% -*- coding: utf-8-unix; time-stamp-format: "%02d-%02m-%:y %02H:%02M:%02S %Z"; sentence-end-double-space: t; -*-
%<*dtx>
\def\bnedtxtimestamp  {Time-stamp: <12-05-2021 22:05:26 CEST>}
\iffalse
%</dtx>
%<*drv>
%% ---------------------------------------------------------------
\def\bnedocdate {2021/05/12}% package bnumexpr documentation date
\def\bnepackdate{2021/05/12}% package bnumexpr date
\def\bneversion {1.4}      % package bnumexpr version
%</drv>
%<*readme>--------------------------------------------------------
| Source:  bnumexpr.dtx
| Version: v1.4, 2021/05/12 (doc: 2021/05/12)
| Author:  Jean-Francois Burnol
| Info:    Expressions with big integers
| License: LPPL 1.3c

bnumexpr usage
==============

The LaTeX package `bnumexpr` allows expandable computations with
integers and the four infix operators `+`, `-`, `*`, `/` using the
expression syntax familiar from the `\numexpr` e-TeX parser, with
these extensions:

- arbitrarily big integers,
- floored division `//`,
- associated modulo `/:`,
- power operators `^` and `**`,
- factorial post-fix operator `!`,
- comma separated expressions,
- the space character as well as the underscore may serve
  to separate groups of digits,
- optional conversion of output to hexadecimal.

The expression parser is a scaled-down variant from the
`\xintiiexpr...\relax`
parser from package [xintexpr](http://ctan.org/pkg/xintexpr).

To support hexadecimal input and output, the package
[xintbinhex](http://ctan.org/pkg/xint) is loaded automatically.

The package loads by default [xintcore](http://ctan.org/pkg/xint)
but the option _custom_ together with macro `\bnumexprsetup` allow to map
the syntax elements to macros from an alternative big integer
expandable engine of the user own choosing,
and then [xintcore](http://ctan.org/pkg/xint) is not loaded.

Note; the possibility not to use the xintcore macros might be
removed in the future: perhaps a future release will maintain during
computations a private internal representation (especially tailored
either for the xintcore macros or new ones which would be included
within `bnumexpr.sty` itself) and the constraints this implies may
render optional use of other macros impossible.

Installation
============

Use your installation manager to install or update `bnumexpr`.

Else, obtain `bnumexpr.dtx`, from CTAN:

> <http://www.ctan.org/pkg/bnumexpr>

Run `"etex bnumexpr.dtx"` to extract these files:

`bnumexpr.sty`
  : this is the style file.

`README.md`

`bnumexprchanges.tex`
  : change history.

`bnumexpr.tex`
  : can be used to generate the documentation:

  :  - with latex+dvipdfmx: `"latex bnumexpr.tex"` (thrice) then
      `"dvipdfmx bnumexpr.dvi"`.

  :  - with pdflatex: `"pdflatex bnumexpr.tex"` (thrice).

  : In both cases files `README.md` and `bnumexprchanges.tex` must
    be located in the same repertory as `bnumexpr.tex` and `bnumexpr.dtx`.

without `bnumexpr.tex`:
  : `"pdflatex bnumexpr.dtx"` (thrice) extracts all files and
    simultaneously generates the pdf documentation.

Finishing the installation:

           bnumexpr.sty   --> TDS:tex/latex/bnumexpr/

           bnumexpr.dtx   --> TDS:source/latex/bnumexpr/

           bnumexpr.pdf   --> TDS:doc/latex/bnumexpr/
              README.me   --> TDS:doc/latex/bnumexpr/

License
=======

Copyright (C) 2014-2021 by Jean-Francois Burnol

| This Work may be distributed and/or modified under the
| conditions of the LaTeX Project Public License 1.3c.
| This version of this license is in

>   <http://www.latex-project.org/lppl/lppl-1-3c.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 "author-maintained".

The Author and Maintainer of this Work is Jean-Francois Burnol.

This Work consists of the main source file `bnumexpr.dtx`
and the derived files

    bnumexpr.sty, bnumexpr.pdf, bnumexpr.tex, bnumexprchanges.tex,
    and README.md

%</readme>--------------------------------------------------------
%<*!readme>
%% ---------------------------------------------------------------
%% The bnumexpr package: Expressions with big integers
%% Copyright (C) 2014-2021 by Jean-Francois Burnol
%%
%</!readme>
%<*changes>-------------------------------------------------------
\item[1.4 (2021/05/12)]
  \begin{itemize}
  \item technology transfer from \xintexprname |1.4| of
    |2020/01/31|. The |\expanded| primitive is now required (TeXLive
    2019).
  \item addition to the syntax of the |"| prefix for hexadecimal
    input.
  \item addition of |\evaltohex| which is like |\bnumeval| with an extra
    conversion step to hexadecimal notation.
  \end{itemize}

\item[1.2e (2019/01/08)]
  Fixes a documentation glitch (extra braces when mentioning |\the\numexpr| or
  |\thebnumexpr|).

\item[1.2d (2019/01/07)]
  \begin{itemize}
  \item requires \xintcorename |1.3d| or later (if not using option |custom|).
  \item adds |\bnumeval|\marg{expression} user interface.
  \end{itemize}

\item[1.2c (2017/12/05)] \textbf{Breaking changes:}
  \begin{itemize}
  \item requires \xintcorename |1.2p| or later (if not using option |custom|).
  \item |divtrunc| key of |\bnumexprsetup| is renamed to |div|.
  \item the |//| and |/:| operators are now by default associated to the
    \emph{floored} division. This is to keep in sync with the change of
    \xintcorename at |1.2p|.
  \item for backwards compatibility, one
    may add to existing document:\newline
    \string\bnumexprsetup\{div=\string\xintiiDivTrunc,
    mod=\string\xintiiModTrunc\}
  \end{itemize}

\item[1.2b (2017/07/09)]
  \begin{itemize}
  \item the |_| may be used to separate visually blocks of digits in long
    numbers.
  \end{itemize}

\item[1.2a (2015/10/14)]
  \begin{itemize}
  \item requires \xintcorename |1.2| or later (if not using option |custom|).
  \item additions to the syntax: factorial |!|, truncated division
    |//|, its associated modulo |/:| and |**| as alternative to |^|.
  \item all options removed except |custom|.
  \item new command |\bnumexprsetup| which replaces the commands such as
    |\bnumexprusesbigintcalc|.
  \item the parser is no more limited to numbers with at most 5000 digits.
  \end{itemize}

\item[1.1b (2014/10/28)]
  \begin{itemize}
  \item README converted to |markdown/pandoc| syntax,
  \item the package now loads only |xintcore|, which belongs to |xint| bundle
    version |1.1| and extracts from the earlier |xint| package the core arithmetic
    operations as used by |bnumexpr|.
  \end{itemize}

\item[1.1a (2014/09/22)]
  \begin{itemize}
  \item added |l3bigint| option to use experimental \LaTeX3
    package of the same name,

  \item added Changes and Readme sections to the documentation,

  \item better |\BNE_protect| mechanism for use of
  |\bnumexpr...\relax| inside an |\edef| (without |\bnethe|). Previous one,
  inherited from |xintexpr.sty 1.09n|, assumed that the |\.=<digits>| dummy
  control sequence encapsulating the computation result had |\relax|
  meaning. But removing this assumption was only a matter of letting
  |\BNE_protect| protect two, not one, tokens. This will be backported to
  next version of \xintexprname, naturally (done with |xintexpr.sty 1.1|).
  \end{itemize}

