A unified parallel processing architecture connects together an extendible number of clusters of multiple numbers of processors to create a high performance parallel processing computer system. Multiple processors are grouped together into four or more physically separable clusters, each cluster having a common cluster shared memory that is symmetrically accessible by all of the processors in that cluster; however, only some of the clusters are adjacently interconnected. Clusters are adjacently interconnected to form a floating shared memory if certain memory access conditions relating to relative memory latency and relative data locality can create an effective shared memory parallel programming environment. A shared memory model can be used with programs that can be executed in the cluster shared memory of a single cluster, or in the floating shared memory that is defined across an extended shared memory space comprised of the cluster shared memories of any set of adjacently interconnected clusters. A distributed memory model can be used with any programs that are to be executed in the cluster shared memories of any non-adjacently interconnected clusters. The adjacent interconnection of multiple clusters of processors to a create a floating shared memory effectively combines all three type of memory models, pure shared memory, extended shared memory and distributed shared memory, into a unified parallel processing architecture.