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    1 /*
    2   Stockfish, a UCI chess playing engine derived from Glaurung 2.1
    3   Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
    4   Copyright (C) 2008-2015 Marco Costalba, Joona Kiiski, Tord Romstad
    5   Copyright (C) 2015-2020 Marco Costalba, Joona Kiiski, Gary Linscott, Tord Romstad
    6 
    7   Stockfish is free software: you can redistribute it and/or modify
    8   it under the terms of the GNU General Public License as published by
    9   the Free Software Foundation, either version 3 of the License, or
   10   (at your option) any later version.
   11 
   12   Stockfish is distributed in the hope that it will be useful,
   13   but WITHOUT ANY WARRANTY; without even the implied warranty of
   14   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   15   GNU General Public License for more details.
   16 
   17   You should have received a copy of the GNU General Public License
   18   along with this program.  If not, see <http://www.gnu.org/licenses/>.
   19 */
   20 
   21 #include <cassert>
   22 
   23 #include "bitboard.h"
   24 #include "endgame.h"
   25 #include "movegen.h"
   26 
   27 using std::string;
   28 
   29 namespace {
   30 
   31   // Table used to drive the king towards the edge of the board
   32   // in KX vs K and KQ vs KR endgames.
   33   constexpr int PushToEdges[SQUARE_NB] = {
   34     100, 90, 80, 70, 70, 80, 90, 100,
   35      90, 70, 60, 50, 50, 60, 70,  90,
   36      80, 60, 40, 30, 30, 40, 60,  80,
   37      70, 50, 30, 20, 20, 30, 50,  70,
   38      70, 50, 30, 20, 20, 30, 50,  70,
   39      80, 60, 40, 30, 30, 40, 60,  80,
   40      90, 70, 60, 50, 50, 60, 70,  90,
   41     100, 90, 80, 70, 70, 80, 90, 100
   42   };
   43 
   44   // Table used to drive the king towards a corner square of the
   45   // right color in KBN vs K endgames.
   46   constexpr int PushToCorners[SQUARE_NB] = {
   47      6400, 6080, 5760, 5440, 5120, 4800, 4480, 4160,
   48      6080, 5760, 5440, 5120, 4800, 4480, 4160, 4480,
   49      5760, 5440, 4960, 4480, 4480, 4000, 4480, 4800,
   50      5440, 5120, 4480, 3840, 3520, 4480, 4800, 5120,
   51      5120, 4800, 4480, 3520, 3840, 4480, 5120, 5440,
   52      4800, 4480, 4000, 4480, 4480, 4960, 5440, 5760,
   53      4480, 4160, 4480, 4800, 5120, 5440, 5760, 6080,
   54      4160, 4480, 4800, 5120, 5440, 5760, 6080, 6400
   55   };
   56 
   57   // Tables used to drive a piece towards or away from another piece
   58   constexpr int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
   59   constexpr int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };
   60 
   61   // Pawn Rank based scaling factors used in KRPPKRP endgame
   62   constexpr int KRPPKRPScaleFactors[RANK_NB] = { 0, 9, 10, 14, 21, 44, 0, 0 };
   63 
   64 #ifndef NDEBUG
   65   bool verify_material(const Position& pos, Color c, Value npm, int pawnsCnt) {
   66     return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;
   67   }
   68 #endif
   69 
   70   // Map the square as if strongSide is white and strongSide's only pawn
   71   // is on the left half of the board.
