Synthesizing nested loop algorithms using nonlinear transformation method

FOR-loops are the main source of parallelism in programs. A nonlinear transformation algorithm for parallelizing the execution of FOR-loop models is proposed. It is shown that by the mapping of nonlinear transformation, iterations of FOR-loops can be executed in a parallel form. The algorithm is useful in exploiting the parallelism of FOR-loops with one or more partitions on the innermost loop. Algorithms to partition and map the nested FOR-loops onto fixed size systolic arrays are discussed. Based on the time and space mapping schemes, all the iterations of FOR-loops can be correctly executed on the array processors in a parallel form