Tuning Technique for Multiple Precision Dense Matrix Multiplication using Prediction of Computational Time

TL;DR

This paper proposes a prediction-based tuning technique to optimize multiple precision dense matrix multiplication, significantly reducing tuning time across various precisions, sizes, and parallelization levels.

Contribution

It introduces a novel method that predicts computational times for different block sizes to efficiently select optimal matrix multiplication configurations.

Findings

Prediction-based tuning reduces optimization time.

Method achieves efficient performance across multiple precisions.

Applicable to various matrix sizes and parallelization levels.

Abstract

Although reliable long precision floating-point arithmetic libraries such as QD and MPFR/GMP are necessary to solve ill-conditioned problems in numerical simulation, long precision BLAS-level computation such as matrix multiplication has not been fully optimized because tuning costs are very high compared to IEEE float and double precision arithmetic. In this study, we develop a technique to shorten this tuning time by using prediction of computational times in several block sizes for the blocking algorithm, and then selecting the fastest matrix multiplication method for tuning multiple precision dense real matrix multiplication in various precisions, matrix sizes, and degrees of parallelization.