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 UndefendedMinor = make_score(25, 10);
177 const Score TrappedRook = make_score(90, 0);
179 // Penalty for a bishop on a1/h1 (a8/h8 for black) which is trapped by
180 // a friendly pawn on b2/g2 (b7/g7 for black). This can obviously only
181 // happen in Chess960 games.
182 const Score TrappedBishopA1H1 = make_score(50, 50);
184 // The SpaceMask[Color] contains the area of the board which is considered
185 // by the space evaluation. In the middle game, each side is given a bonus
186 // based on how many squares inside this area are safe and available for
187 // friendly minor pieces.
188 const Bitboard SpaceMask[] = {
189 (1ULL << SQ_C2) | (1ULL << SQ_D2) | (1ULL << SQ_E2) | (1ULL << SQ_F2) |
190 (1ULL << SQ_C3) | (1ULL << SQ_D3) | (1ULL << SQ_E3) | (1ULL << SQ_F3) |
191 (1ULL << SQ_C4) | (1ULL << SQ_D4) | (1ULL << SQ_E4) | (1ULL << SQ_F4),
192 (1ULL << SQ_C7) | (1ULL << SQ_D7) | (1ULL << SQ_E7) | (1ULL << SQ_F7) |
193 (1ULL << SQ_C6) | (1ULL << SQ_D6) | (1ULL << SQ_E6) | (1ULL << SQ_F6) |
194 (1ULL << SQ_C5) | (1ULL << SQ_D5) | (1ULL << SQ_E5) | (1ULL << SQ_F5)
197 // King danger constants and variables. The king danger scores are taken
198 // from the KingDanger[]. Various little "meta-bonuses" measuring
199 // the strength of the enemy attack are added up into an integer, which
200 // is used as an index to KingDanger[].
202 // KingAttackWeights[PieceType] contains king attack weights by piece type
203 const int KingAttackWeights[] = { 0, 0, 2, 2, 3, 5 };
205 // Bonuses for enemy's safe checks
206 const int QueenContactCheck = 6;
207 const int RookContactCheck = 4;
208 const int QueenCheck = 3;
209 const int RookCheck = 2;
210 const int BishopCheck = 1;
211 const int KnightCheck = 1;
213 // KingExposed[Square] contains penalties based on the position of the
214 // defending king, indexed by king's square (from white's point of view).
215 const int KingExposed[] = {
216 2, 0, 2, 5, 5, 2, 0, 2,
217 2, 2, 4, 8, 8, 4, 2, 2,
218 7, 10, 12, 12, 12, 12, 10, 7,
219 15, 15, 15, 15, 15, 15, 15, 15,
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
226 // KingDanger[Color][attackUnits] contains the actual king danger weighted
227 // scores, indexed by color and by a calculated integer number.
228 Score KingDanger[COLOR_NB][128];
230 // Function prototypes
232 Value do_evaluate(const Position& pos, Value& margin);
235 void init_eval_info(const Position& pos, EvalInfo& ei);
237 template<Color Us, bool Trace>
238 Score evaluate_pieces_of_color(const Position& pos, EvalInfo& ei, Score& mobility);
240 template<Color Us, bool Trace>
241 Score evaluate_king(const Position& pos, EvalInfo& ei, Value margins[]);
243 template<Color Us, bool Trace>
244 Score evaluate_threats(const Position& pos, EvalInfo& ei);
246 template<Color Us, bool Trace>
247 Score evaluate_passed_pawns(const Position& pos, EvalInfo& ei);
250 int evaluate_space(const Position& pos, EvalInfo& ei);
252 Score evaluate_unstoppable_pawns(const Position& pos, EvalInfo& ei);
254 Value interpolate(const Score& v, Phase ph, ScaleFactor sf);
255 Score apply_weight(Score v, Score w);
256 Score weight_option(const std::string& mgOpt, const std::string& egOpt, Score internalWeight);
257 double to_cp(Value v);
263 /// evaluate() is the main evaluation function. It always computes two
264 /// values, an endgame score and a middle game score, and interpolates
265 /// between them based on the remaining material.
267 Value evaluate(const Position& pos, Value& margin) {
268 return do_evaluate<false>(pos, margin);
272 /// trace() is like evaluate() but instead of a value returns a string suitable
273 /// to be print on stdout with the detailed descriptions and values of each
274 /// evaluation term. Used mainly for debugging.
275 std::string trace(const Position& pos) {
276 return Tracing::do_trace(pos);
280 /// init() computes evaluation weights from the corresponding UCI parameters
281 /// and setup king tables.
285 Weights[Mobility] = weight_option("Mobility (Midgame)", "Mobility (Endgame)", WeightsInternal[Mobility]);
286 Weights[PawnStructure] = weight_option("Pawn Structure (Midgame)", "Pawn Structure (Endgame)", WeightsInternal[PawnStructure]);
287 Weights[PassedPawns] = weight_option("Passed Pawns (Midgame)", "Passed Pawns (Endgame)", WeightsInternal[PassedPawns]);
288 Weights[Space] = weight_option("Space", "Space", WeightsInternal[Space]);
289 Weights[KingDangerUs] = weight_option("Cowardice", "Cowardice", WeightsInternal[KingDangerUs]);
290 Weights[KingDangerThem] = weight_option("Aggressiveness", "Aggressiveness", WeightsInternal[KingDangerThem]);
292 const int MaxSlope = 30;
293 const int Peak = 1280;
295 for (int t = 0, i = 1; i < 100; i++)
297 t = std::min(Peak, std::min(int(0.4 * i * i), t + MaxSlope));
299 KingDanger[1][i] = apply_weight(make_score(t, 0), Weights[KingDangerUs]);
300 KingDanger[0][i] = apply_weight(make_score(t, 0), Weights[KingDangerThem]);
310 Value do_evaluate(const Position& pos, Value& margin) {
312 assert(!pos.checkers());
315 Value margins[COLOR_NB];
316 Score score, mobilityWhite, mobilityBlack;
317 Thread* th = pos.this_thread();
319 // margins[] store the uncertainty estimation of position's evaluation
320 // that typically is used by the search for pruning decisions.
