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authorKarl Berry <karl@freefriends.org>2013-11-24 00:00:29 +0000
committerKarl Berry <karl@freefriends.org>2013-11-24 00:00:29 +0000
commitc9f8bd8bf029f005f02efea2a67dade996df2515 (patch)
tree671b749f2efa72f532d714a47ea4d3d79be5b4ce /Master/texmf-dist/source/generic
parent42b82c7597e89fadde85939a364fa8d8aa24f2fa (diff)
xint (23nov13)
git-svn-id: svn://tug.org/texlive/trunk@32224 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/source/generic')
-rw-r--r--Master/texmf-dist/source/generic/xint/xint.dtx2981
-rw-r--r--Master/texmf-dist/source/generic/xint/xint.ins8
2 files changed, 1876 insertions, 1113 deletions
diff --git a/Master/texmf-dist/source/generic/xint/xint.dtx b/Master/texmf-dist/source/generic/xint/xint.dtx
index 2f7cd536ac0..65c15c30343 100644
--- a/Master/texmf-dist/source/generic/xint/xint.dtx
+++ b/Master/texmf-dist/source/generic/xint/xint.dtx
@@ -1,13 +1,14 @@
% -*- coding: iso-latin-1; -*-
%<*doc>
-\def\lasttimestamp{Time-stamp <04-11-2013 13:50:22 CET *>}
+\def\lasttimestamp{Time-stamp <23-11-2013 12:26:51 CET *>}
%</doc>
-% xint.dtx, 1.09f (2013/11/04)
+% xint.dtx, 1.09g (2013/11/22)
%
% Copyright (C) 2013 by Jean-François Burnol
%
% Style files which will self-extract from xint.dtx:
-% (base) xint.sty Expandable operations on long numbers
+% xinttools.sty Expandable and non expandable utilities
+% xint.sty Expandable operations on long numbers
% xintfrac.sty Expandable operations on fractions
% xintexpr.sty Expandable expression parser
% xintbinhex.sty Expandable binary and hexadecimal conversions
@@ -20,9 +21,9 @@
% =======
%
% This work consists of the source file xint.dtx and of its derived files:
-% xint.sty, xintfrac.sty, xintexpr.sty, xintbinhex.sty, xintgcd.sty,
-% xintseries.sty, xintcfrac.sty, as well as xint.ins and the documentation
-% xint.pdf (or xint.dvi).
+% xinttools.sty xint.sty, xintfrac.sty, xintexpr.sty, xintbinhex.sty,
+% xintgcd.sty, xintseries.sty, xintcfrac.sty, as well as xint.ins and the
+% documentation xint.pdf (or xint.dvi).
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either
@@ -54,10 +55,11 @@
%
% To get xint.pdf run pdflatex thrice on xint.dtx
%
+% xinttools.sty |
% xint.sty |
% xintfrac.sty |
-% xintexpr.sty |
-% xintbinhex.sty | --> TDS:tex/generic/xint/
+% xintexpr.sty | --> TDS:tex/generic/xint/
+% xintbinhex.sty |
% xintgcd.sty |
% xintseries.sty |
% xintcfrac.sty |
@@ -67,7 +69,8 @@
% It may be necessary to then refresh the TeX installation filename
% database.
%
-% Usage with LaTeX: \usepackage{xint}
+% Usage with LaTeX: \usepackage{xinttools}
+% \usepackage{xint} % (loads xinttools)
% \usepackage{xintfrac} % (loads xint)
% \usepackage{xintexpr} % (loads xintfrac)
%
@@ -76,7 +79,8 @@
% \usepackage{xintseries} % (loads xintfrac)
% \usepackage{xintcfrac} % (loads xintfrac)
%
-% Usage with TeX: \input xint.sty\relax
+% Usage with TeX: \input xinttools.sty\relax
+% \input xint.sty\relax % (loads xinttools)
% \input xintfrac.sty\relax % (loads xint)
% \input xintexpr.sty\relax % (loads xintfrac)
%
@@ -87,7 +91,8 @@
%
%%
%%----------------------------------------------------------------
-%% The xint bundle (version 1.09f of November 4, 2013)
+%% The xint bundle (version 1.09g of November 22, 2013)
+%<xinttools>%% xinttools: Expandable and non-expandable utilities
%<xint>%% xint: Expandable operations on long numbers
%<xintfrac>%% xintfrac: Expandable operations on fractions
%<xintexpr>%% xintexpr: Expandable expression parser
@@ -99,8 +104,8 @@
%%----------------------------------------------------------------
%%
%<*doc>
-\def\pkgversion{1.09f}
-\def\pkgdate{2013/11/04}
+\def\pkgversion{1.09g}
+\def\pkgdate{2013/11/22}
\def\striptimestamp #1 <#2 #3 #4 #5>{#2 at #3 #4}
\def\getdocdate #1 <#2-#3-#4 #5>{#4/#3/#2}
\edef\docdate{\expandafter\getdocdate\lasttimestamp}
@@ -111,6 +116,7 @@
\generate{\nopreamble
\file{xint.ins}{\from{xint.dtx}{ins}}
\usepreamble\defaultpreamble
+\file{xinttools.sty}{\from{xint.dtx}{xinttools}}
\file{xint.sty}{\from{xint.dtx}{xint}}
\file{xintbinhex.sty}{\from{xint.dtx}{xintbinhex}}
\file{xintgcd.sty}{\from{xint.dtx}{xintgcd}}
@@ -125,8 +131,9 @@
%----------- to .ins file ----------------------------------------
%%
%% This is a generated file. Run tex or latex on this file to
-%% extract xint.sty, xintfrac.sty, xintexpr.sty, xintbinhex.sty,
-%% xintgcd.sty, xintseries.sty and xintcfrac.sty from xint.dtx
+%% extract xinttools.sty, xint.sty, xintfrac.sty, xintexpr.sty,
+%% xintbinhex.sty, xintgcd.sty, xintseries.sty and xintcfrac.sty
+%% from xint.dtx
%%
%% See xint.dtx for the copyright and the conditions for
%% distribution and/or modification of this work.
@@ -134,6 +141,7 @@
\input docstrip.tex
\askforoverwritefalse
\generate{\usepreamble\defaultpreamble
+\file{xinttools.sty}{\from{xint.dtx}{xinttools}}
\file{xint.sty}{\from{xint.dtx}{xint}}
\file{xintbinhex.sty}{\from{xint.dtx}{xintbinhex}}
\file{xintgcd.sty}{\from{xint.dtx}{xintgcd}}
@@ -185,11 +193,12 @@
\def\sectioncouleur{{cyan}}
-% attention à ce 22 hard codé. 23 maintenant,...
+% attention à ce 22 hard codé. 23 maintenant,... 24; et 31 non 32...
\etocsetstyle{section}{}
{}
- {\ifnum\etocthenumber=23 \gdef\sectioncouleur{{joli}}\fi
+ {\ifnum\etocthenumber=24 \gdef\sectioncouleur{{joli}}\fi
+ \ifnum\etocthenumber=32 \gdef\sectioncouleur{[named]{RoyalPurple}}\fi
\savedsectionline{\numberline{\expandafter\textcolor\sectioncouleur
{\etocnumber}}\etocname}
{{\mdseries\etocpage}}%
@@ -490,12 +499,22 @@ pdfpagemode=UseOutlines}
\newcommand\csbh[1]{\texorpdfstring{\csbnolk{#1}}{\textbackslash #1}}
% emploi de \xintFor à partir de 1.09c
-\xintFor #1 in {xint,xintbinhex,xintgcd,xintfrac,xintseries,xintcfrac,xintexpr}
+\xintForpair #1#2 in
+{(xinttools,tools),(xint,xint),(xintbinhex,binhex),(xintgcd,gcd),%
+ (xintfrac,frac),(xintseries,series),(xintcfrac,cfrac),(xintexpr,expr)}
\do
{%
\expandafter\def\csname #1name\endcsname
{\texorpdfstring
- {{\color{joli}\ttfamily\hyphenchar\font45 \bfseries #1}}
+ {\hyperref[sec:#2]%
+ {\color{joli}\bfseries\ttfamily\hyphenchar\font45 #1}}
+ {#1}%
+ \xspace }%
+ \expandafter\def\csname #1nameimp\endcsname
+ {\texorpdfstring
+ {\hyperref[sec:#2imp]%
+ {\color[named]{RoyalPurple}%
+ \bfseries\ttfamily\hyphenchar\font45 #1}}
{#1}%
\xspace }%
}%
@@ -557,32 +576,57 @@ pdfpagemode=UseOutlines}
{\centering
\textsc{Jean-François Burnol}\par
\footnotesize \ttfamily
- jfbu (at) free (dot) fr\\
- Package version: \pkgversion\ (\pkgdate)\\
- Documentation generated from the source file\\
- with timestamp ``\dtxtimestamp''\par
+ jfbu (at) free (dot) fr\par
+ Package version: \pkgversion\ (\pkgdate)%
+ \let\thefootnote\empty
+ \footnote{Documentation generated from the
+ source file with timestamp ``\dtxtimestamp''.}\par
}
+\setcounter{footnote}{0}
+
+\bigskip
+\begin{addmargin}{1cm}\footnotesize
+\makeatletter
+\renewenvironment{description}
+ {\list{}{\topsep\z@ \parsep\z@ \labelwidth\z@ \itemindent-\leftmargin
+ \let\makelabel\descriptionlabel}}
+ {\endlist}
+\makeatother
+\begin{description}
+\item[\xinttoolsname] is loaded by \xintname (hence by all other packages of the
+ bundle, too): it provides utilities of independent interest such as expandable
+ and non-expandable loops.
+
+\item[\xintname] implements with expandable \TeX{} macros additions,
+ subtractions, multiplications, divisions and powers with arbitrarily long
+ numbers.
+
+\item[\xintfracname] extends the scope of \xintname to decimal numbers, to
+ numbers in scientific notation and also to fractions with arbitrarily
+ long such numerators and denominators separated by a forward slash.
+
+\item[\xintexprname] extends \xintfracname with an expandable parser |\xintexpr
+ . . . \relax| of expressions involving arithmetic operations in infix notation
+ on decimal numbers, fractions, numbers in scientific notation, with
+ parentheses, factorial symbol, function names, comparison operators, logic
+ operators, twofold and threefold way conditionals, sub-expressions, macros
+ expanding to the previous items.
+\end{description}
+
+\noindent Further modules:
+%
+\begin{description}
+\item[\xintbinhexname] is for conversions to and from binary and
+ hexadecimal bases.
-\begin{abstract}
-The \xintname package implements with expandable \TeX{} macros the basic
- arithmetic operations of addition, subtraction, multiplication and division,
- applied to arbitrarily long numbers. The \xintfracname package extends the
- scope of \xintname to fractional numbers with arbitrarily long numerators and
- denominators.
-
- \xintexprname provides an expandable parser |\xintexpr . . . \relax|
- of expressions involving arithmetic operations in infix notation on
- decimal numbers, fractions, numbers in scientific notation, with
- parentheses, factorial symbol, function names, comparison operators,
- logic operators, twofold and threefold way conditionals,
- sub-expressions, macros expanding to the previous items.
-
- The \xintbinhexname package is for conversions to and from binary and
- hexadecimal bases, \xintseriesname provides some basic functionality for
- computing in an expandable manner partial sums of series and power series with
- fractional coefficients, \xintgcdname implements the Euclidean algorithm and
- its typesetting, and \xintcfracname deals with the computation of continued
- fractions.
+\item[\xintseriesname] provides some basic functionality for computing in an
+ expandable manner partial sums of series and power series with fractional
+ coefficients.
+
+\item[\xintgcdname] implements the Euclidean algorithm and its typesetting.
+
+\item[\xintcfracname] deals with the computation of continued fractions.
+\end{description}
Most macros, and all of those doing computations, work purely by expansion
without assignments, and may thus be used almost everywhere in \TeX{}.
@@ -590,8 +634,9 @@ The \xintname package implements with expandable \TeX{} macros the basic
The packages may be used with any flavor of \TeX{} supporting the \eTeX{}
extensions. \LaTeX{} users will use |\usepackage| and others |\input| to
load the package components.
-\end{abstract}
+\end{addmargin}
+\bigskip
% 18 octobre 2013, je remets la TOC ici.
% je ne veux pas non plus que la main toc se liste elle-même donc je passe pour
@@ -599,6 +644,9 @@ The \xintname package implements with expandable \TeX{} macros the basic
\etocsetlevel{toctobookmark}{6} % 9 octobre 2013, je fais des petits tricks.
+% 18 novembre 2013, je n'inclus plus la TOC détaillée de
+% xintexpr. Je reconfigure la TOC
+
\etocsettocdepth {subsection}
\renewcommand*{\etocbelowtocskip}{0pt}
@@ -609,41 +657,24 @@ The \xintname package implements with expandable \TeX{} macros the basic
\phantomsection\section* {Contents}
\etoctoccontentsline*{toctobookmark}{Contents}{1}%
}
+
\etocsettagdepth {description}{section}
- \etocsettagdepth {commandsA} {section}
- \etocsettagdepth {xintexpr} {none}
- \etocsettagdepth {commandsB} {none}
- \etocsettagdepth {implementation}{none}
-\tableofcontents
- \etocsettagdepth {description}{none}
\etocsettagdepth {commandsA} {none}
- \etocsettagdepth {xintexpr} {subsection}
+ \etocsettagdepth {xintexpr} {none}
\etocsettagdepth {commandsB} {none}
\etocsettagdepth {implementation}{none}
-\etocsettocstyle {}{}
\tableofcontents
+\etocmulticolstyle [2]{\raggedcolumns}{}
\etocsettagdepth {description}{none}
- \etocsettagdepth {commandsA} {none}
- \etocsettagdepth {xintexpr} {none}
+ \etocsettagdepth {commandsA} {section}
+ \etocsettagdepth {xintexpr} {section}
\etocsettagdepth {commandsB} {section}
- \etocsettagdepth {implementation}{none}
-\etocmulticolstyle [2]{}{}
-\tableofcontents
- \etocsettagdepth {description}{none}
- \etocsettagdepth {commandsA} {none}
- \etocsettagdepth {xintexpr} {none}
- \etocsettagdepth {commandsB} {none}
\etocsettagdepth {implementation}{section}
- \etocsettocstyle {}{}
-\def\sectioncouleur{[named]{RoyalPurple}}
-\begin{addmargin}{3cm}
- \tableofcontents
-\end{addmargin}
+\tableofcontents
\medskip
% pour la suite:
\etocignoredepthtags
-
\etocmulticolstyle [1]{%
\phantomsection\section* {Contents}
\etoctoccontentsline*{toctobookmark}{Contents}{2}%
@@ -654,23 +685,34 @@ The \xintname package implements with expandable \TeX{} macros the basic
\section{Quick introduction}\label{sec:quickintro}
-The \xintname bundle consists of three principal components \xintname,
+The \xintname bundle consists of the three principal components \xintname,
\xintfracname (which loads \xintname), and \xintexprname (which loads
-\xintfracname), and four additional modules. They may be used with Plain \TeX{},
-\LaTeX{} or any other format based on \TeX{}. The package requires the
-\eTeX{} extensions which in modern distributions are made available by default,
-except if you invoke \TeX{} under the name |tex| in command line.
+\xintfracname), and four additional modules. Release |1.09g| has moved the
+macros of \xintname not dealing with the manipulation of big numbers to a
+separate package \xinttoolsname (which is automatically loaded by \xintname), of
+independent interest.
+
+All components may be used as regular packages with \LaTeX{} or loaded directly
+via \string\input{} (e.g. |\input xint.sty\relax|) in any other format based on
+\TeX. Each of them automatically loads those not alreadly loaded it depends
+on.
+
+The \eTeX{} extensions must be enabled; this is the case in modern distributions
+by default, except if you invoke \TeX{} under the name |tex| in command line
+(|etex| should be used then, or |pdftex| in |DVI| output mode).
The goal is too compute \emph{exactly}, purely by expansion, without
count registers nor assignments nor definitions, with arbitrarily big
-numbers and fractions. As will be commented upon more later, this works
-fine when the data has dozens of digits, but multiplying out two @1000@
-digits numbers under this constraint of expandability is expensive; so
-in many situations the package will be used for fixed point (rounding or
-truncating each intermediate result) or floating point computations. The
-``floating point'' macros work with a given arbitrary precision (default
-is @16@ digits; from the remark made above, beyond @100@ digits things
-will start becoming too slow if hundreds of computations are needed). The only
+numbers and fractions.
+% As will be commented upon more later, this works
+% fine when the data has dozens of digits, but multiplying out two @1000@
+% digits numbers under this constraint of expandability is expensive; so
+% in many situations the package will be used for fixed point (rounding or
+% truncating each intermediate result) or floating point computations. The
+% ``floating point'' macros work with a given arbitrary precision (default
+% is @16@ digits; from the remark made above, beyond @100@ digits things
+% will start becoming too slow if hundreds of computations are needed).
+The only
non-algebraic operation which is currently implemented is the extraction
of square roots.
@@ -678,12 +720,12 @@ The package macros expand their arguments\footnote{see in
\autoref{sec:expansions} the related explanations.}; as they are themselves
completely expandable, this means that one may nest them arbitrarily
deep to construct complicated (and still completely expandable) formulas.
-
But one will presumably prefer to use the (expandable!) \csbxint{expr}| ...
\relax| parser as it allows infix notations, function names
(corresponding to some of the package macros), comparison operators,
boolean operators, 2way and 3way conditionals.
+\footnotesize
When producing very long numbers there is the question of printing them on
the page, without going beyond the page limits. In this document, I have most
of the time made use of these macros (not provided by the package:)
@@ -693,8 +735,7 @@ When producing very long numbers there is the question of printing them on
\def\allowsplits #1%
{\ifx #1\relax \else #1\hskip 0pt plus 1pt\relax\expandafter\allowsplits\fi}%
\def\printnumber #1{\expandafter\expandafter\expandafter\allowsplits #1\relax }%
-%% expands twice before printing (all macros from the xint bundle expand in two steps
-%% to their final output).|\par\endgroup
+%% (all macros from the xint bundle expand in two steps to their final output).|\par\endgroup
An alternative (\autoref{fn:np}) is to suitably configure the thousand separator
with the \href{http://ctan.org/pkg/numprint}{numprint} package (does not work in
math mode; I also tried \href{http://ctan.org/pkg/siunitx}{siunitx} but even in
@@ -705,23 +746,35 @@ package\footnote{\url{http://ctan.org/pkg/seqsplit}}
which can be used to achieve this splitting accross lines, and does work
in inline math mode.
-The package \xintname also provides utilities (\autoref{sec:utilsxint}), some
-completely expandable, others not, of independent interest. Their use is
+\normalsize
+The utilities provided by \xinttoolsname (\autoref{sec:tools}), some
+completely expandable, others not, are of independent interest. Their use is
illustrated through various examples: among those, it is shown in
\autoref{ssec:quicksort} how to implement in a completely expandable way the
quick sort algorithm and also how to illustrate it graphically. Other examples
-include some dynamically constructed alignments with cells giving the prime
-numbers (\autoref{ssec:primesI}, \autoref{ssec:primesII}).
+include some dynamically constructed alignments with automatically computed
+prime number cells (\autoref{ssec:primesI}, \autoref{ssec:primesII}).
-Some other traditional computational examples are \hyperref[ssec:Machin]{the
- computations of $\pi$ and $\log 2$} and the computation of the
-\hyperlink{e-convergents}{convergents of $e$} with the help of the
+Some other computational examples are \hyperref[ssec:Machin]{the
+ computations of $\pi$ and $\log 2$} using \xintname and the computation of the
+\hyperlink{e-convergents}{convergents of $e$} with the further help of the
\xintcfracname package.
\section{Recent changes}
\footnotesize
+
+\noindent Release |1.09g| (|[2013/11/22]|):
+\begin{itemize}
+\item package \xinttoolsname is detached from \xintname, to make tools such as
+ \csbxint{For}, \csbxint{ApplyUnbraced}, and \csbxint{iloop} available without
+ the \xintname overhead.
+\item new expandable nestable loops \csbxint{loop} and \csbxint{iloop}.
+\item bugfix: \csbxint{For} and \csbxint{For*} do not modify anymore the value
+ of |\count 255|.
+\end{itemize}
+
\noindent Release |1.09f| (|[2013/11/04]|):
\begin{itemize}
\item new \csbxint{ZapFirstSpaces}, \csbxint{ZapLastSpaces},
@@ -748,6 +801,8 @@ Some other traditional computational examples are \hyperref[ssec:Machin]{the
% changing outputs) to some inner macros.
\end{itemize}
+\clearpage
+
\noindent Release |1.09e| (|[2013/10/29]|):
\begin{itemize}
\item new \csbxint{integers}, \csbxint{dimensions}, \csbxint{rationals} for
@@ -880,7 +935,7 @@ version \fexpan ds the un-braced list items. After
\item Extraction of square roots, for floating point numbers
(\csbxint{FloatSqrt}), and also in
a version adapted to integers (\csbxint{iSqrt}).
-\item New package \xintbinhexname providing \hyperref[sec:combinhex]{conversion
+\item New package \xintbinhexname providing \hyperref[sec:binhex]{conversion
routines} to and from binary and hexadecimal bases.
\end{itemize}
@@ -910,7 +965,7 @@ will replace pointwise |D|; this argument may exceed the |32767| bound.
\item To write the |\xintexpr| parser I benefited from the commented source of
the
\LaTeX3 parser; the |\xintexpr| parser has its own features and peculiarities.
-See \hyperref[sec:comexpr]{its documentation}.
+See \hyperref[sec:expr]{its documentation}.
\end{itemize}
% The |\xintexpr..\relax| and |\xintfloatexpr..\relax| are usable as
@@ -1084,7 +1139,7 @@ with @8@ digits after the decimal mark, and printed.
with the inherent difficulty of keeping up with braces and everything...
\item if such a formula is used thousands of times in a document (for plots?),
this could impact some parts of the \TeX{} program memory (for technical
- reasons explained in \autoref{sec:comexpr}). So, a utility \csbxint{NewExpr}
+ reasons explained in \autoref{sec:expr}). So, a utility \csbxint{NewExpr}
is provided to do the work of translating an |\xintexpr|-ession with
parameters into a chain of macro evaluations.\footnote{As its makes some macro
definitions, it is not an expandable command. It does not need protection
@@ -1999,7 +2054,7 @@ where spaces could break havoc. So the best is to avoid them entirely.
This is entirely otherwise inside an |\xintexpr|-ession, where spaces are
expected to, as a general rule (with possible exceptions related to the
allowed use of braces, see the
-\hyperref[sec:comexpr]{documentation}) be completely
+\hyperref[sec:expr]{documentation}) be completely
harmless, and even recommended for making the source more legible.
Syntax such as |\xintMul\A\B| is accepted and equivalent\footnote{see however
@@ -2329,13 +2384,16 @@ for typesetting: this is just an example of one way to do it.
\section{Utilities for expandable manipulations}
-The package now has more utilities to deal
-expandably with `lists of things', which were treated un-expandably in the
-previous section with \csa{xintAssign} and \csa{xintAssignArray}:
-\csbxint{ReverseOrder} and \csbxint{Length} since the first
-release, \csbxint{Apply} and \csbxint{ListWithSep} since |1.04|,
-\csbxint{RevWithBraces}, \csbxint{CSVtoList}, \csbxint{NthElt} since |1.06|, and
-\csbxint{ApplyUnbraced}, since |1.06b|.
