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Filename : fp-upn.sty
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\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{}%
}