CTAN Comprehensive TeX Archive Network

Directory macros/generic/xint

    Source:  xint.dtx 1.3f 2019/09/10 (doc 2019/09/10)
    Author:  Jean-Francois Burnol
    Info:    Expandable operations on big integers, decimals, fractions
    License: LPPL 1.3f

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

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

Square-root and the four operations achieve correct rounding in the
given arbitrary precision.

Trigonometric functions (direct and inverse) are available with a
maximal precision of 60 digits.

Logarithms and exponentials are available using the poormanlog package
which provides only 8 or 9 digits of precision. This will be increased
in future.


It is possible to use the package both with Plain (\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

The xinttrig and xintlog packages are loaded automatically by xintexpr
and will refuse to be loaded directly.

Further packages: xintbinhex, xintgcd, xintseries and xintcfrac.

Main dependencies are handled automatically. For example xintexpr
automatically loads xinttools and xintfrac (which itself loads xint).
Hexadecimal input requires explicit loading of 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

The LaTeX package polexpr is based upon xintexpr and allows formal
algebra with polynomials, and finding all real roots with arbitrary

With TeX

One does for example:

    \input xintexpr.sty

This will automatically load xintfrac.sty, xinttrig.sty, xintlog.sty and
xinttools.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.


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. The Latexmk and
Pandoc softwares are required to build all the documentation.

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 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 you
can’t use make read the contents of the Makefile for instructions.

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) 2013-2019 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


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,
xinttrig.sty, xintlog.sty, xintbinhex.sty, xintgcd.sty, xintseries.sty,
xintcfrac.sty, xinttools.sty, xint.ins, xint.tex, README, README.md,
pandoctpl.latex, doHTMLs.sh, doPDFs.sh, xint.dvi, xint.pdf, and

Download the contents of this package in one zip archive (2.3M).

xint – Expandable operations on long numbers

The xint bundle main modules are:

utilities of independent interest such as expandable and non-expandable loops,
expandable macros implementing addition, subtraction, multiplication, division, and powers for arbitrarily long integers,
extension of xintcore,
extends the scope of xint to decimal numbers, to numbers using scientific notation and also to (exact) fractions,
provides expandable parsers of numeric expressions using the standard infix notations, parentheses, built-in functions, user definable functions and variables (and more ...) which do either exact evaluations (also with fractions) or floating point evaluations under a user chosen precision.

Further modules of the bundle are: xintkernel (support macros for all the bundle constituents), xintbinhex (conversion to and from hexadecimal and binary bases), xintgcd (provides gcd() and lcm() functions to xintexpr), xintseries (evaluates numerically partial sums of series and power series with fractional coefficients), and xintcfrac (dedicated to the computation and display of continued fractions).

All computations are compatible with expansion-only context.

The packages may be used with Plain , , or (a priori) any other macro format built upon .

Version1.3f 2019-09-10
LicensesThe Project Public License 1.3c
Copyright2013–2019 Jean-François Burnol
MaintainerJean-François Burnol
TDS archivexint.tds.zip
Contained inTeX Live as xint
MiKTeX as xint
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