From: Marco Costalba Date: Mon, 31 Oct 2011 14:37:46 +0000 (+0100) Subject: Document magics bitboards code X-Git-Url: https://git.sesse.net/?p=stockfish;a=commitdiff_plain;h=90890844ade67d8081a5284700cc2ef3ebdbb62d Document magics bitboards code Add comments and rename stuff to better clarify what the magic bitboard initialization code does. No functional change. Signed-off-by: Marco Costalba --- diff --git a/src/bitboard.cpp b/src/bitboard.cpp index 415f9869..758796be 100644 --- a/src/bitboard.cpp +++ b/src/bitboard.cpp @@ -27,15 +27,15 @@ // Global bitboards definitions with static storage duration are // automatically set to zero before enter main(). -Bitboard RMask[64]; -Bitboard RMult[64]; +Bitboard RMasks[64]; +Bitboard RMagics[64]; Bitboard* RAttacks[64]; -int RShift[64]; +int RShifts[64]; -Bitboard BMask[64]; -Bitboard BMult[64]; +Bitboard BMasks[64]; +Bitboard BMagics[64]; Bitboard* BAttacks[64]; -int BShift[64]; +int BShifts[64]; Bitboard SetMaskBB[65]; Bitboard ClearMaskBB[65]; @@ -64,11 +64,11 @@ namespace { CACHE_LINE_ALIGNMENT int BSFTable[64]; - Bitboard RAttacksTable[0x19000]; - Bitboard BAttacksTable[0x1480]; + Bitboard RookTable[0x19000]; // Storage space for rook attacks + Bitboard BishopTable[0x1480]; // Storage space for bishop attacks - void init_sliding_attacks(Bitboard magic[], Bitboard* attack[], Bitboard attTable[], - Bitboard mask[], int shift[], Square delta[]); + void init_magic_bitboards(Bitboard* attacks[], Bitboard magics[], + Bitboard masks[], int shifts[], Square deltas[]); } @@ -228,11 +228,14 @@ void init_bitboards() { set_bit(&StepAttacksBB[make_piece(c, pt)][s], to); } - Square RDelta[] = { DELTA_N, DELTA_E, DELTA_S, DELTA_W }; - Square BDelta[] = { DELTA_NE, DELTA_SE, DELTA_SW, DELTA_NW }; + Square RDeltas[] = { DELTA_N, DELTA_E, DELTA_S, DELTA_W }; + Square BDeltas[] = { DELTA_NE, DELTA_SE, DELTA_SW, DELTA_NW }; - init_sliding_attacks(BMult, BAttacks, BAttacksTable, BMask, BShift, BDelta); - init_sliding_attacks(RMult, RAttacks, RAttacksTable, RMask, RShift, RDelta); + RAttacks[0] = RookTable; + BAttacks[0] = BishopTable; + + init_magic_bitboards(RAttacks, RMagics, RMasks, RShifts, RDeltas); + init_magic_bitboards(BAttacks, BMagics, BMasks, BShifts, BDeltas); for (Square s = SQ_A1; s <= SQ_H8; s++) { @@ -258,28 +261,28 @@ void init_bitboards() { namespace { - Bitboard sliding_attacks(Square sq, Bitboard occupied, Square delta[]) { + Bitboard sliding_attacks(Square sq, Bitboard occupied, Square deltas[]) { Bitboard attacks = 0; for (int i = 0; i < 4; i++) { - Square s = sq + delta[i]; + Square s = sq + deltas[i]; - while (square_is_ok(s) && square_distance(s, s - delta[i]) == 1) + while (square_is_ok(s) && square_distance(s, s - deltas[i]) == 1) { set_bit(&attacks, s); if (bit_is_set(occupied, s)) break; - s += delta[i]; + s += deltas[i]; } } return attacks; } - Bitboard pick_magic(Bitboard mask, RKISS& rk, int booster) { + Bitboard pick_random(Bitboard mask, RKISS& rk, int booster) { Bitboard magic; @@ -300,48 +303,69 @@ namespace { } } - void init_sliding_attacks(Bitboard magic[], Bitboard* attack[], Bitboard attTable[], - Bitboard mask[], int shift[], Square delta[]) { + + // init_magic_bitboards() computes all rook and bishop magics at startup. + // Magic bitboards are used to look up attacks of sliding pieces. As reference + // see chessprogramming.wikispaces.com/Magic+Bitboards. In particular, here we + // use the so called "fancy" approach. + + void init_magic_bitboards(Bitboard* attacks[], Bitboard magics[], + Bitboard masks[], int shifts[], Square deltas[]) { const int MagicBoosters[][8] = { { 3191, 2184, 1310, 3618, 2091, 1308, 2452, 3996 }, { 1059, 3608, 605, 3234, 3326, 38, 2029, 3043 } }; RKISS rk; Bitboard occupancy[4096], reference[4096], edges, b; - int key, maxKey, index, booster, offset = 0; + int key, maxKey, index, booster; for (Square s = SQ_A1; s <= SQ_H8; s++) { + // Board edges are not considered in the relevant occupancies edges = ((Rank1BB | Rank8BB) & ~rank_bb(s)) | ((FileABB | FileHBB) & ~file_bb(s)); - attack[s] = &attTable[offset]; - mask[s] = sliding_attacks(s, EmptyBoardBB, delta) & ~edges; - shift[s] = (CpuIs64Bit ? 