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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) 2015-2016 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 <algorithm>
  22. #include <cassert>
  23.  
  24. #include "bitboard.h"
  25. #include "bitcount.h"
  26. #include "endgame.h"
  27. #include "movegen.h"
  28.  
  29. using std::string;
  30.  
  31. namespace {
  32.  
  33.   // Table used to drive the king towards the edge of the board
  34.   // in KX vs K and KQ vs KR endgames.
  35.   const int PushToEdges[SQUARE_NB] = {
  36.     100, 90, 80, 70, 70, 80, 90, 100,
  37.      90, 70, 60, 50, 50, 60, 70,  90,
  38.      80, 60, 40, 30, 30, 40, 60,  80,
  39.      70, 50, 30, 20, 20, 30, 50,  70,
  40.      70, 50, 30, 20, 20, 30, 50,  70,
  41.      80, 60, 40, 30, 30, 40, 60,  80,
  42.      90, 70, 60, 50, 50, 60, 70,  90,
  43.     100, 90, 80, 70, 70, 80, 90, 100
  44.   };
  45.  
  46.   // Table used to drive the king towards a corner square of the
  47.   // right color in KBN vs K endgames.
  48.   const int PushToCorners[SQUARE_NB] = {
  49.     200, 190, 180, 170, 160, 150, 140, 130,
  50.     190, 180, 170, 160, 150, 140, 130, 140,
  51.     180, 170, 155, 140, 140, 125, 140, 150,
  52.     170, 160, 140, 120, 110, 140, 150, 160,
  53.     160, 150, 140, 110, 120, 140, 160, 170,
  54.     150, 140, 125, 140, 140, 155, 170, 180,
  55.     140, 130, 140, 150, 160, 170, 180, 190,
  56.     130, 140, 150, 160, 170, 180, 190, 200
  57.   };
  58.  
  59.   // Tables used to drive a piece towards or away from another piece
  60.   const int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
  61.   const int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };
  62.  
  63.   // Pawn Rank based scaling factors used in KRPPKRP endgame
  64.   const int KRPPKRPScaleFactors[RANK_NB] = { 0, 9, 10, 14, 21, 44, 0, 0 };
  65.  
  66. #ifndef NDEBUG
  67.   bool verify_material(const Position& pos, Color c, Value npm, int pawnsCnt) {
  68.     return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;
  69.   }
  70. #endif
  71.  
  72.   // Map the square as if strongSide is white and strongSide's only pawn
  73.   // is on the left half of the board.
  74.   Square normalize(const Position& pos, Color strongSide, Square sq) {
  75.  
  76.     assert(pos.count<PAWN>(strongSide) == 1);
  77.  
  78.     if (file_of(pos.square<PAWN>(strongSide)) >= FILE_E)
  79.         sq = Square(sq ^ 7); // Mirror SQ_H1 -> SQ_A1
  80.  
  81.     if (strongSide == BLACK)
  82.         sq = ~sq;
  83.  
  84.     return sq;
  85.   }
  86.  
  87.   // Get the material key of Position out of the given endgame key code
  88.   // like "KBPKN". The trick here is to first forge an ad-hoc FEN string
  89.   // and then let a Position object do the work for us.
  90.   Key key(const string& code, Color c) {
  91.  
  92.     assert(code.length() > 0 && code.length() < 8);
  93.     assert(code[0] == 'K');
  94.  
  95.     string sides[] = { code.substr(code.find('K', 1)),      // Weak
  96.                        code.substr(0, code.find('K', 1)) }; // Strong
  97.  
  98.     std::transform(sides[c].begin(), sides[c].end(), sides[c].begin(), tolower);
  99.  
  100.     string fen =  sides[0] + char(8 - sides[0].length() + '0') + "/8/8/8/8/8/8/"
  101.                 + sides[1] + char(8 - sides[1].length() + '0') + " w - - 0 10";
  102.  
  103.     return Position(fen, false, nullptr).material_key();
  104.   }
  105.  
  106. } // namespace
  107.  
  108.  
  109. /// Endgames members definitions
  110.  
  111. Endgames::Endgames() {
  112.  
  113.   add<KPK>("KPK");
  114.   add<KNNK>("KNNK");
  115.   add<KBNK>("KBNK");
  116.   add<KRKP>("KRKP");
  117.   add<KRKB>("KRKB");
  118.   add<KRKN>("KRKN");
  119.   add<KQKP>("KQKP");
  120.   add<KQKR>("KQKR");
  121.  
