2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2009 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/>.
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 // Bitbase for KP vs K
69 uint8_t KPKBitbase[24576];
71 // Penalty for big distance between king and knight for the defending king
72 // and knight in KR vs KN endgames.
73 const int KRKNKingKnightDistancePenalty[8] = { 0, 0, 4, 10, 20, 32, 48, 70 };
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 /// Mate with KX vs K. This function is used to evaluate positions with
103 /// King and plenty of material vs a lone king. It simply gives the
104 /// attacking side a bonus for driving the defending king towards the edge
105 /// of the board, and for keeping the distance between the two kings small.
107 Value EvaluationFunction<KXK>::apply(const Position& pos) {
109 assert(pos.non_pawn_material(weakerSide) == Value(0));
110 assert(pos.piece_count(weakerSide, PAWN) == Value(0));
112 Square winnerKSq = pos.king_square(strongerSide);
113 Square loserKSq = pos.king_square(weakerSide);
115 Value result = pos.non_pawn_material(strongerSide)
116 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
117 + mate_table(loserKSq)
118 + distance_bonus(square_distance(winnerKSq, loserKSq));
120 if ( pos.piece_count(strongerSide, QUEEN) > 0
121 || pos.piece_count(strongerSide, ROOK) > 0
122 || pos.piece_count(strongerSide, BISHOP) > 1)
123 // TODO: check for two equal-colored bishops!
124 result += VALUE_KNOWN_WIN;
126 return (strongerSide == pos.side_to_move() ? result : -result);
130 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
131 /// defending king towards a corner square of the right color.
133 Value EvaluationFunction<KBNK>::apply(const Position& pos) {
135 assert(pos.non_pawn_material(weakerSide) == Value(0));
136 assert(pos.piece_count(weakerSide, PAWN) == Value(0));
137 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
138 assert(pos.piece_count(strongerSide, BISHOP) == 1);
139 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
140 assert(pos.piece_count(strongerSide, PAWN) == 0);
142 Square winnerKSq = pos.king_square(strongerSide);
143 Square loserKSq = pos.king_square(weakerSide);
144 Square bishopSquare = pos.piece_list(strongerSide, BISHOP, 0);
146 if (square_color(bishopSquare) == BLACK)
148 winnerKSq = flop_square(winnerKSq);
149 loserKSq = flop_square(loserKSq);
152 Value result = VALUE_KNOWN_WIN
153 + distance_bonus(square_distance(winnerKSq, loserKSq))
154 + kbnk_mate_table(loserKSq);
156 return (strongerSide == pos.side_to_move() ? result : -result);
160 /// KP vs K. This endgame is evaluated with the help of a bitbase.
162 Value EvaluationFunction<KPK>::apply(const Position& pos) {
164 assert(pos.non_pawn_material(strongerSide) == Value(0));
165 assert(pos.non_pawn_material(weakerSide) == Value(0));
166 assert(pos.piece_count(strongerSide, PAWN) == 1);
167 assert(pos.piece_count(weakerSide, PAWN) == 0);
169 Square wksq, bksq, wpsq;
172 if (strongerSide == WHITE)
174 wksq = pos.king_square(WHITE);
175 bksq = pos.king_square(BLACK);
176 wpsq = pos.piece_list(WHITE, PAWN, 0);
177 stm = pos.side_to_move();
181 wksq = flip_square(pos.king_square(BLACK));
182 bksq = flip_square(pos.king_square(WHITE));
183 wpsq = flip_square(pos.piece_list(BLACK, PAWN, 0));
184 stm = opposite_color(pos.side_to_move());
187 if (square_file(wpsq) >= FILE_E)
189 wksq = flop_square(wksq);
190 bksq = flop_square(bksq);
191 wpsq = flop_square(wpsq);
194 if (!probe_kpk(wksq, wpsq, bksq, stm))
197 Value result = VALUE_KNOWN_WIN
199 + Value(square_rank(wpsq));
201 return (strongerSide == pos.side_to_move() ? result : -result);
205 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
206 /// a bitbase. The function below returns drawish scores when the pawn is
207 /// far advanced with support of the king, while the attacking king is far
210 Value EvaluationFunction<KRKP>::apply(const Position& pos) {
212 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
213 assert(pos.piece_count(strongerSide, PAWN) == 0);
214 assert(pos.non_pawn_material(weakerSide) == 0);
215 assert(pos.piece_count(weakerSide, PAWN) == 1);
217 Square wksq, wrsq, bksq, bpsq;
218 int tempo = (pos.side_to_move() == strongerSide);
220 wksq = pos.king_square(strongerSide);
221 wrsq = pos.piece_list(strongerSide, ROOK, 0);
222 bksq = pos.king_square(weakerSide);
223 bpsq = pos.piece_list(weakerSide, PAWN, 0);
225 if (strongerSide == BLACK)
227 wksq = flip_square(wksq);
228 wrsq = flip_square(wrsq);
229 bksq = flip_square(bksq);