321 margins[WHITE] = margins[BLACK] = VALUE_ZERO;
323 // Initialize score by reading the incrementally updated scores included
324 // in the position object (material + piece square tables) and adding
325 // Tempo bonus. Score is computed from the point of view of white.
326 score = pos.psq_score() + (pos.side_to_move() == WHITE ? Tempo : -Tempo);
328 // Probe the material hash table
329 ei.mi = Material::probe(pos, th->materialTable, th->endgames);
330 score += ei.mi->material_value();
332 // If we have a specialized evaluation function for the current material
333 // configuration, call it and return.
334 if (ei.mi->specialized_eval_exists())
337 return ei.mi->evaluate(pos);
340 // Probe the pawn hash table
341 ei.pi = Pawns::probe(pos, th->pawnsTable);
342 score += apply_weight(ei.pi->pawns_value(), Weights[PawnStructure]);
344 // Initialize attack and king safety bitboards
345 init_eval_info<WHITE>(pos, ei);
346 init_eval_info<BLACK>(pos, ei);
348 // Evaluate pieces and mobility
349 score += evaluate_pieces_of_color<WHITE, Trace>(pos, ei, mobilityWhite)
350 - evaluate_pieces_of_color<BLACK, Trace>(pos, ei, mobilityBlack);
352 score += apply_weight(mobilityWhite - mobilityBlack, Weights[Mobility]);
354 // Evaluate kings after all other pieces because we need complete attack
355 // information when computing the king safety evaluation.
356 score += evaluate_king<WHITE, Trace>(pos, ei, margins)
357 - evaluate_king<BLACK, Trace>(pos, ei, margins);
359 // Evaluate tactical threats, we need full attack information including king
360 score += evaluate_threats<WHITE, Trace>(pos, ei)
361 - evaluate_threats<BLACK, Trace>(pos, ei);
363 // Evaluate passed pawns, we need full attack information including king
364 score += evaluate_passed_pawns<WHITE, Trace>(pos, ei)
365 - evaluate_passed_pawns<BLACK, Trace>(pos, ei);
367 // If one side has only a king, check whether exists any unstoppable passed pawn
368 if (!pos.non_pawn_material(WHITE) || !pos.non_pawn_material(BLACK))
369 score += evaluate_unstoppable_pawns(pos, ei);
371 // Evaluate space for both sides, only in middle-game.
372 if (ei.mi->space_weight())
374 int s = evaluate_space<WHITE>(pos, ei) - evaluate_space<BLACK>(pos, ei);
375 score += apply_weight(s * ei.mi->space_weight(), Weights[Space]);
378 // Scale winning side if position is more drawish that what it appears
379 ScaleFactor sf = eg_value(score) > VALUE_DRAW ? ei.mi->scale_factor(pos, WHITE)
380 : ei.mi->scale_factor(pos, BLACK);
382 // If we don't already have an unusual scale factor, check for opposite
383 // colored bishop endgames, and use a lower scale for those.
384 if ( ei.mi->game_phase() < PHASE_MIDGAME
385 && pos.opposite_bishops()
386 && sf == SCALE_FACTOR_NORMAL)
388 // Only the two bishops ?
389 if ( pos.non_pawn_material(WHITE) == BishopValueMg
390 && pos.non_pawn_material(BLACK) == BishopValueMg)
392 // Check for KBP vs KB with only a single pawn that is almost
393 // certainly a draw or at least two pawns.
394 bool one_pawn = (pos.count<PAWN>(WHITE) + pos.count<PAWN>(BLACK) == 1);
395 sf = one_pawn ? ScaleFactor(8) : ScaleFactor(32);
398 // Endgame with opposite-colored bishops, but also other pieces. Still
399 // a bit drawish, but not as drawish as with only the two bishops.
