2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2010 Marco Costalba, Joona Kiiski, Tord Romstad
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/>.
33 //// Local definitions
38 // Table used to drive the defending king towards the edge of the board
39 // in KX vs K and KQ vs KR endgames.
40 const uint8_t MateTable[64] = {
41 100, 90, 80, 70, 70, 80, 90, 100,
42 90, 70, 60, 50, 50, 60, 70, 90,
43 80, 60, 40, 30, 30, 40, 60, 80,
44 70, 50, 30, 20, 20, 30, 50, 70,
45 70, 50, 30, 20, 20, 30, 50, 70,
46 80, 60, 40, 30, 30, 40, 60, 80,
47 90, 70, 60, 50, 50, 60, 70, 90,
48 100, 90, 80, 70, 70, 80, 90, 100,
51 // Table used to drive the defending king towards a corner square of the
52 // right color in KBN vs K endgames.
53 const uint8_t KBNKMateTable[64] = {
54 200, 190, 180, 170, 160, 150, 140, 130,
55 190, 180, 170, 160, 150, 140, 130, 140,
56 180, 170, 155, 140, 140, 125, 140, 150,
57 170, 160, 140, 120, 110, 140, 150, 160,
58 160, 150, 140, 110, 120, 140, 160, 170,
59 150, 140, 125, 140, 140, 155, 170, 180,
60 140, 130, 140, 150, 160, 170, 180, 190,
61 130, 140, 150, 160, 170, 180, 190, 200
64 // The attacking side is given a descending bonus based on distance between
65 // the two kings in basic endgames.
66 const int DistanceBonus[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
68 // Penalty for big distance between king and knight for the defending king
69 // and knight in KR vs KN endgames.
70 const int KRKNKingKnightDistancePenalty[8] = { 0, 0, 4, 10, 20, 32, 48, 70 };
72 // Bitbase for KP vs K
73 uint8_t KPKBitbase[24576];
75 // Various inline functions for accessing the above arrays
76 inline Value mate_table(Square s) {
77 return Value(MateTable[s]);
80 inline Value kbnk_mate_table(Square s) {
81 return Value(KBNKMateTable[s]);
84 inline Value distance_bonus(int d) {
85 return Value(DistanceBonus[d]);
88 inline Value krkn_king_knight_distance_penalty(int d) {
89 return Value(KRKNKingKnightDistancePenalty[d]);
92 // Function for probing the KP vs K bitbase
93 int probe_kpk(Square wksq, Square wpsq, Square bksq, Color stm);
102 /// init_bitbases() is called during program initialization, and simply loads
103 /// bitbases from disk into memory. At the moment, there is only the bitbase
104 /// for KP vs K, but we may decide to add other bitbases later.
106 void init_bitbases() {
107 generate_kpk_bitbase(KPKBitbase);
111 /// Mate with KX vs K. This function is used to evaluate positions with
112 /// King and plenty of material vs a lone king. It simply gives the
113 /// attacking side a bonus for driving the defending king towards the edge
114 /// of the board, and for keeping the distance between the two kings small.
116 Value EvaluationFunction<KXK>::apply(const Position& pos) const {
118 assert(pos.non_pawn_material(weakerSide) == Value(0));
119 assert(pos.piece_count(weakerSide, PAWN) == Value(0));
121 Square winnerKSq = pos.king_square(strongerSide);
122 Square loserKSq = pos.king_square(weakerSide);
124 Value result = pos.non_pawn_material(strongerSide)
125 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
126 + mate_table(loserKSq)
127 + distance_bonus(square_distance(winnerKSq, loserKSq));
129 if ( pos.piece_count(strongerSide, QUEEN)
130 || pos.piece_count(strongerSide, ROOK)
131 || pos.piece_count(strongerSide, BISHOP) > 1)
132 // TODO: check for two equal-colored bishops!
133 result += VALUE_KNOWN_WIN;
135 return strongerSide == pos.side_to_move() ? result : -result;
139 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
140 /// defending king towards a corner square of the right color.