   72   Square normalize(const Position& pos, Color strongSide, Square sq) {
   73 
   74     assert(pos.count<PAWN>(strongSide) == 1);
   75 
   76     if (file_of(pos.square<PAWN>(strongSide)) >= FILE_E)
   77         sq = Square(int(sq) ^ 7); // Mirror SQ_H1 -> SQ_A1
   78 
   79     return strongSide == WHITE ? sq : ~sq;
   80   }
   81 
   82 } // namespace
   83 
   84 
   85 namespace Endgames {
   86 
   87   std::pair<Map<Value>, Map<ScaleFactor>> maps;
   88 
   89   void init() {
   90 
   91     add<KPK>("KPK");
   92     add<KNNK>("KNNK");
   93     add<KBNK>("KBNK");
   94     add<KRKP>("KRKP");
   95     add<KRKB>("KRKB");
   96     add<KRKN>("KRKN");
   97     add<KQKP>("KQKP");
   98     add<KQKR>("KQKR");
   99     add<KNNKP>("KNNKP");
  100 
  101     add<KNPK>("KNPK");
  102     add<KNPKB>("KNPKB");
  103     add<KRPKR>("KRPKR");
  104     add<KRPKB>("KRPKB");
  105     add<KBPKB>("KBPKB");
  106     add<KBPKN>("KBPKN");
  107     add<KBPPKB>("KBPPKB");
  108     add<KRPPKRP>("KRPPKRP");
  109   }
  110 }
  111 
  112 
  113 /// Mate with KX vs K. This function is used to evaluate positions with
  114 /// king and plenty of material vs a lone king. It simply gives the
  115 /// attacking side a bonus for driving the defending king towards the edge
  116 /// of the board, and for keeping the distance between the two kings small.
  117 template<>
  118 Value Endgame<KXK>::operator()(const Position& pos) const {
  119 
  120   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  121   assert(!pos.checkers()); // Eval is never called when in check
  122 
  123   // Stalemate detection with lone king
  124   if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
  125       return VALUE_DRAW;
  126 
  127   Square winnerKSq = pos.square<KING>(strongSide);
  128   Square loserKSq = pos.square<KING>(weakSide);
  129 
  130   Value result =  pos.non_pawn_material(strongSide)
  131                 + pos.count<PAWN>(strongSide) * PawnValueEg
  132                 + PushToEdges[loserKSq]
  133                 + PushClose[distance(winnerKSq, loserKSq)];
  134 
  135   if (   pos.count<QUEEN>(strongSide)
  136       || pos.count<ROOK>(strongSide)
  137       ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
  138       || (   (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
  139           && (pos.pieces(strongSide, BISHOP) &  DarkSquares)))
  140       result = std::min(result + VALUE_KNOWN_WIN, VALUE_MATE_IN_MAX_PLY - 1);
  141 
  142   return strongSide == pos.side_to_move() ? result : -result;
  143 }
  144 
  145 
  146 /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
  147 /// defending king towards a corner square that our bishop attacks.
  148 template<>
  149 Value Endgame<KBNK>::operator()(const Position& pos) const {
  150 
  151   assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
  152   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  153 
  154   Square winnerKSq = pos.square<KING>(strongSide);
  155   Square loserKSq = pos.square<KING>(weakSide);
  156   Square bishopSq = pos.square<BISHOP>(strongSide);
  157 
  158   // If our bishop does not attack A1/H8, we flip the enemy king square
  159   // to drive to opposite corners (A8/H1).
  160 
  161   Value result =  VALUE_KNOWN_WIN
  162                 + PushClose[distance(winnerKSq, loserKSq)]
  163                 + PushToCorners[opposite_colors(bishopSq, SQ_A1) ? ~loserKSq : loserKSq];
  164 
  165   assert(abs(result) < VALUE_MATE_IN_MAX_PLY);
  166   return strongSide == pos.side_to_move() ? result : -result;
  167 }
  168 
  169 
  170 /// KP vs K. This endgame is evaluated with the help of a bitbase
  171 template<>
  172 Value Endgame<KPK>::operator()(const Position& pos) const {
  173 
  174   assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
  175   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  176 
  177   // Assume strongSide is white and the pawn is on files A-D
  178   Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
  179   Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  180   Square psq  = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  181 
  182   Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
  183 
  184   if (!Bitbases::probe(wksq, psq, bksq, us))
  185       return VALUE_DRAW;
  186 
  187   Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
  188 
  189   return strongSide == pos.side_to_move() ? result : -result;
  190 }
  191 
  192 
  193 /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
  194 /// a bitbase. The function below returns drawish scores when the pawn is
  195 /// far advanced with support of the king, while the attacking king is far
  196 /// away.
