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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 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 language | English |
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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 Computer-Aided Design
- Artificial Intelligence

## Fingerprint 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