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There’s a kicker here, though, and that’s the counting of neighbors for cells at the edge of the cellmap. When cellmap wrapping is enabled (so that the cellmap becomes essentially a toroid, with each edge joined seamlessly to the opposite edge, as opposed to having a border of off-cells), neighbors that reside on the other edge of the cellmap can’t be accessed by the standard fixed offset, as shown in Figure 17.1. So, in general, we could improve performance by hard-wiring our neighbor-counting for the bit-per-cell cellmap format, but it seems we’d need a lot of conditional code to handle wrapping, and that would slow things back down again.

Figure 17.1 Edge-wrapping complications.

When a problem doesn’t lend itself well to optimization, make it a practice to see if you can change the problem definition to one that allows for greater efficiency. In this case, we’ll change the problem by putting padding bytes around the edge of the cellmap, and duplicating each edge of the cellmap in the padding bytes at the opposite side, as shown in Figure 17.2. That way, a hard-wired neighbor count will find exactly what it should—the opposite edge—without any special code at all.

But doesn’t that extra copying of the edges take time? Sure, but only a little; we can build it into the cellmap copying function, and then frankly we won’t even notice it. Avoiding tens or hundreds of thousands of calls to cell_state(), on the other hand, will be very noticeable. Listing 17.3 shows the alterations to Listing 17.1 required to implement a hard-wired neighbor-counting function. This is a minor change, in truth, implemented in about half an hour and not making the code significantly larger—but Listing 17.3 is 3.6 times faster than Listing 17.1, as shown in Table 17.1. We’re up to about 10 generations per second on a 486; not where we want to be, but it is a vast improvement.

Figure 17.2 The “padding cells” solution.

LISTING 17.3 L17-3.CPP

    /* cellmap class definition, constructor, copy_cells(), set_cell(),
       clear_cell(), cell_state(), count_neighbors(), and
       next_generation() for fast, hard-wired neighbor count approach.
       Otherwise, the same as Listing 17.1 */

    class cellmap {
    private:
       unsigned char *cells;
       unsigned int width;
       unsigned int width_in_bytes;
       unsigned int height;
       unsigned int length_in_bytes;
    public:
       cellmap(unsigned int h, unsigned int v);
       ~cellmap(void);
       void copy_cells(cellmap &sourcemap);
       void set_cell(unsigned int x, unsigned int y);
       void clear_cell(unsigned int x, unsigned int y);
       int cell_state(int x, int y);
       int count_neighbors(int x, int y);
       void next_generation(cellmap& dest_map);
    };

    /* cellmap constructor. Pads around cell storage area with 1 extra
       byte, used for handling edge wrapping. */
    cellmap::cellmap(unsigned int h, unsigned int w)
    {
       width = w;
       width_in_bytes = ((w + 7) / 8) + 2; // pad each side with
                                          // 1 extra byte
       height = h;
       length_in_bytes = width_in_bytes * (h + 2);     // pad top/bottom
                                                       // with 1 extra byte
       cells = new unsigned char[length_in_bytes];     // cell storage
       memset(cells, 0, length_in_bytes);              // clear all cells, to start
    }

    /* Copies one cellmap’s cells to another cellmap. If wrapping is
       enabled, copies edge (wrap) bytes into opposite padding bytes in
       source first, so that the padding bytes off each edge have the
       same values as would be found by wrapping around to the opposite
       edge. Both cellmaps are assumed to be the same size. */
    void cellmap::copy_cells(cellmap &sourcemap)
    {
       unsigned char *cell_ptr;
       int i;

    #if WRAP_EDGES
    // Copy left and right edges into padding bytes on right and left
       cell_ptr = sourcemap.cells + width_in_bytes;
       for (i=0; i<height; i++) {
          *cell_ptr = *(cell_ptr + width_in_bytes - 2);
          *(cell_ptr + width_in_bytes - 1) = *(cell_ptr + 1);
          cell_ptr += width_in_bytes;
       }
    // Copy top and bottom edges into padding bytes on bottom and top
       memcpy(sourcemap.cells, sourcemap.cells + length_in_bytes -
             (width_in_bytes * 2), width_in_bytes);
       memcpy(sourcemap.cells + length_in_bytes - width_in_bytes,
             sourcemap.cells + width_in_bytes, width_in_bytes);
    #endif
       // Copy all cells to the destination
       memcpy(cells, sourcemap.cells, length_in_bytes);
    }