  197 template<>
  198 Value Endgame<KRKP>::operator()(const Position& pos) const {
  199 
  200   assert(verify_material(pos, strongSide, RookValueMg, 0));
  201   assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
  202 
  203   Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
  204   Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
  205   Square rsq  = relative_square(strongSide, pos.square<ROOK>(strongSide));
  206   Square psq  = relative_square(strongSide, pos.square<PAWN>(weakSide));
  207 
  208   Square queeningSq = make_square(file_of(psq), RANK_1);
  209   Value result;
  210 
  211   // If the stronger side's king is in front of the pawn, it's a win
  212   if (forward_file_bb(WHITE, wksq) & psq)
  213       result = RookValueEg - distance(wksq, psq);
  214 
  215   // If the weaker side's king is too far from the pawn and the rook,
  216   // it's a win.
  217   else if (   distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
  218            && distance(bksq, rsq) >= 3)
  219       result = RookValueEg - distance(wksq, psq);
  220 
  221   // If the pawn is far advanced and supported by the defending king,
  222   // the position is drawish
  223   else if (   rank_of(bksq) <= RANK_3
  224            && distance(bksq, psq) == 1
  225            && rank_of(wksq) >= RANK_4
  226            && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
  227       result = Value(80) - 8 * distance(wksq, psq);
  228 
  229   else
  230       result =  Value(200) - 8 * (  distance(wksq, psq + SOUTH)
  231                                   - distance(bksq, psq + SOUTH)
  232                                   - distance(psq, queeningSq));
  233 
  234   return strongSide == pos.side_to_move() ? result : -result;
  235 }
  236 
  237 
  238 /// KR vs KB. This is very simple, and always returns drawish scores. The
  239 /// score is slightly bigger when the defending king is close to the edge.
  240 template<>
  241 Value Endgame<KRKB>::operator()(const Position& pos) const {
  242 
  243   assert(verify_material(pos, strongSide, RookValueMg, 0));
  244   assert(verify_material(pos, weakSide, BishopValueMg, 0));
  245 
  246   Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
  247   return strongSide == pos.side_to_move() ? result : -result;
  248 }
  249 
  250 
  251 /// KR vs KN. The attacking side has slightly better winning chances than
  252 /// in KR vs KB, particularly if the king and the knight are far apart.
  253 template<>
  254 Value Endgame<KRKN>::operator()(const Position& pos) const {
  255 
  256   assert(verify_material(pos, strongSide, RookValueMg, 0));
  257   assert(verify_material(pos, weakSide, KnightValueMg, 0));
  258 
  259   Square bksq = pos.square<KING>(weakSide);
  260   Square bnsq = pos.square<KNIGHT>(weakSide);
  261   Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
  262   return strongSide == pos.side_to_move() ? result : -result;
  263 }
  264 
  265 
  266 /// KQ vs KP. In general, this is a win for the stronger side, but there are a
  267 /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
  268 /// with a king positioned next to it can be a draw, so in that case, we only
  269 /// use the distance between the kings.
  270 template<>
  271 Value Endgame<KQKP>::operator()(const Position& pos) const {
  272 
  273   assert(verify_material(pos, strongSide, QueenValueMg, 0));
  274   assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
  275 
  276   Square winnerKSq = pos.square<KING>(strongSide);
  277   Square loserKSq = pos.square<KING>(weakSide);
  278   Square pawnSq = pos.square<PAWN>(weakSide);
  279 
  280   Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
  281 
  282   if (   relative_rank(weakSide, pawnSq) != RANK_7
  283       || distance(loserKSq, pawnSq) != 1
  284       || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
  285       result += QueenValueEg - PawnValueEg;
  286 
  287   return strongSide == pos.side_to_move() ? result : -result;
  288 }
  289 
  290 
  291 /// KQ vs KR.  This is almost identical to KX vs K:  We give the attacking
  292 /// king a bonus for having the kings close together, and for forcing the
  293 /// defending king towards the edge. If we also take care to avoid null move for
  294 /// the defending side in the search, this is usually sufficient to win KQ vs KR.
