Are the results of bitwise operations on signed integers defined?
For negative operands, << has undefined behavior and the result of >> is implementation-defined (usually as "arithmetic" right shift). << and >> are conceptually not bitwise operators. They're arithmetic operators equivalent to multiplication or division by the appropriate power of two for the operands on which they're well-defined.
As for the genuine bitwise operators ^, ~, |, and &, they operate on the bit representation of the value in the (possibly promoted) type of the operand. Their results are well-defined for each possible choice of signed representation (twos complement, ones complement, or sign-magnitude) but in the latter two cases it's possible that the result will be a trap representation if the implementation treats the "negative zero" representation as a trap. Personally, I almost always use unsigned expressions with bitwise operators so that the result is 100% well-defined in terms of values rather than representations.
Finally, note that this answer as written may only apply to C. C and C++ are very different languages and while I don't know C++ well, I understand it may differ in some of these areas from C...
- A left shift
<<of a negative value has undefined behaviour; - A right shift
>>of a negative value gives an implementation-defined result; - The result of the
&,|and^operators is defined in terms of the bitwise representation of the values. Three possibilities are allowed for the representation of negative numbers in C: two's complement, ones' complement and sign-magnitude. The method used by the implementation will determine the numerical result when these operators are used on negative values.
Note that the value with sign bit 1 and all value bits zero (for two's complement and sign-magnitude), or with sign bit and all value bits 1 (for ones’ complement) is explicitly allowed to be a trap representation, and in this case if you use arguments to these operators that would generate such a value the behaviour is undefined.