\item[1.1 (2014/09/21)] First release. This is down-scaled from the
  (development version of) \xintexprname. Motivation came the previous day
  from a chat with \textsc{Joseph Wright} over big int status in \LaTeX3.
  The |\bnumexpr...\relax| parser can be used on top of big int macros of
  one's choice. Functionalities limited to the basic operations. I leave
  the power operator |^| as an option.
%</changes>-------------------------------------------------------
%<*drv>-----------------------------------------------------------
%% latex bnumexpr.tex (thrice) && dvipdfmx bnumexpr.dvi
%% to produce bnumexpr.pdf
%%
%% or pdflatex bnumexpr.tex (no need to change \Withdvipdfmx toggle,
%% pdf engine will be detected automatically)
%%
\NeedsTeXFormat{LaTeX2e}
\ProvidesFile{bnumexpr.tex}%
[\bnepackdate\space v\bneversion\space driver file for %
  bnumexpr documentation (JFB)]%
\PassOptionsToClass{a4paper,fontsize=11pt}{scrdoc}
\chardef\Withdvipdfmx 1 %
\chardef\NoSourceCode 0 % replace 0 by 1 for not including source code
\input bnumexpr.dtx
%%% Local Variables:
%%% mode: latex
%%% End:
%</drv>-----------------------------------------------------------
%<*dtx>
\fi % end of \iffalse block around generated files
\chardef\noetex 0
\ifx\numexpr\undefined \chardef\noetex 1 \fi
\ifnum\noetex=1 \chardef\extractfiles 0 % extract files, then stop
\else
    \ifx\ProvidesFile\undefined
      \chardef\extractfiles 0 % no LaTeX2e; etex, ... on bnumexpr.dtx
    \else % latex/pdflatex on bnumexpr.tex or on bnumexpr.dtx
      \ifx\Withdvipdfmx\undefined
        % latex run is on bnumexpr.dtx, we will extract all files
        \chardef\extractfiles 1 % 1 = extract and typeset, 2=only typeset
        \chardef\Withdvipdfmx 0 % 0 = pdflatex or latex+dvips, 1 = dvipdfmx
        \chardef\NoSourceCode 0 % 0 = include source code, 1 = do not
        \NeedsTeXFormat{LaTeX2e}%
        \PassOptionsToClass{a4paper,fontsize=11pt}{scrdoc}%
      \else % latex run is on bnumexpr.tex,
        \chardef\extractfiles 2 % no extractions
      \fi
      \ProvidesFile{bnumexpr.dtx}[bundle source (\bnedtxtimestamp)]%
    \fi
\fi
\ifnum\extractfiles<2 % extract files
\def\MessageDeFin{\newlinechar10 \let\Msg\message
\Msg{^^J}%
\Msg{********************************************************************^^J}%
\Msg{*^^J}%
\Msg{* To finish the installation you have to move the following^^J}%
\Msg{* files into a directory searched by TeX:^^J}%
\Msg{*^^J}%
\Msg{*\space\space\space\space bnumexpr.sty^^J}%
\Msg{*^^J}%
\Msg{* To produce the documentation run latex thrice on bnumexpr.tex^^J}%
\Msg{* then dvipdfmx on bnumexpr.dvi. (ignore the dvipdfmx warnings)^^J}%
\Msg{*^^J}%
\Msg{* Happy TeXing!^^J}%
\Msg{*^^J}%
\Msg{********************************************************************^^J}%
}%
\begingroup
    \input docstrip.tex
    \askforoverwritefalse
    \generate{\nopreamble\nopostamble
    \file{README.md}{\from{bnumexpr.dtx}{readme}}
    \usepreamble\defaultpreamble
    \usepostamble\defaultpostamble
    \file{bnumexprchanges.tex}{\from{bnumexpr.dtx}{changes}}
    \file{bnumexpr.tex}{\from{bnumexpr.dtx}{drv}}
    \file{bnumexpr.sty}{\from{bnumexpr.dtx}{package}}}
\endgroup
\fi % end of file extraction
\ifnum\extractfiles=0
% direct tex/etex/xetex on bnumexpr.dtx, files now extracted, stop
  \MessageDeFin\expandafter\end
\fi
% no use of docstrip to extract files if latex compilation was on bnumexpr.tex
\ifdefined\MessageDeFin\AtEndDocument{\MessageDeFin}\fi
%-------------------------------------------------------------------------------
\documentclass {scrdoc}
\ifnum\NoSourceCode=1 \OnlyDescription\fi
\usepackage{ifpdf}
\ifpdf\chardef\Withdvipdfmx 0 \fi
\makeatletter
\ifnum\Withdvipdfmx=1
   \@for\@tempa:=hyperref,bookmark,graphicx,xcolor,pict2e\do
            {\PassOptionsToPackage{dvipdfmx}\@tempa}
   %
   \PassOptionsToPackage{dvipdfm}{geometry}
   \PassOptionsToPackage{bookmarks=true}{hyperref}
   \PassOptionsToPackage{dvipdfmx-outline-open}{hyperref}
   \PassOptionsToPackage{dvipdfmx-outline-open}{bookmark}
   %
   \def\pgfsysdriver{pgfsys-dvipdfm.def}
\else
   \PassOptionsToPackage{bookmarks=true}{hyperref}
\fi
\makeatother

\pagestyle{headings}

\usepackage[T1]{fontenc}

\usepackage[hscale=0.66,vscale=0.75]{geometry}

% requires newtxtt 1.05 or later
\usepackage[zerostyle=a,scaled=0.95,straightquotes]{newtxtt}
\renewcommand\familydefault\ttdefault
\usepackage[noendash]{mathastext}
\renewcommand\familydefault\sfdefault

\usepackage{graphicx}
\usepackage[dvipsnames]{xcolor}
\definecolor{joli}{RGB}{225,95,0}
\definecolor{JOLI}{RGB}{225,95,0}
\definecolor{BLUE}{RGB}{0,0,255}
%\definecolor{niceone}{RGB}{38,128,192}% utilisé avant pour urlcolor
%\colorlet{smallverbcolor}{RoyalPurple}% \colorlet{jfverbcolor}{yellow!5}
\colorlet{smallverbcolor}{NavyBlue}%
\colorlet{softwrapcolor}{blue}
\colorlet{digitscolor}{OrangeRed}

% transféré de xint-manual.tex (maintenant dans xint.dtx)
\DeclareFontFamily{U}{MdSymbolC}{}
\DeclareFontShape {U}{MdSymbolC}{m}{n}{<-> MdSymbolC-Regular}{}

\makeatletter
\newbox\cdbx@SoftWrapIcon
\def\cdbx@SetSoftWrapBox{%
    \setbox\cdbx@SoftWrapIcon\hb@xt@\z@
    {\hb@xt@\fontdimen2\font
        {\hss{\color{softwrapcolor}\usefont{U}{MdSymbolC}{m}{n}\char"97}\hss}%
     \hss}%
   }
\makeatother

