Cache Oblivious Strategies to Exploit Multi-Level Memory on Manycore Systems

Many-core systems are beginning to feature novel large, high-bandwidth intermediate memory as a visible part of the memory hierarchy. This paper discusses how to make use of intermediate memory when composing matrix multiply with transpose to compute $A$ * AT. We re-purpose the cache-oblivious approach developed by Frigo et al. and apply it to the composition of a bandwidth-bound kernel (transpose) with a compute-bound kernel (matrix multiply). Particular focus is on regions of matrix shapes far from square that are not usually considered. Our codes are simpler than optimized codes, but reasonably close in performance. Also, perhaps of more importance is developing a paradigm for how to construct other codes using intermediate memories.