  122.   add<KNPK>("KNPK");
  123.   add<KNPKB>("KNPKB");
  124.   add<KRPKR>("KRPKR");
  125.   add<KRPKB>("KRPKB");
  126.   add<KBPKB>("KBPKB");
  127.   add<KBPKN>("KBPKN");
  128.   add<KBPPKB>("KBPPKB");
  129.   add<KRPPKRP>("KRPPKRP");
  130. }
  131.  
  132.  
  133. template<EndgameType E, typename T>
  134. void Endgames::add(const string& code) {
  135.   map<T>()[key(code, WHITE)] = std::unique_ptr<EndgameBase<T>>(new Endgame<E>(WHITE));
  136.   map<T>()[key(code, BLACK)] = std::unique_ptr<EndgameBase<T>>(new Endgame<E>(BLACK));
  137. }
  138.  
  139.  
  140. /// Mate with KX vs K. This function is used to evaluate positions with
  141. /// king and plenty of material vs a lone king. It simply gives the
  142. /// attacking side a bonus for driving the defending king towards the edge
  143. /// of the board, and for keeping the distance between the two kings small.
  144. template<>
  145. Value Endgame<KXK>::operator()(const Position& pos) const {
  146.  
  147.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  148.   assert(!pos.checkers()); // Eval is never called when in check
  149.  
  150.   // Stalemate detection with lone king
  151.   if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
  152.       return VALUE_DRAW;
  153.  
  154.   Square winnerKSq = pos.square<KING>(strongSide);
  155.   Square loserKSq = pos.square<KING>(weakSide);
  156.  
  157.   Value result =  pos.non_pawn_material(strongSide)
  158.                 + pos.count<PAWN>(strongSide) * PawnValueEg
  159.                 + PushToEdges[loserKSq]
  160.                 + PushClose[distance(winnerKSq, loserKSq)];
  161.  
  162.   if (   pos.count<QUEEN>(strongSide)
  163.       || pos.count<ROOK>(strongSide)
  164.       ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
  165.       ||(pos.count<BISHOP>(strongSide) > 1 && opposite_colors(pos.squares<BISHOP>(strongSide)[0],
  166.                                                               pos.squares<BISHOP>(strongSide)[1])))
  167.       result = std::min(result + VALUE_KNOWN_WIN, VALUE_MATE_IN_MAX_PLY - 1);
  168.  
  169.   return strongSide == pos.side_to_move() ? result : -result;
  170. }
  171.  
  172.  
  173. /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
  174. /// defending king towards a corner square of the right color.
  175. template<>
  176. Value Endgame<KBNK>::operator()(const Position& pos) const {
  177.  
  178.   assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
  179.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  180.  
  181.   Square winnerKSq = pos.square<KING>(strongSide);
  182.   Square loserKSq = pos.square<KING>(weakSide);
  183.   Square bishopSq = pos.square<BISHOP>(strongSide);
  184.  
  185.   // kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a
  186.   // bishop that cannot reach the above squares, we flip the kings in order
  187.   // to drive the enemy toward corners A8 or H1.
  188.   if (opposite_colors(bishopSq, SQ_A1))
  189.   {
  190.       winnerKSq = ~winnerKSq;
  191.       loserKSq  = ~loserKSq;
  192.   }
  193.  
  194.   Value result =  VALUE_KNOWN_WIN
  195.                 + PushClose[distance(winnerKSq, loserKSq)]
  196.                 + PushToCorners[loserKSq];
  197.  
  198.   return strongSide == pos.side_to_move() ? result : -result;
  199. }
  200.  
  201.  
  202. /// KP vs K. This endgame is evaluated with the help of a bitbase.
  203. template<>
  204. Value Endgame<KPK>::operator()(const Position& pos) const {
  205.  
  206.   assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
  207.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  208.  
  209.   // Assume strongSide is white and the pawn is on files A-D
  210.   Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
  211.   Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  212.   Square psq  = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  213.  
  214.   Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
  215.  
  216.   if (!Bitbases::probe(wksq, psq, bksq, us))
  217.       return VALUE_DRAW;
  218.  
  219.   Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));
  220.  
  221.   return strongSide == pos.side_to_move() ? result : -result;
  222. }
  223.  
  224.  
  225. /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
  226. /// a bitbase. The function below returns drawish scores when the pawn is
  227. /// far advanced with support of the king, while the attacking king is far
  228. /// away.
