Choosing a twice more accurate dot product implementation

Stef Graillat; Philippe Langlois; Nicolas Louvet

Choosing a twice more accurate dot product implementation

Stef Graillat ¹ Philippe Langlois Nicolas Louvet

1 PEQUAN - Performance et Qualité des Algorithmes Numériques

LIP6 - Laboratoire d'Informatique de Paris 6

Abstract : The fused multiply and add (FMA) operation computes a floating point multiplication followed by an addition or a subtraction as a single floating point operation. Intel IA-64, IBM RS/6000 and PowerPC architectures implement this FMA operation. The aim of this talk is to study how the FMA improves the computation of dot product with classical and compensated algorithms. The latters double the accuracy of the former at the same working precision. Six algorithms are considered. We present associated theoretical error bounds. Numerical experiments illustrate the actual efficiency in terms of accuracy and running time. We show that the FMA does not improve in a significant way the accuracy of the result whereas it increases significantly the actual speed of the algorithms.

Document type :

Conference papers

Domain :

Computer Science [cs]

Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01351480
Contributor : Lip6 Publications <>
Submitted on : Wednesday, November 21, 2018 - 1:05:07 PM
Last modification on : Thursday, March 21, 2019 - 2:44:24 PM
Long-term archiving on : Friday, February 22, 2019 - 2:19:25 PM

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