Abstract
We investigate the lattice-based array partitioning based on the theory of the Smith Normal Form and we present two elegant techniques for partitioning arrays in parallel DoAll loops for message-passing parallel machines: (1) DoAll loops with constant dependencies for communication-free partitioning: a general solution of all possible communication-free partitioning is derived where the dependencies among array references are described in constant distance vectors. (2) DoAll loops with non-constant dependencies for block-communication partitioning: the dependencies among array references are described in non-constant distance vectors. We derive the partitioning equations which allocate all remote data to a unique processor such that only one block-communication can obtain all the remote data for the computation. By using the Smith Normal Form decomposition, we are also able to verify our partitioning results.
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Tseng, EY., Gaudiot, JL. Automatic Array Partitioning Based on the Smith Normal Form. Int J Parallel Prog 33, 35–56 (2005). https://doi.org/10.1007/s10766-004-1460-2
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DOI: https://doi.org/10.1007/s10766-004-1460-2