2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
4 Copyright (C) 2008-2013 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/>.
30 #include "ucioption.h"
34 enum ExtendedPieceType { // Used for tracing
35 PST = 8, IMBALANCE, MOBILITY, THREAT, PASSED, UNSTOPPABLE, SPACE, TOTAL
40 Score scores[COLOR_NB][TOTAL + 1];
41 std::stringstream stream;
43 void add(int idx, Score term_w, Score term_b = SCORE_ZERO);
44 void row(const char* name, int idx);
45 std::string do_trace(const Position& pos);
48 // Struct EvalInfo contains various information computed and collected
49 // by the evaluation functions.
52 // Pointers to material and pawn hash table entries
56 // attackedBy[color][piece type] is a bitboard representing all squares
57 // attacked by a given color and piece type, attackedBy[color][ALL_PIECES]
58 // contains all squares attacked by the given color.
59 Bitboard attackedBy[COLOR_NB][PIECE_TYPE_NB];
61 // kingRing[color] is the zone around the king which is considered
62 // by the king safety evaluation. This consists of the squares directly
63 // adjacent to the king, and the three (or two, for a king on an edge file)
64 // squares two ranks in front of the king. For instance, if black's king
65 // is on g8, kingRing[BLACK] is a bitboard containing the squares f8, h8,
66 // f7, g7, h7, f6, g6 and h6.
67 Bitboard kingRing[COLOR_NB];
69 // kingAttackersCount[color] is the number of pieces of the given color
70 // which attack a square in the kingRing of the enemy king.
71 int kingAttackersCount[COLOR_NB];
73 // kingAttackersWeight[color] is the sum of the "weight" of the pieces of the
74 // given color which attack a square in the kingRing of the enemy king. The
75 // weights of the individual piece types are given by the variables
76 // QueenAttackWeight, RookAttackWeight, BishopAttackWeight and
77 // KnightAttackWeight in evaluate.cpp
78 int kingAttackersWeight[COLOR_NB];
80 // kingAdjacentZoneAttacksCount[color] is the number of attacks to squares
81 // directly adjacent to the king of the given color. Pieces which attack
82 // more than one square are counted multiple times. For instance, if black's
83 // king is on g8 and there's a white knight on g5, this knight adds
84 // 2 to kingAdjacentZoneAttacksCount[BLACK].
85 int kingAdjacentZoneAttacksCount[COLOR_NB];
88 // Evaluation grain size, must be a power of 2
89 const int GrainSize = 4;
91 // Evaluation weights, initialized from UCI options
92 enum { Mobility, PawnStructure, PassedPawns, Space, KingDangerUs, KingDangerThem };
96 #define S(mg, eg) make_score(mg, eg)
98 // Internal evaluation weights. These are applied on top of the evaluation
99 // weights read from UCI parameters. The purpose is to be able to change
100 // the evaluation weights while keeping the default values of the UCI
101 // parameters at 100, which looks prettier.
103 // Values modified by Joona Kiiski
104 const Score WeightsInternal[] = {
105 S(289, 344), S(233, 201), S(221, 273), S(46, 0), S(271, 0), S(307, 0)
108 // MobilityBonus[PieceType][attacked] contains bonuses for middle and end
109 // game, indexed by piece type and number of attacked squares not occupied by
111 const Score MobilityBonus[][32] = {
113 { S(-35,-30), S(-22,-20), S(-9,-10), S( 3, 0), S(15, 10), S(27, 20), // Knights
114 S( 37, 28), S( 42, 31), S(44, 33) },
115 { S(-22,-27), S( -8,-13), S( 6, 1), S(20, 15), S(34, 29), S(48, 43), // Bishops
116 S( 60, 55), S( 68, 63), S(74, 68), S(77, 72), S(80, 75), S(82, 77),
117 S( 84, 79), S( 86, 81), S(87, 82), S(87, 82) },
118 { S(-17,-33), S(-11,-16), S(-5, 0), S( 1, 16), S( 7, 32), S(13, 48), // Rooks
119 S( 18, 64), S( 22, 80), S(26, 96), S(29,109), S(31,115), S(33,119),
120 S( 35,122), S( 36,123), S(37,124), S(38,124) },
121 { S(-12,-20), S( -8,-13), S(-5, -7), S(-2, -1), S( 1, 5), S( 4, 11), // Queens
122 S( 7, 17), S( 10, 23), S(13, 29), S(16, 34), S(18, 38), S(20, 40),
123 S( 22, 41), S( 23, 41), S(24, 41), S(25, 41), S(25, 41), S(25, 41),
124 S( 25, 41), S( 25, 41), S(25, 41), S(25, 41), S(25, 41), S(25, 41),
125 S( 25, 41), S( 25, 41), S(25, 41), S(25, 41), S(25, 41), S(25, 41),
126 S( 25, 41), S( 25, 41) }
129 // Outpost[PieceType][Square] contains bonuses of knights and bishops, indexed
130 // by piece type and square (from white's point of view).
131 const Value Outpost[][SQUARE_NB] = {
134 V(0), V(0), V(0), V(0), V(0), V(0), V(0), V(0), // Knights
135 V(0), V(0), V(0), V(0), V(0), V(0), V(0), V(0),
136 V(0), V(0), V(4), V(8), V(8), V(4), V(0), V(0),
137 V(0), V(4),V(17),V(26),V(26),V(17), V(4), V(0),
138 V(0), V(8),V(26),V(35),V(35),V(26), V(8), V(0),
139 V(0), V(4),V(17),V(17),V(17),V(17), V(4), V(0) },
141 V(0), V(0), V(0), V(0), V(0), V(0), V(0), V(0), // Bishops
142 V(0), V(0), V(0), V(0), V(0), V(0), V(0), V(0),
143 V(0), V(0), V(5), V(5), V(5), V(5), V(0), V(0),
144 V(0), V(5),V(10),V(10),V(10),V(10), V(5), V(0),
145 V(0),V(10),V(21),V(21),V(21),V(21),V(10), V(0),
146 V(0), V(5), V(8), V(8), V(8), V(8), V(5), V(0) }
149 // Threat[attacking][attacked] contains bonuses according to which piece
150 // type attacks which one.