142 Value EvaluationFunction<KBNK>::apply(const Position& pos) const {
144 assert(pos.non_pawn_material(weakerSide) == Value(0));
145 assert(pos.piece_count(weakerSide, PAWN) == Value(0));
146 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
147 assert(pos.piece_count(strongerSide, BISHOP) == 1);
148 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
149 assert(pos.piece_count(strongerSide, PAWN) == 0);
151 Square winnerKSq = pos.king_square(strongerSide);
152 Square loserKSq = pos.king_square(weakerSide);
153 Square bishopSquare = pos.piece_list(strongerSide, BISHOP, 0);
155 if (same_color_squares(bishopSquare, SQ_A1))
157 winnerKSq = flop_square(winnerKSq);
158 loserKSq = flop_square(loserKSq);
161 Value result = VALUE_KNOWN_WIN
162 + distance_bonus(square_distance(winnerKSq, loserKSq))
163 + kbnk_mate_table(loserKSq);
165 return strongerSide == pos.side_to_move() ? result : -result;
169 /// KP vs K. This endgame is evaluated with the help of a bitbase.
171 Value EvaluationFunction<KPK>::apply(const Position& pos) const {
173 assert(pos.non_pawn_material(strongerSide) == Value(0));
174 assert(pos.non_pawn_material(weakerSide) == Value(0));
175 assert(pos.piece_count(strongerSide, PAWN) == 1);
176 assert(pos.piece_count(weakerSide, PAWN) == 0);
178 Square wksq, bksq, wpsq;
181 if (strongerSide == WHITE)
183 wksq = pos.king_square(WHITE);
184 bksq = pos.king_square(BLACK);
185 wpsq = pos.piece_list(WHITE, PAWN, 0);
186 stm = pos.side_to_move();
190 wksq = flip_square(pos.king_square(BLACK));
191 bksq = flip_square(pos.king_square(WHITE));
192 wpsq = flip_square(pos.piece_list(BLACK, PAWN, 0));
193 stm = opposite_color(pos.side_to_move());
196 if (square_file(wpsq) >= FILE_E)
198 wksq = flop_square(wksq);
199 bksq = flop_square(bksq);
200 wpsq = flop_square(wpsq);
203 if (!probe_kpk(wksq, wpsq, bksq, stm))
206 Value result = VALUE_KNOWN_WIN
208 + Value(square_rank(wpsq));
210 return strongerSide == pos.side_to_move() ? result : -result;
214 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
215 /// a bitbase. The function below returns drawish scores when the pawn is
216 /// far advanced with support of the king, while the attacking king is far
219 Value EvaluationFunction<KRKP>::apply(const Position& pos) const {
221 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
222 assert(pos.piece_count(strongerSide, PAWN) == 0);
223 assert(pos.non_pawn_material(weakerSide) == 0);
224 assert(pos.piece_count(weakerSide, PAWN) == 1);
226 Square wksq, wrsq, bksq, bpsq;
227 int tempo = (pos.side_to_move() == strongerSide);
229 wksq = pos.king_square(strongerSide);
230 wrsq = pos.piece_list(strongerSide, ROOK, 0);
231 bksq = pos.king_square(weakerSide);
232 bpsq = pos.piece_list(weakerSide, PAWN, 0);
234 if (strongerSide == BLACK)
236 wksq = flip_square(wksq);
237 wrsq = flip_square(wrsq);
238 bksq = flip_square(bksq);
239 bpsq = flip_square(bpsq);
242 Square queeningSq = make_square(square_file(bpsq), RANK_1);
245 // If the stronger side's king is in front of the pawn, it's a win
246 if (wksq < bpsq && square_file(wksq) == square_file(bpsq))
247 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
249 // If the weaker side's king is too far from the pawn and the rook,
251 else if ( square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
252 && square_distance(bksq, wrsq) >= 3)
253 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
255 // If the pawn is far advanced and supported by the defending king,
256 // the position is drawish
257 else if ( square_rank(bksq) <= RANK_3
258 && square_distance(bksq, bpsq) == 1
259 && square_rank(wksq) >= RANK_4
260 && square_distance(wksq, bpsq) - tempo > 2)
261 result = Value(80 - square_distance(wksq, bpsq) * 8);
265 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
266 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
267 + Value(square_distance(bpsq, queeningSq) * 8);
269 return strongerSide == pos.side_to_move() ? result : -result;
273 /// KR vs KB. This is very simple, and always returns drawish scores. The
274 /// score is slightly bigger when the defending king is close to the edge.