400 sf = ScaleFactor(50);
403 margin = margins[pos.side_to_move()];
404 Value v = interpolate(score, ei.mi->game_phase(), sf);
406 // In case of tracing add all single evaluation contributions for both white and black
409 Tracing::add(PST, pos.psq_score());
410 Tracing::add(IMBALANCE, ei.mi->material_value());
411 Tracing::add(PAWN, ei.pi->pawns_value());
412 Tracing::add(UNSTOPPABLE, evaluate_unstoppable_pawns(pos, ei));
413 Score w = ei.mi->space_weight() * evaluate_space<WHITE>(pos, ei);
414 Score b = ei.mi->space_weight() * evaluate_space<BLACK>(pos, ei);
415 Tracing::add(SPACE, apply_weight(w, Weights[Space]), apply_weight(b, Weights[Space]));
416 Tracing::add(TOTAL, score);
417 Tracing::stream << "\nUncertainty margin: White: " << to_cp(margins[WHITE])
418 << ", Black: " << to_cp(margins[BLACK])
419 << "\nScaling: " << std::noshowpos
420 << std::setw(6) << 100.0 * ei.mi->game_phase() / 128.0 << "% MG, "
421 << std::setw(6) << 100.0 * (1.0 - ei.mi->game_phase() / 128.0) << "% * "
422 << std::setw(6) << (100.0 * sf) / SCALE_FACTOR_NORMAL << "% EG.\n"
423 << "Total evaluation: " << to_cp(v);
426 return pos.side_to_move() == WHITE ? v : -v;
430 // init_eval_info() initializes king bitboards for given color adding
431 // pawn attacks. To be done at the beginning of the evaluation.
434 void init_eval_info(const Position& pos, EvalInfo& ei) {
436 const Color Them = (Us == WHITE ? BLACK : WHITE);
437 const Square Down = (Us == WHITE ? DELTA_S : DELTA_N);
439 Bitboard b = ei.attackedBy[Them][KING] = pos.attacks_from<KING>(pos.king_square(Them));
440 ei.attackedBy[Us][PAWN] = ei.pi->pawn_attacks(Us);
442 // Init king safety tables only if we are going to use them
443 if (pos.count<QUEEN>(Us) && pos.non_pawn_material(Us) > QueenValueMg + PawnValueMg)
445 ei.kingRing[Them] = b | shift_bb<Down>(b);
446 b &= ei.attackedBy[Us][PAWN];
447 ei.kingAttackersCount[Us] = b ? popcount<Max15>(b) / 2 : 0;
448 ei.kingAdjacentZoneAttacksCount[Us] = ei.kingAttackersWeight[Us] = 0;
450 ei.kingRing[Them] = ei.kingAttackersCount[Us] = 0;
454 // evaluate_outposts() evaluates bishop and knight outposts squares
456 template<PieceType Piece, Color Us>
457 Score evaluate_outposts(const Position& pos, EvalInfo& ei, Square s) {
459 const Color Them = (Us == WHITE ? BLACK : WHITE);
461 assert (Piece == BISHOP || Piece == KNIGHT);
463 // Initial bonus based on square
464 Value bonus = Outpost[Piece == BISHOP][relative_square(Us, s)];
466 // Increase bonus if supported by pawn, especially if the opponent has
467 // no minor piece which can exchange the outpost piece.
468 if (bonus && (ei.attackedBy[Us][PAWN] & s))
470 if ( !pos.pieces(Them, KNIGHT)
471 && !(same_color_squares(s) & pos.pieces(Them, BISHOP)))
472 bonus += bonus + bonus / 2;
476 return make_score(bonus, bonus);
480 // evaluate_pieces<>() assigns bonuses and penalties to the pieces of a given color
482 template<PieceType Piece, Color Us, bool Trace>
483 Score evaluate_pieces(const Position& pos, EvalInfo& ei, Score& mobility, Bitboard mobilityArea) {
487 Score score = SCORE_ZERO;
489 const Color Them = (Us == WHITE ? BLACK : WHITE);
490 const Square* pl = pos.list<Piece>(Us);
492 ei.attackedBy[Us][Piece] = 0;
494 while ((s = *pl++) != SQ_NONE)
496 // Find attacked squares, including x-ray attacks for bishops and rooks
497 b = Piece == BISHOP ? attacks_bb<BISHOP>(s, pos.pieces() ^ pos.pieces(Us, QUEEN))
498 : Piece == ROOK ? attacks_bb< ROOK>(s, pos.pieces() ^ pos.pieces(Us, ROOK, QUEEN))
499 : pos.attacks_from<Piece>(s);
501 ei.attackedBy[Us][Piece] |= b;
503 if (b & ei.kingRing[Them])
505 ei.kingAttackersCount[Us]++;
506 ei.kingAttackersWeight[Us] += KingAttackWeights[Piece];
507 Bitboard bb = (b & ei.attackedBy[Them][KING]);
509 ei.kingAdjacentZoneAttacksCount[Us] += popcount<Max15>(bb);
512 int mob = Piece != QUEEN ? popcount<Max15>(b & mobilityArea)
513 : popcount<Full >(b & mobilityArea);
515 mobility += MobilityBonus[Piece][mob];
517 // Decrease score if we are attacked by an enemy pawn. Remaining part
518 // of threat evaluation must be done later when we have full attack info.
519 if (ei.attackedBy[Them][PAWN] & s)
520 score -= ThreatenedByPawn[Piece];
522 // Otherwise give a bonus if we are a bishop and can pin a piece or can
523 // give a discovered check through an x-ray attack.