+The package now has more utilities to deal expandably with `lists of things',
+which were treated un-expandably in the previous section with \csa{xintAssign}
+and \csa{xintAssignArray}: \csbxint{ReverseOrder} and \csbxint{Length} since the
+first release, \csbxint{Apply} and \csbxint{ListWithSep} since |1.04|,
+\csbxint{RevWithBraces}, \csbxint{CSVtoList}, \csbxint{NthElt} since |1.06|,
+\csbxint{ApplyUnbraced}, since |1.06b|, \csbxint{loop} and \csbxint{iloop} since
+|1.09g|.\footnote{All these utilities, as well as \csbxint{Assign},
+ \csbxint{AssignArray} and the \csbxint{For} loops are now available from the
+ \xinttoolsname package, independently of the big integers facilities of
+ \xintname.}
\edef\z{\xintiPow {2}{100}}
@@ -2370,10 +2428,16 @@ Expandably computing primes is done in \autoref{xintSeq}.
\section{A new kind of for loop}
-As part of the \hyperref[sec:utilsxint]{utilities} coming with the \xintname
+As part of the \hyperref[sec:tools]{utilities} coming with the \xinttoolsname
package, there is a new kind of for loop, \csbxint{For}. Check it out
(\autoref{xintFor}).
+\section{A new kind of expandable loop}
+
+Also included in \xinttoolsname, \csbxint{iloop} is an expandable loop giving
+access to an iteration index, without using count registers. Check it out
+(\autoref{xintiloop}).
+
\section{Exceptions (error messages)}
In situations such as division by zero, the package will insert in the
@@ -2525,6 +2589,7 @@ Lastly, the macros \csa{xintRelaxArray} (of \xintname) and
compatible. \csa{xintTypesetBezoutAlgorithm} also uses the
\csa{endgraf} macro.
+\enlargethispage{\baselineskip}
\section{Installation}
@@ -2557,753 +2622,20 @@ It may be necessary to then refresh the TeX installation filename
database.
+
-\etocdepthtag.toc {commandsA}
-
-\section{Commands of the \xintname package}\label{sec:comxint}
-
-\def\n{\string{N\string}}
-\def\m{\string{M\string}}
-\def\x{\string{x\string}}
-
-In the description of the macros \texttt{\n} (or also \texttt{\m}) stands
-(except if mentioned otherwise) for a (long) number within braces or for a
-control sequence possibly within braces and \hyperref[sec:expansions]{\fexpan
- ding} to such a number
-(without the braces!), or for material within braces which \fexpan ds to such
-a number, as is acceptable on input by the \csbxint{Num} macro: a sequence of
-plus and minus signs, followed by some string of zeros, followed by digits.
-
-The letter \texttt{x} stands for something which will be inserted in-between a
-|\numexpr| and a |\relax|. It will thus be completely expanded and must give an
-integer obeying the \TeX{} bounds. Thus, it may be for example a count register,
-or itself a \csa{numexpr} expression, or just a number written explicitely with
-digits or something like |4*\count 255 + 17|, etc...
-
-For the rules regarding direct use of count registers or \csa{numexpr}
-expression, in the argument to the package macros, see the
-\hyperlink{useofcount}{use of count section} in \autoref{sec:inputs}.
-
-Some of these macros are extended by \xintfracname to accept fractions on input,
-and, generally, to output a fraction. But this means that additions,
-subtractions, multiplications output fractions and not integers; to guarantee
-the integer format on output when the inputs are integers, the original
-integer-only macros \csa{xintAdd}, \csa{xintSub}, \csa{xintMul} remain available
-under the names \csa{xintiAdd}, \csa{xintiSub}, \csa{xintiMul}. Even the
-original integer-only macros may now accept fractions on input as long as they
-are integers in disguise; they still produce on output integers without any
-forward slash mark nor trailing |[n]|. On the other hand macros such as
-|\xintAdd| will output fractions |A/B[n]|, with |B| present even if its value is
-one. To remove this unit denominator and convert the |[n]| part into explicit
-zeros, one has \csbxint{Num} (if one is certain to deal with an integer; see
-also \csbxint{PRaw}). This is mandatory when the computation result is fetched
-into a context where \TeX{} expects a number (assuming it does not exceed
-@2^31@). See the also the \xintfracname \hyperref[sec:comfrac]{documentation}
-for more information on how macros of \xintname are modified after loading
-\xintfracname (or \xintexprname).
-
-
-Package \xintname also provides some general macro programming or token
-manipulation utilities (expandable as well as non-expandable), which are
-described in the next section (\autoref{sec:utilsxint}).
-
-\localtableofcontents
-
-\subsection{\csbh{xintRev}} \label{xintRev}
-
-\csa{xintRev\n} will revert the order of the digits of the number,
-keeping the optional sign. Leading zeros
-resulting from the operation are not removed (see the
-\csa{xintNum} macro for this). This macro and all other
-macros dealing with numbers first expand `fully' their arguments.
-\centeredline{|\xintRev{-123000}|\digitstt{=\xintRev{-123000}}}
-\centeredline{|\xintNum{\xintRev{-123000}}|%
- \digitstt{=\xintNum{\xintRev{-123000}}}}
-
-
-\subsection{\csbh{xintLen}}\label{xintiLen}
-
-\csa{xintLen\n} returns the length of the number, not counting the sign.
-\centeredline{|\xintLen{-12345678901234567890123456789}|\digitstt
- {=\xintLen{-12345678901234567890123456789}}} Extended by \xintfracname to
-fractions: the length of |A/B[n]| is the length of |A| plus the length of |B|
-plus the absolute value of |n| and minus one (an integer input as |N| is
-internally represented in a form equivalent to |N/1[0]| so the minus one means
-that the extended \csa{xintLen}
-behaves the same as the original for integers).
-\centeredline{|\xintLen{-1e3/5.425}|\digitstt
- {=\xintLen{-1e3/5.425}}}
-The length is computed on the |A/B[n]| which would have been returned by
-\csbxint{Raw}: |\xintRaw {-1e3/5.425}|\digitstt{=\xintRaw {-1e3/5.425}}.
-
-Let's point out that the whole thing should sum up to
-less than circa @2^{31}@, but this is a bit theoretical.
-
-|\xintLen| is only for numbers or fractions. See \csbxint{Length} for counting
-tokens (or rather braced groups), more generally.
-
-\subsection{\csbh{xintDigitsOf}}\label{xintDigitsOf}
-
-This is a synonym for \csbxint{AssignArray}, to be used to define
-an array giving all the digits of a given (positive, else the minus sign will
-be treated as first item) number.
-\begingroup\xintDigitsOf\xintiPow {7}{500}\to\digits
-\centeredline{|\xintDigitsOf\xintiPow {7}{500}\to\digits|}
-\noindent @7^500@ has |\digits{0}=|\digits{0} digits, and the 123rd among them
-(starting from the most significant) is
-|\digits{123}=|\digits{123}.
-\endgroup
-
-\subsection{\csbh{xintNum}}\label{xintiNum}
-
-\csa{xintNum\n} removes chains of plus or minus signs, followed by zeros.
-\centeredline{|\xintNum{+---++----+--000000000367941789479}|\digitstt
- {=\xintNum{+---++----+--000000000367941789479}}} Extended by \xintfracname to
-accept also a fraction on input, as long as it reduces to an integer after
-division of the numerator by the denominator.
-\centeredline{|\xintNum{123.48/-0.03}|\digitstt{=\xintNum{123.48/-0.03}}}
-
-
-\subsection{\csbh{xintSgn}}\label{xintiSgn}
-
-\csa{xintSgn\n} returns 1 if the number is positive, 0 if it is
-zero and -1 if it is negative. Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintOpp}}\label{xintiOpp}
-
-\csa{xintOpp\n} returns the opposite |-N| of the number |N|.
-Extended by \xintfracname to fractions.
-
-
-\subsection{\csbh{xintAbs}}\label{xintiAbs}
-
-\csa{xintAbs\n} returns the absolute value of the number. Extended
-by \xintfracname to fractions.
-
-\subsection{\csbh{xintAdd}}\label{xintiAdd}
-
-\csa{xintAdd\n\m} returns the sum of the two numbers. Extended by
-\xintfracname to fractions.
-
-\subsection{\csbh{xintSub}}\label{xintiSub}
-
-\csa{xintSub\n\m} returns the difference |N-M|. Extended by
-\xintfracname to fractions.
-
-\subsection{\csbh{xintCmp}}\label{xintiCmp}
-
-\csa{xintCmp\n\m} returns 1 if |N>M|, 0 if |N=M|, and -1 if |N<M|.
-Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintEq}}\label{xintEq}
-{\small New with release |1.09a|.\par}
-
-\csa{xintEq\n\m} returns 1 if |N=M|, 0 otherwise.
-Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintGt}}\label{xintGt}
-{\small New with release |1.09a|.\par}
-
-% attention dans la doc du 9 octobre j'avais écrit \geq au lieu de >
-
-\csa{xintGt\n\m} returns 1 if |N|$>$|M|, 0 otherwise.
-Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintLt}}\label{xintLt}
-{\small New with release |1.09a|.\par}
-
-% attention dans la doc du 9 octobre j'avais écrit \leq au lieu de <
-
-\csa{xintLt\n\m} returns 1 if |N|$<$|M|, 0 otherwise.
-Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintIsZero}}\label{xintIsZero}
-{\small New with release |1.09a|.\par}
-
-\csa{xintIsZero\n} returns 1 if |N=0|, 0 otherwise.
-Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintNot}}\label{xintNot}
-{\small New with release |1.09c|.\par}
-
-\csa{xintNot} is a synonym for \csa{xintIsZero}.
-
-\subsection{\csbh{xintIsNotZero}}\label{xintIsNotZero}
-{\small New with release |1.09a|.\par}
-
-\csa{xintIsNotZero\n} returns 1 if |N<>0|, 0 otherwise.
-Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintIsOne}}\label{xintIsOne}
-{\small New with release |1.09a|.\par}
-
-\csa{xintIsOne\n} returns 1 if |N=1|, 0 otherwise.
-Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintAND}}\label{xintAND}
-{\small New with release |1.09a|.\par}
-
-\csa{xintAND\n\m} returns 1 if |N<>0| and |M<>0| and zero otherwise.
- Extended by \xintfracname to fractions.
+%\clearpage
-\subsection{\csbh{xintOR}}\label{xintOR}
-{\small New with release |1.09a|.\par}
-
-\csa{xintOR\n\m} returns 1 if |N<>0| or |M<>0| and zero otherwise.
- Extended by \xintfracname to fractions.
-
-
-\subsection{\csbh{xintXOR}}\label{xintXOR}
-{\small New with release |1.09a|.\par}
-
-\csa{xintXOR\n\m} returns 1 if exactly one of |N| or |M| is true (i.e.
-non-zero).
- Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintANDof}}\label{xintANDof}
-{\small New with release |1.09a|.\par}
-
-\csa{xintANDof}|{{a}{b}{c}...}| returns 1 if all are true (i.e. non
-zero) and zero otherwise. The list argument
-may be a macro, it (or rather its first token) is \fexpan ded first (each
-item also is \fexpan ded). Extended by \xintfracname to fractions.
-
-
-\subsection{\csbh{xintORof}}\label{xintORof}
-{\small New with release |1.09a|.\par}
-
-\csa{xintORof}|{{a}{b}{c}...}| returns 1 if at least one is true
-(i.e. does not vanish). The list argument
-may be a macro, it is \fexpan ded first. Extended by \xintfracname to fractions.
-
-
-\subsection{\csbh{xintXORof}}\label{xintXORof}
-{\small New with release |1.09a|.\par}
-
-\csa{xintXORof}|{{a}{b}{c}...}| returns 1 if an odd number of them are
-true (i.e. does not vanish). The list argument may be a macro, it is
-\fexpan ded first. Extended by \xintfracname to fractions.
-
-
-\subsection{\csbh{xintGeq}}\label{xintiGeq}
-
-\csa{xintGeq\n\m} returns 1 if the \emph{absolute value} of the first number is
-at least equal to the absolute value of the second number. If \verb+|N|<|M|+ it
-returns 0. Extended by \xintfracname to fractions (starting with release
-|1.07|). Please note that the macro compares \emph{absolute values}.
-
-\subsection{\csbh{xintMax}}\label{xintiMax}
-
-\csa{xintMax\n\m} returns the largest of the two in the sense of the order
-structure on the relative integers (\emph{i.e.} the right-most number if they
-are put on a line with positive numbers on the right): |\xintiMax
-{-5}{-6}|\digitstt{=\xintiMax{-5}{-6}}. Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintMaxof}}\label{xintMaxof}
-{\small New with release |1.09a|.\par}
-
-\csa{xintMaxof}|{{a}{b}{c}...}| returns the maximum. The list argument
-may be a macro, it is \fexpan ded first. Extended by \xintfracname to
-fractions.
-
-
-\subsection{\csbh{xintMin}}\label{xintiMin}
-
-\csa{xintMin\n\m} returns the smallest of the two in the sense of the order
-structure on the relative integers (\emph{i.e.} the left-most number if they are
-put on a line with positive numbers on the right): |\xintiMin
-{-5}{-6}|\digitstt{=\xintiMin{-5}{-6}}. Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintMinof}}\label{xintMinof}
-{\small New with release |1.09a|.\par}
-
-\csa{xintMinof}|{{a}{b}{c}...}| returns the minimum. The list argument
-may be a macro, it is \fexpan ded first. Extended by \xintfracname to
-fractions.
-
-\subsection{\csbh{xintSum}}\label{xintiSum}
-
-\csa{xintSum}\marg{braced things} after expanding its argument
-expects to find a sequence of tokens (or braced material).
-Each is expanded (with the usual meaning), and the sum of all these numbers is
-returned.
-\centeredline{%
- \csa{xintiSum}|{{123}{-98763450}{\xintFac{7}}{\xintiMul{3347}{591}}}|%
- \digitstt{=\xintiSum{{123}{-98763450}{\xintFac{7}}{\xintiMul{3347}{591}}}}}
-\centeredline{\csa{xintiSum}|{1234567890}|\digitstt{=\xintiSum{1234567890}}}
-An empty sum is no error and returns zero: |\xintiSum
-{}|\digitstt{=\xintiSum {}}. A sum with only one
-term returns that number: |\xintiSum {{-1234}}|\digitstt{=\xintiSum
- {{-1234}}}. Attention that |\xintiSum {-1234}| is not legal input
-and will make the \TeX{} run fail. On the other hand |\xintiSum
-{1234}|\digitstt{=\xintiSum{1234}}. Extended by \xintfracname
-to fractions.
-
-% retiré de la doc le 22 octobre 2013
-
-% \subsection{\csbh{xintSumExpr}}\label{xintiSumExpr}
-
-% \csa{xintSumExpr}\meta{braced things}\csa{relax} is to what \csa{xintSum}
-% expands. The argument is then expanded (with the usual meaning) and should give
-% a list of braced quantities or macros, each one will be expanded in turn.
-% \centeredline{%
-% \csa{xintiSumExpr}| {123}{-98763450}|%
-% |{\xintFac{7}}{\xintiMul{3347}{591}}\relax|\digitstt{=%
-% \xintiSumExpr {123}{-98763450}{\xintFac{7}}{\xintiMul{3347}{591}}\relax}}
-
-% Note: I am not so happy with the name which seems to suggest that the
-% |+| sign should be used instead of braces. Perhaps this will change
-% in the future.
-
-% Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintMul}}\label{xintiMul}
-{\small Modified in release |1.03|.\par}
-
-\csa{xintMul\n\m} returns the product of the two numbers. Starting
-with release |1.03| of \xintname, the macro checks the lengths of
-the two numbers and then activates its algorithm with the best (or
-at least, hoped-so) choice of which one to put first. This makes
-the macro a bit slower for numbers up to 50 digits, but may give
-substantial speed gain when one of the number has 100 digits or more.
-Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintSqr}}\label{xintiSqr}
-
-\csa{xintSqr\n} returns the square. Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintPrd}}\label{xintiPrd}
-
-\csa{xintPrd}\marg{braced things} after expanding its argument expects to find a
-sequence of tokens (or braced material). Each is expanded (with the usual
-meaning), and the product of all these numbers is returned.
-\centeredline{%
- \csa{xintiPrd}|{{-9876}{\xintFac{7}}{\xintiMul{3347}{591}}}|%
- \digitstt{=%
- \xintiPrd{{-9876}{\xintFac{7}}{\xintiMul{3347}{591}}}}}
-\centeredline{\csa{xintiPrd}|{123456789123456789}|\digitstt{=%
- \xintiPrd{123456789123456789}}} An empty product is no error and returns 1:
-|\xintiPrd {}|\digitstt{=\xintiPrd {}}. A product reduced to a single term returns
-this number: |\xintiPrd {{-1234}}|\digitstt{=\xintiPrd {{-1234}}}. Attention that
-|\xintiPrd {-1234}| is not legal input and will make the \TeX{} compilation
-fail. On the other hand |\xintiPrd {1234}|\digitstt{=\xintiPrd {1234}}.
-\centeredline{$\displaystyle 2^{200}3^{100}7^{100}$} \centeredline{|=\xintiPrd
- {{\xintiPow {2}{200}}{\xintiPow {3}{100}}{\xintiPow {7}{100}}}|}
-\digitstt{=\printnumber{\xintNum {\xinttheexpr 2^200*3^100*7^100\relax }}}
-
-Extended by \xintfracname to fractions.
-
-With \xintexprname, the above would be coded simply as \centeredline
-{|\xintthenumexpr 2^200*3^100*7^100\relax |}
-
-% I temporarily remove mention of \xintPrdExpr from the documentation; I
-% really dislike the name now.
-
-% \subsection{\csbh{xintPrdExpr}}\label{xintiPrdExpr}
-
-% {\small Name change in |1.06a|! I apologize, but I suddenly decided that
-% \csa{xintProductExpr} was a bad choice; so I just replaced it by the current
-% name. \par}
-
-% \csa{xintPrdExpr}\marg{argument}\csa{relax} is to what \csa{xintPrd} expands
-% ; its argument is expanded (with the usual meaning) and should give a list of
-% braced numbers or macros. Each will be expanded when it is its turn.
-% \centeredline{\csa{xintiPrdExpr}| 123456789123456789\relax|\digitstt{=%
-% \xintiPrdExpr 123456789123456789\relax}}
-
-% Note: I am not so happy with the name which seems to suggest that the
-% |*| sign should be used instead of braces. Perhaps this will change
-% in the future.
-
-% Extended by \xintfracname to fractions.
-
-\subsection{\csbh{xintPow}}\label{xintiPow}
-
-\csa{xintPow\n\x} returns |N^x|. When |x| is zero, this is 1. If |N| is zero and
-|x<0|, if \verb+|N|>1+ and |x<0| negative, or if \verb+|N|>1+ and |x>999999999|,
-then an error is raised. |2^999999999| has \np{301029996} digits; each exact
-multiplication of two one thousand digits numbers already takes a few seconds,
-so needless to say this bound is completely irrealistic. Already |2^9999| has
-\np{3010} digits,\footnote{on my laptop |\string\xintiPow \{2\}\{9999\}|
- obtains all |3010| digits in about ten or eleven seconds. In contrast, the
- float versions for
- |8|, |16|, |24|, or even more significant figures, do their jobs in circa one
- hundredth of a second (|1.08b|). This is done without |log|/|exp| which are
- not (yet?) implemented in \xintfracname. The \LaTeX3
- \href{http://www.ctan.org/tex-archive/macros/latex/contrib/l3kernel}{l3fp}
- does this with |log|/|exp| and is ten times faster (|16| figures only).} so I
-should perhaps lower the bound to |99999|.
-
-Extended by \xintfracname to fractions (\csbxint{Pow}) and also to floats
-(\csbxint{FloatPow}). Negative
-exponents do not then cause errors anymore. The float version is able to deal
-with things such as
-|2^999999999| without any problem. For example
-|\xintFloatPow[4]{2}{9999}|\digitstt{=\xintFloatPow[4]{2}{9999}} and
-|\xintFloatPow[4]{2}{999999999}|
-\digitstt{=\xintFloatPow[4]{2}{999999999}}.
-
-\subsection{\csbh{xintSgnFork}}\label{xintSgnFork}
-{\small New with release |1.07|. See also \csbxint{ifSgn}.\par}
-
-\csa{xintSgnFork}\verb+{-1|0|1}+\marg{A}\marg{B}\marg{C} expandably
-chooses to execute either the \meta{A}, \meta{B} or \meta{C} code,
-depending on its first argument. This first argument should be anything
-expanding to either |-1|, |0| or |1| (a count register should be
-prefixed by |\the| and a |\numexpr...\relax| also should be prefixed by
-|\the|). This utility is provided to help construct expandable macros
-choosing depending on a condition which one of the package macros to
-use, or which values to confer to their arguments.
-
-\subsection{\csbh{xintifSgn}}\label{xintifSgn}
-{\small New with release |1.09a|.\par}
-
-Similar to \csa{xintSgnFork} except that the first argument may expand to a
-(big) integer (or a fraction if \xintfracname is loaded), and it is its sign
-which decides which of the three branches is taken. Furthermore this first
-argument may be a count register, with no |\the| or |\number| prefix.
-
-\subsection{\csbh{xintifZero}}\label{xintifZero}
-{\small New with release |1.09a|.\par}
-
-\csa{xintifZero}\marg{N}\marg{IsZero}\marg{IsNotZero} expandably checks
-if the first mandatory argument |N| (a number, possibly a fraction if
-\xintfracname is loaded, or a macro expanding to one such) is zero or
-not. It then either executes the first or the second branch.
-
-\subsection{\csbh{xintifNotZero}}\label{xintifNotZero}
-{\small New with release |1.09a|.\par}
-
-\csa{xintifNotZero}\marg{N}\marg{IsNotZero}\marg{IsZero} expandably checks
-if the first mandatory argument |N| (a number, possibly a fraction if
-\xintfracname is loaded, or a macro expanding to one such) is not zero or
-is zero. It then either executes the first or the second branch.
-
-\subsection{\csbh{xintifTrueFalse}}\label{xintifTrueFalse}
-{\small New with release |1.09c|, renamed in |1.09e|.\par}
-
-\csa{xintifTrueFalse}\marg{N}\marg{true branch}\marg{false branch} is a synonym
-for \csbxint{ifNotZero}. It is also available as \csa{xintifTrue} but this later
-name is a bit misleading as the macro must always have a |false| branch,
-possibly an empty brace pair |{}|.
-
-\subsection{\csbh{xintifCmp}}\label{xintifCmp}
-{\small New with release |1.09e|.\par}
-
-\csa{xintifCmp}\marg{A}\marg{B}\marg{if A<B}\marg{if A=B}\marg{if A>B} compares
-its arguments and chooses accordingly the correct branch.
-
-\subsection{\csbh{xintifEq}}\label{xintifEq}
-{\small New with release |1.09a|.\par}
-
-\csa{xintifEq}\marg{A}\marg{B}\marg{YES}\marg{NO} checks equality of its
-two first arguments (numbers, or fractions if \xintfracname is loaded) and does the |YES| or the |NO| branch.
-
-\subsection{\csbh{xintifGt}}\label{xintifGt}
-{\small New with release |1.09a|.\par}
-
-% attention dans la doc du 9 octobre j'avais écrit \geq au lieu de <
-\csa{xintifGt}\marg{A}\marg{B}\marg{YES}\marg{NO} checks if $A>B$ and in that
-case executes the |YES| branch. Extended to fractions (in particular decimal
-numbers) by \xintfracname.
-
-\subsection{\csbh{xintifLt}}\label{xintifLt}
-{\small New with release |1.09a|.\par}
-
-% attention dans la doc du 9 octobre j'avais écrit \leq au lieu de <
-\csa{xintifLt}\marg{A}\marg{B}\marg{YES}\marg{NO} checks if $A<B$ and in that
-case executes the |YES| branch. Extended to fractions (in particular decimal
-numbers) by \xintfracname.
-
-\begin{framed}
- The macros described next are all integer-only on input. With \xintfracname
- loaded their argument is first given to \csbxint{Num} and may thus be
- a fraction, as long as it is in fact an integer in disguise.
