Automatic array partitioning based on the Smith normal form

Authors:
Eric Hung-Yu Tseng;Jean-Luc Gaudiot
Affiliations:
Service Assurance, Spirent Communications, Morgan Hill, CA;Department of EECS, University of California, Irvine, CA
Venue:
International Journal of Parallel Programming
Year:
2005

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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.