Directory `macros/generic/xint`

README.md

% README % xint 1.4o % 2025/09/06

Source:  xint.dtx 1.4o 2025/09/06 (doc 2025/09/06)
Author:  Jean-François Burnol
Info:    Expandable operations on big integers, decimals, fractions
License: LPPL 1.3c

Description

The main functionality is \xintfloateval which parses expressions involving floating point numbers, functions, variables and other syntax elements.

The precision defaults to 16 decimal digits. The logarithm, exponential, direct and inverse trigonometric functions are supported up to 62 digits. The four basic operations and square-root extraction are implemented with correct rounding up to thousands of digits (roughly up to a maximum of 26000 digits for the output).

A variant \xinteval computes with fractions. And \xintiieval handles only (arbitarily large) integers.

All three parsers obtain their result purely expandably. They handle comma separated inputs and nested structures using square brackets. The user can declare custom variables and functions.

Usage

The way of loading xintexpr depends on whether you are using LaTeX or not.

with LaTeX, add \usepackage{xintexpr} to the document preamble,
else, do \input xintexpr.sty and compile with either one of etex, pdftex, xetex, luatex (they all default to the Plain TeX format), or with optex (i.e. luatex with OpTeX format), or with context (luametatex engine).

Example

Here is an example typical of the xintexpr users morning routine since many years (xintexpr was first released in 2013):

\xinteval{reduce(add(1/i^3, i=1..25))}

It expands (in two steps) to:

2560976152652211536408111110189/2131858131361319942957376000000

Repository

It is at https://github.com/jfbu/xint and the issue tracker is at https://github.com/jfbu/xint/issues.

Documentation

Both the user manual and the commented source code are in xint.pdf.

A file CHANGES.html is provided at https://jfbu.github.io/xint. Its source xintchanges.md is part of the CTAN upload, and you can access it in TeXLive using texdoc xintchanges.md.

License

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-François Burnol.

This Work consists of the file xint.dtx and README.md and their derived files such as xint.pdf.

Download the contents of this package in one zip archive (4.0M).

xint – Expandable arbitrary precision floating point and integer operations

Loading xintexpr provides \xinteval and \xintfloateval.

\xintfloateval evaluates numerical expressions. The floating point precision defaults to 16 decimal digits and can be set by user. Trigonometry, exponential and logarithms are implemented up to a maximal precision of 62 decimal digits.

\xinteval computes exactly with integers, fractions, and decimal numbers or numbers in scientific notation. Note though that multiplying two floating point numbers will about double the number of digits, and so on, because the algebra is done exactly.

Both are compatible with expansion-only context.

Loading xintexpr imports automatically various other modules that it depends upon. Among them:

xinttools: utilities such as expandable and non-expandable loops,
xint: macros implementing in particular the basic operations on arbitrarily long integers,
xintbinhex: conversions between decimal and binary, octal, or hexadecimal bases for arbitrarily long integers,
xintfrac: macros implementing in particular the basic operations on arbitrarily large fractions, decimal numbers, or numbers in scientific notation.

Further modules of independent interest include xintgcd, xintseries and xintcfrac.

You can use xintexpr (and the other components) with LaTeX (via \usepackage) or also with Plain TeX, OpTeX, or ConTeXt (via \input xintexpr.sty).

All the components are documented in the file xint.pdf, which also contains the commented source code.

Package	xint
Home page	https://jfbu.github.io/xint
Bug tracker	https://github.com/jfbu/xint/issues
Repository	https://github.com/jfbu/xint
Version	1.4o 2025-09-06
Licenses	The LaTeX Project Public License 1.3c
Copyright	2013–2022, 2025 Jean-François Burnol
Maintainer	Jean-François Burnol
TDS archive	`xint.tds.zip`
Contained in	TeX Live as xint MiKTeX as xint
Topics	Calculation Arithmetic

Directory macros/generic/xint