- CADO-NFS, an implementation of the number field sieve for integer factorization, registered at APP under number IDDN.FR.001.150006.000.S.P.2010.000.10000.
- GF2X
[gitlab],
a library for multiplication in GF(2)[x] (with Richard P. Brent,
Pierrick Gaudry and Emmanuel Thomé).
Also contains code to search for irreducible trinomials over GF(2)
[replaces and superseedes the
`irred-ntl`code]. -
mul_fft-6.1.2.tgz, a GMP-based implementation of
Schönhage-Strassen's large integer multiplication algorithm
(with Pierrick Gaudry and Alexander Kruppa). This code is up to
26%
faster than the one distributed within GMP 6.1.2. It was used by
Andrew Sutherland to set a new record for
genus 1
point-counting over a prime field.
See also the mirror
on Gaudry's web page.
A fixed-length FFT code is
also available for length 2
^{6}[see corresponding mail]. - GMP-ECM: an implementation of Lenstra's Elliptic Curve Method to factor integers. See also the ECMNET page.
- MPC [development version], a library for multiprecision complex arithmetic with exact rounding, based on the MPFR and GNU MP libraries [with Andreas Enge, Philippe Théveny and Patrick Pélissier]
- MPFR: a library for multiple-precision floating-point computation with correct rounding [compiler bugs revealed by MPFR]

- check_exhaustive.c, check_sample.c, check_sample2.c: programs to find large errors of mathematical functions.

- hjacobi.c implements an O(M(n) log n) algorithm for the Jacobi symbol (joint work with Richard Brent).
- double_fac_ui.c implements the double factorial (see this and that).
- WCLR implements the algorithm described in the articles Worst Cases and Lattice Reduction (with Vincent Lefèvre). It is now superseeded by Bacsel (with Guillaume Hanrot, Vincent Lefèvre, and Damien Stehlé) [gitlab]
- DPE, a library for floating-point arithmetic with large exponents (double-precision + exponent), developed with Patrick Pélissier. [Software Heritage archive, cf this paper]
- Epelle: a generic spell-checking mechanism, including a french dictionary (but it can be used for any language, as soon as you have a dictionary).
- intersectplot.mpl, a Maple program to plot the intersection of two 3D surfaces given by implicit equations (with Sylvain Petitjean)
- An implementation of LLL in GMP, translated from that from the NTL library from Victor Shoup
- Lambda-Upsilon-Omega V2.1, an automatic average-case program analyzer developed with Bruno Salvy. This version corrects a problem with Caml-Light 0.74. See also the LUO page from the Algo project.
- MPCHECK 1.1.0, with Nathalie Revol and Patrick Pélissier, a program to check mathematical function libraries (correct rounding, monotonicity, symmetry, output range). [results] Warning: version 1.1.0 only works for the double type (53 bits). [gitlab]
- A sample implementation of MPQS, reusing some nice sieving code written by Scott Contini
- MuPAD, a symbolic computation system I have contributed to in 1994-1995. Unfortunately it never became free, contrary to what was originally planned.
- A program for digital plane recognition (with Yan Gérard and Isabelle Debled-Rennesson)
- An implementation of PSLQ in GMP.
- shift2.c, a implementation in GNU MP of an asymptotically fast algorithm for Taylor shift. Werner Krandick reports a speedup factor of 319 for degree 9,000 and coefficients of 9,000 bits, over von zur Gathen's and Gerhard's convolution method. This work was inspired by High-Performance Implementations of the Descartes Method, by Jeremy R. Johnson, Werner Krandick, Kevin M. Lynch, David G. Richardson, and Anatole D. Ruslanov.
- An implementation in GMP of the Bodrato-Zanoni algorithm for Toom-Cook 4-way. Bodrato and Zanoni extended this to Toom-Cook 5-way, 6-way and 7-way
- A GMP-based implementation of Uspensky's algorithm
(joint work with Fabrice Rouillier)
to isolate all real roots of a polynomial with integer coefficients.
A revised implementation
is available in CADO-NFS
(directory utils, file usp.c).
You might also check the file
src/libqi/kernel/QISolve.cc from the QI library.