Time- and Space-Efficient Evaluation of Some Hypergeometric Constants

Howard Cheng; Guillaume Hanrot; Emmanuel Thomé; Eugene Zima; Paul Zimmermann

doi:10.1145/1277548.1277561

Time- and Space-Efficient Evaluation of Some Hypergeometric Constants

Howard Cheng ¹ Guillaume Hanrot ² Emmanuel Thomé ^{2, *} Eugene Zima ³ Paul Zimmermann ²

* Corresponding author

1 Department of Mathematics and Computer Science

2 CACAO - Curves, Algebra, Computer Arithmetic, and so On

INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications

3 Department of physics and computer science

Abstract : The currently best known algorithms for the numerical evaluation of hypergeometric constants such as $\zeta(3)$ to $d$ decimal digits have time complexity $O(M(d) \log^2 d)$ and space complexity of $O(d \log d)$ or $O(d)$. Following work from Cheng, Gergel, Kim and Zima, we present a new algorithm with the same asymptotic complexity, but more efficient in practice. Our implementation of this algorithm improves slightly over existing programs for the computation of $\pi$, and we announce a new record of 2 billion digits for $\zeta(3)$.

Keywords : high-precision evaluation hypergeometric constants

Document type :

Conference papers

Domain :

Computer Science [cs] / Symbolic Computation [cs.SC]

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