Re: Motion M0046.02: Literals clarified: YES
On 2013-09-15 09:50:20 -0700, Dmitry Nadezhin wrote:
> Michel,
>
> Yes. ulp-count may have more than one digit:
>
> "-10?12" -> [-22.0,+2.0]
>
> Moreover, it is possible to write in the uncertain form any
> semi-infinity interval of any 754 format.
>
> "1?9ue308" -> [1.0e308,+inf] // because 1e309 is larger than max finite b64 value
>
> though it may be awkward
Yes, very awkward. As this doesn't match the Level 1, users should
never do this for this purpose.
> "1?999999999ue300" -> [1.0e300,+inf]
>
> Do you really suggest to extend the uncertain form syntax with
> infinite radius ?
>
> It will be convinient to write semi-infinite intervals in the
> uncertain form, if we allow something like:
>
> "1?ooe100" -> [1.0e100,+inf].
I suppose you meant something like "1?ooue100". But "[1.0e100,+inf]"
is more readable. So, I don't think that supporting infinite radius
is a good idea.
> Nevertheless, interval like [1.0e100,1.0e300] will continue to look
> awkward in the uncertain form.
If you mean that the interval needs to be represented exactly,
then yes. Otherwise the idea behind the uncertain form is that
such an interval can be approximated by [0,1.0e300], and it won't
be awkward any more (the uncertain form is more like fixed point
than floating point, though the accuracy is generally determined
from the maximum exponent of the bounds).
> > I wonder whether it would be useful to mention that the "Uncertain form"
> > is adequate for narrow (and hence bounded) intervals not containing zero,
> > but is severely restricted otherwise.
>
> I agree. It would be useful.
Actually containing zero is not necessarily a problem, and what
"narrow" means depends on the context. If in your application,
your numbers are of the order of magnitude 1e100 and using
double-precision arithmetic is sufficient, then you may regard
[-1,1] as narrow and the fact that this interval contains 0
won't necessarily matter.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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