  229. template<>
  230. Value Endgame<KRKP>::operator()(const Position& pos) const {
  231.  
  232.   assert(verify_material(pos, strongSide, RookValueMg, 0));
  233.   assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
  234.  
  235.   Square wksq = relative_square(strongSide, pos.square<KING>(strongSide));
  236.   Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));
  237.   Square rsq  = relative_square(strongSide, pos.square<ROOK>(strongSide));
  238.   Square psq  = relative_square(strongSide, pos.square<PAWN>(weakSide));
  239.  
  240.   Square queeningSq = make_square(file_of(psq), RANK_1);
  241.   Value result;
  242.  
  243.   // If the stronger side's king is in front of the pawn, it's a win
  244.   if (wksq < psq && file_of(wksq) == file_of(psq))
  245.       result = RookValueEg - distance(wksq, psq);
  246.  
  247.   // If the weaker side's king is too far from the pawn and the rook,
  248.   // it's a win.
  249.   else if (   distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)
  250.            && distance(bksq, rsq) >= 3)
  251.       result = RookValueEg - distance(wksq, psq);
  252.  
  253.   // If the pawn is far advanced and supported by the defending king,
  254.   // the position is drawish
  255.   else if (   rank_of(bksq) <= RANK_3
  256.            && distance(bksq, psq) == 1
  257.            && rank_of(wksq) >= RANK_4
  258.            && distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))
  259.       result = Value(80) - 8 * distance(wksq, psq);
  260.  
  261.   else
  262.       result =  Value(200) - 8 * (  distance(wksq, psq + DELTA_S)
  263.                                   - distance(bksq, psq + DELTA_S)
  264.                                   - distance(psq, queeningSq));
  265.  
  266.   return strongSide == pos.side_to_move() ? result : -result;
  267. }
  268.  
  269.  
  270. /// KR vs KB. This is very simple, and always returns drawish scores.  The
  271. /// score is slightly bigger when the defending king is close to the edge.
  272. template<>
  273. Value Endgame<KRKB>::operator()(const Position& pos) const {
  274.  
  275.   assert(verify_material(pos, strongSide, RookValueMg, 0));
  276.   assert(verify_material(pos, weakSide, BishopValueMg, 0));
  277.  
  278.   Value result = Value(PushToEdges[pos.square<KING>(weakSide)]);
  279.   return strongSide == pos.side_to_move() ? result : -result;
  280. }
  281.  
  282.  
  283. /// KR vs KN. The attacking side has slightly better winning chances than
  284. /// in KR vs KB, particularly if the king and the knight are far apart.
  285. template<>
  286. Value Endgame<KRKN>::operator()(const Position& pos) const {
  287.  
  288.   assert(verify_material(pos, strongSide, RookValueMg, 0));
  289.   assert(verify_material(pos, weakSide, KnightValueMg, 0));
  290.  
  291.   Square bksq = pos.square<KING>(weakSide);
  292.   Square bnsq = pos.square<KNIGHT>(weakSide);
  293.   Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);
  294.   return strongSide == pos.side_to_move() ? result : -result;
  295. }
  296.  
  297.  
  298. /// KQ vs KP. In general, this is a win for the stronger side, but there are a
  299. /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
  300. /// with a king positioned next to it can be a draw, so in that case, we only
  301. /// use the distance between the kings.
  302. template<>
  303. Value Endgame<KQKP>::operator()(const Position& pos) const {
  304.  
  305.   assert(verify_material(pos, strongSide, QueenValueMg, 0));
  306.   assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
  307.  
  308.   Square winnerKSq = pos.square<KING>(strongSide);
  309.   Square loserKSq = pos.square<KING>(weakSide);
  310.   Square pawnSq = pos.square<PAWN>(weakSide);
  311.  
  312.   Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);
  313.  
  314.   if (   relative_rank(weakSide, pawnSq) != RANK_7
  315.       || distance(loserKSq, pawnSq) != 1
  316.       || !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))
  317.       result += QueenValueEg - PawnValueEg;
  318.  
  319.   return strongSide == pos.side_to_move() ? result : -result;
  320. }
  321.  
  322.  
  323. /// KQ vs KR.  This is almost identical to KX vs K:  We give the attacking
  324. /// king a bonus for having the kings close together, and for forcing the
  325. /// defending king towards the edge. If we also take care to avoid null move for
  326. /// the defending side in the search, this is usually sufficient to win KQ vs KR.
  327. template<>
  328. Value Endgame<KQKR>::operator()(const Position& pos) const {
  329.  