230 bpsq = flip_square(bpsq);
233 Square queeningSq = make_square(square_file(bpsq), RANK_1);
236 // If the stronger side's king is in front of the pawn, it's a win
237 if (wksq < bpsq && square_file(wksq) == square_file(bpsq))
238 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
240 // If the weaker side's king is too far from the pawn and the rook,
242 else if ( square_distance(bksq, bpsq) - (tempo^1) >= 3
243 && square_distance(bksq, wrsq) >= 3)
244 result = RookValueEndgame - Value(square_distance(wksq, bpsq));
246 // If the pawn is far advanced and supported by the defending king,
247 // the position is drawish
248 else if ( square_rank(bksq) <= RANK_3
249 && square_distance(bksq, bpsq) == 1
250 && square_rank(wksq) >= RANK_4
251 && square_distance(wksq, bpsq) - tempo > 2)
252 result = Value(80 - square_distance(wksq, bpsq) * 8);
256 - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
257 + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
258 + Value(square_distance(bpsq, queeningSq) * 8);
260 return (strongerSide == pos.side_to_move() ? result : -result);
264 /// KR vs KB. This is very simple, and always returns drawish scores. The
265 /// score is slightly bigger when the defending king is close to the edge.
267 Value EvaluationFunction<KRKB>::apply(const Position& pos) {
269 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
270 assert(pos.piece_count(strongerSide, PAWN) == 0);
271 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
272 assert(pos.piece_count(weakerSide, PAWN) == 0);
273 assert(pos.piece_count(weakerSide, BISHOP) == 1);
275 Value result = mate_table(pos.king_square(weakerSide));
276 return (pos.side_to_move() == strongerSide ? result : -result);
280 /// KR vs KN. The attacking side has slightly better winning chances than
281 /// in KR vs KB, particularly if the king and the knight are far apart.
283 Value EvaluationFunction<KRKN>::apply(const Position& pos) {
285 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
286 assert(pos.piece_count(strongerSide, PAWN) == 0);
287 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
288 assert(pos.piece_count(weakerSide, PAWN) == 0);
289 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
291 Square defendingKSq = pos.king_square(weakerSide);
292 Square nSq = pos.piece_list(weakerSide, KNIGHT, 0);
294 Value result = Value(10) + mate_table(defendingKSq) +
295 krkn_king_knight_distance_penalty(square_distance(defendingKSq, nSq));
297 return (strongerSide == pos.side_to_move())? result : -result;
301 /// KQ vs KR. This is almost identical to KX vs K: We give the attacking
302 /// king a bonus for having the kings close together, and for forcing the
303 /// defending king towards the edge. If we also take care to avoid null move
304 /// for the defending side in the search, this is usually sufficient to be
305 /// able to win KQ vs KR.
307 Value EvaluationFunction<KQKR>::apply(const Position& pos) {
309 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
310 assert(pos.piece_count(strongerSide, PAWN) == 0);
311 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
312 assert(pos.piece_count(weakerSide, PAWN) == 0);
314 Square winnerKSq = pos.king_square(strongerSide);
315 Square loserKSq = pos.king_square(weakerSide);
317 Value result = QueenValueEndgame
319 + mate_table(loserKSq)
320 + distance_bonus(square_distance(winnerKSq, loserKSq));
322 return (strongerSide == pos.side_to_move())? result : -result;
326 Value EvaluationFunction<KBBKN>::apply(const Position& pos) {
328 assert(pos.piece_count(strongerSide, BISHOP) == 2);
329 assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
330 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
331 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
332 assert(pos.pawns() == EmptyBoardBB);
334 Value result = BishopValueEndgame;
335 Square wksq = pos.king_square(strongerSide);
336 Square bksq = pos.king_square(weakerSide);
337 Square nsq = pos.piece_list(weakerSide, KNIGHT, 0);
339 // Bonus for attacking king close to defending king
340 result += distance_bonus(square_distance(wksq, bksq));
342 // Bonus for driving the defending king and knight apart
343 result += Value(square_distance(bksq, nsq) * 32);
345 // Bonus for restricting the knight's mobility
346 result += Value((8 - count_1s_max_15(pos.piece_attacks<KNIGHT>(nsq))) * 8);
348 return (strongerSide == pos.side_to_move() ? result : -result);
352 /// K and two minors vs K and one or two minors or K and two knights against
353 /// king alone are always draw.