276 Value EvaluationFunction<KRKB>::apply(const Position& pos) const {
278 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
279 assert(pos.piece_count(strongerSide, PAWN) == 0);
280 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
281 assert(pos.piece_count(weakerSide, PAWN) == 0);
282 assert(pos.piece_count(weakerSide, BISHOP) == 1);
284 Value result = mate_table(pos.king_square(weakerSide));
285 return strongerSide == pos.side_to_move() ? result : -result;
289 /// KR vs KN. The attacking side has slightly better winning chances than
290 /// in KR vs KB, particularly if the king and the knight are far apart.
292 Value EvaluationFunction<KRKN>::apply(const Position& pos) const {
294 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
295 assert(pos.piece_count(strongerSide, PAWN) == 0);
296 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
297 assert(pos.piece_count(weakerSide, PAWN) == 0);
298 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
300 Square defendingKSq = pos.king_square(weakerSide);
301 Square nSq = pos.piece_list(weakerSide, KNIGHT, 0);
303 int d = square_distance(defendingKSq, nSq);
304 Value result = Value(10)
305 + mate_table(defendingKSq)
306 + krkn_king_knight_distance_penalty(d);
308 return strongerSide == pos.side_to_move() ? result : -result;
312 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
313 /// king a bonus for having the kings close together, and for forcing the
314 /// defending king towards the edge. If we also take care to avoid null move
315 /// for the defending side in the search, this is usually sufficient to be
316 /// able to win KQ vs KR.
318 Value EvaluationFunction<KQKR>::apply(const Position& pos) const {
320 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
321 assert(pos.piece_count(strongerSide, PAWN) == 0);
322 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
323 assert(pos.piece_count(weakerSide, PAWN) == 0);
325 Square winnerKSq = pos.king_square(strongerSide);
326 Square loserKSq = pos.king_square(weakerSide);
328 Value result = QueenValueEndgame
330 + mate_table(loserKSq)
331 + distance_bonus(square_distance(winnerKSq, loserKSq));
333 return strongerSide == pos.side_to_move() ? result : -result;
337 Value EvaluationFunction<KBBKN>::apply(const Position& pos) const {
339 assert(pos.piece_count(strongerSide, BISHOP) == 2);
340 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
341 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
342 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
343 assert(pos.pieces(PAWN) == EmptyBoardBB);
345 Value result = BishopValueEndgame;
346 Square wksq = pos.king_square(strongerSide);
347 Square bksq = pos.king_square(weakerSide);
348 Square nsq = pos.piece_list(weakerSide, KNIGHT, 0);
350 // Bonus for attacking king close to defending king
351 result += distance_bonus(square_distance(wksq, bksq));
353 // Bonus for driving the defending king and knight apart
354 result += Value(square_distance(bksq, nsq) * 32);
356 // Bonus for restricting the knight's mobility
357 result += Value((8 - count_1s_max_15(pos.attacks_from<KNIGHT>(nsq))) * 8);
359 return strongerSide == pos.side_to_move() ? result : -result;
363 /// K and two minors vs K and one or two minors or K and two knights against
364 /// king alone are always draw.
