% -*- coding: utf-8-unix; time-stamp-format: "%02d-%02m-%:y %02H:%02M:%02S %Z"; sentence-end-double-space: t; -*-
%<*dtx>
\def\bnedtxtimestamp  {Time-stamp: <13-05-2021 12:37:08 CEST>}
\iffalse
%</dtx>
%<*drv>
%% ---------------------------------------------------------------
\def\bnedocdate {2021/05/13}% package bnumexpr documentation date
\def\bnepackdate{2021/05/13}% package bnumexpr date
\def\bneversion {1.4a}      % package bnumexpr version
%</drv>
%<*readme>--------------------------------------------------------
| Source:  bnumexpr.dtx
| Version: v1.4a, 2021/05/13 (doc: 2021/05/13)
| 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.

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[1.4a (2021/05/13)]
  \begin{itemize}
  \item fix undefined control sequences errors encountered by the parser in
    case of either extra or missing closing parenthesis (due to a problem
    in technology transfer at |1.4| from upstream \xintexprname).
  \item fix |\BNE_Op_opp| must now be f-expandable (also caused as a
    collateral to the technology transfer).
  \item fix user documentation regarding the constraints applying to the user
    replacement macros for the core algebra, as they have changed at |1.4|.
  \end{itemize}

\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\xintkernelname
   {\href{http://www.ctan.org/pkg/xint}{xintkernel}\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/xintexpr}{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{bnumeval} (\csh{thebnumexpr}), \csh{evaltohex}}
\label{sec:bnumexpr}

\LaTeX\ Package \bnumname provides |\thebnumexpr|\meta{expression}|\relax|:
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 a more core-level |\bnumexpr...\relax| construct%
\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|.}%
, which expands
to a self-contained unit, rather than to explicit digit tokens (and commas).
See \autoref{sec:differences} for some related information.

There is also the 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|
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)}%
\bneshoweval {(92_874_927_979**5-31_9792_7979**6)/30!}%
\bneshoweval {30!/20!/21/22/23/24/25/(26*27*28*29)}%
\bneshoweval {13^50//12^50, 13^50/:12^50}%
\bneshoweval {13^50/12^50, 12^50}%
\bneshoweval {(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}}
\label{sec:differences}

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 contrarily to |\numexpr|, the |\bnumexpr| parser stops only after having
  found (and swallowed) a mandatory ending |\relax| token (it can arise from expansion),

\item in particular note that 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 with |\edef\myVar{\thebnumexpr1+2\relax}|, the computation is of course
  done at time of the |\edef|. But one is also allowed to do
  |\edef\myVar{\bnumexpr1+2\relax}| which prepares |\myVar| as a macro which
  can be inserted in other \bnumname expressions and behave there as a
  self-contained pre-computed unit triggering tacit multiplication, or be
  typeset directly if inserted in the typesetting stream.%
%
\footnote{Prior to |1.4|, one would have had to use |\bnethe\myVar| for
  typesetting, or |\bnumeval{\myVar}|.}
%
  There is no analog with |\numexpr| as |\edef\myVar{\numexpr1+2\relax}| does
  not pre-compute anything and furthermore |\the\numexpr2\myVar\relax| in
  typesetting flow then triggers the |You can't use `\numexpr' in horizontal
  mode| error.

\item expressions may be comma separated. On input, spaces are ignored,
  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,

\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}

As hinted above |\bnumexpr...\relax| differs from |\thebnumexpr...\relax| as
the latter expands to explicit digit tokens, but the former expands to a
private self-contained format which can serve as sub-unit in other
expressions, or be used inside |\edef|.  Since |1.4| the former idiom can also
be inserted directly inside the typesetting stream, or be written out to an
external file where it will expand to some control sequences, braces, and
character tokens, all with their standard catcodes. 

One can use |\numexpr...\relax| as a sub-unit in |\bnumexpr...\relax| but the
reverse does not apply: it would either cause an error or an
anticipated end to the |\numexpr| which will think having hit a |\relax|.

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| control sequence. When using |\bnumeval{...}|
syntax as in
\begin{verbatim}
\ifnum\bnumeval{...}
...
\fi
\end{verbatim}
the end of line will insert a terminating space token. Again, here
|\bnumeval{...}| must produce an integer acceptable to \TeX, i.e. at most
{\number"7FFFFFFF} in absolute value.

\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,
                   opp=\xintiiOpp}%
\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.

The macros serving as custom user replacements must be \emph{f}-expandable.%
%
\footnote{Prior to |1.4|, only \emph{x}-expandability was required. The author
  could relax again the constraint, if asked to do so. Or perhaps simply add
  an option for it.}
%
(except for the computation of factorials, which only has to be
\emph{x}-expandable).

They will by default receive arguments composed of explicit digit tokens, with
no leading zeros, with at most one leading minus sign and no plus sign.

