  In this paper, the singular Ringel-Hall algebra for a tame quiver is
introduced and shown to be isomorphic to the positive part of the quantum
extended Kac-Moody algebra. A PBW basis is constructed and a new class of
perverse sheaves is shown to have purity property. This allows to construct the
canonical bases of the positive part of the quantum extended Kac-Moody algebra.
As an application, the existence of Hall polynomials for tame quiver algebras
is proved.
