[aqrit]

Why not use regular rejection sampling when `limit` is known at compile-time. Does fastrange[1] have fewer rejections due to any excess random bits[2]?

[1] https://github.com/lemire/fastrange

[2] https://github.com/swiftlang/swift/pull/39143

[fanf2]

What do you mean by “regular” rejection sampling?

Fastrange is slightly biased because, as Steve Canon observes in that Swift PR, it is just Knuth’s multiplicative reduction. The point of this post is that it’s possible to simplify Lemire’s nearly-divisionless debiasing when the limit is known at compile time.

I previously experimented with really-divisionless debiasing but I was underwhelmed with the results https://dotat.at/@/2022-04-20-really-divisionless.html

[aqrit]

> “regular” rejection sampling

I was thinking naive: mask off unwanted bits then reject any value above the limit.

It would seem like https://c-faq.com/lib/randrange.html would also move the multiply --or divide by constant-- out of the loop.

[fanf2]

Lemire’s algorithm rejects the fewest possible samples from the random number generator, so it’s generally the fastest. The multiplication costs very little compared to the RNG.