Comment by orlp

The input space is 32 + 32 = 64 bits. The output space is 64 bits. So the best you can do is an 1-to-1 mapping.

However, since a * b = b * a, our input space has a lot of duplicate outputs. So from this alone you can conclude roughly half of the output space must be uncovered by any input pair, simply because there aren't enough input pairs.