Section: Partnerships and Cooperations
National Initiatives
ANR HPAC Project
Participants : ClaudePierre Jeannerod, Nicolas Louvet, Clément Pernet, Nathalie Revol, Damien Stehlé, Philippe Théveny, 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 TaMaDi Project
Participants : Nicolas Brisebarre, Florent de Dinechin, Guillaume Hanrot, Vincent Lefèvre, JeanMichel Muller, Damien Stehlé, Serge Torres.
The TaMaDi project (Table Maker's Dilemma, 20102013) was funded by the ANR and headed by JeanMichel Muller. It started in October 2010 and ended in October 2013. The other French teams involved in the project are the Marelle teamproject of Inria Sophia AntipolisMéditerranée, and the PEQUAN team of LIP6 lab., Paris.
The aim of the project was to find “hardest to round” (HR) cases for the most common functions and floatingpoint formats. In floatingpoint (FP) arithmetic having fully specified “atomic” operations is a keyrequirement for portable, predictable, and provable numerical software. Since 1985, the four arithmetic operations and the square root are IEEE specified (it is required that they should be correctly rounded: the system must always return the floatingpoint number nearest the exact result of the operation). This is not fully the case for the basic mathematical functions (sine, cosine, exponential, etc.). Indeed, the same function, on the same argument value, with the same format, may return significantly different results depending on the environment. As a consequence, numerical programs using these functions suffer from various problems. The lack of specification is due to a problem called the Table Maker's Dilemma (TMD). To compute $f\left(x\right)$ in a given format, where $x$ is a FP number, we must first compute an approximation to $f\left(x\right)$ with a given precision, which we round to the nearest FP number in the considered format. The problem is the following: finding what the accuracy of the approximation must be to ensure that the obtained result is always equal to the “exact” $f\left(x\right)$ rounded to the nearest FP number. In the last years, our teamproject and the CACAO teamproject of Inria NancyGrand Est designed algorithms for finding hardesttoround cases. These algorithms do not allow to tackle with large formats. The TaMaDi project mainly focuses on three aspects:

big precisions: we must get new algorithms for dealing with precisions larger than double precision. Such precisions will become more and more important (even if double precision may be thought as more than enough for a final result, it may not be sufficient for the intermediate results of long or critical calculations);

formal proof: we must provide formal proofs of the critical parts of our methods. Another possibility is to have our programs generating certificates that show the validity of their results. We should then focus on proving the certificates;

aggressive computing: the methods we have designed for generating HR points in double precision require weeks of computation on hundreds of PCs. Even if we design faster algorithms, we must massively parallelize our methods, and study various ways of doing that.
The various documents on the project can be found at http://tamadiwiki.enslyon.fr/tamadiwiki/index.php/Main_Page .
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 highperformance numerical codes. Numerical validation is one aspect of the project, the second one regards numerical reproducibility.