Re: Comments on Motion 27-A "Decorated Intervals"
On 2011-07-15 15:54:48 +0200, Marco Nehmeier wrote:
> Am 15.07.2011 12:14, schrieb Vincent Lefevre:
> >How is the inclusion defined for the elements of DIR?
>
> In section 1.3.4 we stated that the decoration part is ignored.
I thought Section 1.3.4 was about comparison operations (in
some program). Here I meant inclusions in the specification.
The definitions could be the same in both cases, but this is
not obvious.
> >About Remark 5 (and the whole motion), what do the decorations really
> >mean in practice? For instance, consider f(x) = tan(floor(x)*pi+pi/2),
> >implemented as the composition of the various basic functions, and its
> >interval extension. At Level 1, it is ndf for X = [1,1.5], but not at
> >Level 2, where it is con (because of rounding). With X = [1,3], it is
> >con at both Level 1 and Level 2, though f(x) is nowhere defined. So,
> >what confidence con brings here?
>
> The decoration con tells you that that the level 2 computation of the
> function f(x) may have a singularity on the interval x.
I meant: what confidence con brings compared to ndf?
Since
* one can obtain con for a function that is nowhere defined, and
* one can obtain ndf for a function that is not nowhere defined
(due to the tracking rules),
it seems that there isn't a difference between ndf and con.
Regards,
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)