151 const Score Threat[][PIECE_TYPE_NB] = {
153 { S(0, 0), S( 7, 39), S( 0, 0), S(24, 49), S(41,100), S(41,100) }, // KNIGHT
154 { S(0, 0), S( 7, 39), S(24, 49), S( 0, 0), S(41,100), S(41,100) }, // BISHOP
155 { S(0, 0), S( 0, 22), S(15, 49), S(15, 49), S( 0, 0), S(24, 49) }, // ROOK
156 { S(0, 0), S(15, 39), S(15, 39), S(15, 39), S(15, 39), S( 0, 0) } // QUEEN
159 // ThreatenedByPawn[PieceType] contains a penalty according to which piece
160 // type is attacked by an enemy pawn.
161 const Score ThreatenedByPawn[] = {
162 S(0, 0), S(0, 0), S(56, 70), S(56, 70), S(76, 99), S(86, 118)
167 const Score Tempo = make_score(24, 11);
168 const Score BishopPin = make_score(66, 11);
169 const Score RookOn7th = make_score(11, 20);
170 const Score QueenOn7th = make_score( 3, 8);
171 const Score RookOnPawn = make_score(10, 28);
172 const Score QueenOnPawn = make_score( 4, 20);
173 const Score RookOpenFile = make_score(43, 21);
174 const Score RookSemiopenFile = make_score(19, 10);
175 const Score BishopPawns = make_score( 8, 12);
176 const Score MinorBehindPawn = make_score(16, 0);
177 const Score UndefendedMinor = make_score(25, 10);
178 const Score TrappedRook = make_score(90, 0);
180 // Penalty for a bishop on a1/h1 (a8/h8 for black) which is trapped by
181 // a friendly pawn on b2/g2 (b7/g7 for black). This can obviously only
182 // happen in Chess960 games.
183 const Score TrappedBishopA1H1 = make_score(50, 50);
185 // The SpaceMask[Color] contains the area of the board which is considered
186 // by the space evaluation. In the middle game, each side is given a bonus
187 // based on how many squares inside this area are safe and available for
188 // friendly minor pieces.
189 const Bitboard SpaceMask[] = {
190 (1ULL << SQ_C2) | (1ULL << SQ_D2) | (1ULL << SQ_E2) | (1ULL << SQ_F2) |
191 (1ULL << SQ_C3) | (1ULL << SQ_D3) | (1ULL << SQ_E3) | (1ULL << SQ_F3) |
192 (1ULL << SQ_C4) | (1ULL << SQ_D4) | (1ULL << SQ_E4) | (1ULL << SQ_F4),
193 (1ULL << SQ_C7) | (1ULL << SQ_D7) | (1ULL << SQ_E7) | (1ULL << SQ_F7) |
194 (1ULL << SQ_C6) | (1ULL << SQ_D6) | (1ULL << SQ_E6) | (1ULL << SQ_F6) |
195 (1ULL << SQ_C5) | (1ULL << SQ_D5) | (1ULL << SQ_E5) | (1ULL << SQ_F5)
198 // King danger constants and variables. The king danger scores are taken
199 // from the KingDanger[]. Various little "meta-bonuses" measuring
200 // the strength of the enemy attack are added up into an integer, which
201 // is used as an index to KingDanger[].
203 // KingAttackWeights[PieceType] contains king attack weights by piece type
204 const int KingAttackWeights[] = { 0, 0, 2, 2, 3, 5 };
206 // Bonuses for enemy's safe checks
207 const int QueenContactCheck = 6;
208 const int RookContactCheck = 4;
209 const int QueenCheck = 3;
210 const int RookCheck = 2;
211 const int BishopCheck = 1;
212 const int KnightCheck = 1;
214 // KingExposed[Square] contains penalties based on the position of the
215 // defending king, indexed by king's square (from white's point of view).
216 const int KingExposed[] = {
217 2, 0, 2, 5, 5, 2, 0, 2,
218 2, 2, 4, 8, 8, 4, 2, 2,
219 7, 10, 12, 12, 12, 12, 10, 7,
220 15, 15, 15, 15, 15, 15, 15, 15,
221 15, 15, 15, 15, 15, 15, 15, 15,
222 15, 15, 15, 15, 15, 15, 15, 15,
223 15, 15, 15, 15, 15, 15, 15, 15,
224 15, 15, 15, 15, 15, 15, 15, 15
227 // KingDanger[Color][attackUnits] contains the actual king danger weighted
228 // scores, indexed by color and by a calculated integer number.
229 Score KingDanger[COLOR_NB][128];
231 // Function prototypes
233 Value do_evaluate(const Position& pos, Value& margin);
236 void init_eval_info(const Position& pos, EvalInfo& ei);
238 template<Color Us, bool Trace>
239 Score evaluate_pieces_of_color(const Position& pos, EvalInfo& ei, Score& mobility);
241 template<Color Us, bool Trace>
242 Score evaluate_king(const Position& pos, const EvalInfo& ei, Value margins[]);
244 template<Color Us, bool Trace>
245 Score evaluate_threats(const Position& pos, const EvalInfo& ei);
247 template<Color Us, bool Trace>
248 Score evaluate_passed_pawns(const Position& pos, const EvalInfo& ei);
251 int evaluate_space(const Position& pos, const EvalInfo& ei);
253 Score evaluate_unstoppable_pawns(const Position& pos, const EvalInfo& ei);
255 Value interpolate(const Score& v, Phase ph, ScaleFactor sf);
256 Score apply_weight(Score v, Score w);
257 Score weight_option(const std::string& mgOpt, const std::string& egOpt, Score internalWeight);
258 double to_cp(Value v);
264 /// evaluate() is the main evaluation function. It always computes two
265 /// values, an endgame score and a middle game score, and interpolates
266 /// between them based on the remaining material.
268 Value evaluate(const Position& pos, Value& margin) {
269 return do_evaluate<false>(pos, margin);
273 /// trace() is like evaluate() but instead of a value returns a string suitable
274 /// to be print on stdout with the detailed descriptions and values of each
275 /// evaluation term. Used mainly for debugging.
276 std::string trace(const Position& pos) {
277 return Tracing::do_trace(pos);
281 /// init() computes evaluation weights from the corresponding UCI parameters
282 /// and setup king tables.
