> You're out of luck there; no matter what happens you can only generate floating point numbers. If you're worried that the solution lies within the space of fl

> You're out of luck there; no matter what happens you can only generate floating point numbers. If you're worried that the solution lies within the space of floating point numbers, but not within the part that's reachable by generating uniform samples with 1/2^53 resolution, you need to be much, much, much more worried that the solution isn't a floating point number at all. 2^53 is 15 sigfigs. My answer might be around 10 pico-something and I might need a few digits of precision. Then I've thrown away 11 of my sigfigs and there may not be a numerically stable solution with what's left. As you point out, double precision often isn't enough. But it's much more likely to not be enough if we throw large parts of the precision away.