5578

Fast Mersenne prime testing on the GPU

Andrew Thall
Alma College, Alma, MI
Proceedings of the Fourth Workshop on General Purpose Processing on Graphics Processing Units, GPGPU-4, 2011

@inproceedings{thall2011fast,

   title={Fast Mersenne prime testing on the GPU},

   author={Thall, A.},

   booktitle={Proceedings of the Fourth Workshop on General Purpose Processing on Graphics Processing Units},

   pages={6},

   year={2011},

   organization={ACM}

}

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The Lucas-Lehmer test for Mersenne primality can be efficiently parallelized for GPU-based computation. The gpuLucas project implements an irrational-base discrete weighted transform approach (IBDWT) using balanced-integers, non-power-of-two transforms, and carry-save radix representations. gpuLucas uses the CUDA programming language and requires the double-precision floating point capabilities of recent GPUs. Results show up to 7x speedups over benchmark averages for optimized sequential code and factor-of-two speedups over CUDALucas, another GPU-based Lucas-Lehmer tester developed independently and with a different optimization strategy. This work demonstrates techniques for implementing GPU-based number theoretic algorithms on very large numbers, including fast multiplication, prefix-sum-based carry-propagation, and the use of carry-save arithmetic with balanced integers. The work presents timing profiles of convolution-based integer multiplication based on the IBDWT, in particular for non-power-of-two transformations, and establishes the usefulness of the software as a GPU benchmarking application and as a platform for large-integer and polynomial experimentation.
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