text: /*
    Stockfish, a UCI chess playing engine derived from Glaurung 2.1
    Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
    Copyright (C) 2008-2015 Marco Costalba, Joona Kiiski, Tord Romstad
    Copyright (C) 2015-2020 Marco Costalba, Joona Kiiski, Gary Linscott, Tord Romstad
  
    Stockfish is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
  
    Stockfish is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.
  
    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
  */
  
  #include <cassert>
  
  #include "bitboard.h"
  #include "endgame.h"
  #include "movegen.h"
  
  namespace {
  
    // Used to drive the king towards the edge of the board
    // in KX vs K and KQ vs KR endgames.
    // Values range from 27 (center squares) to 90 (in the corners)
    inline int push_to_edge(Square s) {
        int rd = edge_distance(rank_of(s)), fd = edge_distance(file_of(s));
        return 90 - (7 * fd * fd / 2 + 7 * rd * rd / 2);
    }
  
    // Used to drive the king towards A1H8 corners in KBN vs K endgames.
    // Values range from 0 on A8H1 diagonal to 7 in A1H8 corners
    inline int push_to_corner(Square s) {
        return abs(7 - rank_of(s) - file_of(s));
    }
  
    // Drive a piece close to or away from another piece
    inline int push_close(Square s1, Square s2) { return 140 - 20 * distance(s1, s2); }
    inline int push_away(Square s1, Square s2) { return 120 - push_close(s1, s2); }
  
  #ifndef NDEBUG
    bool verify_material(const Position& pos, Color c, Value npm, int pawnsCnt) {
      return pos.non_pawn_material(c) == npm && pos.count<PAWN>(c) == pawnsCnt;
    }
  #endif
  
    // Map the square as if strongSide is white and strongSide's only pawn
    // is on the left half of the board.
    Square normalize(const Position& pos, Color strongSide, Square sq) {
  
      assert(pos.count<PAWN>(strongSide) == 1);
  
      if (file_of(pos.square<PAWN>(strongSide)) >= FILE_E)
          sq = flip_file(sq);
  
      return strongSide == WHITE ? sq : flip_rank(sq);
    }
  
  } // namespace
  
  
  namespace Endgames {
  
    std::pair<Map<Value>, Map<ScaleFactor>> maps;
  
    void init() {
  
      add<KPK>("KPK");
      add<KNNK>("KNNK");
      add<KBNK>("KBNK");
      add<KRKP>("KRKP");
      add<KRKB>("KRKB");
      add<KRKN>("KRKN");
      add<KQKP>("KQKP");
      add<KQKR>("KQKR");
      add<KNNKP>("KNNKP");
  
      add<KRPKR>("KRPKR");
      add<KRPKB>("KRPKB");
      add<KBPKB>("KBPKB");
      add<KBPKN>("KBPKN");
      add<KBPPKB>("KBPPKB");
      add<KRPPKRP>("KRPPKRP");
    }
  }
  
  
  /// Mate with KX vs K. This function is used to evaluate positions with
  /// king and plenty of material vs a lone king. It simply gives the
  /// attacking side a bonus for driving the defending king towards the edge
  /// of the board, and for keeping the distance between the two kings small.
  template<>
  Value Endgame<KXK>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
    assert(!pos.checkers()); // Eval is never called when in check
  
    // Stalemate detection with lone king
    if (pos.side_to_move() == weakSide && !MoveList<LEGAL>(pos).size())
        return VALUE_DRAW;
  
    Square strongKing = pos.square<KING>(strongSide);
    Square weakKing   = pos.square<KING>(weakSide);
  
