8x8 Board

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8x8 Board

The 8x8 Board as basic square-centric board representation is either a two-dimensional array of bytes (or integers), containing piece and empty square codes, indexed by file and rank index, or more commonly a one-dimensional array indexed by a square in a 0..63 range which combines rank or file indices in three consecutive bits each . Such a board representation is often used redundantly in bitboard programs to answer the question which piece (if any) resides on a square efficiently. It has to deal with square mapping accordantly.

Programming

Board Representation

TSCP

TSCP uses two 64 element arrays, containing empty square plus pure piece code, and empty square plus piece color code :.

int color[64];  /* LIGHT, DARK, or EMPTY */
int piece[64];  /* PAWN, KNIGHT, BISHOP, ROOK, QUEEN, KING, or EMPTY */

However, when generating moves, TSCP converts the board data into a bigger array 10x12 Board.

FirstChess

FirstChess uses two 64 integer arrays, for all tasks, including move generating.

int piece[64] = {
    ROOK,  KNIGHT,BISHOP,QUEEN, KING,  BISHOP,KNIGHT,ROOK,
    PAWN,  PAWN,  PAWN,  PAWN,  PAWN,  PAWN,  PAWN,  PAWN,
    EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY,
    EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY,
    EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY,
    EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY,
    PAWN,  PAWN,  PAWN,  PAWN,  PAWN,  PAWN,  PAWN,  PAWN,
    ROOK,  KNIGHT,BISHOP,QUEEN, KING,  BISHOP,KNIGHT,ROOK
};

int color[64] = {
    BLACK, BLACK, BLACK, BLACK, BLACK, BLACK, BLACK, BLACK,
    BLACK, BLACK, BLACK, BLACK, BLACK, BLACK, BLACK, BLACK,
    EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY,
    EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY,
    EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY,
    EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY, EMPTY,
    WHITE, WHITE, WHITE, WHITE, WHITE, WHITE, WHITE, WHITE,
    WHITE, WHITE, WHITE, WHITE, WHITE, WHITE, WHITE, WHITE
};

Banksia

Banksia uses only one vector from C++ standard library :

std::vector<Piece> pieces;

The vector is initialized :

Piece empty(PieceType::empty, Side::none);
for(int i = 0; i < 64; i++) {
    pieces.push_back(empty);
}

Move Generators

Straightforward

Based on the given cell and the size of the board, programs can calculate if the target cells are out of the board. In below code Banksia generates moves for a Rook at position pos:

case PieceType::rook: // both queen and rook here
{
    int col = getColumn(pos);
    for (int y=pos - 1; y >= pos - col; y--) { /* go left */
        gen_addMove(moves, pos, y, captureOnly);
        if (!isEmpty(y)) {
            break;
        }
    }
                
    for (int y=pos + 1; y < pos - col + 8; y++) { /* go right */
        gen_addMove(moves, pos, y, captureOnly);
        if (!isEmpty(y)) {
            break;
        }
    }
                
    for (int y=pos - 8; y >= 0; y -= 8) { /* go up */
        gen_addMove(moves, pos, y, captureOnly);
        if (!isEmpty(y)) {
            break;
        }
    }
                
    for (int y=pos + 8; y < 64; y += 8) { /* go down */
        gen_addMove(moves, pos, y, captureOnly);
        if (!isEmpty(y)) {
           break;
        }
                    
    }
    break;
}

Precalculate data

Some programs pre-calculate data for each cell and extract it when generating moves. That method is well-known mentioned by Hans Eric Sandstroem in GNU Chess version 4.0 document, 6 Sep 1989:

The general idea behind this algoritm is to pre calculate
a lot of data. The data that is pre calculated is every possible move
for every piece from every square disregarding any other pieces on the
board. This pre calculated data is stored in an array that looks like
this:

struct sqdata {
  short nextpos;
  short nextdir;
};
struct sqdata posdata[8][64][64];
/* posdata[piecetype][fromsquare][destinationsquare] */
example:
	the first move for a queen at e8 is stored at;
	posdata[queen][e8][e8].nextpos
	suppose this is e7 and e7 is occupied then the next move
	will be found in;
	posdata[queen][e8][e7].nextdir

To handle the differeces between white and black pawns (they move in
opposite directions) an array ptype has been introduced:

static const short ptype[2][8] = {
  no_piece,pawn,knight,bishop,rook,queen,king,no_piece,
  no_piece,bpawn,knight,bishop,rook,queen,king,no_piece};
           ^^^^^
And it is used like this:
   piecetype = ptype[side][piece]
When generating moves for pieces that are not black pawns, piece
can be used directly in posdata. As in the example above.

Thus the only thing one has to do when generating the moves
is to check for collisions with other pieces. 
the move generation to do this looks like this: (for non pawns)
    p = posdata[piece][sq];
    u = p[sq].nextpos;
    do {
      if (color[u] == neutral) {
	LinkMove(ply,sq,u,xside);
	u = p[u].nextpos;
      }
      else {
	if (color[u] == xside) LinkMove(ply,sq,u,xside);
	u = p[u].nextdir;
      }
    } while (u != sq);

 - I`nt this just beautiful!

The array posdata is initialized in the routine Initialize_moves.
This routine is called just once and it works so no time has been spent
on the structure of this code. GenMoves and CaptureList generates the
moves but the routines ataks, BRscan, Sqatakd, KingScan and trapped
also relies on the move generation algoritm so they have also been
rewritten.

Alternatives

As a lone board representation, the 8x8 board has some efficiency issues with move generation related to off the board test. Therefore more common are approaches dealing with that, that is 10x12 board with surrounding ranks and files, and Vector Attacks with its cheap test and unique square difference property with respect to distance and direction . In Games Playing with Computers, 1972 , Alex Bell introduced an array of 65 squares, where the purpose of square 65 (always empty) is to detect pawns capturing outside the board by a table driven move generator.

See also

• 10x12 Board
• Array of Nibbles
• Bitboards

Square Mapping Considerations

• Vector Attacks

0x88

Publications

• Claude Shannon (1949). Programming a Computer for Playing Chess. pdf from The Computer History Museum
• Alex Bell (1972). Games Playing with Computers. Allen & Unwin, ISBN-13: 978-0080212227

Forum Posts

• Fastest Conversion from 0x88 board to 8x8 board representation by Artem Pyatakov, CCC, July 06, 2001
• Re: Ferret/Gerbil question by Bruce Moreland, CCC, September 21, 2001 » Ferret, Gerbil, 0x88

External Links

• Board representation (chess) - Array based from Wikipedia
• Chess board representations by Robert Hyatt
• Chapter 3: Board Games - 3.1 CHESS from Alex Bell (1972). Games Playing with Computers. Allen & Unwin, ISBN-13: 978-0080212227
• 8 x 8: A Chess Sonata in 8 Movements (1957) directed by Hans Richter, Marcel Duchamp and Jean Cocteau, YouTube Video

Cast : Jean Arp, Paul Bowles, Ceal Bryson, Alexander Calder, Jean Cocteau, Willem de Vogel, Dorothea Tanning

Max Ernst, Richard Huelsenbeck, Frederick Kiesler, Julien Lary, Julien Levy, Jaqueline Matisse, Eugene Pellegrini, Man Ray, Yves Tanguy

References

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