Unbounded and bounded parallelism in BMF. case study: Rank sorting

Abstract. BMF is a formalism that allows us to design parallel programs independently of the target architecture, and to transform the programs into more efficient programs using equational reasoning. We show in this paper that even the abstractness of BMF is very high, bounded and unbounded parallelism can be expressed in this model, and also that BMF allows us to transform a program into different variants, each of them being more appropriate for a specific architecture type. We consider the case-study of rank sorting, for which we construct first a general unbounded parallel program. Then, we transform the program for bounded parallelism, by imposing a limited number of processors. Three variants are obtained. The implementations of the programs onto shared memory, distributed memory, and pipeline architectures are analyzed, too. 1