\usepackage[english]{babel}

\usepackage{hyperref}
\hypersetup{%
%linktoc=all,%
breaklinks=true,%
colorlinks=true,%
urlcolor=SkyBlue,%
linkcolor=PineGreen,%
pdfauthor={Jean-François Burnol},%
pdftitle={The bnumexpr package},%
pdfsubject={Arithmetic with TeX},%
pdfkeywords={Expansion, arithmetic, TeX},%
pdfstartview=FitH,%
pdfpagemode=UseOutlines}
\usepackage{bookmark}

%---- \verb, and verbatim like `environments'. \MicroFont et \MacroFont
\makeatletter
\def\MicroFont {\ttfamily\cdbx@SetSoftWrapBox\color{smallverbcolor}}
%\def\MicroFont {\ttfamily \color[named]{OrangeRed}\cdbx@SetSoftWrapBox }

% \MacroFont est utilisé par macrocode, mais sa définition est figée dans
% \macro@font au \begin{document}

\def\MacroFont {\ttfamily \baselineskip12pt\relax }

%--- November 4, 2014 making quotes straight. (maintenu pour *)
%
% there is no hook in \macrocode after \dospecials etc. Thus I will need to
% take the risk that some future evolution of doc.sty (or perhaps scrdoc)
% invalidates the following.
%
% Actually, I should not at all rely on the doc class, I should do it all by
% myself.

\def\macrocode{\macro@code
               \frenchspacing \@vobeyspaces
               \makestarlowast % \makequotesstraight (obsolète)
               \xmacro@code }

%--- lower * symbol in text

\def\lowast{\raisebox{-.25\height}{*}}
\catcode`* \active
\def\makestarlowast {\let*\lowast\catcode`\*\active}%
\catcode`* 12

%------------obsolete------------
%--- straight quotes, added (finally...) Nov 4, 2014
% \begingroup\makeatletter
%   \catcode`\'\active
%   \catcode`\`\active
% \@firstofone {\endgroup
%   \def\makequotesstraight {% textcomp package has been loaded by newtxtt
%      \let`\textasciigrave
%      \let'\textquotesingle
%      \catcode39\active
%      \catcode96\active }%
% }
%------------

% Tentative, mardi 09 septembre 2014 à 22:41:28

% Modifié mardi 13 octobre 2015 à 15:24:00 pour utilisable en
% argument, et en particulier dans un \footnote{}. Mais utilise
% \scantokens et macro délimitée maintenant.

%\def\jf@makeletter #1{\catcode`#111\relax }

\def\verb #1%
{%
  \relax\leavevmode\null
  \begingroup
   \MicroFont
   \catcode`_ 11 \catcode`! 11 \catcode`: 11 
   \catcode`< 11 \catcode`> 11
  % \scantokens will have a result of inserting a space after cs's.
  % hence the need to have the catcodes of things like _ right.
  % I also need < for > for one occasion in code comments
  % naturally won't work in footnotes though.
  % this code is truly not satisfying, but enough for my needs here.
   \def\@jfverb ##1#1{\let\do\@makeother \dospecials
                      \makestarlowast
  %\let\do\do@noligs  \verbatim@nolig@list % not needed here
                      \@vobeyspaces\everyeof{\noexpand}%
                      \expandafter\@@jfverb\scantokens{##1}\relax}%
  \@jfverb
}%

% Pour v1.2 je laisse tomber les colorbox. À la place je change la couleur
% du texte. J'utilise le violet de xint. (mis dans \Microfont)
% \def\@@@jfverb #1{\ifcat\noexpand#1$% $
%                       \endgroup\else
% %      \penalty\z@
%        \discretionary{\copy\cdbx@SoftWrapIcon}{}{}%
% %      \colorbox{jfverbcolor}{\strut #1}% unfortunately, impacts pdf size
%        #1%
%        \expandafter\@@@jfverb\fi }

\def\@@jfverb #1{\ifcat\noexpand#1\relax\endgroup\else
       \discretionary{\copy\cdbx@SoftWrapIcon}{}{}%
       #1\expandafter\@@jfverb\fi }

\makeatother

% mardi 13 octobre 2015 à 15:32:51
% le | n'est pas encore actif ici!
\catcode`| \active
    \def\bneshow #1%
    {|\thebnumexpr#1\relax|$$\color{digitscolor}\bnumexpr#1\relax$$}
    \def\bneshoweval #1%
    {|\bnumeval{#1}|$$\color{digitscolor}\bnumeval{#1}$$}
    \def\bneshowevaltohex #1%
    {|\evaltohex{#1}|$$\color{digitscolor}\evaltohex{#1}$$}
\catcode`| 12

\DeclareRobustCommand\csa [1]{{\char92\detokenize{#1}}}
\newcommand\csh[1]{\texorpdfstring{\csa{#1}}{\textbackslash\detokenize{#1}}}

\usepackage{xspace}

\def\bnumname
   {\href{http://www.ctan.org/pkg/bnumexpr}{bnumexpr}\xspace }%

\def\bnumnameimp
   {\texorpdfstring
          {\hyperref[sec:bnumexprcode]{{\color{smallverbcolor}\ttzfamily bnumexpr}}}
          {bnumexpr}%
    \xspace }%

\def\xintname
   {\href{http://www.ctan.org/pkg/xint}{xint}\xspace }%
\def\xintcorename
   {\href{http://www.ctan.org/pkg/xint}{xintcore}\xspace }%
\def\xintexprname
   {\href{http://www.ctan.org/pkg/xint}{xintexpr}\xspace }%
\def\xintbinhexname
   {\href{http://www.ctan.org/pkg/xint}{xintbinhex}\xspace }%


% \centeredline: OUR OWN LITTLE MACRO FOR CENTERING LINES
% =======================================================

% 7 mars 2013
% -----------
%
% This macro allows to conveniently center a line inside a paragraph and still
% allow use therein of \verb or other macros changing catcodes.
% A proposito, the \LaTeX \centerline uses \hsize and not \linewidth !
% (which in my humble opinion is bad)

% Actually my \centeredline works nicely in list environments.

% \ignorespaces ajouté le 9 juin 2013.

% Note: \centeredline creates a group

\makeatletter
\newcommand*\centeredline {%
      \ifhmode \\\relax
        \def\centeredline@{\hss\egroup\hskip\z@skip\ignorespaces }%
      \else
        \def\centeredline@{\hss\egroup }%
      \fi
      \afterassignment\@centeredline
      \let\next=}
\def\@centeredline
    {\hbox to \linewidth \bgroup \hss \bgroup \aftergroup\centeredline@ }


\frenchspacing
\usepackage{bnumexpr}

\usepackage{etoc}

\usepackage{framed}
\makeatletter\let\check@percent\relax\makeatother
\begin{document}
\thispagestyle{empty}
\ttzfamily
\pdfbookmark[1]{Title page}{TOP}

{%
\normalfont\Large\parindent0pt \parfillskip 0pt\relax
 \leftskip 2cm plus 1fil \rightskip 2cm plus 1fil
 The \bnumname package\par
}

{\centering
  \textsc{Jean-François Burnol}\par
  \footnotesize
  jfbu (at) free (dot) fr\par
  Package version: \bneversion\ (\bnepackdate);
            documentation date: \bnedocdate.\par
  {From source file \texttt{bnumexpr.dtx}. \bnedtxtimestamp.}\par
}

\etocsetnexttocdepth{section}
\tableofcontents

\section{\csh{thebnumexpr}, \csh{bnumeval}, \csh{evaltohex}}
\label{sec:bnumexpr}

