Black holes and the Uncertainty Principle

Does the singularity at the center of a black hole violate the Heisenberg Uncertainty Principle? By definition it's a point so its position may be known to arbitrarily high precision. It's velocity seems to be able to be measured within bounds, too.

Perhaps it's OK to violate the laws of physics so long as you are inside an event horizon -- no one on the outside will ever find out.

Or more likely the laws of quantum mechanics need to be fixed to apply to regions of spacetime so curved as to be a singularity.