# Efficient implementation of the Hardy-Ramanujan-Rademacher formula

@article{Johansson2012EfficientIO,
title={Efficient implementation of the Hardy-Ramanujan-Rademacher formula},
author={Fredrik Johansson},
journal={Lms Journal of Computation and Mathematics},
year={2012},
volume={15},
pages={341-359}
}
• Fredrik Johansson
• Published 27 May 2012
• Computer Science
• Lms Journal of Computation and Mathematics
We describe how the Hardy-Ramanujan-Rademacher formula can be implemented to allow the partition function p(n) to be computed with softly optimal complexity O(n 1/2+o(1) ) and very little overhead. A new implementation based on these techniques achieves speedups in excess of a factor 500 over previously published software and has been used by the author to calculate p(10 19 ), an exponent twice as large as in previously reported computations. We also investigate performance for multi-evaluation…

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