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diff --git a/Master/texmf-dist/source/latex/oberdiek/bigintcalc.dtx b/Master/texmf-dist/source/latex/oberdiek/bigintcalc.dtx deleted file mode 100644 index 40fa56ed1da..00000000000 --- a/Master/texmf-dist/source/latex/oberdiek/bigintcalc.dtx +++ /dev/null @@ -1,3561 +0,0 @@ -% \iffalse meta-comment -% -% File: bigintcalc.dtx -% Version: 2016/05/16 v1.4 -% Info: Expandable calculations on big integers -% -% Copyright (C) -% 2007, 2011, 2012 Heiko Oberdiek -% 2016-2019 Oberdiek Package Support Group -% https://github.com/ho-tex/oberdiek/issues -% -% This work may be distributed and/or modified under the -% conditions of the LaTeX Project Public License, either -% version 1.3c of this license or (at your option) any later -% version. This version of this license is in -% https://www.latex-project.org/lppl/lppl-1-3c.txt -% and the latest version of this license is in -% https://www.latex-project.org/lppl.txt -% and version 1.3 or later is part of all distributions of -% LaTeX version 2005/12/01 or later. -% -% This work has the LPPL maintenance status "maintained". -% -% The Current Maintainers of this work are -% Heiko Oberdiek and the Oberdiek Package Support Group -% https://github.com/ho-tex/oberdiek/issues -% -% The Base Interpreter refers to any `TeX-Format', -% because some files are installed in TDS:tex/generic//. -% -% This work consists of the main source file bigintcalc.dtx -% and the derived files -% bigintcalc.sty, bigintcalc.pdf, bigintcalc.ins, bigintcalc.drv, -% bigintcalc-test1.tex, bigintcalc-test2.tex, -% bigintcalc-test3.tex. -% -% Distribution: -% CTAN:macros/latex/contrib/oberdiek/bigintcalc.dtx -% CTAN:macros/latex/contrib/oberdiek/bigintcalc.pdf -% -% Unpacking: -% (a) If bigintcalc.ins is present: -% tex bigintcalc.ins -% (b) Without bigintcalc.ins: -% tex bigintcalc.dtx -% (c) If you insist on using LaTeX -% latex \let\install=y\input{bigintcalc.dtx} -% (quote the arguments according to the demands of your shell) -% -% Documentation: -% (a) If bigintcalc.drv is present: -% latex bigintcalc.drv -% (b) Without bigintcalc.drv: -% latex bigintcalc.dtx; ... -% The class ltxdoc loads the configuration file ltxdoc.cfg -% if available. Here you can specify further options, e.g. -% use A4 as paper format: -% \PassOptionsToClass{a4paper}{article} -% -% Programm calls to get the documentation (example): -% pdflatex bigintcalc.dtx -% makeindex -s gind.ist bigintcalc.idx -% pdflatex bigintcalc.dtx -% makeindex -s gind.ist bigintcalc.idx -% pdflatex bigintcalc.dtx -% -% Installation: -% TDS:tex/generic/oberdiek/bigintcalc.sty -% TDS:doc/latex/oberdiek/bigintcalc.pdf -% TDS:source/latex/oberdiek/bigintcalc.dtx -% -%<*ignore> -\begingroup - \catcode123=1 % - \catcode125=2 % - \def\x{LaTeX2e}% -\expandafter\endgroup -\ifcase 0\ifx\install y1\fi\expandafter - \ifx\csname processbatchFile\endcsname\relax\else1\fi - \ifx\fmtname\x\else 1\fi\relax -\else\csname fi\endcsname -%</ignore> -%<*install> -\input docstrip.tex -\Msg{************************************************************************} -\Msg{* Installation} -\Msg{* Package: bigintcalc 2016/05/16 v1.4 Expandable calculations on big integers (HO)} -\Msg{************************************************************************} - -\keepsilent -\askforoverwritefalse - -\let\MetaPrefix\relax -\preamble - -This is a generated file. - -Project: bigintcalc -Version: 2016/05/16 v1.4 - -Copyright (C) - 2007, 2011, 2012 Heiko Oberdiek - 2016-2019 Oberdiek Package Support Group - -This work may be distributed and/or modified under the -conditions of the LaTeX Project Public License, either -version 1.3c of this license or (at your option) any later -version. This version of this license is in - https://www.latex-project.org/lppl/lppl-1-3c.txt -and the latest version of this license is in - https://www.latex-project.org/lppl.txt -and version 1.3 or later is part of all distributions of -LaTeX version 2005/12/01 or later. - -This work has the LPPL maintenance status "maintained". - -The Current Maintainers of this work are -Heiko Oberdiek and the Oberdiek Package Support Group -https://github.com/ho-tex/oberdiek/issues - - -The Base Interpreter refers to any `TeX-Format', -because some files are installed in TDS:tex/generic//. - -This work consists of the main source file bigintcalc.dtx -and the derived files - bigintcalc.sty, bigintcalc.pdf, bigintcalc.ins, bigintcalc.drv, - bigintcalc-test1.tex, bigintcalc-test2.tex, - bigintcalc-test3.tex. - -\endpreamble -\let\MetaPrefix\DoubleperCent - -\generate{% - \file{bigintcalc.ins}{\from{bigintcalc.dtx}{install}}% - \file{bigintcalc.drv}{\from{bigintcalc.dtx}{driver}}% - \usedir{tex/generic/oberdiek}% - \file{bigintcalc.sty}{\from{bigintcalc.dtx}{package}}% -% \usedir{doc/latex/oberdiek/test}% -% \file{bigintcalc-test1.tex}{\from{bigintcalc.dtx}{test1}}% -% \file{bigintcalc-test2.tex}{\from{bigintcalc.dtx}{test2,etex}}% -% \file{bigintcalc-test3.tex}{\from{bigintcalc.dtx}{test2,noetex}}% -} - -\catcode32=13\relax% active space -\let =\space% -\Msg{************************************************************************} -\Msg{*} -\Msg{* To finish the installation you have to move the following} -\Msg{* file into a directory searched by TeX:} -\Msg{*} -\Msg{* bigintcalc.sty} -\Msg{*} -\Msg{* To produce the documentation run the file `bigintcalc.drv'} -\Msg{* through LaTeX.} -\Msg{*} -\Msg{* Happy TeXing!} -\Msg{*} -\Msg{************************************************************************} - -\endbatchfile -%</install> -%<*ignore> -\fi -%</ignore> -%<*driver> -\NeedsTeXFormat{LaTeX2e} -\ProvidesFile{bigintcalc.drv}% - [2016/05/16 v1.4 Expandable calculations on big integers (HO)]% -\documentclass{ltxdoc} -\usepackage{wasysym} -\let\iint\relax -\let\iiint\relax -\usepackage[fleqn]{amsmath} - -\DeclareMathOperator{\opInv}{Inv} -\DeclareMathOperator{\opAbs}{Abs} -\DeclareMathOperator{\opSgn}{Sgn} -\DeclareMathOperator{\opMin}{Min} -\DeclareMathOperator{\opMax}{Max} -\DeclareMathOperator{\opCmp}{Cmp} -\DeclareMathOperator{\opOdd}{Odd} -\DeclareMathOperator{\opInc}{Inc} -\DeclareMathOperator{\opDec}{Dec} -\DeclareMathOperator{\opAdd}{Add} -\DeclareMathOperator{\opSub}{Sub} -\DeclareMathOperator{\opShl}{Shl} -\DeclareMathOperator{\opShr}{Shr} -\DeclareMathOperator{\opMul}{Mul} -\DeclareMathOperator{\opSqr}{Sqr} -\DeclareMathOperator{\opFac}{Fac} -\DeclareMathOperator{\opPow}{Pow} -\DeclareMathOperator{\opDiv}{Div} -\DeclareMathOperator{\opMod}{Mod} -\DeclareMathOperator{\opInt}{Int} -\DeclareMathOperator{\opODD}{ifodd} - -\newcommand*{\Def}{% - \ensuremath{% - \mathrel{\mathop{:}}=% - }% -} -\newcommand*{\op}[1]{% - \textsf{#1}% -} -\usepackage{holtxdoc}[2011/11/22] -\begin{document} - \DocInput{bigintcalc.dtx}% -\end{document} -%</driver> -% \fi -% -% -% -% \GetFileInfo{bigintcalc.drv} -% -% \title{The \xpackage{bigintcalc} package} -% \date{2016/05/16 v1.4} -% \author{Heiko Oberdiek\thanks -% {Please report any issues at \url{https://github.com/ho-tex/oberdiek/issues}}} -% -% \maketitle -% -% \begin{abstract} -% This package provides expandable arithmetic operations -% with big integers that can exceed \TeX's number limits. -% \end{abstract} -% -% \tableofcontents -% -% \section{Documentation} -% -% \subsection{Introduction} -% -% Package \xpackage{bigintcalc} defines arithmetic operations -% that deal with big integers. Big integers can be given -% either as explicit integer number or as macro code -% that expands to an explicit number. \emph{Big} means that -% there is no limit on the size of the number. Big integers -% may exceed \TeX's range limitation of -2147483647 and 2147483647. -% Only memory issues will limit the usable range. -% -% In opposite to package \xpackage{intcalc} -% unexpandable command tokens are not supported, even if -% they are valid \TeX\ numbers like count registers or -% commands created by \cs{chardef}. Nevertheless they may -% be used, if they are prefixed by \cs{number}. -% -% Also \eTeX's \cs{numexpr} expressions are not supported -% directly in the manner of package \xpackage{intcalc}. -% However they can be given if \cs{the}\cs{numexpr} -% or \cs{number}\cs{numexpr} are used. -% -% The operations have the form of macros that take one or -% two integers as parameter and return the integer result. -% The macro name is a three letter operation name prefixed -% by the package name, e.g. \cs{bigintcalcAdd}|{10}{43}| returns -% |53|. -% -% The macros are fully expandable, exactly two expansion -% steps generate the result. Therefore the operations -% may be used nearly everywhere in \TeX, even inside -% \cs{csname}, file names, or other -% expandable contexts. -% -% \subsection{Conditions} -% -% \subsubsection{Preconditions} -% -% \begin{itemize} -% \item -% Arguments can be anything that expands to a number that consists -% of optional signs and digits. -% \item -% The arguments and return values must be sound. -% Zero as divisor or factorials of negative numbers will cause errors. -% \end{itemize} -% -% \subsubsection{Postconditions} -% -% Additional properties of the macros apart from calculating -% a correct result (of course \smiley): -% \begin{itemize} -% \item -% The macros are fully expandable. Thus they can -% be used inside \cs{edef}, \cs{csname}, -% for example. -% \item -% Furthermore exactly two expansion steps calculate the result. -% \item -% The number consists of one optional minus sign and one or more -% digits. The first digit is larger than zero for -% numbers that consists of more than one digit. -% -% In short, the number format is exactly the same as -% \cs{number} generates, but without its range limitation. -% And the tokens (minus