Joint Scheduling and Layout Optimization to Enable Multi-Level Vectorization

We describe a novel loop nest scheduling strategy implemented in the R-Stream compiler 1 : the first scheduling formulation to jointly optimize a trade-off between parallelism, locality, contiguity of array accesses and data layout permutations in a single complete formulation. Our search space contains the maximal amount of vectorization in the program and automatically finds opportunities for automatic multi-level vectorization and simd-ization. Using our model of memory layout, we demonstrate that the amount of contiguous accesses, vectorization and simd-ization can be increased modulo data layout permutations automatically exposed by our technique. This additional degree of freedom opens new opportunities for the scheduler that were previously out of reach. But perhaps the most significant aspect of this work is to encompass an ever increasing number of traditional optimization phases into a single pass. Our approach offers a good solution to the fundamental problem of phase ordering of high-level loop transformations.