[hawski]

IEEE 754 has infinity, it has signed zeros, but it doesn't have the absolute zero. For the math to be entirely correct it is not enough. I wonder why it was done like this.

[pclmulqdq]

+/-0 should generally be thought of as 0. It's just "0 from the right" and "0 from the left." The reason it has +/-0 is for a few specific applications:

- Some people really do want 1/(-x) to be negative infinity when a positive x reaches underflow. This helps with some kinds of numerical simulations since it can preserve the sign bit through underflow.

- Interval arithmetic implementations need to be able to disambiguate closed and open intervals at 0.

If you turn on fast math mode, you can also essentially disable the special treatment of the zeros.

[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.

[kragen]

you're in luck! that's such a frequently asked question that kahan has written several papers about it, and there's a wikipedia page too: https://en.wikipedia.org/wiki/Signed_zero