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

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.

According to the standard, negative zero exists but it is equal to positive zero. For almost all purposes, the two behave the same way and many consider the existence of a negative to be an implementation detail. There are, however, some functions that behave quite differently, namely division and atan2:

#include <math.h>
#include <stdio.h>

int main() {
    double x = 0.0;
    double y = -0.0;
    printf("%.08f == %.08f: %d\n", x, y, x == y);
    printf("%.08f == %.08f: %d\n", 1 / x, 1 / y, 1 / x == 1 / y);
    printf("%.08f == %.08f: %d\n", atan2(x, y), atan2(y, y), atan2(x, y) == atan2(y, y));
}

The result from this code is:

0.00000000 == -0.00000000: 1
1.#INF0000 == -1.#INF0000: 0
3.14159265 == -3.14159265: 0

This would mean that code would correctly handle certain limits without a need for explicit handling. It's not certain that relying on this feature for values close to the limits is a good idea, since a simple calculation error can change the sign and make the value far from correct, but you can still take advantage of it if you avoid calculations that would change the sign.

Yes zero can be signed but the standard requires positive and negative zero to test as equal