Re: confluent hyperg

[Gerard Jungman <jungman at lanl dot gov>]

As far as I know, nobody is working on it. The version which I wrote
is not very good. Lately I have regretted putting it in, but I have
been hoping for some time that it could be fixed.

I am not very satisfied with the implementations that I have
seen (such as SLATEC). I was hoping to find something
better to use as a model, but I never did.

I think that there are some recent results in the literature for
uniform asymptotics, and perhaps other improvements exist as well.

If you have an interest, please go ahead and try to do something
better. I would be interested in seeing your friend's code.

Having a "long double" version makes alot of sense. In fact,
it makes sense for many of the special functions. I would like to
see a general solution for this issue, which would provide long
double versions for all functions, without greatly increased
complexity in the code base. This is not completely trivial
because most of the code assumes "double" arithmetic, and
removing this assumption has always been left as an exercise
for the future.

As far as a "logarithmic" version, that might be quite difficult,
at least starting with the current code. There are many paths
in the current implementation, and possible over/under-flows
would have to be tracked through many of these paths. There must
be a better way.

I know that some people have used arbitrary-precision
packages in an attempt to simplify the evaluation. This
may be useful for some argument values, but it cannot
be a full solution for the problem. And although it would
simplify the 1F1 implementation in some sense, it would
probably increase the total complexity of the code. Of
course, there are also performance issues.

It has been some years since I looked at this. I would
be very glad for any comments or help anyone can offer.


Please post your replies to the full list. I like to
keep all the discussions open, in case others might like
to contribute.

Thanks.
-- 
Gerard Jungman <jungman at lanl dot gov>
Los Alamos National Laboratory


On Tue, 2003-04-15 at 22:39, Krzysztof Pachucki wrote:
> Dear Gerard,
> is anybody working on developing confluent hypergeometric function.
> I have recently reported problems with evaluation of U-function.
> Further problems are related to overflow. It might be very convenient to
> have implementation of confluent hypergs in long double arythmetics.
> In fact friend of mine has developed an analogous quad precision
> version in Fortran, it does not work however in logarithmic case.
> 
> Krzysztof
> 
> 
> On Tue, 15 Apr 2003, Brian Gough wrote:
> 
> > Krzysztof Pachucki writes:
> >  > Dear Brian,
> >  > do you know of any implementation of: gsl_sf_hyperg_1F1_e10_e
> >  > Krzysztof Pachucki
> > 
> > Not to my knowledge, you could try asking on
> > gsl-discuss at sources dot redhat dot com or directly to the author
> > Gerard Jungman jungman at lanl dot gov
> > 
> > Brian
> > 
> > 
> > 
-- 
Gerard Jungman <jungman at lanl dot gov>
Los Alamos National Laboratory