Communication generation for aligned and cyclic(k) distributions using integer lattice

Optimizing communication is a key issue in generating efficient SPMD codes in compiling distributed arrays on data parallel languages, such as High Performance Fortran. In HPF, the array distribution may involve alignment and cyclic(k)-distribution such that the enumeration of the local set and the enumeration of the communication set exhibit regular patterns which can be modeled as integer lattices. In the special case of unit-strided alignment, many techniques of the communication set enumeration have been proposed, while in the general case of the non-unit-strided alignment, inspector-like run-time codes are needed to build repeating pattern table or to scan over local elements such that the communication set can be constructed. Unlike other works on this problem of the general alignment and cyclic(k) distribution, our approach derives an algebraic solution for such an integer lattice that models the communication set by using the Smith-Normal-Form analysis, therefore, efficient enumeration of the communication set can be generated. Based on the integer lattice, we also present our algorithm for the SPMD code generation. In our approach, when the parameters are known, the SPMD program can be efficiently constructed without any inspector-like run-time codes