524 else if ( Piece == BISHOP
525 && (PseudoAttacks[Piece][pos.king_square(Them)] & s)
526 && !more_than_one(BetweenBB[s][pos.king_square(Them)] & pos.pieces()))
529 // Penalty for bishop with same coloured pawns
531 score -= BishopPawns * ei.pi->pawns_on_same_color_squares(Us, s);
533 // Bishop and knight outposts squares
534 if ( (Piece == BISHOP || Piece == KNIGHT)
535 && !(pos.pieces(Them, PAWN) & pawn_attack_span(Us, s)))
536 score += evaluate_outposts<Piece, Us>(pos, ei, s);
538 if ( (Piece == ROOK || Piece == QUEEN)
539 && relative_rank(Us, s) >= RANK_5)
541 // Major piece on 7th rank and enemy king trapped on 8th
542 if ( relative_rank(Us, s) == RANK_7
543 && relative_rank(Us, pos.king_square(Them)) == RANK_8)
544 score += Piece == ROOK ? RookOn7th : QueenOn7th;
546 // Major piece attacking enemy pawns on the same rank/file
547 Bitboard pawns = pos.pieces(Them, PAWN) & PseudoAttacks[ROOK][s];
549 score += popcount<Max15>(pawns) * (Piece == ROOK ? RookOnPawn : QueenOnPawn);
552 // Special extra evaluation for rooks
555 // Give a bonus for a rook on a open or semi-open file
556 if (ei.pi->semiopen(Us, file_of(s)))
557 score += ei.pi->semiopen(Them, file_of(s)) ? RookOpenFile : RookSemiopenFile;
559 if (mob > 3 || ei.pi->semiopen(Us, file_of(s)))
562 Square ksq = pos.king_square(Us);
564 // Penalize rooks which are trapped inside a king. Penalize more if
565 // king has lost right to castle.
566 if ( ((file_of(ksq) < FILE_E) == (file_of(s) < file_of(ksq)))
567 && (rank_of(ksq) == rank_of(s) || relative_rank(Us, ksq) == RANK_1)
568 && !ei.pi->semiopen_on_side(Us, file_of(ksq), file_of(ksq) < FILE_E))
569 score -= (TrappedRook - make_score(mob * 8, 0)) * (pos.can_castle(Us) ? 1 : 2);
572 // An important Chess960 pattern: A cornered bishop blocked by a friendly
573 // pawn diagonally in front of it is a very serious problem, especially
574 // when that pawn is also blocked.
577 && (s == relative_square(Us, SQ_A1) || s == relative_square(Us, SQ_H1)))
579 const enum Piece P = make_piece(Us, PAWN);
580 Square d = pawn_push(Us) + (file_of(s) == FILE_A ? DELTA_E : DELTA_W);
581 if (pos.piece_on(s + d) == P)
582 score -= !pos.is_empty(s + d + pawn_push(Us)) ? TrappedBishopA1H1 * 4
583 : pos.piece_on(s + d + d) == P ? TrappedBishopA1H1 * 2
589 Tracing::scores[Us][Piece] = score;
595 // evaluate_threats<>() assigns bonuses according to the type of attacking piece
596 // and the type of attacked one.
598 template<Color Us, bool Trace>
599 Score evaluate_threats(const Position& pos, EvalInfo& ei) {
601 const Color Them = (Us == WHITE ? BLACK : WHITE);
603 Bitboard b, undefendedMinors, weakEnemies;
604 Score score = SCORE_ZERO;
606 // Undefended minors get penalized even if not under attack
607 undefendedMinors = pos.pieces(Them, BISHOP, KNIGHT)
608 & ~ei.attackedBy[Them][ALL_PIECES];
610 if (undefendedMinors)
611 score += UndefendedMinor;
613 // Enemy pieces not defended by a pawn and under our attack
614 weakEnemies = pos.pieces(Them)
615 & ~ei.attackedBy[Them][PAWN]
616 & ei.attackedBy[Us][ALL_PIECES];
618 // Add bonus according to type of attacked enemy piece and to the
619 // type of attacking piece, from knights to queens. Kings are not
620 // considered because are already handled in king evaluation.
622 for (PieceType pt1 = KNIGHT; pt1 < KING; pt1++)
624 b = ei.attackedBy[Us][pt1] & weakEnemies;
626 for (PieceType pt2 = PAWN; pt2 < KING; pt2++)
627 if (b & pos.pieces(pt2))
628 score += Threat[pt1][pt2];
632 Tracing::scores[Us][THREAT] = score;
638 // evaluate_pieces_of_color<>() assigns bonuses and penalties to all the
639 // pieces of a given color.
641 template<Color Us, bool Trace>
642 Score evaluate_pieces_of_color(const Position& pos, EvalInfo& ei, Score& mobility) {
644 const Color Them = (Us == WHITE ? BLACK : WHITE);
646 Score score = mobility = SCORE_ZERO;
648 // Do not include in mobility squares protected by enemy pawns or occupied by our pieces
649 const Bitboard mobilityArea = ~(ei.attackedBy[Them][PAWN] | pos.pieces(Us, PAWN, KING));
651 score += evaluate_pieces<KNIGHT, Us, Trace>(pos, ei, mobility, mobilityArea);
652 score += evaluate_pieces<BISHOP, Us, Trace>(pos, ei, mobility, mobilityArea);
653 score += evaluate_pieces<ROOK, Us, Trace>(pos, ei, mobility, mobilityArea);
654 score += evaluate_pieces<QUEEN, Us, Trace>(pos, ei, mobility, mobilityArea);
656 // Sum up all attacked squares
657 ei.attackedBy[Us][ALL_PIECES] = ei.attackedBy[Us][PAWN] | ei.attackedBy[Us][KNIGHT]
658 | ei.attackedBy[Us][BISHOP] | ei.attackedBy[Us][ROOK]
659 | ei.attackedBy[Us][QUEEN] | ei.attackedBy[Us][KING];
661 Tracing::scores[Us][MOBILITY] = apply_weight(mobility, Weights[Mobility]);
667 // evaluate_king<>() assigns bonuses and penalties to a king of a given color
669 template<Color Us, bool Trace>
670 Score evaluate_king(const Position& pos, EvalInfo& ei, Value margins[]) {
672 const Color Them = (Us == WHITE ? BLACK : WHITE);
674 Bitboard undefended, b, b1, b2, safe;
676 const Square ksq = pos.king_square(Us);
678 // King shelter and enemy pawns storm
679 Score score = ei.pi->king_safety<Us>(pos, ksq);
681 // King safety. This is quite complicated, and is almost certainly far
682 // from optimally tuned.