\LaTeX\ Package \bnumname provides |\thebnumexpr|\meta{expression}|\relax|:%
%
\footnote{Since |1.4|, one can use |\bnumexpr...\relax| directly in
  typesetting context, it is not mandatory to prefix it with |\bnethe| or to
  use |\thebnumexpr|.}
%
it is analogous to
  |\the\numexpr|\meta{expression}|\relax|, with these extensions:
\begin{itemize}
\item it allows arbitrarily big integers,
\item it computes powers (with either |**| or |^| as infix operator),
\item it computes factorials (with |!| as postfix operator),
\item it has an operator |//| for floored division and |/:| for the
  associated modulo,
\item the space character is ignored and can thus be used to separate in the
  source blocks of digits for better readability of long numbers,
\item also the underscore |_| may be used as visual digit
  separator,
\item comma separated expressions are allowed.
\end{itemize}
There is also an alternative interface |\bnumeval|\marg{expression}, where the
expression is fetched as braced argument. And there is
|\evaltohex|\marg{expression} which does the same as
|\bnumeval|\marg{expression} but with a conversion to hexadecimal notation of
the (possibly comma separated) output. Hexadecimal input uses the |"| prefix.

This package parser is a scaled-down variant of |\xintiiexpr| from package
\xintexprname, dropping support for nested structures, functions, variables,
booleans, etc..., but incorporating by default support for hexadecimal input
as \xintbinhexname will be automatically loaded.

The \eTeX{} extensions are required, this is the default on all modern
installations for \verb?latex|pdflatex? and also for \verb?xelatex|lualatex?.

Further, at |1.4| (|2021/05/12|) the |\expanded| primitive is
required. It is available in all engines since \TeX Live 2019.

By default the arithmetic operations are executed via the \xintcorename
macros, but via option |custom| and usage of |\bnumexprsetup| it is
possible to replace them by expandable macros of a custom origin.

\section{Examples}

\noindent\bneshow {---1 208 637 867 * (2 187 917 891 - 3 109 197 072)}%
\bneshoweval {(13_8089_1090-300_1890_2902)*(1083_1908_3901-109_8290_3890)}%
\bneshow{(92_874_927_979**5-31_9792_7979**6)/30!}%
\bneshoweval {30!/20!/21/22/23/24/25/(26*27*28*29)}%
\bneshow {13^50//12^50, 13^50/:12^50}%
\bneshoweval {13^50/12^50, 12^50}%
\bneshow {(1^10+2^10+3^10+4^10+5^10+6^10+7^10+8^10+9^10)^3}%
\bneshoweval {100!/36^100}%
\bneshoweval {"10*"100*"1000*"A0000, 16^(1+2+3+4)*10}%
\bneshowevaltohex{"7FFFFFFF+1, "400^3, "ABCDEF*"FEDCBA}%

\section{Differences from \csh{numexpr}}

Apart from the extension to big integers (i.e. exceeding the \TeX{} limit at
\number"7FFFFFFF), and the added operators, there are a number of important
differences between |\bnumexpr| and |\numexpr|:

\begin{enumerate}
\item one may embed directly |\bnumexpr...\relax| in another one (or in
  a |\xintexpr...\relax|), but not in a |\numexpr...\relax|: it must
  then be using |\thebnumexpr...| or |\bnethe\bnumexpr...| syntax; on
  the other hand a |\numexpr...\relax| does not need to be prefixed by
  |\the| or |\number| inside |\bnumexpr...\relax|.

\item contrarily to |\numexpr|, the |\bnumexpr| parser stops only after having
  found (and swallowed) a mandatory ending |\relax| token,

\item in particular spaces between digits do not stop |\bnumexpr|, in contrast
  with |\numexpr|:

  |\the\numexpr 3 5+79\relax| expands (in one step) to \expandafter|\the\numexpr 3 5+79\relax|

  |\thebnumexpr 3 5+79\relax| expands (in two steps) to
  \expandafter\expandafter\expandafter|\thebnumexpr 3 5+79\relax|

\item one may do |\edef\variable{\bnumexpr 1+2\relax}|, and then either use
  |\variable| in another |\bnumexpr...\relax|, or print it via
  |\bnethe\variable| (or directly since |1.4|). The computation is done at the time of the |\edef|
  (and two expansion steps suffice). This is again in contrast with
  |\numexpr...\relax| which, without |\the| (or |\number| or
  |\romannumeral|) as prefix would not expand inside an |\edef|,

\item expressions may be comma separated. On input, spaces are ignored,
  naturally, and on output the values are comma separated with a space after
  each comma,

\item |\bnumexpr -(1+1)\relax| is legal contrarily to |\numexpr -(1+1)\relax|
  which raises an error,

\item |\numexpr 2\cnta\relax| is illegal (with |\cnta| a |\count|-variable.)
  But |\bnumexpr 2\cnta\relax| is perfectly legal and will do the tacit
  multiplication,
% \newcount\cnta
% \cnta 1111
% \thebnumexpr 2\cnta\relax

\item more generally, tacit multiplication applies in front of parenthesized
  sub-expressions, or sub |\bnumexpr...\relax| (or |\numexpr...\relax|), or
  also after parentheses in front of numbers,

\item the underscore |_| is accepted within the digits composing a number and
  is silently ignored by |\bnumexpr|.

\end{enumerate}

An important thing to keep in mind is that if one has a calculation
whose result is a small integer, acceptable by \TeX{} in |\ifnum| or
count assignments, this integer produced by |\thebnumexpr| is not
self-delimiting, contrarily to a |\numexpr...\relax| construct: the
situation is exactly as with a |\the\numexpr...\relax|, thus one may
need to terminate the number to avoid premature expansion of following
tokens; for example with the |\space| token.

\section{Printing big numbers}

\LaTeX{} will not split long numbers at the end of lines. I personally
often use helper macros (not in the package) of the following type:

\begin{verbatim}
\def\allowsplits #1{\ifx #1\relax \else #1\hskip 0pt plus 1pt\relax
                    \expandafter\allowsplits\fi}%
\def\printnumber #1{\expandafter\allowsplits \romannumeral-`0#1\relax }%
% \printnumber thus first ``fully'' expands its argument.
\end{verbatim}

\def\allowsplits #1{\ifx #1\relax \else #1\hskip 0pt plus 1pt\relax
                    \expandafter\allowsplits\fi}%
\def\printnumber #1{\expandafter\allowsplits \romannumeral-`0#1\relax }%

\noindent|\thebnumexpr 1000!\relax=|\phantom{0}{\color{digitscolor}\printnumber{\thebnumexpr 1000!\relax}}\par

\section{Expression syntax}

It is the expected one with infix operators and parentheses, the
recognized operators being |+|, |-|, |*|, |/| (rounded division),
|^| (power), |**| (power), |//| (by default floored division),
|/:| (the associated modulo) and |!| (factorial). One can input hexadecimal
numbers as in \TeX\ syntax for number assignments, i.e. using a |"| prefix and
only uppercase letters |ABCDEF|.

The modulo |/:| is by default associated with the floored division |//|, but
using |\bnumexprsetup{mod=...}| it can, like the other operators, be remapped
to any macro of one's choice.

Different computations may be separated by commas. The whole
expression is handled token by token, any component (digit, operator,
parenthesis... even the ending |\relax|) may arise on the spot from
macro expansions.