  330.   assert(verify_material(pos, strongSide, QueenValueMg, 0));
  331.   assert(verify_material(pos, weakSide, RookValueMg, 0));
  332.  
  333.   Square winnerKSq = pos.square<KING>(strongSide);
  334.   Square loserKSq = pos.square<KING>(weakSide);
  335.  
  336.   Value result =  QueenValueEg
  337.                 - RookValueEg
  338.                 + PushToEdges[loserKSq]
  339.                 + PushClose[distance(winnerKSq, loserKSq)];
  340.  
  341.   return strongSide == pos.side_to_move() ? result : -result;
  342. }
  343.  
  344.  
  345. /// Some cases of trivial draws
  346. template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
  347.  
  348.  
  349. /// KB and one or more pawns vs K. It checks for draws with rook pawns and
  350. /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
  351. /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
  352. /// will be used.
  353. template<>
  354. ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
  355.  
  356.   assert(pos.non_pawn_material(strongSide) == BishopValueMg);
  357.   assert(pos.count<PAWN>(strongSide) >= 1);
  358.  
  359.   // No assertions about the material of weakSide, because we want draws to
  360.   // be detected even when the weaker side has some pawns.
  361.  
  362.   Bitboard pawns = pos.pieces(strongSide, PAWN);
  363.   File pawnsFile = file_of(lsb(pawns));
  364.  
  365.   // All pawns are on a single rook file?
  366.   if (    (pawnsFile == FILE_A || pawnsFile == FILE_H)
  367.       && !(pawns & ~file_bb(pawnsFile)))
  368.   {
  369.       Square bishopSq = pos.square<BISHOP>(strongSide);
  370.       Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));
  371.       Square kingSq = pos.square<KING>(weakSide);
  372.  
  373.       if (   opposite_colors(queeningSq, bishopSq)
  374.           && distance(queeningSq, kingSq) <= 1)
  375.           return SCALE_FACTOR_DRAW;
  376.   }
  377.  
  378.   // If all the pawns are on the same B or G file, then it's potentially a draw
  379.   if (    (pawnsFile == FILE_B || pawnsFile == FILE_G)
  380.       && !(pos.pieces(PAWN) & ~file_bb(pawnsFile))
  381.       && pos.non_pawn_material(weakSide) == 0
  382.       && pos.count<PAWN>(weakSide) >= 1)
  383.   {
  384.       // Get weakSide pawn that is closest to the home rank
  385.       Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));
  386.  
  387.       Square strongKingSq = pos.square<KING>(strongSide);
  388.       Square weakKingSq = pos.square<KING>(weakSide);
  389.       Square bishopSq = pos.square<BISHOP>(strongSide);
  390.  
  391.       // There's potential for a draw if our pawn is blocked on the 7th rank,
  392.       // the bishop cannot attack it or they only have one pawn left
  393.       if (   relative_rank(strongSide, weakPawnSq) == RANK_7
  394.           && (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))
  395.           && (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))
  396.       {
  397.           int strongKingDist = distance(weakPawnSq, strongKingSq);
  398.           int weakKingDist = distance(weakPawnSq, weakKingSq);
  399.  
  400.           // It's a draw if the weak king is on its back two ranks, within 2
  401.           // squares of the blocking pawn and the strong king is not
  402.           // closer. (I think this rule only fails in practically
  403.           // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
  404.           // and positions where qsearch will immediately correct the
  405.           // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w)
  406.           if (   relative_rank(strongSide, weakKingSq) >= RANK_7
  407.               && weakKingDist <= 2
  408.               && weakKingDist <= strongKingDist)
  409.               return SCALE_FACTOR_DRAW;
  410.       }
  411.   }
  412.  
  413.   return SCALE_FACTOR_NONE;
  414. }
  415.  
  416.  
  417. /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
  418. /// the third rank defended by a pawn.
  419. template<>
  420. ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
  421.  
  422.   assert(verify_material(pos, strongSide, QueenValueMg, 0));
  423.   assert(pos.count<ROOK>(weakSide) == 1);
  424.   assert(pos.count<PAWN>(weakSide) >= 1);
  425.  
  426.   Square kingSq = pos.square<KING>(weakSide);
  427.   Square rsq = pos.square<ROOK>(weakSide);
  428.  
