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Direc­tory macros/generic/xint

    Source:  xint.dtx 1.2n 2017/08/06 (doc 2017/08/06)
    Author:  Jean-Francois Burnol
    Info:    Expandable operations on big integers, decimals, fractions
    License: LPPL 1.3c

This README is also available as README.pdf and README.html.

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.


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:

    \xinttheexpr mul(add(x(x+1)(x+2), x=y..y+15), y=171286,98762,9296)\relax

evaluates to 15979066346135829902328007959448563667099190784.

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

    \xintDigits:=48;\xintthefloatexpr 123_456_789^1_000.5\relax

But 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

Sub-units xintcore, xint and xintfrac provide the underlying macros, and
xintexpr loads all of them and provides expandable parsers allowing
computations such as the above (and more).


It is possible to use the package with Plain (via \input anywhere) or
with LaTeX (via \usepackage in the preamble).

With LaTeX

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

Further packages: xintbinhex, xintgcd, xintseries and xintcfrac.

Main dependencies are handled automatically. For example xintexpr
automatically loads xintfrac which itself loads xint; but use of the gcd
and lcm functions in expressions require explicit loading of xintgcd,
and hexadecimal notation requires explicit loading of xintbinhex.

Package xintcore is the subset of xint providing only the five
operations on big integers: \xintiiAdd, \xintiiMul, ... It is (by
default) loaded by the (LaTeX only) package bnumexpr which provides a
more light-weight expression parser handling only big integers, the four
operations, the power operation and the factorial.

There is also xinttools which is a separate package providing, among
others, expandable and non-expandable loops such as \xintFor.

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, or \xint_dothis/\xint_orthat.


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:

2.  cd to the download repertory and issue:

        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

            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. Furthermore the
Pandoc software is required.

1.  obtain xint.dtx and Makefile from

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 "tex xint.dtx" or "etex xint.dtx" to extract from xint.dtx all
packages as well as these files:

    the current README with Markdown formatting.

    the changes across successive releases.

    used to generate xint.pdf via "latex xint.tex" (thrice) then
    "dvipdfmx xint.dvi". It is also possible to compile xint.tex with
    xelatex, or with pdflatex (this latter option produces a
    bigger pdf).
    For successful compilation, packages newtxtt, newtxmath, etoc,
    mathastext are needed. Inclusion of the source code is off by
    default, but the toggle can be set in xint.tex.

    A third option is to generate xint.pdf via xelatex xint.dtx or
    pdflatex xint.dtx. Source code is then included by default (but some
    code comments in French use 8bit characters, hence for xelatex an a
    priori conversion of xint.dtx into utf-8 will give a better result).

    this is for UNIX-like systems. Note: this file is only produced with
    "etex xint.dtx", not with "tex xint.dtx". Rename it to Makefile and
    run make on the command line for further help.

doHTMLs.sh and doPDFs.sh
    these are scripts (for UNIX-like systems) which can be used to
    convert the README.md and CHANGES.md to HTML and PDF formats. They
    require Pandoc.

    a Pandoc template used by doPDFs.sh.

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

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


Copyright (C) 2013-2017 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


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.

Down­load the con­tents of this pack­age in one zip archive (1.8M).

xint – Ex­pand­able op­er­a­tions on long num­bers

The bun­dle pro­vides nine pack­ages:

  • xint­core, which pro­vides ex­pand­able macros that im­ple­ment the ba­sic arith­metic op­er­a­tions of ad­di­tion, sub­trac­tion, mul­ti­pli­ca­tion and di­vi­sion, as ap­plied to ar­bi­trar­ily long num­bers rep­re­sented as chains of dig­its with an op­tional mi­nus sign;
  • xint, which ex­tends xint­core with more big in­te­ger op­er­a­tions;
  • xint­tools, which pro­vides util­i­ties of in­de­pen­dent in­ter­est such as ex­pand­able and non-ex­pand­able loops;
  • xint­frac, which com­putes frac­tions us­ing xint;
  • xin­t­expr, which ex­tends xint­frac with an ex­pand­able parser of comma sep­a­rated ex­pres­sions in­volv­ing in­te­gers, frac­tions, boolean, and al­ge­braic op­er­a­tors, and de­clared as well as dummy vari­ables;
  • xint­bin­hex pro­vides con­ver­sions to and from bi­nary and hex­adec­i­mal bases;
  • xintseries, which pro­vides ba­sic func­tion­al­ity for com­put­ing par­tial sums us­ing xint;
  • xint­gcd, which pro­vides im­ple­men­ta­tions of the Eu­clidean al­go­rithm, and of its type­set­ting;
  • xintcfrac, which deals with the com­pu­ta­tion of con­tin­ued frac­tions.

All of the pack­ages’ com­pu­ta­tions are done in a way that they can op­er­ate in an ex­pand­ing en­vi­ron­ment.

The pack­ages may be used ei­ther with Plain or .

Ver­sion1.2n 2017-08-06
Li­cense The Project Public Li­cense 1.3c
Copy­right2013–2017 Jean-François Burnol
Main­tainerJean-François Burnol
TDS archivexint.tds.zip
Con­tained inTeX Live as xint
MiKTeX as xint
Topics per­form and type­set arith­metic prob­lems
per­form cal­cu­la­tions within
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