[Octave-bug-tracker] [bug #47738] expint is inaccurate for certain imaginary inputs

[Colin Macdonald]

Follow-up Comment #6, bug #47738 (project octave):

SciPy uses the specfun Fortran library (unrelated to our specfun pkg)
corresponding to the book "Computation of Special Functions" by Zhang and
Jin.

Largest relative error I've seen in SciPy is 30*eps, which is still large but
at least better.  I'll look at the licensing (SciPy is BSD-style so should be
fine).  Or I can just reimplement the algorithm from their book.  But it has a
500 loop so might be better to compile it.

I need to look further into this anyway, because sinint and cosint are also
poor (cosint uses same implementation as expint but sinint has its own much
worse implementation which blows up for x>300:
https://github.com/cbm755/octsympy/issues/416)

I haven't tested Boost (@Mike do you know what accuracy they claim?  Does it
work for complex inputs?)

@Doug: it looks like the error could be as large as 2e-8, which looks poor.

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