This is not a full program (although it can be run as such), but rather a
reusable subroutine.  Therefore, input is taken directly from memory, and output
is stored back in memory and on the stack.  There is no user interaction.

Input:  Numerator in (1,1)
        Denominator is hard-coded 2
Output: Quotient in (1,1)
        Remainder pushed on the stack
        Nothing else cluttered

The algorithm takes O(numerator) time.  There might exist a faster algorithm but
I don't know it.