Implement the Gamma function with very low relative error

[JSorngard]

Hello!

I found this interesting implementation of the Gamma function by T. Fukushima (same person that published the algorithm I use in the lambert_w crate) in Fortran. It has a lower relative error than the current implementation (often within a single ulp), so I thought I could try implementing it in Rust.

This PR implements this new Gamma function and makes the tests more stringent to show the reduced error.

[JSorngard]

It seems the tests fail because pyo3 expects an older version of python (3.13) than is available on the CI image (3.14).

The tests compile and run fine on my local machine.

I don't know how to fix the problem though.

[JSorngard]

It may be that updating the pyo3 dependency of peroxide will make it able to compile on the latest CI images. I opened that PR in Axect/Peroxide#89.

[JSorngard]

If this PR is interesting then this code might also be interesting as it contains functions for computing the incomplete and complementary incomplete Gamma functions.

[JSorngard]

Should the polynomial function also be exported outside the crate?

[Axect]

Great improvement! Thank you for great contributions!

[Axect]

Should the polynomial function also be exported outside the crate?

I think current implementation pub(crate) is okay enough 👍