Recall the example involving cache reads of a two-dimensional array (shown below). How does a larger matrix and a larger cache affect the performance
of the two pairs of nested loops? What happens if MAX = 8 and the cache can
store four lines? How many hits and misses occur in the reads of A in the first pair of
nested loops? How many hits and misses occur in the second pair? Please show your answer.

double A[MAX][MAX], x[MAX], y[MAX];
. . .
/∗ Initialize A and x, assign y = 0 ∗/
. . .
/∗ First pair of loops ∗/
for (i = 0; i < MAX; i++)
for (j = 0; j < MAX; j++)
y[i] += A[i][j]∗x[j];
. . .
/∗ Assign y = 0 ∗/
. . .
/∗ Second pair of loops ∗/
for (j = 0; j < MAX; j++)
for (i = 0; i < MAX; i++)
y[i] += A[i][j]∗x[j];