ANR HPAC Project

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

ANR TaMaDi Project

Participants : Nicolas Brisebarre, Florent de Dinechin, Guillaume Hanrot, Vincent Lefèvre, Jean-Michel Muller, Damien Stehlé, Serge Torres.

The TaMaDi project (Table Maker's Dilemma, 2010-2013) was funded by the ANR and headed by Jean-Michel Muller. It started in October 2010 and ended in October 2013. The other French teams involved in the project are the Marelle team-project of Inria Sophia Antipolis-Méditerranée, 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 floating-point formats. In floating-point (FP) arithmetic having fully specified “atomic” operations is a key-requirement 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 floating-point 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 team-project and the CACAO team-project of Inria Nancy-Grand Est designed algorithms for finding hardest-to-round cases. These algorithms do not allow to tackle with large formats. The TaMaDi project mainly focuses on three aspects:

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.