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Multiple Regions

In this section we describe how to generate multiple tiled regions in a single loop nest. We can treat the following loop nest of depth 4 as two regions of depth two, and tile the i and j loops together, and tile the k and l loops together.

for (i = 0; i <= N; i++) {
    for (j = 0; j <= N; j++) {
        for (k = 0; k <= N; k++) {
            for (l = 0; l <= N; l++) {
                ...
            }
        }
    }
}

To create blocks of size 100, we'd use the following parameters:

trip[0] = 100; trip[1] = 100; trip[2] = 100; trip[3] = 100;
nregions = 2;
coalesce[0] = FALSE; coalesce[1] = FALSE;
first[0] = 0; first[1] = 2; first[2] = 4;

The resulting code is:

for (i_tile = 0; i_tile <= N; i_tile += 100) {
  for (j_tile = 0; j_tile <= N; j_tile += 100) {
    for (i = i_tile; i <= min(N, i_tile + 99); i++) {
      for (j = max(0, j_tile); j <= min(N, j_tile + 99); j++) {


        for (k_tile = 0; k_tile <= N; k_tile += 100) {
          for (l_tile = 0; l_tile <= N; l_tile += 100) {
            for (k = k_tile; k <= min(N, k_tile + 99); k++) {
              for (l = max(0, l_tile); j <= min(N, l_tile + 99); l++) {
                        ...
              }
            }
          }
        }

      }
    }
  }
}

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