Hybrid static/dynamic scheduling for already optimized dense matrix factorization

TL;DR

This paper introduces a hybrid static/dynamic scheduling strategy for dense matrix factorization that improves performance by balancing data locality and load, outperforming existing static, dynamic, and library routines.

Contribution

The paper proposes a novel hybrid static/dynamic scheduling method for dense matrix factorization that achieves significant performance improvements over fully static, fully dynamic, and existing library routines.

Findings

Up to 64% performance improvement over fully dynamic CALU on AMD NUMA.

Up to 30% improvement over fully static CALU on AMD NUMA.

Speedups of up to 110% over MKL and 82% over PLASMA.

Abstract

We present the use of a hybrid static/dynamic scheduling strategy of the task dependency graph for direct methods used in dense numerical linear algebra. This strategy provides a balance of data locality, load balance, and low dequeue overhead. We show that the usage of this scheduling in communication avoiding dense factorization leads to significant performance gains. On a 48 core AMD Opteron NUMA machine, our experiments show that we can achieve up to 64% improvement over a version of CALU that uses fully dynamic scheduling, and up to 30% improvement over the version of CALU that uses fully static scheduling. On a 16-core Intel Xeon machine, our hybrid static/dynamic scheduling approach is up to 8% faster than the version of CALU that uses a fully static scheduling or fully dynamic scheduling. Our algorithm leads to speedups over the corresponding routines for computing LU factorization in well known libraries. On the 48 core AMD NUMA machine, our best implementation is up to 110% faster than MKL, while on the 16 core Intel Xeon machine, it is up to 82% faster than MKL. Our approach also shows significant speedups compared with PLASMA on both of these systems.