Section: Partnerships and Cooperations
National Initiatives
ANR HPAC Project
Participants : ClaudePierre Jeannerod, Nicolas Louvet, Clément Pernet, Nathalie Revol, Gilles Villard.
“Highperformance 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 JeanGuillaume Dumas (CASYS team, LJK laboratory, Grenoble); it involves AriC as well as the Inria projectteam MOAIS (LIG, Grenoble), the Inria projectteam 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 highperformance libraries for exact linear algebra and algebraic systems on multiprocessor 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 multiprocessor systems and graphics processing units in order to tackle a broader class of problems in latticebased cryptography and algebraic cryptanalysis. HPAC conducts researches along three axes:

A domain specific parallel language (DSL) adapted to highperformance algebraic computations;

Parallel linear algebra kernels and higherlevel mathematical algorithms and library modules;

Library composition, their integration into stateoftheart 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.univparisdiderot.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, JeanMichel 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 computeraided proofs of numerical values, with certified and reasonably tight error bounds, without sacrificing efficiency. Applications to zerofinding, 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 symbolicnumeric 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.
ANR MetaLibm Project
Participants : ClaudePierre Jeannerod, JeanMichel Muller.
MetaLibm is a fouryear project (started in October 2013) focused on the design and implementation of code generators for mathematical functions and filters. The web page of the project is http://www.metalibm.org/ANRMetaLibm/ . It is headed by Florent de Dinechin (INSA Lyon and Socrate team) and, besides Socrate and AriC, also involves teams from LIRMM (Perpignan), LIP6 (Paris), CERN (Geneva), and Kalray (Grenoble). The main goals of the project are to automate the development of mathematical libraries (libm), to extend it beyond standard functions, and to make it unified with similar approaches developed in or useful for signal processing (filter design). Within AriC, we are especially interested in studying the properties of fixedpoint arithmetic and floatingpoint arithmetic that can help develop such a framework.