286 Weights[Mobility] = weight_option("Mobility (Midgame)", "Mobility (Endgame)", WeightsInternal[Mobility]);
287 Weights[PawnStructure] = weight_option("Pawn Structure (Midgame)", "Pawn Structure (Endgame)", WeightsInternal[PawnStructure]);
288 Weights[PassedPawns] = weight_option("Passed Pawns (Midgame)", "Passed Pawns (Endgame)", WeightsInternal[PassedPawns]);
289 Weights[Space] = weight_option("Space", "Space", WeightsInternal[Space]);
290 Weights[KingDangerUs] = weight_option("Cowardice", "Cowardice", WeightsInternal[KingDangerUs]);
291 Weights[KingDangerThem] = weight_option("Aggressiveness", "Aggressiveness", WeightsInternal[KingDangerThem]);
293 const int MaxSlope = 30;
294 const int Peak = 1280;
296 for (int t = 0, i = 1; i < 100; i++)
298 t = std::min(Peak, std::min(int(0.4 * i * i), t + MaxSlope));
300 KingDanger[1][i] = apply_weight(make_score(t, 0), Weights[KingDangerUs]);
301 KingDanger[0][i] = apply_weight(make_score(t, 0), Weights[KingDangerThem]);
311 Value do_evaluate(const Position& pos, Value& margin) {
313 assert(!pos.checkers());
316 Value margins[COLOR_NB];
317 Score score, mobilityWhite, mobilityBlack;
318 Thread* th = pos.this_thread();
320 // margins[] store the uncertainty estimation of position's evaluation
321 // that typically is used by the search for pruning decisions.
322 margins[WHITE] = margins[BLACK] = VALUE_ZERO;
324 // Initialize score by reading the incrementally updated scores included
325 // in the position object (material + piece square tables) and adding
326 // Tempo bonus. Score is computed from the point of view of white.
327 score = pos.psq_score() + (pos.side_to_move() == WHITE ? Tempo : -Tempo);
329 // Probe the material hash table
330 ei.mi = Material::probe(pos, th->materialTable, th->endgames);
331 score += ei.mi->material_value();
333 // If we have a specialized evaluation function for the current material
334 // configuration, call it and return.
335 if (ei.mi->specialized_eval_exists())
338 return ei.mi->evaluate(pos);
341 // Probe the pawn hash table
342 ei.pi = Pawns::probe(pos, th->pawnsTable);
343 score += apply_weight(ei.pi->pawns_value(), Weights[PawnStructure]);
345 // Initialize attack and king safety bitboards
346 init_eval_info<WHITE>(pos, ei);
347 init_eval_info<BLACK>(pos, ei);
349 // Evaluate pieces and mobility
350 score += evaluate_pieces_of_color<WHITE, Trace>(pos, ei, mobilityWhite)
351 - evaluate_pieces_of_color<BLACK, Trace>(pos, ei, mobilityBlack);
353 score += apply_weight(mobilityWhite - mobilityBlack, Weights[Mobility]);
355 // Evaluate kings after all other pieces because we need complete attack
356 // information when computing the king safety evaluation.
357 score += evaluate_king<WHITE, Trace>(pos, ei, margins)
358 - evaluate_king<BLACK, Trace>(pos, ei, margins);
360 // Evaluate tactical threats, we need full attack information including king
361 score += evaluate_threats<WHITE, Trace>(pos, ei)
362 - evaluate_threats<BLACK, Trace>(pos, ei);
364 // Evaluate passed pawns, we need full attack information including king
365 score += evaluate_passed_pawns<WHITE, Trace>(pos, ei)
366 - evaluate_passed_pawns<BLACK, Trace>(pos, ei);
368 // If one side has only a king, check whether exists any unstoppable passed pawn
369 if (!pos.non_pawn_material(WHITE) || !pos.non_pawn_material(BLACK))
370 score += evaluate_unstoppable_pawns(pos, ei);
372 // Evaluate space for both sides, only in middle-game.
373 if (ei.mi->space_weight())
375 int s = evaluate_space<WHITE>(pos, ei) - evaluate_space<BLACK>(pos, ei);
376 score += apply_weight(s * ei.mi->space_weight(), Weights[Space]);
379 // Scale winning side if position is more drawish that what it appears
380 ScaleFactor sf = eg_value(score) > VALUE_DRAW ? ei.mi->scale_factor(pos, WHITE)
381 : ei.mi->scale_factor(pos, BLACK);
383 // If we don't already have an unusual scale factor, check for opposite
384 // colored bishop endgames, and use a lower scale for those.
385 if ( ei.mi->game_phase() < PHASE_MIDGAME
386 && pos.opposite_bishops()
387 && sf == SCALE_FACTOR_NORMAL)
389 // Only the two bishops ?
390 if ( pos.non_pawn_material(WHITE) == BishopValueMg
391 && pos.non_pawn_material(BLACK) == BishopValueMg)
393 // Check for KBP vs KB with only a single pawn that is almost
394 // certainly a draw or at least two pawns.
395 bool one_pawn = (pos.count<PAWN>(WHITE) + pos.count<PAWN>(BLACK) == 1);
396 sf = one_pawn ? ScaleFactor(8) : ScaleFactor(32);
399 // Endgame with opposite-colored bishops, but also other pieces. Still
400 // a bit drawish, but not as drawish as with only the two bishops.
401 sf = ScaleFactor(50);
404 margin = margins[pos.side_to_move()];
405 Value v = interpolate(score, ei.mi->game_phase(), sf);
407 // In case of tracing add all single evaluation contributions for both white and black
410 Tracing::add(PST, pos.psq_score());
411 Tracing::add(IMBALANCE, ei.mi->material_value());
412 Tracing::add(PAWN, ei.pi->pawns_value());
413 Tracing::add(UNSTOPPABLE, evaluate_unstoppable_pawns(pos, ei));
414 Score w = ei.mi->space_weight() * evaluate_space<WHITE>(pos, ei);
415 Score b = ei.mi->space_weight() * evaluate_space<BLACK>(pos, ei);
416 Tracing::add(SPACE, apply_weight(w, Weights[Space]), apply_weight(b, Weights[Space]));
417 Tracing::add(TOTAL, score);
418 Tracing::stream << "\nUncertainty margin: White: " << to_cp(margins[WHITE])
419 << ", Black: " << to_cp(margins[BLACK])
420 << "\nScaling: " << std::noshowpos
421 << std::setw(6) << 100.0 * ei.mi->game_phase() / 128.0 << "% MG, "
422 << std::setw(6) << 100.0 * (1.0 - ei.mi->game_phase() / 128.0) << "% * "
423 << std::setw(6) << (100.0 * sf) / SCALE_FACTOR_NORMAL << "% EG.\n"
424 << "Total evaluation: " << to_cp(v);
427 return pos.side_to_move() == WHITE ? v : -v;
431 // init_eval_info() initializes king bitboards for given color adding
432 // pawn attacks. To be done at the beginning of the evaluation.