355 Value EvaluationFunction<KmmKm>::apply(const Position&) {
360 Value EvaluationFunction<KNNK>::apply(const Position&) {
364 /// KBPKScalingFunction scales endgames where the stronger side has king,
365 /// bishop and one or more pawns. It checks for draws with rook pawns and a
366 /// bishop of the wrong color. If such a draw is detected, ScaleFactor(0) is
367 /// returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
370 ScaleFactor ScalingFunction<KBPK>::apply(const Position& pos) {
372 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
373 assert(pos.piece_count(strongerSide, BISHOP) == 1);
374 assert(pos.piece_count(strongerSide, PAWN) >= 1);
376 // No assertions about the material of weakerSide, because we want draws to
377 // be detected even when the weaker side has some pawns.
379 Bitboard pawns = pos.pawns(strongerSide);
380 File pawnFile = square_file(pos.piece_list(strongerSide, PAWN, 0));
382 // All pawns are on a single rook file ?
383 if ( (pawnFile == FILE_A || pawnFile == FILE_H)
384 && (pawns & ~file_bb(pawnFile)) == EmptyBoardBB)
386 Square bishopSq = pos.piece_list(strongerSide, BISHOP, 0);
387 Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
388 Square kingSq = pos.king_square(weakerSide);
390 if ( square_color(queeningSq) != square_color(bishopSq)
391 && file_distance(square_file(kingSq), pawnFile) <= 1)
393 // The bishop has the wrong color, and the defending king is on the
394 // file of the pawn(s) or the neighboring file. Find the rank of the
398 if (strongerSide == WHITE)
400 for (rank = RANK_7; (rank_bb(rank) & pawns) == EmptyBoardBB; rank--) {}
401 assert(rank >= RANK_2 && rank <= RANK_7);
405 for(rank = RANK_2; (rank_bb(rank) & pawns) == EmptyBoardBB; rank++) {}
406 rank = Rank(rank^7); // HACK to get the relative rank
407 assert(rank >= RANK_2 && rank <= RANK_7);
409 // If the defending king has distance 1 to the promotion square or
410 // is placed somewhere in front of the pawn, it's a draw.
411 if ( square_distance(kingSq, queeningSq) <= 1
412 || relative_rank(strongerSide, kingSq) >= rank)
413 return ScaleFactor(0);
416 return SCALE_FACTOR_NONE;
420 /// KQKRPScalingFunction scales endgames where the stronger side has only
421 /// king and queen, while the weaker side has at least a rook and a pawn.
422 /// It tests for fortress draws with a rook on the third rank defended by
425 ScaleFactor ScalingFunction<KQKRP>::apply(const Position& pos) {
427 assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
428 assert(pos.piece_count(strongerSide, QUEEN) == 1);
429 assert(pos.piece_count(strongerSide, PAWN) == 0);
430 assert(pos.piece_count(weakerSide, ROOK) == 1);
431 assert(pos.piece_count(weakerSide, PAWN) >= 1);
433 Square kingSq = pos.king_square(weakerSide);
434 if ( relative_rank(weakerSide, kingSq) <= RANK_2
435 && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
436 && (pos.rooks(weakerSide) & relative_rank_bb(weakerSide, RANK_3))
437 && (pos.pawns(weakerSide) & relative_rank_bb(weakerSide, RANK_2))
438 && (pos.piece_attacks<KING>(kingSq) & pos.pawns(weakerSide)))
440 Square rsq = pos.piece_list(weakerSide, ROOK, 0);
441 if (pos.pawn_attacks(strongerSide, rsq) & pos.pawns(weakerSide))
442 return ScaleFactor(0);
444 return SCALE_FACTOR_NONE;
448 /// KRPKRScalingFunction scales KRP vs KR endgames. This function knows a
449 /// handful of the most important classes of drawn positions, but is far
450 /// from perfect. It would probably be a good idea to add more knowledge
453 /// It would also be nice to rewrite the actual code for this function,
454 /// which is mostly copied from Glaurung 1.x, and not very pretty.
