2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008 Marco Costalba
6 Stockfish is free software: you can redistribute it and/or modify
7 it under the terms of the GNU General Public License as published by
8 the Free Software Foundation, either version 3 of the License, or
9 (at your option) any later version.
11 Stockfish is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 GNU General Public License for more details.
16 You should have received a copy of the GNU General Public License
17 along with this program. If not, see <http://www.gnu.org/licenses/>.
32 //// Constants and variables
35 /// Evaluation functions
37 // Generic "mate lone king" eval
38 EvaluationFunction<KXK> EvaluateKXK(WHITE), EvaluateKKX(BLACK);
40 // K and two minors vs K and one or two minors
41 EvaluationFunction<KmmKm> EvaluateKmmKm(WHITE);
43 EvaluationFunction<KBNK> EvaluateKBNK(WHITE), EvaluateKKBN(BLACK); // KBN vs K
44 EvaluationFunction<KPK> EvaluateKPK(WHITE), EvaluateKKP(BLACK); // KP vs K
45 EvaluationFunction<KRKP> EvaluateKRKP(WHITE), EvaluateKPKR(BLACK); // KR vs KP
46 EvaluationFunction<KRKB> EvaluateKRKB(WHITE), EvaluateKBKR(BLACK); // KR vs KB
47 EvaluationFunction<KRKN> EvaluateKRKN(WHITE), EvaluateKNKR(BLACK); // KR vs KN
48 EvaluationFunction<KQKR> EvaluateKQKR(WHITE), EvaluateKRKQ(BLACK); // KQ vs KR
49 EvaluationFunction<KBBKN> EvaluateKBBKN(WHITE), EvaluateKNKBB(BLACK); // KBB vs KN
54 ScalingFunction<KBPK> ScaleKBPK(WHITE), ScaleKKBP(BLACK); // KBP vs K
55 ScalingFunction<KQKRP> ScaleKQKRP(WHITE), ScaleKRPKQ(BLACK); // KQ vs KRP
56 ScalingFunction<KRPKR> ScaleKRPKR(WHITE), ScaleKRKRP(BLACK); // KRP vs KR
57 ScalingFunction<KRPPKRP> ScaleKRPPKRP(WHITE), ScaleKRPKRPP(BLACK); // KRPP vs KRP
58 ScalingFunction<KPsK> ScaleKPsK(WHITE), ScaleKKPs(BLACK); // King and pawns vs king
59 ScalingFunction<KBPKB> ScaleKBPKB(WHITE), ScaleKBKBP(BLACK); // KBP vs KB
60 ScalingFunction<KBPKN> ScaleKBPKN(WHITE), ScaleKNKBP(BLACK); // KBP vs KN
61 ScalingFunction<KNPK> ScaleKNPK(WHITE), ScaleKKNP(BLACK); // KNP vs K
62 ScalingFunction<KPKP> ScaleKPKPw(WHITE), ScaleKPKPb(BLACK); // KPKP
66 //// Local definitions
71 // Table used to drive the defending king towards the edge of the board
72 // in KX vs K and KQ vs KR endgames.
73 const uint8_t MateTable[64] = {
74 100, 90, 80, 70, 70, 80, 90, 100,
75 90, 70, 60, 50, 50, 60, 70, 90,
76 80, 60, 40, 30, 30, 40, 60, 80,
77 70, 50, 30, 20, 20, 30, 50, 70,
78 70, 50, 30, 20, 20, 30, 50, 70,
79 80, 60, 40, 30, 30, 40, 60, 80,
80 90, 70, 60, 50, 50, 60, 70, 90,
81 100, 90, 80, 70, 70, 80, 90, 100,
84 // Table used to drive the defending king towards a corner square of the
85 // right color in KBN vs K endgames.
