Re: [pure-lang-users] complex 0

[Eddie R. <er...@bm...>]

On Tue, 2008-09-09 at 00:31 +0200, Albert Graef wrote:
> Eddie Rucker wrote:
> >  > (2.0+:1.0)/0.0;
> >  inf+:inf
> >  > (2.0+:1.0)/(0.0+:0.0);
> >  nan+:nan
> > 
> > Um. Should this be consistent?
> 
> Maybe, not sure. AFAICS, there are three possible perspectives:
> 
> - (2.0+:1.0)/0.0 has an exact 0 in the imaginary part of the divisior, 
> so it's actually a vector multiplied with an infinite scalar, whereas in 
> the case of (2.0+:1.0)/(0.0+:0.0) it's an inexact zero so the general 
> formula must be used which yields nan+:nan because a zero meets a pole 
> in both components. (OTOH, if we take this view then probably 
> (2.0+:1.0)/(0.0+:0) should yield the same result as the former, whereas 
> right now it yields the same result as the latter.)

In Pure, ln 0 => -inf and ln 0.0 -> -inf.  The former is an exact zero
so in real math ln 0 should be undefined. The second is a number close
to zero which yields -inf. So I'm thinking the exact 0 for the imaginary
part of 0.0 should also be promoted to double just like in ln 0. If I'm
wrong then I'm Ok with that.

> - The divisor should be promoted to a complex 0.0+:0.0 in the first 
> case, so you get nan+:nan in either case.
> 
> - The divisior should be promoted to a real 0.0 in the second case, 
> yielding inf+:inf in either case. That's what I get with mzscheme, but 
> it doesn't make any real sense (pun intended) to me because 0.0+:0.0 is 
> *not* the same as 0.0+:0 (or just 0.0) in the IEEE 754 sense (the 
> imaginary zero might as well be just an underflow).

Hm. if we start worrying about 0.0+:0 vs 0.0+:0.0, then should we also
worry about ln 0 vs ln 0.0 too? I think I've already mentioned that
mzscheme says that (log 0) is undefined and (log 0.0) => -inf.0.
Am I'm flogging a dead horse here? Oh woe woe woe is me!

e.r.