The currently best known algorithms for the numerical evaluation of
hypergeometric constants such as ζ(3) to d decimal digits have time
complexity O(M(d)log2d) and space complexity of O(dlogd) 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 π, and we announce a new record of 2 billion digits for
ζ(3)