Re: New extension for Associated Legendre Functions (ALFs)

[Patrick Alken <patrick.alken@colorado.edu>]

I should also mention that I played around with computing
ALFs using quad precision in the recurrence relations. In
doing this you can avoid underflow problems to degrees up
in the 10s of thousands (I only tried up to L,M = 20000).

But unfortunately I don't think sizeof(long double) is standard,
though I do think its guaranteed to be at least 10 bytes
by the latest ansi standard. So for now I left everything
in double precision.

Patrick

On Tue, Mar 17, 2009 at 11:28:52AM +0000, Brian Gough wrote:
> At Mon, 16 Mar 2009 15:31:37 -0600,
> Patrick Alken wrote:
> >   Most current implementations of associated Legendre functions
> > (ALFs), including the current GSL version fail due to underflow
> > above degree and order (L,M) 1900.  A 2002 paper by Holmes and
> > Featherstone shows that with a very simple scaling modification
> > this limit can be extended to 2700 in double precision. I have
> > recently needed to compute high degree ALFs so I have implemented
> > their algorithm and made a new GSL extension if others are interested.
> 
> Great work!
> 
> Incidentally, I found a copy of their paper online at
> http://www.cage.curtin.edu.au/~geogrp/research.html
> http://www.cage.curtin.edu.au/~will/20760279.pdf
> 
> -- 
> Brian Gough