-\end{framed}
-
-\subsection{\csbh{xintifOdd}}\label{xintifOdd}
-{\small New with release |1.09e|.\par}
-
-\csa{xintifOdd}\marg{A}\marg{YES}\marg{NO} checks if $A$ is and odd integer
-and in that case executes the |YES| branch.
-
-
-\subsection{\csbh{xintFac}}\label{xintiFac}
-
-\csa{xintFac\x} returns the factorial. It is an error if the
-argument is negative or at least @10^6@. It is not recommended to
-launch the computation of things such as @100000!@, if you need
-your computer for other tasks. Note that the argument is of the |x| type, it
-must obey the \TeX{} bounds, but on the other hand may involve count registers
-and even arithmetic operations as it will be completely expanded inside a
-|\numexpr|.
-
-With \xintfracname loaded, the macro also
-accepts a fraction as argument, as long as this fraction turns out to be an
-integer: |\xintFac {66/3}|\digitstt{=\xintFac {66/3}}.
-
-% the construct |\xintFac{\xintAdd {2}{3}}| will fail,
-% use either |\xintFac{\xintiAdd {2}{3}}| or |\xintFac{\xintNum{\xintAdd
-% {2}{3}}}|.
-
-% temps obsolètes, mettre à jour
-% On my laptop @1000!@ (2568 digits)
-% is computed in a little less than ten seconds, @2000!@ (5736
-% digits) is computed in a little less than one hundred seconds, and
-% @3000!@ (which has 9131 digits) needs close to seven minutes\dots
-% I have no idea how much time @10000!@ would need (do rather
-% @9999!@ if you can, the algorithm has some overhead at the
-% transition from @N=9999@ to @10000@ and higher; @10000!@ has 35660
-% digits). Not to mention @100000!@ which, from the Stirling formula,
-% should have 456574 digits.
-
-\subsection{\csbh{xintDivision}}\label{xintDivision}
-
-\csa{xintDivision\n\m} returns |{quotient Q}{remainder R}|. This
-is euclidean division: |N = QM + R|, |0|${}\leq{}$\verb+R < |M|+. So the
-remainder is always non-negative and the formula |N = QM + R|
-always holds independently of the signs of |N| or |M|. Division by
-zero is an error (even if |N| vanishes) and returns |{0}{0}|.
-
-This macro is integer only (with \xintfracname loaded it accepts
-fractions on input, but they must be integers in disguise) and not to be
-confused with the \xintfracname macro \csbxint{Div} which divides one
-fraction by another.
-
-\subsection{\csbh{xintQuo}}\label{xintQuo}
-
-\csa{xintQuo\n\m} returns the quotient from the euclidean division. When
-both |N| and |M| are positive one has \csa{xintQuo\n\m}|=\xintiTrunc
-{0}{N/M}| (using package \xintfracname). With \xintfracname loaded it
-accepts fractions on input, but they must be integers in disguise.
-
-\subsection{\csbh{xintRem}}\label{xintRem}
-
-\csa{xintRem\n\m} returns the remainder from the euclidean division.
-With \xintfracname loaded it accepts fractions on input, but they must
-be integers in disguise.
-
-
-
-\subsection{\csbh{xintFDg}}\label{xintFDg}
-
-\csa{xintFDg\n} returns the first digit (most significant) of the
-decimal expansion.
-
-\subsection{\csbh{xintLDg}}\label{xintLDg}
-
-\csa{xintLDg\n} returns the least significant digit. When the
-number is positive, this is the same as the remainder in the
-euclidean division by ten.
-
-\subsection{\csbh{xintMON}, \csbh{xintMMON}}\label{xintMON}\label{xintMMON}
-{\small New in version |1.03|.\par}
-
-\csa{xintMON\n} returns |(-1)^N| and \csa{xintMMON\n} returns
-|(-1)^{N-1}|. \centeredline{|\xintMON {-280914019374101929}|\digitstt{=\xintMON
- {280914019374101929}}, |\xintMMON
-{-280914019374101929}|\digitstt{=\xintMMON {280914019374101929}}}
-
-\subsection{\csbh{xintOdd}}\label{xintOdd}
-
-\csa{xintOdd\n} is 1 if the number is odd and 0 otherwise.
-
-
-\subsection{\csbh{xintiSqrt}, \csbh{xintiSquareRoot}}\label{xintiSqrt}
-\label{xintiSquareRoot}
-{\small New with |1.08|.\par}
-\xintAssign\xintiSquareRoot {17000000000000000000000000}\to\A\B
-
-\noindent\csa{xintiSqrt\n} returns the largest integer whose square is
-at most equal to |N|.
-\centeredline{|\xintiSqrt {2000000000000000000000000000000000000}=|%
-\digitstt{\xintiSqrt{2000000000000000000000000000000000000}}}
-\centeredline{|\xintiSqrt {3000000000000000000000000000000000000}=|%
-\digitstt{\xintiSqrt{3000000000000000000000000000000000000}}}
-\centeredline{|\xintiSqrt {\xintDSH {-120}{2}}=|}%
-\centeredline{\digitstt{\xintiSqrt {\xintDSH {-120}{2}}}}
-\csa{xintiSquareRoot\n} returns |{M}{d}| with |d>0|, |M^2-d=N| and |M|
-smallest (hence |=1+|\csa{xint\-iSqrt}|{N}|).
-\centeredline{|\xintAssign\xintiSquareRoot
- {17000000000000000000000000}\to\A\B|}%
-\centeredline{|\xintiSub{\xintiSqr\A}\B=\A^2-\B|}%
-\centeredline{\digitstt{\xintiSub{\xintiSqr\A}\B=\A\string^2-\B}}
-A rational approximation to
-$\sqrt{|N|}$ is $|M|-\frac{|d|}{|2M|}$ (this is a majorant and the error is at
-most |1/2M|; if |N| is a perfect square |k^2| then |M=k+1| and this gives
-|k+1/(2k+2)|, not |k|).
-
-Package \xintfracname has \csbxint{FloatSqrt} for square
-roots of floating point numbers.
-
-
-\begin{framed}
- The macros described next are strictly for integer-only arguments. These
- arguments are \emph{not} filtered via \csbxint{Num}.
-\end{framed}
-
-\subsection{\csbh{xintInc}, \csbh{xintDec}}
-\label{xintInc}
-\label{xintDec}
-{\small New with |1.08|.\par}
-
-\csa{xintInc\n} is |N+1| and \csa{xintDec\n} is |N-1|. These macros remain
-integer-only, even with \xintfracname loaded.
-
-\subsection{\csbh{xintDouble}, \csbh{xintHalf}}
-\label{xintDouble}
-\label{xintHalf}
-{\small New with |1.08|.\par}
-
-\csa{xintDouble\n} returns |2N| and \csa{xintHalf\n} is |N/2| rounded
-towards zero. These macros remain integer-only, even with \xintfracname loaded.
-
-\subsection{\csbh{xintDSL}}\label{xintDSL}
-
-\csa{xintDSL\n} is decimal shift left, \emph{i.e.} multiplication
-by ten.
-
-\subsection{\csbh{xintDSR}}\label{xintDSR}
-
-\csa{xintDSR\n} is decimal shift right, \emph{i.e.} it removes the last digit
-(keeping the sign), equivalently it is the closest integer to |N/10| when
-starting at zero.
-
-\subsection{\csbh{xintDSH}}\label{xintDSH}
-
-\csa{xintDSH\x\n} is parametrized decimal shift. When |x| is
-negative, it is like iterating \csa{xintDSL} \verb+|x|+ times
-(\emph{i.e.} multiplication by @10^{-@|x|@}@). When |x| positive,
-it is like iterating \csa{DSR} |x| times (and is more efficient), and for a
-non-negative |N| this is thus the same as the
-quotient from the euclidean division by |10^x|.
-
-\subsection{\csbh{xintDSHr}, \csbh{xintDSx}}\label{xintDSHr}\label{xintDSx}
-{\small New in release |1.01|.\par}
-
-\csa{xintDSHr\x\n} expects |x| to be zero or positive and it returns
-then a value |R| which is correlated to the value |Q| returned by
-\csa{xintDSH\x\n} in the following manner:
-\begin{itemize}
-\item if |N| is
- positive or zero, |Q| and |R| are the quotient and remainder in
- the euclidean division by |10^x| (obtained in a more efficient
- manner than using \csa{xintDivision}),
-\item if |N| is negative let
- |Q1| and |R1| be the quotient and remainder in the euclidean
- division by |10^x| of the absolute value of |N|. If |Q1|
- does not vanish, then |Q=-Q1| and |R=R1|. If |Q1| vanishes, then
- |Q=0| and |R=-R1|.
-\item for |x=0|, |Q=N| and |R=0|.
-\end{itemize}
-So one has |N = 10^x Q + R| if |Q| turns out to be zero or
-positive, and |N = 10^x Q - R| if |Q| turns out to be negative,
-which is exactly the case when |N| is at most |-10^x|.
-
-
-\csa{xintDSx\x\n} for |x| negative is exactly as
-\csa{xintDSH\x\n}, \emph{i.e.} multiplication by @10^{-@|x|@}@.
-For |x| zero or positive it returns the two numbers |{Q}{R}|
-described above, each one within braces. So |Q| is
-\csa{xintDSH\x\n}, and |R| is \csa{xintDSHr\x\n}, but computed
-simultaneously.
-
-\begin{flushleft}
- \xintAssign\xintDSx {-1}{-123456789}\to\M
- \noindent{|\xintAssign\xintDSx {-1}{-123456789}\to\M|}\\
- |\meaning\M: |\digitstt{\meaning\M}.\\
- \xintAssign\xintDSx {-20}{1234567689}\to\M
- {|\xintAssign\xintDSx {-20}{123456789}\to\M|}\\
- |\meaning\M: |\digitstt{\meaning\M}.\\
- \xintAssign\xintDSx{0}{-123004321}\to\Q\R
- {|\xintAssign\xintDSx {0}{-123004321}\to\Q\R|}\\
- \noindent|\meaning\Q: |\digitstt{\meaning\Q}, |\meaning\R:
- |\digitstt{\meaning\R.}\\
- |\xintDSH {0}{-123004321}|\digitstt{=\xintDSH {0}{-123004321}},
- |\xintDSHr {0}{-123004321}|\digitstt{=\xintDSHr {0}{-123004321}}\\
- \xintAssign\xintDSx {6}{-123004321}\to\Q\R
- {|\xintAssign\xintDSx {6}{-123004321}\to\Q\R|}\\
- |\meaning\Q: |\digitstt{\meaning\Q},
- |\meaning\R: |\digitstt{\meaning\R.}\\
- |\xintDSH {6}{-123004321}|\digitstt{=\xintDSH {6}{-123004321}},
- |\xintDSHr {6}{-123004321}|\digitstt{=\xintDSHr {6}{-123004321}}\\
- \xintAssign\xintDSx {8}{-123004321}\to\Q\R
- {|\xintAssign\xintDSx {8}{-123004321}\to\Q\R|}\\
- |\meaning\Q: |\digitstt{\meaning\Q},
- |\meaning\R: |\digitstt{\meaning\R.} \\
- |\xintDSH {8}{-123004321}|\digitstt{=\xintDSH {8}{-123004321}},
- |\xintDSHr {8}{-123004321}|\digitstt{=\xintDSHr {8}{-123004321}}\\
- \xintAssign\xintDSx {9}{-123004321}\to\Q\R
- {|\xintAssign\xintDSx {9}{-123004321}\to\Q\R|}\\
- |\meaning\Q: |\digitstt{\meaning\Q},
- |\meaning\R: |\digitstt{\meaning\R.}\\
- |\xintDSH {9}{-123004321}|\digitstt{=\xintDSH {9}{-123004321}},
- |\xintDSHr {9}{-123004321}|\digitstt{=\xintDSHr {9}{-123004321}}\\
-\end{flushleft}
-
-\subsection{\csbh{xintDecSplit}}\label{xintDecSplit}
-
-{\small This has been modified in release |1.01|.\par}
-
-\csa{xintDecSplit\x\n} cuts the number into two pieces (each one within a
-pair of enclosing braces). First the sign if present is \emph{removed}.
-Then, for |x| positive or null, the second piece contains the |x| least
-significant digits (\emph{empty} if |x=0|) and the first piece the remaining
-digits (\emph{empty} when |x| equals or exceeds the length of |N|).
-Leading zeros in the second piece are not removed. When |x| is negative
-the first piece contains the \verb+|x|+ most significant digits and the
-second piece the remaining digits (\emph{empty} if @|x|@ equals or exceeds
-the length of |N|). Leading zeros in this second piece are not removed.
-So the absolute value of the original number is always the concatenation
-of the first and second piece.
-
-{\footnotesize This macro's behavior for |N| non-negative is final and will not
- change. I am still hesitant about what to do with the sign of a
- negative |N|.\par}
-
-
-\xintAssign\xintDecSplit {0}{-123004321}\to\L\R
-\centeredline{|\xintAssign\xintDecSplit {0}{-123004321}\to\L\R|}
-\noindent|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
-\xintAssign\xintDecSplit {5}{-123004321}\to\L\R
-\centeredline{|\xintAssign\xintDecSplit {5}{-123004321}\to\L\R|}
-|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
-\xintAssign\xintDecSplit {9}{-123004321}\to\L\R
-\centeredline{|\xintAssign\xintDecSplit {9}{-123004321}\to\L\R|}
-|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
-\xintAssign\xintDecSplit {10}{-123004321}\to\L\R
-\centeredline{|\xintAssign\xintDecSplit {10}{-123004321}\to\L\R|}
-|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
-\xintAssign\xintDecSplit {-5}{-12300004321}\to\L\R
-\centeredline{|\xintAssign\xintDecSplit {-5}{-12300004321}\to\L\R|}
-|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
-\xintAssign\xintDecSplit {-11}{-12300004321}\to\L\R
-\centeredline{|\xintAssign\xintDecSplit {-11}{-12300004321}\to\L\R|}
-|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
-\xintAssign\xintDecSplit {-15}{-12300004321}\to\L\R
-\centeredline{|\xintAssign\xintDecSplit {-15}{-12300004321}\to\L\R|}
-|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
-
-\subsection{\csbh{xintDecSplitL}}\label{xintDecSplitL}
-
-\csa{xintDecSplitL\x\n} returns the first piece after the action
-of \csa{xintDecSplit}.
-
-\subsection{\csbh{xintDecSplitR}}\label{xintDecSplitR}
-
-\csa{xintDecSplitR\x\n} returns the second piece after the action
-of \csa{xintDecSplit}.
+\etocdepthtag.toc {commandsA}
+\section{Commands of the \xinttoolsname package}
+\label{sec:tools}
-\section{Commands (utilities) of the \xintname package}
-\label{sec:utilsxint}
+These utilities used to be provided within the \xintname package; since |1.09g|
+they have been moved to an independently usable package \xinttoolsname, which
+has none of the \xintname facilities regarding big numbers.
-The completely expandable utilities come first, up to and including
-\csbxint{Seq} (which is listed here because it generates sequences of short
-integers using |\numexpr|, thus does not make use of the big integers macros of
-\xintname).
+The first listed are the completely expandable utilities up to \csbxint{iloop}.
-This section contains various concrete examples of use of these utilities (such
-as \csbxint{ApplyUnbraced}, \csbxint{ApplyInline} and \csbxint{For*}), and ends with a
+This section contains various concrete examples and ends with a
\hyperref[ssec:quicksort]{completely expandable implementation of the Quick Sort
algorithm} together with a graphical illustration of its action.
@@ -3377,7 +2709,7 @@ anyway apart from stripping away all \emph{leading} spaces.
This macro will be mostly of interest to programmers who will know what I will
now be talking about. \emph{The essential points, naturally, are the complete
- expandability and the fact that no brace removal or any other alteration is
+ expandability and the fact that no brace removal nor any other alteration is
done to the input.}
\TeX's input scanner already converts consecutive blanks into single space
@@ -3845,7 +3177,7 @@ many ways, we use again |\xintApplyUnbraced| but with a macro which gobbles
its argument and replaces it with a tabulation character. The \csbxint{For*}
macro would be more elegant here.
%
-\dverb?@
+\dverb?@
\newcounter{primecount}
\newcounter{cellcount}
\newcommand{\NbOfColumns}{13}
@@ -3916,6 +3248,493 @@ empty sequence when the row turns out to already have all its cells.
\centeredline{There are \arabic{primecount} prime numbers up to 1000.}
\end{figure*}
+\subsection{\csbh{xintloop}, \csbh{xintbreakloop}, \csbh{xintbreakloopanddo}, \csbh{xintloopskiptonext}}
+\label{xintloop}
+\label{xintbreakloop}
+\label{xintbreakloopanddo}
+\label{xintloopskiptonext}
+{\small New with release |1.09g|.\par}
+
+|\xintloop|\meta{stuff}|\iftest ... \repeat| is an expandable loop compatible
+with nesting. If a sub-loop is to be used all the material from the start and up
+to the complete subloop inclusive should be braced; these braces will be removed
+and do not create a group.
+
+As this loop and \csbxint{iloop} will primarily be of interest to experienced
+\TeX{} macro programmers, my description will assume that the user is
+knowledgeable enough. The loop and its various constituents are declared short,
+they can not handle |\par| tokens or empty lines.
+
+One can abort the loop with \csbxint{breakloop}; this should not be used in the
+final test, and one should expand the |\fi| from the corresponding test before.
+One has also \csbxint{breakloopanddo} whose first argument will be inserted in
+the token stream after the loop; one may need a macro such as |\xint_afterfi| to
+move the whole thing after the |\fi|, as a simple |\expandafter| will not be
+enough.
+
+One will usually employ some count registers to manage the exit test from the
+loop; this breaks expandability, see \csbxint{iloop} for an expandable integer
+indexed loop. Use in alignments will be complicated by the fact that cells
+create groups, and also from the fact that any encountered unexpandable material
+will cause the \TeX{} input scanner to insert |\endtemplate| on each encountered
+|&| or |\cr|; thus |\xintbreakloop| may not work as expected, but the situation
+can be resolved via |\xint_firstofone{&}| or use of |\TAB| with |\def\TAB{&}|.
+It is thus simpler for alignments to use rather than \csbxint{loop} either the
+expandable \csbxint{ApplyUnbraced} or the non-expandable but alignment
+compatible \csbxint{ApplyInline}, \csbxint{For} or \csbxint{For*}.
+
+As an example, let us suppose we have two macros |\A|\marg{i}\marg{j} and
+|\B|\marg{i}\marg{j} behaving like (small) integer valued matrix entries, and we
+want to define a macro |\C|\marg{i}\marg{j} giving the matrix product (|i| and
+|j| may be count registers). We will assume that |\A[I]| expands to the number
+of rows, |\A[J]| to the number of columns and want the produced |\C| to act in
+the same manner. The code is very dispendious in use of |\count| registers, not
+optimized in any way, not made very robust (the defined macro can not have the
+same name as the first two matrices for example), we just wanted to quickly
+illustrate use of the nesting capabilities of |\xintloop|.\footnote{for a more sophisticated implementation of matrix multiplication, inclusive of determinants, inverses, and display utilities, with entries big integers or decimal numbers or even fractions see \url{http://tex.stackexchange.com/a/143035/4686} from November 11, 2013.}
+\begingroup
+\makeatother
+\begin{verbatim}
+\newcount\rowmax \newcount\colmax \newcount\summax
+\newcount\rowindex \newcount\colindex \newcount\sumindex
+\newcount\tmpcount
+\makeatletter
+\def\MatrixMultiplication #1#2#3{%
+ \rowmax #1[I]\relax
+ \colmax #2[J]\relax
+ \summax #1[J]\relax
+ \rowindex 1
+ \xintloop % loop over row index i
+ {\colindex 1
+ \xintloop % loop over col index k
+ {\tmpcount 0
+ \sumindex 1
+ \xintloop % loop over intermediate index j
+ \advance\tmpcount \numexpr #1\rowindex\sumindex*#2\sumindex\colindex\relax
+ \ifnum\sumindex<\summax
+ \advance\sumindex 1
+ \repeat }%
+ \expandafter\edef\csname\string#3{\the\rowindex.\the\colindex}\endcsname
+ {\the\tmpcount}%
+ \ifnum\colindex<\colmax
+ \advance\colindex 1
+ \repeat }%
+ \ifnum\rowindex<\rowmax
+ \advance\rowindex 1
+ \repeat
+ \expandafter\edef\csname\string#3{I}\endcsname{\the\rowmax}%
+ \expandafter\edef\csname\string#3{J}\endcsname{\the\colmax}%
+ \def #3##1{\ifx[##1\expandafter\Matrix@helper@size
+ \else\expandafter\Matrix@helper@entry\fi #3{##1}}%
+}%
+\def\Matrix@helper@size #1#2#3]{\csname\string#1{#3}\endcsname }%
+\def\Matrix@helper@entry #1#2#3%
+ {\csname\string#1{\the\numexpr#2.\the\numexpr#3}\endcsname }%
+\def\A #1{\ifx[#1\expandafter\A@size
+ \else\expandafter\A@entry\fi {#1}}%
+\def\A@size #1#2]{\ifx I#23\else4\fi}% 3rows, 4columns
+\def\A@entry #1#2{\the\numexpr #1+#2-1\relax}% not pre-computed...
+\def\B #1{\ifx[#1\expandafter\B@size
+ \else\expandafter\B@entry\fi {#1}}%
+\def\B@size #1#2]{\ifx I#24\else3\fi}% 4rows, 3columns
+\def\B@entry #1#2{\the\numexpr #1-#2\relax}% not pre-computed...
+\makeatother
+\MatrixMultiplication\A\B\C \MatrixMultiplication\C\C\D % etc...
+\[\begin{pmatrix}
+ \A11&\A12&\A13&\A14\\
+ \A21&\A22&\A23&\A24\\
+ \A31&\A32&\A33&\A34
+ \end{pmatrix}
+\times
+ \begin{pmatrix}
+ \B11&\B12&\B13\\
+ \B21&\B22&\B23\\
+ \B31&\B32&\B33\\
+ \B41&\B42&\B43
+ \end{pmatrix}
+=
+\begin{pmatrix}
+ \C11&\C12&\C13\\
+ \C21&\C22&\C23\\
+ \C31&\C32&\C33
+\end{pmatrix}\]
+\[\begin{pmatrix}
+ \C11&\C12&\C13\\
+ \C21&\C22&\C23\\
+ \C31&\C32&\C33
+\end{pmatrix}^2 = \begin{pmatrix}
+ \D11&\D12&\D13\\
+ \D21&\D22&\D23\\
+ \D31&\D32&\D33
+\end{pmatrix}\]
+\end{verbatim}
+\newcount\rowmax \newcount\colmax \newcount\summax
+\newcount\rowindex \newcount\colindex \newcount\sumindex
+\newcount\tmpcount
+\makeatletter
+\def\MatrixMultiplication #1#2#3{%
+ \rowmax #1[I]\relax
+ \colmax #2[J]\relax
+ \summax #1[J]\relax
+ \rowindex 1
+ \xintloop % loop over row index i
+ {\colindex 1
+ \xintloop % loop over col index k
+ {\tmpcount 0
+ \sumindex 1
+ \xintloop % loop over intermediate index j
+ \advance\tmpcount \numexpr #1\rowindex\sumindex*#2\sumindex\colindex\relax
+ \ifnum\sumindex<\summax
+ \advance\sumindex 1
+ \repeat }%
+ \expandafter\edef\csname\string#3{\the\rowindex.\the\colindex}\endcsname
+ {\the\tmpcount}%
+ \ifnum\colindex<\colmax
+ \advance\colindex 1
+ \repeat }%
+ \ifnum\rowindex<\rowmax
+ \advance\rowindex 1
+ \repeat
+ \expandafter\edef\csname\string#3{I}\endcsname{\the\rowmax}%
+ \expandafter\edef\csname\string#3{J}\endcsname{\the\colmax}%
+ \def #3##1{\ifx[##1\expandafter\Matrix@helper@size
+ \else\expandafter\Matrix@helper@entry\fi #3{##1}}%
+}%
+\def\Matrix@helper@size #1#2#3]{\csname\string#1{#3}\endcsname }%
+\def\Matrix@helper@entry #1#2#3%
+ {\csname\string#1{\the\numexpr#2.\the\numexpr#3}\endcsname }%
+\def\A #1{\ifx[#1\expandafter\A@size
+ \else\expandafter\A@entry\fi {#1}}%
+\def\A@size #1#2]{\ifx I#23\else4\fi}% 3rows, 4columns
+\def\A@entry #1#2{\the\numexpr #1+#2-1\relax}% not pre-computed...