  295 template<>
  296 Value Endgame<KQKR>::operator()(const Position& pos) const {
  297 
  298   assert(verify_material(pos, strongSide, QueenValueMg, 0));
  299   assert(verify_material(pos, weakSide, RookValueMg, 0));
  300 
  301   Square winnerKSq = pos.square<KING>(strongSide);
  302   Square loserKSq = pos.square<KING>(weakSide);
  303 
  304   Value result =  QueenValueEg
  305                 - RookValueEg
  306                 + PushToEdges[loserKSq]
  307                 + PushClose[distance(winnerKSq, loserKSq)];
  308 
  309   return strongSide == pos.side_to_move() ? result : -result;
  310 }
  311 
  312 
  313 /// KNN vs KP. Simply push the opposing king to the corner
  314 template<>
  315 Value Endgame<KNNKP>::operator()(const Position& pos) const {
  316 
  317   assert(verify_material(pos, strongSide, 2 * KnightValueMg, 0));
  318   assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
  319 
  320   Value result =  2 * KnightValueEg
  321                 - PawnValueEg
  322                 + PushToEdges[pos.square<KING>(weakSide)];
  323 
  324   return strongSide == pos.side_to_move() ? result : -result;
  325 }
  326 
  327 
  328 /// Some cases of trivial draws
  329 template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
  330 
  331 
  332 /// KB and one or more pawns vs K. It checks for draws with rook pawns and
  333 /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
  334 /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
  335 /// will be used.
  336 template<>
  337 ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
  338 
  339   assert(pos.non_pawn_material(strongSide) == BishopValueMg);
  340   assert(pos.count<PAWN>(strongSide) >= 1);
  341 
  342   // No assertions about the material of weakSide, because we want draws to
  343   // be detected even when the weaker side has some pawns.
  344 
  345   Bitboard pawns = pos.pieces(strongSide, PAWN);
  346   File pawnsFile = file_of(lsb(pawns));
  347 
  348   // All pawns are on a single rook file?
  349   if (    (pawnsFile == FILE_A || pawnsFile == FILE_H)
  350       && !(pawns & ~file_bb(pawnsFile)))
  351   {
  352       Square bishopSq = pos.square<BISHOP>(strongSide);
  353       Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
  354       Square kingSq = pos.square<KING>(weakSide);
  355 
  356       if (   opposite_colors(queeningSq, bishopSq)
  357           && distance(queeningSq, kingSq) <= 1)
  358           return SCALE_FACTOR_DRAW;
  359   }
  360 
  361   // If all the pawns are on the same B or G file, then it's potentially a draw
  362   if (    (pawnsFile == FILE_B || pawnsFile == FILE_G)
  363       && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
  364       && pos.non_pawn_material(weakSide) == 0
  365       && pos.count<PAWN>(weakSide) >= 1)
  366   {
  367       // Get weakSide pawn that is closest to the home rank
  368       Square weakPawnSq = frontmost_sq(strongSide, pos.pieces(weakSide, PAWN));
  369 
  370       Square strongKingSq = pos.square<KING>(strongSide);
  371       Square weakKingSq = pos.square<KING>(weakSide);
  372       Square bishopSq = pos.square<BISHOP>(strongSide);
  373 
  374       // There's potential for a draw if our pawn is blocked on the 7th rank,
  375       // the bishop cannot attack it or they only have one pawn left
  376       if (   relative_rank(strongSide, weakPawnSq) == RANK_7
  377           && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
  378           && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
  379       {
  380           int strongKingDist = distance(weakPawnSq, strongKingSq);
  381           int weakKingDist = distance(weakPawnSq, weakKingSq);
  382 
  383           // It's a draw if the weak king is on its back two ranks, within 2
  384           // squares of the blocking pawn and the strong king is not
  385           // closer. (I think this rule only fails in practically
  386           // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
  387           // and positions where qsearch will immediately correct the
  388           // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
  389           if (   relative_rank(strongSide, weakKingSq) >= RANK_7
  390               && weakKingDist <= 2
  391               && weakKingDist <= strongKingDist)
  392               return SCALE_FACTOR_DRAW;
  393       }
  394   }
  395 
  396   return SCALE_FACTOR_NONE;
  397 }
  398 
  399 
  400 /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
  401 /// the third rank defended by a pawn.
