Communication-Free Parallelization via Affine Transformations

The paper describes a parallelization algorithm for programs consisting of arbitrary nestings of loops and sequences of loops. The code produced by our algorithm yields all the degrees of communication-free parallelism that can be obtained via loop fission, fusion, interchange, reversal, skewing, scaling, reindexing and statement reordering. The algorithm first assigns the iterations of instructions in the program to processors via affine processor mappings, then generates the correct code by ensuring that the code executed by each processor is a subsequence of the original sequential execution sequence.

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