456 ScaleFactor ScalingFunction<KRPKR>::apply(const Position &pos) {
458 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
459 assert(pos.piece_count(strongerSide, PAWN) == 1);
460 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
461 assert(pos.piece_count(weakerSide, PAWN) == 0);
463 Square wksq = pos.king_square(strongerSide);
464 Square wrsq = pos.piece_list(strongerSide, ROOK, 0);
465 Square wpsq = pos.piece_list(strongerSide, PAWN, 0);
466 Square bksq = pos.king_square(weakerSide);
467 Square brsq = pos.piece_list(weakerSide, ROOK, 0);
469 // Orient the board in such a way that the stronger side is white, and the
470 // pawn is on the left half of the board.
471 if (strongerSide == BLACK)
473 wksq = flip_square(wksq);
474 wrsq = flip_square(wrsq);
475 wpsq = flip_square(wpsq);
476 bksq = flip_square(bksq);
477 brsq = flip_square(brsq);
479 if (square_file(wpsq) > FILE_D)
481 wksq = flop_square(wksq);
482 wrsq = flop_square(wrsq);
483 wpsq = flop_square(wpsq);
484 bksq = flop_square(bksq);
485 brsq = flop_square(brsq);
488 File f = square_file(wpsq);
489 Rank r = square_rank(wpsq);
490 Square queeningSq = make_square(f, RANK_8);
491 int tempo = (pos.side_to_move() == strongerSide);
493 // If the pawn is not too far advanced and the defending king defends the
494 // queening square, use the third-rank defence.
496 && square_distance(bksq, queeningSq) <= 1
498 && (square_rank(brsq) == RANK_6 || (r <= RANK_3 && square_rank(wrsq) != RANK_6)))
499 return ScaleFactor(0);
501 // The defending side saves a draw by checking from behind in case the pawn
502 // has advanced to the 6th rank with the king behind.
504 && square_distance(bksq, queeningSq) <= 1
505 && square_rank(wksq) + tempo <= RANK_6
506 && (square_rank(brsq) == RANK_1 || (!tempo && abs(square_file(brsq) - f) >= 3)))
507 return ScaleFactor(0);
510 && bksq == queeningSq
511 && square_rank(brsq) == RANK_1
512 && (!tempo || square_distance(wksq, wpsq) >= 2))
513 return ScaleFactor(0);
515 // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
516 // and the black rook is behind the pawn.
519 && (bksq == SQ_H7 || bksq == SQ_G7)
520 && square_file(brsq) == FILE_A
521 && (square_rank(brsq) <= RANK_3 || square_file(wksq) >= FILE_D || square_rank(wksq) <= RANK_5))
522 return ScaleFactor(0);
524 // If the defending king blocks the pawn and the attacking king is too far
525 // away, it's a draw.
527 && bksq == wpsq + DELTA_N
528 && square_distance(wksq, wpsq) - tempo >= 2
529 && square_distance(wksq, brsq) - tempo >= 2)
530 return ScaleFactor(0);
532 // Pawn on the 7th rank supported by the rook from behind usually wins if the
533 // attacking king is closer to the queening square than the defending king,
534 // and the defending king cannot gain tempi by threatening the attacking rook.
537 && square_file(wrsq) == f
538 && wrsq != queeningSq
539 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
540 && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
541 return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
543 // Similar to the above, but with the pawn further back
545 && square_file(wrsq) == f
547 && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
548 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
549 && ( square_distance(bksq, wrsq) + tempo >= 3
550 || ( square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
551 && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
552 return ScaleFactor( SCALE_FACTOR_MAX
553 - (8 * square_distance(wpsq, queeningSq)
554 + 2 * square_distance(wksq, queeningSq)));
556 // If the pawn is not far advanced, and the defending king is somewhere in
557 // the pawn's path, it's probably a draw.
