Quad-Bitboards
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Quad-Bitboards are simply a vector of four bitboards for various purposes. Those vectors are suited for SIMD-instruction sets like SSE2 and may kept for instance in two 128-bit XMM-registers, or AVX2 with one 256-bit YMM-register.
As Board-Definition
One application is to keep one quad-bitboard as compact board-definition with vertical nibbles as piece or empty square codes:
| idx 10 | 6 | 6 | 6 | 6 | 5 | 5 | 5 | 5 | 5 | ~ | 0 | ... | 0 | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| idx 1 | 3 | 2 | 1 | 0 | 9 | 8 | 7 | 6 | 5 | ~ | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 | |||||||
| bb0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | ~ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | black | ||||||
| bb1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | ~ | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | P | . | B | . | Q | ||
| bb2 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | ~ | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | N | B | . | K | |||
| bb3 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | ~ | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | . | . | R | Q | K | ||
| r | n | b | k | q | b | n | r | p | ~ | P | R | N | B | K | Q | B | N | R |
bb3 RQK bb2 NB K bb1 P B Q bb0 black 1 . . 1 1 . . 1 . 1 1 . 1 1 1 . . . 1 1 . 1 . . 1 1 1 1 1 1 1 1 . . . . . . . . . . . . . . . . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 1 1 1 1 1 . . . . . . . . 1 . . 1 1 . . 1 . 1 1 . 1 1 1 . . . 1 1 . 1 . . . . . . . . . .
with following arbitrary square codes:
| empty | square | 0000B |
| white | pawn | 0010B |
| white | knight | 0100B |
| white | bishop | 0110B |
| white | rook | 1000B |
| white | queen | 1010B |
| white | king | 1100B |
| black | pawn | 0011B |
| black | knight | 0101B |
| black | bishop | 0111B |
| black | rook | 1001B |
| black | queen | 1011B |
| black | king | 1101B |
This routine might be used rarely to get a square-centric piece, see also the AVX2 version:
int getPiece (const QBB & qbb, enumSquare sq) {
return ((qbb.bb[0] >> sq) & 1)
+ 2*((qbb.bb[1] >> sq) & 1)
+ 4*((qbb.bb[2] >> sq) & 1)
+ 8*((qbb.bb[3] >> sq) & 1);
}
To get the disjoint bitboards similar to the bitboard board-definition is about some bitwise operations:
black = bb0 occupied = bb1 | bb2 | bb3 odd = bb1 ^ bb2 ^ bb3 // pawn or knight or rook white = bb0 ^ occupied bishops = bb1 & bb2 queens = bb1 & bb3 kings = bb2 & bb3 pawns = odd & bb1 knight = odd & bb2 rooks = odd & bb3
The idea is during make/unmake move to xor the quad-bitboard by from- and to-aspects similar to the hashkey. This implies the information of the moving and possibly captured piece is coded inside the move structure, as well as special moves like double push (triggering ep), castling, en passant and promotions.
