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This paper studies two variants of tiling: iteration space tiling (or loop blocking) and cache-oblivious methods that recursively split the iteration space with divide-and-conquer. The key question to answer is when we should be using one over the other. The answer to this question is complicated for modern architecture due to a number of reasons. In this paper, we present a detailed empirical study to answer this question for a range of kernels that fit the polyhedral model. Our study is basedarXiv:1802.00166v1 fatcat:tsnkzovxmzdg5pbo3lotif3hoe