Chapter 3, Problem 3.59HW

The following code computes the 128-bit product of two 64-bit signed values x and y and stores the result in memory:

Gcc generates the following assembly code implementing the computation:

Thus code uses  three multiplications for (he multiprecision arithmetic required to Implement 128-bit arithmetic on a 64-bit machine. Describe the algorithm used to compute the product, and annotate the assembly code to show how it realizes your algorithm. Hint When extending arguments of x and y to 128 bits, they can be rewritten as x = 2^64. x_{h +}x_i and y = 2⁶⁴ . y_{h +} . y_i  where x_{h ,} x_i, y_{h ,} and y_i are 64-bit  values. Similarly the 128-bit product can be written as p = 2⁶⁴ p_h + p_i where p_h  and  p_i are 64-bit values. show how the code computes the values of p_{h and} p_i in terms of x_{h ,} x_i, y_h, and y_1.