86 const uint8_t KBNKMateTable[64] = {
87 200, 190, 180, 170, 160, 150, 140, 130,
88 190, 180, 170, 160, 150, 140, 130, 140,
89 180, 170, 155, 140, 140, 125, 140, 150,
90 170, 160, 140, 120, 110, 140, 150, 160,
91 160, 150, 140, 110, 120, 140, 160, 170,
92 150, 140, 125, 140, 140, 155, 170, 180,
93 140, 130, 140, 150, 160, 170, 180, 190,
94 130, 140, 150, 160, 170, 180, 190, 200
97 // The attacking side is given a descending bonus based on distance between
98 // the two kings in basic endgames.
99 const int DistanceBonus[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
101 // Bitbase for KP vs K
102 uint8_t KPKBitbase[24576];
104 // Penalty for big distance between king and knight for the defending king
105 // and knight in KR vs KN endgames.
106 const int KRKNKingKnightDistancePenalty[8] = { 0, 0, 4, 10, 20, 32, 48, 70 };
108 // Various inline functions for accessing the above arrays
109 inline Value mate_table(Square s) {
110 return Value(MateTable[s]);
113 inline Value kbnk_mate_table(Square s) {
114 return Value(KBNKMateTable[s]);
117 inline Value distance_bonus(int d) {
118 return Value(DistanceBonus[d]);
121 inline Value krkn_king_knight_distance_penalty(int d) {
122 return Value(KRKNKingKnightDistancePenalty[d]);
125 // Function for probing the KP vs K bitbase
126 int probe_kpk(Square wksq, Square wpsq, Square bksq, Color stm);
135 /// Mate with KX vs K. This function is used to evaluate positions with
136 /// King and plenty of material vs a lone king. It simply gives the
137 /// attacking side a bonus for driving the defending king towards the edge
138 /// of the board, and for keeping the distance between the two kings small.
140 Value EvaluationFunction<KXK>::apply(const Position& pos) {
142 assert(pos.non_pawn_material(weakerSide) == Value(0));
143 assert(pos.piece_count(weakerSide, PAWN) == Value(0));
145 Square winnerKSq = pos.king_square(strongerSide);
146 Square loserKSq = pos.king_square(weakerSide);
148 Value result = pos.non_pawn_material(strongerSide)
149 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
150 + mate_table(loserKSq)
151 + distance_bonus(square_distance(winnerKSq, loserKSq));
153 if ( pos.piece_count(strongerSide, QUEEN) > 0
154 || pos.piece_count(strongerSide, ROOK) > 0
155 || pos.piece_count(strongerSide, BISHOP) > 1)
156 // TODO: check for two equal-colored bishops!
157 result += VALUE_KNOWN_WIN;
159 return (strongerSide == pos.side_to_move() ? result : -result);
163 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
164 /// defending king towards a corner square of the right color.
166 Value EvaluationFunction<KBNK>::apply(const Position& pos) {
168 assert(pos.non_pawn_material(weakerSide) == Value(0));
169 assert(pos.piece_count(weakerSide, PAWN) == Value(0));
170 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
171 assert(pos.piece_count(strongerSide, BISHOP) == 1);
172 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
173 assert(pos.piece_count(strongerSide, PAWN) == 0);
175 Square winnerKSq = pos.king_square(strongerSide);
176 Square loserKSq = pos.king_square(weakerSide);
177 Square bishopSquare = pos.piece_list(strongerSide, BISHOP, 0);
179 if (square_color(bishopSquare) == BLACK)
181 winnerKSq = flop_square(winnerKSq);
182 loserKSq = flop_square(loserKSq);
185 Value result = VALUE_KNOWN_WIN
186 + distance_bonus(square_distance(winnerKSq, loserKSq))
187 + kbnk_mate_table(loserKSq);
189 return (strongerSide == pos.side_to_move() ? result : -result);
193 /// KP vs K. This endgame is evaluated with the help of a bitbase.
