fix complex sph_bessel_j kernel sqrt branch

[lucascolley]

scipy/scipy#23700 (comment) @steppi

AI tools used: ChatGPT

The SciPy tests seem to pass on osx-arm64 with this change.

[steppi]

This looks viable. I suggest putting

inline constexpr double SQRT_PI_2 = 1.2533141373155003;

in a detail namespace in this file, and then replacing the above with

std::complex<T> out = static_cast<T>(detail::SQRT_PI_2) * cyl_bessel_j(n + static_cast<T>(0.5), z) / std::sqrt(z);

using inline constexpr let's us sprinkle constants in whichever headers they are needed without running afoul of the one definition rule.

[steppi]

Thanks @lucascolley. I think this will work. See the comment about defining a constant to use here. Also, the fix is needed in the similar line in each of the spherical bessel functions defined in this header.

[lucascolley]

Do we have the relevant test coverage in this repo?

[steppi]

Do we have the relevant test coverage in this repo?

Yes, all cases from the scipy.special tests as of version 1.16 are included in the test suite here. I guess it's just a matter of adding ubuntu-24.04-arm to the runs-on matrix.

[steppi]

I did not expect that. I'll have to look into why the relevant cases aren't there.

[steppi]

I found that xsref has no tables for the spherical bessel functions. I think this is because the public SciPy functions are regular functions that wrap ufuncs instead of ufuncs themselves. I used a script to automatically generate all of the tables based on what functions get called on what arguments in scipy special's test suite, and private ufuncs with public wrappers only got included if I manually added them.

It shouldn't be too bad to add the tables. I might have time over the weekend.