FLINT : Fast Library for Number Theory

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Authors and credits

Brief project history

FLINT has been developed since 2007 by a large number of people. Initially the library was started by David Harvey and William Hart. Later maintenance of the library was taken over solely by William Hart, who remained the project leader until 2022.

FLINT 2.0 was a clean rewrite from scratch done around 2010 by William Hart, Sebastian Pancratz and Fredrik Johansson. Eventually, the 2.x series greatly expanded the scope of FLINT with new features such as finite fields (implemented by Mike Hansen) and multivariate polynomials (Daniel Schultz), just to mention two examples.

FLINT 3.0, released in 2023, merged three spin-off projects which were previously maintained as separate libraries: Arb and Calcium (started by Fredrik Johansson in 2012 and 2020), and Antic (started by William Hart in 2013). The author list below includes people who contributed to those projects.

If you believe there are names missing or if some information is incorrect, please contact us. See also the automatically-generated list of committers on GitHub.

Current maintainers

Major contributors


William Hart
William Hart
Project leader 2007-2022. Integer and polynomial arithmetic, factorisation and primality testing, SSA style FFT, square root, number fields, general infrastructure, maintenance. Supported by EPSRC Grant EP/G004870/1, DFG Priority programme SPP1489, H2020 OpenDreamKit, DFG SFB-TRR 195.

Fredrik Johansson
Fredrik Johansson
Matrices, polynomial and power series arithmetic, special functions, ball arithmetic, floating-point arithmetic, algebraic numbers, exact real and complex numbers, generic rings, optimisations, maintenance, website design. Supported by FWF Grant Y464-N18, ERC Starting Grant ANTICS 278537, ANR-20-CE48-0014 NuSCAP, Inria.

Daniel Schultz
Daniel Schultz
Multivariate polynomials, threadpool, matrix FFT, LLL improvements, CRT improvements, matrix-vector products, small prime FFT, many speedups and additional functions. Supported by H2020 OpenDreamKit, DFG SFB-TRR 195.
Sebastian Pancratz
Polynomial arithmetic over Z, Z/nZ and Q, p-adic and q-adic arithmetic, including polynomials and matrices. Design of FLINT 2.0. Supported by ERC Grant 204083.

Andy Novocin
Andy Novocin
LLL, polynomial factorisation over Z, polynomial composition.

Mike Hansen
Mike Hansen
Finite fields (small and large F_q), polynomials/matrices over F_q, Finite fields with Zech logarithm representation, fast factorisation of polynomials over F_q, template system. Supported by Macaulay2 developers NSF Grant 1002171.
Tom Bachmann
C++ expressions template wrapper, documentation parser. Supported by Google Summer of Code 2013.

Alex Best
Alex Best
Hermite Normal Form implementation including the Pernet-Stein algorithm and Smith Normal Form implementation including the Iliopoulos and Kannen-Bachem algorithms. Numerous improvements to nullspace, rref and rank computations and integer factoring and other improvements. Supported by Google Summer of Code 2014.

David Harvey
David Harvey
Fast Fourier Transform code, zn_poly for polynomial arithmetic over Z/nZ, mpz_poly, modular computation of Bernoulli numbers (bernmm), profiling and graphing code and many other parts of the FLINT library.
Lina Kulakova
Factorisation for polynomials over F_p for large p. Supported by Google Summer of Code 2012.
Abhinav Baid
LLL implementation, Ogita, Rump, Oishi dot product, Villard algorithm for LLL certification, Schwarz-Rutishauser algorithms for GSO and QR-decomposition. Supported by Google Summer of Code 2014.
Kushagra Singh
ECM and Pollard's Rho and quadratic sieve factoring algorithm implementations. Fast cube root and nth root code for word sized integers. Supported by Google Summer of Code 2015.

