Fully Empirical Autotuned QR Factorization For Multicore Architectures

TL;DR

This paper presents a fully empirical, automatic tuning method for dense QR factorization on multicore architectures, achieving near-optimal performance quickly without relying on complex models.

Contribution

It introduces a novel empirical approach that efficiently prunes the search space for autotuning QR factorization on multicore systems, enabling fast and reliable performance optimization.

Findings

Tuning completes in less than 10 minutes on most platforms.

Achieves 97-100% of the optimal performance.

Method is applicable to multiple hardware architectures.

Abstract

Tuning numerical libraries has become more difficult over time, as systems get more sophisticated. In particular, modern multicore machines make the behaviour of algorithms hard to forecast and model. In this paper, we tackle the issue of tuning a dense QR factorization on multicore architectures. We show that it is hard to rely on a model, which motivates us to design a fully empirical approach. We exhibit few strong empirical properties that enable us to efficiently prune the search space. Our method is automatic, fast and reliable. The tuning process is indeed fully performed at install time in less than one and ten minutes on five out of seven platforms. We achieve an average performance varying from 97% to 100% of the optimum performance depending on the platform. This work is a basis for autotuning the PLASMA library and enabling easy performance portability across hardware systems.