Work efficient higher-order vectorisation

Authors:
Ben Lippmeier;Manuel M.T. Chakravarty;Gabriele Keller;Roman Leshchinskiy;Simon Peyton Jones
Affiliations:
University of New South Wales, Sydney, Australia;University of New South Wales, Sydney, Australia;University of New South Wales, Sydney, Australia;University of New South Wales, Sydney, Australia;Microsoft Research Ltd, Cambridge, United Kingdom
Venue:
Proceedings of the 17th ACM SIGPLAN international conference on Functional programming
Year:
2012

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Abstract

Existing approaches to higher-order vectorisation, also known as flattening nested data parallelism, do not preserve the asymptotic work complexity of the source program. Straightforward examples, such as sparse matrix-vector multiplication, can suffer a severe blow-up in both time and space, which limits the practicality of this method. We discuss why this problem arises, identify the mis-handling of index space transforms as the root cause, and present a solution using a refined representation of nested arrays. We have implemented this solution in Data Parallel Haskell (DPH) and present benchmarks showing that realistic programs, which used to suffer the blow-up, now have the correct asymptotic work complexity. In some cases, the asymptotic complexity of the vectorised program is even better than the original.