683 if ( ei.kingAttackersCount[Them] >= 2
684 && ei.kingAdjacentZoneAttacksCount[Them])
686 // Find the attacked squares around the king which has no defenders
687 // apart from the king itself
688 undefended = ei.attackedBy[Them][ALL_PIECES] & ei.attackedBy[Us][KING];
689 undefended &= ~( ei.attackedBy[Us][PAWN] | ei.attackedBy[Us][KNIGHT]
690 | ei.attackedBy[Us][BISHOP] | ei.attackedBy[Us][ROOK]
691 | ei.attackedBy[Us][QUEEN]);
693 // Initialize the 'attackUnits' variable, which is used later on as an
694 // index to the KingDanger[] array. The initial value is based on the
695 // number and types of the enemy's attacking pieces, the number of
696 // attacked and undefended squares around our king, the square of the
697 // king, and the quality of the pawn shelter.
698 attackUnits = std::min(25, (ei.kingAttackersCount[Them] * ei.kingAttackersWeight[Them]) / 2)
699 + 3 * (ei.kingAdjacentZoneAttacksCount[Them] + popcount<Max15>(undefended))
700 + KingExposed[relative_square(Us, ksq)]
701 - mg_value(score) / 32;
703 // Analyse enemy's safe queen contact checks. First find undefended
704 // squares around the king attacked by enemy queen...
705 b = undefended & ei.attackedBy[Them][QUEEN] & ~pos.pieces(Them);
708 // ...then remove squares not supported by another enemy piece
709 b &= ( ei.attackedBy[Them][PAWN] | ei.attackedBy[Them][KNIGHT]
710 | ei.attackedBy[Them][BISHOP] | ei.attackedBy[Them][ROOK]);
712 attackUnits += QueenContactCheck
714 * (Them == pos.side_to_move() ? 2 : 1);
717 // Analyse enemy's safe rook contact checks. First find undefended
718 // squares around the king attacked by enemy rooks...
719 b = undefended & ei.attackedBy[Them][ROOK] & ~pos.pieces(Them);
721 // Consider only squares where the enemy rook gives check
722 b &= PseudoAttacks[ROOK][ksq];
726 // ...then remove squares not supported by another enemy piece
727 b &= ( ei.attackedBy[Them][PAWN] | ei.attackedBy[Them][KNIGHT]
728 | ei.attackedBy[Them][BISHOP] | ei.attackedBy[Them][QUEEN]);
730 attackUnits += RookContactCheck
732 * (Them == pos.side_to_move() ? 2 : 1);
735 // Analyse enemy's safe distance checks for sliders and knights
736 safe = ~(pos.pieces(Them) | ei.attackedBy[Us][ALL_PIECES]);
738 b1 = pos.attacks_from<ROOK>(ksq) & safe;
739 b2 = pos.attacks_from<BISHOP>(ksq) & safe;
741 // Enemy queen safe checks
742 b = (b1 | b2) & ei.attackedBy[Them][QUEEN];
744 attackUnits += QueenCheck * popcount<Max15>(b);
746 // Enemy rooks safe checks
747 b = b1 & ei.attackedBy[Them][ROOK];
749 attackUnits += RookCheck * popcount<Max15>(b);
751 // Enemy bishops safe checks
752 b = b2 & ei.attackedBy[Them][BISHOP];
754 attackUnits += BishopCheck * popcount<Max15>(b);
756 // Enemy knights safe checks
757 b = pos.attacks_from<KNIGHT>(ksq) & ei.attackedBy[Them][KNIGHT] & safe;
759 attackUnits += KnightCheck * popcount<Max15>(b);
761 // To index KingDanger[] attackUnits must be in [0, 99] range
762 attackUnits = std::min(99, std::max(0, attackUnits));
764 // Finally, extract the king danger score from the KingDanger[]
765 // array and subtract the score from evaluation. Set also margins[]
766 // value that will be used for pruning because this value can sometimes
767 // be very big, and so capturing a single attacking piece can therefore
768 // result in a score change far bigger than the value of the captured piece.
