  We complete the computation of the integral homology of the generalized braid
group $B$ associated to an arbitrary irreducible complex reflection group $W$
of exceptional type. In order to do this we explicitely computed the
recursively-defined differential of a resolution of $\mathbf{Z}$ as a
$\mathbf{Z} B$-module, using parallel computing. We also deduce from this
general computation the rational homology of the Milnor fiber of the
singularity attached to most of these reflection groups.