195 Value EvaluationFunction<KPK>::apply(const Position& pos) {
197 assert(pos.non_pawn_material(strongerSide) == Value(0));
198 assert(pos.non_pawn_material(weakerSide) == Value(0));
199 assert(pos.piece_count(strongerSide, PAWN) == 1);
200 assert(pos.piece_count(weakerSide, PAWN) == 0);
202 Square wksq, bksq, wpsq;
205 if (strongerSide == WHITE)
207 wksq = pos.king_square(WHITE);
208 bksq = pos.king_square(BLACK);
209 wpsq = pos.piece_list(WHITE, PAWN, 0);
210 stm = pos.side_to_move();
214 wksq = flip_square(pos.king_square(BLACK));
215 bksq = flip_square(pos.king_square(WHITE));
216 wpsq = flip_square(pos.piece_list(BLACK, PAWN, 0));
217 stm = opposite_color(pos.side_to_move());
220 if (square_file(wpsq) >= FILE_E)
222 wksq = flop_square(wksq);
223 bksq = flop_square(bksq);
224 wpsq = flop_square(wpsq);
227 if (!probe_kpk(wksq, wpsq, bksq, stm))
230 Value result = VALUE_KNOWN_WIN
232 + Value(square_rank(wpsq));
234 return (strongerSide == pos.side_to_move() ? result : -result);
238 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
239 /// a bitbase. The function below returns drawish scores when the pawn is
240 /// far advanced with support of the king, while the attacking king is far
243 Value EvaluationFunction<KRKP>::apply(const Position& pos) {
245 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
246 assert(pos.piece_count(strongerSide, PAWN) == 0);
247 assert(pos.non_pawn_material(weakerSide) == 0);
248 assert(pos.piece_count(weakerSide, PAWN) == 1);
250 Square wksq, wrsq, bksq, bpsq;
251 int tempo = (pos.side_to_move() == strongerSide);
253 wksq = pos.king_square(strongerSide);
254 wrsq = pos.piece_list(strongerSide, ROOK, 0);
255 bksq = pos.king_square(weakerSide);
256 bpsq = pos.piece_list(weakerSide, PAWN, 0);
258 if (strongerSide == BLACK)
260 wksq = flip_square(wksq);
261 wrsq = flip_square(wrsq);
262 bksq = flip_square(bksq);
263 bpsq = flip_square(bpsq);
266 Square queeningSq = make_square(square_file(bpsq), RANK_1);
269 // If the stronger side's king is in front of the pawn, it's a win
270 if (wksq < bpsq && square_file(wksq) == square_file(bpsq))
271 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
273 // If the weaker side's king is too far from the pawn and the rook,
275 else if ( square_distance(bksq, bpsq) - (tempo^1) >= 3
276 && square_distance(bksq, wrsq) >= 3)
277 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
279 // If the pawn is far advanced and supported by the defending king,
280 // the position is drawish
281 else if ( square_rank(bksq) <= RANK_3
282 && square_distance(bksq, bpsq) == 1
283 && square_rank(wksq) >= RANK_4
284 && square_distance(wksq, bpsq) - tempo > 2)
285 result = Value(80 - square_distance(wksq, bpsq) * 8);
289 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
290 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
291 + Value(square_distance(bpsq, queeningSq) * 8);
293 return (strongerSide == pos.side_to_move() ? result : -result);
297 /// KR vs KB. This is very simple, and always returns drawish scores. The
298 /// score is slightly bigger when the defending king is close to the edge.
300 Value EvaluationFunction<KRKB>::apply(const Position& pos) {
302 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
303 assert(pos.piece_count(strongerSide, PAWN) == 0);
304 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
305 assert(pos.piece_count(weakerSide, PAWN) == 0);
306 assert(pos.piece_count(weakerSide, BISHOP) == 1);
308 Value result = mate_table(pos.king_square(weakerSide));
309 return (pos.side_to_move() == strongerSide ? result : -result);
313 /// KR vs KN. The attacking side has slightly better winning chances than
314 /// in KR vs KB, particularly if the king and the knight are far apart.
