A methodology for generating data distributions to optimize communication

The authors present an algebraic theory, based on the tensor product for describing the semantics of regular data distributions such as block, cyclic, and block-cyclic distributions. These distributions have been proposed in high performance Fortran, an ongoing effort for developing a Fortran extension for massively parallel computing. This algebraic theory has been used for designing and implementing block recursive algorithms on shared-memory and vector multiprocessors. In the present work, the authors extend this theory to generate programs with explicit data distribution commands from tensor product formulas. A methodology to generate data distributions that optimize communication is described. This methodology is demonstrated by generating efficient programs with data distribution for the fast Fourier transform