Add Bernoulli distribution

[dhardy]

Add a Bernoulli distribution (i.e. boolean with probability p).

This is basically just rng.gen() < p, but the uniform distribution used to generate a float has precision limited to ε (smallest representable number above 1); we can do better.

We may decide not to implement this as a distribution but with a simple function calling rng.sample(HighPrecision01) < p or similar.

See also #293: add Rng::gen_bool or similar

[pitdicker]

We went with Rng::gen_bool, so I think this can be closed.

[pitdicker]

After some discussion (#347) we probably still want a Bernoulli distribution, that provides more than 32 bits of accuracy. I.e. that uses rng.sample(HighPrecision01) < p.

[vks]

I'm working on a PR.

What is the reasoning behind Rng::gen_bool and Bernoulli::sample having different accuracies? This seems confusing, if we want to support different accuracies, I think we should also have different distributions, i.e. BernoulliHighPrecision and BernoulliLowPrecision.

[pitdicker]

@vks. Good that you want to make a PR!

As you have been following this repro pretty closely, I think I can ask you this. Making the PR for this distribution is trivial. Before that, can you provide links to the relevant discussions there have been on this issue, and summarize the concerns and possible implementations?

[dhardy]

AFAIK the only advantage of the lower precision variant using "only" 32 bits is that more optimisation can be done when p is a known constant to the compiler — otherwise the version using HighPrecision01 with 52-bits fraction has similar performance (at least in my benches).