Scalable Techniques for Computing Band Linear Recurrences on Massively Parallel and Vector Supercomputers

In this paper, we present a new scalable algorithm, called the Regular Schedule, for parallel evaluation of band linear recurrences (BLR's, i.e., mth-order linear recurrences for m 1). Its scalability and simplicity make it well suited for vector supercomputers and massively parallel computers. We describe our implementation of the Regular Schedule on two types of machines: the Convex C240 and the MasPar MP-2. The scalability of our scheduling techniques is demonstrated on the two machines. Signi cant improvements in CPU performance for a range of programs containing BLR implemented using the Regular Schedule in C over the same programs implemented using the highly-optimized coded-in-assembly BLAS routines [17] are demonstrated on the Convex C240. We also demonstrate the scalability of this schedule on the MasPar MP-2 up to two thousand processors. Our approach can be used both at the user level in parallel programming code containing BLR's, and in compiler parallelization of such programs combined with recurrence recognition techniques for massively parallel and vector supercomputers.