Thread Links Date Links
Thread Prev Thread Next Thread Index Date Prev Date Next Date Index

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

Chenyi Hu wrote:

Jim,
We are taking a step-by-step approach. As far as I know, BLAS-3 is not on the agenda yet. 
Chenyi


James Demmel <demmel@xxxxxxxxxxxxxxx> 9/10/2009 8:42 AM >>>

I know the committee has a lot to do, but if it is going to consider
standardizing accurate versions of the BLAS-1 operations,
what about BLAS-2 and BLAS-3?
Jim Demmel

Dan Zuras Intervals wrote:

Date: Thu, 10 Sep 2009 13:25:08 +0200
From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
To: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
CC: Ulrich Kulisch <Ulrich.Kulisch@xxxxxxxxxxx>, stds-1788@xxxxxxxxxxxxxxxxx, Nathalie Revol <Nathalie.Revol@xxxxxxxxxxx>, vladic@xxxxxxxx, Ronald Boisvert <boisvert@xxxxxxxx> 
Subject: Re: Request for motion [Fwd: Input from IFIP WG 2.5 to IEEE Interval
 Standards Working Group]

Dan Zuras Intervals wrote:


	If we are to pursue this at this time, please include accurate
	versions of all of sum, dot product, sum of squares, & sum of
	absolute values for all supported precisions.

	That the sum is needed is obvious.

	The sum of squares is needed for an accurate 2-norm & is
	different than calling dot product with the same argument
	twice in ways that are important in our context.

	The sum of absolute values is needed for a 1-norm & is pretty
	cheap once you have an accurate sum.

Yes, these are useful. Perhaps also the 2-norm itself!

	Yes.


	Finally, let me caution you that how these things behave on
	empty & NaI elements may turn out to be important to this
	group.
I think only interval-valued results for noninterval inputs should be provided by the standard. Then there are no problems. 
	Well, I am concerned about the elements chosen from empty
	or NaI intervals that end up being elements of the vectors
	in one of these operations.

	As we have not even touched on the issue of representation
	of empty & NaI yet, I thought it important.


If some element is NaN or two terms in the sum are +inf and -inf,
the result should be the empty set; otherwise the tightest enclosing
interval of the exact result should be returned.


Arnold Neumaier

	Arnold,


	Careful here.  Please look at clause 9.4 in 754-2008.

	In the case of sum or dot product you are quite correct.

	But in the case of the norm operations (sum of squares &
	sum of absolute value) the existence of an infinity determines
	the value of the norm even if a NaN element is to be found
	elsewhere in the vector.

	The rules are complicated & vary a bit from operation to
	operation.  They are also controversial & I will not bother
	justifying them again here.

	Let me simply urge caution in defining the exceptional cases.

	Accuracy in the unexceptional case is not the only interesting
	thing about these operations.


				   Dan






--

---------------------------------------------------------------
R. Baker Kearfott,    rbk@xxxxxxxxxxxxx   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
---------------------------------------------------------------