Parallel floating-point expansions for extended-precision GPU computations

Caroline Collange (1) , Mioara Joldes (2, 3) , Jean-Michel Muller (3, 4) , Valentina Popescu (4, 5)

1 PACAP - Pushing Architecture and Compilation for Application Performance
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
3 CNRS - Centre National de la Recherche Scientifique
4 ARIC - Arithmetic and Computing
5 ENS de Lyon - École normale supérieure de Lyon

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.

Mots clés: parallel computations; graphics processing unit; multiple-precision arithmetic; floating-point arithmetic; high precision arithmetic; floating-point expansions

Domaines: Arithmétique des ordinateurs; Calcul parallèle, distribué et partagé [cs.DC]

Caroline 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-01298206⟩