769 score -= KingDanger[Us == Search::RootColor][attackUnits];
770 margins[Us] += mg_value(KingDanger[Us == Search::RootColor][attackUnits]) / 2;
774 Tracing::scores[Us][KING] = score;
780 // evaluate_passed_pawns<>() evaluates the passed pawns of the given color
782 template<Color Us, bool Trace>
783 Score evaluate_passed_pawns(const Position& pos, EvalInfo& ei) {
785 const Color Them = (Us == WHITE ? BLACK : WHITE);
787 Bitboard b, squaresToQueen, defendedSquares, unsafeSquares, supportingPawns;
788 Score score = SCORE_ZERO;
790 b = ei.pi->passed_pawns(Us);
794 Square s = pop_lsb(&b);
796 assert(pos.pawn_is_passed(Us, s));
798 int r = int(relative_rank(Us, s) - RANK_2);
799 int rr = r * (r - 1);
801 // Base bonus based on rank
802 Value mbonus = Value(17 * rr);
803 Value ebonus = Value(7 * (rr + r + 1));
807 Square blockSq = s + pawn_push(Us);
809 // Adjust bonus based on kings proximity
810 ebonus += Value(square_distance(pos.king_square(Them), blockSq) * 5 * rr);
811 ebonus -= Value(square_distance(pos.king_square(Us), blockSq) * 2 * rr);
813 // If blockSq is not the queening square then consider also a second push
814 if (rank_of(blockSq) != (Us == WHITE ? RANK_8 : RANK_1))
815 ebonus -= Value(square_distance(pos.king_square(Us), blockSq + pawn_push(Us)) * rr);
817 // If the pawn is free to advance, increase bonus
818 if (pos.is_empty(blockSq))
820 squaresToQueen = forward_bb(Us, s);
821 defendedSquares = squaresToQueen & ei.attackedBy[Us][ALL_PIECES];
823 // If there is an enemy rook or queen attacking the pawn from behind,
824 // add all X-ray attacks by the rook or queen. Otherwise consider only
825 // the squares in the pawn's path attacked or occupied by the enemy.
826 if ( unlikely(forward_bb(Them, s) & pos.pieces(Them, ROOK, QUEEN))
827 && (forward_bb(Them, s) & pos.pieces(Them, ROOK, QUEEN) & pos.attacks_from<ROOK>(s)))
828 unsafeSquares = squaresToQueen;
830 unsafeSquares = squaresToQueen & (ei.attackedBy[Them][ALL_PIECES] | pos.pieces(Them));
832 // If there aren't enemy attacks huge bonus, a bit smaller if at
833 // least block square is not attacked, otherwise smallest bonus.
834 int k = !unsafeSquares ? 15 : !(unsafeSquares & blockSq) ? 9 : 3;
836 // Big bonus if the path to queen is fully defended, a bit less
837 // if at least block square is defended.
838 if (defendedSquares == squaresToQueen)
841 else if (defendedSquares & blockSq)
842 k += (unsafeSquares & defendedSquares) == unsafeSquares ? 4 : 2;
844 mbonus += Value(k * rr), ebonus += Value(k * rr);
848 // Increase the bonus if the passed pawn is supported by a friendly pawn
849 // on the same rank and a bit smaller if it's on the previous rank.
850 supportingPawns = pos.pieces(Us, PAWN) & adjacent_files_bb(file_of(s));
851 if (supportingPawns & rank_bb(s))
852 ebonus += Value(r * 20);
854 else if (supportingPawns & rank_bb(s - pawn_push(Us)))
855 ebonus += Value(r * 12);
857 // Rook pawns are a special case: They are sometimes worse, and
858 // sometimes better than other passed pawns. It is difficult to find
859 // good rules for determining whether they are good or bad. For now,
860 // we try the following: Increase the value for rook pawns if the
861 // other side has no pieces apart from a knight, and decrease the
862 // value if the other side has a rook or queen.
863 if (file_of(s) == FILE_A || file_of(s) == FILE_H)
865 if (pos.non_pawn_material(Them) <= KnightValueMg)
866 ebonus += ebonus / 4;
867 else if (pos.pieces(Them, ROOK, QUEEN))
868 ebonus -= ebonus / 4;
870 score += make_score(mbonus, ebonus);
875 Tracing::scores[Us][PASSED] = apply_weight(score, Weights[PassedPawns]);
877 // Add the scores to the middle game and endgame eval
878 return apply_weight(score, Weights[PassedPawns]);
882 // evaluate_unstoppable_pawns() evaluates the unstoppable passed pawns for both sides, this is quite
883 // conservative and returns a winning score only when we are very sure that the pawn is winning.
885 Score evaluate_unstoppable_pawns(const Position& pos, EvalInfo& ei) {
887 Bitboard b, b2, blockers, supporters, queeningPath, candidates;
888 Square s, blockSq, queeningSquare;
889 Color c, winnerSide, loserSide;
890 bool pathDefended, opposed;
891 int pliesToGo, movesToGo, oppMovesToGo, sacptg, blockersCount, minKingDist, kingptg, d;
892 int pliesToQueen[] = { 256, 256 };
894 // Step 1. Hunt for unstoppable passed pawns. If we find at least one,
895 // record how many plies are required for promotion.
896 for (c = WHITE; c <= BLACK; c++)
898 // Skip if other side has non-pawn pieces
899 if (pos.non_pawn_material(~c))
902 b = ei.pi->passed_pawns(c);
907 queeningSquare = relative_square(c, file_of(s) | RANK_8);
908 queeningPath = forward_bb(c, s);
910 // Compute plies to queening and check direct advancement
911 movesToGo = rank_distance(s, queeningSquare) - int(relative_rank(c, s) == RANK_2);
912 oppMovesToGo = square_distance(pos.king_square(~c), queeningSquare) - int(c != pos.side_to_move());
913 pathDefended = ((ei.attackedBy[c][ALL_PIECES] & queeningPath) == queeningPath);
915 if (movesToGo >= oppMovesToGo && !pathDefended)
918 // Opponent king cannot block because path is defended and position
919 // is not in check. So only friendly pieces can be blockers.
