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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 onebit granularity can further improve the performance. This paper presents Arbitrary Dynamic Precision Iterative Refinement algorithm (AIR) that minimizes the total significand bitwidth to solve iterative refinement. AIR detects the number of cancellation bits dynamically per iteration and uses the information to provide the least sufficient significand bitwidth 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 language  English 

Article number  102663 
Journal  Parallel Computing 
Volume  97 
Early online date  01 Jun 2020 
DOIs  
Publication status  Published  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 ComputerAided Design
 Artificial Intelligence
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Dive into the research topics of 'AIR: Iterative Refinement Acceleration using Arbitrary Dynamic Precision: Iterative refinement acceleration using arbitrary dynamic precision'. Together they form a unique fingerprint.Projects
 2 Active

R6584CSC: Energy Efficient Trransprecision Techniques for Linear system Solvers
09/04/2018 → …
Project: Research

R6551CSC: Open TransPREcision COMPuting
Woods, R., Karakonstantis, G. & Vandierendonck, H.
03/11/2016 → …
Project: Research