[J3] More Bessel functions

[Ondřej Čertík]

Hi Bill,

On Wed, Jan 20, 2021, at 1:31 PM, Bill Long via J3 wrote:
[...]
> > 
> > Yes, Fortran needs a high quality implementation of all of these (and more), readily available to the user.
> 
> There are professionally written libraries, like NAG, already 
> available.  Also LaPack for some cases.  Perhaps we should argue for 
> robust Fortran interfaces instead, akin to the mpi_f08 module for MPI. 

Yes, exactly: we should argue and agree on a robust API to use for those, but not necessarily putting them into the standard. And that is the purpose of `stdlib` I linked to above.

> 
> 
> > I would argue against putting all these into the Fortran standard today.
> 
> The feature list for F202X is already closed, so F202Y would be the 
> soonest.  Even in the longer run, something like the add-on packages 
> used by C/C++/Python might be a better strategy. 

Yes, add-on seems a better idea.

> 
> 
> > 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).
> 
> “accurate" and “fast" are often conflicting goals. 

Good point. For intrinsic functions, such as `sin` or `erf`, compilers typically use faster but less accurate versions when options like `-ffast-math` are specified. If the special functions are implemented in a third party library, then the library might also provide some similar option to use faster but less accurate versions if requested by the user.

Ondrej