  We investigate the windings around the origin of the two-dimensional Markov
process (X,L) having the stable L\'evy process L and its primitive X as
coordinates, in the non-trivial case when |L| is not a subordinator. First, we
show that these windings have an almost sure limit velocity, extending McKean's
result [McK63] in the Brownian case. Second, we evaluate precisely the upper
tails of the distribution of the half-winding times, connecting the results of
our recent papers [CP14, PS14].
