The symbolic hyperplane transformation for recursively defined arrays

This paper describes a restructuring transformation which can be used to parallelize recurrence relations. The transformation is based on the hyperplane (or wavefront) method, but extends the applicability of the method to irregularly-structured recurrences. We assume that the time of computation of an array element is a linear combination of its indices, and we use a variation of the simplex method to seek a succession of hyperplanes along which array elements can be computed concurrently. Portions of the work reported here have been implemented in the PS automatic program generation system.