Re: Request for motion [Fwd: Input from IFIP WG 2.5 to IEEE Interval Standards Working Group]
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
>