(j3.2006) Special math functions

Lawrie Schonfelder j.l.schonfelder
Tue May 1 08:50:31 EDT 2007

I looked at the draft and it looks rather deficient to me. Apart from the function argument and result types, which are
pretty obvious for all the functions the descriptions simply reproduce one of the mathematical definitions to be found
in a book like Abramovitz and Stegun. There is no attempt to define any of the computational properties that must be
met. To me these would be the only justification for an international standard.
I have long thought that now Fortran included a model definition for its floating point arithmetic it should be possible
to require computational standards in the intrinsic maths functions relative to the model parameters. This could be
particularly useful in many applications. Of course it could be argued that such issues are "quality of implementation"
and not legitimately part of the language standard.
Including the contents page of Abramovitz and Stegun as part of the standard does seem to be of limited use particularly
for the more esoteric functions. For example, if I need the cumulative error function, I may need it with augments close
to the mean or I may be looking at outrider statistics where I need accurate values in the tail. These require quite
different approximation techniques. So simple saying my language gives me the function as part of the standard with no
information as to the computational performance would be useless.

Lawrie Schonfelder
Wirral, UK

> -----Original Message-----
> From: j3-bounces at j3-fortran.org [mailto:j3-bounces at j3-fortran.org]On
> Behalf Of David Muxworthy
> Sent: 01 May 2007 12:45
> To: j3 at j3-fortran.org
> Subject: Re: (j3.2006) Special math functions
> On 1 May 2007, at 02:02, Van Snyder wrote:
> > incomplete Gamma and Beta functions,...Fadeeva (aka plasma
> > dispersion) function,
> >
> > But... I don't see a need for an International Standard in this area.
> What one of the British C folk told me was that they cast envious
> eyes on all the mathematical software available to Fortran users and
> the intention behind this standard was to try to ensure that C became
> more obviously competitive in this area.  The same ends could be
> achieved by interoperability of course and who is to say what
> language the Fortran libraries are actually written in?  But I agree
> an International Standard is a strange way to go about it.
> Cheers,
> David
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