366 Value EvaluationFunction<KmmKm>::apply(const Position&) const {
371 Value EvaluationFunction<KNNK>::apply(const Position&) const {
375 /// KBPKScalingFunction scales endgames where the stronger side has king,
376 /// bishop and one or more pawns. It checks for draws with rook pawns and a
377 /// bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_ZERO is
378 /// returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
381 ScaleFactor ScalingFunction<KBPsK>::apply(const Position& pos) const {
383 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
384 assert(pos.piece_count(strongerSide, BISHOP) == 1);
385 assert(pos.piece_count(strongerSide, PAWN) >= 1);
387 // No assertions about the material of weakerSide, because we want draws to
388 // be detected even when the weaker side has some pawns.
390 Bitboard pawns = pos.pieces(PAWN, strongerSide);
391 File pawnFile = square_file(pos.piece_list(strongerSide, PAWN, 0));
393 // All pawns are on a single rook file ?
394 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
395 && (pawns & ~file_bb(pawnFile)) == EmptyBoardBB)
397 Square bishopSq = pos.piece_list(strongerSide, BISHOP, 0);
398 Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
399 Square kingSq = pos.king_square(weakerSide);
401 if ( !same_color_squares(queeningSq, bishopSq)
402 && file_distance(square_file(kingSq), pawnFile) <= 1)
404 // The bishop has the wrong color, and the defending king is on the
405 // file of the pawn(s) or the neighboring file. Find the rank of the
408 if (strongerSide == WHITE)
410 for (rank = RANK_7; (rank_bb(rank) & pawns) == EmptyBoardBB; rank--) {}
411 assert(rank >= RANK_2 && rank <= RANK_7);
415 for (rank = RANK_2; (rank_bb(rank) & pawns) == EmptyBoardBB; rank++) {}
416 rank = Rank(rank ^ 7); // HACK to get the relative rank
417 assert(rank >= RANK_2 && rank <= RANK_7);
419 // If the defending king has distance 1 to the promotion square or
420 // is placed somewhere in front of the pawn, it's a draw.
421 if ( square_distance(kingSq, queeningSq) <= 1
422 || relative_rank(strongerSide, kingSq) >= rank)
423 return SCALE_FACTOR_ZERO;
426 return SCALE_FACTOR_NONE;
430 /// KQKRPScalingFunction scales endgames where the stronger side has only
431 /// king and queen, while the weaker side has at least a rook and a pawn.
432 /// It tests for fortress draws with a rook on the third rank defended by
435 ScaleFactor ScalingFunction<KQKRPs>::apply(const Position& pos) const {
437 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
438 assert(pos.piece_count(strongerSide, QUEEN) == 1);
439 assert(pos.piece_count(strongerSide, PAWN) == 0);
440 assert(pos.piece_count(weakerSide, ROOK) == 1);
441 assert(pos.piece_count(weakerSide, PAWN) >= 1);
443 Square kingSq = pos.king_square(weakerSide);
444 if ( relative_rank(weakerSide, kingSq) <= RANK_2
445 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
446 && (pos.pieces(ROOK, weakerSide) & relative_rank_bb(weakerSide, RANK_3))
447 && (pos.pieces(PAWN, weakerSide) & relative_rank_bb(weakerSide, RANK_2))
448 && (pos.attacks_from<KING>(kingSq) & pos.pieces(PAWN, weakerSide)))
450 Square rsq = pos.piece_list(weakerSide, ROOK, 0);
451 if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(PAWN, weakerSide))
452 return SCALE_FACTOR_ZERO;
454 return SCALE_FACTOR_NONE;
458 /// KRPKRScalingFunction scales KRP vs KR endgames. This function knows a
459 /// handful of the most important classes of drawn positions, but is far
460 /// from perfect. It would probably be a good idea to add more knowledge
463 /// It would also be nice to rewrite the actual code for this function,
464 /// which is mostly copied from Glaurung 1.x, and not very pretty.
