Formal Specification of Parallel SIMD Execution

Abstract In this paper we define a vector model for parallel SIMD execution. The model is based on the notion of atomic instructions acting on vectors of size Π, where Π is the number of PEs on the machine. The vector model of SIMD execution is independent of any specific computing architecture and can define SIMD execution on a SIMD machine (with Π PEs) or a SIMD simulation on a uniprocessor machine. The vector model enables the formal specification of parallel SIMD languages by providing an underlying mathematical framework for the SIMD paradigm. We provide a semantic definition for an imperative parallel language based on the Maspar MPL language utilising the vector model. The semantic definition provides a complete set of rules for ordering, construction and manipulation of the parallel vectors during the execution of each language construct. This demonstrates how parallel SIMD machines and simulators can use the model to specify the semantics of any operation or language construct. The model can also be used to resolve problems like virtualisation in addition to its implications for ongoing research into the automatic parallelisation of sequential programs.