Re: Request for motion [Fwd: Input from IFIP WG 2.5 to IEEE Interval Standards Working Group]
Dan, et al,
Just for your information, about a decade ago, Jim and I were on the BLAST working group led by Jack. That group tried to establish an Interval BLAS standard including BLAS-1, -2, and -3. The final document is available at http://www.netlib.org/blas/blast-forum/chapter5.pdf. Also, my former graduate student Michael Nooner made a reference implementation which is available at http://www.cs.uca.edu/interval/intbox/ with documentation. We further described the design and implementation as chapter 10 in the book "Knowledge Processing with Interval and Soft Computing" published by Springer last year. Since we did not have a standard on interval computing, the Interval BLAS was listed under Journal of Development in the final document of BLAST.
Regards,
Chenyi
>>> Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx> 9/10/2009 10:26 AM >>>
> Date: Thu, 10 Sep 2009 09:43:41 -0500
> From: "R. Baker Kearfott" <rbk@xxxxxxxxxxxxx>
> To: Chenyi Hu <chu@xxxxxxx>
> CC: James Demmel <demmel@xxxxxxxxxxxxxxx>,
> Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>,
> Nathalie Revol <Nathalie.Revol@xxxxxxxxxxx>,
> stds-1788@xxxxxxxxxxxxxxxxx, Ronald Boisvert <boisvert@xxxxxxxx>,
> Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
> Subject: Re: Request for motion [Fwd: Input from IFIP WG 2.5 to IEEE Interval
> Standards Working Group]
>
> Chenyi, Jim, et al,
>
> Yes, we are taking a step-by-step approach. Also, the dot product
> is BLAS level 1 operation, and we have been given a request to
> consider it :-)
>
> The officers have been discussing among themselves the most
> efficient way of doing the steps, to come to consensus and
> a high-quality final document. One possibility is, essentially,
> voting on pieces of the Vienna proposal. I note the Vienna
> proposal contains statements concerning the accurate dot product.
>
> Concerning BLAS level 2 and BLAS level 3, we'll need to decide
> if this is within our scope and whether it is practical to do
> by the document's delivery date to the Sponsor.
>
> Sincerely,
>
> Baker
>
Begin IMHO
The opening of this rather large can of worms is one of
the reasons I initially wondered if now is the right time
to consider these operations.
Still, the issue of whether or not interval versions of
the BLAS 2 & 3 operations are within the scope of 1788
or not would seem to me to depend on the collective
expertise of our committee members.
For while the higher BLAS functions are derivative in the
same sense as Jim & company think of them, they are also
likely to be implemented directly in floating-point rather
than with our primative interval operations.
I am no expert in this but I have learned enough about
interval linear algebra to know that many of these functions
are computationally intractable when implemented directly in
interval primitives. Rather, it is more likely that such
operations will (at least internally) need to convert to a
midpoint radius form & use accurate floating-point BLAS
together with a Jacobian which will then have to be
converted (conservatively) back into [xlo,xhi] form.
Thus they will require all the expertise our interval
experts can bring to the problem & is (IMHO) something we
should provide for our otherwise inexperienced customers.
Or, at the very least, something we should DEFINE for our
users & provide example libraries for our implementors.
End IMHO
All this will be true whenever we tackle these problems.
On the one hand, it might be better if we knew something
about the details of 1788 before any BLAS are attempted.
On the other hand, given that they are such an important
application for our customers, those who attack this problem
NOW can advise us of the effect of many of our decisions on
their work.
Chickens & eggs come to mind for some reason. :-)
Dan