Behaviour of negative zero (-0.0) in comparison with positive zero (+0.0)

Question

In my code,

float f = -0.0; // Negative 

and compared with negative zero

f == -0.0f

result will be true.

But

float f = 0.0; // Positive

and compared with negative zero

f == -0.0f

also, result will be true instead of false

Why in both cases result to be true?

---

Here is a MCVE to test it (live on coliru):

#include <iostream>

int main()
{
    float f = -0.0;

    std::cout<<"==== > " << f <<std::endl<<std::endl;

    if(f == -0.0f)
    {
        std::cout<<"true"<<std::endl;
    }
    else
    {
        std::cout<<"false"<<std::endl;
    }
}

Output:

==== > -0  // Here print negative zero

true

Answer 1

Floating point arithmetic in C++ is often IEEE-754. This norm differs from the mathematical definition of the real number set.

This norm defines two different representations for the value zero: positive zero and negative zero. It is also defined that those two representations must compare equals, so by definition:

+0.0 == -0.0

As to why it is so, in its paper What Every Computer Scientist Should Know About Floating Point Arithmetic, David Goldberg, 1991-03 (linked in the IEEE-754 page on the IEEE website) writes:

In IEEE arithmetic, it is natural to define log 0 = -∞ and log x to be a NaN when x < 0. Suppose that x represents a small negative number that has underflowed to zero. Thanks to signed zero, x will be negative, so log can return a NaN. However, if there were no signed zero, the log function could not distinguish an underflowed negative number from 0, and would therefore have to return -∞.