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

BEHRENDS, Reimer, HAMMOND, Kevin, JANJIC, Vladimir, KONOVALOV, Alexander, LINTON, Steve, LOIDL, Hans-Wolfgang, MAIER, Patrick and TRINDER, Phil (2016). HPC-GAP: engineering a 21st-century high-performance computer algebra system. Concurrency and Computation: Practice and Experience, 28 (13), 3606-3636.

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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 thatdo 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 HPC 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 32,000 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:	Article
Departments - Does NOT include content added after October 2018:	Faculty of Science, Technology and Arts > Department of Computing
Identification Number:	https://doi.org/10.1002/cpe.3746
Page Range:	3606-3636
Depositing User:	Patrick Maier
Date Deposited:	16 Feb 2018 12:54
Last Modified:	18 Mar 2021 15:31
URI:	https://shura.shu.ac.uk/id/eprint/18621

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