Locality optimization of stencil applications using data dependency graphs

Abstract. This paper proposes tiling techniques based on data depen-dencies and not in code structure. The work presented here leverages and expands previous work by the authors in the domain of non traditional tiling for parallel applications. The main contributions of this paper are: (1) A formal description of tiling from the point of view of the data produced and not from the source code. (2) A mathematical proof for an optimum tiling in terms of maximum reuse for stencil applications, addressing the disparity between computation power and memory bandwidth for many-core architectures. (3) A description and implementation of our tiling technique for well known stencil applications. (4) Experimental evidence that confirms the effectiveness of the tiling proposed to alleviate the disparity between computation power and memory bandwidth for many-core architectures. Our experiments, performed using one of the first Cyclops-64 many-core chips produced, confirm the effectiveness of our approach to reduce the total number of memory operations of stencil applications as well as the running time of the application.