sign, digits) -% have catcode 12 (other). -% \item -% Call by value is simulated. First the arguments are -% converted to numbers. Then these numbers are used -% in the calculations. -% -% Remember that arguments -% may contain expensive macros or \eTeX\ expressions. -% This strategy avoids multiple evaluations of such -% arguments. -% \end{itemize} -% -% \subsection{Error handling} -% -% Some errors are detected by the macros, example: division by zero. -% In this cases an undefined control sequence is called and causes -% a TeX error message, example: \cs{BigIntCalcError:DivisionByZero}. -% The name of the control sequence contains -% the reason for the error. The \TeX\ error may be ignored. -% Then the operation returns zero as result. -% Because the macros are supposed to work in expandible contexts. -% An traditional error message, however, is not expandable and -% would break these contexts. -% -% \subsection{Operations} -% -% Some definition equations below use the function $\opInt$ -% that converts a real number to an integer. The number -% is truncated that means rounding to zero: -% \begin{gather*} -% \opInt(x) \Def -% \begin{cases} -% \lfloor x\rfloor & \text{if $x\geq0$}\\ -% \lceil x\rceil & \text{otherwise} -% \end{cases} -% \end{gather*} -% -% \subsubsection{\op{Num}} -% -% \begin{declcs}{bigintcalcNum} \M{x} -% \end{declcs} -% Macro \cs{bigintcalcNum} converts its argument to a normalized integer -% number without unnecessary leading zeros or signs. -% The result matches the regular expression: -%\begin{quote} -%\begin{verbatim} -%0|-?[1-9][0-9]* -%\end{verbatim} -%\end{quote} -% -% \subsubsection{\op{Inv}, \op{Abs}, \op{Sgn}} -% -% \begin{declcs}{bigintcalcInv} \M{x} -% \end{declcs} -% Macro \cs{bigintcalcInv} switches the sign. -% \begin{gather*} -% \opInv(x) \Def -x -% \end{gather*} -% -% \begin{declcs}{bigintcalcAbs} \M{x} -% \end{declcs} -% Macro \cs{bigintcalcAbs} returns the absolute value -% of integer \meta{x}. -% \begin{gather*} -% \opAbs(x) \Def \vert x\vert -% \end{gather*} -% -% \begin{declcs}{bigintcalcSgn} \M{x} -% \end{declcs} -% Macro \cs{bigintcalcSgn} encodes the sign of \meta{x} as number. -% \begin{gather*} -% \opSgn(x) \Def -% \begin{cases} -% -1& \text{if $x<0$}\\ -% 0& \text{if $x=0$}\\ -% 1& \text{if $x>0$} -% \end{cases} -% \end{gather*} -% These return values can easily be distinguished by \cs{ifcase}: -%\begin{quote} -%\begin{verbatim} -%\ifcase\bigintcalcSgn{<x>} -% $x=0$ -%\or -% $x>0$ -%\else -% $x<0$ -%\fi -%\end{verbatim} -%\end{quote} -% -% \subsubsection{\op{Min}, \op{Max}, \op{Cmp}} -% -% \begin{declcs}{bigintcalcMin} \M{x} \M{y} -% \end{declcs} -% Macro \cs{bigintcalcMin} returns the smaller of the two integers. -% \begin{gather*} -% \opMin(x,y) \Def -% \begin{cases} -% x & \text{if $x<y$}\\ -% y & \text{otherwise} -% \end{cases} -% \end{gather*} -% -% \begin{declcs}{bigintcalcMax} \M{x} \M{y} -% \end{declcs} -% Macro \cs{bigintcalcMax} returns the larger of the two integers. -% \begin{gather*} -% \opMax(x,y) \Def -% \begin{cases} -% x & \text{if $x>y$}\\ -% y & \text{otherwise} -% \end{cases} -% \end{gather*} -% -% \begin{declcs}{bigintcalcCmp} \M{x} \M{y} -% \end{declcs} -% Macro \cs{bigintcalcCmp} encodes the comparison result as number: -% \begin{gather*} -% \opCmp(x,y) \Def -% \begin{cases} -% -1 & \text{if $x<y$}\\ -% 0 & \text{if $x=y$}\\ -% 1 & \text{if $x>y$} -% \end{cases} -% \end{gather*} -% These values can be distinguished by \cs{ifcase}: -%\begin{quote} -%\begin{verbatim} -%\ifcase\bigintcalcCmp{<x>}{<y>} -% $x=y$ -%\or -% $x>y$ -%\else -% $x<y$ -%\fi -%\end{verbatim} -%\end{quote} -% -% \subsubsection{\op{Odd}} -% -% \begin{declcs}{bigintcalcOdd} \M{x} -% \end{declcs} -% \begin{gather*} -% \opOdd(x) \Def -% \begin{cases} -% 1 & \text{if $x$ is odd}\\ -% 0 & \text{if $x$ is even} -% \end{cases} -% \end{gather*} -% -% \subsubsection{\op{Inc}, \op{Dec}, \op{Add}, \op{Sub}} -% -% \begin{declcs}{bigintcalcInc} \M{x} -% \end{declcs} -% Macro \cs{bigintcalcInc} increments \meta{x} by one. -% \begin{gather*} -% \opInc(x) \Def x + 1 -% \end{gather*} -% -% \begin{declcs}{bigintcalcDec} \M{x} -% \end{declcs} -% Macro \cs{bigintcalcDec} decrements \meta{x} by one. -% \begin{gather*} -% \opDec(x) \Def x - 1 -% \end{gather*} -% -% \begin{declcs}{bigintcalcAdd} \M{x} \M{y} -% \end{declcs} -% Macro \cs{bigintcalcAdd} adds the two numbers. -% \begin{gather*} -% \opAdd(x, y) \Def x + y -% \end{gather*} -% -% \begin{declcs}{bigintcalcSub} \M{x} \M{y} -% \end{declcs} -% Macro \cs{bigintcalcSub} calculates the difference. -% \begin{gather*} -% \opSub(x, y) \Def x - y -% \end{gather*} -% -% \subsubsection{\op{Shl}, \op{Shr}} -% -% \begin{declcs}{bigintcalcShl} \M{x} -% \end{declcs} -% Macro \cs{bigintcalcShl} implements shifting to the left that -% means the number is multiplied by two. -% The sign is preserved. -% \begin{gather*} -% \opShl(x) \Def x*2 -% \end{gather*} -% -% \begin{declcs}{bigintcalcShr} \M{x} -% \end{declcs} -% Macro \cs{bigintcalcShr} implements shifting to the right. -% That is equivalent to an integer division by two. -% The sign is preserved. -% \begin{gather*} -% \opShr(x) \Def \opInt(x/2) -% \end{gather*} -% -% \subsubsection{\op{Mul}, \op{Sqr}, \op{Fac}, \op{Pow}} -% -% \begin{declcs}{bigintcalcMul} \M{x} \M{y} -% \end{declcs} -% Macro \cs{bigintcalcMul} calculates the product of -% \meta{x} and \meta{y}. -% \begin{gather*} -% \opMul(x,y) \Def x*y -% \end{gather*} -% -% \begin{declcs}{bigintcalcSqr} \M{x} -% \end{declcs} -% Macro \cs{bigintcalcSqr} returns the square product. -% \begin{gather*} -% \opSqr(x) \Def x^2 -% \end{gather*} -% -% \begin{declcs}{bigintcalcFac} \M{x} -% \end{declcs} -% Macro \cs{bigintcalcFac} returns the factorial of \meta{x}. -% Negative numbers are not permitted. -% \begin{gather*} -% \opFac(x) \Def x!\qquad\text{for $x\geq0$} -% \end{gather*} -% ($0! = 1$) -% -% \begin{declcs}{bigintcalcPow} M{x} M{y} -% \end{declcs} -% Macro \cs{bigintcalcPow} calculates the value of \meta{x} to the -% power of \meta{y}. The error ``division by zero'' is thrown -% if \meta{x} is zero and \meta{y} is negative. -% permitted: -% \begin{gather*} -% \opPow(x,y) \Def -% \opInt(x^y)\qquad\text{for $x\neq0$ or $y\geq0$} -% \end{gather*} -% ($0^0 = 1$) -% -% \subsubsection{\op{Div}, \op{Mul}} -% -% \begin{declcs}{bigintcalcDiv} \M{x} \M{y} -% \end{declcs} -% Macro \cs{bigintcalcDiv} performs an integer division. -% Argument \meta{y} must not be zero. -% \begin{gather*} -% \opDiv(x,y) \Def \opInt(x/y)\qquad\text{for $y\neq0$} -% \end{gather*} -% -% \begin{declcs}{bigintcalcMod} \M{x} \M{y} -% \end{declcs} -% Macro \cs{bigintcalcMod} gets the remainder of the integer -% division. The sign follows the divisor \meta{y}. -% Argument \meta{y} must not be zero. -% \begin{gather*} -% \opMod(x,y) \Def x\mathrel{\%}y\qquad\text{for $y\neq0$} -% \end{gather*} -% The result ranges: -% \begin{gather*} -% -\vert y\vert < \opMod(x,y) \leq 0\qquad\text{for $y<0$}\\ -% 0 \leq \opMod(x,y) < y\qquad\text{for $y\geq0$} -% \end{gather*} -% -% \subsection{Interface for programmers} -% -% If the programmer can ensure some more properties about -% the arguments of the operations, then the following -% macros are a little more efficient. -% -% In general numbers must obey the following constraints: -% \begin{itemize} -% \item Plain number: digit tokens only, no command tokens. -% \item Non-negative. Signs are forbidden. -% \item Delimited by exclamation mark. Curly braces -% around the number are not allowed and will -% break the code. -% \end{itemize} -% -% \begin{declcs}{BigIntCalcOdd} \meta{number} |!| -% \end{declcs} -% |1|/|0| is returned if \meta{number} is odd/even. -% -% \begin{declcs}{BigIntCalcInc} \meta{number} |!| -% \end{declcs} -% Incrementation. -% -% \begin{declcs}{BigIntCalcDec} \meta{number} |!| -% \end{declcs} -% Decrementation, positive number without zero. -% -% \begin{declcs}{BigIntCalcAdd} \meta{number A} |!| \meta{number B} |!| -% \end{declcs} -% Addition, $A\geq B$. -% -% \begin{declcs}{BigIntCalcSub} \meta{number A} |!| \meta{number B} |!| -% \end{declcs} -% Subtraction, $A\geq B$. -% -% \begin{declcs}{BigIntCalcShl} \meta{number} |!| -% \end{declcs} -% Left shift (multiplication with two). -% -% \begin{declcs}{BigIntCalcShr} \meta{number} |!| -% \end{declcs} -% Right shift (integer division by two). -% -% \begin{declcs}{BigIntCalcMul} \meta{number A} |!| \meta{number B} |!| -% \end{declcs} -% Multiplication, $A\geq B$. -% -% \begin{declcs}{BigIntCalcDiv} \meta{number A} |!| \meta{number B} |!| -% \end{declcs} -% Division operation. -% -% \begin{declcs}{BigIntCalcMod} \meta{number A} |!| \meta{number B} |!| -% \end{declcs} -% Modulo operation. -% -% -% \StopEventually{ -% } -% -% \section{Implementation} -% -% \begin{macrocode} -%<*package> -% \end{macrocode} -% -% \subsection{Reload check and package identification} -% Reload check, especially if the package is not used with \LaTeX. -% \begin{macrocode} -\begingroup\catcode61\catcode48\catcode32=10\relax% - \catcode13=5 % ^^M - \endlinechar=13 % - \catcode35=6 % # - \catcode39=12 % ' - \catcode44=12 % , - \catcode45=12 % - - \catcode46=12 % . - \catcode58=12 % : - \catcode64=11 % @ - \catcode123=1 % { - \catcode125=2 % } - \expandafter\let\expandafter\x\csname ver@bigintcalc.sty\endcsname - \ifx\x\relax % plain-TeX, first loading - \else - \def\empty{}% - \ifx\x\empty % LaTeX, first loading, - % variable is initialized, but \ProvidesPackage not yet seen - \else - \expandafter\ifx\csname PackageInfo\endcsname\relax - \def\x#1#2{% - \immediate\write-1{Package #1 Info: #2.