Tessellating Star Stencils

Stencil computations represent a very common class of nested loops in scientific and engineering applications. The exhaustively studied tiling is one of the most powerful transformation techniques to explore the data locality and parallelism. Existing work often uniformly handles different stencil shapes. This paper first presents a concept called natural block to identify the difference between the star and box stencils. Then we propose anew two-level tessellation scheme for star stencils, where the natural block, as well as its successors can tessellate the spatial space and their extensions along the time dimension are able to form a tessellation of the iteration space. Furthermore, a novel implementation technique called double updating is developed for star stencils specifically to improve the in-core data reuse pattern. Evaluation results are provided that demonstrate the effectiveness of the approach.