Re: Alternative atan2 (was Motion 52: final ...)
On 2013-11-27 12:01:03 -0500, Michel Hack wrote:
> We have to be careful here. There is no change in the point library,
> which has only one atan2() function (for each supported format), whose
> Level 1 range is (-pi,+pi] in the notation of Table 10.1, and whose
> Level 2 range is presumably [rdown(-pi),rup(+pi)].
The Level 2 range depends on the interval type (not necessarily
inf-sup) and the implementation. Anyway this doesn't matter for
the alternative atan2.
> However, atan2_sharp() can only be an interval function, and it is
> NOT the interval extension of a point function. So according to our
> definitions it would have to be called an interval mapping, and it
> would not have a decorated version!
Perhaps we could define a decorated version, where decorations are
generalized to multivalued functions. Or consider the fact that
atan2_sharp has a corresponding point function where the result
would be in R/(2pi)Z instead of R. The latter is simpler, IMHO.
> That is bad news, because we do want to detect the case
> atan2_sharp(X,Y) where both X and Y contain 0.
Yes, and just by looking at the interval part of the result, you can't
even detect that. But a user who cares could still test X and/or Y
before calling atan2_sharp(X,Y).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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