}% - }% - \else - \def\x#1#2{\PackageInfo{#1}{#2, stopped}}% - \fi - \x{bigintcalc}{The package is already loaded}% - \aftergroup\endinput - \fi - \fi -\endgroup% -% \end{macrocode} -% Package identification: -% \begin{macrocode} -\begingroup\catcode61\catcode48\catcode32=10\relax% - \catcode13=5 % ^^M - \endlinechar=13 % - \catcode35=6 % # - \catcode39=12 % ' - \catcode40=12 % ( - \catcode41=12 % ) - \catcode44=12 % , - \catcode45=12 % - - \catcode46=12 % . - \catcode47=12 % / - \catcode58=12 % : - \catcode64=11 % @ - \catcode91=12 % [ - \catcode93=12 % ] - \catcode123=1 % { - \catcode125=2 % } - \expandafter\ifx\csname ProvidesPackage\endcsname\relax - \def\x#1#2#3[#4]{\endgroup - \immediate\write-1{Package: #3 #4}% - \xdef#1{#4}% - }% - \else - \def\x#1#2[#3]{\endgroup - #2[{#3}]% - \ifx#1\@undefined - \xdef#1{#3}% - \fi - \ifx#1\relax - \xdef#1{#3}% - \fi - }% - \fi -\expandafter\x\csname ver@bigintcalc.sty\endcsname -\ProvidesPackage{bigintcalc}% - [2016/05/16 v1.4 Expandable calculations on big integers (HO)]% -% \end{macrocode} -% -% \subsection{Catcodes} -% -% \begin{macrocode} -\begingroup\catcode61\catcode48\catcode32=10\relax% - \catcode13=5 % ^^M - \endlinechar=13 % - \catcode123=1 % { - \catcode125=2 % } - \catcode64=11 % @ - \def\x{\endgroup - \expandafter\edef\csname BIC@AtEnd\endcsname{% - \endlinechar=\the\endlinechar\relax - \catcode13=\the\catcode13\relax - \catcode32=\the\catcode32\relax - \catcode35=\the\catcode35\relax - \catcode61=\the\catcode61\relax - \catcode64=\the\catcode64\relax - \catcode123=\the\catcode123\relax - \catcode125=\the\catcode125\relax - }% - }% -\x\catcode61\catcode48\catcode32=10\relax% -\catcode13=5 % ^^M -\endlinechar=13 % -\catcode35=6 % # -\catcode64=11 % @ -\catcode123=1 % { -\catcode125=2 % } -\def\TMP@EnsureCode#1#2{% - \edef\BIC@AtEnd{% - \BIC@AtEnd - \catcode#1=\the\catcode#1\relax - }% - \catcode#1=#2\relax -} -\TMP@EnsureCode{33}{12}% ! -\TMP@EnsureCode{36}{14}% $ (comment!) -\TMP@EnsureCode{38}{14}% & (comment!) -\TMP@EnsureCode{40}{12}% ( -\TMP@EnsureCode{41}{12}% ) -\TMP@EnsureCode{42}{12}% * -\TMP@EnsureCode{43}{12}% + -\TMP@EnsureCode{45}{12}% - -\TMP@EnsureCode{46}{12}% . -\TMP@EnsureCode{47}{12}% / -\TMP@EnsureCode{58}{11}% : (letter!) -\TMP@EnsureCode{60}{12}% < -\TMP@EnsureCode{62}{12}% > -\TMP@EnsureCode{63}{14}% ? (comment!) -\TMP@EnsureCode{91}{12}% [ -\TMP@EnsureCode{93}{12}% ] -\edef\BIC@AtEnd{\BIC@AtEnd\noexpand\endinput} -\begingroup\expandafter\expandafter\expandafter\endgroup -\expandafter\ifx\csname BIC@TestMode\endcsname\relax -\else - \catcode63=9 % ? (ignore) -\fi -? \let\BIC@@TestMode\BIC@TestMode -% \end{macrocode} -% -% \subsection{\eTeX\ detection} -% -% \begin{macrocode} -\begingroup\expandafter\expandafter\expandafter\endgroup -\expandafter\ifx\csname numexpr\endcsname\relax - \catcode36=9 % $ (ignore) -\else - \catcode38=9 % & (ignore) -\fi -% \end{macrocode} -% -% \subsection{Help macros} -% -% \begin{macro}{\BIC@Fi} -% \begin{macrocode} -\let\BIC@Fi\fi -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@AfterFi} -% \begin{macrocode} -\def\BIC@AfterFi#1#2\BIC@Fi{\fi#1}% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@AfterFiFi} -% \begin{macrocode} -\def\BIC@AfterFiFi#1#2\BIC@Fi{\fi\fi#1}% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@AfterFiFiFi} -% \begin{macrocode} -\def\BIC@AfterFiFiFi#1#2\BIC@Fi{\fi\fi\fi#1}% -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\BIC@Space} -% \begin{macrocode} -\begingroup - \def\x#1{\endgroup - \let\BIC@Space= #1% - }% -\x{ } -% \end{macrocode} -% \end{macro} -% -% \subsection{Expand number} -% -% \begin{macrocode} -\begingroup\expandafter\expandafter\expandafter\endgroup -\expandafter\ifx\csname RequirePackage\endcsname\relax - \def\TMP@RequirePackage#1[#2]{% - \begingroup\expandafter\expandafter\expandafter\endgroup - \expandafter\ifx\csname ver@#1.sty\endcsname\relax - \input #1.sty\relax - \fi - }% - \TMP@RequirePackage{pdftexcmds}[2007/11/11]% -\else - \RequirePackage{pdftexcmds}[2007/11/11]% -\fi -% \end{macrocode} -% -% \begin{macrocode} -\begingroup\expandafter\expandafter\expandafter\endgroup -\expandafter\ifx\csname pdf@escapehex\endcsname\relax -% \end{macrocode} -% -% \begin{macro}{\BIC@Expand} -% \begin{macrocode} - \def\BIC@Expand#1{% - \romannumeral0% - \BIC@@Expand#1!\@nil{}% - }% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@Expand} -% \begin{macrocode} - \def\BIC@@Expand#1#2\@nil#3{% - \expandafter\ifcat\noexpand#1\relax - \expandafter\@firstoftwo - \else - \expandafter\@secondoftwo - \fi - {% - \expandafter\BIC@@Expand#1#2\@nil{#3}% - }{% - \ifx#1!% - \expandafter\@firstoftwo - \else - \expandafter\@secondoftwo - \fi - { #3}{% - \BIC@@Expand#2\@nil{#3#1}% - }% - }% - }% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\@firstoftwo} -% \begin{macrocode} - \expandafter\ifx\csname @firstoftwo\endcsname\relax - \long\def\@firstoftwo#1#2{#1}% - \fi -% \end{macrocode} -% \end{macro} -% \begin{macro}{\@secondoftwo} -% \begin{macrocode} - \expandafter\ifx\csname @secondoftwo\endcsname\relax - \long\def\@secondoftwo#1#2{#2}% - \fi -% \end{macrocode} -% \end{macro} -% -% \begin{macrocode} -\else -% \end{macrocode} -% \begin{macro}{\BIC@Expand} -% \begin{macrocode} - \def\BIC@Expand#1{% - \romannumeral0\expandafter\expandafter\expandafter\BIC@Space - \pdf@unescapehex{% - \expandafter\expandafter\expandafter - \BIC@StripHexSpace\pdf@escapehex{#1}20\@nil - }% - }% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@StripHexSpace} -% \begin{macrocode} - \def\BIC@StripHexSpace#120#2\@nil{% - #1% - \ifx\\#2\\% - \else - \BIC@AfterFi{% - \BIC@StripHexSpace#2\@nil - }% - \BIC@Fi - }% -% \end{macrocode} -% \end{macro} -% \begin{macrocode} -\fi -% \end{macrocode} -% -% \subsection{Normalize expanded number} -% -% \begin{macro}{\BIC@Normalize} -% |#1|: result sign\\ -% |#2|: first token of number -% \begin{macrocode} -\def\BIC@Normalize#1#2{% - \ifx#2-% - \ifx\\#1\\% - \BIC@AfterFiFi{% - \BIC@Normalize-% - }% - \else - \BIC@AfterFiFi{% - \BIC@Normalize{}% - }% - \fi - \else - \ifx#2+% - \BIC@AfterFiFi{% - \BIC@Normalize{#1}% - }% - \else - \ifx#20% - \BIC@AfterFiFiFi{% - \BIC@NormalizeZero{#1}% - }% - \else - \BIC@AfterFiFiFi{% - \BIC@NormalizeDigits#1#2% - }% - \fi - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@NormalizeZero} -% \begin{macrocode} -\def\BIC@NormalizeZero#1#2{% - \ifx#2!% - \BIC@AfterFi{ 0}% - \else - \ifx#20% - \BIC@AfterFiFi{% - \BIC@NormalizeZero{#1}% - }% - \else - \BIC@AfterFiFi{% - \BIC@NormalizeDigits#1#2% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@NormalizeDigits} -% \begin{macrocode} -\def\BIC@NormalizeDigits#1!{ #1} -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Num}} -% -% \begin{macro}{\bigintcalcNum} -% \begin{macrocode} -\def\bigintcalcNum#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Normalize - \expandafter\expandafter\expandafter{% - \expandafter\expandafter\expandafter}% - \BIC@Expand{#1}!% -} -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Inv}, \op{Abs}, \op{Sgn}} -% -% -% \begin{macro}{\bigintcalcInv} -% \begin{macrocode} -\def\bigintcalcInv#1{% - \romannumeral0\expandafter\expandafter\expandafter\BIC@Space - \bigintcalcNum{-#1}% -} -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\bigintcalcAbs} -% \begin{macrocode} -\def\bigintcalcAbs#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Abs - \bigintcalcNum{#1}% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Abs} -% \begin{macrocode} -\def\BIC@Abs#1{% - \ifx#1-% - \expandafter\BIC@Space - \else - \expandafter\BIC@Space - \expandafter#1% - \fi -} -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\bigintcalcSgn} -% \begin{macrocode} -\def\bigintcalcSgn#1{% - \number - \expandafter\expandafter\expandafter\BIC@Sgn - \bigintcalcNum{#1}! % -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Sgn} -% \begin{macrocode} -\def\BIC@Sgn#1#2!{% - \ifx#1-% - -1% - \else - \ifx#10% - 0% - \else - 1% - \fi - \fi -} -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Cmp}, \op{Min}, \op{Max}} -% -% \begin{macro}{\bigintcalcCmp} -% \begin{macrocode} -\def\bigintcalcCmp#1#2{% - \number - \expandafter\expandafter\expandafter\BIC@Cmp - \bigintcalcNum{#2}!{#1}% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Cmp} -% \begin{macrocode} -\def\BIC@Cmp#1!#2{% - \expandafter\expandafter\expandafter\BIC@@Cmp - \bigintcalcNum{#2}!#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@Cmp} -% \begin{macrocode} -\def\BIC@@Cmp#1#2!#3#4!{% - \ifx#1-% - \ifx#3-% - \BIC@AfterFiFi{% - \BIC@@Cmp#4!#2!% - }% - \else - \BIC@AfterFiFi{% - -1 % - }% - \fi - \else - \ifx#3-% - \BIC@AfterFiFi{% - 1 % - }% - \else - \BIC@AfterFiFi{% - \BIC@CmpLength#1#2!#3#4!#1#2!#3#4!% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@PosCmp} -% \begin{macrocode} -\def\BIC@PosCmp#1!#2!{% - \BIC@CmpLength#1!#2!#1!#2!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@CmpLength} -% \begin{macrocode} -\def\BIC@CmpLength#1#2!#3#4!{% - \ifx\\#2\\% - \ifx\\#4\\% - \BIC@AfterFiFi\BIC@CmpDiff - \else - \BIC@AfterFiFi{% - \BIC@CmpResult{-1}% - }% - \fi - \else - \ifx\\#4\\% - \BIC@AfterFiFi{% - \BIC@CmpResult1% - }% - \else - \BIC@AfterFiFi{% - \BIC@CmpLength#2!#4!% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@CmpResult} -% \begin{macrocode} -\def\BIC@CmpResult#1#2!#3!{#1 } -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@CmpDiff} -% \begin{macrocode} -\def\BIC@CmpDiff#1#2!#3#4!{% - \ifnum#1<#3 % - \BIC@AfterFi{% - -1 % - }% - \else - \ifnum#1>#3 % - \BIC@AfterFiFi{% - 1 % - }% - \else - \ifx\\#2\\% - \BIC@AfterFiFiFi{% - 0 % - }% - \else - \BIC@AfterFiFiFi{% - \BIC@CmpDiff#2!#4!% - }% - \fi - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\bigintcalcMin} -% \begin{macrocode} -\def\bigintcalcMin#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@MinMax - \bigintcalcNum{#1}!-!