What is the meaning of "producing negative zeroes" in a system that doesn't support it?

Question

C17 6.2.6.2/4 says:

If the implementation does not support negative zeros, the behavior of the &, |, ^, ~, <<, and >> operators with operands that would produce such a value is undefined.

If I have a 2's complement system, it does not support negative zeroes. And it always utilizes all possible combinations of a binary number to express a value. Therefore it is impossible to ever produce a negative zero, no matter which bitwise operation that is used. So what is the meaning of this text?

My take is that this part refers to systems with 1's complement or signed magnitude that does not support negative zeroes, but instead use a padding bit or trap representation. Is this correct?

Answer 1

Yes, I think your interpretation is correct. In two's complement, that are no operations that could generate a negative zero, because the concept here doesn't exist: any value that has the sign bit set is necessarily less than 0.

BTW: It is very likely that the exotic sign representations will be removed from C2x, so all of this will disappear.

Answer 2

Your interpretation is correct.

Going up to paragraph 2 of 6.2.6.2:

For signed integer types, the bits of the object representation shall be divided into three groups: value bits, padding bits, and the sign bit. There need not be any padding bits; signed char shall not have any padding bits. There shall be exactly one sign bit. Each bit that is a value bit shall have the same value as the same bit in the object representation of the corresponding unsigned type (if there are M value bits in the signed type and N in the unsigned type, then M ≤ N ). If the sign bit is zero, it shall not affect the resulting value. If the sign bit is one, the value shall be modified in one of the following ways:

• the corresponding value with sign bit 0 is negated ( sign and magnitude );
• the sign bit has the value − (2^M)( two’s complement );
• the sign bit has the value − (2^M − 1) ( ones’ complement ).

Which of these applies is implementation-defined, as is whether the value with sign bit 1 and all value bits zero (for the first two), or with sign bit and all value bits 1 (for ones’ complement), is a trap representation or a normal value. In the case of sign and magnitude and ones’ complement, if this representation is a normal value it is called a negative zero.

This means an implementation using either one's complement or sign and magnitude has, for a given size integer type, a specific representation which must be either negative zero or a trap representation. It's then up to the implementation to choose which one of those applies.

As an example, suppose a system has sign and magnitude representation and a 32 bit int with no padding. Then the representation that would be negative zero, if it is supported, is 0x80000000.

Now suppose the following operations are performed:

 int x = 0x7fffffff;
 x = ~x;

If the implementation supports negative zero, the ~ operator will generate -0 as the result and store it in x. If it does not, it creates a trap representation and invokes undefined behavior as per paragraph 4.