    Value result =  pos.non_pawn_material(strongSide)
                  + pos.count<PAWN>(strongSide) * PawnValueEg
                  + push_to_edge(weakKing)
                  + push_close(strongKing, weakKing);
  
    if (   pos.count<QUEEN>(strongSide)
        || pos.count<ROOK>(strongSide)
        ||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))
        || (   (pos.pieces(strongSide, BISHOP) & ~DarkSquares)
            && (pos.pieces(strongSide, BISHOP) &  DarkSquares)))
        result = std::min(result + VALUE_KNOWN_WIN, VALUE_TB_WIN_IN_MAX_PLY - 1);
  
    return strongSide == pos.side_to_move() ? result : -result;
  }
  
  
  /// Mate with KBN vs K. This is similar to KX vs K, but we have to drive the
  /// defending king towards a corner square that our bishop attacks.
  template<>
  Value Endgame<KBNK>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, KnightValueMg + BishopValueMg, 0));
    assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  
    Square strongKing   = pos.square<KING>(strongSide);
    Square strongBishop = pos.square<BISHOP>(strongSide);
    Square weakKing     = pos.square<KING>(weakSide);
  
    // If our bishop does not attack A1/H8, we flip the enemy king square
    // to drive to opposite corners (A8/H1).
  
    Value result =  (VALUE_KNOWN_WIN + 3520)
                  + push_close(strongKing, weakKing)
                  + 420 * push_to_corner(opposite_colors(strongBishop, SQ_A1) ? flip_file(weakKing) : weakKing);
  
    assert(abs(result) < VALUE_TB_WIN_IN_MAX_PLY);
    return strongSide == pos.side_to_move() ? result : -result;
  }
  
  
  /// KP vs K. This endgame is evaluated with the help of a bitbase
  template<>
  Value Endgame<KPK>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
    assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  
    // Assume strongSide is white and the pawn is on files A-D
    Square strongKing = normalize(pos, strongSide, pos.square<KING>(strongSide));
    Square strongPawn = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
    Square weakKing   = normalize(pos, strongSide, pos.square<KING>(weakSide));
  
    Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
  
    if (!Bitbases::probe(strongKing, strongPawn, weakKing, us))
        return VALUE_DRAW;
  
    Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(strongPawn));
  
    return strongSide == pos.side_to_move() ? result : -result;
  }
  
  
  /// KR vs KP. This is a somewhat tricky endgame to evaluate precisely without
  /// a bitbase. The function below returns drawish scores when the pawn is
  /// far advanced with support of the king, while the attacking king is far
  /// away.
  template<>
  Value Endgame<KRKP>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, RookValueMg, 0));
    assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
  
    Square strongKing = relative_square(strongSide, pos.square<KING>(strongSide));
    Square weakKing   = relative_square(strongSide, pos.square<KING>(weakSide));
    Square strongRook = relative_square(strongSide, pos.square<ROOK>(strongSide));
    Square weakPawn   = relative_square(strongSide, pos.square<PAWN>(weakSide));
    Square queeningSquare = make_square(file_of(weakPawn), RANK_1);
    Value result;
  
    // If the stronger side's king is in front of the pawn, it's a win
    if (forward_file_bb(WHITE, strongKing) & weakPawn)
        result = RookValueEg - distance(strongKing, weakPawn);
  
    // If the weaker side's king is too far from the pawn and the rook,
    // it's a win.
    else if (   distance(weakKing, weakPawn) >= 3 + (pos.side_to_move() == weakSide)
             && distance(weakKing, strongRook) >= 3)
        result = RookValueEg - distance(strongKing, weakPawn);
  
    // If the pawn is far advanced and supported by the defending king,
    // the position is drawish
    else if (   rank_of(weakKing) <= RANK_3
             && distance(weakKing, weakPawn) == 1
             && rank_of(strongKing) >= RANK_4
             && distance(strongKing, weakPawn) > 2 + (pos.side_to_move() == strongSide))
        result = Value(80) - 8 * distance(strongKing, weakPawn);
  
    else
        result =  Value(200) - 8 * (  distance(strongKing, weakPawn + SOUTH)
                                    - distance(weakKing, weakPawn + SOUTH)
                                    - distance(weakPawn, queeningSquare));
  
    return strongSide == pos.side_to_move() ? result : -result;
  }
  
  
  /// KR vs KB. This is very simple, and always returns drawish scores. The
  /// score is slightly bigger when the defending king is close to the edge.
  template<>
  Value Endgame<KRKB>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, RookValueMg, 0));
    assert(verify_material(pos, weakSide, BishopValueMg, 0));
  
