CABAL

CABAL: Polynomial and power series algebra on a parallel computer. The work on designing or adapting algebra systems to exploit parallel hardware that we have seen to date has concentrated on trying the speed-up that can come from concurrent exploration of branches in search trees or overlapped computation in demanding algorithms. We in this paper, on the other hand, are almost exclusively concerned with the fact that large-scale parallel computers are frequently configured with very large amounts of primary memory. Our system distributes very large formulae across the multiple processors in such a parallel computer in such a way that calculations that would otherwise fail for lack of memory can be completed. Our initial system described here is designed to perform simple polynomial and power series calculations, but even in such apparently limited domains the easing of memory restrictions can sometimes prove useful. Results from our system, called CABAL (Cambridge And Bath ALgebra-system), are included both from runs on small networks of conventional workstations and using a Hitachi SR2201 massively parallel super-computer. The main result is a demonstration of the feasibility of the design.

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