See the Make_random functor in the janestreet Bigint library, which is
built on top of zarith. (It's a functor to produce random distributions
based on both Random.State.t and Base_quickcheck.Generator.t; the functor
itself is not exposed.)

https://github.com/janestreet/bignum/blob/master/bigint/src/bigint.ml

In short, we generate 30-bit chunks of randomness until we have at least
enough bits for our range. We combine those into a number. Usually, we just
modulo that by the range and return it. But to preserve fairness, we first
have to check if the number is in the last fraction-of-range part of the N
bits, and if so retry from scratch. The odds of retry are always less than
50%, so retrying is never too bad.

This is the same trick that Random.int does, but with an unbounded number
of bits instead of a fixed number of bits.

On Wed, Nov 27, 2019 at 4:31 PM François Pottier <francois.pottier@inria.fr>
wrote:

>
> Hello,
>
> I am using zarith and would like to pick a random integer
> comprised between 0 and some bound. I would like a function
> Z.random of type Z.t -> Z.t, but this function seems to be
> missing, and I am not sure how to program it in an efficient
> and correct way. Any suggestions would be welcome. Thanks!
>
> --
> François Pottier
> francois.pottier@inria.fr
> http://gallium.inria.fr/~fpottier/
>


-- 
Carl Eastlund