466 ScaleFactor ScalingFunction<KRPKR>::apply(const Position& pos) const {
468 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
469 assert(pos.piece_count(strongerSide, PAWN) == 1);
470 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
471 assert(pos.piece_count(weakerSide, PAWN) == 0);
473 Square wksq = pos.king_square(strongerSide);
474 Square wrsq = pos.piece_list(strongerSide, ROOK, 0);
475 Square wpsq = pos.piece_list(strongerSide, PAWN, 0);
476 Square bksq = pos.king_square(weakerSide);
477 Square brsq = pos.piece_list(weakerSide, ROOK, 0);
479 // Orient the board in such a way that the stronger side is white, and the
480 // pawn is on the left half of the board.
481 if (strongerSide == BLACK)
483 wksq = flip_square(wksq);
484 wrsq = flip_square(wrsq);
485 wpsq = flip_square(wpsq);
486 bksq = flip_square(bksq);
487 brsq = flip_square(brsq);
489 if (square_file(wpsq) > FILE_D)
491 wksq = flop_square(wksq);
492 wrsq = flop_square(wrsq);
493 wpsq = flop_square(wpsq);
494 bksq = flop_square(bksq);
495 brsq = flop_square(brsq);
498 File f = square_file(wpsq);
499 Rank r = square_rank(wpsq);
500 Square queeningSq = make_square(f, RANK_8);
501 int tempo = (pos.side_to_move() == strongerSide);
503 // If the pawn is not too far advanced and the defending king defends the
504 // queening square, use the third-rank defence.
506 && square_distance(bksq, queeningSq) <= 1
508 && (square_rank(brsq) == RANK_6 || (r <= RANK_3 && square_rank(wrsq) != RANK_6)))
509 return SCALE_FACTOR_ZERO;
511 // The defending side saves a draw by checking from behind in case the pawn
512 // has advanced to the 6th rank with the king behind.
514 && square_distance(bksq, queeningSq) <= 1
515 && square_rank(wksq) + tempo <= RANK_6
516 && (square_rank(brsq) == RANK_1 || (!tempo && abs(square_file(brsq) - f) >= 3)))
517 return SCALE_FACTOR_ZERO;
520 && bksq == queeningSq
521 && square_rank(brsq) == RANK_1
522 && (!tempo || square_distance(wksq, wpsq) >= 2))
523 return SCALE_FACTOR_ZERO;
525 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
526 // and the black rook is behind the pawn.
529 && (bksq == SQ_H7 || bksq == SQ_G7)
530 && square_file(brsq) == FILE_A
531 && (square_rank(brsq) <= RANK_3 || square_file(wksq) >= FILE_D || square_rank(wksq) <= RANK_5))
532 return SCALE_FACTOR_ZERO;
534 // If the defending king blocks the pawn and the attacking king is too far
535 // away, it's a draw.
537 && bksq == wpsq + DELTA_N
538 && square_distance(wksq, wpsq) - tempo >= 2
539 && square_distance(wksq, brsq) - tempo >= 2)
540 return SCALE_FACTOR_ZERO;
542 // Pawn on the 7th rank supported by the rook from behind usually wins if the
543 // attacking king is closer to the queening square than the defending king,
544 // and the defending king cannot gain tempi by threatening the attacking rook.
547 && square_file(wrsq) == f
548 && wrsq != queeningSq
549 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
550 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
551 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
553 // Similar to the above, but with the pawn further back
555 && square_file(wrsq) == f
557 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
558 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
559 && ( square_distance(bksq, wrsq) + tempo >= 3
560 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
561 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
562 return ScaleFactor( SCALE_FACTOR_MAX
563 - 8 * square_distance(wpsq, queeningSq)
564 - 2 * square_distance(wksq, queeningSq));
566 // If the pawn is not far advanced, and the defending king is somewhere in
567 // the pawn's path, it's probably a draw.
568 if (r <= RANK_4 && bksq > wpsq)
570 if (square_file(bksq) == square_file(wpsq))
571 return ScaleFactor(10);
572 if ( abs(square_file(bksq) - square_file(wpsq)) == 1
573 && square_distance(wksq, bksq) > 2)
574 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
576 return SCALE_FACTOR_NONE;
580 /// KRPPKRPScalingFunction scales KRPP vs KRP endgames. There is only a
581 /// single pattern: If the stronger side has no pawns and the defending king
582 /// is actively placed, the position is drawish.
