Re: reference for Fermi-Dirac integral implementation

[Gerard Jungman <jungman at lanl dot gov>]

On 06/21/2013 04:17 AM, mendl@ma.tum.de wrote:
> Dear Gerard Jungman,
>
> could you provide me with a reference (i.e., published paper) for your
> implementation of the Fermi-Dirac integral function for the GNU Scientific
> Library?
>
> I'm currently working on a re-implementation for CUDA, and am thus curious
> to learn about your work. For my case, only single precision accuracy is
> needed, but the CUDA version should run fast since it has to be executed
> many times.
>
> Thanks a lot!
>
> Christian Mendl
> http://christian.mendl.net

Hi. Thanks for the question. I have included the GSL mailing list in my 
reply,
so that the answer can be archived.

The fixed index functions are Chebyshev fits. I may have computed those
myself. If you happen to only need fixed index functions, the best thing
would be to recompute the fits at the fixed precision that you need.

But I assume you are actually asking about the variable index "F_j(x)".
The reference to "Goano" in fermi_dirac.c was unfortunately never spelled
out there. This reference should have been given as follows:

  M. Goano, ACM Trans. Math. Soft. 21 (1995) 221.
  "Algorithm 745: Computation of the Complete and Incomplete 
Fermi-Dirac Integral"

Looking at the code, I see that some of the branches depend on other GSL
functions, including the hypergeometric functions. This is a can of worms,
since the hypergeometric implementations are the most complicated in the
library. Eventually, there must be a better way to do this, but it would
require some original research.

--
G. Jungman