435 void init_eval_info(const Position& pos, EvalInfo& ei) {
437 const Color Them = (Us == WHITE ? BLACK : WHITE);
438 const Square Down = (Us == WHITE ? DELTA_S : DELTA_N);
440 Bitboard b = ei.attackedBy[Them][KING] = pos.attacks_from<KING>(pos.king_square(Them));
441 ei.attackedBy[Us][PAWN] = ei.pi->pawn_attacks(Us);
443 // Init king safety tables only if we are going to use them
444 if (pos.count<QUEEN>(Us) && pos.non_pawn_material(Us) > QueenValueMg + PawnValueMg)
446 ei.kingRing[Them] = b | shift_bb<Down>(b);
447 b &= ei.attackedBy[Us][PAWN];
448 ei.kingAttackersCount[Us] = b ? popcount<Max15>(b) / 2 : 0;
449 ei.kingAdjacentZoneAttacksCount[Us] = ei.kingAttackersWeight[Us] = 0;
451 ei.kingRing[Them] = ei.kingAttackersCount[Us] = 0;
455 // evaluate_outposts() evaluates bishop and knight outposts squares
457 template<PieceType Piece, Color Us>
458 Score evaluate_outposts(const Position& pos, EvalInfo& ei, Square s) {
460 const Color Them = (Us == WHITE ? BLACK : WHITE);
462 assert (Piece == BISHOP || Piece == KNIGHT);
464 // Initial bonus based on square
465 Value bonus = Outpost[Piece == BISHOP][relative_square(Us, s)];
467 // Increase bonus if supported by pawn, especially if the opponent has
468 // no minor piece which can exchange the outpost piece.
469 if (bonus && (ei.attackedBy[Us][PAWN] & s))
471 if ( !pos.pieces(Them, KNIGHT)
472 && !(squares_of_color(s) & pos.pieces(Them, BISHOP)))
473 bonus += bonus + bonus / 2;
477 return make_score(bonus, bonus);
481 // evaluate_pieces<>() assigns bonuses and penalties to the pieces of a given color
483 template<PieceType Piece, Color Us, bool Trace>
484 Score evaluate_pieces(const Position& pos, EvalInfo& ei, Score& mobility, Bitboard mobilityArea) {
488 Score score = SCORE_ZERO;
490 const Color Them = (Us == WHITE ? BLACK : WHITE);
491 const Square* pl = pos.list<Piece>(Us);
493 ei.attackedBy[Us][Piece] = 0;
495 while ((s = *pl++) != SQ_NONE)
497 // Find attacked squares, including x-ray attacks for bishops and rooks
498 b = Piece == BISHOP ? attacks_bb<BISHOP>(s, pos.pieces() ^ pos.pieces(Us, QUEEN))
499 : Piece == ROOK ? attacks_bb< ROOK>(s, pos.pieces() ^ pos.pieces(Us, ROOK, QUEEN))
500 : pos.attacks_from<Piece>(s);
502 ei.attackedBy[Us][Piece] |= b;
504 if (b & ei.kingRing[Them])
506 ei.kingAttackersCount[Us]++;
507 ei.kingAttackersWeight[Us] += KingAttackWeights[Piece];
508 Bitboard bb = (b & ei.attackedBy[Them][KING]);
510 ei.kingAdjacentZoneAttacksCount[Us] += popcount<Max15>(bb);
513 int mob = Piece != QUEEN ? popcount<Max15>(b & mobilityArea)
514 : popcount<Full >(b & mobilityArea);
516 mobility += MobilityBonus[Piece][mob];
518 // Decrease score if we are attacked by an enemy pawn. Remaining part
519 // of threat evaluation must be done later when we have full attack info.
520 if (ei.attackedBy[Them][PAWN] & s)
521 score -= ThreatenedByPawn[Piece];
523 // Otherwise give a bonus if we are a bishop and can pin a piece or can
524 // give a discovered check through an x-ray attack.
525 else if ( Piece == BISHOP
526 && (PseudoAttacks[Piece][pos.king_square(Them)] & s)
527 && !more_than_one(BetweenBB[s][pos.king_square(Them)] & pos.pieces()))
530 // Penalty for bishop with same coloured pawns
532 score -= BishopPawns * ei.pi->pawns_on_same_color_squares(Us, s);
534 if (Piece == BISHOP || Piece == KNIGHT)
536 // Bishop and knight outposts squares
537 if (!(pos.pieces(Them, PAWN) & pawn_attack_span(Us, s)))
538 score += evaluate_outposts<Piece, Us>(pos, ei, s);
540 // Bishop or knight behind a pawn
541 if ( relative_rank(Us, s) < RANK_5
542 && (pos.pieces(PAWN) & (s + pawn_push(Us))))
543 score += MinorBehindPawn;
546 if ( (Piece == ROOK || Piece == QUEEN)
547 && relative_rank(Us, s) >= RANK_5)
549 // Major piece on 7th rank and enemy king trapped on 8th
550 if ( relative_rank(Us, s) == RANK_7
551 && relative_rank(Us, pos.king_square(Them)) == RANK_8)
552 score += Piece == ROOK ? RookOn7th : QueenOn7th;
554 // Major piece attacking enemy pawns on the same rank/file
555 Bitboard pawns = pos.pieces(Them, PAWN) & PseudoAttacks[ROOK][s];
557 score += popcount<Max15>(pawns) * (Piece == ROOK ? RookOnPawn : QueenOnPawn);
560 // Special extra evaluation for rooks
563 // Give a bonus for a rook on a open or semi-open file
564 if (ei.pi->semiopen(Us, file_of(s)))
565 score += ei.pi->semiopen(Them, file_of(s)) ? RookOpenFile : RookSemiopenFile;
567 if (mob > 3 || ei.pi->semiopen(Us, file_of(s)))
570 Square ksq = pos.king_square(Us);
572 // Penalize rooks which are trapped inside a king. Penalize more if
573 // king has lost right to castle.
