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

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

James Demmel wrote:
> 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?

I think these just behave componentwise, hence need not a separate 
specification. (Solving triangular systems would be a different matter
since computations are nested, but I think this is too far away from 
arithmetic to merit inclusion into an interval arithmetic standard.)

BLAS2 and BLAS3 are important as programs since there are important 
implementation issues that drastically affect performance. But they
were not important for the IEEE 754 standard.

But accurate sums and inner products in IEEE 754 would have been a 
standardization issue since they cannot be easily obtained with
standard 754 operations. But the committee apparently saw no need
for it.

An interval standard has a slightly different perspective since
errors accumulate in a worst case way and the cancellation that may
be inherent in sums and inner products may lead to useless bounds.

That's why we need to consider these operations.


Arnold Neumaier