[binarycoffee]

You are right of course, but I would contend that generating as well sub-normal floats is in 99.9% of the cases a needless cost. The reason is that, more often than not, all this extra precision will be immediately lost in subsequent operations.

A very common situation is for instance to plug the random number in a log, in which case you need to use log(1-r) rather than log(r) to avoid an infinite at r=0. The problem is, by doing this simple subtraction you have already lost all the subnormal precision.