574 if ( ((file_of(ksq) < FILE_E) == (file_of(s) < file_of(ksq)))
575 && (rank_of(ksq) == rank_of(s) || relative_rank(Us, ksq) == RANK_1)
576 && !ei.pi->semiopen_on_side(Us, file_of(ksq), file_of(ksq) < FILE_E))
577 score -= (TrappedRook - make_score(mob * 8, 0)) * (pos.can_castle(Us) ? 1 : 2);
580 // An important Chess960 pattern: A cornered bishop blocked by a friendly
581 // pawn diagonally in front of it is a very serious problem, especially
582 // when that pawn is also blocked.
585 && (s == relative_square(Us, SQ_A1) || s == relative_square(Us, SQ_H1)))
587 const enum Piece P = make_piece(Us, PAWN);
588 Square d = pawn_push(Us) + (file_of(s) == FILE_A ? DELTA_E : DELTA_W);
589 if (pos.piece_on(s + d) == P)
590 score -= !pos.is_empty(s + d + pawn_push(Us)) ? TrappedBishopA1H1 * 4
591 : pos.piece_on(s + d + d) == P ? TrappedBishopA1H1 * 2
597 Tracing::scores[Us][Piece] = score;
603 // evaluate_threats<>() assigns bonuses according to the type of attacking piece
604 // and the type of attacked one.
606 template<Color Us, bool Trace>
607 Score evaluate_threats(const Position& pos, const EvalInfo& ei) {
609 const Color Them = (Us == WHITE ? BLACK : WHITE);
611 Bitboard b, undefendedMinors, weakEnemies;
612 Score score = SCORE_ZERO;
614 // Undefended minors get penalized even if not under attack
615 undefendedMinors = pos.pieces(Them, BISHOP, KNIGHT)
616 & ~ei.attackedBy[Them][ALL_PIECES];
618 if (undefendedMinors)
619 score += UndefendedMinor;
621 // Enemy pieces not defended by a pawn and under our attack
622 weakEnemies = pos.pieces(Them)
623 & ~ei.attackedBy[Them][PAWN]
624 & ei.attackedBy[Us][ALL_PIECES];
626 // Add bonus according to type of attacked enemy piece and to the
627 // type of attacking piece, from knights to queens. Kings are not
628 // considered because are already handled in king evaluation.
630 for (PieceType pt1 = KNIGHT; pt1 < KING; pt1++)
632 b = ei.attackedBy[Us][pt1] & weakEnemies;
634 for (PieceType pt2 = PAWN; pt2 < KING; pt2++)
635 if (b & pos.pieces(pt2))
636 score += Threat[pt1][pt2];
640 Tracing::scores[Us][THREAT] = score;
646 // evaluate_pieces_of_color<>() assigns bonuses and penalties to all the
647 // pieces of a given color.
649 template<Color Us, bool Trace>
650 Score evaluate_pieces_of_color(const Position& pos, EvalInfo& ei, Score& mobility) {
652 const Color Them = (Us == WHITE ? BLACK : WHITE);
654 Score score = mobility = SCORE_ZERO;
656 // Do not include in mobility squares protected by enemy pawns or occupied by our pieces
657 const Bitboard mobilityArea = ~(ei.attackedBy[Them][PAWN] | pos.pieces(Us, PAWN, KING));
659 score += evaluate_pieces<KNIGHT, Us, Trace>(pos, ei, mobility, mobilityArea);
660 score += evaluate_pieces<BISHOP, Us, Trace>(pos, ei, mobility, mobilityArea);
661 score += evaluate_pieces<ROOK, Us, Trace>(pos, ei, mobility, mobilityArea);
662 score += evaluate_pieces<QUEEN, Us, Trace>(pos, ei, mobility, mobilityArea);
664 // Sum up all attacked squares
665 ei.attackedBy[Us][ALL_PIECES] = ei.attackedBy[Us][PAWN] | ei.attackedBy[Us][KNIGHT]
666 | ei.attackedBy[Us][BISHOP] | ei.attackedBy[Us][ROOK]
667 | ei.attackedBy[Us][QUEEN] | ei.attackedBy[Us][KING];
669 Tracing::scores[Us][MOBILITY] = apply_weight(mobility, Weights[Mobility]);
675 // evaluate_king<>() assigns bonuses and penalties to a king of a given color
677 template<Color Us, bool Trace>
678 Score evaluate_king(const Position& pos, const EvalInfo& ei, Value margins[]) {
680 const Color Them = (Us == WHITE ? BLACK : WHITE);
682 Bitboard undefended, b, b1, b2, safe;
684 const Square ksq = pos.king_square(Us);
686 // King shelter and enemy pawns storm
687 Score score = ei.pi->king_safety<Us>(pos, ksq);
689 // King safety. This is quite complicated, and is almost certainly far
690 // from optimally tuned.
691 if ( ei.kingAttackersCount[Them] >= 2
692 && ei.kingAdjacentZoneAttacksCount[Them])
694 // Find the attacked squares around the king which has no defenders
695 // apart from the king itself
696 undefended = ei.attackedBy[Them][ALL_PIECES] & ei.attackedBy[Us][KING];
697 undefended &= ~( ei.attackedBy[Us][PAWN] | ei.attackedBy[Us][KNIGHT]
698 | ei.attackedBy[Us][BISHOP] | ei.attackedBy[Us][ROOK]
699 | ei.attackedBy[Us][QUEEN]);
701 // Initialize the 'attackUnits' variable, which is used later on as an
702 // index to the KingDanger[] array. The initial value is based on the
703 // number and types of the enemy's attacking pieces, the number of
704 // attacked and undefended squares around our king, the square of the
705 // king, and the quality of the pawn shelter.
706 attackUnits = std::min(25, (ei.kingAttackersCount[Them] * ei.kingAttackersWeight[Them]) / 2)
707 + 3 * (ei.kingAdjacentZoneAttacksCount[Them] + popcount<Max15>(undefended))
708 + KingExposed[relative_square(Us, ksq)]
709 - mg_value(score) / 32;
711 // Analyse enemy's safe queen contact checks. First find undefended
712 // squares around the king attacked by enemy queen...
