GATE | GATE-CS-2006 | Question 80

A CPU has a 32 KB direct mapped cache with 128-byte block size. Suppose A is a twodimensional array of size 512×512 with elements that occupy 8-bytes each. Consider the following two C code segments, P1 and P2.
P1:

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for (i=0; i<512; i++) {
   for (j=0; j<512; j++) {
      x += A[i][j];
   }
}

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P2:

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for (i=0; i<512; i++) {
   for (j=0; j<512; j++) {
      x += A[j][i];
   }
}

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P1 and P2 are executed independently with the same initial state, namely, the array A is not in the cache and i, j, x are in registers. Let the number of cache misses experienced by P1 be M1 and that for P2 be M2 .

The value of M1 is:
(A) 0
(B) 2048
(C) 16384
(D) 262144


Answer: (C)

Explanation: [P1] runs the loops in a way that access elements of A in row major order and [P2] accesses elements in column major order.
No of cache blocks = CacheSize/BlockSize = 32KB / 128 Byte = 256
No. of array elements in Each Block = BlockSize/ElementSize = 128 Byte / 8 Byte = 16

Total Misses for [P1] = ArraySize * (No. of array elements in Each Block) / (No of cache blocks) = 512 * 512 * 16 / 256 = 16384


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