On optimal temporal locality of stencil codes

Iterative solvers such as the Jacobi and Gauss-Seidel relaxation methods are important, but time-consuming building blocks of many scientific and engineering applications. The performance problems are largely due to cache misses, and can be reduced by tiling the codes. Whereas previous research has shown the usefulness of tiling by experimentally comparing the run times of tiled and original codes, it did not tackle the question as to whether further improvements are possible. In this paper, we give a negative answer, regarding the exploitation of temporal locality in one step of a 2dimensional stencil code. We derive upper and lower bounds that match up to a factor of about 1 + 2/M, where M is the cache size. For the upper bounds, we investigate some modifications of tiling.

• Type: Journal
• Year: 2002
• Where: SAC
• Authors: Claudia Leopold
• Keywords: Applied Computing, Gauss-Seidel Relaxation Methods, Iterative Solvers, SAC 2002, Time-consuming Building