BUG: Incorrect translation of AMOS Fortran code resulting in incorrect/NaN outputs

[hchau630]

This following line in the function kscl in amos.h is incorrectly translated from the original Fortran code:

cs = (exp(std::real(cs)) / tol) * (cos(std::imag(cs)) + sin(std::imag(cs) * std::complex<double>(0, 1)));

The original Fortran code (in zkscl.f) is:

STR = DEXP(CSR)/TOL
CSR = STR*DCOS(CSI)
CSI = STR*DSIN(CSI)

so really it should be translated as

cs = (exp(std::real(cs))/tol)*std::complex<double>(cos(std::imag(cs)), sin(std::imag(cs)));

This resulted in incorrect/NaN outputs for special.kv on certain edge case values. For example

>>> from scipy import special
>>> special.kv(0, 680-1000j)
np.complex128(nan+infj)
>>> special.kv(0, 680-680j)
np.complex128(-4.5537300329442675e-298-0.02992162857456993j)

when really the outputs should be 1.9017e-298+1.7134e-297j and -4.5537e-298-1.8787e-297 respectively.

[steppi]

Thanks for the report @hchau630. Would you like to submit a PR with the fix? If not, I should be able to do it sometime over the next few weeks.

[hchau630]

Sorry probably not, since presumably I'll also have to add some new test cases for the fix and I'm not really familiar with the testing pipeline of xsf. Thanks in advance for fixing the issue.