(click to load snippet)

• function (a, w, h) {
    for (i = 0; i < h; i++) {
      for (j = 0; j < w; j++) {
        a.touch(i,j);
      }
    }
  }
    

• function (a, w, h) {
    for (j = 0; j < w; j++) {
      for (i = 0; i < h; i++) {
        a.touch(i,j);
      }
    }
  }
    

• function (a, w, h) {
    for (i = 0; i < h; i++) {
      for (j = i+1; j < w; j++) {
        a.touch(i,j);
        a.touch(j,i);
      }
    }
  }
    

• function (a, w, h) {
    var transpose_base = function(a, x, y, w, h) {
      for (i = x; i < x+w; i++) {
        for (j = y; j < y+h; j++) {
          if (j >= i) continue;
          /* when iterating over a block that straddles
          the diagonal, only swap the upper triangle */
          a.touch(i,j);
          a.touch(j,i);
        }
      }
    };
    var transpose_block = function(a, x, y, w, h) {
      /* avoid blocks entirely below diagonal */
      if ( (x+w) <= y ) return;
      if (w <= 4 && h <= 4) {
        transpose_base(a, x, y, w, h); return;
      }
      if (w >= h) {
        var mid = Math.floor(w/2);
        transpose_block(a, x    , y,   mid, h);
        transpose_block(a, x+mid, y, w-mid, h);
      } else {
        var mid = Math.floor(h/2);
        transpose_block(a, x,     y, w,   mid);
        transpose_block(a, x, y+mid, w, h-mid);
      }
    };
  
    transpose_block(a, 0, 0, w, h);
  }
    

In the code below, a.touch(i,j) indicates array access a[i][j].