I appreciate the effort to write this up, but I'm not seeing that this has applicability to any real problem. If you put 53 random bits in the mantissa with a

I appreciate the effort to write this up, but I'm not seeing that this has applicability to any real problem. If you put 53 random bits in the mantissa with a fixed exponent, you get a smooth distribution from from [0, 1 - 2^-53] in increments of 2^-53. He seems to be concerned that you will never get a number between(0, 2^-53). True, but you'll also never get any other number between (n * 2^-53,(n+1) * 2^-53) for all the rest of the range. [wrong statement about denormals deleted] His talk about "dividing" to produce the desired range seems misguided. Floating point division is ~10x the cost of any other floating point operations. If you are trying to produce precise floating point numbers, you almost certainly want to be working at the level of bits rather than hoping that division will do the work for you.