Time-and space-efficient evaluation of some hypergeometric constants

Authors:
Howard Cheng;Guillaume Hanrot;Emmanuel Thomé;Paul Zimmermann;Eugene Zima
Affiliations:
Univ. of Lethbridge;INRIA Lorraine/LORIA;INRIA Lorraine/LORIA;INRIA Lorraine/LORIA;Wilfrid Laurier University
Venue:
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Year:
2007

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Abstract

The currently best known algorithms for the numerical evaluation of hypergeometric constants such as Ç(3) to d decimal digits have time complexity O(M(d) log2d) 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 over existing programs for the computation of Π, and we announce a new record of 2 billion digits for Ç(3).