+\def\B #1{\ifx[#1\expandafter\B@size
+ \else\expandafter\B@entry\fi {#1}}%
+\def\B@size #1#2]{\ifx I#24\else3\fi}% 4rows, 3columns
+\def\B@entry #1#2{\the\numexpr #1-#2\relax}% not pre-computed...
+\makeatother
+\MatrixMultiplication\A\B\C \MatrixMultiplication\C\C\D
+\setlength{\unitlength}{1cm}
+% le picture de LaTeX est tout de même assez génial!
+\begin{picture}(0,0)
+\put(6,10){\vtop{\hsize8cm
+\[\begin{pmatrix}
+ \A11&\A12&\A13&\A14\\
+ \A21&\A22&\A23&\A24\\
+ \A31&\A32&\A33&\A34
+ \end{pmatrix}
+\times
+ \begin{pmatrix}
+ \B11&\B12&\B13\\
+ \B21&\B22&\B23\\
+ \B31&\B32&\B33\\
+ \B41&\B42&\B43
+ \end{pmatrix}
+=
+\begin{pmatrix}
+ \C11&\C12&\C13\\
+ \C21&\C22&\C23\\
+ \C31&\C32&\C33
+\end{pmatrix}\]
+\[\begin{pmatrix}
+ \C11&\C12&\C13\\
+ \C21&\C22&\C23\\
+ \C31&\C32&\C33
+\end{pmatrix}^2 = \begin{pmatrix}
+ \D11&\D12&\D13\\
+ \D21&\D22&\D23\\
+ \D31&\D32&\D33
+\end{pmatrix}\]\MatrixMultiplication\C\D\E
+\[\begin{pmatrix}
+ \C11&\C12&\C13\\
+ \C21&\C22&\C23\\
+ \C31&\C32&\C33
+\end{pmatrix}^3 = \begin{pmatrix}
+ \E11&\E12&\E13\\
+ \E21&\E22&\E23\\
+ \E31&\E32&\E33
+\end{pmatrix}\]\MatrixMultiplication\C\E\F
+\[\begin{pmatrix}
+ \C11&\C12&\C13\\
+ \C21&\C22&\C23\\
+ \C31&\C32&\C33
+\end{pmatrix}^4 = \begin{pmatrix}
+ \F11&\F12&\F13\\
+ \F21&\F22&\F23\\
+ \F31&\F32&\F33
+\end{pmatrix}\]}}
+\end{picture}
+\endgroup
+
+\vskip-\baselineskip
+
+\subsection{\csbh{xintiloop}, \csbh{xintiloopindex}, \csbh{xintouteriloopindex},
+ \csbh{xintbreakiloop}, \csbh{xintbreakiloopanddo}, \csbh{xintiloopskiptonext},
+\csbh{xintiloopskipandredo}}
+\label{xintiloop}
+\label{xintbreakiloop}
+\label{xintbreakiloopanddo}
+\label{xintiloopskiptonext}
+\label{xintiloopskipandredo}
+\label{xintiloopindex}
+\label{xintouteriloopindex}
+{\small New with release |1.09g|.\par}
+
+\csa{xintiloop}|[start+delta]|\meta{stuff}|\iftest ... \repeat| is a completely
+expandable nestable loop having access via \csbxint{iloopindex} to the integer
+index of the iteration, with starting value |start| (which may be a |\count|)
+and increment |delta| (\emph{id.}). Currently |[start+delta]| is a
+\emph{mandatory argument}, it is an error to omit it; perhaps a future release
+will make it optional with default |1+1|. A space after the closing square
+bracket is not significant, it will be ignored. Spaces inside the square
+brackets will also be ignored as the two arguments are first given to a
+|\numexpr...\relax|.
+
+As with \csbxint{loop}, this tool will mostly be of interest to advanced users.
+As is the case for its variant, it is declared short and can not handle directly
+|\par| tokens or empty lines. For nesting, one puts inside braces all the
+material from the start (immediately after |[start+delta]|) and up to and
+inclusive of the inner loop, these braces will be removed and do not create a
+loop. In case of nesting, \csbxint{outeriloopindex} gives access to the index of
+the outer loop. If needed one could write on its model a macro giving access to
+the index of the outer outer loop (or even to the |nth| outer loop).
+
+
+The \csa{xintiloopindex} and \csa{xintouteriloopindex} can not be used inside
+braces, and generally speaking this means they should be expanded first when
+given as argument to a macro, and that this macro receives them as delimited
+arguments, not braced ones. Or, but naturally this will break expandability, one
+can assign the value of \csa{xintiloopindex} to some |\count|. Both
+\csa{xintiloopindex} and \csa{xintouteriloopindex} extend to the litteral
+representation of the index, thus in |\ifnum| tests, if it comes last one has to
+correctly end the macro with a |\space|, or encapsulate it in a
+|\numexpr..\relax|.
+
+When the repeat-test of the loop is, for example, |\ifnum\xintiloopindex<10
+\repeat|, this means that the last iteration will be with |\xintiloopindex=10|
+(assuming |delta=1|). There is also |\ifnum\xintiloopindex=10 \else\repeat| to
+get the last iteration to be the one with |\xintiloopindex=10|.
+
+One has \csbxint{breakiloop} and \csbxint{breakiloopanddo} to abort the
+loop, \csbxint{iloopskiptonext} to abort the current iteration and skip to the
+next, \hyperref[xintiloopskipandredo]{\ttfamily\hyphenchar\font45 \char92
+ xintiloopskip\-and\-redo} to skip to the end of the current iteration and redo
+it with the same value of the index (something else will have to change for this
+not to become an eternal loop\dots ).
+
+Inside alignments, if the looped-over text contains a |&| or a |\cr|, any
+un-expandable material before a \csbxint{iloopindex} will make it fail because
+of |\endtemplate|; in such cases one can always either replace |&| by a macro
+expanding to it or replace it by a suitable |\firstofone{&}|, and similarly for
+|\cr|.
+
+As an example, let us construct an |\edef\z{...}| which will define |\z| to be a
+list of prime numbers:
+\dverb|@
+\edef\z
+{\xintiloop [10001+2]%
+ {\xintiloop [3+2]%
+ \ifnum\xintouteriloopindex<\numexpr\xintiloopindex*\xintiloopindex\relax
+ \xintouteriloopindex,
+ \expandafter\xintbreakiloop
+ \fi
+ \ifnum\xintouteriloopindex=\numexpr
+ (\xintouteriloopindex/\xintiloopindex)*\xintiloopindex\relax
+ \else
+ \repeat
+ }% no space here
+ \ifnum \xintiloopindex < 10999 \repeat }%
+\meaning\z|
+\begingroup%\ttfamily
+\edef\z
+{\xintiloop [10001+2]%
+ {\xintiloop [3+2]%
+ \ifnum\xintouteriloopindex<\numexpr\xintiloopindex*\xintiloopindex\relax
+ \xintouteriloopindex,
+ \expandafter\xintbreakiloop
+ \fi
+ \ifnum\xintouteriloopindex=\numexpr
+ (\xintouteriloopindex/\xintiloopindex)*\xintiloopindex\relax
+ \else
+ \repeat
+ }% no space here
+ \ifnum \xintiloopindex < 10999 \repeat }%
+\meaning\z and we should have taken some steps to not have a trailing comma, but
+the point was to show that one can do that in an |\edef|\,!
+\endgroup
+
+Let us create an alignment where each row will contain all divisors of its
+first entry.
+\dverb|@
+\tabskip1ex
+\halign{&\hfil#\hfil\cr
+ \xintiloop [1+1]
+ {\expandafter\bfseries\xintiloopindex &
+ \xintiloop [1+1]
+ \ifnum\xintouteriloopindex=\numexpr
+ (\xintouteriloopindex/\xintiloopindex)*\xintiloopindex\relax
+ \xintiloopindex&\fi
+ \ifnum\xintiloopindex<\xintouteriloopindex\space % \space is CRUCIAL
+ \repeat \cr }%
+ \ifnum\xintiloopindex<30
+ \repeat }|
+
+%
+\noindent We wanted this first entry in bold face, but |\bfseries| leads to
+unexpandable tokens, so the |\expandafter| was necessary for |\xintiloopindex|
+and |\xintouteriloopindex| not to be confronted with a hard to digest
+|\endtemplate|. An alternative way of coding is:
+%
+\dverb|@ \tabskip1ex
+\def\firstofone #1{#1}%
+\halign{&\hfil#\hfil\cr
+ \xintiloop [1+1]
+ {\bfseries\xintiloopindex\firstofone{&}%
+ \xintiloop [1+1] \ifnum\xintouteriloopindex=\numexpr
+ (\xintouteriloopindex/\xintiloopindex)*\xintiloopindex\relax
+ \xintiloopindex\firstofone{&}\fi
+ \ifnum\xintiloopindex<\xintouteriloopindex\space % \space is CRUCIAL
+ \repeat \firstofone{\cr}}%
+ \ifnum\xintiloopindex<30 \repeat }|
+
+\noindent
+Here is the output, thus obtained without any count register:
+\begingroup\catcode`_ 11
+\begin{multicols}2
+\tabskip1ex
+\halign{&\hfil#\hfil\cr
+ \xintiloop [1+1]
+ {\expandafter\bfseries\xintiloopindex &
+ \xintiloop [1+1]
+ \ifnum\xintouteriloopindex=\numexpr
+ (\xintouteriloopindex/\xintiloopindex)*\xintiloopindex\relax
+ \xintiloopindex&\fi
+ \ifnum\xintiloopindex<\xintouteriloopindex\space % CRUCIAL \space HERE
+ \repeat \cr }%
+ \ifnum\xintiloopindex<30
+ \repeat
+}
+\end{multicols}
+\endgroup
+
+\subsection{A table of factorizations}
+
+As one more example with \csbxint{iloop} let us use an alignment to display the
+factorization of some numbers. The loop will actually only play a minor r\^ole
+here, just handling the row index, the row contents being almost entirely
+produced via a macro |\factorize|. The factorizing macro does not use
+|\xintiloop| as it didn't appear to be the convenient tool. As |\factorize| will
+have to be used on |\xintiloopindex|, it has been defined as a delimited macro.
+
+To spare some fractions of a second in the compilation time of this document
+(which has many many other things to do), \number"7FFFFFED{} and
+\number"7FFFFFFF, which turn out to be prime numbers, are not given to
+|factorize| but just typeset directly; this illustrates use of
+\csbxint{iloopskiptonext}.
+
+\begingroup
+\def\MacroFont{\ttfamily\baselineskip12pt\relax \catcode`\" 12 }
+\dverb|@
+\tabskip1ex
+\halign {&\hfil\strut#\hfil\cr\noalign{\hrule}
+ \xintiloop ["7FFFFFE0+1]
+ \expandafter\bf\xintiloopindex &
+ \ifnum\xintiloopindex="7FFFFFED
+ \number"7FFFFFED\cr\noalign{\hrule}
+ \expandafter\xintiloopskiptonext
+ \fi
+ \expandafter\factorize\xintiloopindex.\cr\noalign{\hrule}
+ \ifnum\xintiloopindex<"7FFFFFFE
+ \repeat
+ \bf \number"7FFFFFFF&\number "7FFFFFFF\cr\noalign{\hrule}
+}|\par\smallskip
+\endgroup
+
+The \hyperref[floatfactorize]{table} has been made into a float which appears
+\vpageref{floatfactorize}. Here is now the code for factorization; the
+conditionals use
+the package provided |\xint_firstoftwo| and |\xint_secondoftwo|, one could have
+employed rather \LaTeX{}'s own \texttt{\char92\string@firstoftwo} and
+\texttt{\char92\string@secondoftwo}, or, simpler still in \LaTeX{} context, the
+|\ifnumequal|, |\ifnumless| \dots, utilities from the package |etoolbox| which
+do exactly that under the hood. Only \TeX{} acceptable numbers are treated here,
+but it would be easy to make a translation and use the \xintname macros, thus
+extending the scope to big numbers; naturally up to a cost in speed.
+
+The reason for some strange looking expressions is to avoid arithmetic overflow.
+
+\begingroup
+\def\MacroFont{\ttfamily\baselineskip12pt\relax \catcode`\" 12 }
+\dverb|@
+\catcode`_ 11
+\def\abortfactorize #1\xint_secondoftwo\fi #2#3{\fi}
+
+\def\factorize #1.{\ifnum#1=1 \abortfactorize\fi
+ % avoid overflow if #1="7FFFFFFF
+ \ifnum\numexpr #1-2=\numexpr ((#1/2)-1)*2\relax
+ \expandafter\xint_firstoftwo
+ \else\expandafter\xint_secondoftwo
+ \fi
+ {2&\expandafter\factorize\the\numexpr#1/2.}%
+ {\factorize_b #1.3.}}%
+
+\def\factorize_b #1.#2.{\ifnum#1=1 \abortfactorize\fi
+ % this will avoid overflow which could result from #2*#2
+ \ifnum\numexpr #1-(#2-1)*#2<#2
+ #1\abortfactorize % this #1 is prime
+ \fi
+ % again, avoiding overflow as \numexpr integer division
+ % rounds rather than truncates.
+ \ifnum \numexpr #1-#2=\numexpr ((#1/#2)-1)*#2\relax
+ \expandafter\xint_firstoftwo
+ \else\expandafter\xint_secondoftwo
+ \fi
+ {#2&\expandafter\factorize_b\the\numexpr#1/#2.#2.}%
+ {\expandafter\factorize_b\the\numexpr #1\expandafter.%
+ \the\numexpr #2+2.}}%
+\catcode`_ 8|
+\endgroup
+
+\catcode`_ 11
+\def\abortfactorize #1\xint_secondoftwo\fi #2#3{\fi}
+
+\def\factorize #1.{\ifnum#1=1 \abortfactorize\fi
+ \ifnum\numexpr #1-2=\numexpr ((#1/2)-1)*2\relax
+ \expandafter\xint_firstoftwo
+ \else\expandafter\xint_secondoftwo
+ \fi
+ {2&\expandafter\factorize\the\numexpr#1/2.}%
+ {\factorize_b #1.3.}}%
+
+\def\factorize_b #1.#2.{\ifnum#1=1 \abortfactorize\fi
+ \ifnum\numexpr #1-(#2-1)*#2<#2
+ #1\abortfactorize
+ \fi
+ \ifnum \numexpr #1-#2=\numexpr ((#1/#2)-1)*#2\relax
+ \expandafter\xint_firstoftwo
+ \else\expandafter\xint_secondoftwo
+ \fi
+ {#2&\expandafter\factorize_b\the\numexpr#1/#2.#2.}%
+ {\expandafter\factorize_b\the\numexpr #1\expandafter.%
+ \the\numexpr #2+2.}}%
+\catcode`_ 8
+\begin{figure*}[ht!]
+\centering\phantomsection\label{floatfactorize}
+\tabskip1ex
+\centeredline{\vbox{\halign {&\hfil\strut#\hfil\cr\noalign{\hrule}
+ \xintiloop ["7FFFFFE0+1]
+ \expandafter\bf\xintiloopindex &
+ \ifnum\xintiloopindex="7FFFFFED
+ \number"7FFFFFED\cr\noalign{\hrule}
+ \expandafter\xintiloopskiptonext
+ \fi
+ \expandafter\factorize\xintiloopindex.\cr\noalign{\hrule}
+ \ifnum\xintiloopindex<"7FFFFFFE
+ \repeat
+ \bf \number"7FFFFFFF&\number "7FFFFFFF\cr\noalign{\hrule}
+}}}
+\centeredline{A table of factorizations}
+\end{figure*}
+
\begin{framed}
The next utilities are not compatible with expansion-only context.
@@ -4056,9 +3875,13 @@ where it was reasonable to stop.
\begin{framed}
A macro |\macro| whose definition uses internally an \csbxint{For} loop may be
used inside another \csbxint{For} loop even if the two loops both use the same
- macro parameter. By the way the loop definition inside |\macro| must double
+ macro parameter. Note: the loop definition inside |\macro| must double
the character |#| as is the general rule in \TeX{} with definitions done
inside macros.
+
+ The macros \csa{xintFor} and \csa{xintFor*} are not expandable, one can not
+ use them inside an |\edef|. But they may be used inside alignments (such as a
+ \LaTeX{} |tabular|), as will be shown in examples.
\end{framed}
The spaces between the various declarative elements are all optional;
@@ -4093,7 +3916,7 @@ which encapsulate the item in a macro expanding to that item.
replacement text, just the token |\x|). Input such as |<stuff>,,<stuff>|
creates an empty |#1|, the iteration is not skipped. An empty list does lead
to the use of the replacement text, once, with an empty |#1| (or |#n|). Except
- if the entire list is represented as a single macro (with no parameters),
+ if the entire list is represented as a single macro with no parameters,
\fbox{it must be braced.}
\end{framed}
@@ -4108,24 +3931,9 @@ which encapsulate the item in a macro expanding to that item.
\makeatletter\hbox {\@textsuperscript {\normalfont \thefootnote
}}\makeatother. Spaces at the start, end, or in-between items are gobbled
(but naturally not the spaces which may be inside \emph{braced} items). Except
- if the list argument is a single macro (with no parameters), \fbox{it must be
+ if the list argument is a single macro with no parameters, \fbox{it must be
braced.} Each item which is not braced will be fully expanded (as the |\x|
and |\y| in the example above). An empty list leads to an empty result.
-
- The macro \csbxint{Seq} which generates arithmetic sequences may only be used
- with \csbxint{For*} (numbers from output of |\xintSeq| are braced, not
- separated by commas). \centeredline{|\xintFor* #1 in {\xintSeq
- [+2]{-7}{+2}}\do {stuff with #1}|} will have |#1=-7,-5,-3,-1, and 1|. The
- |#1| as issued from the list produced by \csbxint{Seq} is the litteral
- representation as would be produced by |\arabic| on a \LaTeX{} counter, it is
- not a count register. When used in |\ifnum| tests or other contexts where
- \TeX{} looks for a number it is recommended to use
- |#1\space|\stepcounter{footnote}%
- \makeatletter\hbox {\@textsuperscript {\normalfont \thefootnote
- }}\makeatother, or |#1\relax| if expandability of the process is not an
- issue (for example if the iterated commands do an |\edef| using such a test,
- |\relax| is not a good choice as it will be kept in the complete expansion if
- it is in the true branch of the conditional, whereas |\space| will disappear).
\end{framed}
\begingroup\makeatletter
\def\@footnotetext #1{\insert\footins {\reset@font \footnotesize \interlinepenalty \interfootnotelinepenalty \splittopskip \footnotesep \splitmaxdepth \dp \strutbox \floatingpenalty \@MM \hsize \columnwidth \@parboxrestore \color@begingroup \@makefntext {\rule \z@ \footnotesep \ignorespaces #1\@finalstrut \strutbox }\color@endgroup }}
@@ -4133,14 +3941,53 @@ which encapsulate the item in a macro expanding to that item.
\edef\@thefnmark {\thefootnote}
\@footnotetext{braces around single token items
are optional so this is the same as \texttt{\{123456\}}.}
-\stepcounter{footnote}
-\edef\@thefnmark {\thefootnote}
-\@footnotetext{the \csa{space} will stop the \TeX{} scanning of a number and be
- gobbled in the process; the \csa{relax} stops the scanning but is not
- gobbled. Or one may do \csa{numexpr}\texttt{\#1}\csa{relax}, and then the
- \csa{relax} is gobbled.}
+% \stepcounter{footnote}
+% \edef\@thefnmark {\thefootnote}
+% \@footnotetext{the \csa{space} will stop the \TeX{} scanning of a number and be
+% gobbled in the process; the \csa{relax} stops the scanning but is not
+% gobbled. Or one may do \csa{numexpr}\texttt{\#1}\csa{relax}, and then the
+% \csa{relax} is gobbled.}
\endgroup
-\addtocounter{Hfootnote}{2}
+%\addtocounter{Hfootnote}{2}
+\addtocounter{Hfootnote}{1}
+
+The macro \csbxint{Seq} which generates arithmetic sequences may only be used
+with \csbxint{For*} (numbers from output of |\xintSeq| are braced, not separated
+by commas). \centeredline{|\xintFor* #1 in {\xintSeq [+2]{-7}{+2}}\do {stuff
+ with #1}|} will have |#1=-7,-5,-3,-1, and 1|. The |#1| as issued from the
+list produced by \csbxint{Seq} is the litteral representation as would be
+produced by |\arabic| on a \LaTeX{} counter, it is not a count register. When
+used in |\ifnum| tests or other contexts where \TeX{} looks for a number it is
+recommended to use |#1\space|\footnote{the \csa{space} will stop the \TeX{}
+ scanning of a number and be gobbled in the process; the \csa{relax} stops the
+ scanning but is not gobbled. Or one may do
+ \csa{numexpr}\texttt{\#1}\csa{relax}, and then the \csa{relax} is gobbled.},
+or |#1\relax| if expandability of the process is not an issue (for example if
+the iterated commands do an |\edef| using such a test, |\relax| is not a good
+choice as it will be kept in the complete expansion if it is in the true branch
+of the conditional, whereas |\space| will disappear).
+
+When nesting \csa{xintFor*} loops, using \csa{xintSeq} in the inner loops is
+inefficient, as the arithmetic sequence will be re-created each time. A more
+efficient style is:
+%
+\dverb|@
+ \edef\innersequence {\xintSeq[+2]{-50}{50}}%
+ \xintFor* #1 in {\xintSeq {13}{27}} \do
+ {\xintFor* #2 in \innersequence \do {stuff with #1 and #2}%
+ .. some other macros .. }|
+
+This is a general remark applying for any nesting of loops, one should avoid
+recreating the inner lists of arguments at each iteration of the outer loop.
+However, in the example above, if the |.. some other macros ..| part
+closes a group which was opened before the |\edef\innersequence|, then
+this definition will be lost. An alternative to |\edef|, also efficient,
+exists when dealing with arithmetic sequences: it is to use the
+\csbxint{integers} keyword (described later) which simulates infinite
+arithmetic sequences; the loops will then be terminated via a test |#1|
+(or |#2| etc\dots) and subsequent use of \csbxint{BreakFor}.
+
+
The \csbxint{For} loops are not completely expandable; but they may be nested
and used inside alignments or other contexts where the replacement text closes
@@ -4219,6 +4066,11 @@ Designed to work as expected under nesting. Don't forget an empty brace pair
|{}| if a branch is to do nothing. May be used multiple times in the replacement
text of the loop.
+There is no such thing as an iteration counter provided by the \csa{xintFor}
+loops; the user is invited to define if needed his own count register or
+\LaTeX{} counter, for example with a suitable |\stepcounter| inside the
+replacement text of the loop to update it.
+
\subsection{ \csbh{xintBreakFor}, \csbh{xintBreakForAndDo}}
\label{xintBreakFor}\label{xintBreakForAndDo}
{\small New in |1.09e|.\par}
@@ -4248,22 +4100,22 @@ in the next section which is devoted to ``forever'' loops.