The precedence rules are the expected ones. Tacit multiplication applies in
front of parentheses, and after them, and it has an elevated precedence
compared to multiplication explicitly induced by |*|.

There is currently no user interface to change precedence levels. The
three operators |/|, |//|, |/:| are at the same level of precedence as the
multiplication |*|. The factorial postfix |!| has highest precedence. The
minus signs inherit the precedence level of the previously encountered infix
operators.

In case of equal precedence the operations are left-associative,%
%
\footnote{But it has been announced at \xintexprname \texttt{1.4} that
  probably in future power operator will become right-associative, and if this
  is done, this will be transferred to \bnumname also.}
%
hence:\newline \bneshoweval{2^3^4, (2^3)^4, 2^(3^4)}

The underscore |_| can be used to separate digits in long numbers, for
readability of the input.

\section{Options}

The sole package option is |custom|: it tells \bnumname not to load
package \xintcorename.

\section{\csh{bnumexprsetup}}

Package \bnumname needs that some big integer engine provides the macros doing
the actual computations. By default, it loads package \xintcorename (a subset
of \href{http://www.ctan.org/pkg/xint}{xint}) and uses \csa{bnumexprsetup} in
the following way:
\begin{verbatim}
    \usepackage{xintcore}
    \bnumexprsetup{add=\xintiiAdd, sub=\xintiiSub, mul=\xintiiMul,
                   divround=\xintiiDivRound, div=\xintiiDivFloor,
                   mod=\xintiiMod, pow=\xintiiPow, fac=\xintiiFac}
\end{verbatim}

If
using \csa{bnumexprsetup}, it is not necessary to specify all keys,
for example one can do |\bnumexprsetup{mul=\MyFasterMul}|, and only
multiplication will be changed.

Naturally it is up to the user to load the appropriate package for
the alternative macros.

As per the macros which are the key values, they must have the
following properties:
\begin{enumerate}
\item they must be completely expandable (in the sense of an |\edef|
  or a |\csname...\endcsname|.)
\item they must fully expand their arguments first (in the sense of
  |\romannumeral-`0|.)
\item they must output a number with no leading zeros, at most one
  minus sign and no plus sign. 
\end{enumerate}
The first two items are truly mandatory, the last one may be not
obeyed if the extra key |opp| is used with \csa{bnumexprsetup} to
specify a suitable macro for the opposite of a number. This macro will
be presented not with a braced argument but directly with a sequence
of digits (either as gathered by the parser which skips leading
zeros, or as produced by the other arithmetic macros and then there
could be a minus, or even a plus if macros others than the ones from
\xintcorename have been used).
Thus, |opp| could identify a plus sign |+| upfront and then act
adequately.\footnote{see \csa{BNE_Op_opp} in the code for the
  default.}

Macro |\bnumexprsetup| can be used multiple times in the same document, thus
allowing to switch math engines or to remap operators to some other arithmetic
macros of the same math engine. Its effect obeys the local scope.

At |1.4| release there is no option to customize how the hexadecimal input and
output is handled, it goes necessarily via the \xintbinhexname macros.

\section{Readme}
\begingroup
\makeatletter\def\x{\baselineskip10pt
                    \ttfamily\settowidth\dimen@{X}%
                    %\parindent \dimexpr.5\linewidth-34\dimen@\relax
                    \parindent\z@
                    \let\do\do@noligs\verbatim@nolig@list
                    \let\do\@makeother\dospecials
                    \makestarlowast
                    %\def\par{\leavevmode\null\@@par\penalty\interlinepenalty}%
                    \def\par{\leavevmode\null\@@par\pagebreak[1]}%
                    \@vobeyspaces\obeylines
                    \noindent\kern\parindent\input README.md
\endgroup }\x

\section{Changes}
%\small
\begin{description}
\input bnumexprchanges.tex
\end{description}

\StopEventually{\end{document}\endinput}

\newgeometry{hscale=0.75,vscale=0.75}% ATTENTION \newgeometry fait
                                % un reset de vscale si on ne le
                                % précise pas ici !!!

