Change (0, 1] to (0, 1) without branching

I have a random number generator that outputs values from (0, 1], but I need to give the output to a function that returns infinity at 0 or 1. How can I post-process the generated number to be in (0, 1) without any branches, as this is intended to execute on a GPU?

I suppose one way is to add a tiny constant and then take the value mod 1. In other words, generate from (ɛ, 1 + ɛ], which gets turned into [ɛ, 1). Is there a better way? What should the ɛ be?