High Performance Numerical Validation using Stochastic Arithmetic

Pacôme Eberhart (1) , Julien Brajard (2, 3) , Pierre Fortin (1) , Fabienne Jézéquel (4, 1)

1 PEQUAN - Performance et Qualité des Algorithmes Numériques
2 PARVATI - Processus de la variabilité climatique tropicale et impacts
3 Clime - Coupling environmental data and simulation models for software integration
4 UP2 - Université Panthéon-Assas

In the context of high performance computing, numerical validation becomes increasingly important because of the higher level of parallelism and of the large number of operations. Our approach, Discrete Stochastic Arithmetic, implemented through the CADNA library, has however a high overhead on execution time, especially for very optimised applications, and does not enable the use of vector instructions. In this paper, we present a new CADNA version that will reduce this overhead by up to 85% for both simple and more realistic benchmarks. This new version also enables the use of vector instructions for an additional speedup between 2.5 and 3 times on the AVX2 instruction set extension.

Mots clés: SIMD; HPC; rounding errors; numerical validation; Discrete Stochastic Arithmetic

Domaines: Modélisation et simulation

Pacôme Eberhart, Julien Brajard, Pierre Fortin, Fabienne Jézéquel. High Performance Numerical Validation using Stochastic Arithmetic . Reliable Computing, 2015, 21, pp.35-52. ⟨hal-01254446⟩