920 assert(!pos.checkers());
921 assert((queeningPath & pos.pieces()) == (queeningPath & pos.pieces(c)));
923 // Add moves needed to free the path from friendly pieces and retest condition
924 movesToGo += popcount<Max15>(queeningPath & pos.pieces(c));
926 if (movesToGo >= oppMovesToGo && !pathDefended)
929 pliesToGo = 2 * movesToGo - int(c == pos.side_to_move());
930 pliesToQueen[c] = std::min(pliesToQueen[c], pliesToGo);
934 // Step 2. If either side cannot promote at least three plies before the other side then situation
935 // becomes too complex and we give up. Otherwise we determine the possibly "winning side"
936 if (abs(pliesToQueen[WHITE] - pliesToQueen[BLACK]) < 3)
939 winnerSide = (pliesToQueen[WHITE] < pliesToQueen[BLACK] ? WHITE : BLACK);
940 loserSide = ~winnerSide;
942 // Step 3. Can the losing side possibly create a new passed pawn and thus prevent the loss?
943 b = candidates = pos.pieces(loserSide, PAWN);
949 // Compute plies from queening
950 queeningSquare = relative_square(loserSide, file_of(s) | RANK_8);
951 movesToGo = rank_distance(s, queeningSquare) - int(relative_rank(loserSide, s) == RANK_2);
952 pliesToGo = 2 * movesToGo - int(loserSide == pos.side_to_move());
954 // Check if (without even considering any obstacles) we're too far away or doubled
955 if ( pliesToQueen[winnerSide] + 3 <= pliesToGo
956 || (forward_bb(loserSide, s) & pos.pieces(loserSide, PAWN)))
960 // If any candidate is already a passed pawn it _may_ promote in time. We give up.
961 if (candidates & ei.pi->passed_pawns(loserSide))
964 // Step 4. Check new passed pawn creation through king capturing and pawn sacrifices
970 sacptg = blockersCount = 0;
971 minKingDist = kingptg = 256;
973 // Compute plies from queening
974 queeningSquare = relative_square(loserSide, file_of(s) | RANK_8);
975 movesToGo = rank_distance(s, queeningSquare) - int(relative_rank(loserSide, s) == RANK_2);
976 pliesToGo = 2 * movesToGo - int(loserSide == pos.side_to_move());
978 // Generate list of blocking pawns and supporters
979 supporters = adjacent_files_bb(file_of(s)) & candidates;
980 opposed = forward_bb(loserSide, s) & pos.pieces(winnerSide, PAWN);
981 blockers = passed_pawn_mask(loserSide, s) & pos.pieces(winnerSide, PAWN);
985 // How many plies does it take to remove all the blocking pawns?
988 blockSq = pop_lsb(&blockers);
991 // Check pawns that can give support to overcome obstacle, for instance
992 // black pawns: a4, b4 white: b2 then pawn in b4 is giving support.
995 b2 = supporters & in_front_bb(winnerSide, rank_of(blockSq + pawn_push(winnerSide)));
997 while (b2) // This while-loop could be replaced with LSB/MSB (depending on color)
999 d = square_distance(blockSq, pop_lsb(&b2)) - 2;
1000 movesToGo = std::min(movesToGo, d);
1004 // Check pawns that can be sacrificed against the blocking pawn
1005 b2 = pawn_attack_span(winnerSide, blockSq) & candidates & ~(1ULL << s);
1007 while (b2) // This while-loop could be replaced with LSB/MSB (depending on color)
1009 d = square_distance(blockSq, pop_lsb(&b2)) - 2;
1010 movesToGo = std::min(movesToGo, d);
1013 // If obstacle can be destroyed with an immediate pawn exchange / sacrifice,
1014 // it's not a real obstacle and we have nothing to add to pliesToGo.
1018 // Plies needed to sacrifice against all the blocking pawns
1019 sacptg += movesToGo * 2;
1022 // Plies needed for the king to capture all the blocking pawns
1023 d = square_distance(pos.king_square(loserSide), blockSq);
1024 minKingDist = std::min(minKingDist, d);
1025 kingptg = (minKingDist + blockersCount) * 2;
1028 // Check if pawn sacrifice plan _may_ save the day
1029 if (pliesToQueen[winnerSide] + 3 > pliesToGo + sacptg)
1032 // Check if king capture plan _may_ save the day (contains some false positives)
1033 if (pliesToQueen[winnerSide] + 3 > pliesToGo + kingptg)
1037 // Winning pawn is unstoppable and will promote as first, return big score
1038 Score score = make_score(0, (Value) 1280 - 32 * pliesToQueen[winnerSide]);
1039 return winnerSide == WHITE ? score : -score;
1043 // evaluate_space() computes the space evaluation for a given side. The
1044 // space evaluation is a simple bonus based on the number of safe squares
1045 // available for minor pieces on the central four files on ranks 2--4. Safe
1046 // squares one, two or three squares behind a friendly pawn are counted
1047 // twice. Finally, the space bonus is scaled by a weight taken from the
1048 // material hash table. The aim is to improve play on game opening.
