To make my own objection explicit:

Do you mean that the input integer, respectively the output float, should be uniform over a specific range (defined ahead of time) which the type is capable of representing? Or that it should be uniform over the entire range represented by the type (e.g. 0..65535 for 16-bit unsigned)? Or exactly what? And how should endpoints be handled? Some examples of expected input and output would be helpful, even if e.g. they use rationals rather than exact floating-point values to demonstrate what should be approximated.

What do you mean by endpoints? I've now explained inclusive bounds. I don't know what examples would make sense because I don't know what the float values would look like.

I think that's good enough for now, and I've reopened it. But I mean even simple examples: if we map integers less than 4 to floats less than 1, should [0, 1, 2, 3] map to [0/3, 1/3, 2/3, 3/3] (float approximations thereof), or is it really mapping [0, 1, 2, 3) to [0., 0.25, 0.5, 0.75), or just what?

The problem with talking about "the whole range of possible floats" is that the space of IEEE754 floats is not uniform, even disregarding special values. The space between large values is greater than the space between small values.

I've narrowed the question to U[0, 1]