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\bigintcalcMax} -% \begin{macrocode} -\def\bigintcalcMax#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@MinMax - \bigintcalcNum{#1}!!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@MinMax} -% |#1|: $x$\\ -% |#2|: sign for comparison\\ -% |#3|: $y$ -% \begin{macrocode} -\def\BIC@MinMax#1!#2!#3{% - \expandafter\expandafter\expandafter\BIC@@MinMax - \bigintcalcNum{#3}!#1!#2!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@MinMax} -% |#1|: $y$\\ -% |#2|: $x$\\ -% |#3|: sign for comparison -% \begin{macrocode} -\def\BIC@@MinMax#1!#2!#3!{% - \ifnum\BIC@@Cmp#1!#2!=#31 % - \BIC@AfterFi{ #1}% - \else - \BIC@AfterFi{ #2}% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Odd}} -% -% \begin{macro}{\bigintcalcOdd} -% \begin{macrocode} -\def\bigintcalcOdd#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Odd - \bigintcalcAbs{#1}!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BigIntCalcOdd} -% \begin{macrocode} -\def\BigIntCalcOdd#1!{% - \romannumeral0% - \BIC@Odd#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Odd} -% |#1|: $x$ -% \begin{macrocode} -\def\BIC@Odd#1#2{% - \ifx#2!% - \ifodd#1 % - \BIC@AfterFiFi{ 1}% - \else - \BIC@AfterFiFi{ 0}% - \fi - \else - \expandafter\BIC@Odd\expandafter#2% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Inc}, \op{Dec}} -% -% \begin{macro}{\bigintcalcInc} -% \begin{macrocode} -\def\bigintcalcInc#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@IncSwitch - \bigintcalcNum{#1}!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@IncSwitch} -% \begin{macrocode} -\def\BIC@IncSwitch#1#2!{% - \ifcase\BIC@@Cmp#1#2!-1!% - \BIC@AfterFi{ 0}% - \or - \BIC@AfterFi{% - \BIC@Inc#1#2!{}% - }% - \else - \BIC@AfterFi{% - \expandafter-\romannumeral0% - \BIC@Dec#2!{}% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\bigintcalcDec} -% \begin{macrocode} -\def\bigintcalcDec#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@DecSwitch - \bigintcalcNum{#1}!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@DecSwitch} -% \begin{macrocode} -\def\BIC@DecSwitch#1#2!{% - \ifcase\BIC@Sgn#1#2! % - \BIC@AfterFi{ -1}% - \or - \BIC@AfterFi{% - \BIC@Dec#1#2!{}% - }% - \else - \BIC@AfterFi{% - \expandafter-\romannumeral0% - \BIC@Inc#2!{}% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\BigIntCalcInc} -% \begin{macrocode} -\def\BigIntCalcInc#1!{% - \romannumeral0\BIC@Inc#1!{}% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BigIntCalcDec} -% \begin{macrocode} -\def\BigIntCalcDec#1!{% - \romannumeral0\BIC@Dec#1!{}% -} -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\BIC@Inc} -% \begin{macrocode} -\def\BIC@Inc#1#2!#3{% - \ifx\\#2\\% - \BIC@AfterFi{% - \BIC@@Inc1#1#3!{}% - }% - \else - \BIC@AfterFi{% - \BIC@Inc#2!{#1#3}% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@Inc} -% \begin{macrocode} -\def\BIC@@Inc#1#2#3!#4{% - \ifcase#1 % - \ifx\\#3\\% - \BIC@AfterFiFi{ #2#4}% - \else - \BIC@AfterFiFi{% - \BIC@@Inc0#3!{#2#4}% - }% - \fi - \else - \ifnum#2<9 % - \BIC@AfterFiFi{% -& \expandafter\BIC@@@Inc\the\numexpr#2+1\relax -$ \expandafter\expandafter\expandafter\BIC@@@Inc -$ \ifcase#2 \expandafter1% -$ \or\expandafter2% -$ \or\expandafter3% -$ \or\expandafter4% -$ \or\expandafter5% -$ \or\expandafter6% -$ \or\expandafter7% -$ \or\expandafter8% -$ \or\expandafter9% -$? \else\BigIntCalcError:ThisCannotHappen% -$ \fi - 0#3!{#4}% - }% - \else - \BIC@AfterFiFi{% - \BIC@@@Inc01#3!{#4}% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@@Inc} -% \begin{macrocode} -\def\BIC@@@Inc#1#2#3!#4{% - \ifx\\#3\\% - \ifnum#2=1 % - \BIC@AfterFiFi{ 1#1#4}% - \else - \BIC@AfterFiFi{ #1#4}% - \fi - \else - \BIC@AfterFi{% - \BIC@@Inc#2#3!{#1#4}% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\BIC@Dec} -% \begin{macrocode} -\def\BIC@Dec#1#2!#3{% - \ifx\\#2\\% - \BIC@AfterFi{% - \BIC@@Dec1#1#3!{}% - }% - \else - \BIC@AfterFi{% - \BIC@Dec#2!{#1#3}% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@Dec} -% \begin{macrocode} -\def\BIC@@Dec#1#2#3!#4{% - \ifcase#1 % - \ifx\\#3\\% - \BIC@AfterFiFi{ #2#4}% - \else - \BIC@AfterFiFi{% - \BIC@@Dec0#3!{#2#4}% - }% - \fi - \else - \ifnum#2>0 % - \BIC@AfterFiFi{% -& \expandafter\BIC@@@Dec\the\numexpr#2-1\relax -$ \expandafter\expandafter\expandafter\BIC@@@Dec -$ \ifcase#2 -$? \BigIntCalcError:ThisCannotHappen% -$ \or\expandafter0% -$ \or\expandafter1% -$ \or\expandafter2% -$ \or\expandafter3% -$ \or\expandafter4% -$ \or\expandafter5% -$ \or\expandafter6% -$ \or\expandafter7% -$ \or\expandafter8% -$? \else\BigIntCalcError:ThisCannotHappen% -$ \fi - 0#3!{#4}% - }% - \else - \BIC@AfterFiFi{% - \BIC@@@Dec91#3!{#4}% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@@Dec} -% \begin{macrocode} -\def\BIC@@@Dec#1#2#3!#4{% - \ifx\\#3\\% - \ifcase#1 % - \ifx\\#4\\% - \BIC@AfterFiFiFi{ 0}% - \else - \BIC@AfterFiFiFi{ #4}% - \fi - \else - \BIC@AfterFiFi{ #1#4}% - \fi - \else - \BIC@AfterFi{% - \BIC@@Dec#2#3!{#1#4}% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Add}, \op{Sub}} -% -% \begin{macro}{\bigintcalcAdd} -% \begin{macrocode} -\def\bigintcalcAdd#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Add - \bigintcalcNum{#1}!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Add} -% \begin{macrocode} -\def\BIC@Add#1!#2{% - \expandafter\expandafter\expandafter - \BIC@AddSwitch\bigintcalcNum{#2}!#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\bigintcalcSub} -% \begin{macrocode} -\def\bigintcalcSub#1#2{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Add - \bigintcalcNum{-#2}!{#1}% -} -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\BIC@AddSwitch} -% Decision table for \cs{BIC@AddSwitch}. -% \begin{quote} -% \begin{tabular}[t]{@{}|l|l|l|l|l|@{}} -% \hline -% $x<0$ & $y<0$ & $-x>-y$ & $-$ & $\opAdd(-x,-y)$\\ -% \cline{3-3}\cline{5-5} -% & & else & & $\opAdd(-y,-x)$\\ -% \cline{2-5} -% & else & $-x> y$ & $-$ & $\opSub(-x, y)$\\ -% \cline{3-5} -% & & $-x= y$ & & $0$\\ -% \cline{3-5} -% & & else & $+$ & $\opSub( y,-x)$\\ -% \hline -% else & $y<0$ & $ x>-y$ & $+$ & $\opSub( x,-y)$\\ -% \cline{3-5} -% & & $ x=-y$ & & $0$\\ -% \cline{3-5} -% & & else & $-$ & $\opSub(-y, x)$\\ -% \cline{2-5} -% & else & $ x> y$ & $+$ & $\opAdd( x, y)$\\ -% \cline{3-3}\cline{5-5} -% & & else & & $\opAdd( y, x)$\\ -% \hline -% \end{tabular} -% \end{quote} -% \begin{macrocode} -\def\BIC@AddSwitch#1#2!#3#4!{% - \ifx#1-% x < 0 - \ifx#3-% y < 0 - \expandafter-\romannumeral0% - \ifnum\BIC@PosCmp#2!#4!=1 % -x > -y - \BIC@AfterFiFiFi{% - \BIC@AddXY#2!#4!!!% - }% - \else % -x <= -y - \BIC@AfterFiFiFi{% - \BIC@AddXY#4!#2!!!% - }% - \fi - \else % y >= 0 - \ifcase\BIC@PosCmp#2!#3#4!% -x = y - \BIC@AfterFiFiFi{ 0}% - \or % -x > y - \expandafter-\romannumeral0% - \BIC@AfterFiFiFi{% - \BIC@SubXY#2!#3#4!!!% - }% - \else % -x <= y - \BIC@AfterFiFiFi{% - \BIC@SubXY#3#4!#2!!!% - }% - \fi - \fi - \else % x >= 0 - \ifx#3-% y < 0 - \ifcase\BIC@PosCmp#1#2!#4!% x = -y - \BIC@AfterFiFiFi{ 0}% - \or % x > -y - \BIC@AfterFiFiFi{% - \BIC@SubXY#1#2!#4!!!% - }% - \else % x <= -y - \expandafter-\romannumeral0% - \BIC@AfterFiFiFi{% - \BIC@SubXY#4!#1#2!!!% - }% - \fi - \else % y >= 0 - \ifnum\BIC@PosCmp#1#2!#3#4!=1 % x > y - \BIC@AfterFiFiFi{% - \BIC@AddXY#1#2!#3#4!!!% - }% - \else % x <= y - \BIC@AfterFiFiFi{% - \BIC@AddXY#3#4!#1#2!!!% - }% - \fi - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\BigIntCalcAdd} -% \begin{macrocode} -\def\BigIntCalcAdd#1!#2!{% - \romannumeral0\BIC@AddXY#1!#2!!!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BigIntCalcSub} -% \begin{macrocode} -\def\BigIntCalcSub#1!#2!{% - \romannumeral0\BIC@SubXY#1!#2!!!% -} -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\BIC@AddXY} -% \begin{macrocode} -\def\BIC@AddXY#1#2!#3#4!#5!#6!{% - \ifx\\#2\\% - \ifx\\#3\\% - \BIC@AfterFiFi{% - \BIC@DoAdd0!#1#5!#60!% - }% - \else - \BIC@AfterFiFi{% - \BIC@DoAdd0!#1#5!#3#6!% - }% - \fi - \else - \ifx\\#4\\% - \ifx\\#3\\% - \BIC@AfterFiFiFi{% - \BIC@AddXY#2!{}!#1#5!#60!% - }% - \else - \BIC@AfterFiFiFi{% - \BIC@AddXY#2!{}!#1#5!#3#6!% - }% - \fi - \else - \BIC@AfterFiFi{% - \BIC@AddXY#2!#4!#1#5!#3#6!% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@DoAdd} -% |#1|: carry\\ -% |#2|: reverted result\\ -% |#3#4|: reverted $x$\\ -% |#5#6|: reverted $y$ -% \begin{macrocode} -\def\BIC@DoAdd#1#2!#3#4!#5#6!{% - \ifx\\#4\\% - \BIC@AfterFi{% -& \expandafter\BIC@Space -& \the\numexpr#1+#3+#5\relax#2% -$ \expandafter\expandafter\expandafter\BIC@AddResult -$ \BIC@AddDigit#1#3#5#2% - }% - \else - \BIC@AfterFi{% - \expandafter\expandafter\expandafter\BIC@DoAdd - \BIC@AddDigit#1#3#5#2!#4!#6!% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@AddResult} -% \begin{macrocode} -$ \def\BIC@AddResult#1{% -$ \ifx#10% -$ \expandafter\BIC@Space -$ \else -$ \expandafter\BIC@Space\expandafter#1% -$ \fi -$ }% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@AddDigit} -% |#1|: carry\\ -% |#2|: digit of $x$\\ -% |#3|: digit of $y$ -% \begin{macrocode} -\def\BIC@AddDigit#1#2#3{% - \romannumeral0% -& \expandafter\BIC@@AddDigit\the\numexpr#1+#2+#3!% -$ \expandafter\BIC@@AddDigit\number% -$ \csname -$ BIC@AddCarry% -$ \ifcase#1 % -$ #2% -$ \else -$ \ifcase#2 1\or2\or3\or4\or5\or6\or7\or8\or9\or10\fi -$ \fi -$ \endcsname#3!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@AddDigit} -% \begin{macrocode} -\def\BIC@@AddDigit#1!