Contents II Cache Awareness in Blocking Techniques 76 8

To date, data locality optimizing algorithms mostly aim at providing e cient strategies for blocking and reordering loops. But little research has been devoted to the nal step, i.e., computing the optimal block size. Optimal block sizes are currently computed as if a cache behaves as a local memory, i.e., cache interference phenomena are ignored. Case-studies have already shown that cache interferences can greatly a ect the optimal block size. The purpose of this paper is to propose a methodology for estimating interference misses in a regular do-loop nest, and use that knowledge to derive the optimal block size. First, the di erent types of interference phenomena are identi ed, and a method for predicting their occurrence and evaluating their impact is proposed. Second, current techniques for computing the optimal block size are analytically and experimentally shown to yield far below optimal performance. Third, cache interference phenomena and even TLB behavior are taken into account in the computation of the optimal block size, which proves to yield near-optimal performance, and consequently make blocking techniques safe. Reciprocally, it is also shown that even when no capacity miss occurs, blocking techniques can be used to signi cantly reduce the number of cache interferences.