assembly - Why are signed and unsigned multiplication different instructions on x86(-64)?

Question

I thought the whole point of 2's complement was that operations could be implemented the same way for signed and unsigned numbers. Wikipedia even specifically lists multiply as one of the operations that benefits. So why does x86 have separate instructions for each, mul and imul? Is this still true for x86-64?

Answer 1

Addition and subtraction are the same, as is the low-half of a multiply. A full multiply, however, is not. Simple example:

In 32-bit twos-complement, -1 has the same representation as the unsigned quantity 2**32 - 1. However:

-1 * -1 = +1
(2**32 - 1) * (2**32 - 1) = (2**64 - 2**33 + 1)

(Note that the low 32-bits of both results are the same; that's what I mean when I say the "low-half of the multiply" is the same).