Parallel floating-point expansions for extended-precision GPU computations

Sylvain Collange 1 Mioara Joldes 2, 3 Jean-Michel Muller 3, 4 Valentina Popescu 4, 5
1 PACAP - Pushing Architecture and Compilation for Application Performance
Inria Rennes – Bretagne Atlantique , IRISA-D3 - ARCHITECTURE
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes [Toulouse]
4 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : GPUs are an important hardware development platform for problems where massive parallel computations are needed. Many of these problems require a higher precision than the standard double floating-point (FP) available. One common way of extending the precision is the multiple-component approach, in which real numbers are represented as the unevaluated sum of several standard machine precision FP numbers. This representation is called a FP expansion and it offers the simplicity of using directly available and highly optimized FP operations. In this article we present new data-parallel algorithms for adding and multiplying FP expansions specially designed for extended precision computations on GPUs. These are generalized algorithms that can manipulate FP expansions of different sizes (from double-double up to a few tens of doubles) and ensure a certain worst case error bound on the results.
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Sylvain Collange, Mioara Joldes, Jean-Michel Muller, Valentina Popescu. Parallel floating-point expansions for extended-precision GPU computations. The 27th Annual IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP), Jul 2016, London, United Kingdom. ⟨hal-01298206v2⟩

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