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CSC 236               Tutorial Exercises for Week  9              Fall 2007
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This is the example in section 2.4 of the textbook, rephrased to use the
same notation I use in lecture.

Prove the correctness of the following algorithm.

Recall that the "right shift" operator >> removes some number of bits from
the right end of its first operand (e.g., 11010 >> 1 = 1101).
Similarly, the "left shift" operator << adds 0s to the right end of its
first operand (e.g., 1101 << 1 = 11010).

    mult(m, n):
        # Pre:  m in N, n in Z
        x = m
        y = n
        z = 0
        # Loop Inv:  z = m * n - x * y
        while x != 0:
            if x % 2 == 1:  z += y
            x >>= 1  # right shift, equivalent to x /= 2
            y <<= 1  # left shift, equivalent to y *= 2
        return z
        # Post:  returns m * n