qbb ^= fromTable[move.fromAspects()] ^ toTable[move.toAspects()];
SSE2 Conversions
To Hex Bitboards
A conversion of a quad-bitboard to 16 disjoint bitboards can be done quite efficiently with SSE2 instructions:
void quad2hexBB(U64 h[], const QBB &s) {
__m128i a,b,c,d,e,f, m1;
__m128i* p = (__m128i*) &s;
a = b = d = p[0]; c = p[1];
p = (__m128i*) h;
m1 = _mm_cmpeq_epi8(a, a); // -1
a = _mm_or_si128 (a, c);
d = _mm_and_si128 (d, c); // q3 & q1 : q2 & q0
e = a = _mm_xor_si128 (a, m1); //~q3 & ~q1 : ~q2 & ~q0
b = _mm_xor_si128 (b, d); //~q3 & q1 : ~q2 & q0
f = c = _mm_xor_si128 (c, d); // q3 & ~q1 : q2 & ~q0
a = _mm_unpackhi_epi64 (a, a); //~q3 & ~q1 :~q3 & ~q1
e = _mm_unpacklo_epi64 (e, b); // ~q2 & q0 : ~q2 & ~q0
f = _mm_unpacklo_epi64 (f, d); // q2 & q0 : q2 & ~q0
b = _mm_unpackhi_epi64 (b, b); //~q3 & q1 :~q3 & q1
c = _mm_unpackhi_epi64 (c, c); // q3 & ~q1 : q3 & ~q1
d = _mm_unpackhi_epi64 (d, d); // q3 & q1 : q3 & q1
p[0] = _mm_and_si128 (a, e); //~q3~q2~q1 q0 :~q3~q2~q1~q0
p[1] = _mm_and_si128 (b, e); //~q3~q2 q1 q0 :~q3~q2 q1~q0
p[2] = _mm_and_si128 (a, f); //~q3 q2~q1 q0 :~q3 q2~q1~q0
p[3] = _mm_and_si128 (b, f); //~q3 q2 q1 q0 :~q3 q2 q1~q0
p[4] = _mm_and_si128 (c, e); // q3~q2~q1 q0 : q3~q2~q1~q0
p[5] = _mm_and_si128 (d, e); // q3~q2 q1 q0 : q3~q2 q1~q0
p[6] = _mm_and_si128 (c, f); // q3 q2~q1 q0 : q3 q2~q1~q0
p[7] = _mm_and_si128 (d, f); // q3 q2 q1 q0 : q3 q2 q1~q0
}
To Mailbox
Converting the 64 vertical nibbles to a 8x8 board is more expensive and should be avoided on the fly, let say once per node.
void quadBB2Board(char board[], const QBB &quad) {
static u64 XMM_ALIGN sq2bb_masks[8] = {
0x0101010101010101, 0x0202020202020202,
0x0404040404040404, 0x0808080808080808,
0x1010101010101010, 0x2020202020202020,
0x4040404040404040, 0x8080808080808080,
};
__m128i t0, t1, t2, t3, b0, b1, b2, b3;
__m128i* pm = (__m128i*) sq2bb_masks;
__m128i* pq = (__m128i*) &quad;
__m128i* pb = (__m128i*) board;
// 1. bitboard 0x02:0x01
t0 = pq[0];
t1 = _mm_unpacklo_epi64(t0, t0);
b0 = _mm_and_si128 (t1, pm[0]);
b1 = _mm_srli_epi64 ( _mm_and_si128(t1, pm[1]), 2);
b2 = _mm_srli_epi64 ( _mm_and_si128(t1, pm[2]), 4);
b3 = _mm_srli_epi64 ( _mm_and_si128(t1, pm[3]), 6);
// 2. bitboard 0x04:0x02
t2 = _mm_unpackhi_epi64(t0, t0);
b0 = _mm_or_si128 ( b0, _mm_slli_epi64( _mm_and_si128 (t2, pm[0]), 1));
b1 = _mm_or_si128 ( b1, _mm_srli_epi64( _mm_and_si128 (t2, pm[1]), 1));
b2 = _mm_or_si128 ( b2, _mm_srli_epi64( _mm_and_si128 (t2, pm[2]), 3));
b3 = _mm_or_si128 ( b3, _mm_srli_epi64( _mm_and_si128 (t2, pm[3]), 5));
// 3. bitboard 0x08:0x04
t0 = pq[1];
t1 = _mm_unpacklo_epi64(t0, t0);
b0 = _mm_or_si128 ( b0, _mm_slli_epi64( _mm_and_si128 (t1, pm[0]), 2));
b1 = _mm_or_si128 ( b1, _mm_and_si128 (t1, pm[1]) );
b2 = _mm_or_si128 ( b2, _mm_srli_epi64( _mm_and_si128 (t1, pm[2]), 2));
b3 = _mm_or_si128 ( b3, _mm_srli_epi64( _mm_and_si128 (t1, pm[3]), 4));
// 4. bitboard 0x10:0x08
t2 = _mm_unpackhi_epi64(t0, t0);
b0 = _mm_or_si128 ( b0, _mm_slli_epi64( _mm_and_si128 (t2, pm[0]), 3));
b1 = _mm_or_si128 ( b1, _mm_slli_epi64( _mm_and_si128 (t2, pm[1]), 1));
b2 = _mm_or_si128 ( b2, _mm_srli_epi64( _mm_and_si128 (t2, pm[2]), 1));
b3 = _mm_or_si128 ( b3, _mm_srli_epi64( _mm_and_si128 (t2, pm[3]), 3));
// rotate 8*8 bytes (512 bit) in b0,b1,b2,b3
