Advanced compilation techniques in the PARADIGM compiler for distributed-memory multicomputers

The PARADIGM compiler project provides an automated means to parallelize programs, written in a serial programming model, for efficient execution on distributed-memory multicomputers. .A previous implementation of the compiler based on the PTD representation allowed symbolic array sizes, affine loop bounds and array subscripts, and variable number of processors, provided that arrays were single or multi-dimensionally block distributed. The techniques presented here extend the compiler to also accept multidimensional cyclic and block-cyclic distributions within a uniform symbolic framework. These extensions demand more sophisticated symbolic manipulation capabilities. A novel aspect of our approach is to meet this demand by interfacing PARADIGM with a powerful off-the-shelf symbolic package, Mathematica. This paper describes some of the Mathematica routines that performs various transformations, shows how they are invoked and used by the compiler to overcome the new challenges, and presents experimental results for code involving cyclic and block-cyclic arrays as evidence of the feasibility of the approach.