Re: Motion 31 - incorporating Complete Formats into the standard
> Subject: Re: Motion 31 - incorporating Complete Formats into the standard
> From: John Pryce <j.d.pryce@xxxxxxxxxxxx>
> Date: Sun, 12 Feb 2012 22:13:33 +0000
> To: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
>
> P1788
>
> Before re-submitting the Level 1 text I need some answers relating to motion 9...
>
> . . .
> >>
> >> Regarding "exact" vs "accurate" or "faithful" dot product,
>
> The position paper I have is "The Exact Dot Product as Basic Tool for Long
> Interval Arithmetic" by Ulrich Kulisch and Van Snyder (UKVS for short),
> which seems to be written very much as a spec, since it contains "An
> implementation shall ..." sentences.
>
> > I think that P1788 should not do the job of 754...
>
> . . .
>
Let me comment on just these two issues before you.
In principle, I agree with whoever said 1788 should
not do 754 things again. And, indeed, you will find
the dot products & related reductions as optional in
clause 9.4 of 754-2008.
Alas, we could not agree on making them mandatory &
we could not agree on an accuracy policy.
So if 1788 made them both mandatory & exact (as Ulrich
wishes) it would not be repeating anything from 754.
My second comment is really a question. I am familiar
with the uses of Ulrich's dot product in the context
of linear floating-point problems. But I am not
familiar with how they are used in the interval world.
Are they used in the same way as in floating-point by
using a mid-rad form to compute interval results by
means of an accurate vector or matrix midpoint together
with a Jacobian for the radii?
Or does one just do a dot product in the inf elements
& another on the sup elements to get a narrower dot
product on a vector of intervals in some context that
may be entirely unrelated to linear problems?
I ask partly for my own sake & partly because the
answer might drive your own efforts.
Dan