558 if (r <= RANK_4 && bksq > wpsq)
560 if (square_file(bksq) == square_file(wpsq))
561 return ScaleFactor(10);
562 if ( abs(square_file(bksq) - square_file(wpsq)) == 1
563 && square_distance(wksq, bksq) > 2)
564 return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
566 return SCALE_FACTOR_NONE;
570 /// KRPPKRPScalingFunction scales KRPP vs KRP endgames. There is only a
571 /// single pattern: If the stronger side has no pawns and the defending king
572 /// is actively placed, the position is drawish.
574 ScaleFactor ScalingFunction<KRPPKRP>::apply(const Position &pos) {
576 assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
577 assert(pos.piece_count(strongerSide, PAWN) == 2);
578 assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
579 assert(pos.piece_count(weakerSide, PAWN) == 1);
581 Square wpsq1 = pos.piece_list(strongerSide, PAWN, 0);
582 Square wpsq2 = pos.piece_list(strongerSide, PAWN, 1);
583 Square bksq = pos.king_square(weakerSide);
585 // Does the stronger side have a passed pawn?
586 if ( pos.pawn_is_passed(strongerSide, wpsq1)
587 || pos.pawn_is_passed(strongerSide, wpsq2))
588 return SCALE_FACTOR_NONE;
590 Rank r = Max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
592 if ( file_distance(bksq, wpsq1) <= 1
593 && file_distance(bksq, wpsq2) <= 1
594 && relative_rank(strongerSide, bksq) > r)
597 case RANK_2: return ScaleFactor(10);
598 case RANK_3: return ScaleFactor(10);
599 case RANK_4: return ScaleFactor(15);
600 case RANK_5: return ScaleFactor(20);
601 case RANK_6: return ScaleFactor(40);
602 default: assert(false);
605 return SCALE_FACTOR_NONE;
609 /// KPsKScalingFunction scales endgames with king and two or more pawns
610 /// against king. There is just a single rule here: If all pawns are on
611 /// the same rook file and are blocked by the defending king, it's a draw.
613 ScaleFactor ScalingFunction<KPsK>::apply(const Position &pos) {
615 assert(pos.non_pawn_material(strongerSide) == Value(0));
616 assert(pos.piece_count(strongerSide, PAWN) >= 2);
617 assert(pos.non_pawn_material(weakerSide) == Value(0));
618 assert(pos.piece_count(weakerSide, PAWN) == 0);
620 Bitboard pawns = pos.pawns(strongerSide);
622 // Are all pawns on the 'a' file?
623 if ((pawns & ~FileABB) == EmptyBoardBB)
625 // Does the defending king block the pawns?
626 Square ksq = pos.king_square(weakerSide);
627 if (square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1)
628 return ScaleFactor(0);
629 else if( square_file(ksq) == FILE_A
630 && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB)
631 return ScaleFactor(0);
633 return SCALE_FACTOR_NONE;
635 // Are all pawns on the 'h' file?
636 else if ((pawns & ~FileHBB) == EmptyBoardBB)
638 // Does the defending king block the pawns?
639 Square ksq = pos.king_square(weakerSide);
640 if (square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1)
641 return ScaleFactor(0);
642 else if ( square_file(ksq) == FILE_H
643 && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB)
644 return ScaleFactor(0);
646 return SCALE_FACTOR_NONE;
649 return SCALE_FACTOR_NONE;
653 /// KBPKBScalingFunction scales KBP vs KB endgames. There are two rules:
654 /// If the defending king is somewhere along the path of the pawn, and the
655 /// square of the king is not of the same color as the stronger side's bishop,
656 /// it's a draw. If the two bishops have opposite color, it's almost always
659 ScaleFactor ScalingFunction<KBPKB>::apply(const Position &pos) {
661 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
662 assert(pos.piece_count(strongerSide, BISHOP) == 1);
663 assert(pos.piece_count(strongerSide, PAWN) == 1);
664 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
665 assert(pos.piece_count(weakerSide, BISHOP) == 1);
666 assert(pos.piece_count(weakerSide, PAWN) == 0);
668 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
669 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP, 0);
670 Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP, 0);
671 Square weakerKingSq = pos.king_square(weakerSide);
673 // Case 1: Defending king blocks the pawn, and cannot be driven away
674 if ( square_file(weakerKingSq) == square_file(pawnSq)
675 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
676 && ( square_color(weakerKingSq) != square_color(strongerBishopSq)
677 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
678 return ScaleFactor(0);
680 // Case 2: Opposite colored bishops
681 if (square_color(strongerBishopSq) != square_color(weakerBishopSq))
683 // We assume that the position is drawn in the following three situations:
685 // a. The pawn is on rank 5 or further back.