\label{xintdimensions}\label{xintrationals}
{\small New in |1.09e|.\par}
-If the list argument to \csbxint{For} (or \csbxint{For*}, the two are here
-completely equivalent) is \csbxint{integers} (equivalently \csbxint{egers}) or
-more generally \csbxint{integers}|[||start|\allowbreak|+|\allowbreak|delta||]|
+If the list argument to \csbxint{For} (or \csbxint{For*}, both are equivalent in
+this context) is \csbxint{integers} (equivalently \csbxint{egers}) or more
+generally \csbxint{integers}|[||start|\allowbreak|+|\allowbreak|delta||]|
(\emph{the whole within braces}!)\footnote{the |start+delta| optional
specification may have extra spaces around the plus sign of near the square
brackets, such spaces are removed. The same applies with \csa{xintdimensions}
- and \csa{xintrationals}.}, then \csbxint{For} does an infinite
-iteration where |#1| (or |#2|, \dots, |#9|) will run through the arithmetic
-sequence of (short) integers with initial value |start| and increment |delta|
-(default values: |start=1|, |delta=1|; if the optional argument is present it
-must contains both of them, and they may be explicit integers, or macros or
-count registers. The |#1| (or |#2|, \dots, |#9|) will stand for |\numexpr <opt
-sign><digits>\relax|, and the litteral representation as a string of digits can
-thus be obtained as \fbox{\csa{the\#1}} or |\number#1|. Such a |#1| can be used
-in an |\ifnum| test with no need to be postfixed with a space or a |\relax| and
-one should \emph{not} add them.
+ and \csa{xintrationals}.}, then \csbxint{For} does an infinite iteration where
+|#1| (or |#2|, \dots, |#9|) will run through the arithmetic sequence of (short)
+integers with initial value |start| and increment |delta| (default values:
+|start=1|, |delta=1|; if the optional argument is present it must contains both
+of them, and they may be explicit integers, or macros or count registers. The
+|#1| (or |#2|, \dots, |#9|) will stand for |\numexpr <opt sign><digits>\relax|,
+and the litteral representation as a string of digits can thus be obtained as
+\fbox{\csa{the\#1}} or |\number#1|. Such a |#1| can be used in an |\ifnum| test
+with no need to be postfixed with a space or a |\relax| and one should
+\emph{not} add them.
If the list argument is \csbxint{dimensions} or more generally
\csbxint{dimensions}|[||start|\allowbreak|+|\allowbreak|delta||]| (\emph{within
@@ -4591,11 +4443,11 @@ commas. Spaces around commas and parentheses are ignored.
\end{tabular}$\Biggr)$&}\\\noalign{\vskip1\jot}}%
\end{tabular}}
-\smallskip Only |#1#2|, |#2#3|, \dots, |#8#9| are valid (no error check is
-done on the input syntax\dots). One can nest with
-\csbxint{For}, for disjoint sets of macro parameters. There is also
-\csa{xintForthree} (from |#1#2#3| to |#7#8#9|) and \csa{xintForfour}
-(from |#1#2#3#4| to |#6#7#8#9|).
+\smallskip Only |#1#2|, |#2#3|, |#3#4|, \dots, |#8#9| are valid (no error check
+is done on the input syntax, |#1#3| or similar all end up in errors).
+One can nest with \csbxint{For}, for disjoint sets of macro parameters. There is
+also \csa{xintForthree} (from |#1#2#3| to |#7#8#9|) and \csa{xintForfour} (from
+|#1#2#3#4| to |#6#7#8#9|).
% These three macros |\xintForpair|, |\xintForthree| and |\xintForfour| are to
% be considered in experimental status, and may be removed, replaced or
@@ -4998,7 +4850,745 @@ then one should use the following variants:
It is possible to modify this code to let it do \csa{QSonestep} repeatedly and
stop automatically when the sort is finished.
-\section{Commands of the \xintfracname package}\label{sec:comfrac}
+\section{Commands of the \xintname package}
+\label{sec:xint}
+
+\def\n{\string{N\string}}
+\def\m{\string{M\string}}
+\def\x{\string{x\string}}
+
+In the description of the macros \texttt{\n} (or also \texttt{\m}) stands
+(except if mentioned otherwise) for a (long) number within braces or for a
+control sequence possibly within braces and \hyperref[sec:expansions]{\fexpan
+ ding} to such a number
+(without the braces!), or for material within braces which \fexpan ds to such
+a number, as is acceptable on input by the \csbxint{Num} macro: a sequence of
+plus and minus signs, followed by some string of zeros, followed by digits.
+
+The letter \texttt{x} stands for something which will be inserted in-between a
+|\numexpr| and a |\relax|. It will thus be completely expanded and must give an
+integer obeying the \TeX{} bounds. Thus, it may be for example a count register,
+or itself a \csa{numexpr} expression, or just a number written explicitely with
+digits or something like |4*\count 255 + 17|, etc...
+
+For the rules regarding direct use of count registers or \csa{numexpr}
+expression, in the argument to the package macros, see the
+\hyperlink{useofcount}{use of count section} in \autoref{sec:inputs}.
+
+Some of these macros are extended by \xintfracname to accept fractions on input,
+and, generally, to output a fraction. But this means that additions,
+subtractions, multiplications output fractions and not integers; to guarantee
+the integer format on output when the inputs are integers, the original
+integer-only macros \csa{xintAdd}, \csa{xintSub}, \csa{xintMul} remain available
+under the names \csa{xintiAdd}, \csa{xintiSub}, \csa{xintiMul}. Even the
+original integer-only macros may now accept fractions on input as long as they
+are integers in disguise; they still produce on output integers without any
+forward slash mark nor trailing |[n]|. On the other hand macros such as
+|\xintAdd| will output fractions |A/B[n]|, with |B| present even if its value is
+one. To remove this unit denominator and convert the |[n]| part into explicit
+zeros, one has \csbxint{Num} (if one is certain to deal with an integer; see
+also \csbxint{PRaw}). This is mandatory when the computation result is fetched
+into a context where \TeX{} expects a number (assuming it does not exceed
+@2^31@). See the also the \xintfracname \hyperref[sec:frac]{documentation}
+for more information on how macros of \xintname are modified after loading
+\xintfracname (or \xintexprname).
+
+
+% Package \xintname also provides some general macro programming or token
+% manipulation utilities (expandable as well as non-expandable), which are
+% described in the next section (\autoref{sec:tools}).
+
+\localtableofcontents
+
+\subsection{\csbh{xintRev}} \label{xintRev}
+
+\csa{xintRev\n} will revert the order of the digits of the number,
+keeping the optional sign. Leading zeros
+resulting from the operation are not removed (see the
+\csa{xintNum} macro for this). This macro and all other
+macros dealing with numbers first expand `fully' their arguments.
+\centeredline{|\xintRev{-123000}|\digitstt{=\xintRev{-123000}}}
+\centeredline{|\xintNum{\xintRev{-123000}}|%
+ \digitstt{=\xintNum{\xintRev{-123000}}}}
+
+
+\subsection{\csbh{xintLen}}\label{xintiLen}
+
+\csa{xintLen\n} returns the length of the number, not counting the sign.
+\centeredline{|\xintLen{-12345678901234567890123456789}|\digitstt
+ {=\xintLen{-12345678901234567890123456789}}} Extended by \xintfracname to
+fractions: the length of |A/B[n]| is the length of |A| plus the length of |B|
+plus the absolute value of |n| and minus one (an integer input as |N| is
+internally represented in a form equivalent to |N/1[0]| so the minus one means
+that the extended \csa{xintLen}
+behaves the same as the original for integers).
+\centeredline{|\xintLen{-1e3/5.425}|\digitstt
+ {=\xintLen{-1e3/5.425}}}
+The length is computed on the |A/B[n]| which would have been returned by
+\csbxint{Raw}: |\xintRaw {-1e3/5.425}|\digitstt{=\xintRaw {-1e3/5.425}}.
+
+Let's point out that the whole thing should sum up to
+less than circa @2^{31}@, but this is a bit theoretical.
+
+|\xintLen| is only for numbers or fractions. See \csbxint{Length} for counting
+tokens (or rather braced groups), more generally.
+
+\subsection{\csbh{xintDigitsOf}}\label{xintDigitsOf}
+
+This is a synonym for \csbxint{AssignArray}, to be used to define
+an array giving all the digits of a given (positive, else the minus sign will
+be treated as first item) number.
+\begingroup\xintDigitsOf\xintiPow {7}{500}\to\digits
+\centeredline{|\xintDigitsOf\xintiPow {7}{500}\to\digits|}
+\noindent @7^500@ has |\digits{0}=|\digits{0} digits, and the 123rd among them
+(starting from the most significant) is
+|\digits{123}=|\digits{123}.
+\endgroup
+
+\subsection{\csbh{xintNum}}\label{xintiNum}
+
+\csa{xintNum\n} removes chains of plus or minus signs, followed by zeros.
+\centeredline{|\xintNum{+---++----+--000000000367941789479}|\digitstt
+ {=\xintNum{+---++----+--000000000367941789479}}} Extended by \xintfracname to
+accept also a fraction on input, as long as it reduces to an integer after
+division of the numerator by the denominator.
+\centeredline{|\xintNum{123.48/-0.03}|\digitstt{=\xintNum{123.48/-0.03}}}
+
+
+\subsection{\csbh{xintSgn}}\label{xintiSgn}
+
+\csa{xintSgn\n} returns 1 if the number is positive, 0 if it is
+zero and -1 if it is negative. Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintOpp}}\label{xintiOpp}
+
+\csa{xintOpp\n} returns the opposite |-N| of the number |N|.
+Extended by \xintfracname to fractions.
+
+
+\subsection{\csbh{xintAbs}}\label{xintiAbs}
+
+\csa{xintAbs\n} returns the absolute value of the number. Extended
+by \xintfracname to fractions.
+
+\subsection{\csbh{xintAdd}}\label{xintiAdd}
+
+\csa{xintAdd\n\m} returns the sum of the two numbers. Extended by
+\xintfracname to fractions.
+
+\subsection{\csbh{xintSub}}\label{xintiSub}
+
+\csa{xintSub\n\m} returns the difference |N-M|. Extended by
+\xintfracname to fractions.
+
+\subsection{\csbh{xintCmp}}\label{xintiCmp}
+
+\csa{xintCmp\n\m} returns 1 if |N>M|, 0 if |N=M|, and -1 if |N<M|.
+Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintEq}}\label{xintEq}
+{\small New with release |1.09a|.\par}
+
+\csa{xintEq\n\m} returns 1 if |N=M|, 0 otherwise.
+Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintGt}}\label{xintGt}
+{\small New with release |1.09a|.\par}
+
+% attention dans la doc du 9 octobre j'avais écrit \geq au lieu de >
+
+\csa{xintGt\n\m} returns 1 if |N|$>$|M|, 0 otherwise.
+Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintLt}}\label{xintLt}
+{\small New with release |1.09a|.\par}
+
+% attention dans la doc du 9 octobre j'avais écrit \leq au lieu de <
+
+\csa{xintLt\n\m} returns 1 if |N|$<$|M|, 0 otherwise.
+Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintIsZero}}\label{xintIsZero}
+{\small New with release |1.09a|.\par}
+
+\csa{xintIsZero\n} returns 1 if |N=0|, 0 otherwise.
+Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintNot}}\label{xintNot}
+{\small New with release |1.09c|.\par}
+
+\csa{xintNot} is a synonym for \csa{xintIsZero}.
+
+\subsection{\csbh{xintIsNotZero}}\label{xintIsNotZero}
+{\small New with release |1.09a|.\par}
+
+\csa{xintIsNotZero\n} returns 1 if |N<>0|, 0 otherwise.
+Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintIsOne}}\label{xintIsOne}
+{\small New with release |1.09a|.\par}
+
+\csa{xintIsOne\n} returns 1 if |N=1|, 0 otherwise.
+Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintAND}}\label{xintAND}
+{\small New with release |1.09a|.\par}
+
+\csa{xintAND\n\m} returns 1 if |N<>0| and |M<>0| and zero otherwise.
+ Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintOR}}\label{xintOR}
+{\small New with release |1.09a|.\par}
+
+\csa{xintOR\n\m} returns 1 if |N<>0| or |M<>0| and zero otherwise.
+ Extended by \xintfracname to fractions.
+
+
+\subsection{\csbh{xintXOR}}\label{xintXOR}
+{\small New with release |1.09a|.\par}
+
+\csa{xintXOR\n\m} returns 1 if exactly one of |N| or |M| is true (i.e.
+non-zero).
+ Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintANDof}}\label{xintANDof}
+{\small New with release |1.09a|.\par}
+
+\csa{xintANDof}|{{a}{b}{c}...}| returns 1 if all are true (i.e. non
+zero) and zero otherwise. The list argument
+may be a macro, it (or rather its first token) is \fexpan ded first (each
+item also is \fexpan ded). Extended by \xintfracname to fractions.
+
+
+\subsection{\csbh{xintORof}}\label{xintORof}
+{\small New with release |1.09a|.\par}
+
+\csa{xintORof}|{{a}{b}{c}...}| returns 1 if at least one is true
+(i.e. does not vanish). The list argument
+may be a macro, it is \fexpan ded first. Extended by \xintfracname to fractions.
+
+
+\subsection{\csbh{xintXORof}}\label{xintXORof}
+{\small New with release |1.09a|.\par}
+
+\csa{xintXORof}|{{a}{b}{c}...}| returns 1 if an odd number of them are
+true (i.e. does not vanish). The list argument may be a macro, it is
+\fexpan ded first. Extended by \xintfracname to fractions.
+
+
+\subsection{\csbh{xintGeq}}\label{xintiGeq}
+
+\csa{xintGeq\n\m} returns 1 if the \emph{absolute value} of the first number is
+at least equal to the absolute value of the second number. If \verb+|N|<|M|+ it
+returns 0. Extended by \xintfracname to fractions (starting with release
+|1.07|). Please note that the macro compares \emph{absolute values}.
+
+\subsection{\csbh{xintMax}}\label{xintiMax}
+
+\csa{xintMax\n\m} returns the largest of the two in the sense of the order
+structure on the relative integers (\emph{i.e.} the right-most number if they
+are put on a line with positive numbers on the right): |\xintiMax
+{-5}{-6}|\digitstt{=\xintiMax{-5}{-6}}. Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintMaxof}}\label{xintMaxof}
+{\small New with release |1.09a|.\par}
+
+\csa{xintMaxof}|{{a}{b}{c}...}| returns the maximum. The list argument
+may be a macro, it is \fexpan ded first. Extended by \xintfracname to
+fractions.
+
+
+\subsection{\csbh{xintMin}}\label{xintiMin}
+
+\csa{xintMin\n\m} returns the smallest of the two in the sense of the order
+structure on the relative integers (\emph{i.e.} the left-most number if they are
+put on a line with positive numbers on the right): |\xintiMin
+{-5}{-6}|\digitstt{=\xintiMin{-5}{-6}}. Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintMinof}}\label{xintMinof}
+{\small New with release |1.09a|.\par}
+
+\csa{xintMinof}|{{a}{b}{c}...}| returns the minimum. The list argument
+may be a macro, it is \fexpan ded first. Extended by \xintfracname to
+fractions.
+
+\subsection{\csbh{xintSum}}\label{xintiSum}
+
+\csa{xintSum}\marg{braced things} after expanding its argument
+expects to find a sequence of tokens (or braced material).
+Each is expanded (with the usual meaning), and the sum of all these numbers is
+returned.
+\centeredline{%
+ \csa{xintiSum}|{{123}{-98763450}{\xintFac{7}}{\xintiMul{3347}{591}}}|%
+ \digitstt{=\xintiSum{{123}{-98763450}{\xintFac{7}}{\xintiMul{3347}{591}}}}}
+\centeredline{\csa{xintiSum}|{1234567890}|\digitstt{=\xintiSum{1234567890}}}
+An empty sum is no error and returns zero: |\xintiSum
+{}|\digitstt{=\xintiSum {}}. A sum with only one
+term returns that number: |\xintiSum {{-1234}}|\digitstt{=\xintiSum
+ {{-1234}}}. Attention that |\xintiSum {-1234}| is not legal input
+and will make the \TeX{} run fail. On the other hand |\xintiSum
+{1234}|\digitstt{=\xintiSum{1234}}. Extended by \xintfracname
+to fractions.
+
+% retiré de la doc le 22 octobre 2013
+
+% \subsection{\csbh{xintSumExpr}}\label{xintiSumExpr}
+
+% \csa{xintSumExpr}\meta{braced things}\csa{relax} is to what \csa{xintSum}
+% expands. The argument is then expanded (with the usual meaning) and should give
+% a list of braced quantities or macros, each one will be expanded in turn.
+% \centeredline{%
+% \csa{xintiSumExpr}| {123}{-98763450}|%
+% |{\xintFac{7}}{\xintiMul{3347}{591}}\relax|\digitstt{=%
+% \xintiSumExpr {123}{-98763450}{\xintFac{7}}{\xintiMul{3347}{591}}\relax}}
+
+% Note: I am not so happy with the name which seems to suggest that the
+% |+| sign should be used instead of braces. Perhaps this will change
+% in the future.
+
+% Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintMul}}\label{xintiMul}
+{\small Modified in release |1.03|.\par}
+
+\csa{xintMul\n\m} returns the product of the two numbers. Starting
+with release |1.03| of \xintname, the macro checks the lengths of
+the two numbers and then activates its algorithm with the best (or
+at least, hoped-so) choice of which one to put first. This makes
+the macro a bit slower for numbers up to 50 digits, but may give
+substantial speed gain when one of the number has 100 digits or more.
+Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintSqr}}\label{xintiSqr}
+
+\csa{xintSqr\n} returns the square. Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintPrd}}\label{xintiPrd}
+
+\csa{xintPrd}\marg{braced things} after expanding its argument expects to find a
+sequence of tokens (or braced material). Each is expanded (with the usual
+meaning), and the product of all these numbers is returned.
+\centeredline{%
+ \csa{xintiPrd}|{{-9876}{\xintFac{7}}{\xintiMul{3347}{591}}}|%
+ \digitstt{=%
+ \xintiPrd{{-9876}{\xintFac{7}}{\xintiMul{3347}{591}}}}}
+\centeredline{\csa{xintiPrd}|{123456789123456789}|\digitstt{=%
+ \xintiPrd{123456789123456789}}} An empty product is no error and returns 1:
+|\xintiPrd {}|\digitstt{=\xintiPrd {}}. A product reduced to a single term returns
+this number: |\xintiPrd {{-1234}}|\digitstt{=\xintiPrd {{-1234}}}. Attention that
+|\xintiPrd {-1234}| is not legal input and will make the \TeX{} compilation
+fail. On the other hand |\xintiPrd {1234}|\digitstt{=\xintiPrd {1234}}.
+\centeredline{$\displaystyle 2^{200}3^{100}7^{100}$} \centeredline{|=\xintiPrd
+ {{\xintiPow {2}{200}}{\xintiPow {3}{100}}{\xintiPow {7}{100}}}|}
+\digitstt{=\printnumber{\xintNum {\xinttheexpr 2^200*3^100*7^100\relax }}}
+
+Extended by \xintfracname to fractions.
+
+With \xintexprname, the above would be coded simply as \centeredline
+{|\xintthenumexpr 2^200*3^100*7^100\relax |}
+
+% I temporarily remove mention of \xintPrdExpr from the documentation; I
+% really dislike the name now.
+
+% \subsection{\csbh{xintPrdExpr}}\label{xintiPrdExpr}
+
+% {\small Name change in |1.06a|! I apologize, but I suddenly decided that
+% \csa{xintProductExpr} was a bad choice; so I just replaced it by the current
+% name. \par}
+
+% \csa{xintPrdExpr}\marg{argument}\csa{relax} is to what \csa{xintPrd} expands
+% ; its argument is expanded (with the usual meaning) and should give a list of
+% braced numbers or macros. Each will be expanded when it is its turn.
+% \centeredline{\csa{xintiPrdExpr}| 123456789123456789\relax|\digitstt{=%
+% \xintiPrdExpr 123456789123456789\relax}}
+
+% Note: I am not so happy with the name which seems to suggest that the
+% |*| sign should be used instead of braces. Perhaps this will change
+% in the future.
+
+% Extended by \xintfracname to fractions.
+
+\subsection{\csbh{xintPow}}\label{xintiPow}
+
+\csa{xintPow\n\x} returns |N^x|. When |x| is zero, this is 1. If |N| is zero and
+|x<0|, if \verb+|N|>1+ and |x<0| negative, or if \verb+|N|>1+ and |x>999999999|,
+then an error is raised. |2^999999999| has \np{301029996} digits; each exact
+multiplication of two one thousand digits numbers already takes a few seconds,
+so needless to say this bound is completely irrealistic. Already |2^9999| has
+\np{3010} digits,\footnote{on my laptop |\string\xintiPow \{2\}\{9999\}|
+ obtains all |3010| digits in about ten or eleven seconds. In contrast, the
+ float versions for
+ |8|, |16|, |24|, or even more significant figures, do their jobs in circa one
+ hundredth of a second (|1.08b|). This is done without |log|/|exp| which are
+ not (yet?) implemented in \xintfracname. The \LaTeX3
+ \href{http://www.ctan.org/tex-archive/macros/latex/contrib/l3kernel}{l3fp}
+ does this with |log|/|exp| and is ten times faster (|16| figures only).} so I
+should perhaps lower the bound to |99999|.
+
+Extended by \xintfracname to fractions (\csbxint{Pow}) and also to floats
+(\csbxint{FloatPow}). Negative
+exponents do not then cause errors anymore. The float version is able to deal
+with things such as
+|2^999999999| without any problem. For example
+|\xintFloatPow[4]{2}{9999}|\digitstt{=\xintFloatPow[4]{2}{9999}} and
+|\xintFloatPow[4]{2}{999999999}|
+\digitstt{=\xintFloatPow[4]{2}{999999999}}.
+
+\subsection{\csbh{xintSgnFork}}\label{xintSgnFork}
+{\small New with release |1.07|. See also \csbxint{ifSgn}.\par}
+
+\csa{xintSgnFork}\verb+{-1|0|1}+\marg{A}\marg{B}\marg{C} expandably
+chooses to execute either the \meta{A}, \meta{B} or \meta{C} code,
+depending on its first argument. This first argument should be anything
+expanding to either |-1|, |0| or |1| (a count register should be
+prefixed by |\the| and a |\numexpr...\relax| also should be prefixed by
+|\the|). This utility is provided to help construct expandable macros
+choosing depending on a condition which one of the package macros to
+use, or which values to confer to their arguments.
+
+\subsection{\csbh{xintifSgn}}\label{xintifSgn}
+{\small New with release |1.09a|.\par}
+
+Similar to \csa{xintSgnFork} except that the first argument may expand to a
+(big) integer (or a fraction if \xintfracname is loaded), and it is its sign
+which decides which of the three branches is taken. Furthermore this first
+argument may be a count register, with no |\the| or |\number| prefix.
+
+\subsection{\csbh{xintifZero}}\label{xintifZero}
+{\small New with release |1.09a|.\par}
+
+\csa{xintifZero}\marg{N}\marg{IsZero}\marg{IsNotZero} expandably checks
+if the first mandatory argument |N| (a number, possibly a fraction if
+\xintfracname is loaded, or a macro expanding to one such) is zero or
+not. It then either executes the first or the second branch.
+
+\subsection{\csbh{xintifNotZero}}\label{xintifNotZero}
+{\small New with release |1.09a|.\par}
+
+\csa{xintifNotZero}\marg{N}\marg{IsNotZero}\marg{IsZero} expandably checks
+if the first mandatory argument |N| (a number, possibly a fraction if
+\xintfracname is loaded, or a macro expanding to one such) is not zero or
+is zero. It then either executes the first or the second branch.
+
+\subsection{\csbh{xintifTrueFalse}}\label{xintifTrueFalse}
+{\small New with release |1.09c|, renamed in |1.09e|.\par}
+
+\csa{xintifTrueFalse}\marg{N}\marg{true branch}\marg{false branch} is a synonym
+for \csbxint{ifNotZero}. It is also available as \csa{xintifTrue} but this later
+name is a bit misleading as the macro must always have a |false| branch,
+possibly an empty brace pair |{}|.
