We were computing these functions incorrectly.
I'm not sure what distribution these numbers are, but it isn't the
normal exponential distribution. (We're making the probability of
getting a number of a particular bitlength equal, but the number in
that bitlength thats gets chosen is uniformly chosen)
We weren't using these functions anywhere in our codebase, and they
had a nomenclature error. (There aren't exponentially distributed
integers, instead they would be geometrically distributed)
Dev Ojha
Ethan Buchman