316 Value EvaluationFunction<KRKN>::apply(const Position& pos) {
318 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
319 assert(pos.piece_count(strongerSide, PAWN) == 0);
320 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
321 assert(pos.piece_count(weakerSide, PAWN) == 0);
322 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
324 Square defendingKSq = pos.king_square(weakerSide);
325 Square nSq = pos.piece_list(weakerSide, KNIGHT, 0);
327 Value result = Value(10) + mate_table(defendingKSq) +
328 krkn_king_knight_distance_penalty(square_distance(defendingKSq, nSq));
330 return (strongerSide == pos.side_to_move())? result : -result;
334 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
335 /// king a bonus for having the kings close together, and for forcing the
336 /// defending king towards the edge. If we also take care to avoid null move
337 /// for the defending side in the search, this is usually sufficient to be
338 /// able to win KQ vs KR.
340 Value EvaluationFunction<KQKR>::apply(const Position& pos) {
342 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
343 assert(pos.piece_count(strongerSide, PAWN) == 0);
344 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
345 assert(pos.piece_count(weakerSide, PAWN) == 0);
347 Square winnerKSq = pos.king_square(strongerSide);
348 Square loserKSq = pos.king_square(weakerSide);
350 Value result = QueenValueEndgame
352 + mate_table(loserKSq)
353 + distance_bonus(square_distance(winnerKSq, loserKSq));
355 return (strongerSide == pos.side_to_move())? result : -result;
359 Value EvaluationFunction<KBBKN>::apply(const Position& pos) {
361 assert(pos.piece_count(strongerSide, BISHOP) == 2);
362 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
363 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
364 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
365 assert(pos.pawns() == EmptyBoardBB);
367 Value result = BishopValueEndgame;
368 Square wksq = pos.king_square(strongerSide);
369 Square bksq = pos.king_square(weakerSide);
370 Square nsq = pos.piece_list(weakerSide, KNIGHT, 0);
372 // Bonus for attacking king close to defending king
373 result += distance_bonus(square_distance(wksq, bksq));
375 // Bonus for driving the defending king and knight apart
376 result += Value(square_distance(bksq, nsq) * 32);
378 // Bonus for restricting the knight's mobility
379 result += Value((8 - count_1s_max_15(pos.piece_attacks<KNIGHT>(nsq))) * 8);
381 return (strongerSide == pos.side_to_move() ? result : -result);
385 Value EvaluationFunction<KmmKm>::apply(const Position &pos) {
390 /// KBPKScalingFunction scales endgames where the stronger side has king,
391 /// bishop and one or more pawns. It checks for draws with rook pawns and a
392 /// bishop of the wrong color. If such a draw is detected, ScaleFactor(0) is
393 /// returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
396 ScaleFactor ScalingFunction<KBPK>::apply(const Position& pos) {
398 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
399 assert(pos.piece_count(strongerSide, BISHOP) == 1);
400 assert(pos.piece_count(strongerSide, PAWN) >= 1);
402 // No assertions about the material of weakerSide, because we want draws to
403 // be detected even when the weaker side has some pawns.
405 Bitboard pawns = pos.pawns(strongerSide);
406 File pawnFile = square_file(pos.piece_list(strongerSide, PAWN, 0));
408 // All pawns are on a single rook file ?
409 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
410 && (pawns & ~file_bb(pawnFile)) == EmptyBoardBB)
412 Square bishopSq = pos.piece_list(strongerSide, BISHOP, 0);
413 Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
414 Square kingSq = pos.king_square(weakerSide);
416 if ( square_color(queeningSq) != square_color(bishopSq)
417 && file_distance(square_file(kingSq), pawnFile) <= 1)
419 // The bishop has the wrong color, and the defending king is on the
420 // file of the pawn(s) or the neighboring file. Find the rank of the
424 if (strongerSide == WHITE)
426 for (rank = RANK_7; (rank_bb(rank) & pawns) == EmptyBoardBB; rank--) {}
427 assert(rank >= RANK_2 && rank <= RANK_7);
431 for(rank = RANK_2; (rank_bb(rank) & pawns) == EmptyBoardBB; rank++) {}
432 rank = Rank(rank^7); // HACK to get the relative rank
433 assert(rank >= RANK_2 && rank <= RANK_7);
435 // If the defending king has distance 1 to the promotion square or
436 // is placed somewhere in front of the pawn, it's a draw.