\MakePercentIgnore
%
% \catcode`\<=0 \catcode`\>=11 \catcode`\*=11 \catcode`\/=11
% \let</dtx>\relax
% \def<*package>{\catcode`\<=12 \catcode`\>=12 \catcode`\*=12 \catcode`\/=12 }
%</dtx>
%<*package>
%
% \section{Package \bnumnameimp implementation}
% \label{sec:bnumexprcode}
% \etocdefaultlines
% \localtableofcontents
%
% Comments are sparse.  Actually at |1.4|, there are simply no comments. I
% transferred from \xintexprname its |\expanded| based infra-structure from
% its own |1.4| release of January 2020.  It is a possibility that, even
% though I did remove very large chunks of unneeded macros, in the end, some
% more simplifications could have been considered here.
%
% Error handling by the parser is kept to a minimum; if something goes wrong,
% the offensive token gets discarded, and it is not even always the case that
% some expandable error message is issued.
%
% \subsection{Package identification and catcode setup}
%    \begin{macrocode}
\NeedsTeXFormat{LaTeX2e}%
\ProvidesPackage{bnumexpr}[2021/05/12 v1.4 Expressions with big integers (JFB)]%
%    \end{macrocode}
% \subsection{Load unconditionally xintbinhex}
% Newly done at |1.4|. Formerly, \bnumname had no dependency if loaded
% with option |custom|. But for |1.4| release I have decided to add
% unconditional support for hexadecimal notation.
%
% Let's require the most recent xint date at time of
% writing. We should check for availability of \string\expanded\space but well.
%
%    \begin{macrocode}
\RequirePackage{xintbinhex}[2021/05/10]%
%    \end{macrocode}
% \subsection{\csh{bnumexprsetup}}
%    \begin{macrocode}
{\catcode`! 3 \catcode`_ 11 %
  \gdef\bnumexprsetup #1{\BNE_parsekeys #1,=!,}%
  \gdef\BNE_parsekeys #1=#2#3,%
  {%
    \ifx!#2\expandafter\BNE_parsedone\fi
    \expandafter
    \let\csname BNE_Op_\xint_zapspaces #1 \xint_gobble_i\endcsname%
    =#2\BNE_parsekeys
  }%
  \gdef\BNE_parsedone #1\BNE_parsekeys {}%
}%
%    \end{macrocode}
% \subsection{Package options}
%    \begin{macrocode}
\def\BNEtmpa {0}%
\DeclareOption {custom}{\def\BNEtmpa {1}}%
\ProcessOptions\relax
\edef\BNErestorecatcodes{\XINTrestorecatcodes}%
\XINTsetcatcodes%
\if0\BNEtmpa\expandafter\xint_secondoftwo\fi
\xint_gobble_i{%
    \RequirePackage{xintcore}[2021/05/10]%
    \bnumexprsetup{add=\xintiiAdd, sub=\xintiiSub, mul=\xintiiMul,
                   divround=\xintiiDivRound, div=\xintiiDivFloor,
                   mod=\xintiiMod, pow=\xintiiPow, fac=\xintiiFac}%
}%
%    \end{macrocode}
% Strangely those three are not defined in xintkernel.sty, but only in xint.sty
%    \begin{macrocode}
\long\def\xint_firstofthree  #1#2#3{#1}%
\long\def\xint_secondofthree #1#2#3{#2}%
\long\def\xint_thirdofthree  #1#2#3{#3}%
%    \end{macrocode}
% \subsection{\csh{bnumexpr}, \csh{thebnumexpr}, \csh{bnethe}, \csh{bnumeval}}
%    \begin{macrocode}
\def\XINTfstop {\noexpand\XINTfstop}%
\def\bnumexpr  {\romannumeral0\bnumexpro}%
\def\bnumexpro {\expandafter\BNE_wrap\romannumeral0\bnebareeval }%
\def\BNE_wrap  {\XINTfstop\BNEprint.}%
\def\bnumeval #1%
   {\expanded\expandafter\BNEprint\expandafter.\romannumeral0\bnebareeval#1\relax}%
\def\evaltohex #1%
   {\expanded\expandafter\BNEprinthex\expandafter.\romannumeral0\bnebareeval#1\relax}%
\def\thebnumexpr
   {\expanded\expandafter\BNEprint\expandafter.\romannumeral0\bnebareeval}%
\def\bnebareeval{\BNE_start}%
\def\bnethe#1{\expanded\expandafter\xint_gobble_i\romannumeral`&&@#1}%
\protected\def\BNEprint.#1{{\BNE_print#1.}}%
\def\BNE_print#1{#1\expandafter\BNE_print_a\string}%
\def\BNE_print_a#1{\unless\if#1.\expandafter\BNE_print_b\fi}%
\def\BNE_print_b
   {\expandafter\BNE_print_c\expandafter{\expandafter\xint_gobble_i\string}}%
\def\BNE_print_c#1{, #1\expandafter\BNE_print_a\string}%
\protected\def\BNEprinthex.#1{{\BNE_printhex#1.}}%
\def\BNE_printhex#1{\xintDecToHex{#1}\expandafter\BNE_printhex_a\string}%
\def\BNE_printhex_a#1{\unless\if#1.\expandafter\BNE_printhex_b\fi}%
\def\BNE_printhex_b
   {\expandafter\BNE_printhex_c\expandafter{\expandafter\xint_gobble_i\string}}%
\def\BNE_printhex_c#1{, \xintDecToHex{#1}\expandafter\BNE_printhex_a\string}%
%    \end{macrocode}
% \subsection{\csh{BNE_getnext}}
%    \begin{macrocode}
\def\BNE_getnext #1%
{%
    \expandafter\BNE_put_op_first\romannumeral`&&@%
    \expandafter\BNE_getnext_a\romannumeral`&&@#1%
}%
\def\BNE_put_op_first #1#2#3{\expandafter#2\expandafter#3\expandafter{#1}}%
\def\BNE_getnext_a #1%
{%
    \ifx\relax #1\xint_dothis\BNE_foundprematureend\fi
    \ifx\XINTfstop#1\xint_dothis\BNE_subexpr\fi
    \ifcat\relax#1\xint_dothis\BNE_countetc\fi
    \xint_orthat{}\BNE_getnextfork #1%
}%
\def\BNE_foundprematureend\BNE_getnextfork #1{{}\xint_c_\relax}%
\def\BNE_subexpr #1.#2%
{%
    \expanded{\unexpanded{{#2}}\expandafter}\romannumeral`&&@\BNE_getop
}%
\def\BNE_countetc\BNE_getnextfork#1%
{%
    \if0\ifx\count#11\fi
        \ifx\dimen#11\fi
        \ifx\numexpr#11\fi
        \ifx\dimexpr#11\fi
        \ifx\skip#11\fi
        \ifx\glueexpr#11\fi
        \ifx\fontdimen#11\fi
        \ifx\ht#11\fi
        \ifx\dp#11\fi
        \ifx\wd#11\fi
        \ifx\fontcharht#11\fi
        \ifx\fontcharwd#11\fi
        \ifx\fontchardp#11\fi
        \ifx\fontcharic#11\fi 0\expandafter\BNE_fetch_as_number\fi
   \expandafter\BNE_getnext_a\number #1%
}%
\def\BNE_fetch_as_number
    \expandafter\BNE_getnext_a\number #1%
{%
    \expanded{{{\number#1}}\expandafter}\romannumeral`&&@\BNE_getop
}%
%    \end{macrocode}
% In the case of hitting a |(|, previous release inserted directly a
% |\BNE_oparen|.  But the expansion architecture imported from upstream
% |\xintiiexpr| has been refactored, and the |..._oparen| meaning and
% usage evolved.  We stick with |{}\xint_c_ii^v (| from upstream,
% which works (I am 15 months away from \xintexprname |1.4|).
%    \begin{macrocode}
\def\BNE_getnextfork #1{%
    \if#1+\xint_dothis \BNE_getnext_a \fi
    \if#1-\xint_dothis {{}{}-}\fi
    \if#1(\xint_dothis {{}\xint_c_ii^v (}\fi
    \xint_orthat {\BNE_scan_number #1}%
}%
%    \end{macrocode}
% \subsection{Parsing an integer in decimal or hexadecimal notation}