    Value result = Value(push_to_edge(pos.square<KING>(weakSide)));
    return strongSide == pos.side_to_move() ? result : -result;
  }
  
  
  /// KR vs KN. The attacking side has slightly better winning chances than
  /// in KR vs KB, particularly if the king and the knight are far apart.
  template<>
  Value Endgame<KRKN>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, RookValueMg, 0));
    assert(verify_material(pos, weakSide, KnightValueMg, 0));
  
    Square weakKing   = pos.square<KING>(weakSide);
    Square weakKnight = pos.square<KNIGHT>(weakSide);
    Value result = Value(push_to_edge(weakKing) + push_away(weakKing, weakKnight));
    return strongSide == pos.side_to_move() ? result : -result;
  }
  
  
  /// KQ vs KP. In general, this is a win for the stronger side, but there are a
  /// few important exceptions. A pawn on 7th rank and on the A,C,F or H files
  /// with a king positioned next to it can be a draw, so in that case, we only
  /// use the distance between the kings.
  template<>
  Value Endgame<KQKP>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, QueenValueMg, 0));
    assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
  
    Square strongKing = pos.square<KING>(strongSide);
    Square weakKing   = pos.square<KING>(weakSide);
    Square weakPawn   = pos.square<PAWN>(weakSide);
  
    Value result = Value(push_close(strongKing, weakKing));
  
    if (   relative_rank(weakSide, weakPawn) != RANK_7
        || distance(weakKing, weakPawn) != 1
        || ((FileBBB | FileDBB | FileEBB | FileGBB) & weakPawn))
        result += QueenValueEg - PawnValueEg;
  
    return strongSide == pos.side_to_move() ? result : -result;
  }
  
  
  /// KQ vs KR. This is almost identical to KX vs K: we give the attacking
  /// king a bonus for having the kings close together, and for forcing the
  /// defending king towards the edge. If we also take care to avoid null move for
  /// the defending side in the search, this is usually sufficient to win KQ vs KR.
  template<>
  Value Endgame<KQKR>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, QueenValueMg, 0));
    assert(verify_material(pos, weakSide, RookValueMg, 0));
  
    Square strongKing = pos.square<KING>(strongSide);
    Square weakKing   = pos.square<KING>(weakSide);
  
    Value result =  QueenValueEg
                  - RookValueEg
                  + push_to_edge(weakKing)
                  + push_close(strongKing, weakKing);
  
    return strongSide == pos.side_to_move() ? result : -result;
  }
  
  
  /// KNN vs KP. Very drawish, but there are some mate opportunities if we can
  /// press the weakSide King to a corner before the pawn advances too much.
  template<>
  Value Endgame<KNNKP>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, 2 * KnightValueMg, 0));
    assert(verify_material(pos, weakSide, VALUE_ZERO, 1));
  
    Square weakKing = pos.square<KING>(weakSide);
    Square weakPawn = pos.square<PAWN>(weakSide);
  
    Value result =      PawnValueEg
                 +  2 * push_to_edge(weakKing)
                 - 10 * relative_rank(weakSide, weakPawn);
  
    return strongSide == pos.side_to_move() ? result : -result;
  }
  
  
  /// Some cases of trivial draws
  template<> Value Endgame<KNNK>::operator()(const Position&) const { return VALUE_DRAW; }
  
  
  /// KB and one or more pawns vs K. It checks for draws with rook pawns and
  /// a bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_DRAW
  /// is returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
  /// will be used.
  template<>
  ScaleFactor Endgame<KBPsK>::operator()(const Position& pos) const {
  
    assert(pos.non_pawn_material(strongSide) == BishopValueMg);
    assert(pos.count<PAWN>(strongSide) >= 1);
  
    // No assertions about the material of weakSide, because we want draws to
    // be detected even when the weaker side has some pawns.
  
