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<p>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.</p>
Index Termsnested loop algorithms; nonlinear transformation method; FOR-loop models; nestedFOR-loops; fixed size systolic arrays; space mapping schemes; array processors; parallelform; parallel algorithms; parallel programming

C. Chang and J. Sheu, "Synthesizing Nested Loop Algorithms Using Nonlinear Transformation Method," in IEEE Transactions on Parallel & Distributed Systems, vol. 2, no. , pp. 304-317, 1991.
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