Time-minimal tiling when rise is larger than zero

Abstract. This paper presents a solution to the open problem of finding the optimal tile size to minimise the execution time of a parallelogram-shaped iteration space on a distributed memory machine when the rise of the tiled iteration space is larger than zero. Based on a new communication cost model, which accounts for computation and communication overlap for tiled programs, the problem is formulated as a discrete non-linear optimisation problem and the closed-form optimal tile size is derived. Our experimental results show that the execution times when optimal tile sizes are used are close to the experimentally best. The proposed technique can be used for hand tuning parallel codes and in optimising compilers.