HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Conference papers

Reproducibility and Accuracy for High-Performance Computing

Roman Iakymchuk 1, 2 Caroline 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.
Complete list of metadata

Contributor : Roman Iakymchuk Connect in order to contact the contributor
Submitted on : Friday, April 10, 2015 - 12:06:27 PM
Last modification on : Thursday, December 16, 2021 - 2:04:02 PM


  • HAL Id : hal-01140531, version 1


Roman Iakymchuk, Caroline 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⟩



Record views


Files downloads