The format of these arguments may depend on what the |opp=\foo| replacement
macro does. If the custom |\foo| inserts a |+| when taking the opposite of a
negative number, then the custom macros for arithmetic (and the |\foo| macro
itself) must be able to handle arguments starting optionally with such a |+|.

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

%\clearpage

\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
% \etocmarkbothnouc{Package \bnumnameimp implementation}
%
% 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.
%
% 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.
%
% A few comments at |1.4a|:
% \begin{itemize}
% \item It looked a bit costly and probably would have been mostly useless to
%   end users to integrate in \bnumname support for nested structures via
%   square brackets [, ], which is in \xintexprname since its January 2020
%   |1.4| release.  But some underlying related architecture remains here; we
%   could make some micro-gains probably but diverging from upstream code
%   would make maintenance a nightmare.
% \item The |\bnumexpr\relax| syntax creating an empty ople is by itself now
%   legal, and can be injected (comma separated) in an expression, keeping it
%   invariant, however |\bnumeval{}| ends in a |File ended while scanning use
%   of \BNE_print_c| error because |\BNEprint| makes the tacit requirement
%   that the 1D ople to output has at least one item.
% \item Formerly, the |\csname...\endcsname| encapsulation technique had the
%   after-effect to allow the macros supporting the infix operators to be only
%   x-expandable.  At |1.4|, I could have still allowed only x-expandable
%   macros, but, keeping in sync with upstream, I have used only a
%   |\romannumeral| trigger and did not insert an |\expanded|, so now the
%   support macros must be f-expandable.  The |1.4a| release fixes the related
%   user documentation of |\bnumexprsetup| which was not updated at |1.4|.
%   The support macro for the factorial however needs only be x-expandable.
% \item Also, I simply do not understand why the legacy user documentation
%   said that the support macros were supposed to f-expand their arguments, as
%   they are used only with arguments being explicit digit tokens (and
%   optional minus sign).
% \item I hesitated a bit about making the decimal to hexadecimal and
%   hexadecimal to decimal support macros customizable, but dropped the
%   idea. Loading \xintbinhexname unconditionally has also the advantage to
%   not have to define some \xintkernelname provided helper macros; and it
%   still does not load \xintcorename, so is keeping dependencies somewhat low
%   and the |custom| option significant.
% \item I had fleetingly consider a parser |\hexexpr| where input is
%   hexadecimal with no |"| prefix, but implementing this basically means
%   duplicating with new names a large chunk of the parser code to have parser
%   specific |"getnext"| macros for example.  Not worth it.
% \end{itemize}
%
% \subsection{Package identification and catcode setup}
%    \begin{macrocode}
\NeedsTeXFormat{LaTeX2e}%
\ProvidesPackage{bnumexpr}[2021/05/13 v1.4a 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 \xintname date at time of
% writing. We should check for availability of |\expanded| 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}
% The keys should have been |Add|, |Sub|, \dots, not |add|, |sub|, \dots, so
% internally macros |\BNE_Op_Add| etc\dots\ macro names would be used, but well,
% let's simply leave with this.
%    \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,
                   opp=\xintiiOpp}%
}%
%    \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
\def\BNE_getop_legacy #1%
{%
    \expanded{\unexpanded{{#1}}\expandafter}\romannumeral`&&@\BNE_getop
}%
\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
\catcode`) 11
\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
\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}
% At |1.4|, it is simply a union operator for 1D oples. Inserting directly
% here a |<space><comma>| separator (as in earlier releases) in accumulated
% result would avoid having to do it on output but to the cost of diverging
% from \xintexprname upstream code, and to have to let the |\evaltohex| output
% routine handle comma separated values rather than braced values.
%    \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}
% This |\BNE_Op_opp| causes trouble as at |1.4| it must be f-expandable,
% whereas earlier it expanded inside |\csname...\endcsname| context, so I
% could define it as {\catcode`\#12 |\if-#1\else\if0#10\else-#1\fi\fi|} where
% {\catcode`\#12 |#1|} was the
% first token of unbraced argument but this meant at |1.4| an added
% |\xint_firstofone| here. Well let's return to sanity at |1.4a| and not add
% the |\xint_firstofone| and simply default |\BNE_Op_opp| to |\xintiiOpp|,
% which it should have been all along! And on this occasion let's trim user
% documentation of irrelevant complications.
%    \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`&&@\BNE_Op_opp##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}%
%    \end{macrocode}
% \subsection{The infix operators.}
% I could have at the |1.4| refactoring injected usage of |\expanded| here,
% but kept in sync with upstream \xintexprname code.
%
% Macro names are somewhat bad and there is much risk of confusion in future
% maintenance of |\BNE_Op_| prefix (used for |\BNE_Op_add| etc...; besides
% this should have been |\BNE_Op_Add|) and |\BNE_op_| prefix (used for
% {\catcode`+ 11 |\BNE_op_+|} etc...).
%    \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}
% This one uses |\expanded|.
%    \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{\|}%
\CheckSum {947}%
\makeatletter\check@checksum\makeatother%
\Finale%
%% End of file xint.dtx
