Avoid panics in Binomial BTPE sampler by using u64 values

[mstoeckl]

• Added a CHANGELOG.md entry

Summary

This fixes a panic that can occur when the parameter n for the Binomial sampler is larger than i64::MAX.

Motivation

This should resolve #21 .

Details

The key variable which previously used i64 in binomial::btpe was y, the random coordinate in 0..=n on which the BTPE algorithm performed rejection sampling. Since n is in 0..u64::MAX, y should also be in u64::MAX.

This is a value-breaking change, because e.g. the code now does the float->int cast on the value x_l + v.ln() / lambda_l after checking whether the value is <= 0, instead of before. I don't think this sort of change in boundary rounding should cause any issues (and it may make the sampled distribution closer to the actual target.) I am looking into writing a test to confirm this is OK, but it may be a few weeks before it is ready. (Tested, the new version actually fixes a boundary issue, see test for it in #47.)

[benjamin-lieser]

Thank you a lot, this looks good.

[benjamin-lieser]

You say that even the low significant bits are now correctly distributed. Should we remove the disclaimer from the documentation?

[mstoeckl]

You say that even the low significant bits are now correctly distributed.

No, #47 only checks that the least significant bit is correctly distributed for n below 2^53, as it was before; above 2^53, the following warning remains accurate.

/// The implementation uses `f64` internally, which leads to rounding errors for big numbers.
/// For very large samples (`> 2^53`) the least significant bits of the output will not be random.
/// This means that something like `bin.sample(&mut rand::rng()) % 4` will not follow the correct distribution.
/// The more significant bits should be correctly distributed.