# Directory `macros/generic/xint`

% README % xint 1.4m % 2022/06/10

Source: xint.dtx 1.4m 2022/06/10 (doc 2022/06/11) Author: Jean-Francois Burnol Info: Expandable operations on big integers, decimals, fractions License: LPPL 1.3c

# Description

It is possible to use the package both with Plain (`\input xintexpr.sty`

) or with the LaTeX macro format (`\usepackage{xintexpr}`

).

The basic aim is provide *expandable* computations on (arbitrarily big) integers, fractions, and floating point numbers (at a user chosen precision). The four operations and the square-root extraction achieve the *correct rounding* for the given arbitrary precision. Exponential (natural and to the base ten), logarithm (also to the base 10), fractional powers, direct and inverse trigonometrical functions are available up to 62 digits of precision. The syntax supports dummy variables (to generate sequences of values) and nested structures. Support for user-declared functions and variables is implemented.

Here is an example of everyday typical calculation by `xintexpr`

users:

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

It expands to:

2560976152652211536408111110189/2131858131361319942957376000000

# Usage on the command line

One can use `xintexpr`

as an interactive calculator on the command line. See the xintsession package.

>>> 2^100; @_1 1267650600228229401496703205376 >>> cos(1); @_2 0.5403023058681397 >>> &fp=32 (/usr/local/texlive/2021/texmf-dist/tex/generic/xint/xintlog.sty) (/usr/local/texlive/2021/texmf-dist/tex/generic/xint/xinttrig.sty) fp mode (log and trig reloaded at Digits=32) >>> cos(1); @_3 0.54030230586813971740093660744298 >>> 3^1000; @_4 1.3220708194808066368904552597521e477 >>> &exact exact mode (floating point evaluations use 32 digits) >>> 3^1000; @_5 132207081948080663689045525975... (trimmed for this README)

# Installation

`xint`

is included in TeXLive (hence MacTeX also) and in MikTeX. Thus, use the package manager to update your distribution.

Direct installation of both the macro files and the documentation into a TDS-compliant hierarchy is available via `xint.tds.zip`

and usage of `unzip`

. For example, on a macOS system, installation in user repertory:

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

Admin privileges may be needed if the target repertory requires it.

Else, one can download `xint.dtx`

from https://www.ctan.org/tex-archive/macros/generic/xint and execute `etex xint.dtx`

which will extract all macro files (those with extension `.sty`

). One then only needs to move them to a location where `TeX`

can find them.

To build the documentation one can execute `latex`

directly on `xint.dtx`

(at least three times, perhaps more, so `latexmk`

is recommended) then `dvipdfmx`

or directly `pdflatex`

. The resulting `xint.pdf`

includes both the user manual and the commented source code, with hyperlinks.

For those on Unix-like systems the recommended way is to fetch also `Makefile`

from the location above (or to rename the extracted `Makefile.mk`

into `Makefile`

), then one can execute `make xint.pdf`

(user manual only), or `make sourcexint.pdf`

or `make xint-all.pdf`

. These targets will require `latexmk`

.

Further help can be obtained via `make help`

or from the comments in extracted files `xint.tex`

, `sourcexint.tex`

, and `xint-all.tex`

.

# Documentation

`README.md`

: this file

`CHANGES.html`

: change log as relevant to end users (`texdoc --list xint`

)

`xint.pdf`

: user manual

`sourcexint.pdf`

: commented source code (`texdoc --list xint`

or `texdoc sourcexint`

)

# License

Copyright (C) 2013-2022 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 files `xint.dtx`

and `Makefile`

and extracted files inclusive of the macro files `xint*sty`

as well as derived documentation files such as `xint.pdf`

, `sourcexint.pdf`

and `CHANGES.html`

See `xint.pdf`

for contact information.

Download the contents of this package in one zip archive (3.9M).

## xint – Expandable operations on long numbers

The xint bundle main modules are:

- xinttools
- utilities of independent interest such as expandable and non-expandable loops,
- xintcore
- expandable macros implementing addition, subtraction, multiplication, division, and powers for arbitrarily long integers,
- xint
- extension of xintcore,
- xintfrac
- extends the scope of xint to decimal numbers, to numbers using scientific notation and also to (exact) fractions,
- xintexpr
- 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 TeX, LaTeX, or (a priori) any other macro format built upon TeX.

Package | xint |

Version | 1.4m 2022-06-10 |

Licenses | The LaTeX Project Public License 1.3c |

Copyright | 2013–2022 Jean-François Burnol |

Maintainer | Jean-François Burnol |

TDS archive | `xint.tds.zip` |

Contained in | TeX Live as xint MiKTeX as xint |

Topics | Calculation Arithmetic |