[adrianN]

Choosing a random float is not the same as choosing a random number.

[morelisp]

What applications call for a "random float in [0,1]" with distribution defined in the space of fp representation and not the usual kind?

[adrianN]

For example you when you want to do fuzzing of some algorithm that uses floats, a random float might come in handy.

[morelisp]

In [0,1]?

(I consider this answer nearly disingenuous. It's obviously not what OP was talking about.)