Welcome to Arb’s documentation!


Arb is a C library for arbitrary-precision floating-point ball arithmetic, developed by Fredrik Johansson (fredrik.johansson@gmail.com). It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many transcendental functions. All is done with automatic, rigorous error bounds.

Arb is free software distributed under the GNU Lesser General Public License (LGPL), version 2.1 or later (see License for details).

The git repository is https://github.com/fredrik-johansson/arb/

The documentation website is http://fredrikj.net/arb/

A PDF version of this documentation is available (older versions).


Using ball arithmetic, it is possible to do rigorous root-finding and integration (among other operations) with generic functions. This code should be considered experimental.

Supplementary algorithm notes

Here, we give extra proofs, error bounds, and formulas that would be too lengthy to reproduce in the documentation for each module.