Optimal Evaluation of Fortran-90 Array Expressions for Distributed Memory Machines

The owner-computes strategy has been used for evaluation of Fortran-90 array expressions on distributed memory machines. This strategy simpliies code generation but is often expensive in terms of the total communication cost and size of temporary memory required for its implementation. In this paper, we propose the relaxing of the owner computes strategy, to reduce the total communication and temporary storage cost. We develop cost metrics for measuring the communication and memory cost associated with the evaluation of Fortran-90 array expressions on distributed memory machines. The communication tree is introduced as a useful representation for array expressions involving associative and commutative operators of one kind. Procedures for estimating communication and temporary memory costs for a communication tree are described. An eecient polynomial-time algorithm to determine an evaluation order which minimizes the communication cost is presented. We also present an eecient polynomial-time algorithm to determine the evaluation order which minimizes the memory cost involved in the evaluation of such expressions.