% \iffalse meta-comment
%
% File: bigintcalc.dtx
% Version: 2019/12/15 v1.5
% Info: Expandable calculations on big integers
%
% Copyright (C)
%    2007, 2011, 2012 Heiko Oberdiek
%    2016-2019 Oberdiek Package Support Group
%    https://github.com/ho-tex/bigintcalc/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/bigintcalc/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/bigintcalc/bigintcalc.dtx
%    CTAN:macros/latex/contrib/bigintcalc/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/bigintcalc/bigintcalc.sty
%    TDS:doc/latex/bigintcalc/bigintcalc.pdf
%    TDS:source/latex/bigintcalc/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 2019/12/15 v1.5 Expandable calculations on big integers (HO)}
\Msg{************************************************************************}

\keepsilent
\askforoverwritefalse

\let\MetaPrefix\relax
\preamble

This is a generated file.

Project: bigintcalc
Version: 2019/12/15 v1.5

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/bigintcalc/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/bigintcalc}%
  \file{bigintcalc.sty}{\from{bigintcalc.dtx}{package}}%
}

\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}%
  [2019/12/15 v1.5 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{2019/12/15 v1.5}
% \author{Heiko Oberdiek\thanks
% {Please report any issues at \url{https://github.com/ho-tex/bigintcalc/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}%
  [2019/12/15 v1.5 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/bigintcalc/bigintcalc.dtx}] The source file.
% \item[\CTAN{macros/latex/contrib/bigintcalc/bigintcalc.pdf}] Documentation.
% \end{description}
%
%
% \paragraph{Bundle.} All the packages of the bundle `bigintcalc'
% 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/bigintcalc.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{bigintcalc.tds.zip} in the
% TDS tree (also known as \xfile{texmf} tree) of your choice.
% Example (linux):
% \begin{quote}
%   |unzip bigintcalc.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/bigintcalc/bigintcalc.sty\\
%   bigintcalc.pdf & doc/latex/bigintcalc/bigintcalc.pdf\\
%   bigintcalc.dtx & source/latex/bigintcalc/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}
%   \begin{Version}{2019/12/15 v1.5}
%   \item
%     Documentation updates.
%   \end{Version}
% \end{History}
%
% \PrintIndex
%
% \Finale
\endinput
