Consider the following program:

-#define Size 64

int A[Size; Size], B[Size; Size], C[Size; Size];

int register i, j;

for (j = 0; j< Size; j ++)

for (i = 0; i< Size; i++)

C[i; j] = A[i; j] + B[i; j];

Assume that the program is running on a system using demand paging and the page size is 1 Kilobyte. Each integer is 4 bytes long. It is clear that each array requires a 16-page space. As an example, A[0, 0]-A[0, 63], A[1, 0]-A[1, 63], A[2, 0]-A[2, 63], and A[3, 0]-A[3, 63] will be stored in the first data page. A similar storage pattern can be derived for the rest of array A and for arrays B and C. Assume that the system allocates a 4-page working set for this process. One of the pages will be used by the program and three pages can be used for the data. Also, two index registers are assigned for i and j (so, no memory accesses are needed for references to these two variables).

a. Discuss how frequently the page fault would occur (in terms of number of times C[i, j] = A[i, j] + B[i, j] are executed).

b. Can you modify the program to minimize the page fault frequency?

c. What will be the frequency of page faults after your modification?