  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
$\zeta(3)$.
