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High Performance Numerical Validation using Stochastic Arithmetic

Pacôme Eberhart 1, * Julien Brajard 2, 3 Pierre Fortin 1 Fabienne Jézéquel 4, 1
* Corresponding author
1 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
2 PARVATI - Processus de la variabilité climatique tropicale et impacts
LOCEAN - Laboratoire d'Océanographie et du Climat : Expérimentations et Approches Numériques
Abstract : 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.
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Pacôme Eberhart, Julien Brajard, Pierre Fortin, Fabienne Jézéquel. High Performance Numerical Validation using Stochastic Arithmetic . Reliable Computing, Springer Verlag, 2015, 21, pp.35-52. ⟨hal-01254446⟩

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