \FP@upn@debug{removing top number \string"\FP@vala\string"}% +} +\defpattern\FP@upn[swap]{% + \FP@getstack\FP@vala\FP@getstack\FP@valb% + \FP@upn@debug{exchanging top numbers \string"\FP@vala\string" and \string"\FP@valb\string"}% + \FP@putstack\FP@vala\FP@putstack\FP@valb% +} +\defpattern\FP@upn[copy]{% + \FP@getstack\FP@vala% + \FP@upn@debug{duplicating top number \string"\FP@vala\string"}% + \FP@putstack\FP@vala\FP@putstack\FP@vala% +} + +%left-to-right loop +\defpattern\FP@upn[#2 #3]{\FP@upn[#2]\FP@upn[#3]} +\defpattern\FP@upn[#2 ]{\FP@upn[#2]} +\defpattern\FP@upn[ #2]{\FP@upn[#2]} + +%get result from stacks with one value only +\defpattern\FP@@upn@result[(#2)#3]{\edef#2{#3}} +\defpattern\FP@@upn@result[(#2)]{\FP@errmessage{UPN stack is empty}\edef#2{0}} +\defpattern\FP@@upn@result[(#2)#3,#4]{\FP@errmessage{Evaluation results in multiple values}\edef#2{#3}} +\def\FP@upn@result(#1)#2{\FP@@upn@result[(#2)#1]} + +%save result of upn-expression to macro +\def\FP@saveval[#1#2]{% + \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% +} + +%the main routine +\def\FP@@upn#1#2{% + \bgroup% + \FP@upn@debug{+++ computing upn-expression \string"#2\string"}% + \edef\FP@tmp{[#2]}% + \expandafter\FP@upn\FP@tmp% + \FP@upn@debug{+++ result of upn-expression is \string"\FP@stack\string"}% + \expandafter\FP@upn@result\FP@stack\FP@tmp% + \global\let\FP@tmp\FP@tmp% + \egroup% + \FP@saveval[#1]% +} + +\def\FP@@@upn#1#2{% + \FP@beginmessage{UPN}% + \FP@@upn{#1}{#2}% + \FP@endmessage{}% +} diff --git a/Master/texmf-dist/tex/latex/fp/fp.sty b/Master/texmf-dist/tex/latex/fp/fp.sty new file mode 100644 index 00000000000..8ad1e441b52 --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/fp.sty @@ -0,0 +1,32 @@ +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{fp}[1995/04/02] + +%version information +\def\FP@version{Version 0.8, April 2, 1995} +\message{`Fixed Point Package', \FP@version\space (C) Michael Mehlich} + +\let\FP@save@message\message +\def\message#1{} + +%include all subpackages +\RequirePackage{defpattern} +\RequirePackage{fp-basic} %add, sub, mul, div, abs, neg, lt?, eq?, gt?, + %neg?, pos?, zero?, int? +\RequirePackage{fp-addons} %min, max +\RequirePackage{fp-snap} %trunc, round, clip +\RequirePackage{fp-exp} %e, exp, ln, pow, root +\RequirePackage{fp-trigo} %pi, sin, cos, sincos, tan, cot, tancot, + %arcsin, arccos, arcsincos +\RequirePackage{fp-pas} %pascal +\RequirePackage{fp-random} %seed, random +\RequirePackage{fp-eqn} %lsolve, qsolve +\RequirePackage{fp-upn} %upn +\RequirePackage{fp-eval} %eval + +\let\message\FP@save@message + +\DeclareOption{nomessages}{\FPmessagesfalse} +\DeclareOption{debug}{\FPdebugtrue} +\ProcessOptions + +\endinput diff --git a/Master/texmf-dist/tex/latex/fp/lfp.sty b/Master/texmf-dist/tex/latex/fp/lfp.sty new file mode 100644 index 00000000000..a560a645d6a --- /dev/null +++ b/Master/texmf-dist/tex/latex/fp/lfp.sty @@ -0,0 +1,34 @@ +%load the fp-package for LaTeX2.09 +\chardef\FPcatamp=\the\catcode`\@ +\catcode`@=11 + +\def\NeedsTeXFormat#1{} +\def\ProvidesPackage#1[#2]{} +\def\DeclareOption#1#2{} +\let\ProcessOptions\relax + +\edef\FP@loadedfiles{fp.tex} + +\def\FP@alreadyloaded#1{} +\def\FP@notyetloaded#1{ + \edef\FP@loadedfiles{\FP@loadedfiles,#1} + \input #1.sty +} +\def\RequirePackage#1{% + \let\FP@in@\FP@notyetloaded% + \edef\@tempb{#1}% + \@for\@tempa:=\FP@loadedfiles\do{% + \ifx\@tempa\@tempb% + \let\FP@in@\FP@alreadyloaded% + \fi% + }% + \FP@in@{#1}% +} + +\def\loop#1\repeat{\def\iterate{#1\relax\expandafter\iterate\fi}% + \iterate \let\iterate\relax} +\let\repeat=\fi + +\RequirePackage{fp} + +\catcode`\@=\FPcatamp |