Does float have a negative zero? (-0f)

Question

IEEE floating point numbers have a bit assigned to indicate the sign, which means you can technically have different binary representations of zero (+0 and -0). Is there an

Answer 1

Is there an arithmetic operation I could do for example in C which result in a negative zero floating point value?

Sure:

float negativeZero = -10.0e-30f * 10.0e-30f;

The mathematically precise result of the multiplication is not representable as a floating-point value, so it rounds to the closest representable value, which is -0.0f.

The semantics of negative zero are well defined by the IEEE-754 standard; the only real observable way in which its behavior differs from that of zero in arithmetic expression is that if you divide by it, you will get a different sign of infinity. For example:

1.f /  0.f --> +infinity
1.f / -0.f --> -infinity

Comparisons and addition and subtraction with -0.f give the same result as they would with +0.f (in the default rounding mode). Multiplication can preserve the sign of zero, but as noted, it generally isn't observable.

There are some math library functions whose behavior can vary depending on the sign of zero. For example:

copysignf(1.0f, 0.0f) -->  1.0f
copysignf(1.0f,-0.0f) --> -1.0f

This is more common in the complex functions:

csqrtf(-1.0f + 0.0f*i) --> 0.0f + 1.0f*i
csqrtf(-1.0f - 0.0f*i) --> 0.0f - 1.0f*i

In general, however, you shouldn't need to worry about negative zero.