Pascal Molin
Pascal Molin
Arb discrete Fourier transform (DFT), Dirichlet characters, Dirichlet L-functions, discrete logarithm computation.
Jean Kieffer
Riemann theta functions in any dimension. Various utility functions. Supported by Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation.
Curtis Bright
Mentoring/planning of LLL implementation, numerous patches including 32 bit support.

Albin Ahlbäck
Albin Ahlbäck
Autotools-based build system, optimised assembly for integer multiplication, improvements to xgcd, improved fmpz functions for small inputs, uniformly distributed random numbers, CI improvements, documentation, header file cleanup, maintenance, many general bugfixes and improvements.
Isuru Fernando
Testing, build system maintenance, help merging the projects, other minor fixes. Support for CMake and MSVC builds.
Luca De Feo
Finite field embeddings.
Edouard Rousseau
Finite field embeddings.
Martin Lee
Fast factorisation of polynomials over Z/nZ, faster Brent-Kung modular composition.
Marc Mezzarobba
Fast evaluation of Legendre polynomials, work on the Arb interface in Sage, bug reports, feedback.
Tom Boothby
Improved factoring of unsigned longs, detection of perfect powers.
Andres Goens
F_q module and polynomials over F_q. Supported by DFG Priority program SPP1489.
Jan Tuitman
Helped with the p-adic interface.
Jason Papadopoulos
Block Lanczos code for quadratic sieve and multiprecision complex root finding code for polynomials.
Gonzalo Tornaria
Theta function module, Montgomery multiplication and significant contributions to the Z[x] modular multiplication code.
Burcin Erocal
Wrote the primary FLINT wrapper in the SAGE system (Robert Bradshaw also wrote a preliminary version of this and Martin Albrecht and others have also contributed to it.) Burcin also contributed by writing grant applications via his Lmonade organisation to Google. Supported by DFG Priority programme SPP1489.
Tommy Hofmann
Howell and strong echelon form, representation matrices, many utility functions and other improvements and bug fixes. FLINT integration in Nemo.
Ashish Kedia
Contributed an implementation of the Paterson-Stockmeyer algorithm.
Nitin Kumar
Quadratic sieve. Supported by Google Summer of Code 2015.
Vladimir Glazachev
APRCL primality testing, Shoup multiplication. Supported by Google Summer of Code 2015.
Daniel Roche
Contributed randprime and nextprime functions for the fmpz module and some minpoly code.
Shivin Shrivastava
Fibonacci polynomials and some Taylor shift improvements.
Ben Orchard
MSYS2 binary packages.
Thomas DuBuisson
Logical ops for fmpz module, patches to the build system.
Jean-Pierre Flori
Many build system patches and Sage integration. Code simplifications for Gauss periods, feedback.
Frithjof Schulze
Some fmpz functions and various patches.
Daniel Woodhouse
Contributed an implementation of multivariate multiplication over Z/nZ and used this to implement a fast "saturation" algorithm for Laurent polynomials.
Tomasz Lechowski
Contributed some NTL and Pari polynomial profiling code and researched algorithms for polynomials over finite fields. Supported by Nuffield Foundation.
Daniel Scott
Researched lazy and relaxed algorithms of Joris van der Hoeven. Supported by Warwick University's Undergraduate Research Scholars Scheme.
David Howden
Wrote code for computing Bernoulli numbers mod many primes, including fast polynomial multiplication over Z/pZ specifically for the task. Supported by Warwick University's Undergraduate Research Scholars Scheme.
Daniel Ellam
Helped design a module for p-adic arithmetic for FLINT. Supported by Warwick University's Undergraduate Research Scholars Scheme.
Richard Howell-Peak
Polynomial factorisation and irreducibility testing code for polynomials over Z/pZ. Supported by Warwick University's Undergraduate Research Scholars Scheme.
Peter Shrimpton
Wrote code for a basic prime sieve, Pocklington-Lehmer, Lucas, Fibonacci, BSPW and n-1 primality tests and a Weiferich prime search. Supported by The Nuffield Foundation.
Brian Gladman
MSVC support.
Dana Jacobsen
Tested BPSW primality code up to 2^64 against Feitma's tables and sped up and corrected n_is_prime and n_is_probabprime. Improvements to n_nextprime and n_isprime.
Anubhav Srivastava
Horizontal and vertical concatenation of matrices over Z, and an implementation of the Bodrato matrix squaring algorithm.
Dharak Kharod
Matrix content.
Prabhdeep Singh Walia
Matrix content.
Alena Sergeicheva
Contributed a patch to the build system for individual file testing and also contributed numerous matrix concatenation.
Alex Griffing
Integer factor refinement, sinc function, matrix trace, improved matrix squaring, boolean matrices, improved structured matrix exponentials, Cholesky decomposition, miscellaneous patches.
Vincent Delecroix
Power sums, various polynomial improvements, speedups, root counting and some patches. Work on Sage interface.
Aaditya Thakkar
Strassen multiplication over Z.
Ralf Stephan
Hermite polynomials, Laguerre polynomials, shifted Legendre polynomials, Gegenbauer polynomials. Improvements to inverse trigonometric functions.
Martin Raum
Kronecker product.
xoviat
CMake support.
Claus Fieker
Norms, improved rational solving, flint_abort, qadics without Conway polynomials, minor improvements and bug fixes.
Srivin Srivastava
Fibonacci polynomials, use of Taylor shift in linear composition, other minor contributions.
Jonathan Bober
Original code for Dirichlet characters, C++ compatibility fixes.
Timo Hartmann
Approximate computation of eigenvalues using the QR algorithm (original mpmath implementation used as a basis for the FLINT version).
Juan Arias de Reyna
Riemann-Siegel formula and Riemann zeta zeros (original mpmath implementation used as a basis for the FLINT version).
Ricky Farr
Some convenience functions.
arbguest
Preconditioned linear algebra algorithms.