{% - \ifnum#1<10 % - \BIC@AfterFi{ 0#1}% - \else - \BIC@AfterFi{ #1}% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@AddCarry0} -% \begin{macrocode} -$ \expandafter\def\csname BIC@AddCarry0\endcsname#1{#1}% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@AddCarry10} -% \begin{macrocode} -$ \expandafter\def\csname BIC@AddCarry10\endcsname#1{1#1}% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@AddCarry[1-9]} -% \begin{macrocode} -$ \def\BIC@Temp#1#2{% -$ \expandafter\def\csname BIC@AddCarry#1\endcsname##1{% -$ \ifcase##1 #1\or -$ #2% -$? \else\BigIntCalcError:ThisCannotHappen% -$ \fi -$ }% -$ }% -$ \BIC@Temp 0{1\or2\or3\or4\or5\or6\or7\or8\or9}% -$ \BIC@Temp 1{2\or3\or4\or5\or6\or7\or8\or9\or10}% -$ \BIC@Temp 2{3\or4\or5\or6\or7\or8\or9\or10\or11}% -$ \BIC@Temp 3{4\or5\or6\or7\or8\or9\or10\or11\or12}% -$ \BIC@Temp 4{5\or6\or7\or8\or9\or10\or11\or12\or13}% -$ \BIC@Temp 5{6\or7\or8\or9\or10\or11\or12\or13\or14}% -$ \BIC@Temp 6{7\or8\or9\or10\or11\or12\or13\or14\or15}% -$ \BIC@Temp 7{8\or9\or10\or11\or12\or13\or14\or15\or16}% -$ \BIC@Temp 8{9\or10\or11\or12\or13\or14\or15\or16\or17}% -$ \BIC@Temp 9{10\or11\or12\or13\or14\or15\or16\or17\or18}% -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\BIC@SubXY} -% Preconditions: -% \begin{itemize} -% \item $x > y$, $x \geq 0$, and $y >= 0$ -% \item digits($x$) = digits($y$) -% \end{itemize} -% \begin{macrocode} -\def\BIC@SubXY#1#2!#3#4!#5!#6!{% - \ifx\\#2\\% - \ifx\\#3\\% - \BIC@AfterFiFi{% - \BIC@DoSub0!#1#5!#60!% - }% - \else - \BIC@AfterFiFi{% - \BIC@DoSub0!#1#5!#3#6!% - }% - \fi - \else - \ifx\\#4\\% - \ifx\\#3\\% - \BIC@AfterFiFiFi{% - \BIC@SubXY#2!{}!#1#5!#60!% - }% - \else - \BIC@AfterFiFiFi{% - \BIC@SubXY#2!{}!#1#5!#3#6!% - }% - \fi - \else - \BIC@AfterFiFi{% - \BIC@SubXY#2!#4!#1#5!#3#6!% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@DoSub} -% |#1|: carry\\ -% |#2|: reverted result\\ -% |#3#4|: reverted x\\ -% |#5#6|: reverted y -% \begin{macrocode} -\def\BIC@DoSub#1#2!#3#4!#5#6!{% - \ifx\\#4\\% - \BIC@AfterFi{% - \expandafter\expandafter\expandafter\BIC@SubResult - \BIC@SubDigit#1#3#5#2% - }% - \else - \BIC@AfterFi{% - \expandafter\expandafter\expandafter\BIC@DoSub - \BIC@SubDigit#1#3#5#2!#4!#6!% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@SubResult} -% \begin{macrocode} -\def\BIC@SubResult#1{% - \ifx#10% - \expandafter\BIC@SubResult - \else - \expandafter\BIC@Space\expandafter#1% - \fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@SubDigit} -% |#1|: carry\\ -% |#2|: digit of $x$\\ -% |#3|: digit of $y$ -% \begin{macrocode} -\def\BIC@SubDigit#1#2#3{% - \romannumeral0% -& \expandafter\BIC@@SubDigit\the\numexpr#2-#3-#1!% -$ \expandafter\BIC@@AddDigit\number -$ \csname -$ BIC@SubCarry% -$ \ifcase#1 % -$ #3% -$ \else -$ \ifcase#3 1\or2\or3\or4\or5\or6\or7\or8\or9\or10\fi -$ \fi -$ \endcsname#2!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@SubDigit} -% \begin{macrocode} -& \def\BIC@@SubDigit#1!{% -& \ifnum#1<0 % -& \BIC@AfterFi{% -& \expandafter\BIC@Space -& \expandafter1\the\numexpr#1+10\relax -& }% -& \else -& \BIC@AfterFi{ 0#1}% -& \BIC@Fi -& }% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@SubCarry0} -% \begin{macrocode} -$ \expandafter\def\csname BIC@SubCarry0\endcsname#1{#1}% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@SubCarry10}% -% \begin{macrocode} -$ \expandafter\def\csname BIC@SubCarry10\endcsname#1{1#1}% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@SubCarry[1-9]} -% \begin{macrocode} -$ \def\BIC@Temp#1#2{% -$ \expandafter\def\csname BIC@SubCarry#1\endcsname##1{% -$ \ifcase##1 #2% -$? \else\BigIntCalcError:ThisCannotHappen% -$ \fi -$ }% -$ }% -$ \BIC@Temp 1{19\or0\or1\or2\or3\or4\or5\or6\or7\or8}% -$ \BIC@Temp 2{18\or19\or0\or1\or2\or3\or4\or5\or6\or7}% -$ \BIC@Temp 3{17\or18\or19\or0\or1\or2\or3\or4\or5\or6}% -$ \BIC@Temp 4{16\or17\or18\or19\or0\or1\or2\or3\or4\or5}% -$ \BIC@Temp 5{15\or16\or17\or18\or19\or0\or1\or2\or3\or4}% -$ \BIC@Temp 6{14\or15\or16\or17\or18\or19\or0\or1\or2\or3}% -$ \BIC@Temp 7{13\or14\or15\or16\or17\or18\or19\or0\or1\or2}% -$ \BIC@Temp 8{12\or13\or14\or15\or16\or17\or18\or19\or0\or1}% -$ \BIC@Temp 9{11\or12\or13\or14\or15\or16\or17\or18\or19\or0}% -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Shl}, \op{Shr}} -% -% \begin{macro}{\bigintcalcShl} -% \begin{macrocode} -\def\bigintcalcShl#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Shl - \bigintcalcNum{#1}!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Shl} -% \begin{macrocode} -\def\BIC@Shl#1#2!{% - \ifx#1-% - \BIC@AfterFi{% - \expandafter-\romannumeral0% -& \BIC@@Shl#2!!% -$ \BIC@AddXY#2!#2!!!% - }% - \else - \BIC@AfterFi{% -& \BIC@@Shl#1#2!!% -$ \BIC@AddXY#1#2!#1#2!!!% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BigIntCalcShl} -% \begin{macrocode} -\def\BigIntCalcShl#1!{% - \romannumeral0% -& \BIC@@Shl#1!!% -$ \BIC@AddXY#1!#1!!!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@Shl} -% \begin{macrocode} -& \def\BIC@@Shl#1#2!{% -& \ifx\\#2\\% -& \BIC@AfterFi{% -& \BIC@@@Shl0!#1% -& }% -& \else -& \BIC@AfterFi{% -& \BIC@@Shl#2!#1% -& }% -& \BIC@Fi -& }% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@@Shl} -% |#1|: carry\\ -% |#2|: result\\ -% |#3#4|: reverted number -% \begin{macrocode} -& \def\BIC@@@Shl#1#2!#3#4!{% -& \ifx\\#4\\% -& \BIC@AfterFi{% -& \expandafter\BIC@Space -& \the\numexpr#3*2+#1\relax#2% -& }% -& \else -& \BIC@AfterFi{% -& \expandafter\BIC@@@@Shl\the\numexpr#3*2+#1!#2!#4!% -& }% -& \BIC@Fi -& }% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@@@Shl} -% \begin{macrocode} -& \def\BIC@@@@Shl#1!{% -& \ifnum#1<10 % -& \BIC@AfterFi{% -& \BIC@@@Shl0#1% -& }% -& \else -& \BIC@AfterFi{% -& \BIC@@@Shl#1% -& }% -& \BIC@Fi -& }% -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\bigintcalcShr} -% \begin{macrocode} -\def\bigintcalcShr#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Shr - \bigintcalcNum{#1}!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Shr} -% \begin{macrocode} -\def\BIC@Shr#1#2!{% - \ifx#1-% - \expandafter-\romannumeral0% - \BIC@AfterFi{% - \BIC@@Shr#2!% - }% - \else - \BIC@AfterFi{% - \BIC@@Shr#1#2!% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BigIntCalcShr} -% \begin{macrocode} -\def\BigIntCalcShr#1!{% - \romannumeral0% - \BIC@@Shr#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@Shr} -% \begin{macrocode} -\def\BIC@@Shr#1#2!{% - \ifcase#1 % - \BIC@AfterFi{ 0}% - \or - \ifx\\#2\\% - \BIC@AfterFiFi{ 0}% - \else - \BIC@AfterFiFi{% - \BIC@@@Shr#1#2!!% - }% - \fi - \else - \BIC@AfterFi{% - \BIC@@@Shr0#1#2!!% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@@Shr} -% |#1|: carry\\ -% |#2#3|: number\\ -% |#4|: result -% \begin{macrocode} -\def\BIC@@@Shr#1#2#3!#4!{% - \ifx\\#3\\% - \ifodd#1#2 % - \BIC@AfterFiFi{% -& \expandafter\BIC@ShrResult\the\numexpr(#1#2-1)/2\relax -$ \expandafter\expandafter\expandafter\BIC@ShrResult -$ \csname BIC@ShrDigit#1#2\endcsname - #4!% - }% - \else - \BIC@AfterFiFi{% -& \expandafter\BIC@ShrResult\the\numexpr#1#2/2\relax -$ \expandafter\expandafter\expandafter\BIC@ShrResult -$ \csname BIC@ShrDigit#1#2\endcsname - #4!% - }% - \fi - \else - \ifodd#1#2 % - \BIC@AfterFiFi{% -& \expandafter\BIC@@@@Shr\the\numexpr(#1#2-1)/2\relax1% -$ \expandafter\expandafter\expandafter\BIC@@@@Shr -$ \csname BIC@ShrDigit#1#2\endcsname - #3!#4!% - }% - \else - \BIC@AfterFiFi{% -& \expandafter\BIC@@@@Shr\the\numexpr#1#2/2\relax0% -$ \expandafter\expandafter\expandafter\BIC@@@@Shr -$ \csname BIC@ShrDigit#1#2\endcsname - #3!#4!% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ShrResult} -% \begin{macrocode} -& \def\BIC@ShrResult#1#2!{ #2#1}% -$ \def\BIC@ShrResult#1#2#3!{ #3#1}% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@@@Shr} -% |#1|: new digit\\ -% |#2|: carry\\ -% |#3|: remaining number\\ -% |#4|: result -% \begin{macrocode} -\def\BIC@@@@Shr#1#2#3!#4!{% - \BIC@@@Shr#2#3!#4#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ShrDigit[00-19]} -% \begin{macrocode} -$ \def\BIC@Temp#1#2#3#4{% -$ \expandafter\def\csname BIC@ShrDigit#1#2\endcsname{#3#4}% -$ }% -$ \BIC@Temp 0000% -$ \BIC@Temp 0101% -$ \BIC@Temp 0210% -$ \BIC@Temp 0311% -$ \BIC@Temp 0420% -$ \BIC@Temp 0521% -$ \BIC@Temp 0630% -$ \BIC@Temp 0731% -$ \BIC@Temp 0840% -$ \BIC@Temp 0941% -$ \BIC@Temp 1050% -$ \BIC@Temp 1151% -$ \BIC@Temp 1260% -$ \BIC@Temp 1361% -$ \BIC@Temp 1470% -$ \BIC@Temp 1571% -$ \BIC@Temp 1680% -$ \BIC@Temp 1781% -$ \BIC@Temp 1890% -$ \BIC@Temp 1991% -% \end{macrocode} -% \end{macro} -% -% \subsection{\cs{BIC@Tim}} -% -% \begin{macro}{\BIC@Tim} -% Macro \cs{BIC@Tim} implements ``Number \emph{tim}es digit''.\\ -% |#1|: plain number without sign\\ -% |#2|: digit -\def\BIC@Tim#1!#2{% - \romannumeral0% - \ifcase#2 % 0 - \BIC@AfterFi{ 0}% - \or % 1 - \BIC@AfterFi{ #1}% - \or % 2 - \BIC@AfterFi{% - \BIC@Shl#1!% - }% - \else % 3-9 - \BIC@AfterFi{% - \BIC@@Tim#1!!#2% - }% - \BIC@Fi -} -% \begin{macrocode} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@Tim} -% |#1#2|: number\\ -% |#3|: reverted number -% \begin{macrocode} -\def\BIC@@Tim#1#2!{% - \ifx\\#2\\% - \BIC@AfterFi{% - \BIC@ProcessTim0!#1% - }% - \else - \BIC@AfterFi{% - \BIC@@Tim#2!#1% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ProcessTim} -% |#1|: carry\\ -% |#2|: result\\ -% |#3#4|: reverted number\\ -% |#5|: digit -% \begin{macrocode} -\def\BIC@ProcessTim#1#2!#3#4!#5{% - \ifx\\#4\\% - \BIC@AfterFi{% - \expandafter\BIC@Space -& \the\numexpr#3*#5+#1\relax -$ \romannumeral0\BIC@TimDigit#3#5#1% - #2% - }% - \else - \BIC@AfterFi{% - \expandafter\BIC@@ProcessTim -& \the\numexpr#3*#5+#1% -$ \romannumeral0\BIC@TimDigit#3#5#1% - !#2!#4!#5% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@ProcessTim} -% |#1#2|: carry?, new digit\\ -% |#3|: new number\\ -% |#4|: old number\\ -% |#5|: digit -% \begin{macrocode} -\def\BIC@@ProcessTim#1#2!{% - \ifx\\#2\\% - \BIC@AfterFi{% - \BIC@ProcessTim0#1% - }% - \else - \BIC@AfterFi{% - \BIC@ProcessTim#1#2% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@TimDigit} -% |#1|: digit 0--9\\ -% |#2|: digit 3--9\\ -% |#3|: carry 0--9 -% \begin{macrocode} -$ \def\BIC@TimDigit#1#2#3{% -$ \ifcase#1 % 0 -$ \BIC@AfterFi{ #3}% -$ \or % 1 -$ \BIC@AfterFi{% -$ \expandafter\BIC@Space -$ \number\csname BIC@AddCarry#2\endcsname#3 % -$ }% -$ \else -$ \ifcase#3 % -$ \BIC@AfterFiFi{% -$ \expandafter\BIC@Space -$ \number\csname BIC@MulDigit#2\endcsname#1 % -$ }% -$ \else -$ \BIC@AfterFiFi{% -$ \expandafter\BIC@Space -$ \romannumeral0% -$ \expandafter\BIC@AddXY -$ \number\csname BIC@MulDigit#2\endcsname#1!