Hypercubic Storage Layout and Transforms in Arbitrary Dimensions using GPUs and CUDA

K.A. Hawick and D.P. Playne
Institute of Information and Mathematical Sciences, Massey University, Albany, North Shore 102-904, Auckland, New Zealand
Technical Report CSTN-096, Massey University, 2009


   title={Hypercubic Storage Layout and Transforms in Arbitrary Dimensions using GPUs and CUDA},

   author={Hawick, KA and Playne, DP},

   journal={Computer Science, MAssey University, Tech. Rep. CSTN-096},



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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 (CUDA) concurrent programming language for use on General Purpose Graphical Processing Units (GPGPU). We discuss: general memory layouts; specific optimisations 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.
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