Re: Motion M006.01: discussion period begins, until October 17
On 2016-10-05 08:39:34 -0700, Dmitry Nadezhin wrote:
> Vincent,
>
> > I don't like the word "difficult" in this context, because it
> > may not actually be difficult. I would rather use a word like
> > "advanced" / "enhanced" / "extended".
>
> Do you like a word "accuracy-relaxed string" ?
This is beter, IMHO.
> > In §6.7.5, I would replace "any interval" by constraints obtained
> > with a basic algorithm to have a reasonable behavior, such as:
I think that there was an error in (2). It was:
2. If L < U, then return the hull of x.
It should be like (4), i.e. one should have:
2. If l <= u, return any interval I such that
[l,u] included in I included in hull(L,U).
The only difference is that this is a bit relaxed with rational
literal bounds. But since L < U implies l <= u (used in (4)),
one can remove (2) entirely. I hope that this is now correct.
> I like your suggestion about L and U.
> What will your rules say about semi-infinite interval with rational
> bound like "[p/q, +inf]" ?
This should be similar to the corrected (2) and (4) where U = [l,+oo).
> I think that U is not relevant here and it should return I such that
> [p/q, +oo) included in I include in [hull(hull(p)/hull(q)), +oo).
I suppose that you meant: [inf(hull(hull(p)/hull(q))), +oo)
But saying that U = [l,+oo) is simpler and avoids a dependency on
the rules from (1).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <https://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)