+
+\subsection{\csbh{xintifCmp}}\label{xintifCmp}
+{\small New with release |1.09e|.\par}
+
+\csa{xintifCmp}\marg{A}\marg{B}\marg{if A<B}\marg{if A=B}\marg{if A>B} compares
+its arguments and chooses accordingly the correct branch.
+
+\subsection{\csbh{xintifEq}}\label{xintifEq}
+{\small New with release |1.09a|.\par}
+
+\csa{xintifEq}\marg{A}\marg{B}\marg{YES}\marg{NO} checks equality of its
+two first arguments (numbers, or fractions if \xintfracname is loaded) and does the |YES| or the |NO| branch.
+
+\subsection{\csbh{xintifGt}}\label{xintifGt}
+{\small New with release |1.09a|.\par}
+
+% attention dans la doc du 9 octobre j'avais écrit \geq au lieu de <
+\csa{xintifGt}\marg{A}\marg{B}\marg{YES}\marg{NO} checks if $A>B$ and in that
+case executes the |YES| branch. Extended to fractions (in particular decimal
+numbers) by \xintfracname.
+
+\subsection{\csbh{xintifLt}}\label{xintifLt}
+{\small New with release |1.09a|.\par}
+
+% attention dans la doc du 9 octobre j'avais écrit \leq au lieu de <
+\csa{xintifLt}\marg{A}\marg{B}\marg{YES}\marg{NO} checks if $A<B$ and in that
+case executes the |YES| branch. Extended to fractions (in particular decimal
+numbers) by \xintfracname.
+
+\begin{framed}
+ The macros described next are all integer-only on input. With \xintfracname
+ loaded their argument is first given to \csbxint{Num} and may thus be
+ a fraction, as long as it is in fact an integer in disguise.
+\end{framed}
+
+\subsection{\csbh{xintifOdd}}\label{xintifOdd}
+{\small New with release |1.09e|.\par}
+
+\csa{xintifOdd}\marg{A}\marg{YES}\marg{NO} checks if $A$ is and odd integer
+and in that case executes the |YES| branch.
+
+
+\subsection{\csbh{xintFac}}\label{xintiFac}
+
+\csa{xintFac\x} returns the factorial. It is an error if the
+argument is negative or at least @10^6@. It is not recommended to
+launch the computation of things such as @100000!@, if you need
+your computer for other tasks. Note that the argument is of the |x| type, it
+must obey the \TeX{} bounds, but on the other hand may involve count registers
+and even arithmetic operations as it will be completely expanded inside a
+|\numexpr|.
+
+With \xintfracname loaded, the macro also
+accepts a fraction as argument, as long as this fraction turns out to be an
+integer: |\xintFac {66/3}|\digitstt{=\xintFac {66/3}}.
+
+% the construct |\xintFac{\xintAdd {2}{3}}| will fail,
+% use either |\xintFac{\xintiAdd {2}{3}}| or |\xintFac{\xintNum{\xintAdd
+% {2}{3}}}|.
+
+% temps obsolètes, mettre à jour
+% On my laptop @1000!@ (2568 digits)
+% is computed in a little less than ten seconds, @2000!@ (5736
+% digits) is computed in a little less than one hundred seconds, and
+% @3000!@ (which has 9131 digits) needs close to seven minutes\dots
+% I have no idea how much time @10000!@ would need (do rather
+% @9999!@ if you can, the algorithm has some overhead at the
+% transition from @N=9999@ to @10000@ and higher; @10000!@ has 35660
+% digits). Not to mention @100000!@ which, from the Stirling formula,
+% should have 456574 digits.
+
+\subsection{\csbh{xintDivision}}\label{xintDivision}
+
+\csa{xintDivision\n\m} returns |{quotient Q}{remainder R}|. This
+is euclidean division: |N = QM + R|, |0|${}\leq{}$\verb+R < |M|+. So the
+remainder is always non-negative and the formula |N = QM + R|
+always holds independently of the signs of |N| or |M|. Division by
+zero is an error (even if |N| vanishes) and returns |{0}{0}|.
+
+This macro is integer only (with \xintfracname loaded it accepts
+fractions on input, but they must be integers in disguise) and not to be
+confused with the \xintfracname macro \csbxint{Div} which divides one
+fraction by another.
+
+\subsection{\csbh{xintQuo}}\label{xintQuo}
+
+\csa{xintQuo\n\m} returns the quotient from the euclidean division. When
+both |N| and |M| are positive one has \csa{xintQuo\n\m}|=\xintiTrunc
+{0}{N/M}| (using package \xintfracname). With \xintfracname loaded it
+accepts fractions on input, but they must be integers in disguise.
+
+\subsection{\csbh{xintRem}}\label{xintRem}
+
+\csa{xintRem\n\m} returns the remainder from the euclidean division.
+With \xintfracname loaded it accepts fractions on input, but they must
+be integers in disguise.
+
+
+
+\subsection{\csbh{xintFDg}}\label{xintFDg}
+
+\csa{xintFDg\n} returns the first digit (most significant) of the
+decimal expansion.
+
+\subsection{\csbh{xintLDg}}\label{xintLDg}
+
+\csa{xintLDg\n} returns the least significant digit. When the
+number is positive, this is the same as the remainder in the
+euclidean division by ten.
+
+\subsection{\csbh{xintMON}, \csbh{xintMMON}}\label{xintMON}\label{xintMMON}
+{\small New in version |1.03|.\par}
+
+\csa{xintMON\n} returns |(-1)^N| and \csa{xintMMON\n} returns
+|(-1)^{N-1}|. \centeredline{|\xintMON {-280914019374101929}|\digitstt{=\xintMON
+ {280914019374101929}}, |\xintMMON
+{-280914019374101929}|\digitstt{=\xintMMON {280914019374101929}}}
+
+\subsection{\csbh{xintOdd}}\label{xintOdd}
+
+\csa{xintOdd\n} is 1 if the number is odd and 0 otherwise.
+
+
+\subsection{\csbh{xintiSqrt}, \csbh{xintiSquareRoot}}\label{xintiSqrt}
+\label{xintiSquareRoot}
+{\small New with |1.08|.\par}
+\xintAssign\xintiSquareRoot {17000000000000000000000000}\to\A\B
+
+\noindent\csa{xintiSqrt\n} returns the largest integer whose square is
+at most equal to |N|.
+\centeredline{|\xintiSqrt {2000000000000000000000000000000000000}=|%
+\digitstt{\xintiSqrt{2000000000000000000000000000000000000}}}
+\centeredline{|\xintiSqrt {3000000000000000000000000000000000000}=|%
+\digitstt{\xintiSqrt{3000000000000000000000000000000000000}}}
+\centeredline{|\xintiSqrt {\xintDSH {-120}{2}}=|}%
+\centeredline{\digitstt{\xintiSqrt {\xintDSH {-120}{2}}}}
+\csa{xintiSquareRoot\n} returns |{M}{d}| with |d>0|, |M^2-d=N| and |M|
+smallest (hence |=1+|\csa{xint\-iSqrt}|{N}|).
+\centeredline{|\xintAssign\xintiSquareRoot
+ {17000000000000000000000000}\to\A\B|}%
+\centeredline{|\xintiSub{\xintiSqr\A}\B=\A^2-\B|}%
+\centeredline{\digitstt{\xintiSub{\xintiSqr\A}\B=\A\string^2-\B}}
+A rational approximation to
+$\sqrt{|N|}$ is $|M|-\frac{|d|}{|2M|}$ (this is a majorant and the error is at
+most |1/2M|; if |N| is a perfect square |k^2| then |M=k+1| and this gives
+|k+1/(2k+2)|, not |k|).
+
+Package \xintfracname has \csbxint{FloatSqrt} for square
+roots of floating point numbers.
+
+
+\begin{framed}
+ The macros described next are strictly for integer-only arguments. These
+ arguments are \emph{not} filtered via \csbxint{Num}.
+\end{framed}
+
+\subsection{\csbh{xintInc}, \csbh{xintDec}}
+\label{xintInc}
+\label{xintDec}
+{\small New with |1.08|.\par}
+
+\csa{xintInc\n} is |N+1| and \csa{xintDec\n} is |N-1|. These macros remain
+integer-only, even with \xintfracname loaded.
+
+\subsection{\csbh{xintDouble}, \csbh{xintHalf}}
+\label{xintDouble}
+\label{xintHalf}
+{\small New with |1.08|.\par}
+
+\csa{xintDouble\n} returns |2N| and \csa{xintHalf\n} is |N/2| rounded
+towards zero. These macros remain integer-only, even with \xintfracname loaded.
+
+\subsection{\csbh{xintDSL}}\label{xintDSL}
+
+\csa{xintDSL\n} is decimal shift left, \emph{i.e.} multiplication
+by ten.
+
+\subsection{\csbh{xintDSR}}\label{xintDSR}
+
+\csa{xintDSR\n} is decimal shift right, \emph{i.e.} it removes the last digit
+(keeping the sign), equivalently it is the closest integer to |N/10| when
+starting at zero.
+
+\subsection{\csbh{xintDSH}}\label{xintDSH}
+
+\csa{xintDSH\x\n} is parametrized decimal shift. When |x| is
+negative, it is like iterating \csa{xintDSL} \verb+|x|+ times
+(\emph{i.e.} multiplication by @10^{-@|x|@}@). When |x| positive,
+it is like iterating \csa{DSR} |x| times (and is more efficient), and for a
+non-negative |N| this is thus the same as the
+quotient from the euclidean division by |10^x|.
+
+\subsection{\csbh{xintDSHr}, \csbh{xintDSx}}\label{xintDSHr}\label{xintDSx}
+{\small New in release |1.01|.\par}
+
+\csa{xintDSHr\x\n} expects |x| to be zero or positive and it returns
+then a value |R| which is correlated to the value |Q| returned by
+\csa{xintDSH\x\n} in the following manner:
+\begin{itemize}
+\item if |N| is
+ positive or zero, |Q| and |R| are the quotient and remainder in
+ the euclidean division by |10^x| (obtained in a more efficient
+ manner than using \csa{xintDivision}),
+\item if |N| is negative let
+ |Q1| and |R1| be the quotient and remainder in the euclidean
+ division by |10^x| of the absolute value of |N|. If |Q1|
+ does not vanish, then |Q=-Q1| and |R=R1|. If |Q1| vanishes, then
+ |Q=0| and |R=-R1|.
+\item for |x=0|, |Q=N| and |R=0|.
+\end{itemize}
+So one has |N = 10^x Q + R| if |Q| turns out to be zero or
+positive, and |N = 10^x Q - R| if |Q| turns out to be negative,
+which is exactly the case when |N| is at most |-10^x|.
+
+
+\csa{xintDSx\x\n} for |x| negative is exactly as
+\csa{xintDSH\x\n}, \emph{i.e.} multiplication by @10^{-@|x|@}@.
+For |x| zero or positive it returns the two numbers |{Q}{R}|
+described above, each one within braces. So |Q| is
+\csa{xintDSH\x\n}, and |R| is \csa{xintDSHr\x\n}, but computed
+simultaneously.
+
+\begin{flushleft}
+ \xintAssign\xintDSx {-1}{-123456789}\to\M
+ \noindent{|\xintAssign\xintDSx {-1}{-123456789}\to\M|}\\
+ |\meaning\M: |\digitstt{\meaning\M}.\\
+ \xintAssign\xintDSx {-20}{1234567689}\to\M
+ {|\xintAssign\xintDSx {-20}{123456789}\to\M|}\\
+ |\meaning\M: |\digitstt{\meaning\M}.\\
+ \xintAssign\xintDSx{0}{-123004321}\to\Q\R
+ {|\xintAssign\xintDSx {0}{-123004321}\to\Q\R|}\\
+ \noindent|\meaning\Q: |\digitstt{\meaning\Q}, |\meaning\R:
+ |\digitstt{\meaning\R.}\\
+ |\xintDSH {0}{-123004321}|\digitstt{=\xintDSH {0}{-123004321}},
+ |\xintDSHr {0}{-123004321}|\digitstt{=\xintDSHr {0}{-123004321}}\\
+ \xintAssign\xintDSx {6}{-123004321}\to\Q\R
+ {|\xintAssign\xintDSx {6}{-123004321}\to\Q\R|}\\
+ |\meaning\Q: |\digitstt{\meaning\Q},
+ |\meaning\R: |\digitstt{\meaning\R.}\\
+ |\xintDSH {6}{-123004321}|\digitstt{=\xintDSH {6}{-123004321}},
+ |\xintDSHr {6}{-123004321}|\digitstt{=\xintDSHr {6}{-123004321}}\\
+ \xintAssign\xintDSx {8}{-123004321}\to\Q\R
+ {|\xintAssign\xintDSx {8}{-123004321}\to\Q\R|}\\
+ |\meaning\Q: |\digitstt{\meaning\Q},
+ |\meaning\R: |\digitstt{\meaning\R.} \\
+ |\xintDSH {8}{-123004321}|\digitstt{=\xintDSH {8}{-123004321}},
+ |\xintDSHr {8}{-123004321}|\digitstt{=\xintDSHr {8}{-123004321}}\\
+ \xintAssign\xintDSx {9}{-123004321}\to\Q\R
+ {|\xintAssign\xintDSx {9}{-123004321}\to\Q\R|}\\
+ |\meaning\Q: |\digitstt{\meaning\Q},
+ |\meaning\R: |\digitstt{\meaning\R.}\\
+ |\xintDSH {9}{-123004321}|\digitstt{=\xintDSH {9}{-123004321}},
+ |\xintDSHr {9}{-123004321}|\digitstt{=\xintDSHr {9}{-123004321}}\\
+\end{flushleft}
+
+\subsection{\csbh{xintDecSplit}}\label{xintDecSplit}
+
+{\small This has been modified in release |1.01|.\par}
+
+\csa{xintDecSplit\x\n} cuts the number into two pieces (each one within a
+pair of enclosing braces). First the sign if present is \emph{removed}.
+Then, for |x| positive or null, the second piece contains the |x| least
+significant digits (\emph{empty} if |x=0|) and the first piece the remaining
+digits (\emph{empty} when |x| equals or exceeds the length of |N|).
+Leading zeros in the second piece are not removed. When |x| is negative
+the first piece contains the \verb+|x|+ most significant digits and the
+second piece the remaining digits (\emph{empty} if @|x|@ equals or exceeds
+the length of |N|). Leading zeros in this second piece are not removed.
+So the absolute value of the original number is always the concatenation
+of the first and second piece.
+
+{\footnotesize This macro's behavior for |N| non-negative is final and will not
+ change. I am still hesitant about what to do with the sign of a
+ negative |N|.\par}
+
+
+\xintAssign\xintDecSplit {0}{-123004321}\to\L\R
+\centeredline{|\xintAssign\xintDecSplit {0}{-123004321}\to\L\R|}
+\noindent|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
+\xintAssign\xintDecSplit {5}{-123004321}\to\L\R
+\centeredline{|\xintAssign\xintDecSplit {5}{-123004321}\to\L\R|}
+|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
+\xintAssign\xintDecSplit {9}{-123004321}\to\L\R
+\centeredline{|\xintAssign\xintDecSplit {9}{-123004321}\to\L\R|}
+|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
+\xintAssign\xintDecSplit {10}{-123004321}\to\L\R
+\centeredline{|\xintAssign\xintDecSplit {10}{-123004321}\to\L\R|}
+|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
+\xintAssign\xintDecSplit {-5}{-12300004321}\to\L\R
+\centeredline{|\xintAssign\xintDecSplit {-5}{-12300004321}\to\L\R|}
+|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
+\xintAssign\xintDecSplit {-11}{-12300004321}\to\L\R
+\centeredline{|\xintAssign\xintDecSplit {-11}{-12300004321}\to\L\R|}
+|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
+\xintAssign\xintDecSplit {-15}{-12300004321}\to\L\R
+\centeredline{|\xintAssign\xintDecSplit {-15}{-12300004321}\to\L\R|}
+|\meaning\L: |\digitstt{\meaning\L}, |\meaning\R: |\digitstt{\meaning\R.}
+
+\subsection{\csbh{xintDecSplitL}}\label{xintDecSplitL}
+
+\csa{xintDecSplitL\x\n} returns the first piece after the action
+of \csa{xintDecSplit}.
+
+\subsection{\csbh{xintDecSplitR}}\label{xintDecSplitR}
+
+\csa{xintDecSplitR\x\n} returns the second piece after the action
+of \csa{xintDecSplit}.
+
+
+
+\section{Commands of the \xintfracname package}
+\label{sec:frac}
\def\x{\string{x\string}}
@@ -5014,7 +5604,7 @@ registers and even expressions with
infix arithmetic operators, under some rules which are explained in the previous
\hyperlink{useofcount}{Use of count registers} section.
-As in the \hyperref[sec:comxint]{xint.sty} documentation, |x|
+As in the \hyperref[sec:xint]{xint.sty} documentation, |x|
stands for something which will internally be embedded in a \csa{numexpr}.
It
may thus be a count register or something like |4*\count 255 + 17|, etc..., but
@@ -5675,7 +6265,7 @@ with (big) integers.
\etocdepthtag.toc {xintexpr}
\section{Expandable expressions with the \xintexprname package}%
-\label{sec:comexpr}
+\label{sec:expr}
@@ -6325,7 +6915,8 @@ principles are necessarily different due to the aim of achieving expandability.
\etocdepthtag.toc {commandsB}
-\section{Commands of the \xintbinhexname package}\label{sec:combinhex}
+\section{Commands of the \xintbinhexname package}
+\label{sec:binhex}
This package was first included in the |1.08| release of \xintname. It
provides expandable conversions of arbitrarily long numbers
@@ -6403,7 +6994,7 @@ one hundred hexadecimal digits.
\section{Commands of the \xintgcdname package}
-
+\label{sec:gcd}
This package was included in the original release |1.0| of the \xintname bundle.
@@ -6549,7 +7140,8 @@ and modify it to what is needed.
\xintTypesetBezoutAlgorithm {10000}{1113}
-\section{Commands of the \xintseriesname package}\label{sec:series}
+\section{Commands of the \xintseriesname package}
+\label{sec:series}
Some arguments to the package commands are macros which are expanded only later,
when given their parameters. The arguments serving as indices are systematically
@@ -7694,7 +8286,8 @@ always do it on a value computed with |D+1| truncation.
% \clearpage
-\section{Commands of the \xintcfracname package}
+\section{Commands of the \xintcfracname package}
+\label{sec:cfrac}
This package was first included in release |1.04| of the \xintname bundle.
@@ -8299,7 +8892,8 @@ first place.
\StopEventually{\end{document}\endinput}
\def\storedlinecounts {}
-\def\StoreCodelineNo #1{\edef\storedlinecounts{\storedlinecounts
+\def\StoreCodelineNo #1{\edef\storedlinecounts{%
+ \unexpanded\expandafter{\storedlinecounts}%
{{#1}{\the\c@CodelineNo}}}\c@CodelineNo\z@ }
\makeatother
@@ -8323,45 +8917,40 @@ first place.
%
% \catcode`\<=0 \catcode`\>=11 \catcode`\*=11 \catcode`\/=11
% \let</doc>\relax
-% \def<*xint>{\catcode`\<=12 \catcode`\>=12 \catcode`\*=12 \catcode`\/=12 }
-%
+% \def<*xinttools>{\catcode`\<=12 \catcode`\>=12 \catcode`\*=12 \catcode`\/=12 }
%</doc>
-%<*xint>
-% \section {Package \xintname implementation}
-%
-% With release |1.09a| all macros doing arithmetic operations and a few more
-% apply systematically |\xintnum| to their arguments; this adds a little
-% overhead but this is more convenient for using count registers even with infix
-% notation; also this is what |xintfrac.sty| did all along. Simplifies the
-% discussion in the documentation too.
+%<*xinttools>
% \def\MARGEPAGENO{2.5em}
+% \section {Package \xinttoolsnameimp implementation}
+% \label{sec:toolsimp}
+%
+% Release |1.09g| splits off |xinttools.sty| from |xint.sty|
%
% \localtableofcontents
+%
% \subsection{Catcodes, \protect\eTeX{} and reload detection}
%
% The method for package identification and reload detection is copied verbatim
% from the packages by \textsc{Heiko Oberdiek} (with some modifications starting
-% with
-% release |1.09b|).
+% with release |1.09b|).
%
% The method for catcodes was also inspired by these packages, we proceed
-% slightly differently.
+% slightly differently.
%
% Starting with version |1.06| of the package, also |`| must be
-% catcode-protected,
-% because we replace everywhere in the code the twice-expansion done with
-% |\expandafter| by the systematic use of |\romannumeral-`0|.
+% catcode-protected, because we replace everywhere in the code the
+% twice-expansion done with |\expandafter| by the systematic use of
+% |\romannumeral-`0|.
%
% Starting with version |1.06b| I decide that I suffer from an indigestion of @
% signs, so I replace them all with underscores |_|, \`a la \LaTeX 3.
%
% Release |1.09b| is more economical: some macros are defined already in
-% |xint.sty| and re-used in other modules. All catcode changes have been unified
-% and \csa{XINT_storecatcodes} will be used by each module
-% to redefine |\XINT_restorecatcodes_endinput| in case catcodes have changed
-% in-between the loading of |xint.sty| and the module (not very probable
-% anyhow...).
-%
+% |xint.sty| (now |xinttools.sty|) and re-used in other modules. All catcode
+% changes have been unified and \csa{XINT_storecatcodes} will be used by each
+% module to redefine |\XINT_restorecatcodes_endinput| in case catcodes have
+% changed in-between the loading of |xint.sty| (now |xinttools.sty|) and the
+% module (not very probable but...).
% \begin{macrocode}
\begingroup\catcode61\catcode48\catcode32=10\relax%
\catcode13=5 % ^^M
@@ -8384,7 +8973,7 @@ first place.
\fi
\expandafter
\ifx\csname numexpr\endcsname\relax
- \y{xint}{\numexpr not available, aborting input}%
+ \y{xinttools}{\numexpr not available, aborting input}%
\aftergroup\endinput
\else
\ifx\x\relax % plain-TeX, first loading
@@ -8393,7 +8982,7 @@ first place.
\ifx\x\empty % LaTeX, first loading,
% variable is initialized, but \ProvidesPackage not yet seen
\else
- \y{xint}{I was already loaded, aborting input}%
+ \y{xinttools}{I was already loaded, aborting input}%
\aftergroup\endinput
\fi
\fi
@@ -8488,7 +9077,7 @@ first place.
% escaping me (compatibility with LaTeX 2.09 or other things ??) seems to set
% extra precautions.
%
-% |1.09c| uses e-\TeX{} |\ifdefined|. No |firstoftwo| etc.. yet here.
+% |1.09c| uses e-\TeX{} |\ifdefined|.
% \begin{macrocode}
\ifdefined\ProvidesPackage
\let\XINT_providespackage\relax
@@ -8498,8 +9087,8 @@ first place.
\expandafter\xdef\csname ver@#2.sty\endcsname{#3}}%
\fi
\XINT_providespackage
-\ProvidesPackage {xint}%
- [2013/11/04 v1.09f Expandable operations on long numbers (jfB)]%
+\ProvidesPackage {xinttools}%
+ [2013/11/22 v1.09g Expandable and non-expandable utilities (jfB)]%
% \end{macrocode}
% \subsection{Token management, constants}
% \lverb|In 1.09e \xint_undef replaced everywhere by \xint_bye.|
@@ -8513,75 +9102,31 @@ first place.