713 b = undefended & ei.attackedBy[Them][QUEEN] & ~pos.pieces(Them);
716 // ...then remove squares not supported by another enemy piece
717 b &= ( ei.attackedBy[Them][PAWN] | ei.attackedBy[Them][KNIGHT]
718 | ei.attackedBy[Them][BISHOP] | ei.attackedBy[Them][ROOK]);
720 attackUnits += QueenContactCheck
722 * (Them == pos.side_to_move() ? 2 : 1);
725 // Analyse enemy's safe rook contact checks. First find undefended
726 // squares around the king attacked by enemy rooks...
727 b = undefended & ei.attackedBy[Them][ROOK] & ~pos.pieces(Them);
729 // Consider only squares where the enemy rook gives check
730 b &= PseudoAttacks[ROOK][ksq];
734 // ...then remove squares not supported by another enemy piece
735 b &= ( ei.attackedBy[Them][PAWN] | ei.attackedBy[Them][KNIGHT]
736 | ei.attackedBy[Them][BISHOP] | ei.attackedBy[Them][QUEEN]);
738 attackUnits += RookContactCheck
740 * (Them == pos.side_to_move() ? 2 : 1);
743 // Analyse enemy's safe distance checks for sliders and knights
744 safe = ~(pos.pieces(Them) | ei.attackedBy[Us][ALL_PIECES]);
746 b1 = pos.attacks_from<ROOK>(ksq) & safe;
747 b2 = pos.attacks_from<BISHOP>(ksq) & safe;
749 // Enemy queen safe checks
750 b = (b1 | b2) & ei.attackedBy[Them][QUEEN];
752 attackUnits += QueenCheck * popcount<Max15>(b);
754 // Enemy rooks safe checks
755 b = b1 & ei.attackedBy[Them][ROOK];
757 attackUnits += RookCheck * popcount<Max15>(b);
759 // Enemy bishops safe checks
760 b = b2 & ei.attackedBy[Them][BISHOP];
762 attackUnits += BishopCheck * popcount<Max15>(b);
764 // Enemy knights safe checks
765 b = pos.attacks_from<KNIGHT>(ksq) & ei.attackedBy[Them][KNIGHT] & safe;
767 attackUnits += KnightCheck * popcount<Max15>(b);
769 // To index KingDanger[] attackUnits must be in [0, 99] range
770 attackUnits = std::min(99, std::max(0, attackUnits));
772 // Finally, extract the king danger score from the KingDanger[]
773 // array and subtract the score from evaluation. Set also margins[]
774 // value that will be used for pruning because this value can sometimes
775 // be very big, and so capturing a single attacking piece can therefore
776 // result in a score change far bigger than the value of the captured piece.
777 score -= KingDanger[Us == Search::RootColor][attackUnits];
778 margins[Us] += mg_value(KingDanger[Us == Search::RootColor][attackUnits]);
782 Tracing::scores[Us][KING] = score;
788 // evaluate_passed_pawns<>() evaluates the passed pawns of the given color
790 template<Color Us, bool Trace>
791 Score evaluate_passed_pawns(const Position& pos, const EvalInfo& ei) {
793 const Color Them = (Us == WHITE ? BLACK : WHITE);
795 Bitboard b, squaresToQueen, defendedSquares, unsafeSquares, supportingPawns;
796 Score score = SCORE_ZERO;
798 b = ei.pi->passed_pawns(Us);
802 Square s = pop_lsb(&b);
804 assert(pos.pawn_is_passed(Us, s));
806 int r = int(relative_rank(Us, s) - RANK_2);
807 int rr = r * (r - 1);
809 // Base bonus based on rank
810 Value mbonus = Value(17 * rr);
811 Value ebonus = Value(7 * (rr + r + 1));
815 Square blockSq = s + pawn_push(Us);
817 // Adjust bonus based on kings proximity
818 ebonus += Value(square_distance(pos.king_square(Them), blockSq) * 5 * rr);
819 ebonus -= Value(square_distance(pos.king_square(Us), blockSq) * 2 * rr);
821 // If blockSq is not the queening square then consider also a second push
822 if (rank_of(blockSq) != (Us == WHITE ? RANK_8 : RANK_1))
823 ebonus -= Value(square_distance(pos.king_square(Us), blockSq + pawn_push(Us)) * rr);
825 // If the pawn is free to advance, increase bonus
826 if (pos.is_empty(blockSq))
828 squaresToQueen = forward_bb(Us, s);
829 defendedSquares = squaresToQueen & ei.attackedBy[Us][ALL_PIECES];
831 // If there is an enemy rook or queen attacking the pawn from behind,
832 // add all X-ray attacks by the rook or queen. Otherwise consider only
833 // the squares in the pawn's path attacked or occupied by the enemy.
834 if ( unlikely(forward_bb(Them, s) & pos.pieces(Them, ROOK, QUEEN))
835 && (forward_bb(Them, s) & pos.pieces(Them, ROOK, QUEEN) & pos.attacks_from<ROOK>(s)))
836 unsafeSquares = squaresToQueen;
838 unsafeSquares = squaresToQueen & (ei.attackedBy[Them][ALL_PIECES] | pos.pieces(Them));
840 // If there aren't enemy attacks huge bonus, a bit smaller if at
841 // least block square is not attacked, otherwise smallest bonus.
842 int k = !unsafeSquares ? 15 : !(unsafeSquares & blockSq) ? 9 : 3;
844 // Big bonus if the path to queen is fully defended, a bit less
845 // if at least block square is defended.
846 if (defendedSquares == squaresToQueen)
849 else if (defendedSquares & blockSq)
850 k += (unsafeSquares & defendedSquares) == unsafeSquares ? 4 : 2;
852 mbonus += Value(k * rr), ebonus += Value(k * rr);
856 // Increase the bonus if the passed pawn is supported by a friendly pawn
857 // on the same rank and a bit smaller if it's on the previous rank.
858 supportingPawns = pos.pieces(Us, PAWN) & adjacent_files_bb(file_of(s));
859 if (supportingPawns & rank_bb(s))
860 ebonus += Value(r * 20);
862 else if (supportingPawns & rank_bb(s - pawn_push(Us)))
863 ebonus += Value(r * 12);
865 // Rook pawns are a special case: They are sometimes worse, and
866 // sometimes better than other passed pawns. It is difficult to find
867 // good rules for determining whether they are good or bad. For now,
868 // we try the following: Increase the value for rook pawns if the
869 // other side has no pieces apart from a knight, and decrease the
870 // value if the other side has a rook or queen.