    Bitboard strongPawns = pos.pieces(strongSide, PAWN);
    Bitboard allPawns = pos.pieces(PAWN);
  
    Square strongBishop = pos.square<BISHOP>(strongSide);
    Square weakKing = pos.square<KING>(weakSide);
    Square strongKing = pos.square<KING>(strongSide);
  
    // All strongSide pawns are on a single rook file?
    if (!(strongPawns & ~FileABB) || !(strongPawns & ~FileHBB))
    {
        Square queeningSquare = relative_square(strongSide, make_square(file_of(lsb(strongPawns)), RANK_8));
  
        if (   opposite_colors(queeningSquare, strongBishop)
            && distance(queeningSquare, weakKing) <= 1)
            return SCALE_FACTOR_DRAW;
    }
  
    // If all the pawns are on the same B or G file, then it's potentially a draw
    if ((!(allPawns & ~FileBBB) || !(allPawns & ~FileGBB))
        && pos.non_pawn_material(weakSide) == 0
        && pos.count<PAWN>(weakSide) >= 1)
    {
        // Get the least advanced weakSide pawn
        Square weakPawn = frontmost_sq(strongSide, pos.pieces(weakSide, PAWN));
  
        // There's potential for a draw if our pawn is blocked on the 7th rank,
        // the bishop cannot attack it or they only have one pawn left.
        if (   relative_rank(strongSide, weakPawn) == RANK_7
            && (strongPawns & (weakPawn + pawn_push(weakSide)))
            && (opposite_colors(strongBishop, weakPawn) || !more_than_one(strongPawns)))
        {
            int strongKingDist = distance(weakPawn, strongKing);
            int weakKingDist = distance(weakPawn, weakKing);
  
            // It's a draw if the weak king is on its back two ranks, within 2
            // squares of the blocking pawn and the strong king is not
            // closer. (I think this rule only fails in practically
            // unreachable positions such as 5k1K/6p1/6P1/8/8/3B4/8/8 w
            // and positions where qsearch will immediately correct the
            // problem such as 8/4k1p1/6P1/1K6/3B4/8/8/8 w).
            if (   relative_rank(strongSide, weakKing) >= RANK_7
                && weakKingDist <= 2
                && weakKingDist <= strongKingDist)
                return SCALE_FACTOR_DRAW;
        }
    }
  
    return SCALE_FACTOR_NONE;
  }
  
  
  /// KQ vs KR and one or more pawns. It tests for fortress draws with a rook on
  /// the third rank defended by a pawn.
  template<>
  ScaleFactor Endgame<KQKRPs>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, QueenValueMg, 0));
    assert(pos.count<ROOK>(weakSide) == 1);
    assert(pos.count<PAWN>(weakSide) >= 1);
  
    Square strongKing = pos.square<KING>(strongSide);
    Square weakKing   = pos.square<KING>(weakSide);
    Square weakRook   = pos.square<ROOK>(weakSide);
  
    if (    relative_rank(weakSide,   weakKing) <= RANK_2
        &&  relative_rank(weakSide, strongKing) >= RANK_4
        &&  relative_rank(weakSide,   weakRook) == RANK_3
        && (  pos.pieces(weakSide, PAWN)
            & attacks_bb<KING>(weakKing)
            & pawn_attacks_bb(strongSide, weakRook)))
            return SCALE_FACTOR_DRAW;
  
    return SCALE_FACTOR_NONE;
  }
  
  
  /// KRP vs KR. This function knows a handful of the most important classes of
  /// drawn positions, but is far from perfect. It would probably be a good idea
  /// to add more knowledge in the future.
  ///
  /// It would also be nice to rewrite the actual code for this function,
  /// which is mostly copied from Glaurung 1.x, and isn't very pretty.
  template<>
  ScaleFactor Endgame<KRPKR>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, RookValueMg, 1));
    assert(verify_material(pos, weakSide,   RookValueMg, 0));
  
