A tightly coupled data processing system having high performance characteristics, including at least one general purpose host processor coupled to host processor ports of a High Performance Storage Unit, and a Scientific Processor directly coupled to scientific processor ports of the High Performance Storage Unit is described. The Scientific Processor is under task assignment control of the host processor and shares the same memory space as the host processor, and thereby provides the tight coupling without need of dedicated memory or caching. Provision is also made for the Scientific Processor to share the virtual address space of the host processor. A tightly coupled system is also disclosed wherein a plurality of general purpose host processors are each coupled to one or more High Performance Storage Units, and a Multiple Unit Adapter is utilized to couple an associated Scientific Processor to all of the High Performance Storage Units. Each Scientific Processor includes a parallel operable scalar processor module and a vector processor module.