Generation and optimisation of code using Coxeter lattice paths

Authors:
Thomas J. Ashby;Anthony D. Kennedy;Stephen M. Watt
Affiliations:
University of Edinburgh, Scotland, UK;University of Edinburgh, Scotland, UK;University of Western Ontario, London, Canada
Venue:
Proceedings of the 2007 international workshop on Parallel symbolic computation
Year:
2007

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Abstract

Supercomputing applications usually involve the repeated parallel application of discretized differential operators. Difficulties arise with higher-order discretizations of operators on parallel computers because their communications can overlap processors in complex ways. Their correct and efficient implementation requires careful choreography of computation and communication, taking into account the symmetries of the problem and of the computer's communication network. This paper shows how these symmetries can be used to automate the construction of the code for optimized operator computation. This is done with considerable generality by making the symmetries both of the problem and the computer explicit using the language of finitely presented reection (Coxeter) groups, and using coset enumeration to generate and optimize the required code.