  402 template<>
  403 ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
  404 
  405   assert(verify_material(pos, strongSide, QueenValueMg, 0));
  406   assert(pos.count<ROOK>(weakSide) == 1);
  407   assert(pos.count<PAWN>(weakSide) >= 1);
  408 
  409   Square kingSq = pos.square<KING>(weakSide);
  410   Square rsq = pos.square<ROOK>(weakSide);
  411 
  412   if (    relative_rank(weakSide, kingSq) <= RANK_2
  413       &&  relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
  414       &&  relative_rank(weakSide, rsq) == RANK_3
  415       && (  pos.pieces(weakSide, PAWN)
  416           & pos.attacks_from<KING>(kingSq)
  417           & pos.attacks_from<PAWN>(rsq, strongSide)))
  418           return SCALE_FACTOR_DRAW;
  419 
  420   return SCALE_FACTOR_NONE;
  421 }
  422 
  423 
  424 /// KRP vs KR. This function knows a handful of the most important classes of
  425 /// drawn positions, but is far from perfect. It would probably be a good idea
  426 /// to add more knowledge in the future.
  427 ///
  428 /// It would also be nice to rewrite the actual code for this function,
  429 /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
  430 template<>
  431 ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
  432 
  433   assert(verify_material(pos, strongSide, RookValueMg, 1));
  434   assert(verify_material(pos, weakSide,   RookValueMg, 0));
  435 
  436   // Assume strongSide is white and the pawn is on files A-D
  437   Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
  438   Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  439   Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
  440   Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  441   Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
  442 
  443   File f = file_of(wpsq);
  444   Rank r = rank_of(wpsq);
  445   Square queeningSq = make_square(f, RANK_8);
  446   int tempo = (pos.side_to_move() == strongSide);
  447 
  448   // If the pawn is not too far advanced and the defending king defends the
  449   // queening square, use the third-rank defence.
  450   if (   r <= RANK_5
  451       && distance(bksq, queeningSq) <= 1
  452       && wksq <= SQ_H5
  453       && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
  454       return SCALE_FACTOR_DRAW;
  455 
  456   // The defending side saves a draw by checking from behind in case the pawn
  457   // has advanced to the 6th rank with the king behind.
  458   if (   r == RANK_6
  459       && distance(bksq, queeningSq) <= 1
  460       && rank_of(wksq) + tempo <= RANK_6
  461       && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
  462       return SCALE_FACTOR_DRAW;
  463 
  464   if (   r >= RANK_6
  465       && bksq == queeningSq
  466       && rank_of(brsq) == RANK_1
  467       && (!tempo || distance(wksq, wpsq) >= 2))
  468       return SCALE_FACTOR_DRAW;
  469 
  470   // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
  471   // and the black rook is behind the pawn.
  472   if (   wpsq == SQ_A7
  473       && wrsq == SQ_A8
  474       && (bksq == SQ_H7 || bksq == SQ_G7)
  475       && file_of(brsq) == FILE_A
  476       && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
  477       return SCALE_FACTOR_DRAW;
  478 
  479   // If the defending king blocks the pawn and the attacking king is too far
  480   // away, it's a draw.
  481   if (   r <= RANK_5
  482       && bksq == wpsq + NORTH
  483       && distance(wksq, wpsq) - tempo >= 2
  484       && distance(wksq, brsq) - tempo >= 2)
  485       return SCALE_FACTOR_DRAW;
  486 
  487   // Pawn on the 7th rank supported by the rook from behind usually wins if the
  488   // attacking king is closer to the queening square than the defending king,
  489   // and the defending king cannot gain tempi by threatening the attacking rook.
