------- Comment #6 from dennis dot wassel at googlemail dot com 2009-06-01 12:14 ------- (In reply to comment #3)
> My understanding of infinity in the complex plane is what is called (I > call?) "directed inifinity": if abs((a,b)) goes to +Inf and atan2(a,b) has > a defined value in this limit, then (a,b) goes to infinity in the direction > given by atan2(a,b). However (+/-Inf,+/-Inf) defines only four directions > and is unable to represent general "directed inifinity". So I think that > from a "mathematical" point of view the problem is ill-posed, > (+/-Inf,+/-Inf) is in the same class of "undefined" values as 0/0 or > Inf/Inf, and should give NaNs. Then this is the gist of the matter - my FA textbook does not require the argument to converge, but just the modulus, so our understandings of infinity differ. I agree with Dominique in that mathematically (+/-Inf,+/-Inf) is not well-defined, because the limit of a/b is unknown. > Now atan2(a,b) is DEFINED such that atan2(+0,+/-0)=+/-0, > atan2(-0,+/-0)=+/-Pi, atan2(+Inf,+/-Inf)=+/-Pi/4, > atan2(-Inf,+/-Inf)=+/-3*Pi/4 (it seems that it is even built in the Intel > hardware). With this definition of atan2, it is possible to give a > definition of (+/-Inf,+/-Inf) as the directions of the corners of the > "infinite square". I have nothing against this defintion, except it should > be documented. The mathematicians among us will writhe in agony, but I think this serves the purpose best :) > [...] > In this case the results at compile and run times should be the > same ("least surprising approach"). I strongly support that point, because everything else would be a very nasty gotcha for an average Fortran user like myself. -- http://gcc.gnu.org/bugzilla/show_bug.cgi?id=40318