  429.   if (    relative_rank(weakSide, kingSq) <= RANK_2
  430.       &&  relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4
  431.       &&  relative_rank(weakSide, rsq) == RANK_3
  432.       && (  pos.pieces(weakSide, PAWN)
  433.           & pos.attacks_from<KING>(kingSq)
  434.           & pos.attacks_from<PAWN>(rsq, strongSide)))
  435.           return SCALE_FACTOR_DRAW;
  436.  
  437.   return SCALE_FACTOR_NONE;
  438. }
  439.  
  440.  
  441. /// KRP vs KR. This function knows a handful of the most important classes of
  442. /// drawn positions, but is far from perfect. It would probably be a good idea
  443. /// to add more knowledge in the future.
  444. ///
  445. /// It would also be nice to rewrite the actual code for this function,
  446. /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
  447. template<>
  448. ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
  449.  
  450.   assert(verify_material(pos, strongSide, RookValueMg, 1));
  451.   assert(verify_material(pos, weakSide,   RookValueMg, 0));
  452.  
  453.   // Assume strongSide is white and the pawn is on files A-D
  454.   Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
  455.   Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  456.   Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
  457.   Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  458.   Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
  459.  
  460.   File f = file_of(wpsq);
  461.   Rank r = rank_of(wpsq);
  462.   Square queeningSq = make_square(f, RANK_8);
  463.   int tempo = (pos.side_to_move() == strongSide);
  464.  
  465.   // If the pawn is not too far advanced and the defending king defends the
  466.   // queening square, use the third-rank defence.
  467.   if (   r <= RANK_5
  468.       && distance(bksq, queeningSq) <= 1
  469.       && wksq <= SQ_H5
  470.       && (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != RANK_6)))
  471.       return SCALE_FACTOR_DRAW;
  472.  
  473.   // The defending side saves a draw by checking from behind in case the pawn
  474.   // has advanced to the 6th rank with the king behind.
  475.   if (   r == RANK_6
  476.       && distance(bksq, queeningSq) <= 1
  477.       && rank_of(wksq) + tempo <= RANK_6
  478.       && (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))
  479.       return SCALE_FACTOR_DRAW;
  480.  
  481.   if (   r >= RANK_6
  482.       && bksq == queeningSq
  483.       && rank_of(brsq) == RANK_1
  484.       && (!tempo || distance(wksq, wpsq) >= 2))
  485.       return SCALE_FACTOR_DRAW;
  486.  
  487.   // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
  488.   // and the black rook is behind the pawn.
  489.   if (   wpsq == SQ_A7
  490.       && wrsq == SQ_A8
  491.       && (bksq == SQ_H7 || bksq == SQ_G7)
  492.       && file_of(brsq) == FILE_A
  493.       && (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= RANK_5))
  494.       return SCALE_FACTOR_DRAW;
  495.  
  496.   // If the defending king blocks the pawn and the attacking king is too far
  497.   // away, it's a draw.
  498.   if (   r <= RANK_5
  499.       && bksq == wpsq + DELTA_N
  500.       && distance(wksq, wpsq) - tempo >= 2
  501.       && distance(wksq, brsq) - tempo >= 2)
  502.       return SCALE_FACTOR_DRAW;
  503.  
  504.   // Pawn on the 7th rank supported by the rook from behind usually wins if the
  505.   // attacking king is closer to the queening square than the defending king,
  506.   // and the defending king cannot gain tempi by threatening the attacking rook.
  507.   if (   r == RANK_7
  508.       && f != FILE_A
  509.       && file_of(wrsq) == f
  510.       && wrsq != queeningSq
  511.       && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
  512.       && (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))
  513.       return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));
  514.  
  515.   // Similar to the above, but with the pawn further back
  516.   if (   f != FILE_A
  517.       && file_of(wrsq) == f
  518.       && wrsq < wpsq
  519.       && (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)
  520.       && (distance(wksq, wpsq + DELTA_N) < distance(bksq, wpsq + DELTA_N) - 2 + tempo)
  521.       && (  distance(bksq, wrsq) + tempo >= 3
  522.           || (    distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo
  523.               && (distance(wksq, wpsq + DELTA_N) < distance(bksq, wrsq) + tempo))))
  524.       return ScaleFactor(  SCALE_FACTOR_MAX
  525.                          - 8 * distance(wpsq, queeningSq)
  526.                          - 2 * distance(wksq, queeningSq));
  527.  
  528.   // If the pawn is not far advanced and the defending king is somewhere in
  529.   // the pawn's path, it's probably a draw.
