Re: improving special functions in GSoC 2017

[Robert T. Short]

On 06/25/2016 11:52 PM, John W. Eaton wrote:
> On 06/26/2016 02:08 AM, Colin Macdonald wrote:
> > On 25/06/16 02:54, Marco Caliari wrote:
> > > "Special functions are expected by users to just work".
> >
> > So I just found that our "besselj" gives NaNs for values like "1e10".
> >
> >  >> besselj(1, 1e9)
> > ans = -5.21042264155388e-06
> >  >> besselj(1, 1e10)
> > ans = NaN + NaNi
> >
> >
> > https://savannah.gnu.org/bugs/index.php?48316
> >
> >
> > That's not some wild exotic function: its a common Bessel function!
> >
> >
> > Why are we not just calling some free-licensed library that nails these
> > things?
>
> Amos was the best thing I knew of at the time.  If there is something 
> better now, or a standard library solution, then perhaps we should be 
> using it.  Propose a patch and a test suite.
>
> jwe
There was some discussion of this a few years ago (something like 2011 
or 2012).  At the time Amos was still the best option that we could 
find.  I don't remember all the details, but other libraries (including 
boost) didn't handle things like complex arguments or other some other 
crucial element.  Hopefully things have changed since then, but that was 
the conclusion at that time.  I was not able to find that thread so my 
memory is not refreshed.  I put in a bunch of tests at the time we had 
the discussion.  It seems, though, that I didn't do any for complex 
arguments.  I have no clue how I missed that.

I played around with python (scipy.special) a bit and didn't see any 
obvious issues so it might be worth looking at the library they use.

Bob