Refinement of data parallel programs in Pei

Parallel programs mainly differ from sequential ones in that they include geometrical aspects involved by the hardware architecture. We present in this paper the Pei formalism, which enables to take into account both the geometrical and functional aspects of programs. It provides a refinement calculus mainly used to transform the geometrical characteristics of parallel programs, and we show how it may apply on data parallel programs, in particular for data alignments. Keywords Data fields, Data-parallelism, Program transformation, Refinement. 1 INTRODUCTION Parallel programming is a major challenge for handling efficient computations. It involves two technological issues: a program expressed in some dedicated language which supports a parallel programming model, and a computer and the parallel execution model it implements. Ideally the programming language should be architecture independent whereas the computations efficiency requires a strong-related architecture implementation. ..