AIR: Iterative Refinement Acceleration using Arbitrary Dynamic Precision: Iterative refinement acceleration using arbitrary dynamic precision

JunKyu Lee*, Gregory Peterson, Dimitrios Nikolopoulos, Hans Vandierendonck

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

The increased degree of concurrent operations by lower precision arithmetic enables high performance for iterative refinement. Most of related work present statically defined mixed precision arithmetic approaches, while adapting a level of arithmetic precision dynamically in a loop with one-bit granularity can further improve the performance. This paper presents Arbitrary Dynamic Precision Iterative Refinement algorithm (AIR) that minimizes the total significand bit-width to solve iterative refinement. AIR detects the number of cancellation bits dynamically per iteration and uses the information to provide the least sufficient significand bit-width for the next iteration. We prove that AIR is a backward stable algorithm and can bring up to 2−3× speedups over a mixed precision iterative refinement depending on the characteristics of hardware. Our software demonstration shows that AIR requires only 83% of the significand bits required by mixed precision iterative refinement that solve linear systems for double precision accuracy for backward error with 32 × 32 standard normally distributed matrices.

Original languageEnglish
Article number102663
JournalParallel Computing
Volume97
Early online date01 Jun 2020
DOIs
Publication statusPublished - Sep 2020

Keywords

  • Acceleration
  • Adaptive system
  • Arbitrary precision
  • Dynamic precision
  • High performance
  • Iterative refinement

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computer Networks and Communications
  • Computer Graphics and Computer-Aided Design
  • Artificial Intelligence

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