\def\xint_gobble_vi #1#2#3#4#5#6{}%
\def\xint_gobble_vii #1#2#3#4#5#6#7{}%
\def\xint_gobble_viii #1#2#3#4#5#6#7#8{}%
-\long\def\xint_firstofone #1{#1}% becomes long in 1.09f, 2013/11/01
+\long\def\xint_firstofone #1{#1}% long since 1.09f, 2013/11/01
\xint_firstofone{\let\XINT_sptoken= } % 1.09d, 2013/10/22
-\long\def\xint_firstoftwo #1#2{#1}% made long in 1.09e, 2013/10/28
-\long\def\xint_secondoftwo #1#2{#2}%
+\long\def\xint_firstoftwo #1#2{#1}% long since 1.09e, 2013/10/28
+\long\def\xint_secondoftwo #1#2{#2}% idem
\def\xint_firstoftwo_andstop #1#2{ #1}%
\def\xint_secondoftwo_andstop #1#2{ #2}%
-\def\xint_exchangetwo_keepbraces_andstop #1#2{ {#2}{#1}}%
-\def\xint_firstofthree #1#2#3{#1}%
-\def\xint_secondofthree #1#2#3{#2}%
-\def\xint_thirdofthree #1#2#3{#3}%
\def\xint_minus_andstop { -}%
-\long\def\xint_bye #1\xint_bye {}% becomes long in 1.09f
\def\xint_gob_til_R #1\R {}%
\def\xint_gob_til_W #1\W {}%
\def\xint_gob_til_Z #1\Z {}%
-\def\xint_gob_til_zero #10{}%
-\def\xint_gob_til_one #11{}%
-\def\xint_gob_til_G #1G{}%
-\def\xint_gob_til_minus #1-{}%
-\def\xint_gob_til_zeros_iii #1000{}%
-\def\xint_gob_til_zeros_iv #10000{}%
+\long\def\xint_bye #1\xint_bye {}% long since 1.09f
\let\xint_relax\relax
\def\xint_brelax {\xint_relax }%
-\def\xint_gob_til_relax #1\relax {}%
-\long\def\xint_gob_til_xint_relax #1\xint_relax {}% becomes long in 1.09f
-\def\xint_UDzerofork #10\dummy #2#3\krof {#2}%
-\def\xint_UDsignfork #1-\dummy #2#3\krof {#2}%
-\def\xint_UDwfork #1\W\dummy #2#3\krof {#2}%
-\def\xint_UDzerosfork #100\dummy #2#3\krof {#2}%
-\def\xint_UDonezerofork #110\dummy #2#3\krof {#2}%
-\def\xint_UDzerominusfork #10-\dummy #2#3\krof {#2}%
-\def\xint_UDsignsfork #1--\dummy #2#3\krof {#2}%
+\long\def\xint_gob_til_xint_relax #1\xint_relax {}% long since 1.09f
\def\xint_afterfi #1#2\fi {\fi #1}%
\chardef\xint_c_ 0
-\chardef\xint_c_i 1
-\chardef\xint_c_ii 2
-\chardef\xint_c_iii 3
-\chardef\xint_c_iv 4
-\chardef\xint_c_v 5
\chardef\xint_c_viii 8
-\chardef\xint_c_ix 9
-\chardef\xint_c_x 10
-\newcount\xint_c_x^viii \xint_c_x^viii 100000000
\newtoks\XINT_toks
+\newcount\XINT_count % 1.09g: \xintFor from 1.09f modified \count 255 :-(
% \end{macrocode}
-% \subsection{\csh{xintRev}, \csh{xintReverseOrder}}
-% \lverb|&
-% \xintRev: fait l'expansion avec \romannumeral-`0, vérifie le signe.$\
-% \xintReverseOrder: ne fait PAS l'expansion, ne regarde PAS le signe.|
+% \subsection{ \csh{xintReverseOrder}}
+% \lverb|\xintReverseOrder: does NOT expand its argument|
% \begin{macrocode}
-\def\xintRev {\romannumeral0\xintrev }%
-\def\xintrev #1%
-{%
- \expandafter\XINT_rev_fork
- \romannumeral-`0#1\xint_relax % empty #1 ok, \xint_relax stops expansion
- \xint_bye\xint_bye\xint_bye\xint_bye
- \xint_bye\xint_bye\xint_bye\xint_bye
- \xint_relax
-}%
-\def\XINT_rev_fork #1%
-{%
- \xint_UDsignfork
- #1\dummy {\expandafter\xint_minus_andstop\romannumeral0\XINT_rord_main {}}%
- -\dummy {\XINT_rord_main {}#1}%
- \krof
-}%
-\def\XINT_Rev {\romannumeral0\XINT_rev }%
-\def\xintReverseOrder {\romannumeral0\XINT_rev }%
-\def\XINT_rev #1%
+\def\xintReverseOrder {\romannumeral0\xintreverseorder }%
+\def\xintreverseorder #1%
{%
\XINT_rord_main {}#1%
\xint_relax
@@ -8601,8 +9146,7 @@ first place.
% \end{macrocode}
% \subsection{\csh{xintRevWithBraces}}
% \lverb|New with 1.06. Makes the expansion of its argument and then reverses
-% the
-% resulting tokens or braced tokens, adding a pair of braces to each (thus,
+% the resulting tokens or braced tokens, adding a pair of braces to each (thus,
% maintaining it when it was already there.
%
% As in some other places, 1.09e replaces \Z by \xint_bye, although here it is
@@ -8652,44 +9196,22 @@ first place.
\csname xint_gobble_\romannumeral #1\endcsname
}%
% \end{macrocode}
-% \subsection{\csh{xintLen}, \csh{xintLength}}
-% \lverb|&
-% \xintLen -> fait l'expansion, ne compte PAS le signe.$\
-% \xintLength -> ne fait PAS l'expansion, compte le signe.$\
+% \subsection{\csh{xintLength}}
+% \lverb|\xintLength does NOT expand its argument.$\
+% 1.09g adds the missing \xintlength, which was previously called \XINT_length,
+% and suppresses \XINT_Length$\
% 1.06: improved code is roughly 20$% faster than the one from earlier
% versions. 1.09a, \xintnum inserted. 1.09e: \Z->\xint_bye as this is called
% from \xintNthElt, and there it was necessary not to use \Z. Later use of \Z
% and \W perfectly safe here.|
% \begin{macrocode}
-\def\xintLen {\romannumeral0\xintlen }%
-\def\xintlen #1%
-{%
- \expandafter\XINT_length_fork
- \romannumeral0\xintnum{#1}\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye
-}%
-\def\XINT_Len #1%
-{%
- \romannumeral0\XINT_length_fork
- #1\xint_relax\xint_relax\xint_relax\xint_relax
- \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye
-}%
-\def\XINT_length_fork #1%
-{%
- \expandafter\XINT_length_loop
- \xint_UDsignfork
- #1\dummy {{0}}%
- -\dummy {{0}#1}%
- \krof
-}%
-\def\XINT_Length {\romannumeral0\XINT_length }%
-\def\XINT_length #1%
+\def\xintLength {\romannumeral0\xintlength }%
+\def\xintlength #1%
{%
\XINT_length_loop
{0}#1\xint_relax\xint_relax\xint_relax\xint_relax
\xint_relax\xint_relax\xint_relax\xint_relax\xint_bye
}%
-\let\xintLength\XINT_Length
\def\XINT_length_loop #1#2#3#4#5#6#7#8#9%
{%
\xint_gob_til_xint_relax #9\XINT_length_finish_a\xint_relax
@@ -9245,6 +9767,43 @@ first place.
}%
\def\XINT_seqo_nd #1#2#3#4{\XINT_seqo_nb {#1}{#2}{#3}{#4{#1}}}%
% \end{macrocode}
+%\subsection{\csh{xintloop}, \csh{xintbreakloop}, \csh{xintbreakloopanddo},
+% \csh{xintloopskiptonext}}
+% \lverb|1.09g [2013/11/22]|
+% \begin{macrocode}
+\def\xintloop #1#2\repeat {#1#2\xintloop_again\fi\xint_gobble_i {#1#2}}%
+\def\xintloop_again\fi\xint_gobble_i #1{\fi
+ #1\xintloop_again\fi\xint_gobble_i {#1}}%
+\def\xintbreakloop #1\xintloop_again\fi\xint_gobble_i #2{}%
+\def\xintbreakloopanddo #1#2\xintloop_again\fi\xint_gobble_i #3{#1}%
+\def\xintloopskiptonext #1\xintloop_again\fi\xint_gobble_i #2{%
+ #2\xintloop_again\fi\xint_gobble_i {#2}}%
+% \end{macrocode}
+% \subsection{\csh{xintiloop}, \csh{xintiloopindex}, \csh{xintouteriloopindex},
+% \csh{xintbreakiloop}, \csh{xintbreakiloopanddo}, \csh{xintiloopskiptonext},
+% \csh{xintiloopskipandredo}}
+% \lverb|1.09g [2013/11/22]|
+% \begin{macrocode}
+\def\xintiloop [#1+#2]{%
+ \expandafter\xintiloop_a\the\numexpr #1\expandafter.\the\numexpr #2.}%
+\def\xintiloop_a #1.#2.#3#4\repeat{%
+ #3#4\xintiloop_again\fi\xint_gobble_iii {#1}{#2}{#3#4}}%
+\def\xintiloop_again\fi\xint_gobble_iii #1#2{%
+ \fi\expandafter\xintiloop_again_b\the\numexpr#1+#2.#2.}%
+\def\xintiloop_again_b #1.#2.#3{%
+ #3\xintiloop_again\fi\xint_gobble_iii {#1}{#2}{#3}}%
+\def\xintbreakiloop #1\xintiloop_again\fi\xint_gobble_iii #2#3#4{}%
+\def\xintbreakiloopanddo #1.#2\xintiloop_again\fi\xint_gobble_iii #3#4#5{#1}%
+\def\xintiloopindex #1\xintiloop_again\fi\xint_gobble_iii #2%
+ {#2#1\xintiloop_again\fi\xint_gobble_iii {#2}}%
+\def\xintouteriloopindex #1\xintiloop_again
+ #2\xintiloop_again\fi\xint_gobble_iii #3%
+ {#3#1\xintiloop_again #2\xintiloop_again\fi\xint_gobble_iii {#3}}%
+\def\xintiloopskiptonext #1\xintiloop_again\fi\xint_gobble_iii #2#3{%
+ \expandafter\xintiloop_again_b \the\numexpr#2+#3.#3.}%
+\def\xintiloopskipandredo #1\xintiloop_again\fi\xint_gobble_iii #2#3#4{%
+ #4\xintiloop_again\fi\xint_gobble_iii {#2}{#3}{#4}}%
+% \end{macrocode}
% \subsection{\csh{XINT\_xflet}}
% \lverb|1.09e [2013/10/29]: we expand fully unbraced tokens and swallow arising
% space tokens until the dust settles. For treating cases
@@ -9314,14 +9873,15 @@ first place.
% expand unbraced item elements and this is in fact convenient to simulate
% insertion of lists in others.
%
-% 1.09e: the applied macro is allowed to be long, with items containing
-% explicit \par's.
+% 1.09e: the applied macro is allowed to be long, with items (or the first fixed
+% arguments of he macro, passed together with it as #1 to \xintApplyInline)
+% containing explicit \par's. (1.09g: some missing \long's added)
%
-% 1.09f: terminator used to be z, now Z (still catcode 3).
+% 1.09f: terminator used to be z, now Z (still catcode 3).
%|
% \begin{macrocode}
-\catcode`Z 3%
-\def\xintApplyInline #1#2%
+\catcode`Z 3
+\long\def\xintApplyInline #1#2%
{%
\long\expandafter\def\expandafter\XINT_inline_macro
\expandafter ##\expandafter 1\expandafter {#1{##1}}%
@@ -9330,24 +9890,22 @@ first place.
\def\XINT_inline_b
{%
\ifx\XINT_token Z\expandafter\xint_gobble_i
- \else\expandafter\XINT_inline_d
- \fi
+ \else\expandafter\XINT_inline_d\fi
}%
-\def\XINT_inline_d #1%
+\long\def\XINT_inline_d #1%
{%
- \def\XINT_item{{#1}}\XINT_xflet\XINT_inline_e
+ \long\def\XINT_item{{#1}}\XINT_xflet\XINT_inline_e
}%
\def\XINT_inline_e
{%
\ifx\XINT_token Z\expandafter\XINT_inline_w
- \else\expandafter\XINT_inline_f
- \fi
+ \else\expandafter\XINT_inline_f\fi
}%
\def\XINT_inline_f
{%
\expandafter\XINT_inline_g\expandafter{\XINT_inline_macro {##1}}%
}%
-\def\XINT_inline_g #1%
+\long\def\XINT_inline_g #1%
{%
\expandafter\XINT_inline_macro\XINT_item
\long\def\XINT_inline_macro ##1{#1}\XINT_inline_d
@@ -9401,8 +9959,11 @@ first place.
% If the \XINT_forever branch is taken, the added space will not be a problem
% there.
%
-% [2013/11/03]: 1.09f rewrites the code to allow all macro parameters from #1 to
-% #9 in \xintFor, \xintFor*, and \XINT_forever. |
+% 1.09f rewrites (2013/11/03) the code which now allows all macro parameters
+% from #1 to #9 in \xintFor, \xintFor*, and \XINT_forever.
+%
+% 1.09g \xintFor and \xintFor* modified the value of \count 255, now uses
+% \XINT_count. |
% \begin{macrocode}
\def\XINT_tmpa #1#2{\ifnum #2<#1 \xint_afterfi {{#########2}}\fi}%
\def\XINT_tmpb #1#2{\ifnum #1<#2 \xint_afterfi {{#########2}}\fi}%
@@ -9440,9 +10001,9 @@ first place.
}%
\long\def\XINT_for #1#2in#3#4#5%
{%
- \count 255 #2\relax
+ \XINT_count #2\relax
\expandafter\XINT_toks\expandafter
- {\expandafter\XINT_for_d\the\count 255{#5}}%
+ {\expandafter\XINT_for_d\the\XINT_count{#5}}%
\def\XINT_flet_macro {\expandafter\XINT_for_forever?\space}%
\expandafter\XINT_flet_zapsp #3Z%
}%
@@ -9456,9 +10017,9 @@ first place.
\def\XINT_to_forever\fi #1\xintcsvtolist #2{\fi \XINT_forever #2}%
\long\def\XINT_forx *#1#2in#3#4#5%
{%
- \count 255 #2\relax
+ \XINT_count #2\relax
\expandafter\XINT_toks\expandafter
- {\expandafter\XINT_forx_d\the\count 255{#5}}%
+ {\expandafter\XINT_forx_d\the\XINT_count{#5}}%
\XINT_xflet\XINT_forx_forever? #3Z%
}%
\def\XINT_forx_forever?
@@ -9725,12 +10286,12 @@ first place.
\XINT_restoreescapechar
\expandafter\let\expandafter\xint_temp
\csname\xint_arrayname 0\endcsname
- \count 255 0
+ \XINT_count 0
\loop
\global\expandafter\let
- \csname\xint_arrayname\the\count255\endcsname\relax
- \ifnum \count 255 < \xint_temp
- \advance\count 255 1
+ \csname\xint_arrayname\the\XINT_count\endcsname\relax
+ \ifnum \XINT_count < \xint_temp
+ \advance\XINT_count 1
\repeat
\global\expandafter\let\csname\xint_arrayname 00\endcsname\relax
\global\let #1\relax
@@ -9741,7 +10302,7 @@ first place.
\escapechar -1
\edef\xint_arrayname {\string #2}%
\XINT_restoreescapechar
- \count 255 0
+ \XINT_count 0
\expandafter\XINT_assignarray_loop \romannumeral-`0#1\xint_relax
\csname\xint_arrayname 00\endcsname
\csname\xint_arrayname 0\endcsname
@@ -9752,12 +10313,12 @@ first place.
{%
\def\xint_temp {#1}%
\ifx\xint_brelax\xint_temp
- \expandafter\edef\csname\xint_arrayname 0\endcsname{\the\count 255 }%
+ \expandafter\edef\csname\xint_arrayname 0\endcsname{\the\XINT_count }%
\expandafter\expandafter\expandafter\XINT_assignarray_end_a
\else
- \advance\count 255 1
+ \advance\XINT_count 1
\expandafter\edef
- \csname\xint_arrayname\the\count 255\endcsname{\xint_temp }%
+ \csname\xint_arrayname\the\XINT_count\endcsname{\xint_temp }%
\expandafter\XINT_assignarray_loop
\fi
}%
@@ -9793,6 +10354,205 @@ first place.
}%
}%
\let\xintDigitsOf\xintAssignArray
+\XINT_restorecatcodes_endinput%
+% \end{macrocode}
+%\catcode`\<=0 \catcode`\>=11 \catcode`\*=11 \catcode`\/=11
+%\let</xinttools>\relax
+%\def<*xint>{\catcode`\<=12 \catcode`\>=12 \catcode`\*=12 \catcode`\/=12 }
+%</xinttools>
+%<*xint>
+%
+% \StoreCodelineNo {xinttools}
+%
+% \section{Package \xintnameimp implementation}
+% \label{sec:xintimp}
+%
+% With release |1.09a| all macros doing arithmetic operations and a few more
+% apply systematically |\xintnum| to their arguments; this adds a little
+% overhead but this is more convenient for using count registers even with infix
+% notation; also this is what |xintfrac.sty| did all along. Simplifies the
+% discussion in the documentation too.
+%
+% \localtableofcontents
+%
+% \subsection{Catcodes, \protect\eTeX{} and reload detection}
+%
+% The code for reload detection is copied from \textsc{Heiko
+% Oberdiek}'s packages, and adapted here to check for previous
+% loading of the master \xintname package.
+%
+% The method for catcodes is slightly different, but still
+% directly inspired by these packages.
+%
+% \begin{macrocode}
+\begingroup\catcode61\catcode48\catcode32=10\relax%
+ \catcode13=5 % ^^M
+ \endlinechar=13 %
+ \catcode123=1 % {
+ \catcode125=2 % }
+ \catcode64=11 % @
+ \catcode35=6 % #
+ \catcode44=12 % ,
+ \catcode45=12 % -
+ \catcode46=12 % .
+ \catcode58=12 % :
+ \def\space { }%
+ \let\z\endgroup
+ \expandafter\let\expandafter\x\csname ver@xint.sty\endcsname
+ \expandafter\let\expandafter\w\csname ver@xinttools.sty\endcsname
+ \expandafter
+ \ifx\csname PackageInfo\endcsname\relax
+ \def\y#1#2{\immediate\write-1{Package #1 Info: #2.}}%
+ \else
+ \def\y#1#2{\PackageInfo{#1}{#2}}%
+ \fi
+ \expandafter
+ \ifx\csname numexpr\endcsname\relax
+ \y{xint}{\numexpr not available, aborting input}%
+ \aftergroup\endinput
+ \else
+ \ifx\x\relax % plain-TeX, first loading of xint.sty
+ \ifx\w\relax % but xinttools.sty not yet loaded.
+ \y{xint}{Package xinttools is required}%
+ \y{xint}{Will try \string\input\space xinttools.sty}%
+ \def\z{\endgroup\input xinttools.sty\relax}%
+ \fi
+ \else
+ \def\empty {}%
+ \ifx\x\empty % LaTeX, first loading,
+ % variable is initialized, but \ProvidesPackage not yet seen
+ \ifx\w\relax % xinttools.sty not yet loaded.
+ \y{xint}{Package xinttools is required}%
+ \y{xint}{Will try \string\RequirePackage{xinttools}}%
+ \def\z{\endgroup\RequirePackage{xinttools}}%
+ \fi
+ \else
+ \y{xint}{I was already loaded, aborting input}%
+ \aftergroup\endinput
+ \fi
+ \fi
+ \fi
+\z%
+% \end{macrocode}
+% \subsection{Confirmation of \xinttoolsname loading}
+% \begin{macrocode}
+\begingroup\catcode61\catcode48\catcode32=10\relax%
+ \catcode13=5 % ^^M
+ \endlinechar=13 %
+ \catcode123=1 % {
+ \catcode125=2 % }
+ \catcode64=11 % @
+ \catcode35=6 % #
+ \catcode44=12 % ,
+ \catcode45=12 % -
+ \catcode46=12 % .
+ \catcode58=12 % :
+ \ifdefined\PackageInfo
+ \def\y#1#2{\PackageInfo{#1}{#2}}%
+ \else
+ \def\y#1#2{\immediate\write-1{Package #1 Info: #2.}}%
+ \fi
+ \def\empty {}%
+ \expandafter\let\expandafter\w\csname ver@xinttools.sty\endcsname
+ \ifx\w\relax % Plain TeX, user gave a file name at the prompt
+ \y{xint}{Loading of package xinttools failed, aborting input}%
+ \aftergroup\endinput
+ \fi
+ \ifx\w\empty % LaTeX, user gave a file name at the prompt
+ \y{xint}{Loading of package xinttools failed, aborting input}%
+ \aftergroup\endinput
+ \fi
+\endgroup%
+% \end{macrocode}
+% \subsection{Catcodes}
+% \begin{macrocode}
+\XINTsetupcatcodes%
+% \end{macrocode}
+% \subsection{Package identification}
+% \begin{macrocode}
+\XINT_providespackage
+\ProvidesPackage{xint}%
+ [2013/11/22 v1.09g Expandable operations on long numbers (jfB)]%
+% \end{macrocode}
+% \subsection{Token management, constants}
+% \begin{macrocode}
+\def\xint_firstofthree #1#2#3{#1}%
+\def\xint_secondofthree #1#2#3{#2}%
+\def\xint_thirdofthree #1#2#3{#3}%
+\def\xint_gob_til_zero #10{}%
+\def\xint_gob_til_zeros_iii #1000{}%
+\def\xint_gob_til_zeros_iv #10000{}%
+\def\xint_gob_til_one #11{}%
+\def\xint_gob_til_G #1G{}%
+\def\xint_gob_til_minus #1-{}%
+\def\xint_gob_til_relax #1\relax {}%
+\def\xint_exchangetwo_keepbraces_andstop #1#2{ {#2}{#1}}%
+\def\xint_UDzerofork #10\dummy #2#3\krof {#2}%
+\def\xint_UDsignfork #1-\dummy #2#3\krof {#2}%
+\def\xint_UDwfork #1\W\dummy #2#3\krof {#2}%
+\def\xint_UDzerosfork #100\dummy #2#3\krof {#2}%
+\def\xint_UDonezerofork #110\dummy #2#3\krof {#2}%
+\def\xint_UDzerominusfork #10-\dummy #2#3\krof {#2}%
+\def\xint_UDsignsfork #1--\dummy #2#3\krof {#2}%
+\chardef\xint_c_i 1 % 0 and 8 in xinttools
+\chardef\xint_c_ii 2
+\chardef\xint_c_iii 3
+\chardef\xint_c_iv 4
+\chardef\xint_c_v 5
+\chardef\xint_c_ix 9
+\chardef\xint_c_x 10
+\newcount\xint_c_x^viii \xint_c_x^viii 100000000
+% \end{macrocode}
+% \subsection{\csh{xintRev}}
+% \lverb|&
+% \xintRev: expands fully its argument \romannumeral-`0, and checks the sign.
+% However this last aspect does not appear like a very useful thing. And despite
+% the fact that a special check is made for a sign, actually the input is not
+% given to \xintnum, contrarily to \xintLen. This is all a bit incoherent.
