\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{}% }