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2019/01/06

Source:  xint.dtx 1.3d 2019/01/06 (doc 2019/01/06)
Author:  Jean-Francois Burnol
Info:    Expandable operations on big integers, decimals, fractions

Change log is to be found in CHANGES.pdf or CHANGES.html.

The user manual is xint.pdf, and the commented source code is available as sourcexint.pdf.

Aim

The basic aim is provide expandable computations on integers, fractions, and floating point numbers. For example

\xinttheexpr reduce(37189719/183618963+11390170/17310720)^17\relax

will evaluate exactly the fraction; the result has 462 characters (including the fraction slash.) One can also work with dummy variables:

evaluates to 15979066346135829902328007959448563667099190784.

Float computations are possible at an adjustable precision (default 16).

\xintDigits:=48;\xintthefloatexpr 123_456_789^1_000.5\relax
->3.63692761822782679930738270515740797370813691938e8095

(as this example shows the underscore character can be used to separate visually digits, one can also use the space character for that purpose).

Currently, only integer and half-integer exponents are allowed for the power operation in expressions and only the square-root operation is implemented besides the four arithmetic operations. Square-root and the four operations achieve correct rounding in the given arbitrary precision.

Usage

It is possible to use the package with Plain (using for example \input xintexpr.sty) or with LaTeX (\usepackage{xintexpr}).

With LaTeX

\usepackage{xint}       % expandable arithmetic with big integers
\usepackage{xintfrac}   % decimal numbers, fractions, floats
\usepackage{xinttools}  % expandable and non expandable loops
\usepackage{xintexpr}   % expressions with infix operators

Further packages: xintbinhex, xintgcd, xintseries and xintcfrac.

Main dependencies are handled automatically. For example xintexpr automatically loads xinttools and xintfrac (which itself loads xint). But the gcd()/lcm() functions require extra loading of xintgcd and hexadecimal input requires xintbinhex.

Package xintcore is the subset of xint providing only the five operations on big integers: \xintiiAdd, \xintiiMul, …

The LaTeX package bnumexpr defines a more light-weight parser of arithmetical expressions using big integers, which supports only the four operations, the modulo operation, the power operation, and the factorial. By default it uses the macros from xintcore but this can be customized.

With TeX

One does for example:

\input xintexpr.sty

The packages may be loaded in any catcode context such that letters, digits, \ and % have their standard catcodes.

xintcore.sty and xinttools.sty both import xintkernel.sty which has the catcode handler and package identifier and defines a few utilities such as \oodef/\fdef, \xint_dothis/\xint_orthat, or \xintLength.

Since 1.3b, xintkernel.sty also provides \xintUniformDeviate which is a wrapper of the engine \pdfuniformdeviate or \uniformdeviate done to guarantee more uniformity of the pseudo-random integers. This is used by xintexpr.sty for implementing random() and randrange() functions.

Installation

Method A: using the package manager of your TeX distribution

xint is included in TeXLive (hence also MacTeX) and MikTeX.

There can be a few days of delay between apparition of a new version on CTAN and availability via the distribution package manager.

Method B: manual installation using xint.tds.zip and unzip

Assumes a GNU/Linux-like system (or Mac OS X).

1. obtain xint.tds.zip from CTAN: http://mirror.ctan.org/install/macros/generic/xint.tds.zip

unzip xint.tds.zip -d <TEXMF>

where <TEXMF> is a suitable TDS-compliant destination repertory. For example, with TeXLive:

• Linux, standard access rights, hence sudo is needed, installation into the “local” tree:

sudo unzip xint.tds.zip -d /usr/local/texlive/texmf-local
sudo texhash /usr/local/texlive/texmf-local
• Mac OS X, installation into user home folder (no sudo needed, and it is recommended to not have a ls-R file there, hence no texhash):

unzip xint.tds.zip -d  ~/Library/texmf

Method C: manual installation using Makefile and xint.dtx

The Makefile automatizes rebuilding from xint.dtx all documentation files as well as xint.tds.zip. It is for GNU/Linux-like (inc. Mac OS X) systems, with a teTeX like installation such as TeXLive. The Latexmk and Pandoc softwares are required to build all the documentation.

1. obtain xint.dtx and Makefile from http://mirror.ctan.org/macros/generic/xint.

2. put them in an otherwise empty working repertory, run make or equivalently make help for further instructions.

Method D: installation starting with only xint.dtx

Run etex xint.dtx to extract from xint.dtx all macro files as well as auxiliary files needed for building the documentation. Among them there is Makefile.mk. If you are on a GNU/Linux-type system, rename the file to Makefile and execute make on command line for further help. If not, you will need to examine the contents of this file to see the commands needed to produce the documentation with latexmk (extraction will have created a configuration file .latexmkrc) and pandoc. If not using latexmk, you will need to execute suitable makeindex -s xint-gind.ist calls to produce the indices of macros for inclusion into sourcexint.pdf. It is also possible to get xint.pdf to include the source code. For this, see the instructions in xint.tex.

Finishing the installation in a TDS hierarchy:

• move the style files to TDS:tex/generic/xint/

• xint.dtx goes to TDS:source/generic/xint/

• The documentation (xint.pdf, README.md,…) goes to TDS:doc/generic/xint/

Depending on the destination, it may then be necessary to refresh a filename database.

Copyright (C) 2013-2019 by Jean-Francois Burnol

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

http://www.latex-project.org/lppl/lppl-1-3c.txt

and version 1.3 or later is part of all distributions of LaTeX version 2005/12/01 or later.

This Work has the LPPL maintenance status author-maintained.

The Author of this Work is Jean-Francois Burnol.

This Work consists of the source file xint.dtx and of its derived files: xintkernel.sty, xintcore.sty, xint.sty, xintfrac.sty, xintexpr.sty, xintbinhex.sty, xintgcd.sty, xintseries.sty, xintcfrac.sty, xinttools.sty, xint.ins, xint.tex, README, README.md, README.html, README.pdf, CHANGES.md, CHANGES.html, CHANGES.pdf, pandoctpl.latex, doHTMLs.sh, doPDFs.sh, xint.dvi, xint.pdf, Makefile.mk, xint-gind.ist, and .latexmkrc.