% -$ #3!!!% -$ }% -$ \fi -$ \BIC@Fi -$ }% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@MulDigit[3-9]} -% \begin{macrocode} -$ \def\BIC@Temp#1#2{% -$ \expandafter\def\csname BIC@MulDigit#1\endcsname##1{% -$ \ifcase##1 0% -$ \or ##1% -$ \or #2% -$? \else\BigIntCalcError:ThisCannotHappen% -$ \fi -$ }% -$ }% -$ \BIC@Temp 3{6\or9\or12\or15\or18\or21\or24\or27}% -$ \BIC@Temp 4{8\or12\or16\or20\or24\or28\or32\or36}% -$ \BIC@Temp 5{10\or15\or20\or25\or30\or35\or40\or45}% -$ \BIC@Temp 6{12\or18\or24\or30\or36\or42\or48\or54}% -$ \BIC@Temp 7{14\or21\or28\or35\or42\or49\or56\or63}% -$ \BIC@Temp 8{16\or24\or32\or40\or48\or56\or64\or72}% -$ \BIC@Temp 9{18\or27\or36\or45\or54\or63\or72\or81}% -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Mul}} -% -% \begin{macro}{\bigintcalcMul} -% \begin{macrocode} -\def\bigintcalcMul#1#2{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Mul - \bigintcalcNum{#1}!{#2}% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Mul} -% \begin{macrocode} -\def\BIC@Mul#1!#2{% - \expandafter\expandafter\expandafter\BIC@MulSwitch - \bigintcalcNum{#2}!#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@MulSwitch} -% Decision table for \cs{BIC@MulSwitch}. -% \begin{quote} -% \begin{tabular}[t]{@{}|l|l|l|l|l|@{}} -% \hline -% $x=0$ &\multicolumn{3}{l}{} &$0$\\ -% \hline -% $x>0$ & $y=0$ &\multicolumn2l{}&$0$\\ -% \cline{2-5} -% & $y>0$ & $ x> y$ & $+$ & $\opMul( x, y)$\\ -% \cline{3-3}\cline{5-5} -% & & else & & $\opMul( y, x)$\\ -% \cline{2-5} -% & $y<0$ & $ x>-y$ & $-$ & $\opMul( x,-y)$\\ -% \cline{3-3}\cline{5-5} -% & & else & & $\opMul(-y, x)$\\ -% \hline -% $x<0$ & $y=0$ &\multicolumn2l{}&$0$\\ -% \cline{2-5} -% & $y>0$ & $-x> y$ & $-$ & $\opMul(-x, y)$\\ -% \cline{3-3}\cline{5-5} -% & & else & & $\opMul( y,-x)$\\ -% \cline{2-5} -% & $y<0$ & $-x>-y$ & $+$ & $\opMul(-x,-y)$\\ -% \cline{3-3}\cline{5-5} -% & & else & & $\opMul(-y,-x)$\\ -% \hline -% \end{tabular} -% \end{quote} -% \begin{macrocode} -\def\BIC@MulSwitch#1#2!#3#4!{% - \ifcase\BIC@Sgn#1#2! % x = 0 - \BIC@AfterFi{ 0}% - \or % x > 0 - \ifcase\BIC@Sgn#3#4! % y = 0 - \BIC@AfterFiFi{ 0}% - \or % y > 0 - \ifnum\BIC@PosCmp#1#2!#3#4!=1 % x > y - \BIC@AfterFiFiFi{% - \BIC@ProcessMul0!#1#2!#3#4!% - }% - \else % x <= y - \BIC@AfterFiFiFi{% - \BIC@ProcessMul0!#3#4!#1#2!% - }% - \fi - \else % y < 0 - \expandafter-\romannumeral0% - \ifnum\BIC@PosCmp#1#2!#4!=1 % x > -y - \BIC@AfterFiFiFi{% - \BIC@ProcessMul0!#1#2!#4!% - }% - \else % x <= -y - \BIC@AfterFiFiFi{% - \BIC@ProcessMul0!#4!#1#2!% - }% - \fi - \fi - \else % x < 0 - \ifcase\BIC@Sgn#3#4! % y = 0 - \BIC@AfterFiFi{ 0}% - \or % y > 0 - \expandafter-\romannumeral0% - \ifnum\BIC@PosCmp#2!#3#4!=1 % -x > y - \BIC@AfterFiFiFi{% - \BIC@ProcessMul0!#2!#3#4!% - }% - \else % -x <= y - \BIC@AfterFiFiFi{% - \BIC@ProcessMul0!#3#4!#2!% - }% - \fi - \else % y < 0 - \ifnum\BIC@PosCmp#2!#4!=1 % -x > -y - \BIC@AfterFiFiFi{% - \BIC@ProcessMul0!#2!#4!% - }% - \else % -x <= -y - \BIC@AfterFiFiFi{% - \BIC@ProcessMul0!#4!#2!% - }% - \fi - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BigIntCalcMul} -% \begin{macrocode} -\def\BigIntCalcMul#1!#2!{% - \romannumeral0% - \BIC@ProcessMul0!#1!#2!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ProcessMul} -% |#1|: result\\ -% |#2|: number $x$\\ -% |#3#4|: number $y$ -% \begin{macrocode} -\def\BIC@ProcessMul#1!#2!#3#4!{% - \ifx\\#4\\% - \BIC@AfterFi{% - \expandafter\expandafter\expandafter\BIC@Space - \bigintcalcAdd{\BIC@Tim#2!#3}{#10}% - }% - \else - \BIC@AfterFi{% - \expandafter\expandafter\expandafter\BIC@ProcessMul - \bigintcalcAdd{\BIC@Tim#2!#3}{#10}!#2!#4!% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Sqr}} -% -% \begin{macro}{\bigintcalcSqr} -% \begin{macrocode} -\def\bigintcalcSqr#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Sqr - \bigintcalcNum{#1}!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Sqr} -% \begin{macrocode} -\def\BIC@Sqr#1{% - \ifx#1-% - \expandafter\BIC@@Sqr - \else - \expandafter\BIC@@Sqr\expandafter#1% - \fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@Sqr} -% \begin{macrocode} -\def\BIC@@Sqr#1!{% - \BIC@ProcessMul0!#1!#1!% -} -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Fac}} -% -% \begin{macro}{\bigintcalcFac} -% \begin{macrocode} -\def\bigintcalcFac#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Fac - \bigintcalcNum{#1}!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Fac} -% \begin{macrocode} -\def\BIC@Fac#1#2!{% - \ifx#1-% - \BIC@AfterFi{ 0\BigIntCalcError:FacNegative}% - \else - \ifnum\BIC@PosCmp#1#2!13!<0 % - \ifcase#1#2 % - \BIC@AfterFiFiFi{ 1}% 0! - \or\BIC@AfterFiFiFi{ 1}% 1! - \or\BIC@AfterFiFiFi{ 2}% 2! - \or\BIC@AfterFiFiFi{ 6}% 3! - \or\BIC@AfterFiFiFi{ 24}% 4! - \or\BIC@AfterFiFiFi{ 120}% 5! - \or\BIC@AfterFiFiFi{ 720}% 6! - \or\BIC@AfterFiFiFi{ 5040}% 7! - \or\BIC@AfterFiFiFi{ 40320}% 8! - \or\BIC@AfterFiFiFi{ 362880}% 9! - \or\BIC@AfterFiFiFi{ 3628800}% 10! - \or\BIC@AfterFiFiFi{ 39916800}% 11! - \or\BIC@AfterFiFiFi{ 479001600}% 12! -? \else\BigIntCalcError:ThisCannotHappen% - \fi - \else - \BIC@AfterFiFi{% - \BIC@ProcessFac#1#2!479001600!% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ProcessFac} -% |#1|: $n$\\ -% |#2|: result -% \begin{macrocode} -\def\BIC@ProcessFac#1!#2!{% - \ifnum\BIC@PosCmp#1!12!=0 % - \BIC@AfterFi{ #2}% - \else - \BIC@AfterFi{% - \expandafter\BIC@@ProcessFac - \romannumeral0\BIC@ProcessMul0!#2!#1!% - !#1!% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@ProcessFac} -% |#1|: result\\ -% |#2|: $n$ -% \begin{macrocode} -\def\BIC@@ProcessFac#1!#2!{% - \expandafter\BIC@ProcessFac - \romannumeral0\BIC@Dec#2!{}% - !#1!% -} -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Pow}} -% -% \begin{macro}{\bigintcalcPow} -% |#1|: basis\\ -% |#2|: power -% \begin{macrocode} -\def\bigintcalcPow#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Pow - \bigintcalcNum{#1}!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Pow} -% |#1|: basis\\ -% |#2|: power -% \begin{macrocode} -\def\BIC@Pow#1!#2{% - \expandafter\expandafter\expandafter\BIC@PowSwitch - \bigintcalcNum{#2}!#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@PowSwitch} -% |#1#2|: power $y$\\ -% |#3#4|: basis $x$\\ -% Decision table for \cs{BIC@PowSwitch}. -% \begin{quote} -% \def\M#1{\multicolumn{#1}{l}{}}% -% \begin{tabular}[t]{@{}|l|l|l|l|@{}} -% \hline -% $y=0$ & \M{2} & $1$\\ -% \hline -% $y=1$ & \M{2} & $x$\\ -% \hline -% $y=2$ & $x<0$ & \M{1} & $\opMul(-x,-x)$\\ -% \cline{2-4} -% & else & \M{1} & $\opMul(x,x)$\\ -% \hline -% $y<0$ & $x=0$ & \M{1} & DivisionByZero\\ -% \cline{2-4} -% & $x=1$ & \M{1} & $1$\\ -% \cline{2-4} -% & $x=-1$ & $\opODD(y)$ & $-1$\\ -% \cline{3-4} -% & & else & $1$\\ -% \cline{2-4} -% & else ($\string|x\string|>1$) & \M{1} & $0$\\ -% \hline -% $y>2$ & $x=0$ & \M{1} & $0$\\ -% \cline{2-4} -% & $x=1$ & \M{1} & $1$\\ -% \cline{2-4} -% & $x=-1$ & $\opODD(y)$ & $-1$\\ -% \cline{3-4} -% & & else & $1$\\ -% \cline{2-4} -% & $x<-1$ ($x<0$) & $\opODD(y)$ & $-\opPow(-x,y)$\\ -% \cline{3-4} -% & & else & $\opPow(-x,y)$\\ -% \cline{2-4} -% & else ($x>1$) & \M{1} & $\opPow(x,y)$\\ -% \hline -% \end{tabular} -% \end{quote} -% \begin{macrocode} -\def\BIC@PowSwitch#1#2!#3#4!{% - \ifcase\ifx\\#2\\% - \ifx#100 % y = 0 - \else\ifx#111 % y = 1 - \else\ifx#122 % y = 2 - \else4 % y > 2 - \fi\fi\fi - \else - \ifx#1-3 % y < 0 - \else4 % y > 2 - \fi - \fi - \BIC@AfterFi{ 1}% y = 0 - \or % y = 1 - \BIC@AfterFi{ #3#4}% - \or % y = 2 - \ifx#3-% x < 0 - \BIC@AfterFiFi{% - \BIC@ProcessMul0!#4!#4!% - }% - \else % x >= 0 - \BIC@AfterFiFi{% - \BIC@ProcessMul0!#3#4!#3#4!% - }% - \fi - \or % y < 0 - \ifcase\ifx\\#4\\% - \ifx#300 % x = 0 - \else\ifx#311 % x = 1 - \else3 % x > 1 - \fi\fi - \else - \ifcase\BIC@MinusOne#3#4! % - 3 % |x| > 1 - \or - 2 % x = -1 -? \else\BigIntCalcError:ThisCannotHappen% - \fi - \fi - \BIC@AfterFiFi{ 0\BigIntCalcError:DivisionByZero}% x = 0 - \or % x = 1 - \BIC@AfterFiFi{ 1}% x = 1 - \or % x = -1 - \ifcase\BIC@ModTwo#2! % even(y) - \BIC@AfterFiFiFi{ 1}% - \or % odd(y) - \BIC@AfterFiFiFi{ -1}% -? \else\BigIntCalcError:ThisCannotHappen% - \fi - \or % |x| > 1 - \BIC@AfterFiFi{ 0}% -? \else\BigIntCalcError:ThisCannotHappen% - \fi - \or % y > 2 - \ifcase\ifx\\#4\\% - \ifx#300 % x = 0 - \else\ifx#311 % x = 1 - \else4 % x > 1 - \fi\fi - \else - \ifx#3-% - \ifcase\BIC@MinusOne#3#4! % - 3 % x < -1 - \else - 2 % x = -1 - \fi - \else - 4 % x > 1 - \fi - \fi - \BIC@AfterFiFi{ 0}% x = 0 - \or % x = 1 - \BIC@AfterFiFi{ 1}% x = 1 - \or % x = -1 - \ifcase\BIC@ModTwo#1#2! % even(y) - \BIC@AfterFiFiFi{ 1}% - \or % odd(y) - \BIC@AfterFiFiFi{ -1}% -? \else\BigIntCalcError:ThisCannotHappen% - \fi - \or % x < -1 - \ifcase\BIC@ModTwo#1#2! % even(y) - \BIC@AfterFiFiFi{% - \BIC@PowRec#4!#1#2!1!% - }% - \or % odd(y) - \expandafter-\romannumeral0% - \BIC@AfterFiFiFi{% - \BIC@PowRec#4!#1#2!1!% - }% -? \else\BigIntCalcError:ThisCannotHappen% - \fi - \or % x > 1 - \BIC@AfterFiFi{% - \BIC@PowRec#3#4!#1#2!1!% - }% -? \else\BigIntCalcError:ThisCannotHappen% - \fi -? \else\BigIntCalcError:ThisCannotHappen% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \subsubsection{Help macros} -% -% \begin{macro}{\BIC@ModTwo} -% Macro \cs{BIC@ModTwo} expects a number without sign -% and returns digit |1| or |0| if the number is odd or even. -% \begin{macrocode} -\def\BIC@ModTwo#1#2!{% - \ifx\\#2\\% - \ifodd#1 % - \BIC@AfterFiFi1% - \else - \BIC@AfterFiFi0% - \fi - \else - \BIC@AfterFi{% - \BIC@ModTwo#2!% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \begin{macro}{\BIC@MinusOne} -% Macro \cs{BIC@MinusOne} expects a number and returns -% digit |1| if the number equals minus one and returns |0| otherwise. -% \begin{macrocode} -\def\BIC@MinusOne#1#2!{% - \ifx#1-% - \BIC@@MinusOne#2!% - \else - 0% - \fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@MinusOne} -% \begin{macrocode} -\def\BIC@@MinusOne#1#2!{% - \ifx#11% - \ifx\\#2\\% - 1% - \else - 0% - \fi - \else - 0% - \fi -} -% \end{macrocode} -% \end{macro} -% -% \subsubsection{Recursive calculation} -% -% \begin{macro}{\BIC@PowRec} -%\begin{quote} -%\begin{verbatim} -%Pow(x, y) { -% PowRec(x, y, 1) -%} -%PowRec(x, y, r) { -% if y == 1 then -% return r -% else -% ifodd y then -% return PowRec(x*x, y div 2, r*x) % y div 2 = (y-1)/2 -% else -% return PowRec(x*x, y div 2, r) -% fi -% fi -%} -%\end{verbatim} -%\end{quote} -% |#1|: $x$ (basis)\\ -% |#2#3|: $y$ (power)\\ -% |#4|: $r$ (result) -% \begin{macrocode} -\def\BIC@PowRec#1!#2#3!#4!{% - \ifcase\ifx#21\ifx\\#3\\0 \else1 \fi\else1 \fi % y = 1 - \ifnum\BIC@PosCmp#1!#4!=1 % x > r - \BIC@AfterFiFi{% - \BIC@ProcessMul0!#1!#4!% - }% - \else - \BIC@AfterFiFi{% - \BIC@ProcessMul0!#4!#1!% - }% - \fi - \or - \ifcase\BIC@ModTwo#2#3! % even(y) - \BIC@AfterFiFi{% - \expandafter\BIC@@PowRec\romannumeral0% - \BIC@@Shr#2#3!% - !#1!#4!% - }% - \or % odd(y) - \ifnum\BIC@PosCmp#1!#4!=1 % x > r - \BIC@AfterFiFiFi{% - \expandafter\BIC@@@PowRec\romannumeral0% - \BIC@ProcessMul0!#1!#4!% - !#1!#2#3!% - }% - \else - \BIC@AfterFiFiFi{% - \expandafter\BIC@@@PowRec\romannumeral0% - \BIC@ProcessMul0!#1!#4!% - !#1!#2#3!% - }% - \fi -? \else\BigIntCalcError:ThisCannotHappen% - \fi -? \else\BigIntCalcError:ThisCannotHappen% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@PowRec} -% |#1|: $y/2$\\ -% |#2|: $x$\\ -% |#3|: new $r$ ($r$ or $r*x$) -% \begin{macrocode} -\def\BIC@@PowRec#1!#2!#3!{% - \expandafter\BIC@PowRec\romannumeral0% - \BIC@ProcessMul0!#2!#2!% - !#1!#3!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@@PowRec} -% |#1|: $r*x$ -% |#2|: $x$ -% |#3|: $y$ -% \begin{macrocode} -\def\BIC@@@PowRec#1!#2!#3!{% - \expandafter\BIC@@PowRec\romannumeral0% - \BIC@@Shr#3!% - !#2!#1!% -} -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Div}} -% -% \begin{macro}{\bigintcalcDiv} -% |#1|: $x$\\ -% |#2|: $y$ (divisor) -% \begin{macrocode} -\def\bigintcalcDiv#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Div - \bigintcalcNum{#1}!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Div} -% |#1|: $x$\\ -% |#2|: $y$ -% \begin{macrocode} -\def\BIC@Div#1!#2{% - \expandafter\expandafter\expandafter\BIC@DivSwitchSign - \bigintcalcNum{#2}!#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BigIntCalcDiv} -% \begin{macrocode} -\def\BigIntCalcDiv#1!#2!{% - \romannumeral0% - \BIC@DivSwitchSign#2!#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@DivSwitchSign} -% Decision table for \cs{BIC@DivSwitchSign}. -% \begin{quote} -% \begin{tabular}{@{}|l|l|l|@{}} -% \hline -% $y=0$ & \multicolumn{1}{l}{} & DivisionByZero\\ -% \hline -% $y>0$ & $x=0$ & $0$\\ -% \cline{2-3} -% & $x>0$ & DivSwitch$(+,x,y)$\\ -% \cline{2-3} -% & $x<0$ & DivSwitch$(-,-x,y)$\\ -% \hline -% $y<0$ & $x=0$ & $0$\\ -% \cline{2-3} -% & $x>0$ & DivSwitch$(-,x,-y)$\\ -% \cline{2-3} -% & $x<0$ & DivSwitch$(+,-x,-y)$\\ -% \hline -% \end{tabular} -% \end{quote} -% |#1|: $y$ (divisor)\\ -% |#2|: $x$ -% \begin{macrocode} -\def\BIC@DivSwitchSign#1#2!#3#4!{% - \ifcase\BIC@Sgn#1#2! % y = 0 - \BIC@AfterFi{ 0\BigIntCalcError:DivisionByZero}% - \or % y > 0 - \ifcase\BIC@Sgn#3#4! % x = 0 - \BIC@AfterFiFi{ 0}% - \or % x > 0 - \BIC@AfterFiFi{% - \BIC@DivSwitch{}#3#4!#1#2!% - }% - \else % x < 0 - \BIC@AfterFiFi{% - \BIC@DivSwitch-#4!#1#2!% - }% - \fi - \else % y < 0 - \ifcase\BIC@Sgn#3#4! % x = 0 - \BIC@AfterFiFi{ 0}% - \or % x > 0 - \BIC@AfterFiFi{% - \BIC@DivSwitch-#3#4!#2!% - }% - \else % x < 0 - \BIC@AfterFiFi{% - \BIC@DivSwitch{}#4!#2!% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@DivSwitch} -% Decision table for \cs{BIC@DivSwitch}. -% \begin{quote} -% \begin{tabular}{@{}|l|l|l|@{}} -% \hline -% $y=x$ & \multicolumn{1}{l}{} & sign $1$\\ -% \hline -% $y>x$ & \multicolumn{1}{l}{} & $0$\\ -% \hline -% $y<x$ & $y=1$ & sign $x$\\ -% \cline{2-3} -% & $y=2$ & sign Shr$(x)$\\ -% \cline{2-3} -% & $y=4$ & sign Shr(Shr$(x)$)\\ -% \cline{2-3} -% & else & sign ProcessDiv$(x,y)$\\ -% \hline -% \end{tabular} -% \end{quote} -% |#1|: sign\\ -% |#2|: $x$\\ -% |#3#4|: $y$ ($y\ne 0$) -% \begin{macrocode} -\def\BIC@DivSwitch#1#2!#3#4!{% - \ifcase\BIC@PosCmp#3#4!#2!% y = x - \BIC@AfterFi{ #11}% - \or % y > x - \BIC@AfterFi{ 0}% - \else % y < x - \ifx\\#1\\% - \else - \expandafter-\romannumeral0% - \fi - \ifcase\ifx\\#4\\% - \ifx#310 % y = 1 - \else\ifx#321 % y = 2 - \else\ifx#342 % y = 4 - \else3 % y > 2 - \fi\fi\fi - \else - 3 % y > 2 - \fi - \BIC@AfterFiFi{ #2}% y = 1 - \or % y = 2 - \BIC@AfterFiFi{% - \BIC@@Shr#2!% - }% - \or % y = 4 - \BIC@AfterFiFi{% - \expandafter\BIC@@Shr\romannumeral0% - \BIC@@Shr#2!!% - }% - \or % y > 2 - \BIC@AfterFiFi{% - \BIC@DivStartX#2!#3#4!!!% - }% -? \else\BigIntCalcError:ThisCannotHappen% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ProcessDiv} -% |#1#2|: $x$\\ -% |#3#4|: $y$\\ -% |#5|: collect first digits of $x$\\ -% |#6|: corresponding digits of $y$ -% \begin{macrocode} -\def\BIC@DivStartX#1#2!#3#4!#5!#6!{% - \ifx\\#4\\% - \BIC@AfterFi{% - \BIC@DivStartYii#6#3#4!{#5#1}#2=!% - }% - \else - \BIC@AfterFi{% - \BIC@DivStartX#2!#4!#5#1!#6#3!% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@DivStartYii} -% |#1|: $y$\\ -% |#2|: $x$, |=| -% \begin{macrocode} -\def\BIC@DivStartYii#1!{% - \expandafter\BIC@DivStartYiv\romannumeral0% - \BIC@Shl#1!% - !#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@DivStartYiv} -% |#1|: $2y$\\ -% |#2|: $y$\\ -% |#3|: $x$, |=| -% \begin{macrocode} -\def\BIC@DivStartYiv#1!{% - \expandafter\BIC@DivStartYvi\romannumeral0% - \BIC@Shl#1!% - !#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@DivStartYvi} -% |#1|: $4y$\\ -% |#2|: $2y$\\ -% |#3|: $y$\\ -% |#4|: $x$, |=| -% \begin{macrocode} -\def\BIC@DivStartYvi#1!#2!{% - \expandafter\BIC@DivStartYviii\romannumeral0% - \BIC@AddXY#1!#2!!!% - !#1!#2!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@DivStartYviii} -% |#1|: $6y$\\ -% |#2|: $4y$\\ -% |#3|: $2y$\\ -% |#4|: $y$\\ -% |#5|: $x$, |=| -% \begin{macrocode} -\def\BIC@DivStartYviii#1!#2!{% - \expandafter\BIC@DivStart\romannumeral0% - \BIC@Shl#2!% - !#1!#2!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@DivStart} -% |#1|: $8y$\\ -% |#2|: $6y$\\ -% |#3|: $4y$\\ -% |#4|: $2y$\\ -% |#5|: $y$\\ -% |#6|: $x$, |=| -% \begin{macrocode} -\def\BIC@DivStart#1!#2!#3!#4!#5!#6!{% - \BIC@ProcessDiv#6!!#5!#4!#3!#2!#1!=% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ProcessDiv} -% |#1#2#3|: $x$, |=|\\ -% |#4|: result\\ -% |#5|: $y$\\ -% |#6|: $2y$\\ -% |#7|: $4y$\\ -% |#8|: $6y$\\ -% |#9|: $8y$ -% \begin{macrocode} -\def\BIC@ProcessDiv#1#2#3!#4!#5!{% - \ifcase\BIC@PosCmp#5!#1!% y = #1 - \ifx#2=% - \BIC@AfterFiFi{\BIC@DivCleanup{#41}}% - \else - \BIC@AfterFiFi{% - \BIC@ProcessDiv#2#3!#41!#5!% - }% - \fi - \or % y > #1 - \ifx#2=% - \BIC@AfterFiFi{\BIC@DivCleanup{#40}}% - \else - \ifx\\#4\\% - \BIC@AfterFiFiFi{% - \BIC@ProcessDiv{#1#2}#3!!#5!% - }% - \else - \BIC@AfterFiFiFi{% - \BIC@ProcessDiv{#1#2}#3!#40!#5!% - }% - \fi - \fi - \else % y < #1 - \BIC@AfterFi{% - \BIC@@ProcessDiv{#1}#2#3!#4!#5!% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@DivCleanup} -% |#1|: result\\ -% |#2|: garbage -% \begin{macrocode} -\def\BIC@DivCleanup#1#2={ #1}% -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@@ProcessDiv} -% \begin{macrocode} -\def\BIC@@ProcessDiv#1#2#3!#4!#5!#6!#7!{% - \ifcase\BIC@PosCmp#7!#1!% 4y = #1 - \ifx#2=% - \BIC@AfterFiFi{\BIC@DivCleanup{#44}}% - \else - \BIC@AfterFiFi{% - \BIC@ProcessDiv#2#3!#44!#5!#6!#7!% - }% - \fi - \or % 4y > #1 - \ifcase\BIC@PosCmp#6!#1!% 2y = #1 - \ifx#2=% - \BIC@AfterFiFiFi{\BIC@DivCleanup{#42}}% - \else - \BIC@AfterFiFiFi{% - \BIC@ProcessDiv#2#3!#42!#5!#6!#7!% - }% - \fi - \or % 2y > #1 - \ifx#2=% - \BIC@AfterFiFiFi{\BIC@DivCleanup{#41}}% - \else - \BIC@AfterFiFiFi{% - \BIC@DivSub#1!#5!#2#3!#41!#5!#6!#7!% - }% - \fi - \else % 2y < #1 - \BIC@AfterFiFi{% - \expandafter\BIC@ProcessDivII\romannumeral0% - \BIC@SubXY#1!#6!!!% - !#2#3!#4!#5!23% - #6!#7!% - }% - \fi - \else % 4y < #1 - \BIC@AfterFi{% - \BIC@@@ProcessDiv{#1}#2#3!#4!#5!#6!#7!% - }% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@DivSub} -% Next token group: |#1|-|#2| and next digit |#3|. -% \begin{macrocode} -\def\BIC@DivSub#1!#2!#3{% - \expandafter\BIC@ProcessDiv\expandafter{% - \romannumeral0% - \BIC@SubXY#1!#2!!!% - #3% - }% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ProcessDivII} -% |#1|: $x'-2y$\\ -% |#2#3|: remaining $x$, |=|\\ -% |#4|: result\\ -% |#5|: $y$\\ -% |#6|: first possible result digit\\ -% |#7|: second possible result digit -% \begin{macrocode} -\def\BIC@ProcessDivII#1!#2#3!#4!#5!#6#7{% - \ifcase\BIC@PosCmp#5!#1!% y = #1 - \ifx#2=% - \BIC@AfterFiFi{\BIC@DivCleanup{#4#7}}% - \else - \BIC@AfterFiFi{% - \BIC@ProcessDiv#2#3!#4#7!#5!% - }% - \fi - \or % y > #1 - \ifx#2=% - \BIC@AfterFiFi{\BIC@DivCleanup{#4#6}}% - \else - \BIC@AfterFiFi{% - \BIC@ProcessDiv{#1#2}#3!#4#6!#5!% - }% - \fi - \else % y < #1 - \ifx#2=% - \BIC@AfterFiFi{\BIC@DivCleanup{#4#7}}% - \else - \BIC@AfterFiFi{% - \BIC@DivSub#1!#5!#2#3!#4#7!#5!% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ProcessDivIV} -% |#1#2#3|: $x$, |=|, $x>4y$\\ -% |#4|: result\\ -% |#5|: $y$\\ -% |#6|: $2y$\\ -% |#7|: $4y$\\ -% |#8|: $6y$\\ -% |#9|: $8y$ -% \begin{macrocode} -\def\BIC@@@ProcessDiv#1#2#3!#4!#5!#6!#7!#8!#9!{% - \ifcase\BIC@PosCmp#8!#1!