Applying the Polyhedral Model to Tile Time Loops in Devito

TL;DR

This paper introduces a polyhedral model-based loop tiling optimization for Devito-generated code, significantly reducing runtime by improving data reuse and automating the optimization process.

Contribution

It presents a novel loop tiling method using the polyhedral model specifically for Devito, enhancing performance and automation in finite-difference code generation.

Findings

Up to 27.5% runtime reduction with tiling optimization

Effective data reuse leading to decreased memory traffic

Automation options integrated into Devito framework

Abstract

The run time of many scientific computation applications for numerical methods is heavily dependent on just a few multi-dimensional loop nests. Since these applications are often limited by memory bandwidth rather than computational resources they can benefit greatly from any optimizations which decrease the run time of their loops by improving data reuse and thus reducing the total memory traffic. Some of the most effective of these optimizations are not suitable for development by hand or require advanced software engineering knowledge which is beyond the level of many researchers who are not specialists in code optimization. Several tools exist to automate the generation of high-performance code for numerical methods, such as Devito which produces code for finite-difference approximations typically used in the seismic imaging domain. We present a loop-tiling optimization which can be applied to Devito-generated loops and improves run time by up to 27.5%, and options for automating this optimization in the Devito framework.