RE: Motion M0061.02 : YES
True, a good example is complex numbers, we can use circles or boxes to describe uncertainty, and depending on what we use, we get different results which are not always compatible.
-----Original Message-----
From: stds-1788@xxxxxxxx [mailto:stds-1788@xxxxxxxx] On Behalf Of Vincent Lefevre
Sent: Friday, February 28, 2014 7:53 AM
To: stds-1788
Subject: Re: Motion M0061.02 : YES
On 2014-02-28 09:19:18 +0100, Guillaume Melquiond wrote:
> The last paragraph of 7.5.4 is a bit restrictive too. It might well
> happen that two different implementations are just incomparable. I am
> thinking in particular of elementary functions; which one of two
> implementations is the most accurate presumably depends on the input
> domain (values close to zero, large values, etc) due to their having different argument reduction.
I think that linear ordering may be useful for the end user, and the current "should" is OK. But IMHO, the ordering should just be informative, and not necessarily linear: accuracy mode 1 > accuracy mode 2 when in general f1(X) in included in f2(X), without a guarantee that this is always the case. The idea is to inform the user that he will generally get more accurate results by choosing mode 1 instead of mode 2. The only guaratee is that for inf-sup types (when the hull is unique), the tightest mode gives the most accurate results.
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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <https://www.vinc17.net/> 100% accessible validated (X)HTML - Blog: <https://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)