  We present efficient algorithms for simultaneously computing Kendall's tau
and the jackknife estimator of its variance. For the classical pairwise tau, we
describe a modification of Knight's algorithm (originally designed to compute
only tau) that does so while preserving its $O(n \log_2 n)$ runtime in the
number of observations $n$. We also introduce a novel algorithm computing a
multivariate extension of tau and its jackknife variance in $O(n \log_2^p n)$
time.
