Are you sure positions of units are essentially floats? Given how the units seem to arrange themselves (from what I see), I would guess that it's not close to the full range of floats, and instead there are just a few fractional pixel locations that units snap to. This is just a guess however.

-- If this is the case though, the space could be represented by taking larger integer values (say, a magnitude of 1 or 2 higher) to represent positions at a fractional pixel level (say, in 100ths of a pixel).