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High-level loop transformations are a key instrument in mapping computational kernels to effectively exploit resources in modern processor architectures. However, determining appropriate compositions of loop transformations to achieve this remains a significantly challenging task; current compilers may achieve significantly lower performance than hand-optimized programs. To address this fundamental challenge, we first present a convex characterization of all distinct, semantics-preserving,doi:10.1145/1926385.1926449 dblp:conf/popl/PouchetBBCRSV11 fatcat:h5y7lpv26fdhjcrmemweqffnxu