+% Should be fixed.|
+% \begin{macrocode}
+\def\xintRev {\romannumeral0\xintrev }%
+\def\xintrev #1%
+{%
+ \expandafter\XINT_rev_fork
+ \romannumeral-`0#1\xint_relax % empty #1 ok, \xint_relax stops expansion
+ \xint_bye\xint_bye\xint_bye\xint_bye
+ \xint_bye\xint_bye\xint_bye\xint_bye
+ \xint_relax
+}%
+\def\XINT_rev_fork #1%
+{%
+ \xint_UDsignfork
+ #1\dummy {\expandafter\xint_minus_andstop\romannumeral0\XINT_rord_main {}}%
+ -\dummy {\XINT_rord_main {}#1}%
+ \krof
+}%
+% \end{macrocode}
+% \subsection{\csh{xintLen}}
+% \lverb|\xintLen is ONLY for (possibly long) integers. Gets extended to
+% fractions by xintfrac.sty|
+% \begin{macrocode}
+\def\xintLen {\romannumeral0\xintlen }%
+\def\xintlen #1%
+{%
+ \expandafter\XINT_len_fork
+ \romannumeral0\xintnum{#1}\xint_relax\xint_relax\xint_relax\xint_relax
+ \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye
+}%
+\def\XINT_Len #1% variant which does not expand via \xintnum.
+{%
+ \romannumeral0\XINT_len_fork
+ #1\xint_relax\xint_relax\xint_relax\xint_relax
+ \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye
+}%
+\def\XINT_len_fork #1%
+{%
+ \expandafter\XINT_length_loop
+ \xint_UDsignfork
+ #1\dummy {{0}}%
+ -\dummy {{0}#1}%
+ \krof
+}%
% \end{macrocode}
% \subsection{\csh{XINT\_RQ}}
% \lverb|&
@@ -11640,28 +12400,28 @@ first place.
\def\XINT_mul_minusminus #1#2%
{%
\expandafter\XINT_mul_choice_a
- \expandafter{\romannumeral0\XINT_length {#2}}%
- {\romannumeral0\XINT_length {#1}}{#1}{#2}%
+ \expandafter{\romannumeral0\xintlength {#2}}%
+ {\romannumeral0\xintlength {#1}}{#1}{#2}%
}%
\def\XINT_mul_minusplus #1#2#3%
{%
\expandafter\xint_minus_andstop\romannumeral0\expandafter
\XINT_mul_choice_a
- \expandafter{\romannumeral0\XINT_length {#1#3}}%
- {\romannumeral0\XINT_length {#2}}{#2}{#1#3}%
+ \expandafter{\romannumeral0\xintlength {#1#3}}%
+ {\romannumeral0\xintlength {#2}}{#2}{#1#3}%
}%
\def\XINT_mul_plusminus #1#2#3%
{%
\expandafter\xint_minus_andstop\romannumeral0\expandafter
\XINT_mul_choice_a
- \expandafter{\romannumeral0\XINT_length {#3}}%
- {\romannumeral0\XINT_length {#1#2}}{#1#2}{#3}%
+ \expandafter{\romannumeral0\xintlength {#3}}%
+ {\romannumeral0\xintlength {#1#2}}{#1#2}{#3}%
}%
\def\XINT_mul_plusplus #1#2#3#4%
{%
\expandafter\XINT_mul_choice_a
- \expandafter{\romannumeral0\XINT_length {#2#4}}%
- {\romannumeral0\XINT_length {#1#3}}{#1#3}{#2#4}%
+ \expandafter{\romannumeral0\xintlength {#2#4}}%
+ {\romannumeral0\xintlength {#1#3}}{#1#3}{#2#4}%
}%
\def\XINT_mul_choice_a #1#2%
{%
@@ -11826,7 +12586,7 @@ first place.
\def\XINT_mul_M_zero #1\Z\Z\Z\Z { 0}%
\def\XINT_mul_M_one #1#2#3#4\Z\Z\Z\Z
{%
- \expandafter\xint_cleanupzeros_andstop\romannumeral0\XINT_rev{#4}%
+ \expandafter\xint_cleanupzeros_andstop\romannumeral0\xintreverseorder{#4}%
}%
\def\XINT_mul_N #1#2#3#4#5#6#7%
{%
@@ -11958,7 +12718,7 @@ first place.
}%
\def\XINT_mul_finish_c #1\XINT_mul_finish_ciii \W\W\W\W #2#3\Z\Z\Z\Z
{%
- \expandafter\xint_cleanupzeros_andstop\romannumeral0\XINT_rev{#2}%
+ \expandafter\xint_cleanupzeros_andstop\romannumeral0\xintreverseorder{#2}%
}%
% \end{macrocode}
% \lverb|&
@@ -12122,8 +12882,8 @@ first place.
% Modified with 1.02 and again in 1.03 for greater efficiency. I am
% tempted,
% here and elsewhere, to use \ifcase\XINT_Geq {#1}{1000000000} rather than
-% \ifnum\XINT_Length {#1}>9 but for the time being I leave things as they stand.
-% With release 1.05, rather than using \XINT_Length I opt finally for direct use
+% \ifnum\xintLength {#1}>9 but for the time being I leave things as they stand.
+% With release 1.05, rather than using \xintLength I opt finally for direct use
% of \numexpr (which will throw a suitable number too big message), and to raise
% the \xintError:$\ FactorialOfTooBigNumber for argument larger than 1000000
% (rather than 1000000000). With 1.09a, \xintFac uses \xintnum.|
@@ -12402,7 +13162,7 @@ first place.
\def\XINT_pow_pprod_end\relax\XINT_pow_pprod_compute #1\Z #2%
{%
\expandafter\xint_cleanupzeros_andstop
- \romannumeral0\XINT_rev {#2}%
+ \romannumeral0\xintreverseorder {#2}%
}%
% \end{macrocode}
% \subsection{\csh{xintDivision}, \csh{xintQuo}, \csh{xintRem}}
@@ -12546,7 +13306,7 @@ first place.
\def\XINT_div_prepare #1%
{%
\expandafter \XINT_div_prepareB_aa \expandafter
- {\romannumeral0\XINT_length {#1}}{#1}% B > 0 ici
+ {\romannumeral0\xintlength {#1}}{#1}% B > 0 ici
}%
\def\XINT_div_prepareB_aa #1%
{%
@@ -12607,7 +13367,7 @@ first place.
\def\XINT_div_prepareB_f #1#2#3#4#5\Z
{%
\expandafter \XINT_div_prepareB_g \expandafter
- {\romannumeral0\XINT_rev {#1#2#3#4#5}}{#1#2#3#4}%
+ {\romannumeral0\xintreverseorder {#1#2#3#4#5}}{#1#2#3#4}%
}%
% \end{macrocode}
% \lverb|&
@@ -12627,7 +13387,7 @@ first place.
\def\XINT_div_prepareA_a #1%
{%
\expandafter \XINT_div_prepareA_b \expandafter
- {\romannumeral0\XINT_length {#1}}{#1}% A >0 ici
+ {\romannumeral0\xintlength {#1}}{#1}% A >0 ici
}%
% \end{macrocode}
% \lverb|&
@@ -12907,7 +13667,7 @@ first place.
{%
\expandafter \XINT_div_body_l \expandafter
{\romannumeral0\XINT_div_sub_xpxp
- {\romannumeral0\XINT_mul_Mr {#1}#4\Z\Z\Z\Z }{\XINT_Rev{#2}}}%
+ {\romannumeral0\XINT_mul_Mr {#1}#4\Z\Z\Z\Z }{\xintReverseOrder{#2}}}%
{#3+#1}%
}%
% \end{macrocode}
@@ -13144,7 +13904,7 @@ first place.
\def\XINT_LDg #1{\romannumeral0\XINT_ldg {#1}}%
\def\XINT_ldg #1%
{%
- \expandafter\XINT_ldg_\romannumeral0\XINT_rev {#1}\Z
+ \expandafter\XINT_ldg_\romannumeral0\xintreverseorder {#1}\Z
}%
\def\XINT_ldg_ #1#2\Z{ #1}%
% \end{macrocode}
@@ -13246,16 +14006,16 @@ first place.
\def\XINT_DSR #1{\romannumeral0\XINT_dsr_a {#1}\W\Z }%
\def\XINT_dsr_a
{%
- \expandafter\XINT_dsr_b\romannumeral0\XINT_rev
+ \expandafter\XINT_dsr_b\romannumeral0\xintreverseorder
}%
\def\XINT_dsr_b #1#2#3\Z
{%
\xint_gob_til_W #2\xint_dsr_onedigit\W
\xint_gob_til_minus #2\xint_dsr_onedigit-%
\expandafter\XINT_dsr_removew
- \romannumeral0\XINT_rev {#2#3}%
+ \romannumeral0\xintreverseorder {#2#3}%
}%
-\def\xint_dsr_onedigit #1\XINT_rev #2{ 0}%
+\def\xint_dsr_onedigit #1\xintreverseorder #2{ 0}%
\def\XINT_dsr_removew #1\W { }%
% \end{macrocode}
% \subsection{\csh{xintDSH}, \csh{xintDSHr}}
@@ -13583,7 +14343,7 @@ first place.
\def\XINT_split_fromright #1\Z #2%
{%
\expandafter \XINT_split_fromright_a \expandafter
- {\romannumeral0\XINT_rev {#2}}{#1}{#2}%
+ {\romannumeral0\xintreverseorder {#2}}{#1}{#2}%
}%
\def\XINT_split_fromright_a #1#2%
{%
@@ -13611,7 +14371,7 @@ first place.
}%
\def\XINT_split_fromright_endsplit_ #1#2\W #3\Z #4%
{%
- \expandafter\space\expandafter {\romannumeral0\XINT_rev{#2}}{#1}%
+ \expandafter\space\expandafter {\romannumeral0\xintreverseorder {#2}}{#1}%
}%
\def\XINT_split_fromright_endsplit_i #1#2%
{\XINT_split_fromright_checkiftoofar #2{#2#1}}%
@@ -13853,7 +14613,7 @@ first place.
\def\XINT_sqrt #1\Z
{%
\expandafter\XINT_sqrt_start\expandafter
- {\romannumeral0\XINT_length {#1}}{#1}%
+ {\romannumeral0\xintlength {#1}}{#1}%
}%
\def\XINT_sqrt_start #1%
{%
@@ -14040,7 +14800,8 @@ first place.
%
% \StoreCodelineNo {xint}
%
-% \section{Package \xintbinhexname implementation}
+% \section{Package \xintbinhexnameimp implementation}
+% \label{sec:binheximp}
%
% The commenting is currently (\docdate) very sparse.
%
@@ -14135,11 +14896,6 @@ first place.
\endgroup%
% \end{macrocode}
% \subsection{Catcodes}
-%
-% Perhaps catcodes have changed after the loading of \xintname
-% and prior to the current loading of \xintbinhexname, so we redefine
-% the |\XINT_restorecatcodes_endinput| in this style file.
-%
% \begin{macrocode}
\XINTsetupcatcodes%
% \end{macrocode}
@@ -14147,7 +14903,7 @@ first place.
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintbinhex}%
- [2013/11/04 v1.09f Expandable binary and hexadecimal conversions (jfB)]%
+ [2013/11/22 v1.09g Expandable binary and hexadecimal conversions (jfB)]%
% \end{macrocode}
% \subsection{Constants, etc...}
% \lverb!v1.08!
@@ -14748,7 +15504,8 @@ first place.
%
% \StoreCodelineNo {xintbinhex}
%
-% \section{Package \xintgcdname implementation}
+% \section{Package \xintgcdnameimp implementation}
+% \label{sec:gcdimp}
%
% The commenting is currently (\docdate) very sparse.
%
@@ -14850,7 +15607,7 @@ first place.
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintgcd}%
- [2013/11/04 v1.09f Euclide algorithm with xint package (jfB)]%
+ [2013/11/22 v1.09g Euclide algorithm with xint package (jfB)]%
% \end{macrocode}
% \subsection{\csh{xintGCD}}
% The macros of |1.09a| benefits from the |\xintnum| which has been inserted
@@ -15396,15 +16153,15 @@ first place.
\edef\A{\U2}\edef\B{\U4}\edef\N{\U1}%
\setbox 0 \vbox{\halign {$##$\cr \A\cr \B \cr}}%
\noindent
- \count 255 1
+ \XINT_count 1
\loop
- \hbox to \wd 0 {\hfil$\U{\numexpr 2*\count 255\relax}$}%
- ${} = \U{\numexpr 2*\count 255 + 3\relax}
- \times \U{\numexpr 2*\count 255 + 2\relax}
- + \U{\numexpr 2*\count 255 + 4\relax}$%
- \ifnum \count 255 < \N
+ \hbox to \wd 0 {\hfil$\U{\numexpr 2*\XINT_count\relax}$}%
+ ${} = \U{\numexpr 2*\XINT_count + 3\relax}
+ \times \U{\numexpr 2*\XINT_count + 2\relax}
+ + \U{\numexpr 2*\XINT_count + 4\relax}$%
+ \ifnum \XINT_count < \N
\hfill\break
- \advance \count 255 1
+ \advance \XINT_count 1
\repeat
\par
\endgroup
@@ -15429,24 +16186,24 @@ first place.
\xintAssignArray\xintBezoutAlgorithm {#1}{#2}\to\BEZ
\edef\A{\BEZ2}\edef\B{\BEZ6}\edef\N{\BEZ1}% A = |#1|, B = |#2|
\setbox 0 \vbox{\halign {$##$\cr \A\cr \B \cr}}%
- \count 255 1
+ \XINT_count 1
\loop
\noindent
- \hbox to \wd 0 {\hfil$\BEZ{4*\count 255 - 2}$}%
- ${} = \BEZ{4*\count 255 + 5}
- \times \BEZ{4*\count 255 + 2}
- + \BEZ{4*\count 255 + 6}$\hfill\break
- \hbox to \wd 0 {\hfil$\BEZ{4*\count 255 +7}$}%
- ${} = \BEZ{4*\count 255 + 5}
- \times \BEZ{4*\count 255 + 3}
- + \BEZ{4*\count 255 - 1}$\hfill\break
- \hbox to \wd 0 {\hfil$\BEZ{4*\count 255 +8}$}%
- ${} = \BEZ{4*\count 255 + 5}
- \times \BEZ{4*\count 255 + 4}
- + \BEZ{4*\count 255 }$
+ \hbox to \wd 0 {\hfil$\BEZ{4*\XINT_count - 2}$}%
+ ${} = \BEZ{4*\XINT_count + 5}
+ \times \BEZ{4*\XINT_count + 2}
+ + \BEZ{4*\XINT_count + 6}$\hfill\break
+ \hbox to \wd 0 {\hfil$\BEZ{4*\XINT_count +7}$}%
+ ${} = \BEZ{4*\XINT_count + 5}
+ \times \BEZ{4*\XINT_count + 3}
+ + \BEZ{4*\XINT_count - 1}$\hfill\break
+ \hbox to \wd 0 {\hfil$\BEZ{4*\XINT_count +8}$}%
+ ${} = \BEZ{4*\XINT_count + 5}
+ \times \BEZ{4*\XINT_count + 4}
+ + \BEZ{4*\XINT_count }$
\endgraf
- \ifnum \count 255 < \N
- \advance \count 255 1
+ \ifnum \XINT_count < \N
+ \advance \XINT_count 1
\repeat
\par
\edef\U{\BEZ{4*\N + 4}}%
@@ -15470,7 +16227,8 @@ first place.
%
% \StoreCodelineNo {xintgcd}
%
-% \section{Package \xintfracname implementation}
+% \section{Package \xintfracnameimp implementation}
+% \label{sec:fracimp}
%
% The commenting is currently (\docdate) very sparse.
%
@@ -15572,7 +16330,7 @@ first place.
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintfrac}%
- [2013/11/04 v1.09f Expandable operations on fractions (jfB)]%
+ [2013/11/22 v1.09g Expandable operations on fractions (jfB)]%
\chardef\xint_c_vi 6
\chardef\xint_c_vii 7
\chardef\xint_c_xviii 18
@@ -15733,7 +16491,7 @@ first place.
\def\XINT_frac_Bb #1.\W\Z #2\Z
{%
\expandafter \XINT_frac_T \expandafter
- {\romannumeral0\XINT_length {#1}}{#2#1}%
+ {\romannumeral0\xintlength {#1}}{#2#1}%
}%
\def\XINT_frac_A e\W\Z {\XINT_frac_T {0}{1}{0}}%
\def\XINT_frac_T #1#2#3#4e#5#6\Z
@@ -15758,7 +16516,7 @@ first place.
\def\XINT_frac_Cb #1.\W\Z #2\Z
{%
\expandafter\XINT_frac_D\expandafter
- {\romannumeral0\XINT_length {#1}}{#2#1}%
+ {\romannumeral0\xintlength {#1}}{#2#1}%
}%
\def\XINT_frac_D #1#2#3#4#5#6%
{%
@@ -16440,7 +17198,7 @@ first place.
{%
\xint_gob_til_zero #2\XINT_trunc_zero 0%
\expandafter\XINT_trunc_H\expandafter
- {\the\numexpr\romannumeral0\XINT_length {#1}-#3}{#3}{#1}#2%
+ {\the\numexpr\romannumeral0\xintlength {#1}-#3}{#3}{#1}#2%
}%
\def\XINT_trunc_zero 0#10{ 0}%
\def\XINT_trunc_H #1#2%
@@ -16634,7 +17392,7 @@ first place.
\def\XINT_float_Mc #1#2#3#4#5#6%
{%
\expandafter\XINT_float_N\expandafter
- {\romannumeral0\XINT_length{#6}}{#2}{#5}{#6}{#1}{#3}{#4}%
+ {\romannumeral0\xintlength{#6}}{#2}{#5}{#6}{#1}{#3}{#4}%
}% long de B, P+2, n, B, |A|, A, P
\def\XINT_float_N #1#2%
{%
@@ -17733,12 +18491,12 @@ first place.
\def\XINT_flpow_checkB_b #1#2\Z #3%
{%
\expandafter\XINT_flpow_checkB_c \expandafter
- {\romannumeral0\XINT_length{#2}}{#3}{#2}#1%
+ {\romannumeral0\xintlength{#2}}{#3}{#2}#1%
}%
\def\XINT_flpow_checkB_c #1#2%
{%
\expandafter\XINT_flpow_checkB_d \expandafter
- {\the\numexpr \expandafter\XINT_Length\expandafter
+ {\the\numexpr \expandafter\xintLength\expandafter
{\the\numexpr #1*20/3}+#1+#2+1}%
}%
\def\XINT_flpow_checkB_d #1#2#3#4%
@@ -17876,12 +18634,12 @@ first place.
\def\XINT_flpower_checkB_b #1#2\Z #3%
{%
\expandafter\XINT_flpower_checkB_c \expandafter
- {\romannumeral0\XINT_length{#2}}{#3}{#2}#1%
+ {\romannumeral0\xintlength{#2}}{#3}{#2}#1%
}%
\def\XINT_flpower_checkB_c #1#2%
{%
\expandafter\XINT_flpower_checkB_d \expandafter
- {\the\numexpr \expandafter\XINT_Length\expandafter
+ {\the\numexpr \expandafter\xintLength\expandafter
{\the\numexpr #1*20/3}+#1+#2+1}%
}%
\def\XINT_flpower_checkB_d #1#2#3#4%
@@ -18000,7 +18758,7 @@ first place.
\def\XINT_flsqrt #1#2%
{%
\expandafter\XINT_sqrt_a
- \expandafter{\romannumeral0\XINT_length {#2}}\XINT_flsqrt_big_d {#2}{#1}%
+ \expandafter{\romannumeral0\xintlength {#2}}\XINT_flsqrt_big_d {#2}{#1}%
}%
\def\XINT_flsqrt_big_d #1\or #2\fi #3%
{%
@@ -18131,7 +18889,8 @@ first place.
%
% \StoreCodelineNo {xintfrac}
%
-% \section{Package \xintseriesname implementation}
+% \section{Package \xintseriesnameimp implementation}
+% \label{sec:seriesimp}
%
% The commenting is currently (\docdate) very sparse.
%
@@ -18233,7 +18992,7 @@ first place.
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintseries}%
- [2013/11/04 v1.09f Expandable partial sums with xint package (jfB)]%
+ [2013/11/22 v1.09g Expandable partial sums with xint package (jfB)]%
% \end{macrocode}
% \subsection{\csh{xintSeries}}
% \lverb|&
@@ -18667,7 +19426,8 @@ first place.
%
% \StoreCodelineNo {xintseries}
%
-% \section{Package \xintcfracname implementation}
+% \section{Package \xintcfracnameimp implementation}
+% \label{sec:cfracimp}
%
% The commenting is currently (\docdate) very sparse.
%
@@ -18769,7 +19529,7 @@ first place.
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintcfrac}%
- [2013/11/04 v1.09f Expandable continued fractions with xint package (jfB)]%
+ [2013/11/22 v1.09g Expandable continued fractions with xint package (jfB)]%
% \end{macrocode}
% \subsection{\csh{xintCFrac}}
% \begin{macrocode}
@@ -19733,7 +20493,8 @@ first place.
%
% \StoreCodelineNo {xintcfrac}
%
-% \section{Package \xintexprname implementation}
+% \section{Package \xintexprnameimp implementation}
+% \label{sec:exprimp}
%
% The first version was released in June 2013. I was greatly helped in
% this task of writing an expandable parser of infix operations by the
@@ -19921,7 +20682,7 @@ first place.
% \begin{macrocode}
\XINT_providespackage
\ProvidesPackage{xintexpr}%
- [2013/11/04 v1.09f Expandable expression parser (jfB)]%
+ [2013/11/22 v1.09g Expandable expression parser (jfB)]%
% \end{macrocode}
% \subsection{Helper macros}
% \begin{macrocode}
@@ -20921,11 +21682,11 @@ first place.
\xintApplyInline\mymacro\storedlinecounts
\end{tabular}
\def\mymacroaux #1#2{#2}%
+%
\parbox[t]{10cm}{Total number of code lines:
\digitstt{\xintiSum{\xintApply\mymacro\storedlinecounts}}. Each package starts
- with circa \digitstt{80} lines dealing
- with catcodes, package identification and reloading management, also for Plain
- \TeX\strut. Version
+ with circa \digitstt{80} lines dealing with catcodes, package identification
+ and reloading management, also for Plain \TeX\strut. Version
\texttt{\pkgversion} of \texttt{\pkgdate}.\par}
@@ -20944,7 +21705,7 @@ first place.
Right bracket \] Circumflex \^ Underscore \_
Grave accent \` Left brace \{ Vertical bar \|
Right brace \} Tilde \~}
-\CheckSum {19898}
+\CheckSum {20159}
\makeatletter\check@checksum\makeatother
\Finale
%%
diff --git a/Master/texmf-dist/source/generic/xint/xint.ins b/Master/texmf-dist/source/generic/xint/xint.ins
index 9d8b5299c2f..717d1ac7adb 100644
--- a/Master/texmf-dist/source/generic/xint/xint.ins
+++ b/Master/texmf-dist/source/generic/xint/xint.ins
@@ -1,13 +1,14 @@
%%
%%----------------------------------------------------------------
-%% The xint bundle (version 1.09f of November 4, 2013)
+%% The xint bundle (version 1.09g of November 22, 2013)
%% Copyright (C) 2013 by Jean-Francois Burnol
%%----------------------------------------------------------------
%%
%%
%% This is a generated file. Run tex or latex on this file to
-%% extract xint.sty, xintfrac.sty, xintexpr.sty, xintbinhex.sty,
-%% xintgcd.sty, xintseries.sty and xintcfrac.sty from xint.dtx
+%% extract xinttools.sty, xint.sty, xintfrac.sty, xintexpr.sty,
+%% xintbinhex.sty, xintgcd.sty, xintseries.sty and xintcfrac.sty
+%% from xint.dtx
%%
%% See xint.dtx for the copyright and the conditions for
%% distribution and/or modification of this work.
@@ -15,6 +16,7 @@
\input docstrip.tex
\askforoverwritefalse
\generate{\usepreamble\defaultpreamble
+\file{xinttools.sty}{\from{xint.dtx}{xinttools}}
\file{xint.sty}{\from{xint.dtx}{xint}}
\file{xintbinhex.sty}{\from{xint.dtx}{xintbinhex}}
\file{xintgcd.sty}{\from{xint.dtx}{xintgcd}}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-08 00:27:07 +0000