686 // b. The defending king is somewhere in the pawn's path.
687 // c. The defending bishop attacks some square along the pawn's path,
688 // and is at least three squares away from the pawn.
690 // These rules are probably not perfect, but in practice they work
693 if (relative_rank(strongerSide, pawnSq) <= RANK_5)
694 return ScaleFactor(0);
697 Bitboard ray = ray_bb(pawnSq, (strongerSide == WHITE)? SIGNED_DIR_N : SIGNED_DIR_S);
698 if (ray & pos.kings(weakerSide))
699 return ScaleFactor(0);
700 if( (pos.piece_attacks<BISHOP>(weakerBishopSq) & ray)
701 && square_distance(weakerBishopSq, pawnSq) >= 3)
702 return ScaleFactor(0);
705 return SCALE_FACTOR_NONE;
709 /// KBPPKBScalingFunction scales KBPP vs KB endgames. It detects a few basic
710 /// draws with opposite-colored bishops.
712 ScaleFactor ScalingFunction<KBPPKB>::apply(const Position& pos) {
714 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
715 assert(pos.piece_count(strongerSide, BISHOP) == 1);
716 assert(pos.piece_count(strongerSide, PAWN) == 2);
717 assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
718 assert(pos.piece_count(weakerSide, BISHOP) == 1);
719 assert(pos.piece_count(weakerSide, PAWN) == 0);
721 Square wbsq = pos.piece_list(strongerSide, BISHOP, 0);
722 Square bbsq = pos.piece_list(weakerSide, BISHOP, 0);
724 if (square_color(wbsq) == square_color(bbsq))
725 // Not opposite-colored bishops, no scaling
726 return SCALE_FACTOR_NONE;
728 Square ksq = pos.king_square(weakerSide);
729 Square psq1 = pos.piece_list(strongerSide, PAWN, 0);
730 Square psq2 = pos.piece_list(strongerSide, PAWN, 1);
731 Rank r1 = square_rank(psq1);
732 Rank r2 = square_rank(psq2);
733 Square blockSq1, blockSq2;
735 if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
737 blockSq1 = psq1 + pawn_push(strongerSide);
738 blockSq2 = make_square(square_file(psq2), square_rank(psq1));
742 blockSq1 = psq2 + pawn_push(strongerSide);
743 blockSq2 = make_square(square_file(psq1), square_rank(psq2));
746 switch (file_distance(psq1, psq2))
749 // Both pawns are on the same file. Easy draw if defender firmly controls
750 // some square in the frontmost pawn's path.
751 if ( square_file(ksq) == square_file(blockSq1)
752 && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
753 && square_color(ksq) != square_color(wbsq))
754 return ScaleFactor(0);
756 return SCALE_FACTOR_NONE;
759 // Pawns on neighboring files. Draw if defender firmly controls the square
760 // in front of the frontmost pawn's path, and the square diagonally behind
761 // this square on the file of the other pawn.
763 && square_color(ksq) != square_color(wbsq)
764 && ( bbsq == blockSq2
765 || (pos.piece_attacks<BISHOP>(blockSq2) & pos.bishops(weakerSide))
766 || rank_distance(r1, r2) >= 2))
767 return ScaleFactor(0);
768 else if ( ksq == blockSq2
769 && square_color(ksq) != square_color(wbsq)
770 && ( bbsq == blockSq1
771 || (pos.piece_attacks<BISHOP>(blockSq1) & pos.bishops(weakerSide))))
772 return ScaleFactor(0);
774 return SCALE_FACTOR_NONE;
777 // The pawns are not on the same file or adjacent files. No scaling.