%    \begin{macrocode}
\def\BNE_scan_number #1%
{%
    \if "#1\xint_dothis \BNE_scanhex\fi
    \ifnum \xint_c_ix<1\string#1 \xint_dothis \BNE_startint\fi
    \xint_orthat \BNE_notadigit #1%
}%
\def\BNE_notadigit#1{\BNE_getnext }%
\def\BNE_startint #1%
{%
    \if #10\expandafter\BNE_gobz_a\else\expandafter\BNE_scanint_a\fi #1%
}%
\def\BNE_scanint_a #1#2%
    {\expanded\bgroup{{\iffalse}}\fi #1%
     \expandafter\BNE_scanint_main\romannumeral`&&@#2}%
\def\BNE_gobz_a #1#2%
    {\expanded\bgroup{{\iffalse}}\fi
     \expandafter\BNE_gobz_scanint_main\romannumeral`&&@#2}%
\def\BNE_scanint_main #1%
{%
    \ifcat \relax #1\expandafter\BNE_scanint_hit_cs \fi
    \ifnum\xint_c_ix<1\string#1 \else\expandafter\BNE_scanint_next\fi
    #1\BNE_scanint_again
}%
\def\BNE_scanint_again #1%
{%
    \expandafter\BNE_scanint_main\romannumeral`&&@#1%
}%
\def\BNE_scanint_hit_cs \ifnum#1\fi#2\BNE_scanint_again
{%
    \iffalse{{{\fi}}\expandafter}\romannumeral`&&@\BNE_getop#2%
}%
\def\BNE_scanint_next #1\BNE_scanint_again
{%
    \if    _#1\xint_dothis\BNE_scanint_again\fi
    \xint_orthat
    {\iffalse{{{\fi}}\expandafter}\romannumeral`&&@\BNE_getop#1}%
}%
\def\BNE_gobz_scanint_main #1%
{%
    \ifcat \relax #1\expandafter\BNE_gobz_scanint_hit_cs\fi
    \ifnum\xint_c_x<1\string#1 \else\expandafter\BNE_gobz_scanint_next\fi
    #1\BNE_scanint_again
}%
\def\BNE_gobz_scanint_again #1%
{%
    \expandafter\BNE_gobz_scanint_main\romannumeral`&&@#1%
}%
\def\BNE_gobz_scanint_hit_cs\ifnum#1\fi#2\BNE_scanint_again
{%
    0\iffalse{{{\fi}}\expandafter}\romannumeral`&&@\BNE_getop#2%
}%
\def\BNE_gobz_scanint_next #1\BNE_scanint_again
{%
    \if    _#1\xint_dothis\BNE_gobz_scanint_again\fi
    \if    0#1\xint_dothis\BNE_gobz_scanint_again\fi
    \xint_orthat
    {0\iffalse{{{\fi}}\expandafter}\romannumeral`&&@\BNE_getop#1}%
}%
\def\BNE_hex_in #1.%
{%
    \expanded{{{\xintHexToDec{#1}}}\expandafter}\romannumeral`&&@\BNE_getop
}%
\def\BNE_scanhex #1% #1="
{%
    \expandafter\BNE_hex_in\expanded\bgroup\BNE_scanhex_a
}%
\def\BNE_scanhex_a #1%
{%
    \ifcat #1\relax\xint_dothis{.\iffalse{\fi}#1}\fi
    \xint_orthat {\BNE_scanhex_aa #1}%
}%
\def\BNE_scanhex_aa #1%
{%
    \if\ifnum`#1>`/
       \ifnum`#1>`9
       \ifnum`#1>`@
       \ifnum`#1>`F
       0\else1\fi\else0\fi\else1\fi\else0\fi 1%
       \expandafter\BNE_scanhex_b
    \else
       \if _#1\xint_dothis{\expandafter\BNE_scanhex_bgob}\fi
       \xint_orthat {\xint_afterfi {.\iffalse{\fi}}}%
    \fi
    #1%
}%
\def\BNE_scanhex_b #1#2%
{%
    #1\expandafter\BNE_scanhex_a\romannumeral`&&@#2%
}%
\def\BNE_scanhex_bgob #1#2%
{%
    \expandafter\BNE_scanhex_a\romannumeral`&&@#2%
}%
%    \end{macrocode}
% \subsection{\csh{BNE_getop}}
%    \begin{macrocode}
\def\BNE_getop #1%
{%
    \expandafter\BNE_getop_a\romannumeral`&&@#1%
}%
\catcode`* 11
\def\BNE_getop_a #1%
{%
    \ifx   \relax #1\xint_dothis\xint_firstofthree\fi
    \ifcat \relax #1\xint_dothis\xint_secondofthree\fi
    \ifnum\xint_c_ix<1\string#1 \xint_dothis\xint_secondofthree\fi
    \if    (#1\xint_dothis      \xint_secondofthree\fi %)
    \xint_orthat \xint_thirdofthree
    {\BNE_foundend}%
    {\BNE_precedence_*** *#1}%
    {\expandafter\BNE_scanop_a \string#1}%
}%
\catcode`* 12
\def\BNE_foundend {\xint_c_ \relax}%
\def\BNE_scanop_a #1#2%
{%
    \expandafter\BNE_scanop_b\expandafter#1\romannumeral`&&@#2%
}%
\def\BNE_scanop_b #1#2%
{%
    \ifcat#2\relax\xint_dothis{\BNE_foundop_a #1#2}\fi
    \ifcsname BNE_itself_#1#2\endcsname
    \xint_dothis
        {\expandafter\BNE_scanop_c\csname BNE_itself_#1#2\endcsname}\fi
    \xint_orthat {\BNE_foundop_a #1#2}%
}%
\def\BNE_scanop_c #1#2%
{%
    \expandafter\BNE_scanop_d\expandafter#1\romannumeral`&&@#2%
}%
\def\BNE_scanop_d #1#2%
{%
  \ifcat#2\relax \xint_dothis{\BNE_foundop #1#2}\fi
  \ifcsname BNE_itself_#1#2\endcsname
  \xint_dothis
        {\expandafter\BNE_scanop_c\csname BNE_itself_#1#2\endcsname }\fi
  \xint_orthat {\csname BNE_precedence_#1\endcsname #1#2}%
}%
\def\BNE_foundop_a #1%
{%
    \ifcsname BNE_precedence_#1\endcsname
        \csname BNE_precedence_#1\expandafter\endcsname
        \expandafter #1%
    \else
        \xint_afterfi{\BNE_getop\romannumeral0%
        \XINT_expandableerror
        {"#1" is unknown as operator. (I)nsert one:} }%<<deliberate space
    \fi
}%
\def\BNE_foundop #1{\csname BNE_precedence_#1\endcsname #1}%
%    \end{macrocode}
% \subsection{Expansion spanning; opening and closing parentheses}
%    \begin{macrocode}
\def\BNE_tmpa #1#2#3#4#5%
{%
    \def#1% start
    {%
        \expandafter#2\romannumeral`&&@\BNE_getnext
    }%
    \def#2##1% check
    {%
        \xint_UDsignfork
          ##1{\expandafter#3\romannumeral`&&@#4}%
            -{#3##1}%
        \krof
    }%
    \def#3##1##2% checkp
    {%
        \ifcase ##1%
           \expandafter\BNE_done
        \or\expandafter#5%
        \else
           \expandafter#3\romannumeral`&&@\csname BNE_op_##2\expandafter\endcsname
        \fi
    }%
    \def#5%
    {%
        \XINT_expandableerror
        {An extra ) has been removed. Hit Return, fingers crossed.}%
        \expandafter#2\romannumeral`&&@\expandafter\BNE_put_op_first
        \romannumeral`&&@\BNE_getop_legacy
    }%
}%
\let\BNE_done\space
\expandafter\BNE_tmpa
    \csname BNE_start\expandafter\endcsname
    \csname BNE_check\expandafter\endcsname
    \csname BNE_checkp\expandafter\endcsname
    \csname BNE_op_-xii\expandafter\endcsname
    \csname BNE_extra_)\endcsname
\def\BNE_tmpa #1#2#3#4#5#6%
{%
    \def #1##1% op_(
    {%
        \expandafter #4\romannumeral`&&@\BNE_getnext
    }%
    \def #2##1% op_)
    {%
        \expanded{\unexpanded{\BNE_put_op_first{##1}}\expandafter}\romannumeral`&&@\BNE_getop
    }%
    \def #3% oparen
    {%
        \expandafter #4\romannumeral`&&@\BNE_getnext
    }%
    \def #4##1% check-
    {%
        \xint_UDsignfork
            ##1{\expandafter#5\romannumeral`&&@#6}%
              -{#5##1}%
        \krof
    }%
    \def #5##1##2% checkp
    {%
        \ifcase ##1\expandafter\BNE_missing_)
        \or \csname BNE_op_##2\expandafter\endcsname
