  (This is only a first preliminary version, any suggestions about it will be
welcome.) In this paper it is shown how to compute Riemann's zeta function
$\zeta(s)$ (and Riemann-Siegel $Z(t)$) at any point $s\in\mathbf C$ with a
prescribed error $\varepsilon$ applying the, Riemann-Siegel formula as
described in my paper "High Precision ... I", Math of Comp. 80 (2011)
995--1009.
  This includes the study of how many terms to compute and to what precision to
get the desired result. All possible errors are considered, even those inherent
to the use of floating point representation of the numbers. The result has been
used to implement the computation. The programs have been included in"mpmath",
a public library in Python for the computation of special functions. Hence they
are included also in Sage.
