Re: Motion 52: final "Expressions" text for vote
Let me just remind that an implementor
can get X-X=0 by using inner subtraction:
X-^-X:
http://grouper.ieee.org/groups/1788/private/Motions/Motion12.02.pdf
Regards,
Svetoslav
On 25 Nov 2013 at 3:09, Kreinovich, Vladik wrote:
From: "Kreinovich, Vladik" <vladik@xxxxxxxx>
To: Vincent Lefevre <vincent@xxxxxxxxxx>,
"stds-1788@xxxxxxxxxxxxxxxxx" <stds-1788@xxxxxxxxxxxxxxxxx>
Subject: RE: Motion 52: final "Expressions" text for vote
Date sent: Mon, 25 Nov 2013 03:09:36 +0000
> Dear Vincent, Thanks for your comment. I agree that this is just one of the goals, not THE goal.
>
> Yes, we need intersection, union, etc., but my point is our ulmitae goal is applications -- whether to computations in pure mathematical computing or to problems from engineering and science. While computing the range may not be the only reason, if we have a choice, we should select the one which is most appropriate from the viewpoint of the corresponding application problem.
>
> Re x-x, I think we are in full agreement
> ________________________________________
> From: stds-1788@xxxxxxxx [stds-1788@xxxxxxxx] on behalf of Vincent Lefevre [vincent@xxxxxxxxxx]
> Sent: Sunday, November 24, 2013 6:40 PM
> To: stds-1788@xxxxxxxxxxxxxxxxx
> Subject: Re: Motion 52: final "Expressions" text for vote
>
> On 2013-11-23 22:22:49 +0000, Kreinovich, Vladik wrote:
> > The goal of interval computations is to provide enclosures for
> > ranges of functions of real variables over intervals.
>
> Well, I disagree. This is just *one* of the goals. Another goal is
> to do pure computations on intervals; this includes set operations
> like union (yielding hull on intervals) and intersection.
>
> > Interpretation of expressions should be left to the implementation,
> > it is not a question of mathematcial foundations.
> >
> > It is a question of mathematical foundations of what is the range of
> > x-x when x is in [1,2]. Clearly, the range is 0. It is a question of
> > implementation whether X-X, where X is an interval, would return
> > [0,0] or a wider interval -- as long as what it returns is an
> > enclosure for the exact range.
>
> I disagree or don't think this should be said like that. Say, for
> some language, one could have the following various levels (very
> simplified):
>
> 1. Program text (a sequence of characters).
> 2. Some kind of program graph, after lexical and semantic analysis.
> 3. Another program graph, after some language-specific optimizations.
> For instance, the language could regard for some types, x-x to be
> equivalent to 0.
> 4. For the various "interval expressions", the interpretation in P1788
> (via bindings).
>
> IMHO, in P1788 (4), X-X must not be simplified to [0,0]. But such
> a transformation could be done at the language level (3), before
> regarding the expression as being an interval expression.
>
> > It would be great if we could always return the exact range, but
> > since the problem of computing the exact range is NP-hard, we will
> > inevitably sometimes produce the enclosure with excess width.
>
> One would also need to be careful with requirements on Empty.
> For instance, the exact range of some expression could be Empty,
> but a range computed in an efficient way could be non-Empty.
>
> --
> Vincent Lef`evre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
> 100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/>
> Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)