    // Assume strongSide is white and the pawn is on files A-D
    Square strongKing = normalize(pos, strongSide, pos.square<KING>(strongSide));
    Square strongRook = normalize(pos, strongSide, pos.square<ROOK>(strongSide));
    Square strongPawn = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
    Square weakKing = normalize(pos, strongSide, pos.square<KING>(weakSide));
    Square weakRook = normalize(pos, strongSide, pos.square<ROOK>(weakSide));
  
    File pawnFile = file_of(strongPawn);
    Rank pawnRank = rank_of(strongPawn);
    Square queeningSquare = make_square(pawnFile, RANK_8);
    int tempo = (pos.side_to_move() == strongSide);
  
    // If the pawn is not too far advanced and the defending king defends the
    // queening square, use the third-rank defence.
    if (   pawnRank <= RANK_5
        && distance(weakKing, queeningSquare) <= 1
        && strongKing <= SQ_H5
        && (rank_of(weakRook) == RANK_6 || (pawnRank <= RANK_3 && rank_of(strongRook) != RANK_6)))
        return SCALE_FACTOR_DRAW;
  
    // The defending side saves a draw by checking from behind in case the pawn
    // has advanced to the 6th rank with the king behind.
    if (   pawnRank == RANK_6
        && distance(weakKing, queeningSquare) <= 1
        && rank_of(strongKing) + tempo <= RANK_6
        && (rank_of(weakRook) == RANK_1 || (!tempo && distance<File>(weakRook, strongPawn) >= 3)))
        return SCALE_FACTOR_DRAW;
  
    if (   pawnRank >= RANK_6
        && weakKing == queeningSquare
        && rank_of(weakRook) == RANK_1
        && (!tempo || distance(strongKing, strongPawn) >= 2))
        return SCALE_FACTOR_DRAW;
  
    // White pawn on a7 and rook on a8 is a draw if black's king is on g7 or h7
    // and the black rook is behind the pawn.
    if (   strongPawn == SQ_A7
        && strongRook == SQ_A8
        && (weakKing == SQ_H7 || weakKing == SQ_G7)
        && file_of(weakRook) == FILE_A
        && (rank_of(weakRook) <= RANK_3 || file_of(strongKing) >= FILE_D || rank_of(strongKing) <= RANK_5))
        return SCALE_FACTOR_DRAW;
  
    // If the defending king blocks the pawn and the attacking king is too far
    // away, it's a draw.
    if (   pawnRank <= RANK_5
        && weakKing == strongPawn + NORTH
        && distance(strongKing, strongPawn) - tempo >= 2
        && distance(strongKing, weakRook) - tempo >= 2)
        return SCALE_FACTOR_DRAW;
  
    // Pawn on the 7th rank supported by the rook from behind usually wins if the
    // attacking king is closer to the queening square than the defending king,
    // and the defending king cannot gain tempi by threatening the attacking rook.
    if (   pawnRank == RANK_7
        && pawnFile != FILE_A
        && file_of(strongRook) == pawnFile
        && strongRook != queeningSquare
        && (distance(strongKing, queeningSquare) < distance(weakKing, queeningSquare) - 2 + tempo)
        && (distance(strongKing, queeningSquare) < distance(weakKing, strongRook) + tempo))
        return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(strongKing, queeningSquare));
  
