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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
Inria Rennes – Bretagne Atlantique , IRISA-D3 - ARCHITECTURE
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.
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Contributor : Roman Iakymchuk <>
Submitted on : Friday, April 10, 2015 - 12:06:27 PM
Last modification on : Monday, March 29, 2021 - 2:47:31 PM


  • HAL Id : hal-01140531, version 1


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. ⟨hal-01140531⟩



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