  490   if (   r == RANK_7
  491       && f != FILE_A
  492       && file_of(wrsq) == f
  493       && wrsq != queeningSq
  494       && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
  495       && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
  496       return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
  497 
  498   // Similar to the above, but with the pawn further back
  499   if (   f != FILE_A
  500       && file_of(wrsq) == f
  501       && wrsq < wpsq
  502       && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
  503       && (distance(wksq, wpsq + NORTH) < distance(bksq, wpsq + NORTH) - 2 + tempo)
  504       && (  distance(bksq, wrsq) + tempo >= 3
  505           || (    distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
  506               && (distance(wksq, wpsq + NORTH) < distance(bksq, wrsq) + tempo))))
  507       return ScaleFactor(  SCALE_FACTOR_MAX
  508                          - 8 * distance(wpsq, queeningSq)
  509                          - 2 * distance(wksq, queeningSq));
  510 
  511   // If the pawn is not far advanced and the defending king is somewhere in
  512   // the pawn's path, it's probably a draw.
  513   if (r <= RANK_4 && bksq > wpsq)
  514   {
  515       if (file_of(bksq) == file_of(wpsq))
  516           return ScaleFactor(10);
  517       if (   distance<File>(bksq, wpsq) == 1
  518           && distance(wksq, bksq) > 2)
  519           return ScaleFactor(24 - 2 * distance(wksq, bksq));
  520   }
  521   return SCALE_FACTOR_NONE;
  522 }
  523 
  524 template<>
  525 ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
  526 
  527   assert(verify_material(pos, strongSide, RookValueMg, 1));
  528   assert(verify_material(pos, weakSide, BishopValueMg, 0));
  529 
  530   // Test for a rook pawn
  531   if (pos.pieces(PAWN) & (FileABB | FileHBB))
  532   {
  533       Square ksq = pos.square<KING>(weakSide);
  534       Square bsq = pos.square<BISHOP>(weakSide);
  535       Square psq = pos.square<PAWN>(strongSide);
  536       Rank rk = relative_rank(strongSide, psq);
  537       Direction push = pawn_push(strongSide);
  538 
  539       // If the pawn is on the 5th rank and the pawn (currently) is on
  540       // the same color square as the bishop then there is a chance of
  541       // a fortress. Depending on the king position give a moderate
  542       // reduction or a stronger one if the defending king is near the
  543       // corner but not trapped there.
  544       if (rk == RANK_5 && !opposite_colors(bsq, psq))
  545       {
  546           int d = distance(psq + 3 * push, ksq);
  547 
  548           if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
  549               return ScaleFactor(24);
  550           else
  551               return ScaleFactor(48);
  552       }
  553 
  554       // When the pawn has moved to the 6th rank we can be fairly sure
  555       // it's drawn if the bishop attacks the square in front of the
  556       // pawn from a reasonable distance and the defending king is near
  557       // the corner
  558       if (   rk == RANK_6
  559           && distance(psq + 2 * push, ksq) <= 1
  560           && (PseudoAttacks[BISHOP][bsq] & (psq + push))
  561           && distance<File>(bsq, psq) >= 2)
  562           return ScaleFactor(8);
  563   }
  564 
  565   return SCALE_FACTOR_NONE;
  566 }
  567 
  568 /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
  569 /// pawns and the defending king is actively placed, the position is drawish.
  570 template<>
  571 ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
  572 
  573   assert(verify_material(pos, strongSide, RookValueMg, 2));
  574   assert(verify_material(pos, weakSide,   RookValueMg, 1));
  575 
  576   Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
  577   Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
  578   Square bksq = pos.square<KING>(weakSide);
  579 
  580   // Does the stronger side have a passed pawn?
  581   if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
  582       return SCALE_FACTOR_NONE;
  583 
  584   Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
  585 
  586   if (   distance<File>(bksq, wpsq1) <= 1
  587       && distance<File>(bksq, wpsq2) <= 1
  588       && relative_rank(strongSide, bksq) > r)
  589   {
  590       assert(r > RANK_1 && r < RANK_7);
  591       return ScaleFactor(KRPPKRPScaleFactors[r]);
  592   }
  593   return SCALE_FACTOR_NONE;
  594 }
  595 
  596 
  597 /// K and two or more pawns vs K. There is just a single rule here: If all pawns
  598 /// are on the same rook file and are blocked by the defending king, it's a draw.
