Parallel Recurrence Solvers for Vector and SIMD Supercomputers

Abstract

In this paper we present two algorithms for the parallel solution of first-order linear recurrences, We show that the algorithms can be used to efficiently solve both scalar and blocked versions of the problem on vector and SIMD architectures. The first algorithm is a parallel approach whose resulting code can be explicitly vectorized, making it suitable for efficient execution on vector architectures such as the Cray 2. The second algorithm is a modified recursive approach designed to reduce the communication overhead encountered in SIMD architectures such as the Connection Machine 2 (CM-2). We present the performance exhibited by the parallel algorithm implementations on the Cray 2 and CM-2 for both scalar and blocked versions of the recurrence problem.