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155 lines
6.1 KiB
155 lines
6.1 KiB
\NeedsTeXFormat{LaTeX2e}
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\ProvidesPackage{fp-eval}[1995/04/03]
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%version information
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\def\FP@evalversion{0.9a}
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\message{%
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`Fixed Point Calculator',%
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\space\space\space\space%
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\space\space\space\space%
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Version \FP@evalversion%
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\space(C) Michael Mehlich%
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\space\space\space\space\space\space\space%
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\space\space\space\space\space\space%
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}
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%resolve dependencies
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\RequirePackage{defpattern}
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\RequirePackage{fp-upn}
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%%%public area (macros which may be used)%%%
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\def\FPeval#1#2{\FP@eval{#1}{#2}} % #1 := eval(#2)
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%%%private fp-area (don't use these macros)%%%
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%%%%%make postfix notation from prefix/infix notation
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%%%handle constants and function applications
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%constants
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\defpattern\FP@gen@app[#2]{#2}
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%function applications from prefix to postfix
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\defpattern\FP@gen@app[add #2]{#2 add}
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\defpattern\FP@gen@app[sub #2]{#2 sub}
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\defpattern\FP@gen@app[mul #2]{#2 mul}
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\defpattern\FP@gen@app[div #2]{#2 div}
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\defpattern\FP@gen@app[abs #2]{#2 abs}
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\defpattern\FP@gen@app[neg #2]{#2 neg}
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\defpattern\FP@gen@app[sgn #2]{#2 sgn}
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\defpattern\FP@gen@app[min #2]{#2 min}
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\defpattern\FP@gen@app[max #2]{#2 max}
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\defpattern\FP@gen@app[round #2]{#2 round}
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\defpattern\FP@gen@app[trunc #2]{#2 trunc}
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\defpattern\FP@gen@app[clip #2]{#2 clip}
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\defpattern\FP@gen@app[exp #2]{#2 exp}
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\defpattern\FP@gen@app[ln #2]{#2 ln}
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\defpattern\FP@gen@app[pow #2]{#2 pow}
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\defpattern\FP@gen@app[root #2]{#2 root}
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\defpattern\FP@gen@app[seed #2]{#2 seed}
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\defpattern\FP@gen@app[random #2]{#2 random}
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\defpattern\FP@gen@app[sin #2]{#2 sin}
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\defpattern\FP@gen@app[cos #2]{#2 cos}
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\defpattern\FP@gen@app[sincos #2]{#2 sincos}
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\defpattern\FP@gen@app[tan #2]{#2 tan}
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\defpattern\FP@gen@app[cot #2]{#2 cot}
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\defpattern\FP@gen@app[tancot #2]{#2 tancot}
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\defpattern\FP@gen@app[arcsin #2]{#2 arcsin}
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\defpattern\FP@gen@app[arccos #2]{#2 arccos}
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\defpattern\FP@gen@app[arcsincos #2]{#2 arcsincos}
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\defpattern\FP@gen@app[arctan #2]{#2 arctan}
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\defpattern\FP@gen@app[arccot #2]{#2 arccot}
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\defpattern\FP@gen@app[arctancot #2]{#2 arctancot}
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\defpattern\FP@gen@app[pop #2]{#2 pop}
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\defpattern\FP@gen@app[swap #2]{#2 swap}
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\defpattern\FP@gen@app[copy #2]{#2 copy}
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\defpattern\FP@gen@app[ #2]{\FP@gen@app[#2]}
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\def\FP@gen@app@handle#1{\FP@gen@app[#1]}
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%%%handle ^, right to left
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\defpattern\FP@gen@exp[#2]{\FP@gen@app@handle{#2}}
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\defpattern\FP@gen@exp[#2^#3]{\FP@gen@exp[#3] \FP@gen@exp[#2] pow}
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\def\FP@gen@exp@handle#1{\FP@gen@exp[#1]}
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%%%handle * and /, left to right
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%handle two or more occurrences of * and /
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\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}}
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\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}}
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%split second * or / if exists
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\defpattern\FP@gen@mul@split@two@div[#2|#3|#4|#5|#6]{\FP@gen@mul@splitted[#2|#3|#4|#5|#6]}
