SAGA and CONDENSE: a two-phase approach for the implementation of recurrence equations on multiprocessor architectures

The automation of parallel implementations of algorithms, specifically those arising in scientific and engineering applications, is investigated. Since many of these computations can be formulated as coupled system of recurrence equations, they exhibit a high degree of repetitiveness and regularity. These properties are utilized to generate efficient, and in certain cases optimal, schedules and processor assignments on particular multiprocessor configurations. The process of determining a parallel implementation consists of two successive stages, named SAGA and CONDENSE. SAGA generates a minimal-time systolic implementation with a number of processors that is likely to be problem-dependent. If the problem size exceeds the size of the target architecture, CONDENSE groups the processors in the array given by SAGA so that each group is assigned, or condensed, to one processor of the target architecture. The condensation is done so as to minimize the total run time and is guided by the systolic array from SAGA.<>