Hitting each representable floating point number with an equal probability does not generate an approximately uniform distribution of [0,1). For a sufficiently

Hitting each representable floating point number with an equal probability does not generate an approximately uniform distribution of [0,1). For a sufficiently small positive number, eps, you have to have equal probabilities of numbers falling in [0,eps) and [0.5,0.5+eps) for a uniform distribution, and using random bits would fail this requirement.