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Fast Library for Number Theory

Number theory library written in C

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Source updated January 16, 2026

The Fast Library for Number Theory (FLINT) is a C library for number theory applications. It implements efficient versions of various ring arithmetics as well as derived functionality such as integer factorization using a quadratic sieve. The library is designed to be compiled with the GNU Multi-Precision Library (GMP) and is released under the GNU General Public License. It is developed by William Hart of the University of Kaiserslautern (formerly University of Warwick) and David Harvey of University of New South Wales (formerly Harvard University) to address the speed limitations of the PARI and NTL libraries.

FLINT along with a Cython wrapper for it is distributed with SageMath. The development of FLINT has led to significant contributions in the areas of integer factorization and polynomial arithmetic. For example as of May, 2007 on certain platforms FLINT factors integers in the quadratic sieve range faster than any other general implementation, and as of February, 2008 it does arithmetic in $\mathbb {Z} [x]$ faster than any other package.

01Functionality

Core:

Ring arithmetic (integers, rationals, algebraic, real, complex and p-adic numbers, finite fields, and number fields)
- Exact real numbers (formerly the separate Calcium library)
- Arbitrary-precision approximate real numbers with ball arithmetic (formerly the separate Arb library)
Polynomials (univariate and multivariate), power series, and matrices building on top of ring arithmetics.

Based on core:

Primality testing (APRCL, Miller-Rabin, BPSW, etc.)
Integer factorization (trial factor, quadratic sieve, Pollard's rho, Lenstra ECM)
Multivariate polynomial GCD and factorisation
FFTs
Multimodular reconstruction
Special functions
Exact and approximate linear algebra
LLL
Finite field embeddings
... and more.

02Use in research

FLINT maintains a webpage listing peer-reviewed papers, preprints, and other academic products making use of its functionality.

Watch videos about Fast Library for Number TheoryExplainers and documentaries on YouTube (opens in a new tab)

Sources and credits

This article is adapted from the Wikipedia article “Fast Library for Number Theory”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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