Re: Why (IMO) you should vote Yes to Motion 14.02
> Date: Wed, 30 Jun 2010 18:40:31 +0200
> From: Christian Keil <c.keil@xxxxxxxxxxxxx>
> To: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
> Cc: stds-1788@xxxxxxxxxxxxxxxxx
> Subject: Re: Why (IMO) you should vote Yes to Motion 14.02
>
> . . .
>
> > Thus some form in which the bound may be recovered by, x + eps
> > or even x + x*eps would be acceptable so long as those
> > operations can be performed exactly.
>
> Isn't this and your later argument about the requirement on the sum in
> mid-rad formats exactly this inferring too much? I said "the note
> could be interpreted to define the nature of the level 2 datum having
> endpoints in F". You say that is inferring too much. The next step in
> my argument would be: well in this case the text doesn't define the
> nature of the level 2 datum and therefor doesn't require the bounds to
> be in F. The note on the triple representation uses a sum to represent
> each bound but doesn't say where the operation is to take place and
> what kind of result it should have, most importantly it doesn't
> require the sum to be executed in F. All of this comes IMHO from the
> definition of the level 2 datum. So probably if this Motion is
> referring to Section 5 of the standard that part has to be figured out
> before a final conclusion of this one---or this one has to be general
> enough to support an (in a limited way) arbitrary Section 5 (probably
> with minor adjustments).
>
> On to the more fundamental issue...
>
> Christian
Much of what you say here is true but I'm not sure where
you're going with this.
I am not saying that all possible mid x rad pairs exactly
sum to an element of F. What I am saying is that a mid-rad
form can be RESTRICTED to those pairs that exactly sum to
an element of F. The use of
mid <-- mid
rad <-- roundAway(mid + rad) - mid
is one such restriction. There may be others.
And, while I did not think about it in quite the same way
as you seem to be, I AM saying that the extracted endpoints
shall be elements of F or shall be exactly equal to elements
of F. Whether extracted from an inf-sup, a mid-rad, or a
mid-rad1-rad2.
And the part I'm not sure of in your comments here is the
thing about 'where that operation is to take place'.
If you mean, is it to happen when the bound is extracted?
Then, yes, I believe that is when it happens.
But if you mean, is it to be done in the same floating-point
arithmetic as is associated with F? Then I have to admit I
haven't thought about that. I don't know. I would certainly
insist that the result, when converted to an element of F, be
converted exactly (or losslessly, as you say in your next
note). But if there is some advantage to be had by doing
that arithmetic in some other way, I see no need to prevent
it.
Then again, neither do I see any utility in it.
Do I misunderstand your meaning here, Christian?
Dan