    // Similar to the above, but with the pawn further back
    if (   pawnFile != FILE_A
        && file_of(strongRook) == pawnFile
        && strongRook < strongPawn
        && (distance(strongKing, queeningSquare) < distance(weakKing, queeningSquare) - 2 + tempo)
        && (distance(strongKing, strongPawn + NORTH) < distance(weakKing, strongPawn + NORTH) - 2 + tempo)
        && (  distance(weakKing, strongRook) + tempo >= 3
            || (    distance(strongKing, queeningSquare) < distance(weakKing, strongRook) + tempo
                && (distance(strongKing, strongPawn + NORTH) < distance(weakKing, strongPawn) + tempo))))
        return ScaleFactor(  SCALE_FACTOR_MAX
                           - 8 * distance(strongPawn, queeningSquare)
                           - 2 * distance(strongKing, queeningSquare));
  
    // If the pawn is not far advanced and the defending king is somewhere in
    // the pawn's path, it's probably a draw.
    if (pawnRank <= RANK_4 && weakKing > strongPawn)
    {
        if (file_of(weakKing) == file_of(strongPawn))
            return ScaleFactor(10);
        if (   distance<File>(weakKing, strongPawn) == 1
            && distance(strongKing, weakKing) > 2)
            return ScaleFactor(24 - 2 * distance(strongKing, weakKing));
    }
    return SCALE_FACTOR_NONE;
  }
  
  template<>
  ScaleFactor Endgame<KRPKB>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, RookValueMg, 1));
    assert(verify_material(pos, weakSide, BishopValueMg, 0));
  
    // Test for a rook pawn
    if (pos.pieces(PAWN) & (FileABB | FileHBB))
    {
        Square weakKing = pos.square<KING>(weakSide);
        Square weakBishop = pos.square<BISHOP>(weakSide);
        Square strongKing = pos.square<KING>(strongSide);
        Square strongPawn = pos.square<PAWN>(strongSide);
        Rank pawnRank = relative_rank(strongSide, strongPawn);
        Direction push = pawn_push(strongSide);
  
        // If the pawn is on the 5th rank and the pawn (currently) is on
        // the same color square as the bishop then there is a chance of
        // a fortress. Depending on the king position give a moderate
        // reduction or a stronger one if the defending king is near the
        // corner but not trapped there.
        if (pawnRank == RANK_5 && !opposite_colors(weakBishop, strongPawn))
        {
            int d = distance(strongPawn + 3 * push, weakKing);
  
            if (d <= 2 && !(d == 0 && weakKing == strongKing + 2 * push))
                return ScaleFactor(24);
            else
                return ScaleFactor(48);
        }
  
        // When the pawn has moved to the 6th rank we can be fairly sure
        // it's drawn if the bishop attacks the square in front of the
        // pawn from a reasonable distance and the defending king is near
        // the corner
        if (   pawnRank == RANK_6
            && distance(strongPawn + 2 * push, weakKing) <= 1
            && (attacks_bb<BISHOP>(weakBishop) & (strongPawn + push))
            && distance<File>(weakBishop, strongPawn) >= 2)
            return ScaleFactor(8);
    }
  
    return SCALE_FACTOR_NONE;
  }
  
  /// KRPP vs KRP. There is just a single rule: if the stronger side has no passed
  /// pawns and the defending king is actively placed, the position is drawish.
  template<>
  ScaleFactor Endgame<KRPPKRP>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, RookValueMg, 2));
    assert(verify_material(pos, weakSide,   RookValueMg, 1));
  
    Square strongPawn1 = pos.squares<PAWN>(strongSide)[0];
    Square strongPawn2 = pos.squares<PAWN>(strongSide)[1];
    Square weakKing = pos.square<KING>(weakSide);
  
    // Does the stronger side have a passed pawn?
    if (pos.pawn_passed(strongSide, strongPawn1) || pos.pawn_passed(strongSide, strongPawn2))
        return SCALE_FACTOR_NONE;
  
    Rank pawnRank = std::max(relative_rank(strongSide, strongPawn1), relative_rank(strongSide, strongPawn2));
  
    if (   distance<File>(weakKing, strongPawn1) <= 1
        && distance<File>(weakKing, strongPawn2) <= 1
        && relative_rank(strongSide, weakKing) > pawnRank)
    {
        assert(pawnRank > RANK_1 && pawnRank < RANK_7);
        return ScaleFactor(7 * pawnRank);
    }
    return SCALE_FACTOR_NONE;
  }
  
