Orchestrating Production Computer Algebra Components into Portable Parallel Programs

This paper demonstrates that it is possible to obtain good, scalable parallel performance by coordinating multiple instances of unaltered sequential computational algebra systems in order to deliver a single parallel system. The paper presents the first substantial parallel performance results for SymGrid-Par, a system that orchestrates computational algebra components into a high-performance parallel application. We show that SymGrid-Par is capable of exploiting different parallel/multicore architectures without any change to the computational algebra component. Ultimately, our intention is to extend our system so that it is capable of orchestrating heterogeneous computations across a high-performance computational Grid. For now, we illustrate our approach with a single, unmodified production computational algebra system, GAP, running on two common commodity architectures — a homogeneous cluster and an eight-core system. Computational algebra applications are large, specialised, and symbolic, rather than the more commonly studied numerical applications. They also exhibit high levels of irregularity, and multiple levels of irregularity. We demonstrate that for three small but representative algebraic computations, good parallel speedup is possible relative to a sequential GAP system running on a single processor/core. We compare the performance of the orchestrated system with that of parGAP, an established parallel implementation of GAP, demonstrating