Question

This is the original code

for (j = 0; j <= 30; j++) {
  for (k = 0; k <= 30; k++) {
    x[j][k] = y[j][k] + z[j][k];
  }
}

And the code below is after applying a common sub-expression elimination optimization

for (j = 0; j <= 30; j++) {
  for (k = 0; k <= 30; k++) {
    t2 = C1 * j + W * k;
    x[t2] = y[t2] + z[t2];
  }
}

How does the common sub-expression elimination helps to improve performance in this case ? Its only array indices that is optimized ?

Answer 1

Any half-decent modern compiler will already be performing this optimisation.

Furthermore part of the index calculation should be hoisted into the outer loop:

for (j = 0; j <= 30; j++) {
  t1 = C1 * j;
  for (k = 0; k <= 30; k++) {
    t2 = t1 + W * k;
    x[t2] = y[t2] + z[t2];
  }
}