  
  /// K and two or more pawns vs K. There is just a single rule here: if all pawns
  /// are on the same rook file and are blocked by the defending king, it's a draw.
  template<>
  ScaleFactor Endgame<KPsK>::operator()(const Position& pos) const {
  
    assert(pos.non_pawn_material(strongSide) == VALUE_ZERO);
    assert(pos.count<PAWN>(strongSide) >= 2);
    assert(verify_material(pos, weakSide, VALUE_ZERO, 0));
  
    Square weakKing = pos.square<KING>(weakSide);
    Bitboard strongPawns = pos.pieces(strongSide, PAWN);
  
    // If all pawns are ahead of the king on a single rook file, it's a draw.
    if (!((strongPawns & ~FileABB) || (strongPawns & ~FileHBB)) &&
        !(strongPawns & ~passed_pawn_span(weakSide, weakKing)))
        return SCALE_FACTOR_DRAW;
  
    return SCALE_FACTOR_NONE;
  }
  
  
  /// KBP vs KB. There are two rules: if the defending king is somewhere along the
  /// path of the pawn, and the square of the king is not of the same color as the
  /// stronger side's bishop, it's a draw. If the two bishops have opposite color,
  /// it's almost always a draw.
  template<>
  ScaleFactor Endgame<KBPKB>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, BishopValueMg, 1));
    assert(verify_material(pos, weakSide,   BishopValueMg, 0));
  
    Square strongPawn = pos.square<PAWN>(strongSide);
    Square strongBishop = pos.square<BISHOP>(strongSide);
    Square weakBishop = pos.square<BISHOP>(weakSide);
    Square weakKing = pos.square<KING>(weakSide);
  
    // Case 1: Defending king blocks the pawn, and cannot be driven away
    if (   (forward_file_bb(strongSide, strongPawn) & weakKing)
        && (   opposite_colors(weakKing, strongBishop)
            || relative_rank(strongSide, weakKing) <= RANK_6))
        return SCALE_FACTOR_DRAW;
  
    // Case 2: Opposite colored bishops
    if (opposite_colors(strongBishop, weakBishop))
        return SCALE_FACTOR_DRAW;
  
    return SCALE_FACTOR_NONE;
  }
  
  
  /// KBPP vs KB. It detects a few basic draws with opposite-colored bishops
  template<>
  ScaleFactor Endgame<KBPPKB>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, BishopValueMg, 2));
    assert(verify_material(pos, weakSide,   BishopValueMg, 0));
  
    Square strongBishop = pos.square<BISHOP>(strongSide);
    Square weakBishop   = pos.square<BISHOP>(weakSide);
  
    if (!opposite_colors(strongBishop, weakBishop))
        return SCALE_FACTOR_NONE;
  
    Square weakKing = pos.square<KING>(weakSide);
    Square strongPawn1 = pos.squares<PAWN>(strongSide)[0];
    Square strongPawn2 = pos.squares<PAWN>(strongSide)[1];
    Square blockSq1, blockSq2;
  
    if (relative_rank(strongSide, strongPawn1) > relative_rank(strongSide, strongPawn2))
    {
        blockSq1 = strongPawn1 + pawn_push(strongSide);
        blockSq2 = make_square(file_of(strongPawn2), rank_of(strongPawn1));
    }
    else
    {
        blockSq1 = strongPawn2 + pawn_push(strongSide);
        blockSq2 = make_square(file_of(strongPawn1), rank_of(strongPawn2));
    }
  
