Re: Alternative atan2 (was Motion 52: final ...)
Lee Winter wrote:
> There is no justification for changing the name or specifications of
> the classic atan2(). It needs to return an interval within +/-tau/2.
> However, the addition of a non-inflationary function, say atan2_sharp(),
> would be valuable. In addition to a different name, it needs a careful
> definition of its specification.
I assume "tau" means "2pi".
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)].
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! That is bad news, because we do
want to detect the case atan2_sharp(X,Y) where both X and Y contain 0.
Looks like we need a special case here.
Btw, the fact that atan2_sharp() is not an interval extension of a
point function argues strongly in favour of keeping the basic atan2(),
which is the interval extension of its corresponding point function.
Michel.
---Sent: 2013-11-27 17:32:45 UTC