  530.   if (r <= RANK_4 && bksq > wpsq)
  531.   {
  532.       if (file_of(bksq) == file_of(wpsq))
  533.           return ScaleFactor(10);
  534.       if (   distance<File>(bksq, wpsq) == 1
  535.           && distance(wksq, bksq) > 2)
  536.           return ScaleFactor(24 - 2 * distance(wksq, bksq));
  537.   }
  538.   return SCALE_FACTOR_NONE;
  539. }
  540.  
  541. template<>
  542. ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
  543.  
  544.   assert(verify_material(pos, strongSide, RookValueMg, 1));
  545.   assert(verify_material(pos, weakSide, BishopValueMg, 0));
  546.  
  547.   // Test for a rook pawn
  548.   if (pos.pieces(PAWN) & (FileABB | FileHBB))
  549.   {
  550.       Square ksq = pos.square<KING>(weakSide);
  551.       Square bsq = pos.square<BISHOP>(weakSide);
  552.       Square psq = pos.square<PAWN>(strongSide);
  553.       Rank rk = relative_rank(strongSide, psq);
  554.       Square push = pawn_push(strongSide);
  555.  
  556.       // If the pawn is on the 5th rank and the pawn (currently) is on
  557.       // the same color square as the bishop then there is a chance of
  558.       // a fortress. Depending on the king position give a moderate
  559.       // reduction or a stronger one if the defending king is near the
  560.       // corner but not trapped there.
  561.       if (rk == RANK_5 && !opposite_colors(bsq, psq))
  562.       {
  563.           int d = distance(psq + 3 * push, ksq);
  564.  
  565.           if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 2 * push))
  566.               return ScaleFactor(24);
  567.           else
  568.               return ScaleFactor(48);
  569.       }
  570.  
  571.       // When the pawn has moved to the 6th rank we can be fairly sure
  572.       // it's drawn if the bishop attacks the square in front of the
  573.       // pawn from a reasonable distance and the defending king is near
  574.       // the corner
  575.       if (   rk == RANK_6
  576.           && distance(psq + 2 * push, ksq) <= 1
  577.           && (PseudoAttacks[BISHOP][bsq] & (psq + push))
  578.           && distance<File>(bsq, psq) >= 2)
  579.           return ScaleFactor(8);
  580.   }
  581.  
  582.   return SCALE_FACTOR_NONE;
  583. }
  584.  
  585. /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
  586. /// pawns and the defending king is actively placed, the position is drawish.
  587. template<>
  588. ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
  589.  
  590.   assert(verify_material(pos, strongSide, RookValueMg, 2));
  591.   assert(verify_material(pos, weakSide,   RookValueMg, 1));
  592.  
  593.   Square wpsq1 = pos.squares<PAWN>(strongSide)[0];
  594.   Square wpsq2 = pos.squares<PAWN>(strongSide)[1];
  595.   Square bksq = pos.square<KING>(weakSide);
  596.  
  597.   // Does the stronger side have a passed pawn?
  598.   if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))
  599.       return SCALE_FACTOR_NONE;
  600.  
  601.   Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));
  602.  
  603.   if (   distance<File>(bksq, wpsq1) <= 1
  604.       && distance<File>(bksq, wpsq2) <= 1
  605.       && relative_rank(strongSide, bksq) > r)
  606.   {
  607.       assert(r > RANK_1 && r < RANK_7);
  608.       return ScaleFactor(KRPPKRPScaleFactors[r]);
  609.   }
  610.   return SCALE_FACTOR_NONE;
  611. }
  612.  
  613.  
  614. /// K and two or more pawns vs K. There is just a single rule here: If all pawns
  615. /// are on the same rook file and are blocked by the defending king, it's a draw.
  616. template<>
  617. ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
  618.  
  619.   assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
  620.   assert(pos.count<PAWN>(strongSide) >= 2);
  621.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  622.  
  623.   Square ksq = pos.square<KING>(weakSide);
  624.   Bitboard pawns = pos.pieces(strongSide, PAWN);
  625.  
  626.   // If all pawns are ahead of the king, on a single rook file and
  627.   // the king is within one file of the pawns, it's a draw.
  628.   if (   !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))
  629.       && !((pawns & ~FileABB) && (pawns & ~FileHBB))
  630.       &&  distance<File>(ksq, lsb(pawns)) <= 1)
  631.       return SCALE_FACTOR_DRAW;
  632.  
  633.   return SCALE_FACTOR_NONE;
  634. }
  635.  
  636.  
