[hawski]

But still, why there is no absolute 0 - the third zero? I would prefer something like this:

  1 / +0 == +inf
  1 / -0 == -inf
  1 / 0 == nan
  abs(-0) == 0

But it is not possible as there is no unsigned/absolute zero: 0 means +0. I guess it makes things much simpler, but IMHO it makes it a bit less useful and strange.

[pclmulqdq]

I think if you treat infinity as a special case of NaN (which it basically is for many math systems), you get the behavior you want. A lot of people think that +/-0 represent +/-epsilon, but they really don't. +0 is the default 0, and -0 is what you get when you underflow specifically from the left.