BUG: special: fix algorithmic error in ratevl in cephes/polevl.h

[ZhibingSun]

Reference issue

Closes #20697.

What does this implement/fix?

It fixed an algorithmic error in ratevl in cephes/polevl.h.

Additional information

[tupui]

Thanks @ZhibingSun

[lucascolley]

and congrats on your first contribution to SciPy!

[steppi]

I think it's fine to keep this comment here, but just want to point out that this may change in the future, especially as we work on unifying the cephes, amos, specfun, cdflib, faddeeva, etc. codebases.

[ZhibingSun]

Sure. I just checked the code for $erf(x)$ and $erfc(x)$ in special/Faddeeva.cc, which I think have better performance than the ones in cephes/ndtr.h, so is it possible to improve the performance of the functions in cephes/ndtr.h in the future, i.e., $erf(x)$, $erfc(x)$, and $ndtr(x)$?.

[steppi]

We actually found that cephes has better accuracy for real valued ndtr, erf, and erfc. See #19492 (comment).

I just meant that it's not unlikely that ratevl will end up being used again in another function, and I want to make sure to keep in mind that if so, this comment will need to be updated.