Reproducibility and Accuracy for High-Performance Computing

Roman Iakymchuk 1, 2 Sylvain Collange 3 David Defour 4 Stef Graillat 2
2 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
3 ALF - Amdahl's Law is Forever
IRISA-D3 - ARCHITECTURE, Inria Rennes – Bretagne Atlantique
4 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : On modern multi-core, many-core, and heterogeneous architectures, floating-point computations, especially reductions, may become non-deterministic and, therefore, non-reproducible mainly due to the non-associativity of floating-point operations. We introduce an approach to compute the correctly rounded sums of large floating-point vectors accurately and efficiently, achieving deterministic results by construction. Our multi-level algorithm consists of two main stages: a filtering stage that relies on fast vectorized floating-point expansions, and an accumulation stage based on superaccumulators in a high-radix carry-save representation. We extend this approach to dot product and matrix-matrix multiplication. In this talk, I will present the reproducible and accurate (rounding to the nearest) algorithms for summation, dot product, and matrix-matrix multiplication as well as their implementations in parallel environments such as Intel server CPUs, Intel Xeon Phi, and both NVIDIA and AMD GPUs. I will show that the performance of our algorithms is comparable with the standard implementations.
Type de document :
Communication dans un congrès
RAIM: Rencontres Arithmétiques de l’Informatique Mathématique, Apr 2015, Rennes, France. 2015
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https://hal.archives-ouvertes.fr/hal-01140531
Contributeur : Roman Iakymchuk <>
Soumis le : vendredi 10 avril 2015 - 12:06:27
Dernière modification le : lundi 9 octobre 2017 - 15:32:12

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  • HAL Id : hal-01140531, version 1

Citation

Roman Iakymchuk, Sylvain Collange, David Defour, Stef Graillat. Reproducibility and Accuracy for High-Performance Computing. RAIM: Rencontres Arithmétiques de l’Informatique Mathématique, Apr 2015, Rennes, France. 2015. 〈hal-01140531〉

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