> XOR is just a particular case of subtraction, it is not a different kind of operation.

It's different in that there's no carry propagation.

▲ adrian_b 4 hours ago | parent [-]

That is not a property specific to XOR.

Whenever you do addition/subtraction modulo some power of two, the carry does not propagate over the boundaries that correspond to the size of the modulus.

For instance, you can make the 128-bit register XMM1 to be zero in one of the following ways:

  PXOR  XMM1, XMM1   ; Subtraction modulo 2^1
  PSUBB XMM1, XMM1   ; Subtraction modulo 2^8
  PSUBW XMM1, XMM1   ; Subtraction modulo 2^16
  PSUBD XMM1, XMM1   ; Subtraction modulo 2^32
  PSUBQ XMM1, XMM1   ; Subtraction modulo 2^64

In all these 5 instructions, the carry propagates inside chunks corresponding to the size of the modulus and the carry does not propagate between chunks.

For XOR, i.e. subtraction modulo 2^1, the size of a chunk is just 1 bit, so the propagation of the carry inside the chunk happens to do nothing.

There are no special rules for XOR, its behavior is the same as for any other subtraction, any behavior that seems special is caused by the facts that the numbers 1 (size in bits of the integer residue) and 0 (number of carry propagations inside a number having the size of the residue) are somewhat more special numbers than the other cardinal numbers.

When you do not do those 5 operations inside a single ALU, but with separate adders, the shorter is the number of bits over which the carry must propagate, the faster is the logic device. But when a single ALU does all 5, the speed of the ALU is a little slower than the slowest of those 5 (a little slower because there are additional control gates for selecting the desired operation).

The other bitwise operations are also just particular cases of more general vector operations. Each of the 3 most important bitwise operations is the 1-bit limit of 2 operations which are distinct for numbers with sizes greater than 1 bit, but which are equivalent for 1-bit numbers. While XOR is just addition or subtraction of 1-bit numbers, AND is just minimum or multiplication of 1-bit numbers, and OR is just maximum of 1-bit numbers or the 1-bit version of the function that gives the probability for 1 of 2 events to happen (i.e. difference between sum and product).

	▲	gpderetta 4 hours ago \| parent [-]
		And in practice it is very likely that XOR and the variously sized vector ADDs and SUBs are implemented exactly by the same ALU circuitry, parameterized by a bitmasks of the carry lines to enable (none for XOR, all except the vector size boundaries for the vector operations).