% 6y = #1 - \ifx#2=% - \BIC@AfterFiFi{\BIC@DivCleanup{#46}}% - \else - \BIC@AfterFiFi{% - \BIC@ProcessDiv#2#3!#46!#5!#6!#7!#8!#9!% - }% - \fi - \or % 6y > #1 - \BIC@AfterFi{% - \expandafter\BIC@ProcessDivII\romannumeral0% - \BIC@SubXY#1!#7!!!% - !#2#3!#4!#5!45% - #6!#7!#8!#9!% - }% - \else % 6y < #1 - \ifcase\BIC@PosCmp#9!#1!% 8y = #1 - \ifx#2=% - \BIC@AfterFiFiFi{\BIC@DivCleanup{#48}}% - \else - \BIC@AfterFiFiFi{% - \BIC@ProcessDiv#2#3!#48!#5!#6!#7!#8!#9!% - }% - \fi - \or % 8y > #1 - \BIC@AfterFiFi{% - \expandafter\BIC@ProcessDivII\romannumeral0% - \BIC@SubXY#1!#8!!!% - !#2#3!#4!#5!67% - #6!#7!#8!#9!% - }% - \else % 8y < #1 - \BIC@AfterFiFi{% - \expandafter\BIC@ProcessDivII\romannumeral0% - \BIC@SubXY#1!#9!!!% - !#2#3!#4!#5!89% - #6!#7!#8!#9!% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \subsection{\op{Mod}} -% -% \begin{macro}{\bigintcalcMod} -% |#1|: $x$\\ -% |#2|: $y$ -% \begin{macrocode} -\def\bigintcalcMod#1{% - \romannumeral0% - \expandafter\expandafter\expandafter\BIC@Mod - \bigintcalcNum{#1}!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@Mod} -% |#1|: $x$\\ -% |#2|: $y$ -% \begin{macrocode} -\def\BIC@Mod#1!#2{% - \expandafter\expandafter\expandafter\BIC@ModSwitchSign - \bigintcalcNum{#2}!#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BigIntCalcMod} -% \begin{macrocode} -\def\BigIntCalcMod#1!#2!{% - \romannumeral0% - \BIC@ModSwitchSign#2!#1!% -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ModSwitchSign} -% Decision table for \cs{BIC@ModSwitchSign}. -% \begin{quote} -% \begin{tabular}{@{}|l|l|l|@{}} -% \hline -% $y=0$ & \multicolumn{1}{l}{} & DivisionByZero\\ -% \hline -% $y>0$ & $x=0$ & $0$\\ -% \cline{2-3} -% & else & ModSwitch$(+,x,y)$\\ -% \hline -% $y<0$ & \multicolumn{1}{l}{} & ModSwitch$(-,-x,-y)$\\ -% \hline -% \end{tabular} -% \end{quote} -% |#1#2|: $y$\\ -% |#3#4|: $x$ -% \begin{macrocode} -\def\BIC@ModSwitchSign#1#2!#3#4!{% - \ifcase\ifx\\#2\\% - \ifx#100 % y = 0 - \else1 % y > 0 - \fi - \else - \ifx#1-2 % y < 0 - \else1 % y > 0 - \fi - \fi - \BIC@AfterFi{ 0\BigIntCalcError:DivisionByZero}% - \or % y > 0 - \ifcase\ifx\\#4\\\ifx#300 \else1 \fi\else1 \fi % x = 0 - \BIC@AfterFiFi{ 0}% - \else - \BIC@AfterFiFi{% - \BIC@ModSwitch{}#3#4!#1#2!% - }% - \fi - \else % y < 0 - \ifcase\ifx\\#4\\% - \ifx#300 % x = 0 - \else1 % x > 0 - \fi - \else - \ifx#3-2 % x < 0 - \else1 % x > 0 - \fi - \fi - \BIC@AfterFiFi{ 0}% - \or % x > 0 - \BIC@AfterFiFi{% - \BIC@ModSwitch--#3#4!#2!% - }% - \else % x < 0 - \BIC@AfterFiFi{% - \BIC@ModSwitch-#4!#2!% - }% - \fi - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ModSwitch} -% Decision table for \cs{BIC@ModSwitch}. -% \begin{quote} -% \begin{tabular}{@{}|l|l|l|@{}} -% \hline -% $y=1$ & \multicolumn{1}{l}{} & $0$\\ -% \hline -% $y=2$ & ifodd$(x)$ & sign $1$\\ -% \cline{2-3} -% & else & $0$\\ -% \hline -% $y>2$ & $x<0$ & -% $z\leftarrow x-(x/y)*y;\quad (z<0)\mathbin{?}z+y\mathbin{:}z$\\ -% \cline{2-3} -% & $x>0$ & $x - (x/y) * y$\\ -% \hline -% \end{tabular} -% \end{quote} -% |#1|: sign\\ -% |#2#3|: $x$\\ -% |#4#5|: $y$ -% \begin{macrocode} -\def\BIC@ModSwitch#1#2#3!#4#5!{% - \ifcase\ifx\\#5\\% - \ifx#410 % y = 1 - \else\ifx#421 % y = 2 - \else2 % y > 2 - \fi\fi - \else2 % y > 2 - \fi - \BIC@AfterFi{ 0}% y = 1 - \or % y = 2 - \ifcase\BIC@ModTwo#2#3! % even(x) - \BIC@AfterFiFi{ 0}% - \or % odd(x) - \BIC@AfterFiFi{ #11}% -? \else\BigIntCalcError:ThisCannotHappen% - \fi - \or % y > 2 - \ifx\\#1\\% - \else - \expandafter\BIC@Space\romannumeral0% - \expandafter\BIC@ModMinus\romannumeral0% - \fi - \ifx#2-% x < 0 - \BIC@AfterFiFi{% - \expandafter\expandafter\expandafter\BIC@ModX - \bigintcalcSub{#2#3}{% - \bigintcalcMul{#4#5}{\bigintcalcDiv{#2#3}{#4#5}}% - }!#4#5!% - }% - \else % x > 0 - \BIC@AfterFiFi{% - \expandafter\expandafter\expandafter\BIC@Space - \bigintcalcSub{#2#3}{% - \bigintcalcMul{#4#5}{\bigintcalcDiv{#2#3}{#4#5}}% - }% - }% - \fi -? \else\BigIntCalcError:ThisCannotHappen% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ModMinus} -% \begin{macrocode} -\def\BIC@ModMinus#1{% - \ifx#10% - \BIC@AfterFi{ 0}% - \else - \BIC@AfterFi{ -#1}% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% \begin{macro}{\BIC@ModX} -% |#1#2|: $z$\\ -% |#3|: $x$ -% \begin{macrocode} -\def\BIC@ModX#1#2!#3!{% - \ifx#1-% z < 0 - \BIC@AfterFi{% - \expandafter\BIC@Space\romannumeral0% - \BIC@SubXY#3!#2!!!% - }% - \else % z >= 0 - \BIC@AfterFi{ #1#2}% - \BIC@Fi -} -% \end{macrocode} -% \end{macro} -% -% \begin{macrocode} -\BIC@AtEnd% -% \end{macrocode} -% -% \begin{macrocode} -%</package> -% \end{macrocode} -%% \section{Installation} -% -% \subsection{Download} -% -% \paragraph{Package.} This package is available on -% CTAN\footnote{\CTANpkg{bigintcalc}}: -% \begin{description} -% \item[\CTAN{macros/latex/contrib/oberdiek/bigintcalc.dtx}] The source file. -% \item[\CTAN{macros/latex/contrib/oberdiek/bigintcalc.pdf}] Documentation. -% \end{description} -% -% -% \paragraph{Bundle.} All the packages of the bundle `oberdiek' -% are also available in a TDS compliant ZIP archive. There -% the packages are already unpacked and the documentation files -% are generated. The files and directories obey the TDS standard. -% \begin{description} -% \item[\CTANinstall{install/macros/latex/contrib/oberdiek.tds.zip}] -% \end{description} -% \emph{TDS} refers to the standard ``A Directory Structure -% for \TeX\ Files'' (\CTANpkg{tds}). Directories -% with \xfile{texmf} in their name are usually organized this way. -% -% \subsection{Bundle installation} -% -% \paragraph{Unpacking.} Unpack the \xfile{oberdiek.tds.zip} in the -% TDS tree (also known as \xfile{texmf} tree) of your choice. -% Example (linux): -% \begin{quote} -% |unzip oberdiek.tds.zip -d ~/texmf| -% \end{quote} -% -% \subsection{Package installation} -% -% \paragraph{Unpacking.} The \xfile{.dtx} file is a self-extracting -% \docstrip\ archive. The files are extracted by running the -% \xfile{.dtx} through \plainTeX: -% \begin{quote} -% \verb|tex bigintcalc.dtx| -% \end{quote} -% -% \paragraph{TDS.} Now the different files must be moved into -% the different directories in your installation TDS tree -% (also known as \xfile{texmf} tree): -% \begin{quote} -% \def\t{^^A -% \begin{tabular}{@{}>{\ttfamily}l@{ $\rightarrow$ }>{\ttfamily}l@{}} -% bigintcalc.sty & tex/generic/oberdiek/bigintcalc.sty\\ -% bigintcalc.pdf & doc/latex/oberdiek/bigintcalc.pdf\\ -% bigintcalc.dtx & source/latex/oberdiek/bigintcalc.dtx\\ -% \end{tabular}^^A -% }^^A -% \sbox0{\t}^^A -% \ifdim\wd0>\linewidth -% \begingroup -% \advance\linewidth by\leftmargin -% \advance\linewidth by\rightmargin -% \edef\x{\endgroup -% \def\noexpand\lw{\the\linewidth}^^A -% }\x -% \def\lwbox{^^A -% \leavevmode -% \hbox to \linewidth{^^A -% \kern-\leftmargin\relax -% \hss -% \usebox0 -% \hss -% \kern-\rightmargin\relax -% }^^A -% }^^A -% \ifdim\wd0>\lw -% \sbox0{\small\t}^^A -% \ifdim\wd0>\linewidth -% \ifdim\wd0>\lw -% \sbox0{\footnotesize\t}^^A -% \ifdim\wd0>\linewidth -% \ifdim\wd0>\lw -% \sbox0{\scriptsize\t}^^A -% \ifdim\wd0>\linewidth -% \ifdim\wd0>\lw -% \sbox0{\tiny\t}^^A -% \ifdim\wd0>\linewidth -% \lwbox -% \else -% \usebox0 -% \fi -% \else -% \lwbox -% \fi -% \else -% \usebox0 -% \fi -% \else -% \lwbox -% \fi -% \else -% \usebox0 -% \fi -% \else -% \lwbox -% \fi -% \else -% \usebox0 -% \fi -% \else -% \lwbox -% \fi -% \else -% \usebox0 -% \fi -% \end{quote} -% If you have a \xfile{docstrip.cfg} that configures and enables \docstrip's -% TDS installing feature, then some files can already be in the right -% place, see the documentation of \docstrip. -% -% \subsection{Refresh file name databases} -% -% If your \TeX~distribution -% (\TeX\,Live, \mikTeX, \dots) relies on file name databases, you must refresh -% these. For example, \TeX\,Live\ users run \verb|texhash| or -% \verb|mktexlsr|. -% -% \subsection{Some details for the interested} -% -% \paragraph{Unpacking with \LaTeX.} -% The \xfile{.dtx} chooses its action depending on the format: -% \begin{description} -% \item[\plainTeX:] Run \docstrip\ and extract the files. -% \item[\LaTeX:] Generate the documentation. -% \end{description} -% If you insist on using \LaTeX\ for \docstrip\ (really, -% \docstrip\ does not need \LaTeX), then inform the autodetect routine -% about your intention: -% \begin{quote} -% \verb|latex \let\install=y\input{bigintcalc.dtx}| -% \end{quote} -% Do not forget to quote the argument according to the demands -% of your shell. -% -% \paragraph{Generating the documentation.} -% You can use both the \xfile{.dtx} or the \xfile{.drv} to generate -% the documentation. The process can be configured by the -% configuration file \xfile{ltxdoc.cfg}. For instance, put this -% line into this file, if you want to have A4 as paper format: -% \begin{quote} -% \verb|\PassOptionsToClass{a4paper}{article}| -% \end{quote} -% An example follows how to generate the -% documentation with pdf\LaTeX: -% \begin{quote} -%\begin{verbatim} -%pdflatex bigintcalc.dtx -%makeindex -s gind.ist bigintcalc.idx -%pdflatex bigintcalc.dtx -%makeindex -s gind.ist bigintcalc.idx -%pdflatex bigintcalc.dtx -%\end{verbatim} -% \end{quote} -% -% \begin{History} -% \begin{Version}{2007/09/27 v1.0} -% \item -% First version. -% \end{Version} -% \begin{Version}{2007/11/11 v1.1} -% \item -% Use of package \xpackage{pdftexcmds} for \LuaTeX\ support. -% \end{Version} -% \begin{Version}{2011/01/30 v1.2} -% \item -% Already loaded package files are not input in \hologo{plainTeX}. -% \end{Version} -% \begin{Version}{2012/04/08 v1.3} -% \item -% Fix: \xpackage{pdftexcmds} wasn't loaded in case of \hologo{LaTeX}. -% \end{Version} -% \begin{Version}{2016/05/16 v1.4} -% \item -% Documentation updates. -% \end{Version} -% \end{History} -% -% \PrintIndex -% -% \Finale -\endinput |