Reproducible and Accurate Matrix Multiplication for High-Performance Computing

Sylvain Collange 1 David Defour 2 Stef Graillat 3 Roman Iakymchuk 3
1 ALF - Amdahl's Law is Forever
Inria Rennes – Bretagne Atlantique , IRISA-D3 - ARCHITECTURE
2 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
3 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : On modern multi-core, many-core, and heterogeneous architectures, floating-point computations may become non-deterministic and thus non-reproducible mainly due to non-associativity of floating-point operations. We introduce an algorithm to compute a product of two floating-point matrices that delivers reproducible results with the best possible accuracy. Our multi-level algorithm relies on fast vectorized floating-point expansions and as well as superaccumulators in a high-radix carry-save representation. We present implementations on recent Intel Xeon Phi accelerators and both AMD and NVIDIA GPUs.
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SCAN 2014 - 16th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, Sep 2014, Wuerzburg, Germany. 16th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, pp.42-43, 2014, 〈http://www.scan2014.uni-wuerzburg.de/start/〉
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Sylvain Collange, David Defour, Stef Graillat, Roman Iakymchuk. Reproducible and Accurate Matrix Multiplication for High-Performance Computing. SCAN 2014 - 16th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, Sep 2014, Wuerzburg, Germany. 16th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, pp.42-43, 2014, 〈http://www.scan2014.uni-wuerzburg.de/start/〉. 〈hal-01215627〉

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