t0 = _mm_srli_epi64 ( _mm_unpackhi_epi64(b0,b0), 1);
t1 = _mm_srli_epi64 ( _mm_unpackhi_epi64(b1,b1), 1);
t2 = _mm_srli_epi64 ( _mm_unpackhi_epi64(b2,b2), 1);
t3 = _mm_srli_epi64 ( _mm_unpackhi_epi64(b3,b3), 1);
b0 = _mm_unpacklo_epi8 (b0, t0);
b1 = _mm_unpacklo_epi8 (b1, t1);
b2 = _mm_unpacklo_epi8 (b2, t2);
b3 = _mm_unpacklo_epi8 (b3, t3);
t0 = _mm_unpacklo_epi16(b0, b1);
t1 = _mm_unpackhi_epi16(b0, b1);
t2 = _mm_unpacklo_epi16(b2, b3);
t3 = _mm_unpackhi_epi16(b2, b3);
pb[0] = _mm_unpacklo_epi32(t0, t2);
pb[1] = _mm_unpackhi_epi32(t0, t2);
pb[2] = _mm_unpacklo_epi32(t1, t3);
pb[3] = _mm_unpackhi_epi32(t1, t3);
}
As Sliding Piece Generators
Another application is to perform parallel prefix Kogge-Stone algorithms with quad-bitboards. That allows to propagate four or up to 15 bitboards with one direction fill.
qbb.bb[0] = white rooks or queens qbb.bb[1] = black rooks or queens qbb.bb[2] = black king qbb.bb[3] = white king
Using an appropriate C++ QBB-class with overloaded operators using SSE2-intrinsics, allows to write it in usual syntax...
void nortOccl(QBB &gen /* in, out */, U64 pro64) {
QBB pro(pro64);
gen |= pro & (gen << 8);
pro = pro & (pro << 8);
gen |= pro & (gen << 16);
pro = pro & (pro << 16);
gen |= pro & (gen << 32);
}
Quotes
Quote by Gerd Isenberg [1]
A quad-bitboard is simply a dense board-structure, where arbitrary piece-code-nibbles reside vertically in four bitboards. Together with hashkeys (normal and pawnhash), ep and castle states, movecount, reversable movecount, and some more the whole board structure takes 64-bytes - and make/unmake is almost one simdwise "xor/add/and" instruction with delta[moveNr] on that board-structure. Quad-bitboards with up to 15 arbitrary codes may be used in fill-algorithms, to generate the multiplexed quad-bitboard in one run with one common empty square propagator. But multiplexing and demultiplexing makes it rather hard to use efficiently. One simpler coding scheme, where each bitboard is a disjoint set, is following:
bb0: white rooks or queens bb1: white king bb2: black king bb3: black rooks or queens
Now we can fill this quad-bitboard left and right wise (and for the other directions as well). We can aggregate the real sliding attacks for the taboo sets of the opponent king. We can do simdwise leftFill(bb1:bb0) & rightFill(bb3:bb2) and rightFill(bb1:bb0) & leftFill(bb3:bb2) to get inbetween sets of sliders with opponent king. In case of a sliding check (no piece inbetween) we can use this set as possible target set of check-breaking moves. Otherwise we can intersect it with own pieces to get pinned pieces (in total and by direction) or with opposite pieces to get discovered checkers...
See also
Forum Posts
- Quad-bitboards by Pradu, Winboard Forum, November 12, 2006
- Hashing a quadboard from scratch by Edoardo Manino, CCC, November 23, 2016 » Hash Table
- Quad-bard vs bitboard : is it faster ? by Jean-Francois Romang, CCC, May 04, 2018
External Links
- QBBEngine- a didactic engine by Fabio Gobbato » QBBEngine
- Wes Montgomery - Four on Six, BBC Two, London, May 7, 1965, YouTube Video
- feat. Stan Tracey, Jackie Dougan, Rick Laird
References
- ↑ Re: Quad-bitboards by Gerd Isenberg, Winboard Forum, November 12, 2006