437 if ( square_distance(kingSq, queeningSq) <= 1
438 || relative_rank(strongerSide, kingSq) >= rank)
439 return ScaleFactor(0);
442 return SCALE_FACTOR_NONE;
446 /// KQKRPScalingFunction scales endgames where the stronger side has only
447 /// king and queen, while the weaker side has at least a rook and a pawn.
448 /// It tests for fortress draws with a rook on the third rank defended by
451 ScaleFactor ScalingFunction<KQKRP>::apply(const Position& pos) {
453 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
454 assert(pos.piece_count(strongerSide, QUEEN) == 1);
455 assert(pos.piece_count(strongerSide, PAWN) == 0);
456 assert(pos.piece_count(weakerSide, ROOK) == 1);
457 assert(pos.piece_count(weakerSide, PAWN) >= 1);
459 Square kingSq = pos.king_square(weakerSide);
460 if ( relative_rank(weakerSide, kingSq) <= RANK_2
461 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
462 && (pos.rooks(weakerSide) & relative_rank_bb(weakerSide, RANK_3))
463 && (pos.pawns(weakerSide) & relative_rank_bb(weakerSide, RANK_2))
464 && (pos.piece_attacks<KING>(kingSq) & pos.pawns(weakerSide)))
466 Square rsq = pos.piece_list(weakerSide, ROOK, 0);
467 if (pos.pawn_attacks(strongerSide, rsq) & pos.pawns(weakerSide))
468 return ScaleFactor(0);
470 return SCALE_FACTOR_NONE;
474 /// KRPKRScalingFunction scales KRP vs KR endgames. This function knows a
475 /// handful of the most important classes of drawn positions, but is far
476 /// from perfect. It would probably be a good idea to add more knowledge
479 /// It would also be nice to rewrite the actual code for this function,
480 /// which is mostly copied from Glaurung 1.x, and not very pretty.
482 ScaleFactor ScalingFunction<KRPKR>::apply(const Position &pos) {
484 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
485 assert(pos.piece_count(strongerSide, PAWN) == 1);
486 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
487 assert(pos.piece_count(weakerSide, PAWN) == 0);
489 Square wksq = pos.king_square(strongerSide);
490 Square wrsq = pos.piece_list(strongerSide, ROOK, 0);
491 Square wpsq = pos.piece_list(strongerSide, PAWN, 0);
492 Square bksq = pos.king_square(weakerSide);
493 Square brsq = pos.piece_list(weakerSide, ROOK, 0);
495 // Orient the board in such a way that the stronger side is white, and the
496 // pawn is on the left half of the board.
497 if (strongerSide == BLACK)
499 wksq = flip_square(wksq);
500 wrsq = flip_square(wrsq);
501 wpsq = flip_square(wpsq);
502 bksq = flip_square(bksq);
503 brsq = flip_square(brsq);
505 if (square_file(wpsq) > FILE_D)
507 wksq = flop_square(wksq);
508 wrsq = flop_square(wrsq);
509 wpsq = flop_square(wpsq);
510 bksq = flop_square(bksq);
511 brsq = flop_square(brsq);
514 File f = square_file(wpsq);
515 Rank r = square_rank(wpsq);
516 Square queeningSq = make_square(f, RANK_8);
517 int tempo = (pos.side_to_move() == strongerSide);
519 // If the pawn is not too far advanced and the defending king defends the
520 // queening square, use the third-rank defence.
522 && square_distance(bksq, queeningSq) <= 1
524 && (square_rank(brsq) == RANK_6 || (r <= RANK_3 && square_rank(wrsq) != RANK_6)))
525 return ScaleFactor(0);
527 // The defending side saves a draw by checking from behind in case the pawn
528 // has advanced to the 6th rank with the king behind.
