Algorithm 979: Recursive Algorithms for Dense Linear Algebra -- The ReLAPACK Collection

TL;DR

This paper introduces ReLAPACK, an open-source library of recursive algorithms for dense linear algebra that simplifies tuning and often outperforms traditional blocked algorithms and optimized libraries.

Contribution

ReLAPACK provides a collection of recursive algorithms that replace blocked LAPACK routines, achieving high performance with minimal tuning effort.

Findings

ReLAPACK outperforms reference LAPACK in many scenarios.

ReLAPACK surpasses the performance of optimized libraries.

Recursive algorithms require less tuning than blocked algorithms.

Abstract

To exploit both memory locality and the full performance potential of highly tuned kernels, dense linear algebra libraries such as LAPACK commonly implement operations as blocked algorithms. However, to achieve next-to-optimal performance with such algorithms, significant tuning is required. On the other hand, recursive algorithms are virtually tuning free, and yet attain similar performance. In this paper, we first analyze and compare blocked and recursive algorithms in terms of performance, and then introduce ReLAPACK, an open-source library of recursive algorithms to seamlessly replace most of LAPACK's blocked algorithms. In many scenarios, ReLAPACK clearly outperforms reference LAPACK, and even improves upon the performance of optimizes libraries.