[J3] More Bessel functions

[Ondřej Čertík]

On Tue, Jan 19, 2021, at 7:26 PM, Steven G. Kargl via J3 wrote:
> On Tue, Jan 19, 2021 at 02:49:59PM -0800, Van Snyder via J3 wrote:
> > On Tue, 2021-01-19 at 12:28 -0700, Ondřej Čertík via J3 wrote:
> > > On Tue, Jan 19, 2021, at 12:11 PM, Steven G. Kargl via J3 wrote:
> > > > On Tue, Jan 19, 2021 at 10:45:22AM -0800, Van Snyder via J3 wrote:
> > > > > On Tue, 2021-01-19 at 16:38 +0000, Nathan Sircombe via J3 wrote:
> > > > > > They’re not implemented in libm as far as I can tell -
> > > > > > https://www.gnu.org/software/libc/manual/html_node/Special-Functions.html
> > > > > > 
> > > > > > …so you don’t get them ‘for free’, although GSL has
> > > > > > animplementation.
> > > > > 
> > > > > There are more things in heaven and earth, Horatio, than are
> > > > > dreamt ofin your philosophy.There are more sources of freely-
> > > > > available reliable mathematicalsoftware than libm.
> > > > 
> > > > Isn't your second sentence an argument against adding these
> > > > functions to the Fortran standard?
> > > > As Bill points out, Abramowitz and Stegun is a rather thickbook on
> > > > special functions.  It is now updated and availablefor free at 
> > > > https://dlmf.nist.gov.  The NIST site contains linksto software,
> > > > e.g., https://dlmf.nist.gov/10.77.  Should theFortran standard
> > > > include all of the functions covered by NIST?
> > 
> > The advantage of standards is they are, well, standard.
> > One can find software for just about any special function. Typically
> > several routines, with different interfaces.
> 
> I think that this is slippery slope.
> 
> I suspect that solving linear algebra problems far out
> paces the need for BESSEL_I0(x), etc.  Should the Standard
> include standardized interfaces for some, many, or all of
> the BLAS and LAPACK routines?  Perhaps, the Standard should
> include an intrinsic module named ISO_MATRIX that encapsulates
> BLAS and LAPACK interfaces.
> 
> I also suspect forward and inverse FFTs far out pace
> the need for BESSEL_I0(x).  Again, should the Standard
> include standardized interfaces and an ISO_FOURIER intrinsic
> module?  Should it only include radix-2 FFTs?  I would
> advocate for Clive Temperton's prime factor FFT algorithms.

Yes, Fortran needs a high quality implementation of all of these (and more), readily available to the user. I would argue against putting all these into the Fortran standard today. However, all these are in scope and planned for stdlib:

https://github.com/fortran-lang/stdlib/

And that is a great start to put all these, with a community discussed and agreed upon API, and a good (i.e., numerically accurate and fast) reference implementation (leveraging / reusing software that is already available whenever possible).

Ondrej