871 if (file_of(s) == FILE_A || file_of(s) == FILE_H)
873 if (pos.non_pawn_material(Them) <= KnightValueMg)
874 ebonus += ebonus / 4;
875 else if (pos.pieces(Them, ROOK, QUEEN))
876 ebonus -= ebonus / 4;
878 score += make_score(mbonus, ebonus);
883 Tracing::scores[Us][PASSED] = apply_weight(score, Weights[PassedPawns]);
885 // Add the scores to the middle game and endgame eval
886 return apply_weight(score, Weights[PassedPawns]);
890 // evaluate_unstoppable_pawns() evaluates the unstoppable passed pawns for both sides, this is quite
891 // conservative and returns a winning score only when we are very sure that the pawn is winning.
893 Score evaluate_unstoppable_pawns(const Position& pos, const EvalInfo& ei) {
895 Bitboard b, b2, blockers, supporters, queeningPath, candidates;
896 Square s, blockSq, queeningSquare;
897 Color c, winnerSide, loserSide;
898 bool pathDefended, opposed;
899 int pliesToGo, movesToGo, oppMovesToGo, sacptg, blockersCount, minKingDist, kingptg, d;
900 int pliesToQueen[] = { 256, 256 };
902 // Step 1. Hunt for unstoppable passed pawns. If we find at least one,
903 // record how many plies are required for promotion.
904 for (c = WHITE; c <= BLACK; c++)
906 // Skip if other side has non-pawn pieces
907 if (pos.non_pawn_material(~c))
910 b = ei.pi->passed_pawns(c);
915 queeningSquare = relative_square(c, file_of(s) | RANK_8);
916 queeningPath = forward_bb(c, s);
918 // Compute plies to queening and check direct advancement
919 movesToGo = rank_distance(s, queeningSquare) - int(relative_rank(c, s) == RANK_2);
920 oppMovesToGo = square_distance(pos.king_square(~c), queeningSquare) - int(c != pos.side_to_move());
921 pathDefended = ((ei.attackedBy[c][ALL_PIECES] & queeningPath) == queeningPath);
923 if (movesToGo >= oppMovesToGo && !pathDefended)
926 // Opponent king cannot block because path is defended and position
927 // is not in check. So only friendly pieces can be blockers.
928 assert(!pos.checkers());
929 assert((queeningPath & pos.pieces()) == (queeningPath & pos.pieces(c)));
931 // Add moves needed to free the path from friendly pieces and retest condition
932 movesToGo += popcount<Max15>(queeningPath & pos.pieces(c));
934 if (movesToGo >= oppMovesToGo && !pathDefended)
937 pliesToGo = 2 * movesToGo - int(c == pos.side_to_move());
938 pliesToQueen[c] = std::min(pliesToQueen[c], pliesToGo);
942 // Step 2. If either side cannot promote at least three plies before the other side then situation
943 // becomes too complex and we give up. Otherwise we determine the possibly "winning side"
944 if (abs(pliesToQueen[WHITE] - pliesToQueen[BLACK]) < 3)
947 winnerSide = (pliesToQueen[WHITE] < pliesToQueen[BLACK] ? WHITE : BLACK);
948 loserSide = ~winnerSide;
950 // Step 3. Can the losing side possibly create a new passed pawn and thus prevent the loss?
951 b = candidates = pos.pieces(loserSide, PAWN);
957 // Compute plies from queening
958 queeningSquare = relative_square(loserSide, file_of(s) | RANK_8);
959 movesToGo = rank_distance(s, queeningSquare) - int(relative_rank(loserSide, s) == RANK_2);
960 pliesToGo = 2 * movesToGo - int(loserSide == pos.side_to_move());
962 // Check if (without even considering any obstacles) we're too far away or doubled
963 if ( pliesToQueen[winnerSide] + 3 <= pliesToGo
964 || (forward_bb(loserSide, s) & pos.pieces(loserSide, PAWN)))
968 // If any candidate is already a passed pawn it _may_ promote in time. We give up.
969 if (candidates & ei.pi->passed_pawns(loserSide))
972 // Step 4. Check new passed pawn creation through king capturing and pawn sacrifices
978 sacptg = blockersCount = 0;
979 minKingDist = kingptg = 256;
981 // Compute plies from queening
982 queeningSquare = relative_square(loserSide, file_of(s) | RANK_8);
983 movesToGo = rank_distance(s, queeningSquare) - int(relative_rank(loserSide, s) == RANK_2);
984 pliesToGo = 2 * movesToGo - int(loserSide == pos.side_to_move());
986 // Generate list of blocking pawns and supporters
987 supporters = adjacent_files_bb(file_of(s)) & candidates;
988 opposed = forward_bb(loserSide, s) & pos.pieces(winnerSide, PAWN);
989 blockers = passed_pawn_mask(loserSide, s) & pos.pieces(winnerSide, PAWN);
993 // How many plies does it take to remove all the blocking pawns?
996 blockSq = pop_lsb(&blockers);
999 // Check pawns that can give support to overcome obstacle, for instance
1000 // black pawns: a4, b4 white: b2 then pawn in b4 is giving support.
1003 b2 = supporters & in_front_bb(winnerSide, rank_of(blockSq + pawn_push(winnerSide)));
1005 while (b2) // This while-loop could be replaced with LSB/MSB (depending on color)
1007 d = square_distance(blockSq, pop_lsb(&b2)) - 2;
1008 movesToGo = std::min(movesToGo, d);
1012 // Check pawns that can be sacrificed against the blocking pawn
1013 b2 = pawn_attack_span(winnerSide, blockSq) & candidates & ~(1ULL << s);
1015 while (b2) // This while-loop could be replaced with LSB/MSB (depending on color)
1017 d = square_distance(blockSq, pop_lsb(&b2)) - 2;
1018 movesToGo = std::min(movesToGo, d);
1021 // If obstacle can be destroyed with an immediate pawn exchange / sacrifice,
1022 // it's not a real obstacle and we have nothing to add to pliesToGo.