  599 template<>
  600 ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
  601 
  602   assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
  603   assert(pos.count<PAWN>(strongSide) >= 2);
  604   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  605 
  606   Square ksq = pos.square<KING>(weakSide);
  607   Bitboard pawns = pos.pieces(strongSide, PAWN);
  608 
  609   // If all pawns are ahead of the king, on a single rook file and
  610   // the king is within one file of the pawns, it's a draw.
  611   if (   !(pawns & ~forward_ranks_bb(weakSide, ksq))
  612       && !((pawns & ~FileABB) && (pawns & ~FileHBB))
  613       &&  distance<File>(ksq, lsb(pawns)) <= 1)
  614       return SCALE_FACTOR_DRAW;
  615 
  616   return SCALE_FACTOR_NONE;
  617 }
  618 
  619 
  620 /// KBP vs KB. There are two rules: if the defending king is somewhere along the
  621 /// path of the pawn, and the square of the king is not of the same color as the
  622 /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
  623 /// it's almost always a draw.
  624 template<>
  625 ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
  626 
  627   assert(verify_material(pos, strongSide, BishopValueMg, 1));
  628   assert(verify_material(pos, weakSide,   BishopValueMg, 0));
  629 
  630   Square pawnSq = pos.square<PAWN>(strongSide);
  631   Square strongBishopSq = pos.square<BISHOP>(strongSide);
  632   Square weakBishopSq = pos.square<BISHOP>(weakSide);
  633   Square weakKingSq = pos.square<KING>(weakSide);
  634 
  635   // Case 1: Defending king blocks the pawn, and cannot be driven away
  636   if (   file_of(weakKingSq) == file_of(pawnSq)
  637       && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
  638       && (   opposite_colors(weakKingSq, strongBishopSq)
  639           || relative_rank(strongSide, weakKingSq) <= RANK_6))
  640       return SCALE_FACTOR_DRAW;
  641 
  642   // Case 2: Opposite colored bishops
  643   if (opposite_colors(strongBishopSq, weakBishopSq))
  644       return SCALE_FACTOR_DRAW;
  645 
  646   return SCALE_FACTOR_NONE;
  647 }
  648 
  649 
  650 /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
  651 template<>
  652 ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
  653 
  654   assert(verify_material(pos, strongSide, BishopValueMg, 2));
  655   assert(verify_material(pos, weakSide,   BishopValueMg, 0));
  656 
  657   Square wbsq = pos.square<BISHOP>(strongSide);
  658   Square bbsq = pos.square<BISHOP>(weakSide);
  659 
  660   if (!opposite_colors(wbsq, bbsq))
  661       return SCALE_FACTOR_NONE;
  662 
  663   Square ksq = pos.square<KING>(weakSide);
  664   Square psq1 = pos.squares<PAWN>(strongSide)[0];
  665   Square psq2 = pos.squares<PAWN>(strongSide)[1];
  666   Square blockSq1, blockSq2;
  667 
  668   if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
  669   {
  670       blockSq1 = psq1 + pawn_push(strongSide);
  671       blockSq2 = make_square(file_of(psq2), rank_of(psq1));
  672   }
  673   else
  674   {
  675       blockSq1 = psq2 + pawn_push(strongSide);
  676       blockSq2 = make_square(file_of(psq1), rank_of(psq2));
  677   }
  678 
  679   switch (distance<File>(psq1, psq2))
  680   {
  681   case 0:
  682     // Both pawns are on the same file. It's an easy draw if the defender firmly
  683     // controls some square in the frontmost pawn's path.
  684     if (   file_of(ksq) == file_of(blockSq1)
  685         && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
  686         && opposite_colors(ksq, wbsq))
  687         return SCALE_FACTOR_DRAW;
  688     else
  689         return SCALE_FACTOR_NONE;
  690 
  691   case 1:
  692     // Pawns on adjacent files. It's a draw if the defender firmly controls the
  693     // square in front of the frontmost pawn's path, and the square diagonally
  694     // behind this square on the file of the other pawn.
