An Algebraic Approach to Cache Memory Characterization for Block Recursive Algorithms

Multiprocessor systems usually have cache or local memory in the memory hierarchy. Obtaining good performance on these systems requires that a program utilizes the cache ef-ciently. In this paper, we address the issue of generating eecient cache based algorithms from tensor product formulas. Tensor product formulas have been used for expressing block recursive algorithms like Strassen's matrix multiplication and fast Fourier transforms. These formulas can be translated into eecient parallel programs for shared and distributed memory multiprocessors. We analyze the utilization of a set associative cache for programs generated from ten-sor product formulas. Simulation results are shown to be consistent with the analysis. Strategies are presented to algebraically transform a formula such that the resulting program has a better cache utilization.