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

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).

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