On compiling array expressions for Efficient execution on distributed-memory machines

Efficient generation of communication sets and local index sets is important for evaluation of array expressions in scientific languages such as Fortran-90 and High Performance Fortran implemented on distributed-memory machines. We show that for arrays affinely aligned with templates that are distributed on multiple processors with a block-cyclic distribution, the local memory access sequence and communication sets can be efficiently enumerated using closed forms. First, closed form solutions are presented for arrays that are aligned with identity templates that are distributed using block or cyclic distributions. These closed forms are then used with a uirtual processor approach to give an efficient solution for arrays with block-cyclic distributions. These results are extended to arrays affinely aligned to arbitrary templates that have regular distributions. We present performance results on an iPSC/860 processor, that demonstrate the low runtime overhead of this scheme.