530 && square_distance(bksq, queeningSq) <= 1
531 && square_rank(wksq) + tempo <= RANK_6
532 && (square_rank(brsq) == RANK_1 || (!tempo && abs(square_file(brsq) - f) >= 3)))
533 return ScaleFactor(0);
536 && bksq == queeningSq
537 && square_rank(brsq) == RANK_1
538 && (!tempo || square_distance(wksq, wpsq) >= 2))
539 return ScaleFactor(0);
541 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
542 // and the black rook is behind the pawn.
545 && (bksq == SQ_H7 || bksq == SQ_G7)
546 && square_file(brsq) == FILE_A
547 && (square_rank(brsq) <= RANK_3 || square_file(wksq) >= FILE_D || square_rank(wksq) <= RANK_5))
548 return ScaleFactor(0);
550 // If the defending king blocks the pawn and the attacking king is too far
551 // away, it's a draw.
553 && bksq == wpsq + DELTA_N
554 && square_distance(wksq, wpsq) - tempo >= 2
555 && square_distance(wksq, brsq) - tempo >= 2)
556 return ScaleFactor(0);
558 // Pawn on the 7th rank supported by the rook from behind usually wins if the
559 // attacking king is closer to the queening square than the defending king,
560 // and the defending king cannot gain tempi by threatening the attacking rook.
563 && square_file(wrsq) == f
564 && wrsq != queeningSq
565 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
566 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
567 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
569 // Similar to the above, but with the pawn further back
571 && square_file(wrsq) == f
573 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
574 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
575 && ( square_distance(bksq, wrsq) + tempo >= 3
576 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
577 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
578 return ScaleFactor( SCALE_FACTOR_MAX
579 - (8 * square_distance(wpsq, queeningSq)
580 + 2 * square_distance(wksq, queeningSq)));
582 // If the pawn is not far advanced, and the defending king is somewhere in
583 // the pawn's path, it's probably a draw.
584 if (r <= RANK_4 && bksq > wpsq)
586 if (square_file(bksq) == square_file(wpsq))
587 return ScaleFactor(10);
588 if ( abs(square_file(bksq) - square_file(wpsq)) == 1
589 && square_distance(wksq, bksq) > 2)
590 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
592 return SCALE_FACTOR_NONE;
596 /// KRPPKRPScalingFunction scales KRPP vs KRP endgames. There is only a
597 /// single pattern: If the stronger side has no pawns and the defending king
598 /// is actively placed, the position is drawish.
600 ScaleFactor ScalingFunction<KRPPKRP>::apply(const Position &pos) {
602 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
603 assert(pos.piece_count(strongerSide, PAWN) == 2);
604 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
605 assert(pos.piece_count(weakerSide, PAWN) == 1);
607 Square wpsq1 = pos.piece_list(strongerSide, PAWN, 0);
608 Square wpsq2 = pos.piece_list(strongerSide, PAWN, 1);
609 Square bksq = pos.king_square(weakerSide);
611 // Does the stronger side have a passed pawn?
612 if ( pos.pawn_is_passed(strongerSide, wpsq1)
613 || pos.pawn_is_passed(strongerSide, wpsq2))
614 return SCALE_FACTOR_NONE;
616 Rank r = Max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
618 if ( file_distance(bksq, wpsq1) <= 1
619 && file_distance(bksq, wpsq2) <= 1
620 && relative_rank(strongerSide, bksq) > r)
623 case RANK_2: return ScaleFactor(10);
624 case RANK_3: return ScaleFactor(10);
625 case RANK_4: return ScaleFactor(15);
626 case RANK_5: return ScaleFactor(20);
627 case RANK_6: return ScaleFactor(40);
628 default: assert(false);
631 return SCALE_FACTOR_NONE;
635 /// KPsKScalingFunction scales endgames with king and two or more pawns
636 /// against king. There is just a single rule here: If all pawns are on
637 /// the same rook file and are blocked by the defending king, it's a draw.