D.H.J. Polymath
D.H.J. Polymath
Riemann xi function, Riemann zeta zeros.
Joel Dahne
Feedback and improvements for Legendre functions, nth derivatives for Arb polynomials, minmax function.
Vincent Neiger
Many utility functions for nmod_mat and associated modules.
Julian Rüth
Serialization support.
David Berghaus
Modular splitting evaluation of polynomials. Aliased window matrix multiplication.
Matthias Gessinger
Graeffe transforms.
Erik Postma
Improved handling of infinities and wide intervals in Arb functions.
Mathieu Gouttenoire
Primality testing for Gaussian integers.
Michael Abshoff
Original build system, project infrastructure.

Other contributors

The following people have contributed patches, bug reports, documentation improvements, or other significant support. The list is certainly incomplete.

Other credits

Citing FLINT

A general citation of the following form is recommended:

The FLINT team. FLINT: Fast Library for Number Theory, 2023. Version 3.0.0, https://flintlib.org.
@manual{flint,
    key = {FLINT},
    author = {The {FLINT} team},
    title = {{FLINT}: {F}ast {L}ibrary for {N}umber {T}heory},
    year = {2023},
    note = {Version 3.0.0, \url{https://flintlib.org}}
}

Please consider also looking up whether there is a paper discussing the specific feature(s) in FLINT which you are using. In many cases, there is such a paper! For example, research using the ball arithmetic component of FLINT (Arb) may cite:

F. Johansson. "Arb: efficient arbitrary-precision midpoint-radius interval arithmetic", IEEE Transactions on Computers, 66(8):1281-1292, 2017. DOI: 10.1109/TC.2017.2690633

Research using FLINT's number fields may cite:

William B. Hart. "ANTIC: Algebraic number theory in C", Computeralgebra-Rundbrief: Vol. 56, 2015

Many other references can be found in the bibliography of the FLINT documentation.

Last updated: 2024-04-21 12:36:41 GMT

Contact: Fredrik Johansson, flint-devel mailing list