778 return SCALE_FACTOR_NONE;
783 /// KBPKNScalingFunction scales KBP vs KN endgames. There is a single rule:
784 /// If the defending king is somewhere along the path of the pawn, and the
785 /// square of the king is not of the same color as the stronger side's bishop,
788 ScaleFactor ScalingFunction<KBPKN>::apply(const Position &pos) {
790 assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
791 assert(pos.piece_count(strongerSide, BISHOP) == 1);
792 assert(pos.piece_count(strongerSide, PAWN) == 1);
793 assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
794 assert(pos.piece_count(weakerSide, KNIGHT) == 1);
795 assert(pos.piece_count(weakerSide, PAWN) == 0);
797 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
798 Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP, 0);
799 Square weakerKingSq = pos.king_square(weakerSide);
801 if ( square_file(weakerKingSq) == square_file(pawnSq)
802 && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
803 && ( square_color(weakerKingSq) != square_color(strongerBishopSq)
804 || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
805 return ScaleFactor(0);
807 return SCALE_FACTOR_NONE;
811 /// KNPKScalingFunction scales KNP vs K endgames. There is a single rule:
812 /// If the pawn is a rook pawn on the 7th rank and the defending king prevents
813 /// the pawn from advancing, the position is drawn.
815 ScaleFactor ScalingFunction<KNPK>::apply(const Position &pos) {
817 assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
818 assert(pos.piece_count(strongerSide, KNIGHT) == 1);
819 assert(pos.piece_count(strongerSide, PAWN) == 1);
820 assert(pos.non_pawn_material(weakerSide) == Value(0));
821 assert(pos.piece_count(weakerSide, PAWN) == 0);
823 Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
824 Square weakerKingSq = pos.king_square(weakerSide);
826 if ( pawnSq == relative_square(strongerSide, SQ_A7)
827 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
828 return ScaleFactor(0);
830 if ( pawnSq == relative_square(strongerSide, SQ_H7)
831 && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
832 return ScaleFactor(0);
834 return SCALE_FACTOR_NONE;
838 /// KPKPScalingFunction scales KP vs KP endgames. This is done by removing
839 /// the weakest side's pawn and probing the KP vs K bitbase: If the weakest
840 /// side has a draw without the pawn, she probably has at least a draw with
841 /// the pawn as well. The exception is when the stronger side's pawn is far
842 /// advanced and not on a rook file; in this case it is often possible to win
843 /// (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
845 ScaleFactor ScalingFunction<KPKP>::apply(const Position &pos) {
847 assert(pos.non_pawn_material(strongerSide) == Value(0));
848 assert(pos.non_pawn_material(weakerSide) == Value(0));
849 assert(pos.piece_count(WHITE, PAWN) == 1);
850 assert(pos.piece_count(BLACK, PAWN) == 1);
852 Square wksq, bksq, wpsq;
855 if (strongerSide == WHITE)
857 wksq = pos.king_square(WHITE);
858 bksq = pos.king_square(BLACK);
859 wpsq = pos.piece_list(WHITE, PAWN, 0);
860 stm = pos.side_to_move();
864 wksq = flip_square(pos.king_square(BLACK));
865 bksq = flip_square(pos.king_square(WHITE));
866 wpsq = flip_square(pos.piece_list(BLACK, PAWN, 0));
867 stm = opposite_color(pos.side_to_move());
870 if (square_file(wpsq) >= FILE_E)
872 wksq = flop_square(wksq);
873 bksq = flop_square(bksq);
874 wpsq = flop_square(wpsq);
877 // If the pawn has advanced to the fifth rank or further, and is not a
878 // rook pawn, it's too dangerous to assume that it's at least a draw.
879 if ( square_rank(wpsq) >= RANK_5
880 && square_file(wpsq) != FILE_A)
881 return SCALE_FACTOR_NONE;
883 // Probe the KPK bitbase with the weakest side's pawn removed. If it's a
884 // draw, it's probably at least a draw even with the pawn.
885 if (probe_kpk(wksq, wpsq, bksq, stm))
886 return SCALE_FACTOR_NONE;
888 return ScaleFactor(0);
892 /// init_bitbases() is called during program initialization, and simply loads
893 /// bitbases from disk into memory. At the moment, there is only the bitbase
894 /// for KP vs K, but we may decide to add other bitbases later.
896 void init_bitbases() {
897 generate_kpk_bitbase(KPKBitbase);
903 // Probe the KP vs K bitbase:
905 int probe_kpk(Square wksq, Square wpsq, Square bksq, Color stm) {
907 int wp = int(square_file(wpsq)) + (int(square_rank(wpsq)) - 1) * 4;
908 int index = int(stm) + 2*int(bksq) + 128*int(wksq) + 8192*wp;
910 assert(index >= 0 && index < 24576*8);
911 return KPKBitbase[index/8] & (1 << (index&7));