Re: Motion: Number format (Motion 33?)
> > If we require these properties from numeric types, should not we
> > formulate similar requirements to interval datatype.
>
> I think so.
What do you think about formulation of requirements to F and requirements to T in the same motion ?
> > 2) Interval [0,0] mut be in T (as A3)
>
> I'm not sure. Are there operations that would return this interval
> explicitly? If neg() is not in the standard, [0,0] must be in T so
> that the user can write [0,0] - x to get something equivalent to -x.
Can anybody think of interval type T that doesn't contain [0,0] ?
> > 3) For any bounded notempty interval [u,v] in T exists singleton interval [x,x] in T
> > such that x \in [u,v]
>
> Can anyone think of a format for which this wouldn't be true?
>
> To avoid some surprises, perhaps the following could be added:
> the hull of a symmetric interval must be symmetric.
This is a good point. I agree with this requirement on T.
> > If we accept these requirements on P1788 interval datatypes,
> > then for each interval datatype T we can build canonic number format
> > that consists of all singletons [x,x] in T and
> > of special datum -oo, +oo, NaN .
> > It is still necessary to choose rounding function.
> >
> > Aren't these additional requirements (1)-(3) on interval datatypes too much ?
>
> Perhaps (3), except if the goal is to have a canonic number format.
Yes. The goal is a canonic number format.
I keep in mind Lee Winter's idea in the last paragraph of:
http://grouper.ieee.org/groups/1788/email/msg04903.html
At least, operation "center: T->T" could be better for centered form than "mid: T->F".
center(x) for nonempty x returns some singleton interval contained in x.
-Dima
----- Исходное сообщение -----
От: vincent@xxxxxxxxxx
Кому: stds-1788@xxxxxxxxxxxxxxxxx
Отправленные: Воскресенье, 15 Апрель 2012 г 3:43:31 GMT +04:00 Абу-Даби, Маскат
Тема: Re: Motion: Number format (Motion 33?)
On 2012-04-14 05:25:47 -0700, Dmitry Nadezhin wrote:
> If we require these properties from numeric types, should not we
> formulate similar requirements to interval datatype.
I think so.
[...]
> Shouldn't we make this definition stricter and require from T properties similar to requirements
> to "P1788 number format":
> 1) Datatype T must be symmetric - in interval x is in T then -x is in T (as A4).
Perhaps (and require the -x operation to be exact).
> 2) Interval [0,0] mut be in T (as A3)
I'm not sure. Are there operations that would return this interval
explicitly? If neg() is not in the standard, [0,0] must be in T so
that the user can write [0,0] - x to get something equivalent to -x.
> 3) For any bounded notempty interval [u,v] in T exists singleton interval [x,x] in T
> such that x \in [u,v]
Can anyone think of a format for which this wouldn't be true?
To avoid some surprises, perhaps the following could be added:
the hull of a symmetric interval must be symmetric.
> If we accept these requirements on P1788 interval datatypes,
> then for each interval datatype T we can build canonic number format
> that consists of all singletons [x,x] in T and
> of special datum -oo, +oo, NaN .
> It is still necessary to choose rounding function.
>
> Aren't these additional requirements (1)-(3) on interval datatypes too much ?
Perhaps (3), except if the goal is to have a canonic number format.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)