    /* Turns cell on. x and y are offset by 1 byte down and to the right, to compensate for the
    padding bytes around the cellmap. */
    void cellmap::set_cell(unsigned int x, unsigned int y)
    {
       unsigned char *cell_ptr =
             cells + ((y + 1) * width_in_bytes) + ((x / 8) + 1);

       *(cell_ptr) |= 0x80 >> (x & 0x07);
    }

    /* Turns cell off. x and y are offset by 1 byte down and to the right,
    to compensate for the padding bytes around the cell map. */
    void cellmap::clear_cell(unsigned int x, unsigned int y)
    {
       unsigned char *cell_ptr =
             cells + ((y + 1) * width_in_bytes) + ((x / 8) + 1);

       *(cell_ptr) &= ~(0x80 >> (x & 0x07));
    }

    /* Returns cell state (1=on or 0=off). x and y are offset by 1 byte
       down and to the right, to
    compensate for the padding bytes around
       the cell map. */
    int cellmap::cell_state(int x, int y)
    {
       unsigned char *cell_ptr =
             cells + ((y + 1) * width_in_bytes) + ((x / 8) + 1);

       return (*cell_ptr & (0x80 >> (x & 0x07))) ? 1 : 0;
    }

    /* Counts the number of neighboring on-cells for specified cell. */
    int cellmap::count_neighbors(int x, int y)
    {
       unsigned char *cell_ptr, mask;
       unsigned int neighbor_count;

       // Point to upper left neighbor
       cell_ptr = cells + ((y * width_in_bytes) + ((x + 7) / 8));
       mask = 0x80 >> ((x - 1) & 0x07);
       // Count upper left neighbor
       neighbor_count = (*cell_ptr & mask) ? 1 : 0;
       // Count left neighbor
       if ((*(cell_ptr + width_in_bytes) & mask)) neighbor_count++;
       // Count lower left neighbor
       if ((*(cell_ptr + (width_in_bytes * 2)) & mask)) neighbor_count++;

       // Point to upper neighbor
       if ((mask >>= 1) == 0) {
          mask = 0x80;
          cell_ptr++;
       }
       // Count upper neighbor
       if ((*cell_ptr & mask)) neighbor_count++;
       // Count lower neighbor
       if ((*(cell_ptr + (width_in_bytes * 2)) & mask))  neighbor_count++;

       // Point to upper right neighbor
       if ((mask >>= 1) == 0) {
          mask = 0x80;
          cell_ptr++;
       }
       // Count upper right neighbor
       if ((*cell_ptr & mask)) neighbor_count++;
       // Count right neighbor
       if ((*(cell_ptr + width_in_bytes) & mask)) neighbor_count++;
       // Count lower right neighbor
       if ((*(cell_ptr + (width_in_bytes * 2)) & mask))  neighbor_count++;

       return neighbor_count;
    }

    /* Calculates the next generation of current_map and stores it in
       next_map. */
    void cellmap::next_generation(cellmap& next_map)
    {
       unsigned int x, y, neighbor_count;

       for (y=0; y<height; y++) {
          for (x=0; x<width; x++) {
             neighbor_count = count_neighbors(x, y);
             if (cell_state(x, y) == 1) {
                if ((neighbor_count != 2) && (neighbor_count != 3)) {
                   next_map.clear_cell(x, y);    // turn it off
                   draw_pixel(x, y, OFF_COLOR);
                }
             } else {
                if (neighbor_count == 3) {
                   next_map.set_cell(x, y);      // turn it on
                   draw_pixel(x, y, ON_COLOR);
                }
             }
          }
       }
    }

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Graphics Programming Black Book © 2001 Michael Abrash