Re: Motion 52: final "Expressions" text for vote
Vincent Lefèvre replied:
> On 2013-11-25 15:35:13 -0500, Michel Hack wrote:
> > I just skimmed the article, and if I understand it correctly, the point
> > it makes is that, for intervals, the restriction of the atan2() range
> > to [-\pi, +\pi] would force some evaluations to return the essentially
> > useless [-\pi, +\pi] instead of a sharp enclosure that straddles \pi.
> >
> > The same may apply to the other inverse-trig functions.
>
> I think that atan2 is a bit particular. Do you have an example
> with a conventional inverse-trig function (asin, acos, atan)?
I have now read Bill Walster's article in more detail. The regular
inverse-trig functions are not affected, and Bill's definition of
the point function atan2() is the same as ours in Table 10.1.
As issue is the interval version of atan2(), which, in order to
permit sharp results, should not be required to be the strict
interval extension of the corresponding point function: for
certain inputs, one or the other bound of the result must be
allowed to be extended outward by 2pi. This will allow sharp
results straddling pi or -pi.
This is independent of cset vs set-based flavour, in my opinion.
So -- should we allow this special dispensation, with an explanation?
After all, we already allow violating transcendental bounds by a small
amount in order to preserve containment.
Michel.
P.S. In a way, this is the same issue facing division by an interval
containing zero. In that case we defined div2() to allow the
return of a pair of tight enclosures instead of Entire. Here
we can actually stitch those two intervals together because the
pole happens to be finite.
---Sent: 2013-11-26 19:34:49 UTC