Accuracy Versus Time: A Case Study with Summation Algorithms

Philippe Langlois (1) , Matthieu Martel (1) , Laurent Thévenoux (1)

1 ELIAUS - Electronique, Informatique, Automatique et Systèmes

In this article, we focus on numerical algorithms for which, in practice, parallelism and accuracy do not cohabit well. In order to increase parallelism, expressions are reparsed implicitly using mathematical laws like associativity and this reduces the accuracy. Our approach consists in performing an exhaustive study: we generate all the algorithms equivalent to the original one and compatible with our relaxed time constraint. Next we compute the worst errors which may arise during their evaluation, for several relevant sets of data. Our main conclusion is that relaxing very slightly the time constraints by choosing algorithms whose critical paths are a bit longer than the optimal makes it possible to strongly optimize the accuracy. We extend these results to the case of bounded parallelism and to accurate sum algorithms that use compensation techniques.

Domaines: Arithmétique des ordinateurs; Performance et fiabilité [cs.PF]

Philippe Langlois, Matthieu Martel, Laurent Thévenoux. Accuracy Versus Time: A Case Study with Summation Algorithms. PASCO'10 : Parallel Symbolic Computation 2010, Jul 2010, Grenoble, France. pp.121-130, ⟨10.1145/1837210.1837229⟩. ⟨hal-00477511⟩