    switch (distance<File>(strongPawn1, strongPawn2))
    {
    case 0:
      // Both pawns are on the same file. It's an easy draw if the defender firmly
      // controls some square in the frontmost pawn's path.
      if (   file_of(weakKing) == file_of(blockSq1)
          && relative_rank(strongSide, weakKing) >= relative_rank(strongSide, blockSq1)
          && opposite_colors(weakKing, strongBishop))
          return SCALE_FACTOR_DRAW;
      else
          return SCALE_FACTOR_NONE;
  
    case 1:
      // Pawns on adjacent files. It's a draw if the defender firmly controls the
      // square in front of the frontmost pawn's path, and the square diagonally
      // behind this square on the file of the other pawn.
      if (   weakKing == blockSq1
          && opposite_colors(weakKing, strongBishop)
          && (   weakBishop == blockSq2
              || (attacks_bb<BISHOP>(blockSq2, pos.pieces()) & pos.pieces(weakSide, BISHOP))
              || distance<Rank>(strongPawn1, strongPawn2) >= 2))
          return SCALE_FACTOR_DRAW;
  
      else if (   weakKing == blockSq2
               && opposite_colors(weakKing, strongBishop)
               && (   weakBishop == blockSq1
                   || (attacks_bb<BISHOP>(blockSq1, pos.pieces()) & pos.pieces(weakSide, BISHOP))))
          return SCALE_FACTOR_DRAW;
      else
          return SCALE_FACTOR_NONE;
  
    default:
      // The pawns are not on the same file or adjacent files. No scaling.
      return SCALE_FACTOR_NONE;
    }
  }
  
  
  /// KBP vs KN. There is a single rule: if the defending king is somewhere along
  /// the path of the pawn, and the square of the king is not of the same color as
  /// the stronger side's bishop, it's a draw.
  template<>
  ScaleFactor Endgame<KBPKN>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, BishopValueMg, 1));
    assert(verify_material(pos, weakSide, KnightValueMg, 0));
  
    Square strongPawn = pos.square<PAWN>(strongSide);
    Square strongBishop = pos.square<BISHOP>(strongSide);
    Square weakKing = pos.square<KING>(weakSide);
  
    if (   file_of(weakKing) == file_of(strongPawn)
        && relative_rank(strongSide, strongPawn) < relative_rank(strongSide, weakKing)
        && (   opposite_colors(weakKing, strongBishop)
            || relative_rank(strongSide, weakKing) <= RANK_6))
        return SCALE_FACTOR_DRAW;
  
    return SCALE_FACTOR_NONE;
  }
  
  
  /// KP vs KP. This is done by removing the weakest side's pawn and probing the
  /// KP vs K bitbase: if the weakest side has a draw without the pawn, it probably
  /// has at least a draw with the pawn as well. The exception is when the stronger
  /// side's pawn is far advanced and not on a rook file; in this case it is often
  /// possible to win (e.g. 8/4k3/3p4/3P4/6K1/8/8/8 w - - 0 1).
  template<>
  ScaleFactor Endgame<KPKP>::operator()(const Position& pos) const {
  
    assert(verify_material(pos, strongSide, VALUE_ZERO, 1));
    assert(verify_material(pos, weakSide,   VALUE_ZERO, 1));
  
    // Assume strongSide is white and the pawn is on files A-D
    Square strongKing = normalize(pos, strongSide, pos.square<KING>(strongSide));
    Square weakKing   = normalize(pos, strongSide, pos.square<KING>(weakSide));
    Square strongPawn = normalize(pos, strongSide, pos.square<PAWN>(strongSide));
  
    Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;
  
    // If the pawn has advanced to the fifth rank or further, and is not a
    // rook pawn, it's too dangerous to assume that it's at least a draw.
    if (rank_of(strongPawn) >= RANK_5 && file_of(strongPawn) != FILE_A)
        return SCALE_FACTOR_NONE;
  
    // Probe the KPK bitbase with the weakest side's pawn removed. If it's a draw,
    // it's probably at least a draw even with the pawn.
    return Bitbases::probe(strongKing, strongPawn, weakKing, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;
  }
  