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Re: Alternative atan2 (was Re: Motion 52: final ...)

Lee,

Would you like to propose such a specification?

George Corliss


On Nov 27, 2013, at 10:30 AM, Lee Winter <lee.j.i.winter@xxxxxxxxx> wrote:

> On Wed, Nov 27, 2013 at 7:39 AM, Vincent Lefevre <vincent@xxxxxxxxxx> wrote:
>> On 2013-11-27 11:46:19 +0000, John Pryce wrote:
>>> I think atan2 is the only one that can be "improved" by this method.
>> 
>> I also think so.
>> 
>>> Basically, for any box (yy,xx) in R^2 that doesn't contain (0,0),
>>> but meets the usual branch cut of atan2, the idea is to rotate the
>>> branch cut out of the way of the box. Depending on the rule for
>>> which direction to rotate, one gets different answers for the range
>>> of the resulting function. Bill, is that right?
>>> 
>>> It's a neat idea. Jürgen, would you consider adding this to function
>>> to our list (recommended, I would say)? Who supports this?
>> 
>> IMHO, the alternative function should have a different name, so that
>> it is not confused with the usual atan2 function (standardized in
>> ISO C, POSIX and IEEE 754-2008 at least). This traditional atan2
>> function should still be supported in P1788, as it could be useful
>> to obtain proved results (enclosures...) on this function.
> 
> Absolute agreement here.
> 
> 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 suggest that atan2_sharp() be specified such that it returns the
> same two points as atan2(), with one end point adjusted by tau so that
> the result is (i) sharp, and (ii) centered as closely as possible on
> the true mathematical result.
> 
> Lee Winter
> Nashua, New Hampshire
> United States of America

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