64 : 32) - count_1s(mask[s]); + // Given a square 's', the mask is the bitboard of sliding attacks from + // 's' computed on an empty board. The index must be big enough to contain + // all the attacks for each possible subset of the mask and so is 2 power + // the number of 1s of the mask. Hence we deduce the size of the shift to + // apply to the 64 or 32 bits word to get the index. + masks[s] = sliding_attacks(s, EmptyBoardBB, deltas) & ~edges; + shifts[s] = (CpuIs64Bit ? 64 : 32) - count_1s(masks[s]); - // Use Carry-Rippler trick to enumerate all subsets of mask[s] + // Use Carry-Rippler trick to enumerate all subsets of masks[s] and + // store the corresponding sliding attacks in reference[]. b = maxKey = 0; do { occupancy[maxKey] = b; - reference[maxKey++] = sliding_attacks(s, b, delta); - b = (b - mask[s]) & mask[s]; + reference[maxKey++] = sliding_attacks(s, b, deltas); + b = (b - masks[s]) & masks[s]; } while (b); - offset += maxKey; + // Set the offset for the table of the next square. We have individual + // table sizes for each square with "Fancy Magic Bitboards". + if (s < SQ_H8) + attacks[s + 1] = attacks[s] + maxKey; + booster = MagicBoosters[CpuIs64Bit][rank_of(s)]; - // Then find a possible magic and the corresponding attacks + // Find a magic for square 's' picking up an (almost) random number + // until we find the one that passes the verification test. do { - magic[s] = pick_magic(mask[s], rk, booster); - memset(attack[s], 0, maxKey * sizeof(Bitboard)); + magics[s] = pick_random(masks[s], rk, booster); + memset(attacks[s], 0, maxKey * sizeof(Bitboard)); + // A good magic must map every possible occupancy to an index that + // looks up the correct sliding attack in the attacks[s] database. + // Note that we build up the database for square 's' as a side + // effect of verifying the magic. for (key = 0; key < maxKey; key++) { - index = CpuIs64Bit ? unsigned((occupancy[key] * magic[s]) >> shift[s]) - : unsigned(occupancy[key] * magic[s] ^ (occupancy[key] >> 32) * (magic[s] >> 32)) >> shift[s]; + index = CpuIs64Bit ? unsigned((occupancy[key] * magics[s]) >> shifts[s]) + : unsigned(occupancy[key] * magics[s] ^ (occupancy[key] >> 32) * (magics[s] >> 32)) >> shifts[s]; - if (!attack[s][index]) - attack[s][index] = reference[key]; + if (!attacks[s][index]) + attacks[s][index] = reference[key]; - else if (attack[s][index] != reference[key]) + else if (attacks[s][index] != reference[key]) break; } } while (key != maxKey); diff --git a/src/bitboard.h b/src/bitboard.h index fa1f9d20..c6136549 100644 --- a/src/bitboard.h +++ b/src/bitboard.h @@ -60,14 +60,14 @@ extern Bitboard SquaresInFrontMask[2][64]; extern Bitboard PassedPawnMask[2][64]; extern Bitboard AttackSpanMask[2][64]; -extern uint64_t RMult[64]; -extern int RShift[64]; -extern Bitboard RMask[64]; +extern uint64_t RMagics[64]; +extern int RShifts[64]; +extern Bitboard RMasks[64]; extern Bitboard* RAttacks[64]; -extern uint64_t BMult[64]; -extern int BShift[64]; -extern Bitboard BMask[64]; +extern uint64_t BMagics[64]; +extern int BShifts[64]; +extern Bitboard BMasks[64]; extern Bitboard* BAttacks[64]; extern Bitboard BishopPseudoAttacks[64]; @@ -172,25 +172,25 @@ inline Bitboard in_front_bb(Color c, Square s) { #if defined(IS_64BIT) inline Bitboard rook_attacks_bb(Square s, Bitboard occ) { - return RAttacks[s][((occ & RMask[s]) * RMult[s]) >> RShift[s]]; + return RAttacks[s][((occ & RMasks[s]) * RMagics[s]) >> RShifts[s]]; } inline Bitboard bishop_attacks_bb(Square s, Bitboard occ) { - return BAttacks[s][((occ & BMask[s]) * BMult[s]) >> BShift[s]]; + return BAttacks[s][((occ & BMasks[s]) * BMagics[s]) >> BShifts[s]]; } #else // if !defined(IS_64BIT) inline Bitboard rook_attacks_bb(Square s, Bitboard occ) { - Bitboard b = occ & RMask[s]; + Bitboard b = occ & RMasks[s]; return RAttacks[s] - [unsigned(int(b) * int(RMult[s]) ^ int(b >> 32) * int(RMult[s] >> 32)) >> RShift[s]]; + [unsigned(int(b) * int(RMagics[s]) ^ int(b >> 32) * int(RMagics[s] >> 32)) >> RShifts[s]]; } inline Bitboard bishop_attacks_bb(Square s, Bitboard occ) { - Bitboard b = occ & BMask[s]; + Bitboard b = occ & BMasks[s]; return BAttacks[s] - [unsigned(int(b) * int(BMult[s]) ^ int(b >> 32) * int(BMult[s] >> 32)) >> BShift[s]]; + [unsigned(int(b) * int(BMagics[s]) ^ int(b >> 32) * int(BMagics[s] >> 32)) >> BShifts[s]]; } #endif