ENH: special: translate sph_bessel to C++, refactor cyl_bessel

[izaid]

This PR translates and refactors various Bessel functions, both spherical and cylindrical. Currently a work in progress.

[izaid]

@steppi This is done, ready for review.

[izaid]

Right, I did a bit more here. Namely some other clean-up that needed to happen: standardising functions with multiple outputs to take references instead of pointers, remove sf_error.c so only sf_error.cc exists, etc. A lot of things are in better shape. Done here.

[steppi]

OK, there's a lot going on here @izaid . I'm going to give you a pass, because I know this is the last week you'll be able to devote to SciPy for a while, so I think it's fine to err on the side of getting as much as possible done. This was tough to review though due to a combination of many unrelated changes, and difficulty determining what was essential. The only change I've seen that is needed is ensuring Python.h is the first included header wherever it appears.

Let me know if the following list of changes is exhaustive.

1. A large number of formatting changes.
2. Passing references instead of pointers for ufuncs with multiple return values.
3. _spherical_bessel.pxd translated into C++.
4. Cylindrical bessel functions moved out of amos and into bessel.h.
   Can you give an account of what other changes, if any, were made besides moving
   these to a new file and changing some function names?
5. sf_error.cc and sf_error.c combined to a single file, sf_error.c.
6. New header scipy/special/special.h for functions where SciPy behavior deviate from behavior in C++ library (returning multiple values, where is from an independent function, runtime warning for noninteger parameters, returning NAN when result should be 0.
7. New header for exponential integrals, translation of scaled_exp1 into C++ header.

Did I miss anything?

[steppi]

@izaid and I talked about this offline, we both agree that having these files in the folder scipy/special makes the special in the filename redundant. We're just leaving it like this for now because there's already a generated _ufuncs.pyx which generates _ufuncs.c, and we want a way to distinguish between these until the generated ufuncs from _generate_pyx.py are moved to the new ufunc infrastructure.

[steppi]

Ideally, these pure formatting changes should be left out of big PRs like this. Keep it as is, it just slows down review because I have to check that nothing essential has changed here.

[steppi]

For the sake of anyone watching from the sidelines, the naming may seem confusing because special is temporarily overloaded right now in our naming scheme. When the C++ library of special functions gets a name, X, these files will become X_wrappers.cpp and X_wrappers.h. The function names here will be things like X_itstruve0 etc. Having things like that seems reasonable to me.

[izaid]

Yes, so the idea here is that the C wrappers are X_whatever for a C++ function X::whatever. Right now, X is "special", but we expect that to change in the future. This is pretty standard practice.

[izaid]

OK, there's a lot going on here @izaid . I'm going to give you a pass, because I know this is the last week you'll be able to devote to SciPy for a while, so I think it's fine to err on the side of getting as much as possible done. This was tough to review though due to a combination of many unrelated changes, and difficulty determining what was essential. The only change I've seen that is needed is ensuring Python.h is the first included header wherever it appears.

Let me know if the following list of changes is exhaustive.

1. A large number of formatting changes.

2. Passing references instead of pointers for ufuncs with multiple return values.

3. _spherical_bessel.pxd translated into C++.

4. Cylindrical bessel functions moved out of `amos` and into `bessel.h`.
   Can you give an account of what other changes, if any, were made besides moving
   these to a new file and changing some function names?

5. sf_error.cc and sf_error.c combined to a single file, sf_error.c.

6. New header `scipy/special/special.h` for functions where SciPy behavior deviate from behavior in C++ library (returning multiple values, where is from an independent function, runtime warning for noninteger parameters, returning `NAN` when result should be 0.

7. New header for exponential integrals, translation of scaled_exp1 into C++ header.

Did I miss anything?

OK, there's a lot going on here @izaid . I'm going to give you a pass, because I know this is the last week you'll be able to devote to SciPy for a while, so I think it's fine to err on the side of getting as much as possible done. This was tough to review though due to a combination of many unrelated changes, and difficulty determining what was essential. The only change I've seen that is needed is ensuring Python.h is the first included header wherever it appears.

Let me know if the following list of changes is exhaustive.

1. A large number of formatting changes.

2. Passing references instead of pointers for ufuncs with multiple return values.

3. _spherical_bessel.pxd translated into C++.

4. Cylindrical bessel functions moved out of `amos` and into `bessel.h`.
   Can you give an account of what other changes, if any, were made besides moving
   these to a new file and changing some function names?

5. sf_error.cc and sf_error.c combined to a single file, sf_error.c.

6. New header `scipy/special/special.h` for functions where SciPy behavior deviate from behavior in C++ library (returning multiple values, where is from an independent function, runtime warning for noninteger parameters, returning `NAN` when result should be 0.

7. New header for exponential integrals, translation of scaled_exp1 into C++ header.

Did I miss anything?

That's pretty comprehensive! A lot of refactoring and things to make life easier, plus translation of the spherical Bessel functions. I've made the changes requested now too.

[steppi]

I'm happy with this now.