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The memory behavior of cache oblivious stencil computations

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Abstract

We present and evaluate a cache oblivious algorithm for stencil computations, which arise for example in finite-difference methods. Our algorithm applies to arbitrary stencils in n-dimensional spaces. On an “ideal cache” of size Z, our algorithm saves a factor of Θ(Z 1/n) cache misses compared to a naive algorithm, and it exploits temporal locality optimally throughout the entire memory hierarchy. We evaluate our algorithm in terms of the number of cache misses, and demonstrate that the memory behavior agrees with our theoretical predictions. Our experimental evaluation is based on a finite-difference solution of a heat diffusion problem, as well as a Gauss-Seidel iteration and a 2-dimensional LBMHD program, both reformulated as cache oblivious stencil computations.

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Authors and Affiliations

  1. IBM Austin Research Laboratory, 11501 Burnet Road, Austin, TX, 78758, USA

    Matteo Frigo & Volker Strumpen

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  1. Matteo Frigo
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  2. Volker Strumpen
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Correspondence to Volker Strumpen.

Additional information

This work was supported in part by the Defense Advanced Research Projects Agency (DARPA) under contract No. NBCH30390004.

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Frigo, M., Strumpen, V. The memory behavior of cache oblivious stencil computations. J Supercomput 39, 93–112 (2007). https://doi.org/10.1007/s11227-007-0111-y

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