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Bitboards,
also called bitsets or bitmaps, are among other things used to represent the board inside a chess program in a piece centric manner. Bitboards, are in essence, finite sets of up to 64 elements - all the squares of a chessboard, one bit per square. Other board games with greater board sizes may be use set-wise representations as well [1] , but classical chess has the advantage that one 64-bit word or register covers the whole board. Even more bitboard friendly is Checkers with 32-bit bitboards and less piece-types than chess [2] .
Samuel Bak - Boards Meeting [3]

The Board of Sets

To represent the board we typically need one bitboard for each piece-type and color - likely encapsulated inside a class or structure, or as an array of bitboards as part of a position object. A one-bit inside a bitboard implies the existence of a piece of this piece-type on a certain square - one to one associated by the bit-position.

Bitboard Basics

Of course bitboards are not only about the existence of pieces - it is a general purpose, set-wise data-structure fitting in one 64-bit register. For example, a bitboard can represent things like attack- and defend sets, move-target sets and so on.

General Bitboard Techniques

The fundamental bitboard basics.

Pattern and Attacks

This is basically about chess, how to calculate attack-sets and various pattern for evaluation and move generation purposes.

Move Generation Issues

Bitboard aspects on move generation and static exchange evaluation (SEE).

Miscellaneous



Defining Bitboards

To be aware of their scalar 64-bit origin, we use so far a type defined unsigned integer U64 in our C or C++ source snippets, the scalar 64-bit long in Java. Feel free to define a distinct type or wrap U64 into classes for better abstraction and type-safety during compile time. The macro C64 will append a suffix to 64-bit constants as required by some compilers:
typedef unsigned __int64 U64;    // for the old microsoft compilers
typedef unsigned long long  U64; // supported by MSC 13.00+ and C99
#define C64(constantU64) constantU64##ULL

Bitboard-History

The general approach of Bitsets was first proposed by Mikhail R. Shura-Bura in 1952 [4] [5]. The bitboard method for holding a board game appears to have been invented in the mid 1950's, by Arthur Samuel and was used in his checkers program. In computer chess bitboards were first described by Georgy Adelson-Velsky et al. in 1967 [6] , reprinted 1970 [7] . Bitboards were used in Kaissa and in Chess. The invention and publication of Rotated Bitboards by Robert Hyatt [8] and Peter Gillgasch with Ernst A. Heinz in the 90s was another milestone in the history of bitboards. Steffan Westcott's innovations, too expensive on 32-bit x86 processors, should be revisited with x86-64 and SIMD instructions in mind. With the advent of fast 64-bit multiplication along with faster memory, Magic Bitboards as proposed by Lasse Hansen [9] and refined by Pradu Kannan [10] have surpassed Rotated.

Analysis

The use of bitboards has spawned numerous discussions about their costs and benefits. The major points to consider are:
  • Bitboards can have a high information density.
  • Single populated or even empty Bitboards have a low information density.
  • Bitboards are weak in answering questions like what piece if any resides on square x. One reason to keep a redundant mailbox board representation with some additional update costs during make/unmake.
  • Bitboards can operate on all squares in parallel using bitwise instructions. This is one of the main arguments used by proponents of bitboards, because it allows for a flexibility in evaluation.
  • Bitboards are rather handicapped on 32 bit processors, as each bitwise computation must be split into two or more instructions [11] . As most modern processors are now 64 bit, this point is somewhat diminished [12] .
  • Bitboards often rely on bit-twiddling and various optimization tricks and special instructions for certain hardware architectures, such as bitscan and population count. Optimal code requires machine dependent header-files in C/C++. Portable code is likely not optimal for all processors.
  • Some operations on bitboards are less general, f.i. shifts. This requires additional code overhead.

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External Links


References

  1. ^ Reijer Grimbergen (2007). Using Bitboards for Move Generation in Shogi. ICGA Journal, Vol. 30, No. 1, pdf
  2. ^ Checker Bitboards Tutorial by Jonathan Kreuzer
  3. ^ Chess in the Art of Samuel Bak, Center for Holocaust & Genocide Studies, University of Minnesota
  4. ^ Lazar A. Lyusternik, Aleksandr A. Abramov, Victor I. Shestakov, Mikhail R. Shura-Bura (1952). Programming for High-Speed Electronic Computers. (Программирование для электронных счетных машин)
  5. ^ Andrey Ershov, Mikhail R. Shura-Bura (1980). The Early Development of Programming in the USSR. in Nicholas C. Metropolis (ed.) A History of Computing in the Twentieth Century. Academic Press, preprint pp. 43
  6. ^ Early Reference on Bit-Boards by Tony Warnock from rec.games.chess, October 29, 1994
  7. ^ Georgy Adelson-Velsky, Vladimir Arlazarov, Alexander Bitman, Alexander Zhivotovsky and Anatoly Uskov (1970). Programming a Computer to Play Chess. Russian Mathematical Surveys, Vol. 25, pp. 221-262.
  8. ^ Robert Hyatt (1999). Rotated Bitmaps, a New Twist on an Old Idea. ICCA Journal, Vol. 22, No. 4
  9. ^ Fast(er) bitboard move generator by Lasse Hansen, Winboard Forum, June 14, 2006
  10. ^ List of magics for bitboard move generation by Pradu Kannan, Winboard Forum, August 23, 2006
  11. ^ Efficient Bitboard Implementation on 32-bit Architecture by Roberto Waldteufel, CCC, October 25, 1998
  12. ^ Speedup by bitboards by Onno Garms, Winboard Forum, July 13, 2007
  13. ^ Bitboard user's information request by Robert Hyatt, CCC, October 05, 1999
  14. ^ Robert Hyatt (1999). Rotated Bitmaps, a New Twist on an Old Idea. ICCA Journal, Vol. 22, No. 4


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