> Honestly, I think It's the best we can actually guarantee.

A bit of a late follow-up, but worth recording here in context, as it didn't occur to me at the time we were originally discussing here.

If one looks at the C++11 standard, they are quite explicit about the fact that a uniform RNG (in the terms of the standard) produces _uniformly distributed unsigned integral types in the closed interval [min, max]_.

Now, the requirement of integral types I think could be debated, but I do think that the requirement that a uniform RNG type produces numbers in a closed interval with explicit and inclusive min and max is probably an essential constraint for well-defined functionality built on top of UniformRNG sources of randomness.