High-Performance Computer Algebra: A Hecke Algebra Case Study

MAIER, Patrick, LIVESEY, Daria, LOIDL, Hans-Wolfgang and TRINDER, Phil (2014). High-Performance Computer Algebra: A Hecke Algebra Case Study. In: Euro-Par 2014 Parallel Processing. Springer, 415-426.

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Official URL: https://doi.org/10.1007/978-3-319-09873-9_35
Link to published version:: https://doi.org/10.1007/978-3-319-09873-9_35


We describe the first ever parallelisation of an algebraic computation at modern HPC scale. Our case study poses challenges typical of the domain: it is a multi-phase application with dynamic task creation and irregular parallelism over complex control and data structures. Our starting point is a sequential algorithm for finding invariant bilinear forms in the representation theory of Hecke algebras, implemented in the GAP computational group theory system. After optimising the sequential code we develop a parallel algorithm that exploits the new skeleton-based SGP2 framework to parallelise the three most computationally-intensive phases. To this end we develop a new domain-specific skeleton, parBufferTryReduce. We report good parallel performance both on a commodity cluster and on a national HPC, delivering speedups up to 548 over the optimised sequential implementation on 1024 cores.

Item Type: Book Section
Departments: Faculty of Science, Technology and Arts > Computing
Identification Number: https://doi.org/10.1007/978-3-319-09873-9_35
Depositing User: Patrick Maier
Date Deposited: 28 Feb 2018 13:30
Last Modified: 28 Feb 2018 21:47
URI: http://shura.shu.ac.uk/id/eprint/18618

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