Optimal Temporal Blocking for Stencil Computation

Temporal blocking is a class of algorithms which reduces the required memory bandwidth (B/F ratio) of a given stencil computation, by "blocking" multiple time steps. In this paper, we prove that a lower limit exists for the reduction of the B/F attainable by temporal blocking, under certain conditions. We introduce the PiTCH tiling, an example of temporal blocking method that achieves the optimal B/F ratio. We estimate the performance of PiTCH tiling for various stencil applications on several modern CPUs. We show that PiTCH tiling achieves 1.5 similar to 2 times better B/F reduction in three-dimensional applications, compared to other temporal blocking schemes. We also show that PiTCH tiling can remove the bandwidth bottleneck from most of the stencil applications considered.