584 ScaleFactor ScalingFunction<KRPPKRP>::apply(const Position& pos) const {
586 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
587 assert(pos.piece_count(strongerSide, PAWN) == 2);
588 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
589 assert(pos.piece_count(weakerSide, PAWN) == 1);
591 Square wpsq1 = pos.piece_list(strongerSide, PAWN, 0);
592 Square wpsq2 = pos.piece_list(strongerSide, PAWN, 1);
593 Square bksq = pos.king_square(weakerSide);
595 // Does the stronger side have a passed pawn?
596 if ( pos.pawn_is_passed(strongerSide, wpsq1)
597 || pos.pawn_is_passed(strongerSide, wpsq2))
598 return SCALE_FACTOR_NONE;
600 Rank r = Max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
602 if ( file_distance(bksq, wpsq1) <= 1
603 && file_distance(bksq, wpsq2) <= 1
604 && relative_rank(strongerSide, bksq) > r)
607 case RANK_2: return ScaleFactor(10);
608 case RANK_3: return ScaleFactor(10);
609 case RANK_4: return ScaleFactor(15);
610 case RANK_5: return ScaleFactor(20);
611 case RANK_6: return ScaleFactor(40);
612 default: assert(false);
615 return SCALE_FACTOR_NONE;
619 /// KPsKScalingFunction scales endgames with king and two or more pawns
620 /// against king. There is just a single rule here: If all pawns are on
621 /// the same rook file and are blocked by the defending king, it's a draw.
623 ScaleFactor ScalingFunction<KPsK>::apply(const Position& pos) const {
625 assert(pos.non_pawn_material(strongerSide) == Value(0));
626 assert(pos.piece_count(strongerSide, PAWN) >= 2);
627 assert(pos.non_pawn_material(weakerSide) == Value(0));
628 assert(pos.piece_count(weakerSide, PAWN) == 0);
630 Square ksq = pos.king_square(weakerSide);
631 Bitboard pawns = pos.pieces(PAWN, strongerSide);
633 // Are all pawns on the 'a' file?
634 if ((pawns & ~FileABB) == EmptyBoardBB)
636 // Does the defending king block the pawns?
637 if ( square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
638 || ( square_file(ksq) == FILE_A
639 && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB))
640 return SCALE_FACTOR_ZERO;
642 // Are all pawns on the 'h' file?
643 else if ((pawns & ~FileHBB) == EmptyBoardBB)
645 // Does the defending king block the pawns?
646 if ( square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
647 || ( square_file(ksq) == FILE_H
648 && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB))
649 return SCALE_FACTOR_ZERO;
651 return SCALE_FACTOR_NONE;
655 /// KBPKBScalingFunction scales KBP vs KB endgames. There are two rules:
656 /// If the defending king is somewhere along the path of the pawn, and the
657 /// square of the king is not of the same color as the stronger side's bishop,
658 /// it's a draw. If the two bishops have opposite color, it's almost always
661 ScaleFactor ScalingFunction<KBPKB>::apply(const Position& pos) const {
663 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
664 assert(pos.piece_count(strongerSide, BISHOP) == 1);
665 assert(pos.piece_count(strongerSide, PAWN) == 1);
666 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
667 assert(pos.piece_count(weakerSide, BISHOP) == 1);
668 assert(pos.piece_count(weakerSide, PAWN) == 0);
670 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
671 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP, 0);
672 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP, 0);
673 Square weakerKingSq = pos.king_square(weakerSide);
675 // Case 1: Defending king blocks the pawn, and cannot be driven away
676 if ( square_file(weakerKingSq) == square_file(pawnSq)
677 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
678 && ( !same_color_squares(weakerKingSq, strongerBishopSq)
679 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
680 return SCALE_FACTOR_ZERO;
682 // Case 2: Opposite colored bishops
683 if (!same_color_squares(strongerBishopSq, weakerBishopSq))
685 // We assume that the position is drawn in the following three situations:
687 // a. The pawn is on rank 5 or further back.