  695     if (   ksq == blockSq1
  696         && opposite_colors(ksq, wbsq)
  697         && (   bbsq == blockSq2
  698             || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
  699             || distance<Rank>(psq1, psq2) >= 2))
  700         return SCALE_FACTOR_DRAW;
  701 
  702     else if (   ksq == blockSq2
  703              && opposite_colors(ksq, wbsq)
  704              && (   bbsq == blockSq1
  705                  || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
  706         return SCALE_FACTOR_DRAW;
  707     else
  708         return SCALE_FACTOR_NONE;
  709 
  710   default:
  711     // The pawns are not on the same file or adjacent files. No scaling.
  712     return SCALE_FACTOR_NONE;
  713   }
  714 }
  715 
  716 
  717 /// KBP vs KN. There is a single rule: If the defending king is somewhere along
  718 /// the path of the pawn, and the square of the king is not of the same color as
  719 /// the stronger side's bishop, it's a draw.
  720 template<>
  721 ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
  722 
  723   assert(verify_material(pos, strongSide, BishopValueMg, 1));
  724   assert(verify_material(pos, weakSide, KnightValueMg, 0));
  725 
  726   Square pawnSq = pos.square<PAWN>(strongSide);
  727   Square strongBishopSq = pos.square<BISHOP>(strongSide);
  728   Square weakKingSq = pos.square<KING>(weakSide);
  729 
  730   if (   file_of(weakKingSq) == file_of(pawnSq)
  731       && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
  732       && (   opposite_colors(weakKingSq, strongBishopSq)
  733           || relative_rank(strongSide, weakKingSq) <= RANK_6))
  734       return SCALE_FACTOR_DRAW;
  735 
  736   return SCALE_FACTOR_NONE;
  737 }
  738 
  739 
  740 /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
  741 /// and the defending king prevents the pawn from advancing, the position is drawn.
  742 template<>
  743 ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
  744 
  745   assert(verify_material(pos, strongSide, KnightValueMg, 1));
  746   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  747 
  748   // Assume strongSide is white and the pawn is on files A-D
  749   Square pawnSq     = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  750   Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  751 
  752   if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
  753       return SCALE_FACTOR_DRAW;
  754 
  755   return SCALE_FACTOR_NONE;
  756 }
  757 
  758 
  759 /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
  760 /// Otherwise the position is drawn.
  761 template<>
  762 ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
  763 
  764   assert(verify_material(pos, strongSide, KnightValueMg, 1));
  765   assert(verify_material(pos, weakSide, BishopValueMg, 0));
  766 
  767   Square pawnSq = pos.square<PAWN>(strongSide);
  768   Square bishopSq = pos.square<BISHOP>(weakSide);
  769   Square weakKingSq = pos.square<KING>(weakSide);
  770 
  771   // King needs to get close to promoting pawn to prevent knight from blocking.
  772   // Rules for this are very tricky, so just approximate.
  773   if (forward_file_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
  774       return ScaleFactor(distance(weakKingSq, pawnSq));
  775 
  776   return SCALE_FACTOR_NONE;
  777 }
  778 
  779 
  780 /// KP vs KP. This is done by removing the weakest side's pawn and probing the
  781 /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
  782 /// has at least a draw with the pawn as well. The exception is when the stronger
  783 /// side's pawn is far advanced and not on a rook file; in this case it is often
  784 /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
  785 template<>
  786 ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
  787 
  788   assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
  789   assert(verify_material(pos, weakSide,   VALUE_ZERO, 1));
  790 
  791   // Assume strongSide is white and the pawn is on files A-D
  792   Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
  793   Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  794   Square psq  = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  795 
  796   Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
  797 
  798   // If the pawn has advanced to the fifth rank or further, and is not a
  799   // rook pawn, it's too dangerous to assume that it's at least a draw.
  800   if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
  801       return SCALE_FACTOR_NONE;
  802 
  803   // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
  804   // it's probably at least a draw even with the pawn.
  805   return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;
  806 }