Oh, I know very well who iq is :) And for a visual demo it might make perfect sense to sacrifice completeness of a solution for speed / code size. But to me, "pick a random number from {k/2^23 : 0 <= k < 2^23, k ∈ ℕ}" and "pick a random number uniformly at random from [0, 1)" are not the same.

All operations (add/sub, mul/div, sin, exp, log, etc...), with IEEE754 floats are defined using real arithmetic, and then assumed to round to the nearest representable floating point value. I don't see why random number generation, at least as a default before micro-optimizing, should be any different.