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This paper presents a new parallelization method for reductions of arrays with subscripted subscripts on scalable shared memory multiprocessors. The mapping of computations is based on grouping reduction loop iterations into sets that are further assigned to the cooperating threads of computation. Iterations belonging to the same set are chosen in such a way that update different entries in the reduction array. That is, the loop distribution implies a conflict-free write distribution of the reduction array. The iteration sets are set up by building a loop-index prefetching data structure that allows to reorder properly the loop iterations. The proposed method is general, scalable, and easy to implement on a compiler. In addition it deals in a uniform way with one and multiple subscript arrays. In case of multiple indirection arrays, writes on the reduction array affecting different sets are solved by defining conflict-free supersets. A performance evaluation is presented. From the experimental results and performance analysis, the proposed method appears as a clear alternative to the array expansion and privatized buffer techniques, used on state-of-the-art parallelizing compilers, like Polaris or SUIF. The scalability problem that those techniques exhibit is missing in our method, as the memory overhead presented does not depend on the number of processors.

A compiler method for the parallel execution of irregular reductions in scalable shared memory multiprocessors