  637. /// KBP vs KB. There are two rules: if the defending king is somewhere along the
  638. /// path of the pawn, and the square of the king is not of the same color as the
  639. /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
  640. /// it's almost always a draw.
  641. template<>
  642. ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
  643.  
  644.   assert(verify_material(pos, strongSide, BishopValueMg, 1));
  645.   assert(verify_material(pos, weakSide,   BishopValueMg, 0));
  646.  
  647.   Square pawnSq = pos.square<PAWN>(strongSide);
  648.   Square strongBishopSq = pos.square<BISHOP>(strongSide);
  649.   Square weakBishopSq = pos.square<BISHOP>(weakSide);
  650.   Square weakKingSq = pos.square<KING>(weakSide);
  651.  
  652.   // Case 1: Defending king blocks the pawn, and cannot be driven away
  653.   if (   file_of(weakKingSq) == file_of(pawnSq)
  654.       && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
  655.       && (   opposite_colors(weakKingSq, strongBishopSq)
  656.           || relative_rank(strongSide, weakKingSq) <= RANK_6))
  657.       return SCALE_FACTOR_DRAW;
  658.  
  659.   // Case 2: Opposite colored bishops
  660.   if (opposite_colors(strongBishopSq, weakBishopSq))
  661.   {
  662.       // We assume that the position is drawn in the following three situations:
  663.       //
  664.       //   a. The pawn is on rank 5 or further back.
  665.       //   b. The defending king is somewhere in the pawn's path.
  666.       //   c. The defending bishop attacks some square along the pawn's path,
  667.       //      and is at least three squares away from the pawn.
  668.       //
  669.       // These rules are probably not perfect, but in practice they work
  670.       // reasonably well.
  671.  
  672.       if (relative_rank(strongSide, pawnSq) <= RANK_5)
  673.           return SCALE_FACTOR_DRAW;
  674.       else
  675.       {
  676.           Bitboard path = forward_bb(strongSide, pawnSq);
  677.  
  678.           if (path & pos.pieces(weakSide, KING))
  679.               return SCALE_FACTOR_DRAW;
  680.  
  681.           if (  (pos.attacks_from<BISHOP>(weakBishopSq) & path)
  682.               && distance(weakBishopSq, pawnSq) >= 3)
  683.               return SCALE_FACTOR_DRAW;
  684.       }
  685.   }
  686.   return SCALE_FACTOR_NONE;
  687. }
  688.  
  689.  
  690. /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
  691. template<>
  692. ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
  693.  
  694.   assert(verify_material(pos, strongSide, BishopValueMg, 2));
  695.   assert(verify_material(pos, weakSide,   BishopValueMg, 0));
  696.  
  697.   Square wbsq = pos.square<BISHOP>(strongSide);
  698.   Square bbsq = pos.square<BISHOP>(weakSide);
  699.  
  700.   if (!opposite_colors(wbsq, bbsq))
  701.       return SCALE_FACTOR_NONE;
  702.  
  703.   Square ksq = pos.square<KING>(weakSide);
  704.   Square psq1 = pos.squares<PAWN>(strongSide)[0];
  705.   Square psq2 = pos.squares<PAWN>(strongSide)[1];
  706.   Rank r1 = rank_of(psq1);
  707.   Rank r2 = rank_of(psq2);
  708.   Square blockSq1, blockSq2;
  709.  
  710.   if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))
  711.   {
  712.       blockSq1 = psq1 + pawn_push(strongSide);
  713.       blockSq2 = make_square(file_of(psq2), rank_of(psq1));
  714.   }
  715.   else
  716.   {
  717.       blockSq1 = psq2 + pawn_push(strongSide);
  718.       blockSq2 = make_square(file_of(psq1), rank_of(psq2));
  719.   }
  720.  
  721.   switch (distance<File>(psq1, psq2))
  722.   {
  723.   case 0:
  724.     // Both pawns are on the same file. It's an easy draw if the defender firmly
  725.     // controls some square in the frontmost pawn's path.
  726.     if (   file_of(ksq) == file_of(blockSq1)
  727.         && relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)
  728.         && opposite_colors(ksq, wbsq))
  729.         return SCALE_FACTOR_DRAW;
  730.     else
  731.         return SCALE_FACTOR_NONE;
  732.  
  733.   case 1:
  734.     // Pawns on adjacent files. It's a draw if the defender firmly controls the
  735.     // square in front of the frontmost pawn's path, and the square diagonally
  736.     // behind this square on the file of the other pawn.
