A new multiplication algorithm for extended precision using floating-point expansions - Archive ouverte HAL Access content directly
Conference Papers Year : 2016

A new multiplication algorithm for extended precision using floating-point expansions

Abstract

Some important computational problems must use a floating-point (FP) precision several times higher than the hardware-implemented available one. These computations critically rely on software libraries for high-precision FP arithmetic. The representation of a high-precision data type crucially influences the corresponding arithmetic algorithms. Recent work showed that algorithms for FP expansions, that is, a representation based on unevaluated sum of standard FP types, benefit from various high-performance support for native FP, such as low latency, high throughput, vectorization, threading, etc. Bailey's QD library and its corresponding Graphics Processing Unit (GPU) version, GQD, are such examples. Despite using native FP arithmetic as the key operations, QD and GQD algorithms are focused on double-double or quad-double representations and do not generalize efficiently or naturally to a flexible number of components in the FP expansion. In this paper, we introduce a new multiplication algorithm for FP expansion with flexible precision, up to the order of tens of FP elements in mind. The main feature consists in the partial products being accumulated in a special designed data structure that has the regularity of a fixed-point representation while allowing the computation to be naturally carried out using native FP types. This allows us to easily avoid unnecessary computation and to present rigorous accuracy analysis transparently. The algorithm, its correctness and accuracy proofs and some performance comparisons with existing libraries are all contributions of this paper.
Fichier principal
Vignette du fichier
ARITH23-CamReady.pdf (303.61 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01298195 , version 1 (05-04-2016)

Identifiers

  • HAL Id : hal-01298195 , version 1

Cite

Jean-Michel Muller, Valentina Popescu, Ping Tak Peter Tang. A new multiplication algorithm for extended precision using floating-point expansions. ARITH23, Jul 2016, Santa Clara, United States. ⟨hal-01298195⟩
243 View
400 Download

Share

Gmail Mastodon Facebook X LinkedIn More