688 // b. The defending king is somewhere in the pawn's path.
689 // c. The defending bishop attacks some square along the pawn's path,
690 // and is at least three squares away from the pawn.
692 // These rules are probably not perfect, but in practice they work
695 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
696 return SCALE_FACTOR_ZERO;
699 Bitboard ray = ray_bb(pawnSq, (strongerSide == WHITE)? SIGNED_DIR_N : SIGNED_DIR_S);
700 if (ray & pos.pieces(KING, weakerSide))
701 return SCALE_FACTOR_ZERO;
703 if ( (pos.attacks_from<BISHOP>(weakerBishopSq) & ray)
704 && square_distance(weakerBishopSq, pawnSq) >= 3)
705 return SCALE_FACTOR_ZERO;
708 return SCALE_FACTOR_NONE;
712 /// KBPPKBScalingFunction scales KBPP vs KB endgames. It detects a few basic
713 /// draws with opposite-colored bishops.
715 ScaleFactor ScalingFunction<KBPPKB>::apply(const Position& pos) const {
717 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
718 assert(pos.piece_count(strongerSide, BISHOP) == 1);
719 assert(pos.piece_count(strongerSide, PAWN) == 2);
720 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
721 assert(pos.piece_count(weakerSide, BISHOP) == 1);
722 assert(pos.piece_count(weakerSide, PAWN) == 0);
724 Square wbsq = pos.piece_list(strongerSide, BISHOP, 0);
725 Square bbsq = pos.piece_list(weakerSide, BISHOP, 0);
727 if (same_color_squares(wbsq, bbsq))
728 // Not opposite-colored bishops, no scaling
729 return SCALE_FACTOR_NONE;
731 Square ksq = pos.king_square(weakerSide);
732 Square psq1 = pos.piece_list(strongerSide, PAWN, 0);
733 Square psq2 = pos.piece_list(strongerSide, PAWN, 1);
734 Rank r1 = square_rank(psq1);
735 Rank r2 = square_rank(psq2);
736 Square blockSq1, blockSq2;
738 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
740 blockSq1 = psq1 + pawn_push(strongerSide);
741 blockSq2 = make_square(square_file(psq2), square_rank(psq1));
745 blockSq1 = psq2 + pawn_push(strongerSide);
746 blockSq2 = make_square(square_file(psq1), square_rank(psq2));
749 switch (file_distance(psq1, psq2))
752 // Both pawns are on the same file. Easy draw if defender firmly controls
753 // some square in the frontmost pawn's path.
754 if ( square_file(ksq) == square_file(blockSq1)
755 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
756 && !same_color_squares(ksq, wbsq))
757 return SCALE_FACTOR_ZERO;
759 return SCALE_FACTOR_NONE;
762 // Pawns on neighboring files. Draw if defender firmly controls the square
763 // in front of the frontmost pawn's path, and the square diagonally behind
764 // this square on the file of the other pawn.
766 && !same_color_squares(ksq, wbsq)
767 && ( bbsq == blockSq2
768 || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(BISHOP, weakerSide))
769 || rank_distance(r1, r2) >= 2))
770 return SCALE_FACTOR_ZERO;
772 else if ( ksq == blockSq2
773 && !same_color_squares(ksq, wbsq)
774 && ( bbsq == blockSq1
775 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(BISHOP, weakerSide))))
776 return SCALE_FACTOR_ZERO;
778 return SCALE_FACTOR_NONE;
781 // The pawns are not on the same file or adjacent files. No scaling.