  737.     if (   ksq == blockSq1
  738.         && opposite_colors(ksq, wbsq)
  739.         && (   bbsq == blockSq2
  740.             || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))
  741.             || distance(r1, r2) >= 2))
  742.         return SCALE_FACTOR_DRAW;
  743.  
  744.     else if (   ksq == blockSq2
  745.              && opposite_colors(ksq, wbsq)
  746.              && (   bbsq == blockSq1
  747.                  || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(weakSide, BISHOP))))
  748.         return SCALE_FACTOR_DRAW;
  749.     else
  750.         return SCALE_FACTOR_NONE;
  751.  
  752.   default:
  753.     // The pawns are not on the same file or adjacent files. No scaling.
  754.     return SCALE_FACTOR_NONE;
  755.   }
  756. }
  757.  
  758.  
  759. /// KBP vs KN. There is a single rule: If the defending king is somewhere along
  760. /// the path of the pawn, and the square of the king is not of the same color as
  761. /// the stronger side's bishop, it's a draw.
  762. template<>
  763. ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
  764.  
  765.   assert(verify_material(pos, strongSide, BishopValueMg, 1));
  766.   assert(verify_material(pos, weakSide, KnightValueMg, 0));
  767.  
  768.   Square pawnSq = pos.square<PAWN>(strongSide);
  769.   Square strongBishopSq = pos.square<BISHOP>(strongSide);
  770.   Square weakKingSq = pos.square<KING>(weakSide);
  771.  
  772.   if (   file_of(weakKingSq) == file_of(pawnSq)
  773.       && relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)
  774.       && (   opposite_colors(weakKingSq, strongBishopSq)
  775.           || relative_rank(strongSide, weakKingSq) <= RANK_6))
  776.       return SCALE_FACTOR_DRAW;
  777.  
  778.   return SCALE_FACTOR_NONE;
  779. }
  780.  
  781.  
  782. /// KNP vs K. There is a single rule: if the pawn is a rook pawn on the 7th rank
  783. /// and the defending king prevents the pawn from advancing, the position is drawn.
  784. template<>
  785. ScaleFactor Endgame<KNPK>::operator()(const Position& pos) const {
  786.  
  787.   assert(verify_material(pos, strongSide, KnightValueMg, 1));
  788.   assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  789.  
  790.   // Assume strongSide is white and the pawn is on files A-D
  791.   Square pawnSq     = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  792.   Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  793.  
  794.   if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)
  795.       return SCALE_FACTOR_DRAW;
  796.  
  797.   return SCALE_FACTOR_NONE;
  798. }
  799.  
  800.  
  801. /// KNP vs KB. If knight can block bishop from taking pawn, it's a win.
  802. /// Otherwise the position is drawn.
  803. template<>
  804. ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {
  805.  
  806.   Square pawnSq = pos.square<PAWN>(strongSide);
  807.   Square bishopSq = pos.square<BISHOP>(weakSide);
  808.   Square weakKingSq = pos.square<KING>(weakSide);
  809.  
  810.   // King needs to get close to promoting pawn to prevent knight from blocking.
  811.   // Rules for this are very tricky, so just approximate.
  812.   if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))
  813.       return ScaleFactor(distance(weakKingSq, pawnSq));
  814.  
  815.   return SCALE_FACTOR_NONE;
  816. }
  817.  
  818.  
  819. /// KP vs KP. This is done by removing the weakest side's pawn and probing the
  820. /// KP vs K bitbase: If the weakest side has a draw without the pawn, it probably
  821. /// has at least a draw with the pawn as well. The exception is when the stronger
  822. /// side's pawn is far advanced and not on a rook file; in this case it is often
  823. /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
  824. template<>
  825. ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
  826.  
  827.   assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
  828.   assert(verify_material(pos, weakSide,   VALUE_ZERO, 1));
  829.  
  830.   // Assume strongSide is white and the pawn is on files A-D
  831.   Square wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));
  832.   Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));
  833.   Square psq  = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  834.  
  835.   Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
  836.  
  837.   // If the pawn has advanced to the fifth rank or further, and is not a
  838.   // rook pawn, it's too dangerous to assume that it's at least a draw.
  839.   if (rank_of(psq) >= RANK_5 && file_of(psq) != FILE_A)
  840.       return SCALE_FACTOR_NONE;
  841.  
  842.   // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
  843.   // it's probably at least a draw even with the pawn.
  844.   return Bitbases::probe(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;
  845. }
  846.