Section: Partnerships and Cooperations

National Initiatives

ANR HPAC Project

Participants : Claude-Pierre Jeannerod, Nicolas Louvet, Clément Pernet, Nathalie Revol, Philippe Théveny, Gilles Villard.

“High-performance Algebraic Computing” (HPAC) is a four year ANR project that started in January 2012. The Web page of the project is http://hpac.gforge.inria.fr/ . HPAC is headed by Jean-Guillaume Dumas (CASYS team, LJK laboratory, Grenoble); it involves AriC as well as the Inria project-team MOAIS (LIG, Grenoble), the Inria project-team PolSys (LIP6 lab., Paris), the ARITH group (LIRMM laboratory, Montpellier), and the HPC Project company.

The overall ambition of HPAC is to provide international reference high-performance libraries for exact linear algebra and algebraic systems on multi-processor architecture and to influence parallel programming approaches for algebraic computing. The central goal is to extend the efficiency of the LinBox and FGb libraries to new trend parallel architectures such as clusters of multi-processor systems and graphics processing units in order to tackle a broader class of problems in lattice-based cryptography and algebraic cryptanalysis. HPAC conducts researches along three axes:

• A domain specific parallel language (DSL) adapted to high-performance algebraic computations;

• Parallel linear algebra kernels and higher-level mathematical algorithms and library modules;

• Library composition, their integration into state-of-the-art software, and innovative high performance solutions for cryptology challenges.

ANR DYNA3S Project

Participants : Guillaume Hanrot, Gilles Villard.

Dyna3s is a four year ANR project that started in October 2013. The Web page of the project is http://www.liafa.univ-paris-diderot.fr/dyna3s/ . It is headed by Valérie Berthé (U. Paris 7) and involves also the University of Caen.

The aim is to study algorithms that compute the greatest common divisor (gcd) from the point of view of dynamical systems. A gcd algorithm is considered as a discrete dynamical system by focusing on integer input. We are mainly interested in the computation of the gcd of several integers. Another motivation comes from discrete geometry, a framework where the understanding of basic primitives, discrete lines and planes, relies on algorithm of the Euclidean type.

ANR FastRelax Project

Participants : Nicolas Brisebarre, Guillaume Hanrot, Vincent Lefèvre, Jean-Michel Muller, Bruno Salvy, Serge Torres, Silviu Filip, Sébastien Maulat.

FastRelax stands for “Fast and Reliable Approximation”. It is a four year ANR project started in October 2014. The web page of the project is http://fastrelax.gforge.inria.fr/ . It is headed by B. Salvy and involves AriC as well as members of the Marelle Team (Sophia), of the Mac group (LAAS, Toulouse), of the Specfun and Toccata Teams (Saclay), as well as of the Pequan group in UVSQ and a colleague in the Plume group of LIP.

The aim of this project is to develop computer-aided proofs of numerical values, with certified and reasonably tight error bounds, without sacrificing efficiency. Applications to zero-finding, numerical quadrature or global optimization can all benefit from using our results as building blocks. We expect our work to initiate a “fast and reliable” trend in the symbolic-numeric community. This will be achieved by developing interactions between our fields, designing and implementing prototype libraries and applying our results to concrete problems originating in optimal control theory.

PEPS Quarenum

Participants : Nicolas Louvet, Nathalie Revol.

“Quarenum” is an abbreviation for Qualité et Reproductibilité Numériques dans le Calcul Scientifique Haute Performance. This project focuses on the numerical quality of scientific software, more precisely of high-performance numerical codes. Numerical validation is one aspect of the project, the second one regards numerical reproducibility.