639 ScaleFactor ScalingFunction<KPsK>::apply(const Position &pos) {
641 assert(pos.non_pawn_material(strongerSide) == Value(0));
642 assert(pos.piece_count(strongerSide, PAWN) >= 2);
643 assert(pos.non_pawn_material(weakerSide) == Value(0));
644 assert(pos.piece_count(weakerSide, PAWN) == 0);
646 Bitboard pawns = pos.pawns(strongerSide);
648 // Are all pawns on the 'a' file?
649 if ((pawns & ~FileABB) == EmptyBoardBB)
651 // Does the defending king block the pawns?
652 Square ksq = pos.king_square(weakerSide);
653 if (square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1)
654 return ScaleFactor(0);
655 else if( square_file(ksq) == FILE_A
656 && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB)
657 return ScaleFactor(0);
659 return SCALE_FACTOR_NONE;
661 // Are all pawns on the 'h' file?
662 else if ((pawns & ~FileHBB) == EmptyBoardBB)
664 // Does the defending king block the pawns?
665 Square ksq = pos.king_square(weakerSide);
666 if (square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1)
667 return ScaleFactor(0);
668 else if ( square_file(ksq) == FILE_H
669 && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB)
670 return ScaleFactor(0);
672 return SCALE_FACTOR_NONE;
675 return SCALE_FACTOR_NONE;
679 /// KBPKBScalingFunction scales KBP vs KB endgames. There are two rules:
680 /// If the defending king is somewhere along the path of the pawn, and the
681 /// square of the king is not of the same color as the stronger side's bishop,
682 /// it's a draw. If the two bishops have opposite color, it's almost always
685 ScaleFactor ScalingFunction<KBPKB>::apply(const Position &pos) {
687 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
688 assert(pos.piece_count(strongerSide, BISHOP) == 1);
689 assert(pos.piece_count(strongerSide, PAWN) == 1);
690 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
691 assert(pos.piece_count(weakerSide, BISHOP) == 1);
692 assert(pos.piece_count(weakerSide, PAWN) == 0);
694 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
695 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP, 0);
696 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP, 0);
697 Square weakerKingSq = pos.king_square(weakerSide);
699 // Case 1: Defending king blocks the pawn, and cannot be driven away
700 if ( square_file(weakerKingSq) == square_file(pawnSq)
701 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
702 && ( square_color(weakerKingSq) != square_color(strongerBishopSq)
703 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
704 return ScaleFactor(0);
706 // Case 2: Opposite colored bishops
707 if (square_color(strongerBishopSq) != square_color(weakerBishopSq))
709 // We assume that the position is drawn in the following three situations:
711 // a. The pawn is on rank 5 or further back.
712 // b. The defending king is somewhere in the pawn's path.
713 // c. The defending bishop attacks some square along the pawn's path,
714 // and is at least three squares away from the pawn.
716 // These rules are probably not perfect, but in practice they work
719 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
720 return ScaleFactor(0);
723 Bitboard ray = ray_bb(pawnSq, (strongerSide == WHITE)? SIGNED_DIR_N : SIGNED_DIR_S);
724 if (ray & pos.kings(weakerSide))
725 return ScaleFactor(0);
726 if( (pos.piece_attacks<BISHOP>(weakerBishopSq) & ray)
727 && square_distance(weakerBishopSq, pawnSq) >= 3)
728 return ScaleFactor(0);
731 return SCALE_FACTOR_NONE;
735 /// KBPKNScalingFunction scales KBP vs KN endgames. There is a single rule:
736 /// If the defending king is somewhere along the path of the pawn, and the
737 /// square of the king is not of the same color as the stronger side's bishop,
740 ScaleFactor ScalingFunction<KBPKN>::apply(const Position &pos) {
742 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
743 assert(pos.piece_count(strongerSide, BISHOP) == 1);
744 assert(pos.piece_count(strongerSide, PAWN) == 1);
745 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
746 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
747 assert(pos.piece_count(weakerSide, PAWN) == 0);
749 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
750 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP, 0);
751 Square weakerKingSq = pos.king_square(weakerSide);
753 if ( square_file(weakerKingSq) == square_file(pawnSq)
754 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
755 && ( square_color(weakerKingSq) != square_color(strongerBishopSq)
756 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
757 return ScaleFactor(0);
759 return SCALE_FACTOR_NONE;
763 /// KNPKScalingFunction scales KNP vs K endgames. There is a single rule:
764 /// If the pawn is a rook pawn on the 7th rank and the defending king prevents
765 /// the pawn from advancing, the position is drawn.
