Solving linear recurrences with loop raking

Abstract

The article presents a variation of the partition method for solving m/sup th/-order linear recurrences that is well-suited to vector multiprocessors. The algorithm fully utilizes both vector and multiprocessor capabilities, and reduces the number of memory accesses as compared to the more commonly used version of the partition method. The variation uses a general loop restructuring technique called loop raking. The article describes an implementation of this technique on the CRAY Y-MP and presents performance results on first- and second-order linear recurrences, as well as on Livermore loops, 5, 11 and 19, which are based on linear recurrences.<>