1026 // Plies needed to sacrifice against all the blocking pawns
1027 sacptg += movesToGo * 2;
1030 // Plies needed for the king to capture all the blocking pawns
1031 d = square_distance(pos.king_square(loserSide), blockSq);
1032 minKingDist = std::min(minKingDist, d);
1033 kingptg = (minKingDist + blockersCount) * 2;
1036 // Check if pawn sacrifice plan _may_ save the day
1037 if (pliesToQueen[winnerSide] + 3 > pliesToGo + sacptg)
1040 // Check if king capture plan _may_ save the day (contains some false positives)
1041 if (pliesToQueen[winnerSide] + 3 > pliesToGo + kingptg)
1045 // Winning pawn is unstoppable and will promote as first, return big score
1046 Score score = make_score(0, (Value) 1280 - 32 * pliesToQueen[winnerSide]);
1047 return winnerSide == WHITE ? score : -score;
1051 // evaluate_space() computes the space evaluation for a given side. The
1052 // space evaluation is a simple bonus based on the number of safe squares
1053 // available for minor pieces on the central four files on ranks 2--4. Safe
1054 // squares one, two or three squares behind a friendly pawn are counted
1055 // twice. Finally, the space bonus is scaled by a weight taken from the
1056 // material hash table. The aim is to improve play on game opening.
1058 int evaluate_space(const Position& pos, const EvalInfo& ei) {
1060 const Color Them = (Us == WHITE ? BLACK : WHITE);
1062 // Find the safe squares for our pieces inside the area defined by
1063 // SpaceMask[]. A square is unsafe if it is attacked by an enemy
1064 // pawn, or if it is undefended and attacked by an enemy piece.
1065 Bitboard safe = SpaceMask[Us]
1066 & ~pos.pieces(Us, PAWN)
1067 & ~ei.attackedBy[Them][PAWN]
1068 & (ei.attackedBy[Us][ALL_PIECES] | ~ei.attackedBy[Them][ALL_PIECES]);
1070 // Find all squares which are at most three squares behind some friendly pawn
1071 Bitboard behind = pos.pieces(Us, PAWN);
1072 behind |= (Us == WHITE ? behind >> 8 : behind << 8);
1073 behind |= (Us == WHITE ? behind >> 16 : behind << 16);
1075 // Since SpaceMask[Us] is fully on our half of the board
1076 assert(unsigned(safe >> (Us == WHITE ? 32 : 0)) == 0);
1078 // Count safe + (behind & safe) with a single popcount
1079 return popcount<Full>((Us == WHITE ? safe << 32 : safe >> 32) | (behind & safe));
1083 // interpolate() interpolates between a middle game and an endgame score,
1084 // based on game phase. It also scales the return value by a ScaleFactor array.
1086 Value interpolate(const Score& v, Phase ph, ScaleFactor sf) {
1088 assert(mg_value(v) > -VALUE_INFINITE && mg_value(v) < VALUE_INFINITE);
1089 assert(eg_value(v) > -VALUE_INFINITE && eg_value(v) < VALUE_INFINITE);
1090 assert(ph >= PHASE_ENDGAME && ph <= PHASE_MIDGAME);
1092 int ev = (eg_value(v) * int(sf)) / SCALE_FACTOR_NORMAL;
1093 int result = (mg_value(v) * int(ph) + ev * int(128 - ph)) / 128;
1094 return Value((result / GrainSize) * GrainSize); // Sign independent
1097 // apply_weight() weights score v by score w trying to prevent overflow
1098 Score apply_weight(Score v, Score w) {
1099 return make_score((int(mg_value(v)) * mg_value(w)) / 0x100,
1100 (int(eg_value(v)) * eg_value(w)) / 0x100);
1103 // weight_option() computes the value of an evaluation weight, by combining
1104 // two UCI-configurable weights (midgame and endgame) with an internal weight.
1106 Score weight_option(const std::string& mgOpt, const std::string& egOpt, Score internalWeight) {
1108 // Scale option value from 100 to 256
1109 int mg = Options[mgOpt] * 256 / 100;
1110 int eg = Options[egOpt] * 256 / 100;
1112 return apply_weight(make_score(mg, eg), internalWeight);
1116 // Tracing functions definitions
1118 double to_cp(Value v) { return double(v) / double(PawnValueMg); }
1120 void Tracing::add(int idx, Score wScore, Score bScore) {
1122 scores[WHITE][idx] = wScore;
1123 scores[BLACK][idx] = bScore;
1126 void Tracing::row(const char* name, int idx) {
1128 Score wScore = scores[WHITE][idx];
1129 Score bScore = scores[BLACK][idx];
1132 case PST: case IMBALANCE: case PAWN: case UNSTOPPABLE: case TOTAL:
1133 stream << std::setw(20) << name << " | --- --- | --- --- | "
1134 << std::setw(6) << to_cp(mg_value(wScore)) << " "
1135 << std::setw(6) << to_cp(eg_value(wScore)) << " \n";
1138 stream << std::setw(20) << name << " | " << std::noshowpos
1139 << std::setw(5) << to_cp(mg_value(wScore)) << " "
1140 << std::setw(5) << to_cp(eg_value(wScore)) << " | "
1141 << std::setw(5) << to_cp(mg_value(bScore)) << " "
1142 << std::setw(5) << to_cp(eg_value(bScore)) << " | "
1144 << std::setw(6) << to_cp(mg_value(wScore - bScore)) << " "
1145 << std::setw(6) << to_cp(eg_value(wScore - bScore)) << " \n";
1149 std::string Tracing::do_trace(const Position& pos) {
1152 stream << std::showpoint << std::showpos << std::fixed << std::setprecision(2);
1153 std::memset(scores, 0, 2 * (TOTAL + 1) * sizeof(Score));
1156 do_evaluate<true>(pos, margin);
1158 std::string totals = stream.str();
1161 stream << std::setw(21) << "Eval term " << "| White | Black | Total \n"
1162 << " | MG EG | MG EG | MG EG \n"
1163 << "---------------------+-------------+-------------+---------------\n";
1165 row("Material, PST, Tempo", PST);
1166 row("Material imbalance", IMBALANCE);
1168 row("Knights", KNIGHT);
1169 row("Bishops", BISHOP);
1171 row("Queens", QUEEN);
1172 row("Mobility", MOBILITY);
1173 row("King safety", KING);
1174 row("Threats", THREAT);
1175 row("Passed pawns", PASSED);
1176 row("Unstoppable pawns", UNSTOPPABLE);
1177 row("Space", SPACE);
1179 stream << "---------------------+-------------+-------------+---------------\n";
1180 row("Total", TOTAL);
1183 return stream.str();