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Hypercubic storage layout and transforms in arbitrary dimensions using GPUs and CUDA

Hawick, K. A.; Playne, D. P.


K. A. Hawick

D. P. Playne


Many simulations in the physical sciences are expressed in terms of rectilinear arrays of variables. It is attractive to develop such simulations for use in 1-, 2-, 3- or arbitrary physical dimensions and also in a manner that supports exploitation of data-parallelism on fast modern processing devices. We report on data layouts and transformation algorithms that support both conventional and data-parallel memory layouts. We present our implementations expressed in both conventional serial C code as well as in NVIDIA's Compute Unified Device Architecture concurrent programming language for use on general purpose graphical processing units. We discuss: general memory layouts; specific optimizations possible for dimensions that are powers-of-two and common transformations, such as inverting, shifting and crinkling. We present performance data for some illustrative scientific applications of these layouts and transforms using several current GPU devices and discuss the code and speed scalability of this approach.


Hawick, K. A., & Playne, D. P. (2011). Hypercubic storage layout and transforms in arbitrary dimensions using GPUs and CUDA. Concurrency and Computation: Practice and Experience, 23(10), 1027-1050.

Journal Article Type Article
Online Publication Date Aug 28, 2010
Publication Date 2011-07
Deposit Date Nov 13, 2014
Journal Concurrency And Computation-Practice & Experience
Print ISSN 1532-0626
Electronic ISSN 1532-0634
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 23
Issue 10
Pages 1027-1050
Keywords Theoretical Computer Science; Computer Networks and Communications; Computational Theory and Mathematics; Software; Computer Science Applications
Public URL
Contract Date Nov 13, 2014