RFC: implement a biased rand(a:b) (fix #20582)

[rfourquet]

See #20582 for details. This basically uses a+floor(Int,n*rand()) to get a random number in a:a+n-1. This can be significantly faster than regular rand(a:b), but introduces a bias. I don't have a strong opininion about this, but thought that having a PR could move the discussion forward.

This also implements rand(fast(a)) where a is an array, but for some reason this allocates, which trumps the benefits. I have no idea why this is so, as the implementation is simpler for rand(fast(a)) than for rand(a)... any help to sort this out would be appreciated!

[Keno]

Have we verified that we can't make the algorithm in #29004 faster than this? I'm a bit surprised that generating a random Float would be faster than that.

[rfourquet]

Have we verified that we can't make the algorithm in #29004 faster than this

I think that in the linked discourse thread it was shown to be slighly slower than the biased algo, but faster if the input is converted to Int32 first.
I will investigate a bit more. Maybe the algorithm in #29004 should replace our current default implementation.

I'm a bit surprised that generating a random Float would be faster than that.

I guess it depends on the used RNG. For MersenneTwister, Float64 is what is generated natively, and generating a UInt64 integer requires more random bits than for a Float64.

[affans]

I think the algorithm in #29004 should be used. It's worth it to have a miniscule reduction in speed if it means removing the bias. Some applications/scientific simulations may need to generate millions of random numbers, and I don't think it's a good idea if rand() will introduce bias.

If we want to go with the biased implementation then it needs to documented.

[StefanKarpinski]

I have to say I don't really like this approach. Sure, I get that this just makes the tradeoff of fast and biased versus slower and unbiased explicit, but I'd much rather have my cake and eat it too, by using something like #29004 / https://discourse.julialang.org/t/rand-1-10-vs-int-round-10-rand/14339 to do faster unbiased sampling. It seems premature to declare failure and force the user to chose between fast and correct here.

[affans]

@rfourquet Would you be able to implement the new algorithm? I am new to contributing but I think I could probably give this a try. Is there a way I can push to my commits to this PR or do I have to make my own?

[rfourquet]

Welcome @affans ! Seeing activity in the discourse thread in the last two days prompted me to implement this, so I will open another PR soon.

[affans]

@rfourquet Thanks! would you remember to tag me so that I can follow along. I feel like this is an intermediate PR I can follow and learn the internals of Julia.

[rfourquet]

I think this should be in a package at best.