        \else
          \expandafter #5\romannumeral`&&@\csname BNE_op_##2\expandafter\endcsname
        \fi
    }%
}%
\expandafter\BNE_tmpa
    \csname BNE_op_(\expandafter\endcsname
    \csname BNE_op_)\expandafter\endcsname
    \csname BNE_oparen\expandafter\endcsname
    \csname BNE_check-_)\expandafter\endcsname
    \csname BNE_checkp_)\expandafter\endcsname
    \csname BNE_op_-xii\endcsname
\catcode`) 11
\let\BNE_precedence_)\xint_c_i
\def\BNE_missing_) 
   {\XINT_expandableerror{Sorry to report a missing ) at the end of this journey.}%
    \xint_c_ \BNE_done }%
\catcode`) 12
%    \end{macrocode}
% \subsection{The comma as binary operator}
%    \begin{macrocode}
\def\BNE_tmpa #1#2#3#4#5%
{%
    \def #1##1% \BNE_op_,
    {%
      \expanded{\unexpanded{#2{##1}}\expandafter}%
      \romannumeral`&&@\expandafter#3\romannumeral`&&@\BNE_getnext
    }%
    \def #2##1##2##3##4{##2##3{##1##4}}% \BNE_exec_,
    \def #3##1% \BNE_check-_,
    {%
      \xint_UDsignfork
        ##1{\expandafter#4\romannumeral`&&@#5}%
          -{#4##1}%
      \krof
    }%
    \def #4##1##2% \BNE_checkp_,
    {%
      \ifnum ##1>\xint_c_iii
        \expandafter#4%
           \romannumeral`&&@\csname BNE_op_##2\expandafter\endcsname
      \else
        \expandafter##1\expandafter##2%
      \fi
    }%
}%
\expandafter\BNE_tmpa
    \csname BNE_op_,\expandafter\endcsname
    \csname BNE_exec_,\expandafter\endcsname
    \csname BNE_check-_,\expandafter\endcsname
    \csname BNE_checkp_,\expandafter\endcsname
    \csname BNE_op_-xii\endcsname
\expandafter\let\csname BNE_precedence_,\endcsname\xint_c_iii
%    \end{macrocode}
% \subsection{The minus as prefix operator of variable precedence level}
%    \begin{macrocode}
\def\BNE_tmpb #1#2#3#4#5%
{%
    \def #1% \BNE_op_-<level>
    {%
      \expandafter #2\romannumeral`&&@\expandafter#3%
      \romannumeral`&&@\BNE_getnext
    }%
    \def #2##1##2##3% \BNE_exec_-<level>
    {%
      \expandafter ##1\expandafter ##2\expandafter
       {\expandafter{\romannumeral`&&@\expandafter\BNE_Op_opp\xint_firstofone##3}}%
    }%
    \def #3##1% \BNE_check-_-<level>
    {%
      \xint_UDsignfork
        ##1{\expandafter #4\romannumeral`&&@#1}%
          -{#4##1}%
      \krof
    }%
    \def #4##1##2% \BNE_checkp_-<level>
    {%
      \ifnum ##1>#5%
        \expandafter #4%
        \romannumeral`&&@\csname BNE_op_##2\expandafter\endcsname
      \else
        \expandafter ##1\expandafter ##2%
      \fi
    }%
}%
\def\BNE_tmpa #1%
{%
\expandafter\BNE_tmpb
    \csname BNE_op_-#1\expandafter\endcsname
    \csname BNE_exec_-#1\expandafter\endcsname
    \csname BNE_check-_-#1\expandafter\endcsname
    \csname BNE_checkp_-#1\expandafter\endcsname
    \csname xint_c_#1\endcsname
}%
\BNE_tmpa {xii}%
\BNE_tmpa {xiv}%
\BNE_tmpa {xvi}%
\BNE_tmpa {xviii}%
\def\BNE_Op_opp #1{\if-#1\else\if0#10\else-#1\fi\fi }%
%    \end{macrocode}
% \subsection{The infix operators.}
%    \begin{macrocode}
\def\BNE_defbin_c #1#2#3#4#5#6#7%
{%
  \def #1##1% \BNE_op_<op>
  {%
    \expanded{\unexpanded{#2{##1}}\expandafter}%
    \romannumeral`&&@\expandafter#3\romannumeral`&&@\BNE_getnext
  }%
  \def #2##1##2##3##4% \BNE_exec_<op>
  {%
    \expandafter##2\expandafter##3\expandafter
      {\expandafter{\romannumeral`&&@#6##1##4}}%
  }%
  \def #3##1% \BNE_check-_<op>
  {%
    \xint_UDsignfork
      ##1{\expandafter#4\romannumeral`&&@#5}%
        -{#4##1}%
    \krof
  }%
  \def #4##1##2% \BNE_checkp_<op>
  {%
    \ifnum ##1>#7%
      \expandafter#4%
      \romannumeral`&&@\csname BNE_op_##2\expandafter\endcsname
    \else 
      \expandafter ##1\expandafter ##2%
    \fi
  }%
}%
\def\BNE_defbin_b #1#2#3#4%
{%
  \expandafter\BNE_defbin_c
  \csname BNE_op_#1\expandafter\endcsname
  \csname BNE_exec_#1\expandafter\endcsname
  \csname BNE_check-_#1\expandafter\endcsname
  \csname BNE_checkp_#1\expandafter\endcsname
  \csname BNE_op_-#3\expandafter\endcsname
  \csname #4\expandafter\endcsname
  \csname BNE_precedence_#1\endcsname
  \expandafter
  \let\csname BNE_precedence_#1\expandafter\endcsname
      \csname xint_c_#2\endcsname
}%
\BNE_defbin_b {//} {xiv}{xiv}{BNE_Op_div}%
\BNE_defbin_b {/:} {xiv}{xiv}{BNE_Op_mod}%
\BNE_defbin_b  +   {xii}{xii}{BNE_Op_add}%
\BNE_defbin_b  -   {xii}{xii}{BNE_Op_sub}%
\BNE_defbin_b  *   {xiv}{xiv}{BNE_Op_mul}%
\BNE_defbin_b  /   {xiv}{xiv}{BNE_Op_divround}%
\BNE_defbin_b  ^   {xviii}{xviii}{BNE_Op_pow}%
\expandafter\def\csname BNE_itself_**\endcsname {^}%
\expandafter\def\csname BNE_itself_//\endcsname {//}%
\expandafter\def\csname BNE_itself_/:\endcsname {/:}%
\expandafter\let\csname BNE_precedence_***\endcsname \xint_c_xvi
%    \end{macrocode}
% \subsection{! as postfix factorial operator}
%    \begin{macrocode}
\catcode`! 11
\let\BNE_precedence_! \xint_c_xx
\def\BNE_op_! #1%
{%
    \expandafter\BNE_put_op_first
    \expanded{{{\BNE_Op_fac#1}}\expandafter}\romannumeral`&&@\BNE_getop
}%
%    \end{macrocode}
% \subsection{Cleanup}
%    \begin{macrocode}
\let\BNEtmpa\relax \let\BNE_tmpa\relax \let\BNE_tmpb\relax \let\BNE_tmpc\relax
\BNErestorecatcodes%
%    \end{macrocode}
% \MakePercentComment
%</package>
%<*dtx>
\DeleteShortVerb{\|}
\CharacterTable
 {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
  Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
  Digits        \0\1\2\3\4\5\6\7\8\9
  Exclamation   \!     Double quote  \"     Hash (number) \#
  Dollar        \$     Percent       \%     Ampersand     \&
  Acute accent  \'     Left paren    \(     Right paren   \)
  Asterisk      \*     Plus          \+     Comma         \,
  Minus         \-     Point         \.     Solidus       \/
  Colon         \:     Semicolon     \;     Less than     \<
  Equals        \=     Greater than  \>     Question mark \?
  Commercial at \@     Left bracket  \[     Backslash     \\
  Right bracket \]     Circumflex    \^     Underscore    \_
  Grave accent  \`     Left brace    \{     Vertical bar  \|
  Right brace   \}     Tilde         \~}
\CheckSum {949}
\makeatletter\check@checksum\makeatother
\Finale
%% End of file xint.dtx