782 return SCALE_FACTOR_NONE;
787 /// KBPKNScalingFunction scales KBP vs KN endgames. There is a single rule:
788 /// If the defending king is somewhere along the path of the pawn, and the
789 /// square of the king is not of the same color as the stronger side's bishop,
792 ScaleFactor ScalingFunction<KBPKN>::apply(const Position& pos) const {
794 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
795 assert(pos.piece_count(strongerSide, BISHOP) == 1);
796 assert(pos.piece_count(strongerSide, PAWN) == 1);
797 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
798 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
799 assert(pos.piece_count(weakerSide, PAWN) == 0);
801 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
802 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP, 0);
803 Square weakerKingSq = pos.king_square(weakerSide);
805 if ( square_file(weakerKingSq) == square_file(pawnSq)
806 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
807 && ( !same_color_squares(weakerKingSq, strongerBishopSq)
808 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
809 return SCALE_FACTOR_ZERO;
811 return SCALE_FACTOR_NONE;
815 /// KNPKScalingFunction scales KNP vs K endgames. There is a single rule:
816 /// If the pawn is a rook pawn on the 7th rank and the defending king prevents
817 /// the pawn from advancing, the position is drawn.
819 ScaleFactor ScalingFunction<KNPK>::apply(const Position& pos) const {
821 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
822 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
823 assert(pos.piece_count(strongerSide, PAWN) == 1);
824 assert(pos.non_pawn_material(weakerSide) == Value(0));
825 assert(pos.piece_count(weakerSide, PAWN) == 0);
827 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
828 Square weakerKingSq = pos.king_square(weakerSide);
830 if ( pawnSq == relative_square(strongerSide, SQ_A7)
831 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
832 return SCALE_FACTOR_ZERO;
834 if ( pawnSq == relative_square(strongerSide, SQ_H7)
835 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
836 return SCALE_FACTOR_ZERO;
838 return SCALE_FACTOR_NONE;
842 /// KPKPScalingFunction scales KP vs KP endgames. This is done by removing
843 /// the weakest side's pawn and probing the KP vs K bitbase: If the weakest
844 /// side has a draw without the pawn, she probably has at least a draw with
845 /// the pawn as well. The exception is when the stronger side's pawn is far
846 /// advanced and not on a rook file; in this case it is often possible to win
847 /// (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
849 ScaleFactor ScalingFunction<KPKP>::apply(const Position& pos) const {
851 assert(pos.non_pawn_material(strongerSide) == Value(0));
852 assert(pos.non_pawn_material(weakerSide) == Value(0));
853 assert(pos.piece_count(WHITE, PAWN) == 1);
854 assert(pos.piece_count(BLACK, PAWN) == 1);
856 Square wksq, bksq, wpsq;
859 if (strongerSide == WHITE)
861 wksq = pos.king_square(WHITE);
862 bksq = pos.king_square(BLACK);
863 wpsq = pos.piece_list(WHITE, PAWN, 0);
864 stm = pos.side_to_move();
868 wksq = flip_square(pos.king_square(BLACK));
869 bksq = flip_square(pos.king_square(WHITE));
870 wpsq = flip_square(pos.piece_list(BLACK, PAWN, 0));
871 stm = opposite_color(pos.side_to_move());
874 if (square_file(wpsq) >= FILE_E)
876 wksq = flop_square(wksq);
877 bksq = flop_square(bksq);
878 wpsq = flop_square(wpsq);
881 // If the pawn has advanced to the fifth rank or further, and is not a
882 // rook pawn, it's too dangerous to assume that it's at least a draw.
883 if ( square_rank(wpsq) >= RANK_5
884 && square_file(wpsq) != FILE_A)
885 return SCALE_FACTOR_NONE;
887 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a
888 // draw, it's probably at least a draw even with the pawn.
889 return probe_kpk(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_ZERO;
895 // Probe the KP vs K bitbase
897 int probe_kpk(Square wksq, Square wpsq, Square bksq, Color stm) {
899 int wp = square_file(wpsq) + 4 * (square_rank(wpsq) - 1);
900 int index = int(stm) + 2 * bksq + 128 * wksq + 8192 * wp;
902 assert(index >= 0 && index < 24576 * 8);
904 return KPKBitbase[index / 8] & (1 << (index & 7));