Replaces the Poisson rejection method implementation

[JamboChen]

• Added a CHANGELOG.md entry

Summary

As discussed in #1515, this PR replaces the implementation of poisson::RejectionMethod with a new algorithm based on the paper .

Motivation

The new implementation offers improved performance and maintains better sampling distribution, especially for extreme values of lambda (> 1e9).

Details

In terms of performance, here are the benchmarks I ran, with the current implementation as the baseline:

poisson/100             time:   [45.5242 cycles 45.6734 cycles 45.8337 cycles]
                        change: [-86.572% -86.507% -86.438%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 5 outliers among 100 measurements (5.00%)
  2 (2.00%) low mild
  2 (2.00%) high mild
  1 (1.00%) high severe
poisson/variable        time:   [5494.6626 cycles 5508.2882 cycles 5523.2298 cycles]
                        thrpt:  [5523.2298 cycles/100 5508.2882 cycles/100 5494.6626 cycles/100]
                 change:
                        time:   [-76.728% -76.573% -76.430%] (p = 0.00 < 0.05)
                        thrpt:  [+324.27% +326.85% +329.69%]
                        Performance has improved.
Found 5 outliers among 100 measurements (5.00%)
  1 (1.00%) low mild
  3 (3.00%) high mild
  1 (1.00%) high severe

[JamboChen]

This test fails

The sampled mean is 14.7370005, which should be within the 99% confidence interval of poisson mean, and it passes the ks test with lambda=15.

[dhardy]

I expect that test is less useful than the KS test, so feel free to remove it.

This PR should also enable KS tests for larger lambda?

[JamboChen]

I randomly tested between 10 and 1000. I also tested for lambda=1e9, 1e10 and it passed, larger numbers take too long (>30min) so no results yet

[benjamin-lieser]

I have checked the code and it does seems to match the verbal description in the paper, I really can't read fortran. I have not checked the math in the paper.

The simple avg_test can be safely ignored in my opinion.

I would add a few more values to the KS test
let parameters = [0.1, 1.0, 7.5, 45.0, 98.0, 230.0, 4567.5, 4.4541e7];

[benjamin-lieser]

Can you add the changelog?

[dhardy]

Thanks @benjamin-lieser and @JamboChen!

I'll go ahead with the release.