HPC-GAP: engineering a 21st-century high-performance computer algebra system

Behrends, R., Hammond, K., Janjic, V., Konovalov, A., Linton, S., Loidl, H.-W., Maier, P. and Trinder, P. (2016) HPC-GAP: engineering a 21st-century high-performance computer algebra system. Concurrency and Computation: Practice and Experience, 28(13), pp. 3606-3636. (doi:10.1002/cpe.3746)

Behrends, R., Hammond, K., Janjic, V., Konovalov, A., Linton, S., Loidl, H.-W., Maier, P. and Trinder, P. (2016) HPC-GAP: engineering a 21st-century high-performance computer algebra system. Concurrency and Computation: Practice and Experience, 28(13), pp. 3606-3636. (doi:10.1002/cpe.3746)

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Abstract

Symbolic computation has underpinned a number of key advances in Mathematics and Computer Science. Applications are typically large and potentially highly parallel, making them good candidates for parallel execution at a variety of scales from multi-core to high-performance computing systems. However, much existing work on parallel computing is based around numeric rather than symbolic computations. In particular, symbolic computing presents particular problems in terms of varying granularity and irregular task sizes that do not match conventional approaches to parallelisation. It also presents problems in terms of the structure of the algorithms and data. This paper describes a new implementation of the free open-source GAP computational algebra system that places parallelism at the heart of the design, dealing with the key scalability and cross-platform portability problems. We provide three system layers that deal with the three most important classes of hardware: individual shared memory multi-core nodes, mid-scale distributed clusters of (multi-core) nodes and full-blown high-performance computing systems, comprising large-scale tightly connected networks of multi-core nodes. This requires us to develop new cross-layer programming abstractions in the form of new domain-specific skeletons that allow us to seamlessly target different hardware levels. Our results show that, using our approach, we can achieve good scalability and speedups for two realistic exemplars, on high-performance systems comprising up to 32000 cores, as well as on ubiquitous multi-core systems and distributed clusters. The work reported here paves the way towards full-scale exploitation of symbolic computation by high-performance computing systems, and we demonstrate the potential with two major case studies.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Trinder, Professor Phil and Maier, Dr Patrick
Authors: Behrends, R., Hammond, K., Janjic, V., Konovalov, A., Linton, S., Loidl, H.-W., Maier, P., and Trinder, P.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Concurrency and Computation: Practice and Experience
Publisher:John Wiley and Sons
ISSN:1532-0626
ISSN (Online):1532-0634
Published Online:15 January 2016
Copyright Holders:Copyright © 2016 The Authors
First Published:First published in Concurrency and Computation: Practice and Experience 2016
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
644791Adaptive Just-In-Time Parallelisation (AJITPar)Phil TrinderEngineering & Physical Sciences Research Council (EPSRC)EP/L000687/1COM - COMPUTING SCIENCE