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\defpattern\FP@gen@mul@split@two@div[#2|#3|#4/#5|#6|#7]{\FP@gen@mul@splitted[#2|#3|#4|/|#5#6#7]}
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\defpattern\FP@gen@mul@split@two[#2|/|#3]{\FP@gen@exp@handle{#2} \FP@gen@exp@handle{#3} div}
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\defpattern\FP@gen@mul@split@two[#2|*|#3]{\FP@gen@exp@handle{#2} \FP@gen@exp@handle{#3} mul}
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\defpattern\FP@gen@mul@split@two[#2|#3|#4/#5]{\FP@gen@mul@splitted[#2|#3|#4|/|#5]}
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\defpattern\FP@gen@mul@split@two[#2|#3|#4*#5]{\FP@gen@mul@split@two@div[#2|#3|#4|*|#5]}
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%split first * or / if exists
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\defpattern\FP@gen@mul@split@one@div[#2|#3|#4]{\FP@gen@mul@split@two[#2|#3|#4]}
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\defpattern\FP@gen@mul@split@one@div[#2/#3|#4|#5]{\FP@gen@mul@split@two[#2|/|#3#4#5]}
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\defpattern\FP@gen@mul@split@one[#2]{\FP@gen@exp@handle{#2}}
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\defpattern\FP@gen@mul@split@one[#2/#3]{\FP@gen@mul@split@two[#2|/|#3]}
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\defpattern\FP@gen@mul@split@one[#2*#3]{\FP@gen@mul@split@one@div[#2|*|#3]}
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%generate code for a series of * and /
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\def\FP@gen@mul@handle#1{\FP@gen@mul@split@one[#1]}
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%%%handle + and -, left to right
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%handle two or more occurrences of + and -
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\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}}
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\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}}
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%split second + or - if exists
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\defpattern\FP@gen@add@split@two@minus[#2|#3|#4|#5|#6]{\FP@gen@add@splitted[#2|#3|#4|#5|#6]}
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\defpattern\FP@gen@add@split@two@minus[#2|#3|#4-#5|#6|#7]{\FP@gen@add@splitted[#2|#3|#4|-|#5#6#7]}
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\defpattern\FP@gen@add@split@two[#2|-|#3]{\FP@gen@mul@handle{#2} \FP@gen@mul@handle{#3} sub}
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\defpattern\FP@gen@add@split@two[#2|+|#3]{\FP@gen@mul@handle{#2} \FP@gen@mul@handle{#3} add}
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\defpattern\FP@gen@add@split@two[#2|#3|#4-#5]{\FP@gen@add@splitted[#2|#3|#4|-|#5]}
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\defpattern\FP@gen@add@split@two[#2|#3|#4+#5]{\FP@gen@add@split@two@minus[#2|#3|#4|+|#5]}
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%split first + or - if exists
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\defpattern\FP@gen@add@split@one@minus[#2|#3|#4]{\FP@gen@add@split@two[#2|#3|#4]}
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\defpattern\FP@gen@add@split@one@minus[#2-#3|#4|#5]{\FP@gen@add@split@two[#2|-|#3#4#5]}
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\defpattern\FP@gen@add@split@one[#2]{\FP@gen@mul@handle{#2}}
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\defpattern\FP@gen@add@split@one[#2-#3]{\FP@gen@add@split@two[#2|-|#3]}
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\defpattern\FP@gen@add@split@one[#2+#3]{\FP@gen@add@split@one@minus[#2|+|#3]}
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%generate code for a series of + and -
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\def\FP@gen@add@handle#1{\FP@gen@add@split@one[#1]}
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%%%handle , and : as argument lists for functions with surrounding ( and )
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\defpattern\FP@gen@komma[#2]{\FP@gen@add@handle{#2}}
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\defpattern\FP@gen@komma[#2,#3]{\FP@gen@komma[#2] \FP@gen@komma[#3] }
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\defpattern\FP@gen@komma[#2:#3]{\FP@gen@komma[#2] \FP@gen@komma[#3] }
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%%%generate code for each paranthesis
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\def\FP@gen@code#1{\FP@gen@komma[#1]}
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%%%handle paranthesis
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\defpattern\FP@kl@handle@one[#2|#3|#4]{\FP@kl@handle[#2 \FP@gen@code{#3}#4]}
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\defpattern\FP@kl@handle@one[#2|#3(#4|#5]{\FP@kl@handle@one[#2(#3|#4|#5]}
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\defpattern\FP@kl@handle[#2]{\FP@gen@code{#2}}
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\defpattern\FP@kl@handle[#2(#3)#4]{%
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\FP@kl@handle@one[#2|#3|#4]%
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}
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\defpattern\FP@gen[#2]{\FP@kl@handle[#2]}
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\defpattern\FP@gen[#2(-#3]{\FP@gen[#2(0-#3]}
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\defpattern\FP@gen[#2(+#3]{\FP@gen[#2(#3]}
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\defpattern\FP@gen[#2( #3]{\FP@gen[#2(#3]}
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\def\FP@mkupn#1{%
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\expandafter\FP@gen\expandafter[#1]%
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}
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%%%%%compute expression via upn
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\def\FP@eval#1#2{%
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\FP@beginmessage{EVAL}%
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\FPupn{#1}{\FP@mkupn{#2}}%
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\FP@endmessage{}%
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}
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