We can substantially improve on this by handling multiple markers at a time. Since seven cases can be distinguished by three bits, we can compose a sequence of operations which maps a pair of padded 2-bit genotypes to seven different 3-bit values in the appropriate manner. On 64-bit machines, 20 3-bit values can be packed into a machine word—for example, let bits 0-2 describe the relation at marker #0, bits 3-5 describe the relation at marker #1, and so forth, all the way up to bits 57-59 describing the relation at marker #19—so this representation lets us instruct the processor to act on 20 markers simultaneously.