767 ScaleFactor ScalingFunction<KNPK>::apply(const Position &pos) {
769 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
770 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
771 assert(pos.piece_count(strongerSide, PAWN) == 1);
772 assert(pos.non_pawn_material(weakerSide) == Value(0));
773 assert(pos.piece_count(weakerSide, PAWN) == 0);
775 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
776 Square weakerKingSq = pos.king_square(weakerSide);
778 if ( pawnSq == relative_square(strongerSide, SQ_A7)
779 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
780 return ScaleFactor(0);
782 if ( pawnSq == relative_square(strongerSide, SQ_H7)
783 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
784 return ScaleFactor(0);
786 return SCALE_FACTOR_NONE;
790 /// KPKPScalingFunction scales KP vs KP endgames. This is done by removing
791 /// the weakest side's pawn and probing the KP vs K bitbase: If the weakest
792 /// side has a draw without the pawn, she probably has at least a draw with
793 /// the pawn as well. The exception is when the stronger side's pawn is far
794 /// advanced and not on a rook file; in this case it is often possible to win
795 /// (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
797 ScaleFactor ScalingFunction<KPKP>::apply(const Position &pos) {
799 assert(pos.non_pawn_material(strongerSide) == Value(0));
800 assert(pos.non_pawn_material(weakerSide) == Value(0));
801 assert(pos.piece_count(WHITE, PAWN) == 1);
802 assert(pos.piece_count(BLACK, PAWN) == 1);
804 Square wksq, bksq, wpsq;
807 if (strongerSide == WHITE)
809 wksq = pos.king_square(WHITE);
810 bksq = pos.king_square(BLACK);
811 wpsq = pos.piece_list(WHITE, PAWN, 0);
812 stm = pos.side_to_move();
816 wksq = flip_square(pos.king_square(BLACK));
817 bksq = flip_square(pos.king_square(WHITE));
818 wpsq = flip_square(pos.piece_list(BLACK, PAWN, 0));
819 stm = opposite_color(pos.side_to_move());
822 if (square_file(wpsq) >= FILE_E)
824 wksq = flop_square(wksq);
825 bksq = flop_square(bksq);
826 wpsq = flop_square(wpsq);
829 // If the pawn has advanced to the fifth rank or further, and is not a
830 // rook pawn, it's too dangerous to assume that it's at least a draw.
831 if ( square_rank(wpsq) >= RANK_5
832 && square_file(wpsq) != FILE_A)
833 return SCALE_FACTOR_NONE;
835 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a
836 // draw, it's probably at least a draw even with the pawn.
837 if (probe_kpk(wksq, wpsq, bksq, stm))
838 return SCALE_FACTOR_NONE;
840 return ScaleFactor(0);
844 /// init_bitbases() is called during program initialization, and simply loads
845 /// bitbases from disk into memory. At the moment, there is only the bitbase
846 /// for KP vs K, but we may decide to add other bitbases later.
848 void init_bitbases() {
849 generate_kpk_bitbase(KPKBitbase);
855 // Probe the KP vs K bitbase:
857 int probe_kpk(Square wksq, Square wpsq, Square bksq, Color stm) {
859 int wp = int(square_file(wpsq)) + (int(square_rank(wpsq)) - 1) * 4;
860 int index = int(stm) + 2*int(bksq) + 128*int(wksq) + 8192*wp;
862 assert(index >= 0 && index < 24576*8);
863 return KPKBitbase[index/8] & (1 << (index&7));