1050 int evaluate_space(const Position& pos, EvalInfo& ei) {
1052 const Color Them = (Us == WHITE ? BLACK : WHITE);
1054 // Find the safe squares for our pieces inside the area defined by
1055 // SpaceMask[]. A square is unsafe if it is attacked by an enemy
1056 // pawn, or if it is undefended and attacked by an enemy piece.
1057 Bitboard safe = SpaceMask[Us]
1058 & ~pos.pieces(Us, PAWN)
1059 & ~ei.attackedBy[Them][PAWN]
1060 & (ei.attackedBy[Us][ALL_PIECES] | ~ei.attackedBy[Them][ALL_PIECES]);
1062 // Find all squares which are at most three squares behind some friendly pawn
1063 Bitboard behind = pos.pieces(Us, PAWN);
1064 behind |= (Us == WHITE ? behind >> 8 : behind << 8);
1065 behind |= (Us == WHITE ? behind >> 16 : behind << 16);
1067 // Since SpaceMask[Us] is fully on our half of the board
1068 assert(unsigned(safe >> (Us == WHITE ? 32 : 0)) == 0);
1070 // Count safe + (behind & safe) with a single popcount
1071 return popcount<Full>((Us == WHITE ? safe << 32 : safe >> 32) | (behind & safe));
1075 // interpolate() interpolates between a middle game and an endgame score,
1076 // based on game phase. It also scales the return value by a ScaleFactor array.
1078 Value interpolate(const Score& v, Phase ph, ScaleFactor sf) {
1080 assert(mg_value(v) > -VALUE_INFINITE && mg_value(v) < VALUE_INFINITE);
1081 assert(eg_value(v) > -VALUE_INFINITE && eg_value(v) < VALUE_INFINITE);
1082 assert(ph >= PHASE_ENDGAME && ph <= PHASE_MIDGAME);
1084 int ev = (eg_value(v) * int(sf)) / SCALE_FACTOR_NORMAL;
1085 int result = (mg_value(v) * int(ph) + ev * int(128 - ph)) / 128;
1086 return Value((result + GrainSize / 2) & ~(GrainSize - 1));
1089 // apply_weight() weights score v by score w trying to prevent overflow
1090 Score apply_weight(Score v, Score w) {
1091 return make_score((int(mg_value(v)) * mg_value(w)) / 0x100,
1092 (int(eg_value(v)) * eg_value(w)) / 0x100);
1095 // weight_option() computes the value of an evaluation weight, by combining
1096 // two UCI-configurable weights (midgame and endgame) with an internal weight.
1098 Score weight_option(const std::string& mgOpt, const std::string& egOpt, Score internalWeight) {
1100 // Scale option value from 100 to 256
1101 int mg = Options[mgOpt] * 256 / 100;
1102 int eg = Options[egOpt] * 256 / 100;
1104 return apply_weight(make_score(mg, eg), internalWeight);
1108 // Tracing functions definitions
1110 double to_cp(Value v) { return double(v) / double(PawnValueMg); }
1112 void Tracing::add(int idx, Score wScore, Score bScore) {
1114 scores[WHITE][idx] = wScore;
1115 scores[BLACK][idx] = bScore;
1118 void Tracing::row(const char* name, int idx) {
1120 Score wScore = scores[WHITE][idx];
1121 Score bScore = scores[BLACK][idx];
1124 case PST: case IMBALANCE: case PAWN: case UNSTOPPABLE: case TOTAL:
1125 stream << std::setw(20) << name << " | --- --- | --- --- | "
1126 << std::setw(6) << to_cp(mg_value(wScore)) << " "
1127 << std::setw(6) << to_cp(eg_value(wScore)) << " \n";
1130 stream << std::setw(20) << name << " | " << std::noshowpos
1131 << std::setw(5) << to_cp(mg_value(wScore)) << " "
1132 << std::setw(5) << to_cp(eg_value(wScore)) << " | "
1133 << std::setw(5) << to_cp(mg_value(bScore)) << " "
1134 << std::setw(5) << to_cp(eg_value(bScore)) << " | "
1136 << std::setw(6) << to_cp(mg_value(wScore - bScore)) << " "
1137 << std::setw(6) << to_cp(eg_value(wScore - bScore)) << " \n";
1141 std::string Tracing::do_trace(const Position& pos) {
1143 Search::RootColor = pos.side_to_move();
1146 stream << std::showpoint << std::showpos << std::fixed << std::setprecision(2);
1147 std::memset(scores, 0, 2 * (TOTAL + 1) * sizeof(Score));
1150 do_evaluate<true>(pos, margin);
1152 std::string totals = stream.str();
1155 stream << std::setw(21) << "Eval term " << "| White | Black | Total \n"
1156 << " | MG EG | MG EG | MG EG \n"
1157 << "---------------------+-------------+-------------+---------------\n";
1159 row("Material, PST, Tempo", PST);
1160 row("Material imbalance", IMBALANCE);
1162 row("Knights", KNIGHT);
1163 row("Bishops", BISHOP);
1165 row("Queens", QUEEN);
1166 row("Mobility", MOBILITY);
1167 row("King safety", KING);
1168 row("Threats", THREAT);
1169 row("Passed pawns", PASSED);
1170 row("Unstoppable pawns", UNSTOPPABLE);
1171 row("Space", SPACE);
1173 stream << "---------------------+-------------+-------------+---------------\n";
1174 row("Total", TOTAL);
1177 return stream.str();